Modulation

Contents
1

Amplitude modulation

1.1

Forms of amplitude modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.1.1

ITU designations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2.1

Continuous waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2.2

Early technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2.3

Vacuum tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2.4

Single-sideband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3

Simplied analysis of standard AM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4

Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.5

Power and spectrum eciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.6

Modulation index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.7

Modulation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.7.1

Low-level generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.7.2

High-level generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.8

Demodulation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.9

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.11 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Modulation

2.1

Analog modulation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1.1

List of analog modulation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Digital modulation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.2.1

Fundamental digital modulation methods . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.2.2

Modulator and detector principles of operation . . . . . . . . . . . . . . . . . . . . . . . .

11

2.2.3

List of common digital modulation techniques . . . . . . . . . . . . . . . . . . . . . . . .

12

2.2.4

Automatic digital modulation recognition (ADMR) . . . . . . . . . . . . . . . . . . . . .

12

2.2.5

Digital baseband modulation or line coding . . . . . . . . . . . . . . . . . . . . . . . . . .

13

2.3

Pulse modulation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

2.4

Miscellaneous modulation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

2.5

Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

2.6

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

1.2

2.2

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CONTENTS
2.7

References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

2.8

External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

Radio

15

3.1

Etymology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

3.2

Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

3.2.1

Transmitter and modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

3.2.2

Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

3.2.3

Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

3.2.4

Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

3.2.5

Receiver and demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3.2.6

Radio band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3.3

Communication systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3.4

History

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

3.5

Uses of radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

3.5.1

Audio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

3.5.2

Telephony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

3.5.3

Video . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

3.5.4

Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

3.5.5

Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

3.5.6

Data (digital radio) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

3.5.7

Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

3.5.8

Amateur radio service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

3.5.9

Unlicensed radio services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

3.5.10 Radio control (RC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

3.6

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

3.7

Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

3.8

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

3.9

External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

Carrier wave

26

4.1

Carrierless modulation systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

4.2

Carrier leakage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

4.3

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

4.4

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

Frequency modulation

27

5.1

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

5.1.1

Sinusoidal baseband signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

5.1.2

Modulation index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

5.1.3

Bessel functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

5.1.4

Carsons rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

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iii

5.2

Noise reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

5.3

Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

5.3.1

Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

5.3.2

Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

5.4.1

Magnetic tape storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

5.4.2

Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

5.4.3

Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

5.5

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

5.6

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

5.7

External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

5.8

Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

5.4

Frequency
6.1

Denitions

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

6.2

Units

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

6.3

Period versus frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

6.4

Related types of frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

6.5

In wave propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

6.6

Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

6.6.1

By counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

6.6.2

By stroboscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

6.6.3

By frequency counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

6.6.4

Heterodyne methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

6.7.1

Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

6.7.2

Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

6.7.3

Line current

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

6.8

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

6.9

Notes and references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

6.10 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

6.11 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

Radiotelephone

37

7.1

Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

7.1.1

Mode of emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

7.1.2

Modes of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

7.2.1

Privacy and selective calling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

7.3.1

Conventional telephone use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

7.3.2

Marine use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

6.7

32

7.2
7.3

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CONTENTS
7.4

Regulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

7.5

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

7.6

Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

7.7

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

Two-way radio

40

8.1

History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

8.2

Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

8.2.1

Conventional versus trunked . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

8.2.2

Simplex versus duplex channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

8.2.3

Push-to-Talk (PTT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

8.2.4

Analog versus digital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

8.2.5

Data over two-way radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

8.2.6

Engineered versus not engineered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

8.2.7

Options, duty cycle, and conguration . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

8.2.8

Life of equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

8.3

Two-way radio frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

8.4

UHF versus VHF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

8.5

Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

8.6

Other two-way radio devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

8.6.1

Two-way radio rental business . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

8.7

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

8.8

References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

8.9

External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

Airband

49

9.1

Spectrum usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

9.1.1

Other bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

9.1.2

Channel spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

9.1.3

Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

9.1.4

Audio properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

9.1.5

Digital radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

9.2

Unauthorised use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

9.3

See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

9.4

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

10 Citizens band radio

52

10.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

10.1.1 United States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

10.1.2 Australia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

10.1.3 Canada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

10.1.4 Indonesia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

CONTENTS

10.1.5 Malaysia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

10.1.6 United Kingdom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

10.2 Frequency allocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

10.2.1 Standard Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

10.2.2 Intermediate Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

10.2.3 SSB usage

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

10.2.4 Country-specic variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

10.3 Current use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

10.4 Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

10.5 Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

10.6 Working skip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

10.7 Freebanding and export radios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

10.8 Callbook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

10.9 Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

10.10See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

10.11References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

10.12Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

10.13External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

11 Quadrature amplitude modulation

64

11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

11.2 Analog QAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

11.2.1 Fourier analysis of QAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

11.3 Quantized QAM

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11.3.1 Ideal structure

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11.4 Quantized QAM performance

65
66

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

11.4.1 Rectangular QAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

11.4.2 Non-rectangular QAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

11.4.3 Hierarchical QAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

11.5 Interference and noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

11.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

11.7 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

11.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

12 Medium wave

70

12.1 Propagation characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

12.2 Use in the Americas

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

12.3 Use in Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

12.4 Stereo and digital transmissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

12.5 Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

12.5.1 Receiving antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

12.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

vi

CONTENTS
12.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

12.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

13 AM broadcasting

74

13.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

13.1.1 Early technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

13.1.2 Vacuum tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

13.1.3 Beginning of broadcasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

13.1.4 Market concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

13.1.5 Radio networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

13.1.6 Shortwave broadcasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

13.1.7 Golden Age of Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

13.1.8 Shortcomings of AM broadcasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

13.1.9 Competing media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

13.1.10 AM stereo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

13.2 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

13.3 Broadcast frequency bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

13.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

13.5 Other distribution methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

13.6 Microbroadcasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

13.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

13.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

13.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

14 Heterodyne

86

14.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

14.1.1 Superheterodyne receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

14.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

14.2.1 Up and down converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

14.2.2 Analog videotape recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

14.2.3 Music synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

14.2.4 Optical heterodyning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

14.3 Mathematical principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

14.3.1 Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

14.3.2 Output of a mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

14.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

14.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

14.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

14.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

15 Detector (radio)
15.1 Amplitude modulation detectors

91
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

CONTENTS

vii

15.1.1 Envelope detector

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

15.1.2 Product detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

15.2 Frequency and phase modulation detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

15.2.1 Phase detector

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

15.2.2 The Foster-Seeley discriminator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

15.2.3 Ratio detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

15.2.4 Quadrature detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

15.2.5 Other FM detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

15.3 Phase-locked loop detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

15.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

15.5 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

15.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

16 Rectier

95

16.1 Rectier devices

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

16.2 Rectier circuits

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

16.2.1 Single-phase rectiers

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

16.2.2 Three-phase rectiers

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

16.2.3 Voltage-multiplying rectiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

16.3 Rectier eciency

16.4 Rectier losses

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99

16.5 Rectier output smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

16.6 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
16.7 Rectication technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
16.7.1 Electromechanical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
16.7.2 Electrolytic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
16.7.3 Plasma type

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

16.7.4 Diode vacuum tube (valve) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

16.7.5 Solid state
16.8 Current research

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

16.9 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

16.10References
17 Fleming valve

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
107

17.1 How it works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

17.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
17.2.1 Oscillation valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
17.2.2 Power applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
17.3 References and notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
17.3.1 Citations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
17.3.2 Patents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
17.4 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

viii

CONTENTS

18 Continuous wave

110

18.1 Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

18.1.1 Key clicks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
18.2 Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
18.3 Laser physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
18.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
18.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
19 Alexanderson alternator
19.1 History

112

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

19.1.1 Prior developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

19.1.2 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
19.1.3 Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
19.1.4 US Navy stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
19.2 Design

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

19.2.1 Frequency control

19.3 Performance advantages

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

19.4 Disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

19.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
19.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
19.7 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

19.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

20 Lee de Forest

116

20.1 Early life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

20.2 Early radio work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
20.3 American De Forest Wireless Telegraph Company . . . . . . . . . . . . . . . . . . . . . . . . . . 117
20.4 Radio Telephone Company . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
20.4.1 Arc radiotelephone development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
20.4.2 Initial broadcasting experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
20.4.3 Grid Audion detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
20.5 Employment at Federal Telegraph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
20.5.1 Audio frequency amplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
20.6 Reorganized Radio Telephone Company . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
20.6.1 Regeneration controversy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
20.6.2 Renewed broadcasting activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
20.7 Phonolm sound-on-lm process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
20.8 Later years and death . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
20.9 Legacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
20.10Awards and recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
20.11Personal life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
20.11.1 Marriages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

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ix

20.11.2 Politics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

20.11.3 Religious views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
20.12Quotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
20.13Patents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
20.14See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
20.15References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
20.16Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
20.17External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
21 Amplier
21.1 History

129
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

21.2 Figures of merit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

21.3 Amplier categorisation
21.3.1 Active devices

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

21.3.2 Amplier architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

21.3.3 Applications

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

21.4 Classication of amplier stages and systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

21.4.1 Input and output variables
21.4.2 Common terminal

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

21.4.3 Unilateral or bilateral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

21.4.4 Inverting or non-inverting
21.4.5 Function

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

21.4.6 Interstage coupling method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

21.4.7 Frequency range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
21.5 Power amplier classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
21.5.1 Conduction angle classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
21.5.2 Class A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
21.5.3 Class B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
21.5.4 Class AB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
21.5.5 Class C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
21.5.6 Class D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
21.5.7 Additional classes

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

21.6 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

21.6.1 Amplier circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
21.6.2 Notes on implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
21.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
21.8 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

21.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

22 Transmitter

148

22.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

22.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

CONTENTS
22.3 How it works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
22.4 Legal restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
22.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
22.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
22.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

23 Arc converter

153

23.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

23.2 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
23.3 Keying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
23.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
23.5 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

23.6 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

23.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
24 Microphone

157

24.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

24.2 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
24.3 Varieties

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

24.3.1 Condenser

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

24.3.2 Dynamic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

24.3.3 Ribbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
24.3.4 Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
24.3.5 Piezoelectric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
24.3.6 Fiber optic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
24.3.7 Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
24.3.8 Liquid

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

24.3.9 MEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

24.3.10 Speakers as microphones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
24.4 Capsule design and directivity

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

24.5 Polar patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

24.5.1 Omnidirectional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
24.5.2 Unidirectional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
24.5.3 Bi-directional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
24.5.4 Shotgun and parabolic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
24.5.5 Boundary or PZM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
24.6 Application-specic designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
24.7 Powering

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

24.8 Connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

24.8.1 Impedance-matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
24.8.2 Digital microphone interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
24.9 Measurements and specications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

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24.10Measurement microphones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

24.10.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
24.11Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
24.12Windscreens

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

24.13See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

24.14References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
24.15External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
25 FM broadcasting

174

25.1 Broadcast bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

25.2 Modulation characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
25.2.1 Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
25.2.2 Pre-emphasis and de-emphasis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
25.2.3 Stereo FM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
25.2.4 Quadraphonic FM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
25.2.5 Other subcarrier services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
25.2.6 Dolby FM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
25.3 Distance covered by stereo FM transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
25.4 Adoption of FM broadcasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
25.4.1 United States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
25.4.2 Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
25.4.3 Australia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
25.4.4 New Zealand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
25.4.5 Turkey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
25.4.6 Other countries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
25.4.7 ITU Conferences about FM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
25.5 Small-scale use of the FM broadcast band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
25.5.1 Consumer use of FM transmitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
25.5.2 Microbroadcasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
25.5.3 Clandestine use of FM transmitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
25.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
25.6.1 FM broadcasting by country . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
25.6.2 FM broadcasting (technical) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
25.6.3 Lists

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

25.6.4 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

25.7 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

25.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

26 Radio broadcasting

183

26.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

26.2 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
26.2.1 Shortwave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

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CONTENTS
26.2.2 AM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
26.2.3 FM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
26.2.4 Pirate radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
26.2.5 Terrestrial digital radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
26.2.6 Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
26.3 Program formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
26.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
26.5 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

26.6 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

26.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
27 Single-sideband modulation

189

27.1 Basic concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

27.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
27.3 Mathematical formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
27.3.1 Lower sideband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
27.4 Practical implementations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
27.4.1 Bandpass ltering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
27.4.2 Hartley modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
27.4.3 Weaver modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
27.4.4 Full, reduced, and suppressed carrier SSB . . . . . . . . . . . . . . . . . . . . . . . . . . 192
27.5 Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
27.6 SSB as a speech-scrambling technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
27.7 Vestigial sideband (VSB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
27.8 Frequencies for LSB and USB in amateur radio voice communication . . . . . . . . . . . . . . . . 194
27.9 Extended single sideband (eSSB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
27.10Amplitude-companded single-sideband modulation (ACSSB) . . . . . . . . . . . . . . . . . . . . 194
27.11ITU designations

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

27.12Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
27.13See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
27.14References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
27.15General references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
27.16Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
28 Longwave

196

28.1 Non-broadcast use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

28.1.1 Non-directional beacons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
28.1.2 Time signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
28.1.3 Military communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
28.1.4 LowFER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
28.1.5 Historic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
28.2 Broadcasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

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28.2.1 Carrier frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

28.2.2 Long distance reception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
28.2.3 List of long-wave broadcasting transmitters . . . . . . . . . . . . . . . . . . . . . . . . . . 198
28.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
28.4 Notes and references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
28.5 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
29 Double-sideband suppressed-carrier transmission

200

29.1 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

29.2 Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
29.3 Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
29.3.1 Distortion and attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
29.4 How it works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
29.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
29.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
30 Product detector

203

30.1 A simple product detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

30.1.1 Mathematical model of the simple product detector . . . . . . . . . . . . . . . . . . . . . 203
30.1.2 Drawbacks of the simple product detector . . . . . . . . . . . . . . . . . . . . . . . . . . 203
30.2 Another example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
30.2.1 Mathematical model of the detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
30.3 A more sophisticated product detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
30.4 Advantages and disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
31 Envelope detector

205

31.1 Denition of the envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

31.2 Diode detector

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

31.3 Precision detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

31.4 Drawbacks

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

31.5 Demodulation of signals

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

31.6 Audio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

31.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
31.8 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

31.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

32 Double-sideband reduced-carrier transmission

207

32.1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

32.2 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
33 Automatic gain control

208

33.1 How it works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

33.2 Example use cases

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

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33.2.1 AM radio receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
33.2.2 Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
33.2.3 Audio/video

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

33.2.4 Vogad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

33.2.5 Telephone recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
33.2.6 Biological . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
33.3 Recovery times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
33.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
33.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
34 Broadcasting

211

34.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

34.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
34.3 Economic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
34.4 Recorded and live forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
34.5 Social impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
34.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
34.7 Notes and references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
34.8 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
34.9 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
34.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
35 Linear amplier

216

35.1 Explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

35.2 Amplier classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
35.3 Amateur radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
35.4 Broadcast radio stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
35.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
35.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
36 Pulse-width modulation

218

36.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

36.2 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
36.2.1 Delta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
36.2.2 Delta-sigma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
36.2.3 Space vector modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
36.2.4 Direct torque control (DTC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
36.2.5 Time proportioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
36.2.6 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
36.2.7 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
36.2.8 PWM sampling theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
36.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

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36.3.1 Servos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

36.3.2 Telecommunications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
36.3.3 Power delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
36.3.4 Voltage regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
36.3.5 Audio eects and amplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
36.3.6 Electrical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
36.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
36.5 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

36.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

37 Ampliphase

224

37.1 How it works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

37.2 Development

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

37.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

37.4 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
38 Doherty amplier

225

38.1 Successor developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

38.2 Footnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
38.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
39 AM stereo

227

39.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

39.1.1 Timeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
39.2 Broadcasting systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
39.2.1 Harris System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
39.2.2 Magnavox System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
39.2.3 Motorola C-QUAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
39.2.4 Kahn-Hazeltine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
39.2.5 Belar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
39.3 Adoption in the United States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
39.4 Global adoption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
39.5 Current status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
39.6 Surround sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
39.7 Decline in use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
39.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
39.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
40 Shortwave radio

232

40.1 Frequency classications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

40.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
40.2.1 Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
40.2.2 Amateur use of shortwave propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

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40.3 Propagation characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
40.4 Types of modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
40.5 Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
40.6 Shortwave broadcasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
40.6.1 Frequency allocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
40.6.2 Advantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
40.6.3 Disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
40.7 Shortwave listening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
40.8 Amateur radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
40.9 Utility stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
40.10Unusual signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
40.11Shortwave broadcasts and music . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
40.12Shortwaves future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
40.13See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
40.14References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
40.15External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

41 Amplitude modulation signalling system

41.1 Broadcasting

241

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

41.2 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

42 Sideband

242

42.1 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

42.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
43 Types of radio emissions

244

43.1 Designation details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

43.1.1 Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
43.1.2 Type of modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
43.1.3 Type of modulating signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
43.1.4 Type of transmitted information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
43.1.5 Details of information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
43.1.6 Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
43.2 Common examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
43.2.1 Broadcasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
43.2.2 Two-way radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
43.2.3 Low-speed data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
43.3 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
43.4 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
44 Modulation (disambiguation)

246

44.1 Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

44.2 Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

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44.3 Music . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

44.3.1 Classical compositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
44.3.2 Albums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
45 Electronics

247

45.1 Branches of electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

45.2 Electronic devices and components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
45.3 History of electronic components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
45.4 Types of circuits

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

45.4.1 Analog circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

45.4.2 Digital circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
45.5 Heat dissipation and thermal management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
45.6 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
45.7 Electronics theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
45.8 Electronics lab

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

45.9 Computer aided design (CAD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

45.10Construction methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
45.11Degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
45.12See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
45.13References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

45.14Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

45.15External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
46 Telecommunication

252

46.1 Etymology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

46.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
46.2.1 Beacons and pigeons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
46.2.2 Telegraph and telephone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
46.2.3 Radio and television . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
46.2.4 Computers and the Internet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
46.3 Key concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
46.3.1 Basic elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
46.3.2 Analog versus digital communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
46.3.3 Telecommunication networks

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

46.3.4 Communication channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

46.3.5 Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
46.4 Society

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

46.4.1 Economic impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

46.4.2 Social impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
46.4.3 Other impacts

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

46.5 Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

46.6 Modern media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

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46.6.1 Worldwide equipment sales
46.6.2 Telephone

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

46.6.3 Radio and television

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

46.6.4 Internet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

46.6.5 Local area networks and wide area networks . . . . . . . . . . . . . . . . . . . . . . . . . 260
46.7 Transmission capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
46.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
46.9 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

46.9.1 Citations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

46.9.2 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
46.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
47 Waveform

265

47.1 Examples of waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

47.2 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
47.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
47.4 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
47.5 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
48 Analog signal

267

48.1 Advantages and disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

48.2 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
48.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
49 Baseband

269

49.1 Various uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

49.1.1 Baseband bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
49.1.2 Baseband channel

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

49.1.3 Digital baseband transmission

49.1.4 Baseband processor
49.1.5 Baseband signal

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

49.1.6 Equivalent baseband signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

49.2 Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
49.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
49.4 References
50 Demodulation
50.1 History

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
271

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

50.2 Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

50.3 AM radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
50.4 FM radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
50.5 PM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
50.6 QAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

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50.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

50.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
51 Low-pass lter

273

51.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

51.1.1 Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
51.1.2 Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
51.1.3 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
51.2 Ideal and real lters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
51.3 Continuous-time low-pass lters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
51.3.1 Laplace notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
51.4 Electronic low-pass lters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
51.4.1 First order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
51.4.2 Second order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
51.4.3 Higher order passive lters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
51.4.4 Active electronic realization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
51.4.5 Discrete-time realization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
51.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
51.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
51.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
52 Digital data

279

52.1 Symbol to digital conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

52.2 Properties of digital information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
52.3 Historical digital systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
52.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
52.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
52.6 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
53 Public switched telephone network

282

53.1 History (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

53.2 Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
53.3 Regulation

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

53.4 Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

53.4.1 Network topology

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

53.4.2 Digital channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

53.4.3 Impact on IP standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
53.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
53.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
53.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
54 Channel (communications)

285

54.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

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54.2 Channel models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
54.2.1 Digital channel models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
54.2.2 Analog channel models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
54.3 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
54.4 Channel performance measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
54.5 Multi-terminal channels, with application to cellular systems . . . . . . . . . . . . . . . . . . . . . 287
54.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
54.7 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288

55 Band-pass lter

289

55.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

55.2 Q factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
55.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
55.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
55.5 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

55.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

56 Frequency-division multiplexing

291

56.1 How it works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

56.2 Telephone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
56.2.1 Group and supergroup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
56.3 Other examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
56.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
56.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
57 Line code

294

57.1 Line coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

57.2 Disparity

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

57.3 Polarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

57.4 Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
57.5 Other considerations

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

57.6 Common line codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

57.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
57.8 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

57.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

58 Local area network

298

58.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298

58.2 Cabling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
58.3 Wireless media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
58.4 Technical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
58.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
58.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

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58.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

59 Narrowband

301

59.1 Two-way radio narrowband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

59.2 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
59.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
59.4 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
60 Wideband

302

60.1 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

60.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
60.3 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
61 Data transmission

303

61.1 Distinction between related subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303

61.2 Protocol layers and sub-topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
61.3 Applications and history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
61.4 Serial and parallel transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
61.5 Types of communication channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
61.6 Asynchronous and synchronous data transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
61.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
61.8 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
62 Carrier frequency

307

63 Frequency modulation synthesis

308

63.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

63.2 Spectral analysis

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

63.3 Footnote . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

63.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
63.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
63.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
64 Constant envelope

311

64.1 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

64.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
65 Angle modulation

312

65.1 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312

66 Phase modulation

313

66.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

66.2 Modulation index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
66.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314

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67 Bit rate

315

67.1 Prexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

67.2 In data communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
67.2.1 Gross bit rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
67.2.2 Information rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
67.2.3 Network throughput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
67.2.4 Goodput (data transfer rate) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
67.2.5 Progress trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
67.3 Multimedia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
67.4 Encoding bit rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
67.4.1 Audio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
67.4.2 Video . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
67.4.3 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
67.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
67.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
67.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
68 Symbol rate

321

68.1 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

68.1.1 Relationship to gross bitrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
68.1.2 Modems for passband transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
68.1.3 Line codes for baseband transmission

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 322

68.1.4 Digital television and OFDM example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322

68.1.5 Relationship to chip rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
68.1.6 Relationship to bit error rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
68.2 Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
68.2.1 Binary modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
68.2.2 N-ary modulation, N greater than 2
68.2.3 Data rate versus error rate

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

68.3 Signicant condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

68.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
68.5 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

68.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

69 Digital signal

325

69.1 Denitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

69.1.1 In digital electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
69.1.2 In signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
69.1.3 In communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
69.2 Logic signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
69.3 Logic voltage levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
69.4 Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

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69.5 Clocking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

69.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
69.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
70 Digital-to-analog converter

328

70.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

70.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
70.2.1 Audio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
70.2.2 Video . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
70.2.3 Mechanical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
70.3 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
70.4 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
70.5 Figures of merit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
70.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
70.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
70.8 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
70.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
71 Analog transmission

333

71.1 Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

71.2 Modes of transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
71.3 Types of analog transmissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
71.4 Benets and drawbacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
71.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
71.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
72 Phase-shift keying

335

72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

72.1.1 Denitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
72.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
72.3 Binary phase-shift keying (BPSK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
72.3.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
72.3.2 Bit error rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
72.4 Quadrature phase-shift keying (QPSK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
72.4.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
72.4.2 Bit error rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
72.4.3 Variants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
72.5 Higher-order PSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
72.5.1 Bit error rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
72.6 Dierential phase-shift keying (DPSK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
72.6.1 Dierential encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
72.6.2 Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

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72.6.3 Example: Dierentially encoded BPSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

72.7 Channel capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

72.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
72.9 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
72.10References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
73 Frequency-shift keying
73.1 Implementations of FSK Modems

345
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

73.2 Other forms of FSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

73.2.1 Continuous-phase frequency-shift keying

. . . . . . . . . . . . . . . . . . . . . . . . . . 345

73.2.2 Gaussian frequency-shift keying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

73.2.3 Minimum-shift keying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
73.2.4 Gaussian minimum shift keying

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346

73.2.5 Audio FSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346

73.2.6 Continuous 4 level FM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
73.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
73.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
73.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
73.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
74 Amplitude-shift keying

348

74.1 Probability of error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

74.2 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
74.3 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
75 Binary number

351

75.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

75.1.1 Egypt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
75.1.2 China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
75.1.3 India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
75.1.4 Other cultures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
75.1.5 Western predecessors to Leibniz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
75.1.6 Leibniz and the I Ching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
75.1.7 Later developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
75.2 Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
75.3 Counting in binary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
75.3.1 Decimal counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
75.3.2 Binary counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
75.4 Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
75.5 Binary arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
75.5.1 Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
75.5.2 Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

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75.5.3 Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

75.5.4 Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
75.5.5 Square root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
75.6 Bitwise operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
75.7 Conversion to and from other numeral systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
75.7.1 Decimal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
75.7.2 Hexadecimal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
75.7.3 Octal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
75.8 Representing real numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
75.9 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
75.10Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
75.11References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
75.12External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
76 Bit

362

76.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

76.2 Physical representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
76.2.1 Transmission and processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
76.2.2 Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
76.3 Unit and symbol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
76.3.1 Multiple bits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
76.4 Information capacity and information compression . . . . . . . . . . . . . . . . . . . . . . . . . . 363
76.5 Bit-based computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
76.6 Other information units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
76.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
76.8 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
76.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
76.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
77 Baud

366

77.1 Denitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

77.2 Relationship to gross bit rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
77.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
77.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
77.5 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
78 Constellation diagram

368

78.1 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368

78.2 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
78.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
79 Complex number

370

79.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

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79.1.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
79.1.2 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
79.1.3 Complex plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
79.1.4 History in brief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

79.2 Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372

79.2.1 Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
79.2.2 Ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
79.3 Elementary operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
79.3.1 Conjugate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
79.3.2 Addition and subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
79.3.3 Multiplication and division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
79.3.4 Reciprocal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
79.3.5 Square root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
79.4 Polar form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
79.4.1 Absolute value and argument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
79.4.2 Multiplication and division in polar form . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
79.5 Exponentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
79.5.1 Eulers formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
79.5.2 Natural logarithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
79.5.3 Integer and fractional exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
79.6 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
79.6.1 Field structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
79.6.2 Solutions of polynomial equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
79.6.3 Algebraic characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
79.6.4 Characterization as a topological eld . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
79.7 Formal construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
79.7.1 Formal development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
79.7.2 Matrix representation of complex numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 378
79.8 Complex analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378
79.8.1 Complex exponential and related functions . . . . . . . . . . . . . . . . . . . . . . . . . . 378
79.8.2 Holomorphic functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
79.9 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
79.9.1 Control theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
79.9.2 Improper integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
79.9.3 Fluid dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
79.9.4 Dynamic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
79.9.5 Electromagnetism and electrical engineering . . . . . . . . . . . . . . . . . . . . . . . . . 380
79.9.6 Signal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
79.9.7 Quantum mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
79.9.8 Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
79.9.9 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

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79.9.10 Algebraic number theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

79.9.11 Analytic number theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
79.10History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
79.11Generalizations and related notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
79.12See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
79.13Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
79.14References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
79.14.1 Mathematical references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
79.14.2 Historical references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
79.15Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
79.16External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
80 Imaginary unit

386

80.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

80.2 i and i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
80.3 Proper use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
80.4 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
80.4.1 Square roots

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388

80.4.2 Cube roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388

80.4.3 Multiplication and division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
80.4.4 Powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
80.4.5 Factorial

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

80.4.6 Other operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

80.5 Alternative notations

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

80.6 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

80.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390
80.8 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390
80.9 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390

80.10Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390

80.11External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390
81 Passband

391

81.1 Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391

81.2 Digital transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
81.3 Details

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

81.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

81.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
82 Radio frequency
82.1 Special properties of RF current

393
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

82.2 Radio communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

82.3 Frequency bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394

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82.4 In medicine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394

82.5 Eects on the human body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
82.5.1 Extremely low frequency RF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
82.5.2 Microwaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
82.5.3 General RF exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
82.6 As a weapon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
82.7 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
82.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
82.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
82.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396
83 Pulse shaping

397

83.1 Need for pulse shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

83.2 Pulse shaping lters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
83.2.1 Sinc lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
83.2.2 Raised-cosine lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
83.2.3 Gaussian lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
83.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
83.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
84 Digital signal processing

399

84.1 Signal sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

84.2 Domains

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

84.2.1 Time and space domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

84.2.2 Frequency domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
84.2.3 Z-plane analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
84.2.4 Wavelet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
84.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
84.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
84.5 Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
84.6 Related elds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
84.7 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
84.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
84.9 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
85 Direct digital synthesizer

404

85.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404

85.2 Performance

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404

85.2.1 Frequency agility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404

85.2.2 Phase noise and jitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
85.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
85.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

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85.5 External links and further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

86 Fading

406

86.1 Key concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406

86.2 Slow versus fast fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
86.3 Block fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
86.4 Selective fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
86.5 Fading models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
86.6 Mitigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
86.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
86.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
86.9 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
86.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
87 Attenuation

410

87.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410

87.2 Ultrasound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410
87.2.1 Attenuation coecient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410
87.3 Light attenuation in water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
87.4 Earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
87.5 Electromagnetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
87.5.1 Radiography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
87.5.2 Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
87.5.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
87.5.4 Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
87.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
87.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
87.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
88 Superheterodyne receiver

415

88.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

88.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
88.1.2 Invention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416
88.1.3 Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416
88.2 Design and principle of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
88.2.1 Circuit description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
88.2.2 Local oscillator and mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
88.2.3 Intermediate frequency amplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
88.2.4 Bandpass lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
88.2.5 Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
88.3 Advanced designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
88.3.1 Other uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

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88.3.2 Modern designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420
88.4 Advantages and disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420
88.4.1 Image frequency (f ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420
88.4.2 Local oscillator radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
88.4.3 Local oscillator sideband noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
88.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
88.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
88.7 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
88.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422

89 Undersampling

423

89.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423

89.2 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
89.3 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

90 Matched lter

426

90.1 Derivation of the matched lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426

90.1.1 Derivation via matrix algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426
90.1.2 Derivation via Lagrangian

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427

90.2 The matched lter as a least squares estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428

90.2.1 Derivation

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428

90.2.2 Implications

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429

90.3 Frequency-domain interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429

90.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
90.4.1 Matched lter in radar and sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
90.4.2 Matched lter in digital communications . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
90.4.3 Matched lter in gravitational-wave astronomy

. . . . . . . . . . . . . . . . . . . . . . . 431

90.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

90.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
90.7 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

90.8 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432

91 Intersymbol interference
91.1 Causes

433

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

91.1.1 Multipath propagation

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

91.1.2 Bandlimited channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

91.2 Eects on eye patterns
91.3 Countering ISI

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434

91.4 Intentional Intersymbol interference

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434

91.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434

91.6 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

91.7 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

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91.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

92 Phase synchronization

436

92.1 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436

92.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436
92.3 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436
93 Asynchronous communication

437

93.1 Physical layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437

93.2 Data link layer and higher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
93.3 Application layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
93.4 Electronically mediated communication

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437

93.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437

93.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438
94 Multiple frequency-shift keying

439

94.1 MFSK Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

94.1.1 2-tone MFSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
94.1.2 MFSK in HF communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
94.1.3 VHF & UHF communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
94.2 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
94.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
94.4 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
95 Dual-tone multi-frequency signaling

443

95.1 Multifrequency signaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

95.2 #, *, A, B, C, and D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444
95.3 Keypad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444
95.4 Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
95.5 Other multiple frequency signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
95.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
95.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
95.8 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
95.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
96 On-o keying

446

96.1 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446

96.2 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446
96.3 References
97 8VSB

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446
447

97.1 Modulation Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447

97.2 Throughput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
97.3 Power saving advantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447

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97.4 Disputes over ATSCs use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

97.5 8VSB vs COFDM

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

97.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

97.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448
97.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
98 Polar modulation
98.1 History

450

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

98.2 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

98.3 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
99 Continuous phase modulation
99.1 Phase memory

451

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

99.2 Phase trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

99.3 Partial response CPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
99.4 Continuous-phase frequency-shift keying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
99.4.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452
99.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452
99.6 References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452

100Minimum-shift keying
100.1Mathematical representation

453
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

100.2Gaussian minimum-shift keying

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

100.3See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454

100.4Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454
100.5References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454
101Orthogonal frequency-division multiplexing

455

101.1Example of applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455

101.1.1 Wired . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
101.1.2 Wireless . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
101.2Key features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
101.2.1 Summary of advantages

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456

101.2.2 Summary of disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456

101.3Characteristics and principles of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
101.3.1 Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
101.3.2 Implementation using the FFT algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
101.3.3 Guard interval for elimination of intersymbol interference . . . . . . . . . . . . . . . . . . 457
101.3.4 Simplied equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
101.3.5 Channel coding and interleaving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
101.3.6 Adaptive transmission

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

101.3.7 OFDM extended with multiple access . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

101.3.8 Space diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

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101.3.9 Linear transmitter power amplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460

101.4Eciency comparison between single carrier and multicarrier . . . . . . . . . . . . . . . . . . . . 460
101.5Idealized system model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461
101.5.1 Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461
101.5.2 Receiver

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461

101.6Mathematical description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461

101.7Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
101.7.1 OFDM system comparison table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
101.7.2 ADSL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
101.7.3 Powerline Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
101.7.4 Wireless local area networks (LAN) and metropolitan area networks (MAN) . . . . . . . . 462
101.7.5 Wireless personal area networks (PAN) . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
101.7.6 Terrestrial digital radio and television broadcasting

. . . . . . . . . . . . . . . . . . . . . 462

101.7.7 Ultra-wideband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

101.7.8 FLASH-OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463
101.8History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464
101.9See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464
101.10References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465
101.11Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
101.12External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
102Wavelet modulation

467

102.1See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467

102.2References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467

103Trellis modulation

468

103.1A new modulation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468

103.2See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
103.3In popular culture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
103.4Relevant papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
103.5References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
103.6External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
104Spread spectrum

470

104.1Spread-spectrum telecommunications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470

104.2Invention of frequency hopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471
104.3Spread-spectrum clock signal generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471
104.4See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472
104.5Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472
104.6Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472
104.7External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
105Direct-sequence spread spectrum

474

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105.1History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
105.2Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
105.3Transmission method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
105.4Benets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
105.5Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
105.6See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
105.7References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
105.8External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
106Chirp spread spectrum

476

106.1Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476
106.2Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476
106.3See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
106.4References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
106.5External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
107Frequency-hopping spread spectrum

478

107.1Spread-spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
107.2Military use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
107.3Civilian use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
107.4Technical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
107.5Multiple inventors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
107.6Variations of FHSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
107.7See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
107.8Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
107.9References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
107.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
108Channel access method

481

108.1Fundamental types of channel access schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481

108.1.1 Frequency-division multiple access (FDMA) . . . . . . . . . . . . . . . . . . . . . . . . . 481
108.1.2 Time division multiple access (TDMA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
108.1.3 Code division multiple access (CDMA)/Spread spectrum multiple access (SSMA) . . . . . 482
108.1.4 Space division multiple access (SDMA) . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
108.1.5 Power division multiple access (PDMA) . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
108.2List of channel access methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
108.2.1 Circuit mode and channelization methods . . . . . . . . . . . . . . . . . . . . . . . . . . 482
108.2.2 Packet mode methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
108.2.3 Duplexing methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
108.3Hybrid channel access scheme application examples . . . . . . . . . . . . . . . . . . . . . . . . . 483
108.4Denition within certain application areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
108.4.1 Local and metropolitan area networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

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108.4.2 Satellite communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

108.4.3 Switching centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
108.5Classications in the literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
108.6See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
108.7Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
108.8References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
109Multi-carrier code division multiple access

485

109.1Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
109.2Downlink: MC-CDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
109.3Variants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
109.4References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486
109.5Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486
109.6See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486
110Orthogonal frequency-division multiple access

487

110.1Key features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487

110.1.1 Claimed advantages over OFDM with time-domain statistical multiplexing . . . . . . . . . 487
110.1.2 Claimed OFDMA Advantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
110.1.3 Recognised disadvantages of OFDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
110.2Characteristics and principles of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
110.3Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
110.4Trademark and patents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
110.5See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
110.6Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
110.7References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
110.8External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
111Class-D amplier

490

111.1Basic operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490

111.2Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
111.3Signal modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
111.4Design challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
111.4.1 Switching speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
111.4.2 Electromagnetic interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
111.4.3 Power supply design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
111.5Error control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
111.6Advantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
111.7Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
111.8See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493
111.9References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493
111.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

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112RF power amplier

494

112.1Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
112.2Wideband amplier design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
112.3References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
112.4External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
113Code division multiple access

496

113.1History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496
113.2Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496
113.3Steps in CDMA modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497
113.4Code division multiplexing (synchronous CDMA) . . . . . . . . . . . . . . . . . . . . . . . . . . 497
113.4.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
113.5Asynchronous CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499
113.5.1 Advantages of asynchronous CDMA over other techniques . . . . . . . . . . . . . . . . . 499
113.5.2 Spread-spectrum characteristics of CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . 500
113.6Collaborative CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500
113.7See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
113.8Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
113.9References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
113.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
114Software-dened radio

502

114.1Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502
114.2Operating principles

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502

114.2.1 Ideal concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503

114.2.2 Receiver architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
114.3History

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503

114.3.1 SPEAKeasy phase I

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504

114.3.2 SPEAKeasy phase II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504

114.4Current usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505
114.4.1 Military . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505
114.4.2 Amateur and home use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505
114.5See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506
114.6References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506

114.7Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507

114.8External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507
115Cognitive radio

509

115.1Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
115.2History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
115.3Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510
115.4Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510

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115.4.1 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510

115.4.2 Versus intelligent antenna (IA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
115.5Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
115.6Simulation of CR networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512
115.7Future plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512
115.8See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512
115.9References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512
115.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
116Manchester code

514

116.1Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514
116.2Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514
116.3Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514
116.3.1 Manchester encoding as phase-shift keying

. . . . . . . . . . . . . . . . . . . . . . . . . 515

116.3.2 Conventions for representation of data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515

116.4See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
116.5References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
117Non-return-to-zero

516

117.1Unipolar non-return-to-zero level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516

117.2Bipolar non-return-to-zero level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
117.3Non-return-to-zero space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
117.4Non-return-to-zero inverted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
117.5See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518
117.6References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518
118Unipolar encoding

519

118.1See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519

119Bipolar encoding

520

119.1Alternate mark inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520

119.2Voltage Build-up

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520

119.3Synchronization and Zeroes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520

119.4Error detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521
119.5Other T1 encoding schemes

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

119.6See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

119.7References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

120Pulse wave

522

120.1See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522

120.2References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522
121Discrete-time signal

523

121.1Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523

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121.2See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523

121.3References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523

122Forward error correction

524

122.1How it works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524

122.2Averaging noise to reduce errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524
122.3Types of FEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
122.4Concatenated FEC codes for improved performance . . . . . . . . . . . . . . . . . . . . . . . . . 525
122.5Low-density parity-check (LDPC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
122.6Turbo codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
122.7Local decoding and testing of codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
122.8Interleaving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
122.8.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
122.8.2 Disadvantages of interleaving

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

122.9List of error-correcting codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

122.10See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528
122.11References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528
122.12Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528
122.13External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529
123Pulse-amplitude modulation

530

123.1Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
123.2Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
123.2.1 Ethernet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
123.2.2 Photo biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
123.2.3 Electronic drivers for LED lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
123.2.4 Digital television . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531
123.3See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531
123.4References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531
124Pulse-position modulation

532

124.1History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532
124.2Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532
124.3Sensitivity to multipath interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532
124.4Non-coherent detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532
124.5PPM vs. M-FSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533
124.6Applications for RF communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533
124.6.1 PPM encoding for radio control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533
124.7See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533
124.8References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533
125Pulse-code modulation

534

125.1History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534

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125.2Implementations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
125.3Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
125.4Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
125.5Standard sampling precision and rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536
125.6Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536
125.7Digitization as part of the PCM process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536
125.8Encoding for serial transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
125.9Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
125.10See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
125.11Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
125.12References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
125.13Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
125.14External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539
126Dierential pulse-code modulation

540

126.1Option 1: dierence between two consecutive quantized samples . . . . . . . . . . . . . . . . . . . 540

126.2Option 2: analysis by synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540
126.3See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540
126.4References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540
127Adaptive dierential pulse-code modulation

541

127.1In telephony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541

127.2Split-band or subband ADPCM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541
127.3Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541
127.4References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541
128Delta modulation

543

128.1Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543
128.2Transfer characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543
128.3Output signal power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544
128.4Bit-rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544
128.5Adaptive delta modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544
128.6Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544
128.7SBS Application 24 kbps delta modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544
128.8See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545
128.9Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545
128.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545
129Delta-sigma modulation
129.1Motivation

546

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546

129.1.1 Why convert an analog signal into a stream of pulses? . . . . . . . . . . . . . . . . . . . . 546

129.1.2 Why delta-sigma modulation? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546
129.1.3 Why the delta-sigma analog to digital conversion? . . . . . . . . . . . . . . . . . . . . . . 547

xl

CONTENTS
129.2Analog to digital conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547
129.2.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547
129.2.2 Analysis

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547

129.2.3 Practical Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548

129.2.4 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550
129.3Digital to analog conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551
129.3.1 Discussion

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551

129.4Relationship to -modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551

129.5Principle

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

129.6Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552
129.6.1 2nd order and higher order modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552
129.6.2 3-level and higher quantizer
129.6.3 Decimation structures

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

129.7Quantization theory formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

129.8Oversampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553
129.8.1 Example of decimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553
129.9Naming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553
129.10See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
129.11References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
129.12External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
130Continuously variable slope delta modulation

555

130.1Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555
130.2SBS application 24 kbit/s delta modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555
130.3References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556

131Pulse-density modulation

557

131.1Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557
131.2Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557
131.3Analog-to-digital conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557
131.4Digital-to-analog conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558
131.5Relationship to biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558
131.6Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558
131.7Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558
131.8See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559
131.9References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559
131.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559
132Morse code

560

132.1Development and history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560

132.2User prociency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562
132.3International Morse Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563

CONTENTS

xli

132.3.1 Aviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563

132.3.2 Amateur radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563
132.3.3 Other uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564
132.3.4 Applications for the general public . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
132.3.5 Morse code as an assistive technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
132.4Representation, timing and speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
132.4.1 Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
132.4.2 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
132.4.3 Spoken representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
132.4.4 Speed in words per minute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
132.4.5 Farnsworth speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567
132.4.6 Alternative display of common characters in International Morse code . . . . . . . . . . . . 567
132.4.7 Link budget issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567
132.5Learning methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567
132.5.1 Mnemonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568
132.6Letters, numbers, punctuation, prosigns for Morse code and non-English variants . . . . . . . . . . 568
132.6.1 Prosigns

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568

132.6.2 Symbol representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568

132.6.3 Non-Latin extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569
132.6.4 Unusual variants

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569

132.7Decoding software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569

132.8See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569
132.9References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569
132.10External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
132.11Text and image sources, contributors, and licenses . . . . . . . . . . . . . . . . . . . . . . . . . . 571
132.11.1Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571
132.11.2Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599
132.11.3Content license . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624

Chapter 1

Amplitude modulation
1.1 Forms of amplitude modulation

Amplitude modulation (AM) is a modulation technique

used in electronic communication, most commonly for
transmitting information via a radio carrier wave. In amplitude modulation, the amplitude (signal strength) of the
carrier wave is varied in proportion to the waveform being transmitted. That waveform may, for instance, correspond to the sounds to be reproduced by a loudspeaker, or
the light intensity of television pixels. This technique contrasts with frequency modulation, in which the frequency
of the carrier signal is varied, and phase modulation, in
which its phase is varied.

In electronics and telecommunications, modulation

means varying some aspect of a higher frequency
continuous wave carrier signal with an informationbearing modulation waveform, such as an audio signal
which represents sound, or a video signal which represents images, so the carrier will carry the information.
When it reaches its destination, the information signal is
AM was the earliest modulation method used to trans- extracted from the modulated carrier by demodulation.
mit voice by radio. It was developed during the rst two In amplitude modulation, the amplitude or strength
decades of the 20th century beginning with Roberto Lan- of the carrier oscillations is what is varied. For examdell De Moura and Reginald Fessenden's radiotelephone ple, in AM radio communication, a continuous wave
experiments in 1900.[1] It remains in use today in many radio-frequency signal (a sinusoidal carrier wave) has its
forms of communication; for example it is used in amplitude modulated by an audio waveform before transportable two way radios, VHF aircraft radio, Citizens mission. The audio waveform modies the amplitude
Band Radio, and in computer modems (in the form of of the carrier wave and determines the envelope of the
QAM). AM is often used to refer to mediumwave AM waveform. In the frequency domain, amplitude moduradio broadcasting.
lation produces a signal with power concentrated at the
carrier frequency and two adjacent sidebands. Each sideband is equal in bandwidth to that of the modulating signal, and is a mirror image of the other. Standard AM is
thus sometimes called double-sideband amplitude modulation (DSB-AM) to distinguish it from more sophisticated modulation methods also based on AM.
One disadvantage of all amplitude modulation techniques
(not only standard AM) is that the receiver amplies and
detects noise and electromagnetic interference in equal
proportion to the signal. Increasing the received signal
to noise ratio, say, by a factor of 10 (a 10 decibel improvement), thus would require increasing the transmitter
power by a factor of 10. This is in contrast to frequency
modulation (FM) and digital radio where the eect of
such noise following demodulation is strongly reduced so
long as the received signal is well above the threshold for
reception. For this reason AM broadcast is not favored
for music and high delity broadcasting, but rather for
voice communications and broadcasts (sports, news, talk
radio etc.).

Fig 1: An audio signal (top) may be carried by a carrier signal

using AM or FM methods.

Another disadvantage of AM is that it is inecient in

power usage; at least two-thirds of the power is concentrated in the carrier signal. The carrier signal con1

CHAPTER 1. AMPLITUDE MODULATION

tains none of the original information being transmitted 1.1.1 ITU designations
(voice, video, data, etc.). However its presence provides
a simple means of demodulation using envelope detec- In 1982, the International Telecommunication Union
tion, providing a frequency and phase reference to ex- (ITU) designated the types of amplitude modulation:
tract the modulation from the sidebands. In some modulation systems based on AM, a lower transmitter power
is required through partial or total elimination of the car- 1.2 History
rier component, however receivers for these signals are
more complex and costly. The receiver may regenerate a copy of the carrier frequency (usually as shifted
to the intermediate frequency) from a greatly reduced
pilot carrier (in reduced-carrier transmission or DSBRC) to use in the demodulation process. Even with the
carrier totally eliminated in double-sideband suppressedcarrier transmission, carrier regeneration is possible using a Costas phase-locked loop. This doesn't work however for single-sideband suppressed-carrier transmission
(SSB-SC), leading to the characteristic Donald Duck
sound from such receivers when slightly detuned. Single sideband is nevertheless used widely in amateur radio
and other voice communications both due to its power efciency and bandwidth eciency (cutting the RF bandwidth in half compared to standard AM). On the other
hand, in medium wave and short wave broadcasting, standard AM with the full carrier allows for reception using
inexpensive receivers. The broadcaster absorbs the extra
power cost to greatly increase potential audience.
An additional function provided by the carrier in standard
AM, but which is lost in either single or double-sideband
suppressed-carrier transmission, is that it provides an amplitude reference. In the receiver, the automatic gain control (AGC) responds to the carrier so that the reproduced
audio level stays in a xed proportion to the original modulation. On the other hand, with suppressed-carrier transmissions there is no transmitted power during pauses in
the modulation, so the AGC must respond to peaks of
the transmitted power during peaks in the modulation.
This typically involves a so-called fast attack, slow decay
circuit which holds the AGC level for a second or more
following such peaks, in between syllables or short pauses
in the program. This is very acceptable for communications radios, where compression of the audio aids intelligibility. However it is absolutely undesired for music
or normal broadcast programming, where a faithful reproduction of the original program, including its varying One of the crude pre-vacuum tube AM transmitters, a Telefunken
arc transmitter from 1906. The carrier wave is generated by 6
modulation levels, is expected.
A trivial form of AM which can be used for transmitting binary data is on-o keying, the simplest form of
amplitude-shift keying, in which ones and zeros are represented by the presence or absence of a carrier. Ono keying is likewise used by radio amateurs to transmit
Morse code where it is known as continuous wave (CW)
operation, even though the transmission is not strictly
continuous. A more complex form of AM, Quadrature
amplitude modulation is now more commonly used with
digital data, while making more ecient use of the available bandwidth.

electric arcs in the vertical tubes, connected to a tuned circuit.

Modulation is done by the large carbon microphone (cone shape)
in the antenna lead.

Although AM was used in a few crude experiments in

multiplex telegraph and telephone transmission in the late
1800s,[2] the practical development of amplitude modulation is synonymous with the development between 1900
and 1920 of "radiotelephone" transmission, that is, the
eort to send sound (audio) by radio waves. The rst
radio transmitters, called spark gap transmitters, transmitted information by wireless telegraphy, using dierent
length pulses of carrier wave to spell out text messages in

1.2. HISTORY

3
sidered the rst AM public entertainment broadcast on
Christmas Eve, 1906. He also discovered the principle
on which AM modulation is based, heterodyning, and invented one of the rst detectors able to rectify and receive AM, the electrolytic detector or liquid baretter, in
1902. Other radio detectors invented for wireless telegraphy, such as the Fleming valve (1904) and the crystal
detector (1906) also proved able to rectify AM signals,
so the technological hurdle was generating AM waves;
receiving them was not a problem.

1.2.2 Early technologies

Early experiments in AM radio transmission, conducted
by Fessenden, Valdamar Poulsen, Ernst Ruhmer, Quirino
Majorana, Charles Harrold, and Lee De Forest, were
hampered by the lack of a technology for amplication.
The rst practical continuous wave AM transmitters were
based on either the huge, expensive Alexanderson alternator, developed 1906-1910, or versions of the Poulsen
arc transmitter (arc converter), invented in 1903. The
modications necessary to transmit AM were clumsy and
One of the rst vacuum tube AM radio transmitters, built by resulted in very low quality audio. Modulation was usuMeissner in 1913 with an early triode tube by Robert von Lieben. ally accomplished by a carbon microphone inserted diHe used it in a historic 36 km (24 mi) voice transmission from rectly in the antenna or ground wire; its varying resistance
Berlin to Nauen, Germany. Compare its small size with above varied the current to the antenna. The limited power hantransmitter.
dling ability of the microphone severely limited the power
of the rst radiotelephones; many of the microphones
Morse code. They couldn't transmit audio because the were water-cooled.
carrier consisted of strings of damped waves, pulses of
radio waves that declined to zero, that sounded like a buzz
in receivers. In eect they were already amplitude mod- 1.2.3 Vacuum tubes
ulated.
The discovery in 1912 of the amplifying ability of the
Audion vacuum tube, invented in 1906 by Lee De Forest, solved these problems. The vacuum tube feedback
1.2.1 Continuous waves
oscillator, invented in 1912 by Edwin Armstrong and
The rst AM transmission was made by Canadian re- Alexander Meissner, was a cheap source of continuous
searcher Reginald Fessenden on 23 December 1900 using waves and could be easily modulated to make an AM
a spark gap transmitter with a specially designed high fre- transmitter. Modulation did not have to be done at the
quency 10 kHz interrupter, over a distance of 1 mile (1.6 output but could be applied to the signal before the nal
km) at Cobb Island, Maryland, USA. His rst transmitted amplier tube, so the microphone or other audio source
words were, Hello. One, two, three, four. Is it snowing didn't have to handle high power. Wartime research
where you are, Mr. Thiessen?". The words were barely greatly advanced the art of AM modulation, and after
the war the availability of cheap tubes sparked a great
intelligible above the background buzz of the spark.
Fessenden was a signicant gure in the development of increase in the number of radio stations experimenting
AM radio. He was one of the rst researchers to real- with AM transmission of news or music. The vacuum
ize, from experiments like the above, that the existing tube was responsible for the rise of AM radio broadcasttechnology for producing radio waves, the spark trans- ing around 1920, the rst electronic mass entertainment
mitter, was not usable for amplitude modulation, and that medium. Amplitude modulation was virtually the only
a new kind of transmitter, one that produced sinusoidal type used for radio broadcasting until FM broadcasting
continuous waves, was needed. This was a radical idea at began after World War 2.
the time, because experts believed the impulsive spark
was necessary to produce radio frequency waves, and
Fessenden was ridiculed. He invented and helped develop one of the rst continuous wave transmitters - the
Alexanderson alternator, with which he made what is con-

At the same time as AM radio began, telephone companies such as AT&T were developing the other large application for AM: sending multiple telephone calls through
a single wire by modulating them on separate carrier frequencies, called frequency division multiplexing.[2]

1.2.4

CHAPTER 1. AMPLITUDE MODULATION

Single-sideband

John Renshaw Carson in 1915 did the rst mathematical analysis of amplitude modulation, showing that a signal and carrier frequency combined in a nonlinear device
would create two sidebands on either side of the carrier
frequency, and passing the modulated signal through another nonlinear device would extract the original baseband signal.[2] His analysis also showed only one sideband
was necessary to transmit the audio signal, and Carson
patented single-sideband modulation (SSB) on 1 December 1915.[2] This more advanced variant of amplitude
modulation was adopted by AT&T for longwave transatlantic telephone service beginning 7 January 1927. After
WW2 it was developed by the military for aircraft communication.

Using prosthaphaeresis identities, y(t) can be shown to be

the sum of three sine waves:

[sin(2(fc + fm )t + ) + sin(2(fc fm )t
y(t) = Asin(2fc t)+ AM
2
Therefore, the modulated signal has three components:
the carrier wave c(t) which is unchanged, and two pure
sine waves (known as sidebands) with frequencies slightly
above and below the carrier frequency fc.

1.4 Spectrum

|M()|

1.3 Simplied analysis of standard

AM

A
|Y()|

A
M(+c )

M(c )

Fig 2: Double-sided spectra of baseband and AM signals.

Illustration of Amplitude Modulation

Consider a carrier wave (sine wave) of frequency fc and

amplitude A given by:

c(t) = A sin(2fc t)
Let m(t) represent the modulation waveform. For this
example we shall take the modulation to be simply a sine
wave of a frequency fm, a much lower frequency (such as
an audio frequency) than fc:

m(t) = M cos(2fm t + )

Of course a useful modulation signal m(t) will generally

not consist of a single sine wave, as treated above. However, by the principle of Fourier decomposition, m(t) can
be expressed as the sum of a number of sine waves of
various frequencies, amplitudes, and phases. Carrying
out the multiplication of 1+m(t) with c(t) as above then
yields a result consisting of a sum of sine waves. Again
the carrier c(t) is present unchanged, but for each frequency component of m at there are two sidebands at
frequencies fc + and fc - . The collection of the former frequencies above the carrier frequency is known as
the upper sideband, and those below constitute the lower
sideband. In a slightly dierent way of looking at it, we
can consider the modulation m(t) to consist of an equal
mix of positive and negative frequency components (as
results from a formal Fourier transform of a real valued
quantity) as shown in the top of Fig. 2. Then one can
view the sidebands as that modulation m(t) having simply
been shifted in frequency by fc as depicted at the bottom
right of Fig. 2 (formally, the modulated signal also contains identical components at negative frequencies, shown
at the bottom left of Fig. 2 for completeness).

where M is the amplitude of the modulation. We shall insist that M<1 so that (1+m(t)) is always positive. If M>1
then overmodulation occurs and reconstruction of message signal from the transmitted signal would lead in loss
of original signal. Amplitude modulation results when the If we just look at the short-term spectrum of modulation,
carrier c(t) is multiplied by the positive quantity (1+m(t)): changing as it would for a human voice for instance, then
we can plot the frequency content (horizontal axis) as a
function of time (vertical axis) as in Fig. 3. It can again be
seen that as the modulation frequency content varies, at
In this simple case M is identical to the modulation in- any point in time there is an upper sideband generated acdex, discussed below. With M=0.5 the amplitude mod- cording to those frequencies shifted above the carrier freulated signal y(t) thus corresponds to the top graph (la- quency, and the same content mirror-imaged in the lower
belled 50% Modulation) in Figure 4.
sideband below the carrier frequency. At all times, the

1.6. MODULATION INDEX

5
pensive receivers using envelope detection. Even (analog)
television, with a (largely) suppressed lower sideband, includes sucient carrier power for use of envelope detection. But for communications systems where both transmitters and receivers can be optimized, suppression of
both one sideband and the carrier represent a net advantage and are frequently employed.

1.6 Modulation index

The AM modulation index is a measure based on the ratio
of the modulation excursions of the RF signal to the level
of the unmodulated carrier. It is thus dened as:
Fig 3: The spectrogram of an AM voice broadcast shows the two
sidebands (green) on either side of the carrier (red) with time
proceeding in the vertical direction.

h=

peak value of m(t)

M
=
A
A

carrier itself remains constant, and of greater power than where M and A are the modulation amplitude and carthe total sideband power.
rier amplitude, respectively; the modulation amplitude is
the peak (positive or negative) change in the RF amplitude from its unmodulated value. Modulation index is
1.5 Power and spectrum eciency normally expressed as a percentage, and may be displayed
on a meter connected to an AM transmitter.
So if h = 0.5 , carrier amplitude varies by 50% above
(and below) its unmodulated level, as is shown in the rst
waveform, below. For h = 1.0 , it varies by 100% as
shown in the illustration below it. With 100% modulation the wave amplitude sometimes reaches zero, and
this represents full modulation using standard AM and
is often a target (in order to obtain the highest possible signal to noise ratio) but mustn't be exceeded. Increasing the modulating signal beyond that point, known
as overmodulation, causes a standard AM modulator
(see below) to fail, as the negative excursions of the
wave envelope cannot become less than zero, resulting in
distortion (clipping) of the received modulation. Transmitters typically incorporate a limiter circuit to avoid
overmodulation, and/or a compressor circuit (especially
for
voice communications) in order to still approach
Another improvement over standard AM is obtained
100%
modulation for maximum intelligibility above the
through reduction or suppression of the carrier componoise.
Such
circuits are sometimes referred to as a vogad.
nent of the modulated spectrum. In Figure 2 this is the
spike in between the sidebands; even with full (100%) However it is possible to talk about a modulation index
sine wave modulation, the power in the carrier com- exceeding 100%, without introducing distortion, in the
ponent is twice that in the sidebands, yet it carries no case of double-sideband reduced-carrier transmission. In
unique information. Thus there is a great advantage in that case, negative excursions beyond zero entail a reeciency in reducing or totally suppressing the carrier, versal of the carrier phase, as shown in the third waveeither in conjunction with elimination of one sideband form below. This cannot be produced using the e(single-sideband suppressed-carrier transmission) or with cient high-level (output stage) modulation techniques (see
both sidebands remaining (double sideband suppressed below) which are widely used especially in high power
carrier). While these suppressed carrier transmissions are broadcast transmitters. Rather, a special modulator proecient in terms of transmitter power, they require more duces such a waveform at a low level followed by a linear
sophisticated receivers employing synchronous detection amplier. Whats more, a standard AM receiver using
and regeneration of the carrier frequency. For that rea- an envelope detector is incapable of properly demodulatson, standard AM continues to be widely used, especially ing such a signal. Rather, synchronous detection is rein broadcast transmission, to allow for the use of inex- quired. Thus double-sideband transmission is generally
The RF bandwidth of an AM transmission (refer to Figure 2, but only considering positive frequencies) is twice
the bandwidth of the modulating (or "baseband") signal,
since the upper and lower sidebands around the carrier
frequency each have a bandwidth as wide as the highest modulating frequency. Although the bandwidth of an
AM signal is narrower than one using frequency modulation (FM), it is twice as wide as single-sideband techniques; it thus may be viewed as spectrally inecient.
Within a frequency band, only half as many transmissions (or channels) can thus be accommodated. For
this reason television employs a variant of single-sideband
(known as vestigial sideband, somewhat of a compromise
in terms of bandwidth) in order to reduce the required
channel spacing.

CHAPTER 1. AMPLITUDE MODULATION

not referred to as AM even though it generates an identical RF waveform as standard AM as long as the modulation index is below 100%. Such systems more often
attempt a radical reduction of the carrier level compared
to the sidebands (where the useful information is present)
to the point of double-sideband suppressed-carrier transmission where the carrier is (ideally) reduced to zero. In
all such cases the term modulation index loses its value
as it refers to the ratio of the modulation amplitude to a
rather small (or zero) remaining carrier amplitude.
Amplitude
1.5

50% Modulation

0.5
0

Anode (plate) modulation. A tetrodes plate and screen grid voltage is modulated via an audio transformer. The resistor R1 sets
the grid bias; both the input and output are tuned circuits with
inductive coupling.

0.5

1.5
Time
Amplitude
2

100% Modulation

Message wave envelope

Carrier wave

typically at a frequency less than the desired RF-output

frequency. The analog signal must then be shifted in frequency and linearly amplied to the desired frequency
and power level (linear amplication must be used to prevent modulation distortion).[4] This low-level method for
AM is used in many Amateur Radio transceivers.[5]

2
Time
Amplitude
2.5

150% Modulation

1.7.2 High-level generation

0.5
0
0.5

2.5
Time

Fig 4: Modulation depth. In the diagram, the unmodulated carrier has an amplitude of 1.

1.7 Modulation methods

Modulation circuit designs may be classied as lowor high-level (depending on whether they modulate
in a low-power domainfollowed by amplication for
transmissionor in the high-power domain of the transmitted signal).[3]

1.7.1

AM may also be generated at a low level, using analog

methods described in the next section.

Low-level generation

In modern radio systems, modulated signals are generated via digital signal processing (DSP). With DSP many
types of AM are possible with software control (including DSB with carrier, SSB suppressed-carrier and independent sideband, or ISB). Calculated digital samples are
converted to voltages with a digital to analog converter,

High-power AM transmitters (such as those used for AM

broadcasting) are based on high-eciency class-D and
class-E power amplier stages, modulated by varying the
supply voltage.[6]
Older designs (for broadcast and amateur radio) also generate AM by controlling the gain of the transmitters nal
amplier (generally class-C, for eciency). The following types are for vacuum tube transmitters (but similar
options are available with transistors):[7]
Plate modulation: In plate modulation, the plate
voltage of the RF amplier is modulated with the
audio signal. The audio power requirement is 50
percent of the RF-carrier power.
Heising (constant-current) modulation: RF amplier plate voltage is fed through a choke (highvalue inductor). The AM modulation tube plate
is fed through the same inductor, so the modulator tube diverts current from the RF amplier. The
choke acts as a constant current source in the audio
range. This system has a low power eciency.
Control grid modulation: The operating bias and
gain of the nal RF amplier can be controlled by
varying the voltage of the control grid. This method

1.10. REFERENCES
requires little audio power, but care must be taken
to reduce distortion.
Clamp tube (screen grid) modulation: The
screen-grid bias may be controlled through a clamp
tube, which reduces voltage according to the modulation signal. It is dicult to approach 100-percent
modulation while maintaining low distortion with
this system.
Doherty modulation: One tube provides the power
under carrier conditions and another operates only
for positive modulation peaks. Overall eciency is
good, and distortion is low.

7
Sideband, for some explanation of what this is.
Types of radio emissions, for the emission types designated by the ITU
Airband
Citizens Band Radio
Quadrature amplitude modulation
DSB-SC

1.10 References

Outphasing modulation: Two tubes are operated

in parallel, but partially out of phase with each Notes
other. As they are dierentially phase modulated
their combined amplitude is greater or smaller. Ef[1] http://www.aminharadio.com/radio/files/
ciency is good and distortion low when properly adArtigo-Revista-PCP-USA.pdf
justed.
Pulse width modulation (PWM) or Pulse duration modulation (PDM): A highly ecient high
voltage power supply is applied to the tube plate.
The output voltage of this supply is varied at an audio rate to follow the program. This system was pioneered by Hilmer Swanson and has a number of
variations, all of which achieve high eciency and
sound quality.

1.8 Demodulation methods

The simplest form of AM demodulator consists of a diode
which is congured to act as envelope detector. Another
type of demodulator, the product detector, can provide
better-quality demodulation with additional circuit complexity.

1.9 See also

AM radio
AM stereo
Mediumwave band used for AM broadcast radio
Longwave band used for AM broadcast radio
Frequency modulation

[2] Bray, John (2002). Innovation and the Communications

Revolution: From the Victorian Pioneers to Broadband Internet. Inst. of Electrical Engineers. pp. 59, 6162.
ISBN 0852962185.
[3] A.P.Godse and U.A.Bakshi (2009). Communication Engineering. Technical Publications. p. 36. ISBN 978-818431-089-4.
[4] Silver, Ward, ed. (2011). Ch. 15 DSP and Software Radio Design. The ARRL Handbook for Radio Communications (Eighty-eighth ed.). American Radio Relay League.
ISBN 978-0-87259-096-0.
[5] Silver, Ward, ed. (2011). Ch. 14 Transceivers.
The ARRL Handbook for Radio Communications (Eightyeighth ed.). American Radio Relay League. ISBN 978-087259-096-0.
[6] Frederick H. Raab; et al. (May 2003). RF and Microwave Power Amplier and Transmitter Technologies
- Part 2. High Frequency Design: 22.
[7] Laurence Gray and Richard Graham (1961).
Transmitters. McGraw-Hill. pp. 141.

Radio

Sources
Newkirk, David and Karlquist, Rick (2004). Mixers, modulators and demodulators. In D. G. Reed
(ed.), The ARRL Handbook for Radio Communications (81st ed.), pp. 15.115.36. Newington:
ARRL. ISBN 0-87259-196-4.

Shortwave radio almost universally uses AM, narrow FM occurring above 25 MHz.
Modulation, for a list of other modulation techniques
Amplitude modulation signalling system (AMSS), a
digital system for adding low bitrate information to
an AM signal.

1.11 External links

Amplitude Modulation by Jakub Serych, Wolfram
Demonstrations Project.
Amplitude Modulation, by S Sastry.

CHAPTER 1. AMPLITUDE MODULATION

Amplitude Modulation, an introduction
Federation of American Scientists.

by

Amplitude Modulation tutorial video with example

transmitter circuit.
Amplitude Modulation tutorial including related
topics of modulators, demodulators, etc . .

Chapter 2

Modulation
For other uses, see Modulation (disambiguation).

In music synthesizers, modulation may be used to synthesise waveforms with an extensive overtone spectrum using a small number of oscillators. In this case the carrier
frequency is typically in the same order or much lower
than the modulating waveform (see frequency modulation synthesis or ring modulation synthesis).

In electronics and telecommunications, modulation is

the process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that typically contains information to be transmitted.
In telecommunications, modulation is the process of conveying a message signal, for example a digital bit stream
or an analog audio signal, inside another signal that can
be physically transmitted. Modulation of a sine waveform
transforms a baseband message signal into a passband signal.

2.1 Analog modulation methods

A modulator is a device that performs modulation. A

demodulator (sometimes detector or demod) is a device
that performs demodulation, the inverse of modulation.
A modem (from modulatordemodulator) can perform
both operations.
The aim of analog modulation is to transfer an analog
baseband (or lowpass) signal, for example an audio signal
or TV signal, over an analog bandpass channel at a dierent frequency, for example over a limited radio frequency
band or a cable TV network channel.
The aim of digital modulation is to transfer a digital bit
stream over an analog bandpass channel, for example over A low-frequency message signal (top) may be carried by an AM
the public switched telephone network (where a bandpass or FM radio wave.
lter limits the frequency range to 3003400 Hz) or over
In analog modulation, the modulation is applied continua limited radio frequency band.
ously in response to the analog information signal.
Analog and digital modulation facilitate frequency division multiplexing (FDM), where several low pass information signals are transferred simultaneously over the
2.1.1 List of analog modulation techniques
same shared physical medium, using separate passband
channels (several dierent carrier frequencies).
Common analog modulation techniques are:
The aim of digital baseband modulation methods, also
known as line coding, is to transfer a digital bit stream
Amplitude modulation (AM) (here the amplitude of
over a baseband channel, typically a non-ltered copper
the carrier signal is varied in accordance to the inwire such as a serial bus or a wired local area network.
stantaneous amplitude of the modulating signal)
The aim of pulse modulation methods is to transfer a
Double-sideband modulation (DSB)
narrowband analog signal, for example a phone call over
a wideband baseband channel or, in some of the schemes,
Double-sideband modulation with carrier
as a bit stream over another digital transmission system.
(DSB-WC) (used on the AM radio broadcasting band)
9

10

CHAPTER 2. MODULATION
Double-sideband
suppressed-carrier
transmission (DSB-SC)
Double-sideband reduced carrier transmission (DSB-RC)
Single-sideband modulation (SSB, or SSBAM)
Single-sideband modulation with carrier
(SSB-WC)
Single-sideband modulation suppressed
carrier modulation (SSB-SC)

1 second

symbol

10

00

11

01

Vestigial sideband modulation (VSB, or VSBAM)

Quadrature amplitude modulation (QAM)
Angle modulation, which is approximately constant
envelope
Frequency modulation (FM) (here the frequency of the carrier signal is varied in accordance to the instantaneous amplitude of the
modulating signal)
Phase modulation (PM) (here the phase shift
of the carrier signal is varied in accordance
with the instantaneous amplitude of the modulating signal)
Transpositional Modulation (TM), in which
the waveform inection is modied resulting
in a signal where each quarter cycle is transposed in the modulation process. TM is a
pesudo-analog modulation (AM). Where an
AM carrier also carries a phase variable phase
f(). TM is f(AM,)

2.2 Digital modulation methods

Schematic of 4 baud (8 bit/s) data link containing arbitrarily chosen values.

melody consisting of 1000 tones per second,

the symbol rate is 1000 symbols/second, or
baud. Since each tone (i.e., symbol) represents
a message consisting of two digital bits in this
example, the bit rate is twice the symbol rate,
i.e. 2000 bits per second. This is similar to the
technique used by dialup modems as opposed
to DSL modems.
According to one denition of digital signal, the modulated signal is a digital signal. According to another denition, the modulation is a form of digital-to-analog conversion. Most textbooks would consider digital modulation schemes as a form of digital transmission, synonymous to data transmission; very few would consider it as
analog transmission.

2.2.1 Fundamental
methods

digital

modulation

In digital modulation, an analog carrier signal is moduThe most fundamental digital modulation techniques are
lated by a discrete signal. Digital modulation methods
based on keying:
can be considered as digital-to-analog conversion, and
the corresponding demodulation or detection as analog PSK (phase-shift keying): a nite number of phases
to-digital conversion. The changes in the carrier signal
are used.
are chosen from a nite number of M alternative symbols
(the modulation alphabet).
FSK (frequency-shift keying): a nite number of
frequencies are used.
A simple example: A telephone line is
ASK (amplitude-shift keying): a nite number of
designed for transferring audible sounds, for
amplitudes are used.
example tones, and not digital bits (zeros and
ones). Computers may however communicate
QAM (quadrature amplitude modulation): a nite
over a telephone line by means of modems,
number of at least two phases and at least two amwhich are representing the digital bits by tones,
plitudes are used.
called symbols. If there are four alternative
symbols (corresponding to a musical instruIn QAM, an inphase signal (or I, with one example bement that can generate four dierent tones,
ing a cosine waveform) and a quadrature phase signal
one at a time), the rst symbol may represent
(or Q, with an example being a sine wave) are amplitude
the bit sequence 00, the second 01, the third
modulated with a nite number of amplitudes, and then
10 and the fourth 11. If the modem plays a

2.2. DIGITAL MODULATION METHODS

summed. It can be seen as a two-channel system, each
channel using ASK. The resulting signal is equivalent to
a combination of PSK and ASK.
In all of the above methods, each of these phases, frequencies or amplitudes are assigned a unique pattern of
binary bits. Usually, each phase, frequency or amplitude
encodes an equal number of bits. This number of bits
comprises the symbol that is represented by the particular phase, frequency or amplitude.

11
Carry out the modulation, for example by multiplying the sine and cosine waveform with the I and Q
signals, resulting in the equivalent low pass signal being frequency shifted to the modulated passband signal or RF signal. Sometimes this is achieved using
DSP technology, for example direct digital synthesis using a waveform table, instead of analog signal
processing. In that case the above DAC step should
be done after this step.

6. Amplication and analog bandpass ltering to avoid

If the alphabet consists of M = 2N alternative symbols,
harmonic distortion and periodic spectrum.
each symbol represents a message consisting of N bits. If
the symbol rate (also known as the baud rate) is fS symbols/second (or baud), the data rate is N fS bit/second.
At the receiver side, the demodulator typically performs:
For example, with an alphabet consisting of 16 alternative
symbols, each symbol represents 4 bits. Thus, the data
1. Bandpass ltering.
rate is four times the baud rate.
2. Automatic gain control, AGC (to compensate for
In the case of PSK, ASK or QAM, where the carrier
attenuation, for example fading).
frequency of the modulated signal is constant, the modulation alphabet is often conveniently represented on a
3. Frequency shifting of the RF signal to the equivaconstellation diagram, showing the amplitude of the I siglent baseband I and Q signals, or to an intermediate
nal at the x-axis, and the amplitude of the Q signal at the
frequency (IF) signal, by multiplying the RF signal
y-axis, for each symbol.
with a local oscillator sinewave and cosine wave frequency (see the superheterodyne receiver principle).

2.2.2

Modulator and detector principles of

operation

PSK and ASK, and sometimes also FSK, are often generated and detected using the principle of QAM. The I
and Q signals can be combined into a complex-valued
signal I+jQ (where j is the imaginary unit). The resulting so called equivalent lowpass signal or equivalent
baseband signal is a complex-valued representation of
the real-valued modulated physical signal (the so-called
passband signal or RF signal).
These are the general steps used by the modulator to
transmit data:

4. Sampling and analog-to-digital conversion (ADC)

(sometimes before or instead of the above point, for
example by means of undersampling).
5. Equalization ltering, for example a matched lter, compensation for multipath propagation, time
spreading, phase distortion and frequency selective
fading, to avoid intersymbol interference and symbol distortion.
6. Detection of the amplitudes of the I and Q signals,
or the frequency or phase of the IF signal.
7. Quantization of the amplitudes, frequencies or
phases to the nearest allowed symbol values.

1. Group the incoming data bits into codewords, one

for each symbol that will be transmitted.

8. Mapping of the quantized amplitudes, frequencies

or phases to codewords (bit groups).

2. Map the codewords to attributes, for example amplitudes of the I and Q signals (the equivalent low
pass signal), or frequency or phase values.

9. Parallel-to-serial conversion of the codewords into a

bit stream.

10. Pass the resultant bit stream on for further process3. Adapt pulse shaping or some other ltering to limit
ing such as removal of any error-correcting codes.
the bandwidth and form the spectrum of the equivalent low pass signal, typically using digital signal
As is common to all digital communication systems, the
processing.
design of both the modulator and demodulator must be
4. Perform digital to analog conversion (DAC) of the done simultaneously. Digital modulation schemes are
I and Q signals (since today all of the above is possible because the transmitter-receiver pair have prior
normally achieved using digital signal processing, knowledge of how data is encoded and represented in
the communications system. In all digital communicaDSP).
tion systems, both the modulator at the transmitter and
5. Generate a high frequency sine carrier waveform, the demodulator at the receiver are structured so that they
and perhaps also a cosine quadrature component. perform inverse operations.

12

CHAPTER 2. MODULATION

Non-coherent modulation methods do not require a receiver reference clock signal that is phase synchronized
with the sender carrier signal. In this case, modulation
symbols (rather than bits, characters, or data packets)
are asynchronously transferred. The opposite is coherent
modulation.

2.2.3

List of common digital modulation

techniques

The most common digital modulation techniques are:

Trellis coded modulation (TCM), also known as

Trellis modulation
Spread-spectrum techniques
Direct-sequence spread spectrum (DSSS)
Chirp spread spectrum (CSS) according to
IEEE 802.15.4a CSS uses pseudo-stochastic
coding
Frequency-hopping spread spectrum (FHSS)
applies a special scheme for channel release

MSK and GMSK are particular cases of continuous phase

modulation. Indeed, MSK is a particular case of the subfamily of CPM known as continuous-phase frequency Binary PSK (BPSK), using M=2 symbols
shift keying (CPFSK) which is dened by a rectangular
Quadrature PSK (QPSK), using M=4 symbols frequency pulse (i.e. a linearly increasing phase pulse) of
one symbol-time duration (total response signaling).
8PSK, using M=8 symbols

Phase-shift keying (PSK)

16PSK, using M=16 symbols

OFDM is based on the idea of frequency-division multiplexing (FDM), but the multiplexed streams are all parts
Dierential PSK (DPSK)
of a single original stream. The bit stream is split into
Dierential QPSK (DQPSK)
several parallel data streams, each transferred over its
own sub-carrier using some conventional digital modu Oset QPSK (OQPSK)
lation scheme. The modulated sub-carriers are summed
/4QPSK
to form an OFDM signal. This dividing and recombining helps with handling channel impairments. OFDM is
Frequency-shift keying (FSK)
considered as a modulation technique rather than a mul Audio frequency-shift keying (AFSK)
tiplex technique, since it transfers one bit stream over
Multi-frequency shift keying (M-ary FSK or one communication channel using one sequence of socalled OFDM symbols. OFDM can be extended to multiMFSK)
user channel access method in the orthogonal frequency Dual-tone multi-frequency (DTMF)
division multiple access (OFDMA) and multi-carrier
code division multiple access (MC-CDMA) schemes, alAmplitude-shift keying (ASK)
lowing several users to share the same physical medium
On-o keying (OOK), the most common ASK form by giving dierent sub-carriers or spreading codes to different users.
M-ary vestigial sideband modulation, for exOf the two kinds of RF power amplier, switching amample 8VSB
pliers (Class D ampliers) cost less and use less batQuadrature amplitude modulation (QAM), a com- tery power than linear ampliers of the same output
power. However, they only work with relatively constantbination of PSK and ASK
amplitude-modulation signals such as angle modulation
Polar modulation like QAM a combination of (FSK or PSK) and CDMA, but not with QAM and
PSK and ASK
OFDM. Nevertheless, even though switching ampliers
are completely unsuitable for normal QAM constellaContinuous phase modulation (CPM) methods
tions, often the QAM modulation principle are used to
drive switching ampliers with these FM and other wave Minimum-shift keying (MSK)
forms, and sometimes QAM demodulators are used to
Gaussian minimum-shift keying (GMSK)
receive the signals put out by these switching ampliers.
Continuous-phase frequency-shift keying
(CPFSK)

Orthogonal
frequency-division
(OFDM) modulation

multiplexing

2.2.4 Automatic digital modulation recognition (ADMR)

Discrete multitone (DMT), including adaptive Automatic digital modulation recognition in intelligent
communication systems is one of the most important ismodulation and bit-loading
sues in software dened radio and cognitive radio. Ac Wavelet modulation
cording to incremental expanse of intelligent receivers,

2.4. MISCELLANEOUS MODULATION TECHNIQUES

13

automatic modulation recognition becomes a challenging

Pulse-width modulation (PWM) and Pulse-depth
topic in telecommunication systems and computer engimodulation (PDM)
neering. Such systems have many civil and military appli Pulse-position modulation (PPM)
cations. Moreover, blind recognition of modulation type
is an important problem in commercial systems, especially in software dened radio. Usually in such systems, Analog-over-digital methods
there are some extra information for system conguration, but considering blind approaches in intelligent re Pulse-code modulation (PCM)
ceivers, we can reduce information overload and increase
Dierential PCM (DPCM)
transmission performance.[1] Obviously, with no knowledge of the transmitted data and many unknown param Adaptive DPCM (ADPCM)
eters at the receiver, such as the signal power, carrier frequency and phase osets, timing information, etc., blind
Delta modulation (DM or -modulation)
identication of the modulation is a dicult task. This
Delta-sigma modulation ()
becomes even more challenging in real-world scenarios with multipath fading, frequency-selective and time Continuously variable slope delta modulation
varying channels.[2]
(CVSDM), also called Adaptive-delta modulation
There are two main approaches to automatic modula(ADM)
tion recognition. The rst approach uses likelihood-based
Pulse-density modulation (PDM)
methods to assign an input signal to a proper class. Another recent approach is based on feature extraction.

2.2.5

Digital baseband modulation or line

coding

Main article: Line code

The term digital baseband modulation (or digital baseband transmission) is synonymous to line codes. These
are methods to transfer a digital bit stream over an analog baseband channel (a.k.a. lowpass channel) using
a pulse train, i.e. a discrete number of signal levels,
by directly modulating the voltage or current on a cable. Common examples are unipolar, non-return-to-zero
(NRZ), Manchester and alternate mark inversion (AMI)
codings.[3]

2.3 Pulse modulation methods

Pulse modulation schemes aim at transferring a narrowband analog signal over an analog baseband channel as
a two-level signal by modulating a pulse wave. Some
pulse modulation schemes also allow the narrowband analog signal to be transferred as a digital signal (i.e., as a
quantized discrete-time signal) with a xed bit rate, which
can be transferred over an underlying digital transmission system, for example, some line code. These are not
modulation schemes in the conventional sense since they
are not channel coding schemes, but should be considered
as source coding schemes, and in some cases analog-todigital conversion techniques.
Analog-over-analog methods
Pulse-amplitude modulation (PAM)

2.4 Miscellaneous
techniques

modulation

The use of on-o keying to transmit Morse code

at radio frequencies is known as continuous wave
(CW) operation.
Adaptive modulation
Space modulation is a method whereby signals are
modulated within airspace such as that used in
instrument landing systems.

2.5 Further reading

Multipliers vs. Modulators Analog Dialogue, June
2013

2.6 See also

Neuromodulation
Demodulation
Electrical resonance
Heterodyne
Modulation order
Types of radio emissions
Communications channel
Channel access methods

14
Channel coding
Line code
Telecommunication
Modem
RF modulator
Codec
Ring modulation

2.7 References
[1] M. Hadi Valipour, M. Mehdi Homayounpour and M.
Amin Mehralian, Automatic digital modulation recognition in presence of noise using SVM and PSO, in Proceedings of 2012 Sixth International Symposium on Telecommunications (IST), pp 378-382, Nov 2012, Tehran, Iran.
[2] Dobre, Octavia A., Ali Abdi, Yeheskel Bar-Ness, and Wei
Su. Communications, IET 1, no. 2 (2007): 137-156.
(2007). Survey of automatic modulation classication
techniques: classical approaches and new trends (PDF).
IET Communications: 137156.
[3] Ke-Lin Du & M. N. S. Swamy (2010). Wireless Communication Systems: From RF Subsystems to 4G Enabling
Technologies. Cambridge University Press. p. 188. ISBN
978-0-521-11403-5.

2.8 External links

Interactive presentation of soft-demapping for
AWGN-channel in a web-demo Institute of
Telecommunications, University of Stuttgart
Modem(Modulation and Demodulation)

CHAPTER 2. MODULATION

Chapter 3

Radio
This article is about science and technology. For broadcasting, see Radio broadcasting. For other uses, see
Radio (disambiguation).
Radio is the technology of using radio waves to carry

Classic radio receiver dial

modulation). Radio systems also need an antenna to convert electric currents into radio waves, and vice versa. An
antenna can be used for both transmitting and receiving.
The electrical resonance of tuned circuits in radios allow
individual stations to be selected. The electromagnetic
wave is intercepted by a tuned receiving antenna. A radio
receiver receives its input from an antenna and converts it
into a form usable for the consumer, such as sound, pictures, digital data, measurement values, navigational positions, etc.[2] Radio frequencies occupy the range from
a 3 kHz to 300 GHz, although commercially important
uses of radio use only a small part of this spectrum.[3]
A radio communication system sends signals by radio.[4]
The radio equipment involved in communication systems
includes a transmitter and a receiver, each having an
The Alexandra Palace, here: mast of the broadcasting station
antenna and appropriate terminal equipment such as a
information, such as sound, by systematically modulating microphone at the transmitter and a loudspeaker at the
[5]
some property of electromagnetic energy waves transmit- receiver in the case of a voice-communication system.
ted through space, such as their amplitude, frequency,
phase, or pulse width.[n 1] When radio waves strike
an electrical conductor, the oscillating elds induce an 3.1 Etymology
alternating current in the conductor. The information in
the waves can be extracted and transformed back into its The term radio is derived from the Latin word radius,
original form.
meaning spoke of a wheel, beam of light, ray. It was
Radio systems need a transmitter to modulate (change)
some property of the energy produced to impress a signal
on it, for example using amplitude modulation or angle
modulation (which can be frequency modulation or phase

rst applied to communications in 1881 when, at the suggestion of French scientist Ernest Mercadier, Alexander
Graham Bell adopted radiophone (meaning radiated
sound) as an alternate name for his photophone optical

15

16

CHAPTER 3. RADIO

transmission system.[6] However, this invention would not Radio Times since its founding in the early 1920s.
be widely adopted.
In recent years the more general term wireless has
Following Heinrich Hertz's establishment of the existence gained renewed popularity, even for devices using elecof electromagnetic radiation in the late 1880s, a vari- tromagnetic radiation, through the rapid growth of shortety of terms were initially used for the phenomenon, range computer networking, e.g., Wireless Local Area
with early descriptions of the radiation itself including Network (WLAN), Wi-Fi, and Bluetooth, as well as moHertzian waves, electric waves, and ether waves, bile telephony, e.g., GSM and UMTS cell phones. Towhile phrases describing its use in communications in- day, the term radio species the transceiver device or
cluded spark telegraphy, space telegraphy, aerogra- chip, whereas wireless refers to the lack of physical
phy and, eventually and most commonly, wireless teleg- connections; thus equipment employs embedded radio
raphy. However, wireless included a broad variety of transceivers, but operates as wireless devices over wirerelated electronic technologies, including electrostatic in- less sensor networks.
duction, electromagnetic induction and aquatic and earth
conduction, so there was a need for a more precise term
referring exclusively to electromagnetic radiation.
3.2 Processes
The rst use of radio- in conjunction with electromagnetic radiation appears to have been by French physicist douard Branly, who in 1890 developed a version
of a coherer receiver he called a radio-conducteur.[7] The
radio- prex was later used to form additional descriptive compound and hyphenated words, especially in Europe, for example, in early 1898 the British publication
The Practical Engineer included a reference to the radiotelegraph and radiotelegraphy,[8] while the French
text of both the 1903 and 1906 Berlin Radiotelegraphic
Conventions includes the phrases radiotlgraphique and
radiotlgrammes.
The use of radio as a standalone word dates back
to at least December 30, 1904, when instructions issued by the British Post Oce for transmitting telegrams specied that The word 'Radio'... is sent in
the Service Instructions.[9] This practice was universally
adopted, and the word radio introduced internationally, by the 1906 Berlin Radiotelegraphic Convention,
which included a Service Regulation specifying that Radiotelegrams shall show in the preamble that the service
is 'Radio'".
The switch to radio in place of wireless took place
slowly and unevenly in the English-speaking world. Lee
de Forest helped popularize the new word in the United
Statesin early 1907 he founded the DeForest Radio
Telephone Company, and his letter in the June 22, 1907
Electrical World about the need for legal restrictions
warned that Radio chaos will certainly be the result until such stringent regulation is enforced.[10] The United
States Navy would also play a role. Although its translation of the 1906 Berlin Convention used the terms wireless telegraph and wireless telegram, by 1912 it began
to promote the use of radio instead. The term started
to become preferred by the general public in the 1920s
with the introduction of broadcasting. (Broadcasting is
based upon an agricultural term meaning roughly scattering seeds widely.) British Commonwealth countries
continued to commonly use the term wireless until the
mid-20th century, though the magazine of the British
Broadcasting Corporation in the UK has been called

Radio communication. Information such as sound is converted

by a transducer such as a microphone to an electrical signal,
which modulates a radio wave sent from a transmitter. A receiver
intercepts the radio wave and extracts the information-bearing
electronic signal, which is converted back using another transducer such as a speaker.

Radio systems used for communication have the following elements. With more than 100 years of development,
each process is implemented by a wide range of methods,
specialised for dierent communications purposes.

3.2.1 Transmitter and modulation

Main article: Radio transmitter
See also: Radio transmitter design
Each system contains a transmitter, This consists of a
source of electrical energy, producing alternating current
of a desired frequency of oscillation. The transmitter contains a system to modulate (change) some property of the
energy produced to impress a signal on it. This modulation might be as simple as turning the energy on and
o, or altering more subtle properties such as amplitude,
frequency, phase, or combinations of these properties.
The transmitter sends the modulated electrical energy to a
tuned resonant antenna; this structure converts the rapidly
changing alternating current into an electromagnetic wave
that can move through free space (sometimes with a particular polarization).
Amplitude modulation of a carrier wave works by varying the strength of the transmitted signal in proportion to
the information being sent. For example, changes in the

3.2. PROCESSES

17

An audio signal (top) may be carried by an AM or FM radio

wave.

signal strength can be used to reect the sounds to be reproduced by a speaker, or to specify the light intensity of
television pixels. It was the method used for the rst audio radio transmissions, and remains in use today. AM
is often used to refer to the medium wave broadcast band
(see AM radio), but it is used in various radiotelephone
services such as the Citizen Band, amateur radio and es- Rooftop television antennas. Yagi-Uda antennas like these six are
pecially in aviation, due to its ability to be received under widely used at VHF and UHF frequencies.
very weak signal conditions and its immunity to capture
eect, allowing more than one signal to be heard simulduce a tiny voltage at its terminals, that is applied to a
taneously.
receiver to be amplied. Some antennas can be used for
Frequency modulation varies the frequency of the carrier. both transmitting and receiving, even simultaneously, deThe instantaneous frequency of the carrier is directly pro- pending on the connected equipment.
portional to the instantaneous value of the input signal.
FM has the "capture eect" whereby a receiver only receives the strongest signal, even when others are present. 3.2.3 Propagation
Digital data can be sent by shifting the carriers frequency
among a set of discrete values, a technique known as Main article: Radio propagation
frequency-shift keying. FM is commonly used at Very
high frequency (VHF) radio frequencies for high-delity
broadcasts of music and speech (see FM broadcasting). Once generated, electromagnetic waves travel through
space either directly, or have their path altered by
Analog TV sound is also broadcast using FM.
reection, refraction or diraction. The intensity of
Angle modulation alters the instantaneous phase of the the waves diminishes due to geometric dispersion (the
carrier wave to transmit a signal. It may be either FM or inverse-square law); some energy may also be absorbed
phase modulation (PM).
by the intervening medium in some cases. Noise will generally alter the desired signal; this electromagnetic interference comes from natural sources, as well as from ar3.2.2 Antenna
ticial sources such as other transmitters and accidental
radiators. Noise is also produced at every step due to the
inherent properties of the devices used. If the magniMain article: Antenna (radio)
An antenna (or aerial) is an electrical device which con- tude of the noise is large enough, the desired signal will
verts electric currents into radio waves, and vice versa. It no longer be discernible; the signal-to-noise ratio is the
is usually used with a radio transmitter or radio receiver. fundamental limit to the range of radio communications.
In transmission, a radio transmitter supplies an electric
current oscillating at radio frequency (i.e. high frequency
AC) to the antennas terminals, and the antenna radiates 3.2.4 Resonance
the energy from the current as electromagnetic waves (radio waves). In reception, an antenna intercepts some of Main article: Electrical resonance
the power of an electromagnetic wave in order to pro- See also: LC circuit

18

CHAPTER 3. RADIO

3.2.6 Radio band

Electrical resonance of tuned circuits in radios allow individual stations to be selected. A resonant circuit will Main article: Radio frequency
respond strongly to a particular frequency, and much less
so to diering frequencies. This allows the radio receiver
to discriminate between multiple signals diering in fre- Radio frequencies occupy the range from a 3 kHz to 300
GHz, although commercially important uses of radio use
quency.
only a small part of this spectrum.[12] Other types of
electromagnetic radiation, with frequencies above the RF
range, are infrared, visible light, ultraviolet, X-rays and
gamma rays. Since the energy of an individual photon of
3.2.5 Receiver and demodulation
radio frequency is too low to remove an electron from an
atom, radio waves are classied as non-ionizing radiation.
Main article: Radio receiver
See also: Radio receiver design, Crystal radio, and
Communications receiver
The electromagnetic wave is intercepted by a tuned re-

3.3 Communication systems

A radio communication system sends signals by radio.[13]
Types of radio communication systems deployed depend
on technology, standards, regulations, radio spectrum
allocation, user requirements, service positioning, and
investment.[14]
The radio equipment involved in communication systems
includes a transmitter and a receiver, each having an
antenna and appropriate terminal equipment such as a
A crystal receiver, consisting of an antenna, adjustable microphone at the transmitter and a loudspeaker at the
electromagnetic coil, crystal rectier, capacitor, headphones and receiver in the case of a voice-communication system.[15]
ground connection.

The power consumed in a transmitting station varies depending on the distance of communication and the transmission conditions. The power received at the receiving
station is usually only a tiny fraction of the transmitters
output, since communication depends on receiving the
information, not the energy, that was transmitted.

ceiving antenna; this structure captures some of the energy of the wave and returns it to the form of oscillating electrical currents. At the receiver, these currents are
demodulated, which is conversion to a usable signal form
by a detector sub-system. The receiver is "tuned" to re- Classical radio communications systems use frequencyspond preferentially to the desired signals, and reject undivision multiplexing (FDM) as a strategy to split up and
desired signals.
share the available radio-frequency bandwidth for use by
Early radio systems relied entirely on the energy collected dierent parties communications concurrently. Modern
by an antenna to produce signals for the operator. Ra- radio communication systems include those that divide
dio became more useful after the invention of electronic up a radio-frequency band by time-division multiplexing
devices such as the vacuum tube and later the transistor, (TDM) and code-division multiplexing (CDM) as alterwhich made it possible to amplify weak signals. Today ra- natives to the classical FDM strategy. These systems ofdio systems are used for applications from walkie-talkie fer dierent tradeos in supporting multiple users, bechildrens toys to the control of space vehicles, as well as yond the FDM strategy that was ideal for broadcast radio
for broadcasting, and many other applications.
but less so for applications such as mobile telephony.
A radio receiver receives its input from an antenna, uses
electronic lters to separate a wanted radio signal from all
other signals picked up by this antenna, amplies it to a
level suitable for further processing, and nally converts
through demodulation and decoding the signal into a form
usable for the consumer, such as sound, pictures, digital
data, measurement values, navigational positions, etc.[11]

A radio communication system may send information

only one way. For example, in broadcasting a single transmitter sends signals to many receivers. Two stations may
take turns sending and receiving, using a single radio frequency; this is called simplex. By using two radio frequencies, two stations may continuously and concurrently
send and receive signals - this is called "duplex" operation.

3.5. USES OF RADIO

3.4 History

19

3.5 Uses of radio

For a broader coverage related to this topic, see Radio
spectrum Applications.

Main article: History of radio

In 1864 James Clerk Maxwell showed mathematically
that electromagnetic waves could propagate through free
space.[16] The eects of electromagnetic waves (thenunexplained "action at a distance" sparking behavior)
were actually observed before and after Maxwells work
by many inventors and experimenters including Luigi
Galvani (1791), Peter Samuel Munk (1835), Joseph
Henry (1842), Samuel Alfred Varley (1852), Edwin
Houston, Elihu Thomson, Thomas Edison (1875) and
David Edward Hughes (1878).[17][18][19] Edison gave the
eect the name "etheric force"[20] and Hughes detected
a spark impulse up to 500 yards (460 m) with a portable
receiver, but none could identify what caused the phenomenon and it was usually written o as electromagnetic
induction.[21] In 1886 Heinrich Rudolf Hertz noticed the
same sparking phenomenon and, in published experiments (1887-1888), was able to demonstrate the existence of electromagnetic waves in an experiment conrming Maxwells theory of electromagnetism. The discovery
of these Hertzian waves (radio waves) prompted many
experiments by physicists. An August 1894 lecture by
the British physicist Oliver Lodge, where he transmitted
and received Hertzian waves at distances up to 50 meters, was followed up a year later with experiments by
Indian physicist Jagadish Bose in radio microwave optics
and construction of a radio based lightning detector by
Russian physicist Alexander Stepanovich Popov. Starting in late 1894, Guglielmo Marconi began pursuing the
idea of building a wireless telegraphy system based on
Hertzian waves (radio). Marconi gained a patent on the
system in 1896 and developed it into a commercial communication system over the next few years.[22]

Early uses were maritime, for sending telegraphic messages using Morse code between ships and land. The earliest users included the Japanese Navy scouting the Russian eet during the Battle of Tsushima in 1905. One of
the most memorable uses of marine telegraphy was during the sinking of the RMS Titanic in 1912, including
communications between operators on the sinking ship
and nearby vessels, and communications to shore stations
listing the survivors.
Radio was used to pass on orders and communications
between armies and navies on both sides in World War
I; Germany used radio communications for diplomatic
messages once it discovered that its submarine cables had
been tapped by the British. The United States passed
on President Woodrow Wilson's Fourteen Points to Germany via radio during the war. Broadcasting began from
San Jose, California in 1909,[23] and became feasible in
the 1920s, with the widespread introduction of radio receivers, particularly in Europe and the United States. Besides broadcasting, point-to-point broadcasting, including telephone messages and relays of radio programs, became widespread in the 1920s and 1930s. Another use of
radio in the pre-war years was the development of detection and locating of aircraft and ships by the use of radar
(RAdio Detection And Ranging).

Today, radio takes many forms, including wireless networks and mobile communications of all types, as well as
radio broadcasting. Before the advent of television, commercial radio broadcasts included not only news and music, but dramas, comedies, variety shows, and many other
forms of entertainment (the era from the late 1920s to
the mid-1950s is commonly called radios Golden Age).
Radio was unique among methods of dramatic presentation in that it used only sound. For more, see radio proEarly 20th century radio systems transmitted messages
gramming.
by continuous wave code only. Early attempts at developing a system of amplitude modulation for voice and
music were demonstrated in 1900 and 1906, but had little success. World War I accelerated the development of 3.5.1 Audio
radio for military communications, and in this era the rst
vacuum tubes were applied to radio transmitters and re- One-way
ceivers. Electronic amplication was a key development
in changing radio from an experimental practice by ex- Main article: Radio broadcasting
perts into a home appliance. After the war, commercial AM radio uses amplitude modulation, in which the amradio broadcasting began in the 1920s and became an im- plitude of the transmitted signal is made proportional to
portant mass medium for entertainment and news.
the sound amplitude captured (transduced) by the miWorld War II again accelerated development of radio for crophone, while the transmitted frequency remains unthe wartime purposes of aircraft and land communica- changed. Transmissions are aected by static and intion, radio navigation and radar. After the war, the ex- terference because lightning and other sources of radio
periments in television that had been interrupted were re- emissions on the same frequency add their amplitudes to
sumed, and it also became an important home entertain- the original transmitted amplitude.
ment medium.

In the early part of the 20th century, American AM ra-

20

Bakelite radio at the Bakelite Museum, Orchard Mill, Williton,

Somerset, UK.

CHAPTER 3. RADIO

Bush House, old home of the BBC World Service.

FM broadcast radio sends music and voice with less noise

than AM radio. It is often mistakenly thought that FM is
higher delity than AM, but that is not true. AM is capable of the same audio bandwidth that FM employs. AM
receivers typically use narrower lters in the receiver to
recover the signal with less noise. AM stereo receivers
can reproduce the same audio bandwidth that FM does
due to the wider lter used in an AM stereo receiver,
but today, AM radios limit the audio bandpass to 35
kHz. In frequency modulation, amplitude variation at the
microphone causes the transmitter frequency to uctuate.
Because the audio signal modulates the frequency and not
the amplitude, an FM signal is not subject to static and
A Fisher 500 AM/FM hi- receiver from 1959.
interference in the same way as AM signals. Due to its
need for a wider bandwidth, FM is transmitted in the Very
High Frequency (VHF, 30 MHz to 300 MHz) radio specdio stations broadcast with powers as high as 500 kW, trum.
and some could be heard worldwide; these stations transmitters were commandeered for military use by the US VHF radio waves act more like light, traveling in straight
Government during World War II. Currently, the max- lines; hence the reception range is generally limited to
imum broadcast power for a civilian AM radio station about 50200 miles (80322 km). During unusual upin the United States and Canada is 50 kW, and the ma- per atmospheric conditions, FM signals are occasionally
jority of stations that emit signals this powerful were reected back towards the Earth by the ionosphere, regrandfathered in (see List of 50 kW AM radio stations sulting in long distance FM reception. FM receivers are
in the United States). In 1986 KTNN received the last subject to the capture eect, which causes the radio to
granted 50,000-watt class A license. These 50 kW sta- only receive the strongest signal when multiple signals aptions are generally called "clear channel" stations (not to pear on the same frequency. FM receivers are relatively
be confused with Clear Channel Communications), be- immune to lightning and spark interference.
cause within North America each of these stations has High power is useful in penetrating buildings, diracting
exclusive use of its broadcast frequency throughout part around hills, and refracting in the dense atmosphere near
or all of the broadcast day.
the horizon for some distance beyond the horizon. Conse-

3.5. USES OF RADIO

21

quently, 100,000-watt FM stations can regularly be heard Marine voice radios can use single sideband voice (SSB)
up to 100 miles (160 km) away, and farther, 150 miles in the shortwave High Frequency (HF3 MHz to 30
(240 km), if there are no competing signals.
MHz) radio spectrum for very long ranges or Marine
A few old, grandfathered stations do not conform to VHF radio / narrowband FM in the VHF spectrum for
these power rules. WBCT-FM (93.7) in Grand Rapids, much shorter ranges. Narrowband FM sacrices delity
Michigan, US, runs 320,000 watts ERP, and can increase to make more channels available within the radio specto 500,000 watts ERP by the terms of its original license. trum, by using a smaller range of radio frequencies, usuSuch a huge power level does not usually help to increase ally with ve kHz of deviation, versus the 75 kHz used
by commercial FM broadcasts, and 25 kHz used for TV
range as much as one might expect, because VHF frequencies travel in nearly straight lines over the horizon sound.
and o into space. Nevertheless, when there were fewer
FM stations competing, this station could be heard near
Bloomington, Illinois, US, almost 300 miles (480 km)
away.

Government, police, re and commercial voice services

also use narrowband FM on special frequencies. Early
police radios used AM receivers to receive one-way dispatches.

FM subcarrier services are secondary signals transmitted

in a piggyback fashion along with the main program.
Special receivers are required to utilize these services.
Analog channels may contain alternative programming,
such as reading services for the blind, background music or stereo sound signals. In some extremely crowded
metropolitan areas, the sub-channel program might be an
alternate foreign-language radio program for various ethnic groups. Sub-carriers can also transmit digital data,
such as station identication, the current songs name,
web addresses, or stock quotes. In some countries, FM
radios automatically re-tune themselves to the same channel in a dierent district by using sub-bands.

Civil and military HF (high frequency) voice services use

shortwave radio to contact ships at sea, aircraft and isolated settlements. Most use single sideband voice (SSB),
which uses less bandwidth than AM.[24] On an AM radio SSB sounds like ducks quacking, or the adults in a
Charlie Brown cartoon. Viewed as a graph of frequency
versus power, an AM signal shows power where the frequencies of the voice add and subtract with the main radio
frequency. SSB cuts the bandwidth in half by suppressing
the carrier and one of the sidebands. This also makes the
transmitter about three times more powerful, because it
doesn't need to transmit the unused carrier and sideband.

Two-way
Main article: Two-way radio
Aviation voice radios use Aircraft band VHF AM. AM
is used so that multiple stations on the same channel can
be received. (Use of FM would result in stronger stations blocking out reception of weaker stations due to
FMs capture eect). Aircraft y high enough that their
transmitters can be received hundreds of miles away, even
though they are using VHF.

TETRA, Terrestrial Trunked Radio is a digital cell phone

system for military, police and ambulances. Commercial
services such as XM, WorldSpace and Sirius oer encrypted digital satellite radio.

3.5.2 Telephony
Mobile phones transmit to a local cell site (transmitter/receiver) that ultimately connects to the public
switched telephone network (PSTN) through an optic
ber or microwave radio and other network elements.
When the mobile phone nears the edge of the cell sites
radio coverage area, the central computer switches the
phone to a new cell. Cell phones originally used FM, but
now most use various digital modulation schemes. Recent developments in Sweden (such as DROPme) allow
for the instant downloading of digital material from a radio broadcast (such as a song) to a mobile phone.
Satellite phones use satellites rather than cell towers to
communicate.

3.5.3 Video

Degen DE1103, an advanced world mini-receiver with single

sideband modulation and dual conversion

Analog television sends the picture as AM and the sound

as AM or FM, with the sound carrier a xed frequency
(4.5 MHz in the NTSC system) away from the video carrier. Analog television also uses a vestigial sideband on
the video carrier to reduce the bandwidth required.
Digital television uses 8VSB modulation in North Amer-

22

CHAPTER 3. RADIO

ica (under the ATSC digital television standard), and

COFDM modulation elsewhere in the world (using the
DVB-T standard). A ReedSolomon error correction
code adds redundant correction codes and allows reliable reception during moderate data loss. Although many
current and future codecs can be sent in the MPEG
transport stream container format, as of 2006 most systems use a standard-denition format almost identical to
DVD: MPEG-2 video in Anamorphic widescreen and
MPEG layer 2 (MP2) audio. High-denition television
is possible simply by using a higher-resolution picture,
but H.264/AVC is being considered as a replacement
video codec in some regions for its improved compression. With the compression and improved modulation
involved, a single channel can contain a high-denition
program and several standard-denition programs.

gation potential to civil aircraft.

3.5.5 Radar
Main article: Radar
Radar (Radio Detection And Ranging) detects objects at
a distance by bouncing radio waves o them. The delay
caused by the echo measures the distance. The direction
of the beam determines the direction of the reection.
The polarization and frequency of the return can sense
the type of surface. Navigational radars scan a wide area
two to four times per minute. They use very short waves
that reect from earth and stone. They are common on
commercial ships and long-distance commercial aircraft.

General purpose radars generally use navigational radar

frequencies, but modulate and polarize the pulse so the
receiver can determine the type of surface of the reecMain article: Radio navigation
tor. The best general-purpose radars distinguish the rain
of heavy storms, as well as land and vehicles. Some can
All satellite navigation systems use satellites with preci- superimpose sonar data and map data from GPS position.
sion clocks. The satellite transmits its position, and the Search radars scan a wide area with pulses of short ratime of the transmission. The receiver listens to four dio waves. They usually scan the area two to four times
satellites, and can gure its position as being on a line that a minute. Sometimes search radars use the Doppler efis tangent to a spherical shell around each satellite, deter- fect to separate moving vehicles from clutter. Targeting
mined by the time-of-ight of the radio signals from the radars use the same principle as search radar but scan a
satellite. A computer in the receiver does the math.
much smaller area far more often, usually several times a
Radio direction-nding is the oldest form of radio nav- second or more. Weather radars resemble search radars,
igation. Before 1960 navigators used movable loop an- but use radio waves with circular polarization and a wavetennas to locate commercial AM stations near cities. length to reect from water droplets. Some weather radar
In some cases they used marine radiolocation beacons, use the Doppler eect to measure wind speeds.

3.5.4

Navigation

which share a range of frequencies just above AM radio

with amateur radio operators. LORAN systems also used
time-of-ight radio signals, but from radio stations on the 3.5.6
ground.

Data (digital radio)

Very High Frequency Omnidirectional Range (VOR),

systems (used by aircraft), have an antenna array that
transmits two signals simultaneously. A directional signal rotates like a lighthouse at a xed rate. When the directional signal is facing north, an omnidirectional signal
pulses. By measuring the dierence in phase of these
two signals, an aircraft can determine its bearing or radial from the station, thus establishing a line of position.
An aircraft can get readings from two VORs and locate
its position at the intersection of the two radials, known
as a "x.
When the VOR station is collocated with DME (Distance
Measuring Equipment), the aircraft can determine its
bearing and range from the station, thus providing a x
from only one ground station. Such stations are called
VOR/DMEs. The military operates a similar system
of navaids, called TACANs, which are often built into
VOR stations. Such stations are called VORTACs. Because TACANs include distance measuring equipment,
VOR/DME and VORTAC stations are identical in navi-

2008 Pure One Classic digital radio

Most new radio systems are digital, including Digital TV,

satellite radio, and Digital Audio Broadcasting. The oldest form of digital broadcast was spark gap telegraphy,
used by pioneers such as Marconi. By pressing the key,

3.5. USES OF RADIO

the operator could send messages in Morse code by energizing a rotating commutating spark gap. The rotating commutator produced a tone in the receiver, where
a simple spark gap would produce a hiss, indistinguishable from static. Spark-gap transmitters are now illegal,
because their transmissions span several hundred megahertz. This is very wasteful of both radio frequencies and
power.
The next advance was continuous wave telegraphy, or
CW (Continuous Wave), in which a pure radio frequency,
produced by a vacuum tube electronic oscillator was
switched on and o by a key. A receiver with a local oscillator would "heterodyne" with the pure radio frequency,
creating a whistle-like audio tone. CW uses less than 100
Hz of bandwidth. CW is still used, these days primarily by amateur radio operators (hams). Strictly, on-o
keying of a carrier should be known as Interrupted Continuous Wave or ICW or on-o keying (OOK).

23
sions. Commercial use of spread spectrum began in the
1980s. Bluetooth, most cell phones, and the 802.11b version of Wi-Fi each use various forms of spread spectrum.
Systems that need reliability, or that share their frequency with other services, may use coded orthogonal
frequency-division multiplexing or COFDM. COFDM
breaks a digital signal into as many as several hundred
slower subchannels. The digital signal is often sent as
QAM on the subchannels. Modern COFDM systems use
a small computer to make and decode the signal with
digital signal processing, which is more exible and far
less expensive than older systems that implemented separate electronic channels.

COFDM resists fading and ghosting because the narrowchannel QAM signals can be sent slowly. An adaptive
system, or one that sends error-correction codes can also
resist interference, because most interference can aect
only a few of the QAM channels. COFDM is used for
Radioteletype equipment usually operates on short-wave Wi-Fi, some cell phones, Digital Radio Mondiale, Eureka
(HF) and is much loved by the military because they cre- 147, and many other local area network, digital TV and
ate written information without a skilled operator. They radio standards.
send a bit as one of two tones using frequency-shift keying. Groups of ve or seven bits become a character
printed by a teleprinter. From about 1925 to 1975, ra- 3.5.7 Heating
dioteletype was how most commercial messages were
sent to less developed countries. These are still used by Main article: Radio-frequency heating
the military and weather services.
Aircraft use a 1200 Baud radioteletype service over VHF
to send their ID, altitude and position, and get gate
and connecting-ight data. Microwave dishes on satellites, telephone exchanges and TV stations usually use
quadrature amplitude modulation (QAM). QAM sends
data by changing both the phase and the amplitude of
the radio signal. Engineers like QAM because it packs
the most bits into a radio signal when given an exclusive
(non-shared) xed narrowband frequency range. Usually
the bits are sent in frames that repeat. A special bit
pattern is used to locate the beginning of a frame.

Radio-frequency energy generated for heating of objects

is generally not intended to radiate outside of the generating equipment, to prevent interference with other radio
signals. Microwave ovens use intense radio waves to heat
food. Diathermy equipment is used in surgery for sealing
of blood vessels. Induction furnaces are used for melting
metal for casting, and induction hobs for cooking.

3.5.8 Amateur radio service

Modern GPS receivers.

Communication systems that limit themselves to a xed

narrowband frequency range are vulnerable to jamming. Amateur radio station with multiple receivers and transceivers
A variety of jamming-resistant spread spectrum techniques were initially developed for military use, most fa- Amateur radio, also known as ham radio, is a hobby
mously for Global Positioning System satellite transmis- in which enthusiasts are licensed to communicate on a

24

CHAPTER 3. RADIO

number of bands in the radio frequency spectrum noncommercially and for their own experiments. They may
also provide emergency and service assistance in exceptional circumstances. This contribution has been very
benecial in saving lives in many instances.[25]
Radio amateurs use a variety of modes, including ecient ones like Morse code and experimental ones like
Low-Frequency Experimental Radio. Several forms of
radio were pioneered by radio amateurs and later became
commercially important, including FM, single-sideband
(SSB), AM, digital packet radio and satellite repeaters.
Some amateur frequencies may be disrupted illegally by
power-line internet service.

3.5.9

Unlicensed radio services

Unlicensed, government-authorized personal radio services such as Citizens band radio in Australia, most of
the Americas, and Europe, and Family Radio Service and
Multi-Use Radio Service in North America exist to provide simple, usually short range communication for individuals and small groups, without the overhead of licensing. Similar services exist in other parts of the world.
These radio services involve the use of handheld units.
Wi-Fi also operates in unlicensed radio bands and is very
widely used to network computers.
Free radio stations, sometimes called pirate radio or
clandestine stations, are unauthorized, unlicensed, illegal broadcasting stations. These are often low power
transmitters operated on sporadic schedules by hobbyists,
community activists, or political and cultural dissidents.
Some pirate stations operating oshore in parts of Europe and the United Kingdom more closely resembled
legal stations, maintaining regular schedules, using high
power, and selling commercial advertising time.[26][27]

3.5.10

Radio control (RC)

Radio remote controls use radio waves to transmit control data to a remote object as in some early forms
of guided missile, some early TV remotes and a range
of model boats, cars and airplanes. Large industrial
remote-controlled equipment such as cranes and switching locomotives now usually use digital radio techniques
to ensure safety and reliability.

3.7 Notes
[1] While the term 'radio-' is actually the combining form of
radiant (e.g., radioactive, radiotherapy), the process that
was originally called radiotelegraphy has become so common that it is nearly always called just 'radio' and the associated electromagnetic waves are called radio waves. In
practice, radio frequencies are signicantly below that of
visible light from about 3 kHz to 300 GHz.[1]

3.8 References
[1] Dictionary of Electronics By Rudolf F. Graf (1974). Page
467.
[2] Radio-Electronics, ''Radio Receiver Technology''".
Radio-electronics.com. Retrieved 2014-08-02.
[3] The Electromagnetic Spectrum, University of Tennessee,
Dept. of Physics and Astronomy
[4] Clint Smith, Curt Gervelis (2003). Wireless Network Performance Handbook. McGraw-Hill Professional. ISBN
0-07-140655-7.
[5] R. K. Puri (2004). Solid State Physics and Electronics. S.
Chand. ISBN 81-219-1475-2.
[6] Production of Sound by Radiant Energy by Alexander
Graham Bell, Popular Science Monthly, July, 1881, pages
329-330: "[W]e have named the apparatus for the production and reproduction of sound in this way the photophone, because an ordinary beam of light contains the
rays which are operative. To avoid in future any misunderstandings upon this point, we have decided to adopt the
term "radiophone", proposed by M. Mercadier, as a general term signifying the production of sound by any form
of radiant energy...
[7] The Genesis of Wireless Telegraphy by A. Frederick
Collins, Electrical World and Engineer, May 10, 1902,
page 811.
[8] Wireless Telegraphy, The Practical Engineer, February
25, 1898, page 174. Dr. O. J. Lodge, who preceded Marconi in making experiments in what may be called ray
telegraphy or radiotelegraphy by a year or two, has devised
a new method of sending and receiving the messages. The
reader will understand that in the radiotelegraph electric
waves forming the signals of the message start from the
sending instrument and travel in all directions like rays of
light from a lamp, only they are invisible.

In Madison Square Garden, at the Electrical Exhibi- [9]

tion of 1898, Nikola Tesla successfully demonstrated a
radio-controlled boat.[28] He was awarded U.S. patent
No. 613,809 for a Method of and Apparatus for Con[10]
trolling Mechanism of Moving Vessels or Vehicles.[29]

3.6 See also

Outline of radio

Wireless Telegraphy, The Electrical Review (London),

January 20, 1905, page 108, quoting from the British Post
Oces December 30, 1904 Post Oce Circular.
Interference with Wireless Messages, Electrical World,
June 22, 1907, page 1270.

[11] Radio-Electronics, ''Radio Receiver Technology''".

Radio-electronics.com. Retrieved 2014-08-02.
[12] The Electromagnetic Spectrum, University of Tennessee,
Dept. of Physics and Astronomy

3.9. EXTERNAL LINKS

[13] Clint Smith, Curt Gervelis (2003). Wireless Network Performance Handbook. McGraw-Hill Professional. ISBN
0-07-140655-7.
[14] Macario, R. C. V. (1996). Modern personal radio systems. IEE telecommunications series, 33. London: Institution of Electrical Engineers. Page 3.
[15] R. K. Puri (2004). Solid State Physics and Electronics. S.
Chand. ISBN 81-219-1475-2.
[16] web.pdx.edu/~{}bseipel/Lecture%20notes%206-%
20203%20EMwaves.pdf
[17] T. K. Sarkar, Robert Mailloux, Arthur A. Oliner, M.
Salazar-Palma, Dipak L. Sengupta , History of Wireless,
John Wiley & Sons - 2006, pages 258-261
[18] Christopher H. Sterling, Encyclopedia of Radio 3Volume, Routledge - 2004, page 831
[19] Anand Kumar Sethi, The Business of Electronics: A Concise History, Palgrave Macmillan - 2013, page 22
[20] ieeeghn.org, IEEE Global History Network, Etheric Force
[21] W. Bernard Carlson, Innovation as a Social Process: Elihu
Thomson and the Rise of General Electric, Cambridge
University Press - 2003, pages 57-58
[22] U.S. Supreme Court. Retrieved 2012-04-23.
[23] The History Of KQW Radio - KCBS. Bayarearadio.org.
Retrieved 2009-07-22.
[24] Audio example of SSB. Retrieved 2014-08-02.
[25] "Amateur Radio Saved Lives in South Asia". Arrl.org.
2004-12-29. Archived from the original on 2007-10-13.
[26] Free radio: electronic civil disobedience by Lawrence C.
Soley. Published by Westview Press, 1998. ISBN 0-81339064-8, ISBN 978-0-8133-9064-2
[27] Rebel Radio: The Full Story of British Pirate Radio by John
Hind, Stephen Mosco. Published by Pluto Press, 1985.
ISBN 0-7453-0055-3, ISBN 978-0-7453-0055-9
[28] Tesla - Master of Lightning: Remote Control. PBS. Retrieved 2009-07-22.
[29] Tesla - Master of Lightning: Selected Tesla Patents.
PBS. Retrieved 2009-07-22.

3.9 External links

25

Chapter 4

Carrier wave
In telecommunications, a carrier wave, carrier signal,
or just carrier, is a waveform (usually sinusoidal) that is
modulated (modied) with an input signal for the purpose
of conveying information.[1] This carrier wave is usually
a much higher frequency than the input signal. The purpose of the carrier is usually either to transmit the information through space as an electromagnetic wave (as in
radio communication), or to allow several carriers at different frequencies to share a common physical transmission medium by frequency division multiplexing (as, for
example, a cable television system). The term is also used
for an unmodulated emission in the absence of any modulating signal.[2]

4.2 Carrier leakage

Carrier leakage is interference caused by cross-talk or a
DC oset. It is present as an unmodulated sine wave
within the signals bandwidth, whose amplitude is independent of the signals amplitude. See frequency mixers,
to read further about carrier leakage or local oscillator
feedthrough.

4.3 See also

Carrier recovery

Most radio systems in the 20th century used frequency

modulation (FM) or amplitude modulation (AM) to make
the carrier carry information. In the case of singlesideband modulation (SSB), the carrier is suppressed (and
in some forms of SSB, eliminated). The carrier must be
reintroduced at the receiver by a beat frequency oscillator (BFO). The frequency of a radio or television station
is actually the carrier waves center frequency.

Carrier system
Carrier tone
Frequency-division multiplexing
Sideband

4.4 References
4.1 Carrierless modulation systems

[1] Carrier wave with no modulation transports no information.. University Of Texas. Archived from the original on
2008-04-14. Retrieved 2008-05-30.

Newer forms of radio communication (such as spread

spectrum and ultra-wideband) do not use a conventional
sinusoidal carrier wave, nor does OFDM (which is used
in DSL and in the European standard for HDTV).

OFDM may be thought of as an array of symmetrical carrier waves. The rules governing carrier-wave
propagation aect OFDM dierently from 8VSB.
Some forms of spread spectrum transmission (and
most forms of ultra-wideband) are mathematically
dened as being devoid of carrier waves. Transmitter implementations typically produce residual carriers which may (or may not) be detectable or transmitted.
26

[2] Federal Standard 1037C and MIL-STD-188

Chapter 5

Frequency modulation

A signal may be carried by an AM or FM radio wave.

In telecommunications and signal processing, frequency

modulation (FM) is the encoding of information in a
carrier wave by varying the instantaneous frequency of
the wave. This contrasts with amplitude modulation, in
which the amplitude of the carrier wave varies, while the
frequency remains constant.
FM has better noise (RFI) rejection than AM, as shown in this
In analog frequency modulation, such as FM radio broad- dramatic New York publicity demonstration by General Electric
casting of an audio signal representing voice or music, in 1940. The radio has both AM and FM receivers. With a milthe instantaneous frequency deviation, the dierence be- lion volt arc as a source of interference behind it, the AM receiver
tween the frequency of the carrier and its center fre- produced only a roar of static, while the FM receiver clearly reproduced a music program from Armstrongs experimental FM
quency, is proportional to the modulating signal.
transmitter W2XMN in New Jersey.

Digital data can be encoded and transmitted via FM by

shifting the carriers frequency among a predened set
of frequencies representing digits - for example one frequency can represent a binary 1 and a second can represent binary 0. This modulation technique is known
as frequency-shift keying (FSK). FSK is widely used in
modems and fax modems, and can also be used to send
Morse code.[1] Radioteletype also uses FSK.[2]
Frequency modulation is widely used for FM radio
broadcasting. It is also used in telemetry, radar, seismic prospecting, and monitoring newborns for seizures
via EEG,[3] two-way radio systems, music synthesis, magnetic tape-recording systems and some videotransmission systems. In radio transmission, an advantage of frequency modulation is that it has a larger signalto-noise ratio and therefore rejects radio frequency inter-

ference better than an equal power amplitude modulation

(AM) signal. For this reason, most music is broadcast
over FM radio.
Frequency modulation has a close relationship with phase
modulation; phase modulation is often used as an intermediate step to achieve frequency modulation. Mathematically both of these are considered a special case of
quadrature amplitude modulation (QAM).

27

28

CHAPTER 5. FREQUENCY MODULATION

5.1 Theory

5.1.2 Modulation index

If the information to be transmitted (i.e., the baseband

signal) is xm (t) and the sinusoidal carrier is xc (t) =
Ac cos(2fc t) , where fc is the carriers base frequency,
and Ac is the carriers amplitude, the modulator combines
the carrier with the baseband data signal to get the transmitted signal:

As in other modulation systems, the modulation index

indicates by how much the modulated variable varies
around its unmodulated level. It relates to variations in
the carrier frequency:

h=
(

y(t) = Ac cos 2
f ( )d
0
)
( t
[fc + f xm ( )] d
= Ac cos 2
0
(
)
t
= Ac cos 2fc t + 2f
xm ( )d
0

f
f |xm (t)|
=
fm
fm

where fm is the highest frequency component present

in the modulating signal xm(t), and f is the peak
frequency-deviationi.e. the maximum deviation of the
instantaneous frequency from the carrier frequency. For
a sine wave modulation, the modulation index is seen to
be the ratio of the peak frequency deviation of the carrier
wave to the frequency of the modulating sine wave.

where f = Kf Am , Kf being the sensitivity of the If h 1 , the modulation is called narrowband FM, and
frequency modulator and Am being the amplitude of the its bandwidth is approximately 2fm . Sometimes modulation index h<0.3 rad is considered as Narrowband FM
modulating signal or baseband signal.
otherwise Wideband FM.
In this equation, f ( ) is the instantaneous frequency of
the oscillator and f is the frequency deviation, which For digital modulation systems, for example Binary Frerepresents the maximum shift away from fc in one direc- quency Shift Keying (BFSK), where a binary signal modulates the carrier, the modulation index is given by:
tion, assuming xm(t) is limited to the range 1.
While most of the energy of the signal is contained within
fc f, it can be shown by Fourier analysis that a wider
range of frequencies is required to precisely represent an
FM signal. The frequency spectrum of an actual FM signal has components extending innitely, although their
amplitude decreases and higher-order components are often neglected in practical design problems.[4]

h=

f
f
= 1 = 2f Ts
fm
2Ts

where Ts is the symbol period, and fm = 2T1 s is used as

the highest frequency of the modulating binary waveform
by convention, even though it would be more accurate to
say it is the highest fundamental of the modulating binary
waveform. In the case of digital modulation, the carrier
5.1.1 Sinusoidal baseband signal
fc is never transmitted. Rather, one of two frequencies
is transmitted, either fc + f or fc f , depending on
Mathematically, a baseband modulated signal may be ap- the binary state 0 or 1 of the modulation signal.
proximated by a sinusoidal continuous wave signal with a
If h 1 , the modulation is called wideband FM and
frequency fm.This method is also named as Single-tone
its bandwidth is approximately 2f . While wideband
Modulation.The integral of such a signal is:
FM uses more bandwidth, it can improve the signal-tonoise ratio signicantly; for example, doubling the value
t
of f , while keeping fm constant, results in an eightAm cos(2fm t)
xm ( )d =
fold improvement in the signal-to-noise ratio.[5] (Com2fm
0
pare this with Chirp spread spectrum, which uses exIn this case, the expression for y(t) above simplies to:
tremely wide frequency deviations to achieve processing gains comparable to traditional, better-known spreadspectrum modes).
(
)
f
y(t) = Ac cos 2fc t
cos (2fm t)
With a tone-modulated FM wave, if the modulation frefm
quency is held constant and the modulation index is inwhere the amplitude Am of the modulating sinusoid is creased, the (non-negligible) bandwidth of the FM sigrepresented by the peak deviation f (see frequency de- nal increases but the spacing between spectra remains the
viation).
same; some spectral components decrease in strength as
The harmonic distribution of a sine wave carrier modu- others increase. If the frequency deviation is held conlated by such a sinusoidal signal can be represented with stant and the modulation frequency increased, the spacing
Bessel functions; this provides the basis for a mathemat- between spectra increases.
ical understanding of frequency modulation in the fre- Frequency modulation can be classied as narrowband if
quency domain.
the change in the carrier frequency is about the same as

5.2. NOISE REDUCTION

the signal frequency, or as wideband if the change in the
carrier frequency is much higher (modulation index >1)
than the signal frequency. [6] For example, narrowband
FM is used for two way radio systems such as Family
Radio Service, in which the carrier is allowed to deviate only 2.5 kHz above and below the center frequency
with speech signals of no more than 3.5 kHz bandwidth.
Wideband FM is used for FM broadcasting, in which music and speech are transmitted with up to 75 kHz deviation from the center frequency and carry audio with up to
a 20-kHz bandwidth.

5.1.3

Bessel functions

For the case of a carrier modulated by a single sine wave,

the resulting frequency spectrum can be calculated using Bessel functions of the rst kind, as a function of
the sideband number and the modulation index. The carrier and sideband amplitudes are illustrated for dierent
modulation indices of FM signals. For particular values
of the modulation index, the carrier amplitude becomes
zero and all the signal power is in the sidebands.[4]

29
where W is the highest frequency in the modulating signal but non-sinusoidal in nature and D is the Deviation
ratio which the ratio of frequency deviation to highest frequency of modulating non-sinusoidal signal.

5.2 Noise reduction

A major advantage of FM in a communications circuit,
compared for example with AM, is the possibility of improved Signal-to-noise ratio (SNR). Compared with an
optimum AM scheme, FM typically has poorer SNR below a certain signal level called the noise threshold, but
above a higher level the full improvement or full quieting threshold the SNR is much improved over AM.
The improvement depends on modulation level and deviation. For typical voice communications channels, improvements are typically 5-15 dB. FM broadcasting using wider deviation can achieve even greater improvements. Additional techniques, such as pre-emphasis of
higher audio frequencies with corresponding de-emphasis
in the receiver, are generally used to improve overall SNR
in FM circuits. Since FM signals have constant amplitude, FM receivers normally have limiters that remove
AM noise, further improving SNR.[7][8]

Since the sidebands are on both sides of the carrier, their

count is doubled, and then multiplied by the modulating frequency to nd the bandwidth. For example, 3
kHz deviation modulated by a 2.2 kHz audio tone produces a modulation index of 1.36. Suppose that we
limit ourselves to only those sidebands that have a rel- 5.3 Implementation
ative amplitude of at least 0.01. Then, examining the
chart shows this modulation index will produce three 5.3.1 Modulation
sidebands. These three sidebands, when doubled, gives
us (6 * 2.2 kHz) or a 13.2 kHz required bandwidth.
FM signals can be generated using either direct or indirect
frequency modulation:

5.1.4

Carsons rule

Main article: Carson bandwidth rule

A rule of thumb, Carsons rule states that nearly all (~98
percent) of the power of a frequency-modulated signal
lies within a bandwidth BT of:
BT = 2(f + fm )
= 2fm ( + 1)

Direct FM modulation can be achieved by directly

feeding the message into the input of a VCO.
For indirect FM modulation, the message signal
is integrated to generate a phase-modulated signal.
This is used to modulate a crystal-controlled oscillator, and the result is passed through a frequency
multiplier to give an FM signal. In this modulation
narrowband FM is generated leading to wideband
FM later and hence the modulation is known as Indirect FM modulation.[9]

where f , as dened above, is the peak deviation of the

instantaneous frequency f (t) from the center carrier fre5.3.2 Demodulation
quency fc , is the Modulation index which is the ratio
of frequency deviation to highest frequency in the moduSee also: Detectors
lating signal and fm is the highest frequency in the modulating signal. Condition for application of Carsons rule
Many FM detector circuits exist. A common method
is only sinusoidal signals.
for recovering the information signal is through a FosterBT = 2(f + W )
Seeley discriminator. A phase-locked loop can be used as
an FM demodulator. Slope detection demodulates an FM
signal by using a tuned circuit which has its resonant fre= 2W (D + 1)
quency slightly oset from the carrier. As the frequency

30

CHAPTER 5. FREQUENCY MODULATION

rises and falls the tuned circuit provides a changing amplitude of response, converting FM to AM. AM receivers
may detect some FM transmissions by this means, although it does not provide an ecient means of detection
for FM broadcasts.

5.4 Applications
5.4.1

Magnetic tape storage

FM is also used at intermediate frequencies by analog

VCR systems (including VHS) to record the luminance
(black and white) portions of the video signal. Commonly, the chrominance component is recorded as a conventional AM signal, using the higher-frequency FM signal as bias. FM is the only feasible method of recording
the luminance (black and white) component of video to
(and retrieving video from) magnetic tape without distortion; video signals have a large range of frequency components from a few hertz to several megahertz, too wide
for equalizers to work with due to electronic noise below 60 dB. FM also keeps the tape at saturation level,
acting as a form of noise reduction; a limiter can mask
variations in playback output, and the FM capture eect
removes print-through and pre-echo. A continuous pilottone, if added to the signal as was done on V2000 and
many Hi-band formats can keep mechanical jitter under
control and assist timebase correction.

An American FM radio transmitter in Bualo, NY at WEDG

modulation (FM) radio.[11] He patented the regenerative

circuit in 1914, the superheterodyne receiver in 1918 and
the super-regenerative circuit in 1922.[12] Armstrong presented his paper, A Method of Reducing Disturbances in
Radio Signaling by a System of Frequency Modulation,
These FM systems are unusual, in that they have a ratio
(which rst described FM radio) before the New York
of carrier to maximum modulation frequency of less than
section of the Institute of Radio Engineers on November
two; contrast this with FM audio broadcasting, where the
6, 1935. The paper was published in 1936.[13]
ratio is around 10,000. Consider, for example, a 6-MHz
carrier modulated at a 3.5-MHz rate; by Bessel analysis, As the name implies, wideband FM (WFM) requires a
the rst sidebands are on 9.5 and 2.5 MHz and the second wider signal bandwidth than amplitude modulation by
sidebands are on 13 MHz and 1 MHz. The result is a an equivalent modulating signal; this also makes the sigreversed-phase sideband on +1 MHz; on demodulation, nal more robust against noise and interference. Frethis results in unwanted output at 61 = 5 MHz. The quency modulation is also more robust against signalsystem must be designed so that this unwanted output is amplitude-fading phenomena. As a result, FM was chosen as the modulation standard for high frequency, high
reduced to an acceptable level.[10]
delity radio transmission, hence the term "FM radio"
(although for many years the BBC called it VHF radio because commercial FM broadcasting uses part of
5.4.2 Sound
the VHF bandthe FM broadcast band). FM receivers
FM is also used at audio frequencies to synthesize sound. employ a special detector for FM signals and exhibit a
This technique, known as FM synthesis, was popularized phenomenon known as the capture eect, in which the
by early digital synthesizers and became a standard fea- tuner captures the stronger of two stations on the same
ture in several generations of personal computer sound frequency while rejecting the other (compare this with a
similar situation on an AM receiver, where both stations
cards.
can be heard simultaneously). However, frequency drift
or a lack of selectivity may cause one station to be over5.4.3 Radio
taken by another on an adjacent channel. Frequency drift
was a problem in early (or inexpensive) receivers; inadeMain article: FM broadcasting
quate selectivity may aect any tuner.
An FM signal can also be used to carry a stereo signal;
Edwin Howard Armstrong (18901954) was an Ameri- this is done with multiplexing and demultiplexing before
can electrical engineer who invented wideband frequency and after the FM process. The FM modulation and de-

5.7. EXTERNAL LINKS

modulation process is identical in stereo and monaural
processes. A high-eciency radio-frequency switching
amplier can be used to transmit FM signals (and other
constant-amplitude signals). For a given signal strength
(measured at the receiver antenna), switching ampliers
use less battery power and typically cost less than a linear
amplier. This gives FM another advantage over other
modulation methods requiring linear ampliers, such as
AM and QAM.

31

[6] B. P. Lathi, Communication Systems, John Wiley and

Sons, 1968 ISBN 0-471-51832-8, p, 214217
[7] H. P. Westman, ed. (1970). Reference Data for Radio
Engineers (Fifth ed.). Howard W. Sams & Co. p. 21-11.
[8] Alan Bloom (2010). Chapter 8. Modulation. In H.
Ward Silver and Mark J. Wilson (Eds). The ARRL Handbook for Radio Communications. American Radio Relay
League. p. 8.7. ISBN 978-0-87259-146-2.

FM is commonly used at VHF radio frequencies for [9] Communication Systems 4th Ed, Simon Haykin, 2001
high-delity broadcasts of music and speech. Analog
[10]
FM Systems Of Exceptional Bandwidth
TV sound is also broadcast using FM. Narrowband FM
Proc. IEEE vol 112, no. 9, p. 1664, Septemis used for voice communications in commercial and
ber 1965
amateur radio settings. In broadcast services, where audio delity is important, wideband FM is generally used. [11] A. Michael Noll (2001). Principles of modern communications technology. Artech House. p. 104. ISBN 978-1In two-way radio, narrowband FM (NBFM) is used to
58053-284-6.
conserve bandwidth for land mobile, marine mobile and
other radio services.
[12] US 1342885

5.5 See also

Amplitude modulation
Continuous-wave frequency-modulated radar
Chirp
FM broadcasting

[13] Armstrong, E. H. (May 1936). A Method of Reducing

Disturbances in Radio Signaling by a System of Frequency
Modulation. Proceedings of the IRE. IRE. 24 (5): 689
740. doi:10.1109/JRPROC.1936.227383.

5.7 External links

Frequency modulation tutorial video with example
waveforms and FM transmitter circuit.

FM stereo
FM-UWB (FM and Ultra Wideband)
History of radio
Modulation, for a list of other modulation techniques

5.6 References
[1] Stan Gibilisco (2002). Teach yourself electricity and electronics. McGraw-Hill Professional. p. 477. ISBN 978-007-137730-0.
[2] David B. Rutledge (1999). The Electronics of Radio.
Cambridge University Press. p. 310. ISBN 978-0-52164645-1.
[3] B. Boashash, editor, Time-Frequency Signal Analysis
and Processing A Comprehensive Reference, Elsevier
Science, Oxford, 2003; ISBN 0-08-044335-4
[4] T.G. Thomas, S. C. Sekhar Communication Theory, TataMcGraw Hill 2005, ISBN 0-07-059091-5 page 136
[5] Der, Lawrence, Ph.D., Frequency Modulation (FM) Tutorial, http://www.silabs.com/Marcom%20Documents/
Resources/FMTutorial.pdf, Silicon Laboratories, Inc.,
accessed 2013 February 24, p. 5

5.8 Further reading

A. Bruce Carlson. Communication Systems, 4th
edition. McGraw-Hill Science/Engineering/Math.
2001. ISBN 0-07-011127-8, ISBN 978-0-07011127-1.
Gary L. Frost. Early FM Radio: Incremental Technology in Twentieth-Century America. Baltimore:
Johns Hopkins University Press, 2010. ISBN 08018-9440-9, ISBN 978-0-8018-9440-4.
Ken Seymour, AT&T Wireless (Mobility). Frequency Modulation, The Electronics Handbook, pp
1188-1200, 1st Edition, 1996. 2nd Edition, 2005
CRC Press, Inc., ISBN 0-8493-8345-5 (1st Edition).

Chapter 6

Frequency
This article is about the rates of waves, oscillations, and
vibrations. For the rates of non-cyclic phenomena, see
Aperiodic frequency. For the general concept beyond the
temporal domain, see Frequency (statistics). For other
uses, see Frequency (disambiguation).
For a broader coverage related to this topic, see Temporal
rate.
Frequency is the number of occurrences of a repeating
event per unit time.[1] It is also referred to as temporal
frequency, which emphasizes the contrast to spatial frequency and angular frequency. The period is the duration
of time of one cycle in a repeating event, so the period
is the reciprocal of the frequency.[2] For example, if a
newborn babys heart beats at a frequency of 120 times a
minute, its periodthe time interval between beatsis
half a second (that is, 60 seconds divided by 120 beats).
Frequency is an important parameter used in science and
engineering to specify the rate of oscillatory and vibratory
phenomena, such as mechanical vibrations, audio (sound)
signals, radio waves, and light.

6.1 Denitions
For cyclical processes, such as rotation, oscillations, or
waves, frequency is dened as a number of cycles per
unit time. In physics and engineering disciplines, such as
optics, acoustics, and radio, frequency is usually denoted
by a Latin letter f or by the Greek letter or (nu) (see
e.g. Plancks formula).
Period (in units of time) X Ordinary frequency (in number of cycles per unit of time) = 1 cycle.

These three dots are ashing, or cycling, periodicallyfrom

lowest frequency (0.5 hertz) to highest frequency (2.0 hertz),
top to bottom. For each ashing dot: f is the frequency in
hertz, (Hz)or the number of events per second (i.e., cycles per
second)that the dot ashes; while T is the period, or time, in
seconds (s) of each cycle, (i.e., the number of seconds per cycle).
Note T and f are reciprocal values to each other.

Therefore, the period, usually denoted by T, is the duration of one cycle, and is the reciprocal of the frequency
f:

6.2 Units

f=

1cycle
.
T

The SI unit of frequency is the hertz (Hz), named after

the German physicist Heinrich Hertz; one hertz means
that an event repeats once per second. A previous name
for this unit was cycles per second (cps). The SI unit for
32

6.5. IN WAVE PROPAGATION

33
For other uses, see Frequency (disambiguation).

As time elapseshere moving left to right on the horizontal

axisthe ve sinusoidal waves vary, or cycle, regularly at different rates. The red wave (top) has the lowest frequency (i.e.,
cycles at the slowest rate) while the purple wave (bottom) has the
highest frequency (cycles at the fastest rate).

Angular frequency, usually denoted by the Greek

letter (omega), is dened as the rate of change
of angular displacement, , (during rotation), or the
rate of change of the phase of a sinusoidal waveform (e.g. in oscillations and waves), or as the rate
of change of the argument to the sine function:

y(t) = sin ((t)) = sin(t) = sin(2f t)

period is the second.
A traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min
or rpm. 60 rpm equals one hertz.[3]

d
= = 2f
dt
Angular frequency is commonly measured in
radians per second (rad/s) but, for discretetime signals, can also be expressed as radians per sample time, which is a dimensionless
quantity.

6.3 Period versus frequency

As a matter of convenience, longer and slower waves,
such as ocean surface waves, tend to be described by wave
period rather than frequency. Short and fast waves, like
audio and radio, are usually described by their frequency
instead of period. These commonly used conversions are
listed below:

Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more
spatial displacement axes. E.g.:

6.4 Related types of frequency

y(t) = sin ((t, x)) = sin(t + kx)

d
=k
dx
Wavenumber, k, is the spatial frequency analogue of angular temporal frequency and is
measured in radians per meter. In the case of
more than one spatial dimension, wavenumber
is a vector quantity.

6.5 In wave propagation

Further information: Wave propagation
For periodic waves in nondispersive media (that is, media
in which the wave speed is independent of frequency),
frequency has an inverse relationship to the wavelength,
(lambda). Even in dispersive media, the frequency f of
a sinusoidal wave is equal to the phase velocity v of the
wave divided by the wavelength of the wave:
Diagram of the relationship between the dierent types of frequency and other wave properties.

f=

v
.

34

CHAPTER 6. FREQUENCY

In the special case of electromagnetic waves moving frequency will vibrate with large amplitude, visible next
through a vacuum, then v = c, where c is the speed of to the scale.
light in a vacuum, and this expression becomes:

f=

c
.

6.6.2 By stroboscope

An older method of measuring the frequency of rotating

When waves from a monochrome source travel from one
or vibrating objects is to use a stroboscope. This is an
medium to another, their frequency remains the same
intense repetitively ashing light (strobe light) whose freonly their wavelength and speed change.
quency can be adjusted with a calibrated timing circuit.
The strobe light is pointed at the rotating object and the
frequency adjusted up and down. When the frequency of
6.6 Measurement
the strobe equals the frequency of the rotating or vibrating
object, the object completes one cycle of oscillation and
returns to its original position between the ashes of light,
See also: Frequency meter
so when illuminated by the strobe the object appears stationary. Then the frequency can be read from the calibrated readout on the stroboscope. A downside of this
6.6.1 By counting
method is that an object rotating at an integral multiple
of the strobing frequency will also appear stationary.
Calculating the frequency of a repeating event is accomplished by counting the number of times that event occurs
within a specic time period, then dividing the count by 6.6.3 By frequency counter
the length of the time period. For example, if 71 events
occur within 15 seconds the frequency is:

f=

71
4.7 Hz
15 s

If the number of counts is not very large, it is more accurate to measure the time interval for a predetermined
number of occurrences, rather than the number of occurrences within a specied time.[4] The latter method introduces a random error into the count of between zero
and one count, so on average half a count. This is called
gating error and causes an average error in the calculated
frequency of f = 1/(2 Tm), or a fractional error of f
/ f = 1/(2 f Tm) where Tm is the timing interval and f
is the measured frequency. This error decreases with frequency, so it is a problem at low frequencies where the
number of counts N is small.

Modern frequency counter

Higher frequencies are usually measured with a frequency

counter. This is an electronic instrument which measures the frequency of an applied repetitive electronic
signal and displays the result in hertz on a digital display.
It uses digital logic to count the number of cycles during a time interval established by a precision quartz time
base. Cyclic processes that are not electrical in nature,
such as the rotation rate of a shaft, mechanical vibrations, or sound waves, can be converted to a repetitive
electronic signal by transducers and the signal applied to
a frequency counter. Frequency counters can currently
cover the range up to about 100 GHz. This represents
the limit of direct counting methods; frequencies above
this must be measured by indirect methods.

6.6.4 Heterodyne methods

resonant-reed frequency meter, an obsolete device used
from about 1900 to the 1940s for measuring the frequency of alternating current. It consists of a strip of
metal with reeds of graduated lengths, vibrated by an
electromagnet. When the unknown frequency is applied
to the electromagnet, the reed which is resonant at that

Above the range of frequency counters, frequencies of

electromagnetic signals are often measured indirectly by
means of heterodyning (frequency conversion). A reference signal of a known frequency near the unknown frequency is mixed with the unknown frequency in a non-

6.8. SEE ALSO

linear mixing device such as a diode. This creates a
heterodyne or beat signal at the dierence between the
two frequencies. If the two signals are close together in
frequency the heterodyne is low enough to be measured
by a frequency counter. This process only measures the
dierence between the unknown frequency and the reference frequency, which must be determined by some other
method. To reach higher frequencies, several stages of
heterodyning can be used. Current research is extending this method to infrared and light frequencies (optical
heterodyne detection).

6.7 Examples
6.7.1

Light

35
where c is the speed of light (c in a vacuum, or less in
other media), f is the frequency and is the wavelength.
In dispersive media, such as glass, the speed depends
somewhat on frequency, so the wavelength is not quite
inversely proportional to frequency.

6.7.2 Sound
Main article: Audio frequency
Sound propagates as mechanical vibration waves of pressure and displacement, in air or other substances.[5] Frequency is the property of sound that most determines
pitch.[6]
The frequencies an ear can hear are limited to a specic
range of frequencies. The audible frequency range for
humans is typically given as being between about 20 Hz
and 20,000 Hz (20 kHz), though the high frequency limit
usually reduces with age. Other species have dierent
hearing ranges. For example, some dog breeds can perceive vibrations up to 60,000 Hz.[7]
In many media, such as air, the speed of sound is approximately independent of frequency, so the wavelength of
the sound waves (distance between repetitions) is approximately inversely proportional to frequency.

Complete spectrum of electromagnetic radiation with the visible

portion highlighted

6.7.3 Line current

Main articles: Light and Electromagnetic radiation

Main article: Utility frequency

Visible light is an electromagnetic wave, consisting of

oscillating electric and magnetic elds traveling through
space. The frequency of the wave determines its color:
41014 Hz is red light, 81014 Hz is violet light, and between these (in the range 4-81014 Hz) are all the other
colors of the rainbow. An electromagnetic wave can have
a frequency less than 41014 Hz, but it will be invisible to the human eye; such waves are called infrared (IR)
radiation. At even lower frequency, the wave is called
a microwave, and at still lower frequencies it is called a
radio wave. Likewise, an electromagnetic wave can have
a frequency higher than 81014 Hz, but it will be invisible to the human eye; such waves are called ultraviolet
(UV) radiation. Even higher-frequency waves are called
X-rays, and higher still are gamma rays.

In Europe, Africa, Australia, Southern South America,

most of Asia, and Russia, the frequency of the alternating
current in household electrical outlets is 50 Hz (close to
the tone G), whereas in North America and Northern
South America, the frequency of the alternating current
in household electrical outlets is 60 Hz (between the tones
B and B; that is, a minor third above the European frequency). The frequency of the 'hum' in an audio recording can show where the recording was made, in countries
using a European, or an American, grid frequency.

6.8 See also

See also: Frequency (disambiguation)

All of these waves, from the lowest-frequency radio waves See also: Category:Units of frequency.
to the highest-frequency gamma rays, are fundamentally
the same, and they are all called electromagnetic radiation. They all travel through a vacuum at the same speed
Audio frequency
(the speed of light), giving them wavelengths inversely
Bandwidth (signal processing)
proportional to their frequencies.
Cuto frequency
c = f

Downsampling

36

CHAPTER 6. FREQUENCY

6.10 Further reading

Electronic lter
Frequency band

Giancoli, D.C. (1988). Physics for Scientists and

Engineers (2nd ed.). Prentice Hall. ISBN 0-13669201-X.

Frequency converter
Frequency domain
Frequency distribution

6.11 External links

Frequency extender

Conversion: frequency to wavelength and back

Frequency grid

Conversion: period, cycle duration, periodic time to

frequency

Frequency modulation
Frequency spectrum

Keyboard frequencies = naming of notes - The English and American system versus the German system

Interaction frequency
Natural frequency
Negative frequency

Teaching resource for 14-16yrs on sound including

frequency

Periodicity (disambiguation)

A simple tutorial on how to build a frequency meter

Pink noise

Frequency - diracdelta.co.uk JavaScript calculation.

Preselector

A frequency generator with sound, useful for hearing

tests

Radar signal characteristics

Signaling (telecommunications)
Spread spectrum
Spectral component
Transverter
Upsampling
Quefrency

6.9 Notes and references

[1] Denition of FREQUENCY.
2016.

Retrieved 3 October

[2] Denition of PERIOD. Retrieved 3 October 2016.

[3] Davies, A. (1997). Handbook of Condition Monitoring:
Techniques and Methodology. New York: Springer. ISBN
978-0-412-61320-3.
[4] Bakshi, K.A.; A.V. Bakshi; U.A. Bakshi (2008).
Electronic Measurement Systems. US: Technical Publications. pp. 414. ISBN 978-81-8431-206-5.
[5] Denition of SOUND. Retrieved 3 October 2016.
[6] Pilhofer, Michael (2007). Music Theory for Dummies.
For Dummies. p. 97. ISBN 9780470167946.
[7] Elert, Glenn; Timothy Condon (2003). Frequency Range
of Dog Hearing. The Physics Factbook. Retrieved 200810-22.

Chapter 7

Radiotelephone
For the 19th century optical telecommunication inven- 7.1.1 Mode of emission
tion by Alexander Graham Bell and Sumner Tainter, see
Photophone.
The word phone has a long precedent beginning with early
A radiotelephone (or radiophone) is a communications
US wireless voice systems. The term means voice as opposed to telegraph or Morse code. This would include
systems tting into the category of two-way radio or oneway voice broadcasts such as coastal maritime weather.
The term is still popular in the amateur radio community
and in US Federal Communications Commission regulations.

7.1.2 Modes of operation

A standard landline telephone allows both users to talk
and listen simultaneously; eectively there are two open
channels between the two end-to-end users of the system. In a radiotelephone system, this form of working,
known as full-duplex, require a radio system to simultaneously transmit and receive on two separate channels,
which both wastes bandwidth and presents some technical
challenges. It is, however, the most comfortable method
of voice communication for users, and it is currently used
in cell phones and was used in the former IMTS.

Comparison of an amateur radio handheld transceiver, cell

phone, and matchbox

system for transmission of speech over radio. Radiotelephone systems are not necessarily interconnected with the
public land line telephone network. Radiotelephony
means transmission of sound (audio) by radio, in contrast
to radiotelegraphy (transmission of telegraph signals) or
video transmission. Where a two-way radio system is arranged for speaking and listening at a mobile station, and
where it can be interconnected to the public switched telephone system, the system can provide mobile telephone
service.

7.1 Design

The most common method of working for radiotelephones is half-duplex, operation, which allows one person to talk and the other to listen alternately. If a single
channel is used, both ends take turns to transmit on it.
An eavesdropper would hear both sides of the conversation. Dual-frequency working splits the communication
into two separate channels, but only one is used to transmit at a time. The end users have the same experience
as single frequency simplex but an eavesdropper with one
receiver would only hear one side of the conversation.
The user presses a special switch on the transmitter when
they wish to talkthis is called the press-to-talk switch
or PTT (colloquially, sometimes called the tit). It is
usually tted on the side of the microphone or other obvious position. Users may use a special code-word such
as over to signal that they have nished transmitting, or
it may follow from the conversation.

37

38

7.2 Features
Radiotelephones may operate at any frequency where
they are licensed to do so, though typically they are used
in the various bands between 60 and 900 MHz. They may
use simple modulation schemes such as AM or FM, or
more complex techniques such as digital coding, spread
spectrum, and so on. Licensing terms for a given band
will usually specify the type of modulation to be used. For
example, airband radiotelephones used for air to ground
communication between pilots and controllers operates
in the VHF band from 118.0 to 136.975 MHz, using amplitude modulation.

CHAPTER 7. RADIOTELEPHONE
a far greater number of addresses. In addition, special
features (such as broadcast modes and emergency overrides) can be designed in, using special addresses set aside
for the purpose. A mobile unit can also broadcast a Selcall sequence with its unique address to the base, so the
user can know before the call is picked up which unit is
calling. In practice many selcall systems also have automatic transponding built in, which allows the base station to interrogate a mobile even if the operator is not
present. Such transponding systems usually have a status
code that the user can set to indicate what they are doing. Features like this, while very simple, are one reason
why they are very popular with organisations that need to
manage a large number of remote mobile units. Selcall
is widely used, though is becoming superseded by much
more sophisticated digital systems.

Radiotelephone receivers are usually designed to a very

high standard, and are usually of the double-conversion
superhet design. Likewise, transmitters are carefully designed to avoid unwanted interference and feature power
outputs from a few tens of milliwatts to perhaps 50 watts
for a mobile unit, up to a couple of hundred watts for a 7.3
base station. Multiple channels are often provided using
a frequency synthesizer.
7.3.1

Uses
Conventional telephone use

Receivers usually features a squelch circuit to cut o

the audio output from the receiver when there is no Main article: Mobile radio telephone
transmission to listen to. This is in contrast to broadcast
receivers, which often dispense with this.
Mobile radio telephone systems such as Mobile Telephone Service and Improved Mobile Telephone Service
allowed a mobile unit to have a telephone number allow7.2.1 Privacy and selective calling
ing access from the general telephone network, although
some systems required mobile operators to set up calls
Main article: Selective calling
to mobile stations. Mobile radio telephone systems before the introduction of cellular telephone services suffered
from few usable channels, heavy congestion, and
Often, on a small network system, there are many mobile
very
high
operating costs.
units and one main base station. This would be typical for
police or taxi services for example. To help direct messages to the correct recipients and avoid irrelevant traf7.3.2 Marine use
c on the networks being a distraction to other units, a
variety of means have been devised to create addressing
The Marine Radiotelephone Service or HF ship-to-shore
systems.
operates on shortwave radio frequencies, using singleThe crudest and oldest of these is called CTCSS, or Con- sideband modulation. The usual method is that a ship
tinuous Tone-Controlled Squelch System. This consists calls a shore station, and the shore stations marine operof superimposing a precise very low frequency tone on ator connects the caller to the public switched telephone
the audio signal. Only the receiver tuned to this specic network. This service is retained for safety reasons, but
tone is able to receive the signal: this receiver shuts o in practice has been made obsolete by satellite telephones
the audio when the tone is not present or is a dierent fre- (particularly INMARSAT) and VoIP telephone and email
quency. By assigning a unique frequency to each mobile, via satellite internet.
private channels can be imposed on a public network.
However this is only a convenience featureit does not Short wave radio is used because it bounces between the
ionosphere and the ground, giving a modest 1,000 watt
guarantee privacy.
transmitter (the standard power) a worldwide range.
A more commonly used system is called Selective Calling
or Selcall. This also uses audio tones, but these are not re- Most shore stations monitor several frequencies. The frestricted to sub-audio tones and are sent as a short burst in quencies with the longest range are usually near 20 MHz,
sequence. The receiver will be programmed to respond but the ionospheric weather (propagation) can dramationly to a unique set of tones in a precise sequence, and cally change which frequencies work best.
only then will it open the audio circuits for open-channel Single-sideband (SSB) is used because the short wave
conversation with the base station. This system is much bands are crowded with many users, and SSB permits
more versatile than CTCSS, as relatively few tones yield a single voice channel to use a narrower range of radio

7.6. NOTES
frequencies (bandwidth), about 3.5 kHz. In comparison,
AM radio uses about 8 kHz, and narrowband (voice or
communication-quality) FM uses 9 kHz.
Marine radiotelephony rst became common in the
1930s, and was used extensively for communications to
ships and aircraft over water. In that time, most longrange aircraft had long-wire antennas that would be let
out during a call, and reeled-in afterward. Marine radiotelephony originally used AM mode in the 2-3 MHz
region before the transition to SSB and the adoption of
various higher frequency bands in addition to the 2 MHz
frequencies.
One of the most important uses of marine radiotelephony
has been to change ships itineraries, and to perform other
business at sea.
Some ships, including almost all military ships, carry
teletypewriters, and use them to communicate over short
wave. This is called marine radiotelegraphy". The
equipment is a shortwave radio transceiver with an attachment that generates and receives audio tones in order to
drive the teletypewiter.

7.4 Regulations
In the United States, since the Communications Act of
1934 the Federal Communications Commission (FCC)
has issued various commercial radiotelephone operator
licenses and permits to qualied applicants. These allow them to install, service, and maintain voice-only radio transmitter systems for use on ships and aircraft.[1]
(Until deregulation in the 1990s they were also required
for commercial domestic radio and television broadcast
systems. Because of treaty obligations they are still required for engineers of international shortwave broadcast
stations.) The certicate currently issued is the general
radiotelephone operator license.

7.5 See also

ASTRA2Connect Maritime Broadband
AT&T High Seas Service
Car phone
Improved Mobile Telephone Service
Inmarsat
Mobile radio telephone
Mobile Telephone Service
Two-way radio

39

7.6 Notes
[1] http://www.narte.org/h/fccabout.asp

7.7 References
Bruce, Robert V. Bell: Alexander Bell and the Conquest of Solitude. Ithaca, New York: Cornell University Press, 1990. ISBN 0-8014-9691-8.
Carson, Mary Kay (2007). 8. Alexander Graham Bell: Giving Voice To The World. Sterling Biographies. 387 Park Avenue South, New York, NY
10016: Sterling Publishing Co., Inc. pp. 7678.
ISBN 978-1-4027-3230-0. OCLC 182527281.

Chapter 8

Two-way radio
This article is about two-way radio in general. For handheld two-way radios, see Walkie-talkie.
A two-way radio is a radio that can do both transmit

8.1 History
Installation of receivers and transmitters at the same
xed location allowed exchange of messages wirelessly.
As early as 1907, two-way telegraphy trac across the
Atlantic Ocean was commercially available. By 1912
commercial and military ships carried both transmitters
and receivers, allowing two-way communication in close
to real-time with a ship that was out of sight of land.
The rst truly mobile two-way radio was developed in
Australia in 1923 by Senior Constable Frederick William
Downie of the Victorian Police. The Victoria Police were
the rst in the world to use wireless communication in
cars, putting an end to the inecient status reports via
public telephone boxes which had been used until that
time. The rst sets took up the entire back seat of the
Lancia patrol cars.[4]

Several modern two-way hand-held radios compatible with the

Project 25 digital radio standard (Mobile and base station radios
not shown)

As radio equipment became more powerful, compact,

and easier to use, smaller vehicles had two-way radio
communication equipment installed. Installation of radio equipment in aircraft allowed scouts to report back
and receive a signal (a transceiver), unlike a broadcast observations in real-time, not requiring the pilot to drop
messages to troops on the ground below or to land and
receiver which only receives content. A two-way radio
(transceiver) allows the operator to have a conversation make a personal report.
with other similar radios operating on the same radio In 1933, the Bayonne, New Jersey police department
frequency (channel). Two-way radios are available in successfully operated a two-way system between a cenmobile, stationary base and hand-held portable congu- tral xed station and radio transceivers installed in porations. Hand-held radios are often called walkie-talkies, lice cars; this allowed rapidly directing police response in
emergencies.[5] During World War II walkie-talkie handhandie-talkies, or just hand-helds.
Two-way radio systems usually operate in a half-duplex held radio transceivers were extensively used by air and
mode; that is, the operator can talk, or he can listen, ground troops, both by the Allies and the Axis.
but not at the same time. A push-to-talk or Press To
Transmit button activates the transmitter; when it is released the receiver is active. A mobile phone or cellular
telephone is an example of a two-way radio that does
both transmits and receives at the same time,i.e., in fullduplex mode. Full-duplex is generally achieved by the
use of two dierent frequencies or by frequency-sharing
methods to carry the two directions of the conversation
simultaneously.[1] Methods for mitigating the self interference caused by simultaneous same-frequency transmission and reception include using two antennas,[2] or
dynamic solid-state lters.[3]

Early two-way schemes allowed only one station to transmit at a time while others listened, since all signals were
on the same radio frequency this was called simplex
mode. Code and voice operations required a simple
communication protocol to allow all stations to cooperate in using the single radio channel, so that one stations
transmissions were not obscured by anothers. By using
receivers and transmitters tuned to dierent frequencies,
and solving the problems introduced by operation of a
receiver immediately next to a transmitter, simultaneous
transmission and reception was possible at each end of a
radio link, in so-called "full duplex" mode.

40

8.2. TYPES
The rst radio systems could not transmit voice. This required training of operators in use of Morse code. On a
ship, the radio operating ocers (sometimes shortened to
radio ocers) typically had no other duties than handling radio messages. When voice transmission became
possible, dedicated operators were no longer required and
two-way use became more common. Todays two-way
mobile radio equipment is nearly as simple to use as a
household telephone, from the point of view of operating personnel, thereby making two-way communications
a useful tool in a wide range of personal, commercial and
military roles.

8.2 Types
Two-way radio systems can be classied in several ways
depending on their attributes.

41
There are a wide variety of scan congurations which
vary from one system to another. Some radios have scan
features that receive the primary selected channel at full
volume and other channels in a scan list at reduced volume. This helps the user distinguish between the primary
channel and others without looking at the radio control
panel. An overview:
A scanning feature can be dened and preset: when
in scanning mode, a predetermined set of channels is
scanned. Channels are not changeable by the radio
user.
Some radios allow an option for user-selected scan:
this allows either lockout of pre-selected channels or
adding channels to a scan list by the operator. The
radio may revert to a default scan list each time it
is powered o or may permanently store the most
recent changes.

In professional radios, scan features are programmable

and have many options. Scan features can aect system
latency. If the radio has a twenty channel scan list and
Conventional
some channels have CTCSS, it can take several seconds to
search the entire list. The radio must stop on each channel
Conventional radios operate on xed RF channels. In the
with a signal and check for a valid CTCSS before resumcase of radios with multiple channels, they operate on one
ing scanning. This can cause missed messages.
channel at a time. The proper channel is selected by a
user. The user operates a channel selector (dial or but- For this reason, scan features are either not used or scan
tons) on the radio control panel to pick the appropriate lists are intentionally kept short in emergency applications. Part of APCO Project 16 set standards for chanchannel.
nel access times and delays caused by system overhead.
In multi-channel systems, channels are used for sepaScan features can further increase these delays. One study
rate purposes.[6] A channel may be reserved for a spesaid delays of longer than 0.4 seconds (400 milliseconds)
cic function or for a geographic area. In a functional
in emergency services are not recommended.[7] No delay
channel system, one channel may allow City of Springfrom user push-to-talk until the users voice is heard in
eld road repair crews to talk to the City of Springelds
the radios speaker is an unattainable ideal.
road maintenance oce. A second channel may allow
road repair crews to communicate with state highway department crews. In a geographic system, a taxi company Talk-back on scan Some conventional radios use, or
may use one channel to communicate in the Boston, Mas- have an option for, a talk-back-on-scan function. If the
sachusetts area and a second channel when taxis are in user transmits when the radio is in a scan mode, it may
Providence, Rhode Island. In marine radio operations, transmit on the last channel received instead of the seone channel is used as an emergency and calling channel, lected channel. This may allow users of multi-channel
so that stations may make contact then move to a separate radios to reply to the last message without looking at the
working channel for continued communication.
radio to see which channel it was on. Without this feature,
Motorola uses the term mode to refer to channels on some the user would have to use the channel selector to switch
conventional two-way radio models. In this use, a mode to the channel where the last message occurred. (This
consists of a radio frequency channel and all channel- option can cause confusion and users must be trained to
dependent options such as selective calling, channel scan- understand this feature.)

8.2.1

Conventional versus trunked

ning, power level, and more.

Scanning in conventional radios Some conventional
radios scan more than one channel. That is, the receiver
searches more than one channel for a valid transmission.
A valid transmission may be a radio channel with any signal or a combination of a radio channel with a specic
CTCSS (or Selective calling) code.

This is an incomplete list of some conventional radio

types:
Commercial and Public Safety Radio
Marine VHF radio
Family Radio Service (sometimes referred to by the
abbreviation FRS)

42

CHAPTER 8. TWO-WAY RADIO

UNICOM

8.2.2 Simplex versus duplex channels

Amateur Radio

Simplex

Trunked
Main article: Trunked radio system
In a trunked radio system, the system logic automatically
picks the physical radio frequency channel. There is a
protocol that denes a relationship between the radios and
the radio backbone which supports them. The protocol
allows channel assignments to happen automatically.
Digital trunked systems may carry simultaneous conversations on one physical channel. In the case of a digital
trunked radio system, the system also manages time slots
on a single physical channel. The function of carrying simultaneous conversations over a single channel is called
multiplexing.
Instead of channels, radios are related by groups which
may be called, groups, talk groups, or divided into a hierarchy such as eet and subeet, or agency-eet-subeet.
These can be thought of as virtual channels which appear
and disappear as conversations occur.
Systems make arrangements for handshaking and connections between radios by one of these two methods:

Simplex channel systems use a single channel for transmit

and receive. This is typical of aircraft VHF AM, Citizens Band and marine radios. Simplex systems are often
legacy systems that have existed since the 1930s. The architecture allows old radios to work with new ones in a
single network. In the case of all ships worldwide or all
aircraft worldwide, the large number of radios installed,
(the installed base,) can take decades to upgrade. Simplex systems often use open architectures that allow any
radio meeting basic standards to be compatible with the
entire system.
Advantage: as the simplest system conguration,
there is reliability since only two radios are needed
to establish communication between them, without
any other infrastructure.
Disadvantages: The simplex conguration oers
communication over the shortest range or distance
because mobile units must be in eective range of
each other. The available channel bandwidth limits the number of simultaneous conversations, since
dead air time cannot be easily used for additional
communication.

A computer assigns channels over a dedicated con- Duplex

trol channel. The control channel sends a continual
data stream. All radios in the system monitor the
data stream until commanded by the computer to
join a conversation on an assigned channel.
Electronics embedded in each radio communicate
using a protocol of tones or data in order to establish
a conversation, (scan-based).
If all physical channels are busy, some systems include a
protocol to queue or stack pending requests until a channel becomes available.
Some trunked radios scan more than one talk group or
agency-eet-subeet.
Visual clues a radio may be trunked include the 1) lack
of a squelch knob or adjustment, 2) no monitor button or
switch, and 3) a chirp (made famous by Nextel) showing
the channel is available and ready at the moment the pushto-talk is pressed.
This is an incomplete list of some trunked radio types:
TETRA
Logic Trunked Radio (abbreviated LTR)
SmartZone and SmartNet
EDACS

Duplex means two channels are used: one in each direction.

Duplex channel systems transmit and receive on dierent discrete channels. This denes systems where equipment cannot communicate without some infrastructure
such as a repeater, base station or Talk-Through Base.

8.2. TYPES
Most common in the US is a repeater conguration where
a base station is congured to simultaneously re-transmit
the audio received from mobile units. This makes the mobiles, or hand-helds, able to communicate amongst one
another anywhere within reception range of the base station or repeater. Typically the base or repeater station
has a high antenna and high power, which allows much
greater range, compared with a ground vehicle or handheld transceiver.

43

8.2.4 Analog versus digital

One example of analog radios are AM aircraft radios used
to communicate with control towers and air trac controllers. Another is a Family Radio Service walkie talkie.
Analog equipment is less complex than the simplest digital.

Advantage: In high-quality equipment, better ability

to communicate in cases where a received signal is
Duplex systems can be divided into two types. The term
weak or noisy.
half-duplex refers to systems where use of a push-to-talk
switch is required to communicate. Full duplex refers to
Disadvantage: Only one conversation at a time can
systems like mobile telephones with a capability to simuloccur on each channel.
taneously receive and transmit. Repeaters are by nature
full duplex, most mobiles and almost all handhelds are
Examples of digital communication technologies are all
half duplex.
modern cellphones plus TETRA considered to be the best
Advantage: duplex channels usually allow repeater standard in digital radio and being the baseline infrastrucoperation which extends range (in most cases due ture for whole of country networks, including manufacto increased transmit power and improved aerial lo- turers such as DAMM, Rohill, Cassidian, Sepura and othcation / height) especially where hand-held radios ers, APCO Project 25, a standard for digital public safety
radios, and nally other systems such as Motorolas Moare in use.
toTRBO, HQTs DMR, Nextels iDEN, Hyteras DMR,
Disadvantage: If a radio cannot reach the repeater,
EMCs DMR, and NXDN implemented by Icom as IDAS
it cannot communicate.
and by Kenwood as NEXEDGE. Only NXDN and Mototrbo are proprietary DMR is an ETSI open standard.
Hybrid simplex/duplex
Advantage: More simultaneous talking paths are
Some systems use a mix of the two where radios use dupossible and information such as unit ID, status butplex as a default but can communicate simplex on the base
tons, or text messages can be embedded into a sinstation channel if out-of-range.[8] In the US, the capabilgle digital radio channel. The interoperability stanity to talk simplex on a duplex channel with a repeater is
dard of TETRA means that any brand TETRA radio
sometimes called talk-around, direct, or car-to-car.
can work with any Brand TETRA infrastructure, not
locking the user into expensive and proprietary systems.

8.2.3

Push-to-Talk (PTT)

Disadvantage: Radios must be designed to the same,

compatible standard, radios can become obsolete
quickly (although this is mitigated by properly implemented interoperability standards such as those
set down by ETSI for TETRA), cost more to purchase, and are more complicated.

In two-way radios with headsets, a push-to-talk button

may be included on a cord or wireless electronics box
clipped to the users clothing. In re trucks or an ambulance a button may be present where the corded headset
plugs into the radio wiring. Aircraft typically have corded
headsets and a separate push-to-talk button on the control yoke or control stick. Dispatch consoles often have
a hand-operated push-to-talk buttons along with a foot
switch or pedal. If the dispatchers hands are on a computer keyboard, the user can step on the foot pedal to
transmit. Some systems have muting so the dispatcher
can be on a telephone call and the caller cannot hear what
is said over the radio. Their headset microphone will
mute if they transmit. This relieves the dispatcher of explaining every radio message to a caller.

8.2.5 Data over two-way radio

In some circumstances, voice-operated transmit (VOX) is

used in place of a push-to-talk button. Possible uses are
handicapped users who cannot push a button, Amateur
radio operators, reghters, crane operators, or others
performing critical tasks where hands must be free but
communication is still necessary.

Some two-way digital systems carry both audio and data

over a single data stream. Systems of this type include
NXDN and APCO Project 25. Other more advanced
systems under the TETRA standard are capable of joining time slots together to improve data bandwidth, allowing advanced data polling and telemetry applications over

In some cases, two-way radio is used to communicate

analog or digital data. Systems can be simplex or duplex and may employ selective calling features such as
CTCSS. In full-duplex systems, data can be sent real-time
between two points. In simplex or half-duplex, data can
be sent with a time lag between many points.

44

CHAPTER 8. TWO-WAY RADIO

radio. The method of encoding and decoding the au- in an urban area. System designers use radio frequency
dio stream is called a codec, such as the AMBE or the models, terrain models, and signal propagation modeling
ACELP family of codecs.
software in an attempt to accurately estimate where radios
After market GPS tracking and mobile messaging devices will work within a dened geographic area. The models
can be interfaced with popular two-way radio models pro- help designers choose equipment, equipment locations,
antennas, and estimate how well signals will penetrate
viding a range of features.
buildings. These models will be backed-up by drive testing and actual eld signal level measurements. Designers
adjust antenna patterns, add or move equipment sites, and
Analog
design antenna networks in a way that will accomplish the
[11]
Analog systems may communicate a single condition, intended level of performance.
such as water level in a livestock tank. A transmitter at
the tank site continually sends a signal with a constant audio tone. The tone would change in pitch to indicate the
tanks water level. A meter at the remote end would vary,
corresponding to the tone pitch, to indicate the amount
of water present in the livestock tank. Similar methods
can be used to telemeter any analog condition. This type
of radio system serves a purpose equivalent to a fourto-twenty milliampere loop.[9] In the US, mid-band 72
76 MHz or UHF 450470 MHz interstitial channels are
often used for these systems. Some systems multiplex
telemetry of several analog conditions by limiting each to
a separate range of tone pitches, for example.[10]

Some systems are not engineered. Legacy systems are existing systems which were never designed to meet a system performance objective. They may have started with
a base station and a group of mobile radios. Over a period of years, they have equipment added on in a building block style. Legacy systems may perform adequately
even though they were not professionally designed as a
coherent system. A user may purchase and locate a base
station with an expectation that similar systems used in
the past worked acceptably. A City Road Department
may have a system that works acceptably, so the Parks
Department may build a new similar system and nd it
equally usable. General Mobile Radio Service systems
are not usually engineered.

Digital
Digital systems may communicate text messages from
computer-aided dispatch (CAD). For example, a display
in a tow truck may give a textual location for a call and
any related details. The tow truck driver may press an acknowledge button, sending data in the opposite direction
and agging the call as received by the driver. They can
be used for analog telemetry systems, such as the livestock tank levels, as described above. Another possibility is the lubricating oil pressure in a transit bus engine,
or the current speed of the bus. Analog conditions are
translated into data words. Some systems send radio paging messages which can either 1) beep a paging receiver,
2) send a numeric message, or 3) send a text message.

8.2.7 Options, duty cycle, and conguration

Digital systems typically use data rates in the 1,200

19,200 kilobit-per-second rates and may employ modulation schemes such as frequency shift keying, audio frequency shift keying, or quadrature phase shift keying to
encode characters. Modern equipment have the same capabilities to carry data as are found in Internet Protocol.
Working within the systems protocol constraints, virtually anything can be sent or received.

8.2.6

Engineered versus not engineered

Engineered systems are designed to perform close to a

specication or standard. They are designed as systems
with all equipment matched to perform together. For example, a modern, local government two-way radio system
in the US may be designed to provide 95% area coverage

Example of control arrangement on a congured P25-capable

hand-held radio.

1940s tube-type land mobile two way radios often had

one channel and were carrier squelch. Because radios
were costly and there were fewer radio users, it might be
the case that no one else nearby used the same channel.

8.2. TYPES

45

A transmit and receive crystal had to be ordered for the

desired channel frequency, then the radio had to be tuned
or aligned to work on the channel. 12-volt mobile, tubetype radios drew several amperes on standby and tens-ofamperes on transmit. Equipment worked ideally when
new. The performance of vacuum tubes gradually degraded over time. US regulations required an indicator
lamp showing the transmitter had power applied and was
ready to transmit and a second indicator, (usually red,)
that showed the transmitter was on. In radios with options, wire jumpers and discrete components were used
to select options. To change a setting, the technician soldered an option jumper wire then made any corresponding adjustments.
Motorola MOTOTRBO Repeater DR3000 with duplexer mounted
Many mobile and handhelds have a limited duty cycle. in Flightcase, 100% Duty cycle up to 40 W output
Duty Cycle is the ratio of listening time to transmit time
and is generally dependent on how well the transmitter
of ambulances, for example, could be pressed into sercan shed the heat from the heat sink on the rear of the ravice as command post at a major incident. Unfortunately
dio. A 10% duty cycle (common on handhelds) translates
budgets frequently get in the way and intermittent duty
to 10 seconds of transmit time to 90 seconds of receive
radios are purchased.
time. Some mobile and base equipment is specied at
dierent power levels for example 100% duty cycle at Time delay is always associated with radio systems, but
it is apparent in spacecraft communications. NASA reg25 watts and 15% at 40 watts.[12]
ularly communicates with exploratory spacecraft where a
The trend is toward increasing complexity. Modern
round-trip message time is measured in hours (like out
handheld and mobile radios can have capacities as high
past Jupiter). For Apollo program and Space Shuttle,
as 255 channels. Most are synthesized: the internal elecQuindar tones were used for transmit PTT control.
tronics in modern radios operate over a range of frequencies with no tuning adjustments. High-end models may
have several hundred optional settings and require a com8.2.8 Life of equipment
puter and software to congure. Sometimes, controls on
the radio are referred to as programmable. By changing
Though the general life term for the two way radio is 5
conguration settings, a system designer could choose to
to 7 years and 1 to 2 years for its accessories but still the
set up a button on the radios control panel to function as:
usage, atmosphere and environment plays a major role to
decide its life term (radios are often deployed in harsh
turn scan on or o,
environments where more fragile communication equipment such as phones and tablets may fail). There are so
alert another mobile radio, (selective calling),
many speculations on the life term of two way radios and
their accessories i.e. batteries, chargers, head set etc.
turn on an outside speaker, or
select repeater locations.
In most modern radios these settings are done with specialized software (provided by the manufacturer) and a
connection to a laptop computer.

In government systems, equipment may be replaced

based on budgeting rather than any plan or expected service life. Funding in government agencies may be cyclical
or sporadic. Managers may replace computing systems,
vehicles, or budget computer and vehicle support costs
while ignoring two-way radio equipment. Equipment
may remain in use even though maintenance costs are unreasonable when viewed from an eciency standpoint.[13]

Microprocessor-based radios can draw less than 0.2 amperes on standby and up to tens-of-amperes on highDierent system elements will have diering service lifepowered, 100 watt transmitters.
Base stations, repeaters, and high-quality mobile radios times. These may be aected by who uses the equipment.
often have specications that include a duty cycle. A An individual contacted at one county government agency
repeater should always be continuous duty. This means claimed equipment used by 24-hour services wears out
the radio is designed to transmit in a continuous broad- much faster than equipment used by those who work in
cast without transmitter overheating and resulting failure. positions staed eight hours a day.
Handhelds are intermittent duty, mobile radios and base
station radios are available in normal or continuous duty
congurations. Continuous duty is preferred in mobile
emergency equipment because any one of an entire eet

One document says seven years is beyond the expected

lifetime of walkie-talkies in police service. Batteries are
cited as needing replacement more often. Twelve-yearold dispatch consoles mentioned in the same document

46

CHAPTER 8. TWO-WAY RADIO

were identied as usable. These were compared to prob- frequency by its channel number. Organizations, such as
lematic 21-year-old consoles used elsewhere in the same electric power utilities or police departments, may have
system.[14]
several assigned frequencies in use with arbitrarily asAnother source says system backbone equipment like signed channel numbers. For example, one police departconsoles and base stations are expected to have a fteen- ments Channel 1 might be known to another departyear life. Mobile radios are expected to last ten years. ment as Channel 3 or may not even be available. PubWalkie talkies typically last eight.[15] In a State of Cali- lic service agencies have an interest in maintaining some
fornia document, the Department of General Services re- common frequencies for inter-area or inter-service coordination in emergencies (modern term: interoperability).
ports expected service life for a communications console
used in the Department of Forestry and Fire Protection Each country allocates radio frequencies to dierent twois 10 years.[16]
way services, in accordance with international agreements. In the United States some examples of two-way
services are: Citizens Band, FRS, GMRS, MURS, and
BRS.
8.3 Two-way radio frequencies
Two-way radios can operate on many dierent
frequencies, and these frequencies are assigned differently in dierent countries. Typically channelized
operations are used, so that operators need not tune
equipment to a particular frequency but instead can use
one or more pre-selected frequencies, easily chosen by a
dial, a pushbutton or other means. For example, in the
United States, there is a block of 5 channels (pre-selected
radio frequencies) are allocated to the Multiple Use
Radio System. A dierent block of 22 channels are
assigned, collectively, to the General Mobile Radio
Service and Family Radio Service. The Citizens Radio
Service (""CB"") has 40 channels.

Amateur radio operators nearly always use frequencies

rather than channel numbers, since there is no regulatory
or operating requirement for xed channels in this context. Even amateur radio equipment will have memory
features to allow rapidly setting the transmitter and receiver to favorite frequencies.

8.4 UHF versus VHF

The most common two-way radio systems operate in the
VHF and UHF parts of the radio spectrum. Because this
part of the spectrum is heavily used for broadcasting and
multiple competing uses, spectrum management has become an important activity of governments to regulate radio users in the interests of ecient and non-interfering
use of radio. Both bands are widely applied for dierent
users.

In an analog, conventional system, (the simplest type

of system) a frequency or channel serves as a physical medium or link carrying communicated information.
The performance of a radio system is partly dependent on
the characteristics of frequency band used. The selection UHF has a shorter wavelength which makes it easier for
of a frequency for a two-way radio system is aected, in the signal to nd its way through smaller wall openings to
part, by:[17]
the inside of a building. The longer wavelength of VHF
means it can transmit further under normal conditions.
government licensing and regulations.
For most applications, lower radio frequencies are better
for longer range and through vegetation. A broadcasting
local congestion or availability of frequencies.
TV station illustrates this. A typical VHF TV station op terrain, since radio signals travel dierently in forests erates at about 100,000 watts and has a coverage radius
range of about 60 miles. A UHF TV station with a 60and urban viewsheds.
mile coverage radius requires transmitting at 3,000,000
the presence of noise, interference, or intermodula- watts. Another factor with higher frequencies (UHF) is
that smaller sized objects will absorb or reect the ention.
ergy more which causes range loss and/or multipath re sky wave interference below 5060 MHz and ections which can weaken a signal by causing an Out of
tropospheric bending at VHF.
Time/Out of Phase signal to reach the antenna of the receiver (this is what caused the Ghost image on old over
in the US, some frequencies require approval of a
the air television).
frequency coordination committee.
If an application requires working mostly outdoors, a
A channel number is just a shorthand notation for a fre- VHF radio is probably the best choice, especially if a base
quency. It is, for instance, easier to remember Channel station radio indoors is used and an external antenna is
1 than to remember 26.965 MHz (US CB Channel 1) added. The higher the antenna is placed, the further the
or 462.5625 MHz (FRS/GMRS channel 1), or 156.05 radio can transmit and receive.
MHz (Marine channel 1). It is necessary to identify If the radios are used mainly inside buildings, then UHF
which radio service is under discussion when specifying a is likely the best solution since its shorter wavelength trav-

8.7. SEE ALSO

47

els through small openings in the building better. There 8.6.1 Two-way radio rental business
are also repeaters that can be installed that can relay any
frequencies signal (VHF or UHF) to increase the com- As two-way radios became the leading method of twomunication distance.
way communication, industries like movie and television
There are more available channels with UHF. Since the production companies, security companies, event comrange of UHF is also not as far as VHF under most con- panies, sporting events and others needed to nd a soditions, there is less chance of distant radios interfering lution to use two way radios that was cost-eective and
with the signal. UHF is less aected than VHF by man- economically smart. Instead of buying two-way radios
made electrical noise. So as you see, radio technology is these companies began renting two-way radios short term
very dynamic and you must make the choice of what to and long term. The two-way radio rentals is a signicant
and important component of two-way radio businesses.
use based on your individual situation.
Many have become reluctant to buy two way radios because of the duration of their event or the necessity to
save money. Renting two way radios has brought comfort to customers in renting two way radios because the
8.5 Range
price and non commitment to owning such two way communication devices. Customers can rent anything from
The useful direct range of a two-way radio system detwo-way radios to two-way radio equipment like speaker
pends on radio propagation conditions, which are a funcmicrophones or repeaters.
tion of frequency, antenna height and characteristics, atmospheric noise, reection and refraction within the atmosphere, transmitter power and receiver sensitivity, and
required signal-to-noise ratio for the chosen modulation 8.7 See also
method. An engineered two-way radio system will calculate the coverage of any given base station with an
TETRA (Terrestrial Trunked Radio)
estimate of the reliability of the communication at that
Astro (Motorola)
range. Two-way systems operating in the VHF and UHF
bands, where many land mobile systems operate, rely on
Digital Mobile Radio
line-of-sight propagation for the reliable coverage area.
The shadowing eect of tall buildings may block recep PMR446
tion in areas within the line-of-sight range which can be
achieved in open countryside free of obstructions. The
Family Radio Service
approximate line-of-sight distance to the radio horizon
can be estimated from : horizon in kilometers = 3.569
GE Marc V
times the square root of the antenna height in meters.
Project 25
There are other factors that aect the range of a twoway radio such as weather, exact frequency used, and
Quik Call I
obstructions.[18]
Mobile radio

8.6 Other two-way radio devices

Not all two way radios are hand-held devices. The same
technology that is used in two way radios can be placed in
other radio forms. An example of this is a wireless callbox. A wireless callbox is a device that can be used for
voice communication at security gates and doors. Not
only can they be used to talk to people at these entry
points, personnel can remotely unlock the door so the visitor can enter. There are also customer service callboxes
that can be placed around a business that a customer can
use to summon help from a two-way radio equipped store
employee.
Another use of two-way radio technology is for a wireless PA system. A wireless PA is essentially a one-way
two way radio that enables broadcasting messages from
handheld two-way radios or base station intercoms.

Motorola Saber
Professional Mobile Radio
Specialized Mobile Radio

8.8 References
[1] Goldsmith, Andrea (8 Aug 2005). Wireless ComCambridge University Press.
ISBN
munications.
9780521837163. Retrieved 20 April 2016.
[2] Duarte, Melissa; Sabharwal, Ashutosh (2010). FullDuplex Wireless Communications Using O-The-Shelf
Radios: Feasibility and First Results (PDF). WARP
Project. Retrieved 20 April 2016.
[3] Choi, Charles Q. Chip Could Double Wireless Data Capacity. IEEE Spectrum. Retrieved 20 April 2016.

48

CHAPTER 8. TWO-WAY RADIO

[4] Haldane, Robert. (1995) The Peoples Force, A history of

the Victoria Police. Melbourne University Press. ISBN
0-522-84674-2, 1995
[5] IEEE History Milestones retrieved Oct. 2, 2007
[6] One example of purpose-specic channel assignments is
described in Ivanov, D. A., V. P. Savelyev, and P. V. Shemanski, Organization of Communications, Fundamentals of Tactical Command and Control: A Soviet View, Soviet Military Thought Series #18, (Washington, D.C.: Superintendent of Documents, 1977) Library of Congress
Control Number: 84602565. This is a US Air Force translation of a Soviet-era, Russian-language book. See also,
Inadequate System Capacity, Special Report: Improving Fireghter Communications, USFA-TR-099/January
1999, (Emmitsburg, Maryland: U.S. Fire Administration, 1999) pp. 18-19 and 5.2 Present System, The
California Highway Patrol Communications Technology
Research Project on 800 MHz, 80-C477, (Sacramento,
California: Department of General Services, Communications Technology Division, 1982,) pp. V-4 - V-6.
[7] 3.4.1 User Equipment General Deciencies, San Rafael
Police Radio Committee: Report to Mayor and City Council, (San Rafael, California: City of San Rafael, 1995,) pp.
12.
[8] For an example of talk around use, see Problem Reporting, Special Report: Improving Fireghter Communications, USFA-TR-099/January 1999, (Emmitsburg, Maryland: U.S. Fire Administration, 1999) pp. 25-26. This article also conrms the denition of the phrase talk around.
[9] For examples, see, Mikhailov, K. E. Communications
Facilities on the Volga-Moscow Transmission Line,
Long-Distance Electrical Transmission between the V. I.
Lenin Hydroelectric Station and Moscow, (Jerusalem: Israeli Program for Scientic Translations, 1965).
[10] For an electrocardiogram telemetry example, see Planning Emergency Medical Communications: Volume 2,
Local/Regional-Level Planning Guide, (Washington, D.C.:
National Highway Trac Safety Administration, US Department of Transportation, 1995) pp. 48.
[11] For two examples of drive testing and eld measurements
of received signal levels, see:
Section II: Radio Propagation Studies, The California Highway Patrol Communications Technology Research Project on 800 MHz, 80-C477,
(Sacramento, California: Department of General
Services, Communications Technology Division,
1982,) pp. II-1 - II-34.
Ossanna, Jr., Joseph F., A Model For Mobile
Radio Fading Due to Building Reections: Theoretical and Experimental Fading Waveform Power
Spectra, Bell System Technical Journal, November
1964, pp. 2935-2971. 800 MHz trivia: this article
shows that signal fades occur at audio frequencies
near CTCSS tones, explaining why only DCS was
used in Motorola 800 MHz systems in the 1970s.
[12] Kenwood TKR-850 specication sheet

[13] For one example, see: Plan Element S-7: Rationalized Funding and Plan Element L-2: Permanent Contra Costa Public Safety Radio Authority, Contra Costa
County Public Safety Mobile Radio Master Plan, (Fairfax,
Virginia: Federal Engineering, Inc., 2002,) pp. 45, 49.
[14] For one example, see: 3.2.10.1 Current System Problems, Trunked Radio System: Request For Proposals,
(Oklahoma City, Oklahoma: Oklahoma City Municipal
Facilities Authority, Public Safety Capital Projects Oce,
2000) pp. 56.
[15] 2.4 Equipment Inventory, San Rafael Police Radio Committee: Report to Mayor and City Council, (San Rafael,
California: City of San Rafael, 1995,) pp. 8.
[16] 8000 Exhibits:Equipment Replacement Costs for a Typical Three Position CDF Command and Control Center,
8000 Telecommunications Manual, (Sacramento, California: State of California, Department of Forestry and Fire
Protection, 2006) Adobe PDF le on console costs.
[17] See, Appendix B - FCC Regulations, California EMS
Communications Plan: Final Draft, (Sacramento, California: State of California EMS Authority, September 2000)
pp.38. and Arizona Phase II Final Report: Statewide Radio Inter-operability Needs Assessment, Macro Corporation and The State of Arizona, 2004.
[18] 2-Way Radio Range: How Far Can Two-Way Radios
Communicate?"

8.9 External links

P25 Phase 2 Forum, for more information on P25
Phase 2
DMR (Digital Mobile Radio) Association
TETRA Association
Project 25 Technology Interest Group
Harris PSPC

Chapter 9

Airband
This article is about the radio spectrum used in aviation.
For bands named Air, see Air (disambiguation) Artists.
Airband or Aircraft band is the name for a group of

A typical aircraft VHF radio. The display shows an active frequency of 123.5MHz and a standby frequency of 121.5 MHz.
The two are exchanged using the button marked with a doubleheaded arrow. The tuning control on the right only aects the
standby frequency.

frequencies in the VHF radio spectrum allocated to radio

communication in civil aviation, sometimes also referred
to as VHF, or phonetically as Victor. Dierent sections
of the band are used for radionavigational aids and air
trac control.[1][2][3]
In most countries a license to operate airband equipment
is required and the operator is tested on competency in
procedures, language and the use of the phonetic alphabet.[2][4]

9.1 Spectrum usage

Antenna array at Amsterdam Airport Schiphol

The VHF airband uses the frequencies between 108 and

137 MHz. The lowest 10 MHz of the band, from 108
117.95 MHz, is split into 200 narrow-band channels of sion range of an aircraft ying at cruise altitude (35,000
is about 200 mi (322 km) in good weather
50 kHz. These are reserved for navigational aids such as ft (10,668 m)),
[2][3][5][6]
conditions.
VOR beacons, and precision approach systems such as
ILS localizers.[2][3]
As of 2012, most countries divide the upper 19 MHz into
760 channels for amplitude modulation voice transmissions, on frequencies from 118136.975 MHz, in steps
of 25 kHz. In Europe, it is becoming common to further divide those channels into three (8.33 kHz channel
spacing), potentially permitting 2,280 channels. Some
channels between 123.100 and 135.950 are available in
the US to other users such as government agencies, commercial company advisory, search and rescue, military
aircraft, glider and ballooning air-to-ground, ight test
and national aviation authority use. A typical transmis-

9.1.1 Other bands

Aeronautical voice communication is also conducted
in other frequency bands, including satellite voice on
Inmarsat or Iridium,[7] and high frequency voice. Usually these other frequency bands are only used in oceanic
and remote areas, though they work over wider areas or
even globally. Military aircraft also use a dedicated UHFAM band from 225.0399.95 MHz for air-to-air and airto-ground, including air trac control communication.
This band has a designated emergency and guard channel

49

50

CHAPTER 9. AIRBAND

of 243.0 MHz.[2][8]
Some types of navaids, such as non-directional beacons
and Distance Measuring Equipment, do not operate on
these frequencies; in the case of NDBs, the low frequency
and medium frequency bands are used between 190415
kHz and 510535 kHz. The ILS glide path operates in the
UHF frequency range of 329.3335.0 MHz, and DME
also uses UHF from 9621150 MHz.[2]

9.1.2

Channel spacing

9.1.4 Audio properties

The audio quality in the airband is limited by the RF
bandwidth used. In the newer channel spacing scheme,
the largest bandwidth of an airband channel might be limited to 8.33 kHz, so the highest possible audio frequency
is 4.165 kHz.[16] In the 25 kHz channel spacing scheme,
an upper audio frequency of 12.5 kHz would be theoretically possible.[16] However, most airband voice transmissions never actually reach these limits. Usually, the whole
transmission is contained within a 6 kHz to 8 kHz bandwidth, corresponding to an upper audio frequency of 3
kHz to 4 kHz.[16] This frequency, while low compared to
the top of the human hearing range, is sucient to convey speech. Dierent aircraft, control towers and other
users transmit with dierent bandwidths and audio characteristics.

Channel spacing for voice communication on the airband

was originally 200 kHz until 1947,[9] providing 70 channels from 118 to 132 MHz. Some radios of that time
provided receive-only coverage below 118 MHz for a total of 90 channels. From 19471958 the spacing became
100 kHz; from 1954 split once again to 50 kHz and the
upper limit extended to 135.95 MHz (360 channels), and
then to 25 kHz in 1972 to provide 720 usable channels. 9.1.5 Digital radio
On 1 January 1990 the frequencies between 136.000 and
A switch to digital radios has been contemplated, as this
136.975 MHz were added, resulting in 760 channels.[5]
would greatly increase capacity by reducing the bandIncreasing air trac congestion has led to further subwidth required to transmit speech. Other benets from
division into narrow-band 8.33 kHz channels in the
digital coding of voice transmissions include decreased
ICAO European region; all aircraft ying are required
susceptibility to electrical interference and jamming. The
to have communication equipment for this channel
change-over to digital radio has yet to happen, partly bespacing.[2][10][11][12] Outside of Europe, 8.33 kHz chancause the mobility of aircraft necessitates complete internels are permitted in many countries but not widely used
national cooperation to move to a new system and also the
as of 2012.
time implementation for subsequent changeover.[17][18]
The emergency communication channel 121.5 MHz is the Another factor delaying the move to any digital mode is
only channel that retains 100 kHz channel spacing in the the need to retain the ability for one station to override
US; there are no channel allocations between 121.4 and another in an emergency.
121.5 or between 121.5 and 121.6[13]

9.1.3

Modulation

Aircraft communications radio operations worldwide use

amplitude modulation, predominantly A3E double sideband with full carrier on VHF and UHF, and J3E single
sideband with suppressed carrier on HF. Besides being
simple, power-ecient and compatible with legacy equipment, AM and SSB permit stronger stations to override
weaker or interfering stations. Additionally, this method
does not suer from the capture eect found in FM. Even
if a pilot is transmitting, a control tower can talk over
that transmission and other aircraft will hear a somewhat
garbled mixture of both transmissions, rather than just
one or the other. Even if both transmissions are received
with identical signal strength, a heterodyne will be heard
where no such indication of blockage would be evident in
an FM system.[14]

9.2 Unauthorised use

It is illegal in most countries to transmit on the Airband
frequencies without a suitable license, although an individual license may not be required, for instance in the US
where aircraft stations are licensed by rule..[19] Many
countries regulations also restrict communications in the
airband. For instance, in Canada, airband communications are limited to those required for the safety and navigation of an aircraft; the general operation of the aircraft;
and the exchange of messages on behalf of the public. In
addition, a person may operate radio apparatus only to
transmit a non-superuous signal or a signal containing
non-profane or non-obscene radiocommunications.[2]

Listening to airband frequencies without a license is

also an oence in some countries, including the UK,[20]
though enforcement may vary. Such activity has been
Alternative analog modulation schemes are under discus- the subject of international situations between govsion, such as the CLIMAX[15] multi-carrier system and ernments when tourists bring airband equipment into
oset carrier techniques to permit more ecient utiliza- countries which ban the possession and use of such
tion of spectrum.
equipment.[21][22]

9.4. REFERENCES

9.3 See also

Aircraft Communications Addressing and Reporting System
Air trac ow management
Air trac control
Avionics
Control tower
Future Air Navigation System
Radio horizon

9.4 References
[1] H. P. Westman (ed), Reference Data for Radio Engineers
Fifth Edition, Howard W. Sams and Co, 1968, page 1-6
[2] Transport Canada (April 2014). Com - 5.0 radio communications (PDF). Retrieved 27 April 2013.
[3] Aviation Radio Bands and Frequencies. Smeter network
2011. Retrieved 16 February 2011.
[4] Radio Telephony Training Syllabus (PDF). Cotswold
Gliding Club - date undisclosed. Retrieved 16 February
2011.
[5] Requirements for 760 channel VHF radio for Aeronautical operations (PDF). Federal aviation agency 1992. Retrieved 2011-02-14.
[6] VII. ELECTRONIC AIDS TO INSTRUMENT FLYING. FAA test company - date undisclosed. Retrieved
2011-02-17.
[7] Iridium Satellite Voice (SATVOICE) with Safety Services (PDF). Retrieved 2016-09-18.
[8] DAOT 5: C-12-118-000/MB-000 Operating Instructions
CH118 Helicopter (unclassied), Change 2, 23 April
1987, Page 1-51. Department of National Defence
[9] 8.33 kHz Channel spacing what is this?". Roger-Wilco.
2010-04-03. Retrieved 2012-05-10.
[10] Mise en oeuvre de lespacement 8.33 kHz au-dessous
du FL 195
[11] Aircraft frequencies for UK and Europe. Garfnet organisation 2009. Retrieved 14 February 2011.
[12] 8.33kHz Programme. Eurocontrol. Retrieved 200712-24.
[13] 47 C.F.R. 87.173 as of 2012
[14] EECE 252 Project Report, Amplitude Modulated Radio
Applications in Aviation 17 April 2012
[15] EuroControl, CLIMAX/8.33: To extend 8.33 kHz benets, ICAO, October 2007

51

[16] Poole, Ian. Amplitude Modulation, AM Spectrum

& Bandwidth. Radio-Electronics.com. Retrieved 26
September 2015.
[17] Aordable real-time digital voice transmission using
Voip technology. Command NAVAIR 2 January 2010.
Retrieved 16 February 2011.
[18] Aircraft centric digital CNS (PDF). CITA 2010. Retrieved 14 February 2011.
[19] 47 C.F.R. 87.18 as of 2012
[20] Guidance on Receive-Only Radio Scanners Ofcom
[21] Greek drama in capital. Algarve resident 2011. Retrieved 16 February 2011.
[22] Plane-spotters 'ignored warnings. BBC News, 25 April
2002. Retrieved: 14 March 2007. Quote: Note-taking
in conjunction with other activities may be detrimental (to
Greek security).

Chapter 10

Citizens band radio

communications. Like many other two-way radio services, citizens band channels are shared by many users.
Only one station may transmit at a time; other stations
must listen and wait for the shared channel to be available. It is customary for stations waiting to use a shared
channel to broadcast the single word Break during a lull
in the conversation. (Citation needed. Not an accurate
representation of radio etiquette.) This informs people
using the channel that others are waiting.

Typical 1980s CB base station, used with outdoor antenna. This

radio may also be used in an automobile, since it is powered by
13.8V DC. Shown with Astatic Power D-104 desk mic

A number of countries have created similar radio services, with varying technical standards and requirements
for licensing. While they may be known by other names,
such as the General Radio Service in Canada,[1] they often use similar frequencies (26 to 28 MHz), have similar
uses, and similar technical standards. Although licenses
may be required, eligibility is generally simple. Some
countries also have personal radio services in the UHF
band, such as the European PMR446 and the Australian
UHF CB.

10.1 History
10.1.1 United States
Main article: CB usage in the United States

Origins

Cobra 18 WX ST II mobile CB radio with microphone

Citizens band radio (also known as CB radio) is, in

many countries, a system of short-distance radio communications between individuals typically on a selection of
40 channels within the 27 MHz (11 m) band. Citizens
band is distinct from other personal radio service allocations such as FRS, GMRS, MURS, UHF CB and the
Amateur Radio Service (ham radio). In many countries, CB operation does not require a license, and (unlike
amateur radio) it may be used for business or personal A QSL card issued by a US CB station in 1963.
52

10.1. HISTORY

53

The citizens band radio service originated in the United

States as one of several personal radio services regulated
by the Federal Communications Commission (FCC).
These services began in 1945 to permit citizens a radio
band for personal communication (e.g., radio-controlled
model airplanes and family and business communications). In 1948, the original CB radios were designed
for operation on the 460470 MHz UHF band.[2] There
were two classes of CB radio: A and B. Class B radios had simpler technical requirements, and were limited to a smaller frequency range. Al Gross established
the Citizens Radio Corporation during the late 1940s to
manufacture Class B handhelds for the general public.[3]

of tractor-trailers in eastern Pennsylvania using the citizens band radio in his truck. His name was J.W. Edwards and his handle (or radio name) was River Rat.
The blockade began on I-80 and quickly spread throughout the country, with River Rats messages literally being
relayed from one area of trucks to the next.[8] The radios were crucial for independent truckers; many were
paid by the mile, which meant their productivity was impacted by the 55-mph speed limit.[7] The use of CB radios in 1970s lms such as Smokey and the Bandit (1977)
and Convoy (1978), popular novelty songs such as C.W.
McCall's "Convoy" (1975) and on television series such
as Movin' On (debuted in 1974) and The Dukes of Hazzard
(debuted 1979) established CB radio as a nationwide
Ultra-high frequency (UHF) radios, at the time, were neicraze
in the USA in the mid- to late 1970s.
ther practical nor aordable for the average consumer.
[4]
On September 11, 1958 the Class D CB service was Originally, CB required a purchased license ($20 in the
created on 27 MHz, and this band became what is pop- early 1970s, reduced to $4 on March 1, 1975) and the
ularly known today as Citizens Band. There were only use of a callsign; however, when the CB craze was at its
23 channels at the time; the rst 22 were taken from the peak many people ignored this requirement and invented
former amateur radio service 11-meter band, and channel their own nicknames (known as handles). Rules on au23 was shared with radio-controlled devices. Some hob- thorized use of CB radio (along with lax enforcement)
byists continue to use the designation 11 meters to refer led to widespread disregard of the regulations (notably in
to the Citizens Band and adjoining frequencies. Part 95 antenna height, distance communications, licensing, call
of the Code of Federal Regulations regulates the Class signs and transmitter power).
D CB service, on the 27 MHz band, since the 1970s and Betty Ford, the former First Lady of the United States,
continuing today.[5] Most of the 460470 MHz band was used the CB handle First Mama.[9] Voice actor Mel
reassigned for business and public-safety use; Class A CB Blanc was also an active CB operator, often using Bugs
is the forerunner of the General Mobile Radio Service or Day as his handle and talking on the air in the Los
(GMRS). Class B CB is a more distant ancestor of the Angeles area in one of his many voice characters. He
Family Radio Service. The Multi-Use Radio Service is
appeared in an interview (with clips having fun talking
another two-way radio service in the VHF high band. An to children on his home CB radio station) in the NBC
unsuccessful petition was led in 1973 to create a Class E
Knowledge television episode about CB radio in 1978.[10]
CB service at 220 MHz, which was opposed by amateur Similar to internet chat rooms a quarter-century later, CB
radio organizations.[6] and others. There are several other
allowed people to get to know one another in a quasiclasses of personal radio services for specialized purposes anonymous manner. As with the internet, CB radio usage
(such as remote control devices).
allowed the worst characteristics of anonymity.
During the 1960s, the service was popular among Originally, there were 23 CB channels in the U.S.; the 40small businesses (e.g., electricians, plumbers, carpen- channel band plan was implemented in 1977. Channel 9
ters), truck drivers and radio hobbyists. By the late 1960s was ocially reserved for emergency use by the FCC in
advances in solid-state electronics allowed the weight, 1969.[11] Channel 10 was originally often used for highsize, and cost of the radios to fall, giving the public access way travel communications east of the Mississippi River,
to a communications medium previously only available and channel 19 west of the Mississippi; channel 19 then
to specialists.[7] CB clubs were formed; a CB slang lan- became the preferred highway channel in most areas, as it
guage evolved alongside 10-codes, similar to those used did not have adjacent-channel interference problems with
in emergency services.
channel 9. Many CBers called channel 19 the truckers
1970s popularity
After the 1973 oil crisis the U.S. government imposed a
nationwide 55 mph speed limit, and fuel shortages and
rationing were widespread. CB radio was used (especially by truckers) to locate service stations with better
supplies of fuel, to notify other drivers of speed traps,
and to organize blockades and convoys in a 1974 strike
protesting the new speed limit and other trucking regulations. One leader was able to almost single-handedly
coordinate an interstate highway blockade of hundreds

channel. Channel 11 was originally restricted by the

FCC for use as the calling channel.
The original FCC output power limitation for CB radios
was 5-watts DC input to the nal amplier stage, which
was a reference to the earlier radios equipped with tubes.
With solid state radios becoming more common in the
1970s, this specication was rewritten by the FCC at the
same time the authorized channels were increased to 40.
The current specication is simply 4-watts output (AM)
or 12-watts output (SSB)" as measured at the antenna
connector on the back of the radio. The old specication

54
was often used in false advertising by some manufacturers who would claim their CB radios had 5-watts long
after the specication had changed to 4-watts output. The
older 23-channel radios built under the old specications
typically had an output of around 3.5 to 3.8 watts output when measured at the antenna connector. The FCC
simply rounded-up the old 5-watts DC input to the nal
amplier stage specication to the new 4-watts output
as measured at the antenna connector on the back of the
radio, resulting in a far simpler and easier specication.
Initially, the FCC intended for CB to be the poor mans
business-band radio, and CB regulations were structured similarly to those regulating the business band radio service. Until 1975,[12] only channels 915 and
23[13] could be used for inter-station calls (to other licensees). Channels 18 and 1622 were reserved for
intra-station communications (among units with the
same license).[14] After the inter-station/intra-station rule
was dropped, channel 11 was reserved as a calling frequency (for the purpose of establishing communications);
however, this was withdrawn in 1977.[15] During this
early period, many CB radios had inter-station channels
colored on their dials, while the other channels were clear
or normally colored (except channel 9, which was usually colored red). It was common for a town to adopt an
inter-station channel as its home channel. This helped
prevent overcrowding on Channel 11, enabling a CBer to
monitor a towns home channel to contact another CBer
from that town instead of a making a general call on
Channel 11.
Boating and the U.S. Coast Guard
Since CB was coming down in price and VHF Marine
Band was still expensive, many boaters put CB radios on
their boats. Business caught on to this market, and introduced marine CBs containing a weather band (WX).
There was a lot of controversy about whether or not the
Coast Guard should monitor CB radio, but they did, using Motorola base stations installed at their search and
rescue stations. The Coast Guard stopped this practice in
the late 1980s and recommends VHF Marine Band radios
for boaters.[16]
21st-century use
CB has lost much of its original appeal due to development of mobile phones, the internet and the Family Radio
Service. Changing radio propagation for long-distance
communications due to the 11-year sunspot cycle is a
factor at these frequencies. In addition, CB may have
become a victim of its own popularity; with millions of
users on a nite number of frequencies during the mid-tolate 1970s and early 1980s, channels often were noisy and
communication dicult. This caused a waning of interest among hobbyists. Business users (such as tow-truck
operators, plumbers and electricians) moved to the VHF

CHAPTER 10. CITIZENS BAND RADIO

business-band frequencies. The business band requires
an FCC license, and usually results in an assignment to
a single frequency. The advantages of fewer users sharing a frequency, greater authorized output power, clarity
of FM transmission, lack of interference by distant stations due to skip propagation, and consistent communications made the VHF (Very High Frequency) radio an
attractive alternative to the overcrowded CB channels.
Channel 9 is restricted by the FCC to only emergency
communications and roadside assistance.[17] Most highway travelers monitor channel 19. CB radio is still used
by truck drivers, and remains an eective means of obtaining information about road construction, accidents
and police speed traps.

10.1.2 Australia
Before CB was authorized in Australia, there were handheld 27 MHz walkie-talkies which utilized several
frequencies between the present CB channels, such as
27.240 MHz.[18][19] By the mid-1970s, hobbyists were
experimenting with handheld radios and unauthorized 23
Channel American CB radios. At that time in Australia,
the 11-meter band was still used by licensed ham operators and Emergency Services,[20] but not yet available
for CB use. A number of CB clubs had formed by this
time which assigned call signs to members, exchanged
QSL cards, and lobbied for the legalisation of CB. In
1977 Having legalised Australian CB and allowed the import and sale of American and Japanese 23 channel sets
the government then drafted new interim regulations for
Australian 18 channel transceivers.The new RB249 regulations came in on January 1, 1978 and the last ocial
registrations for 23 channel sets was January 31, 1978. If
you did not have your 23 Channel CB registered by this
date it was illegal to use it and could no longer be eligible to get licensed. The 18 channel band plan used 16
channels of the 23 channel CB radios plus 2 extra channels. 27.095 and 27.195 to make up the 18 channels.
Channels 1,2,3,4,10,21 and 23 where deleted from this
18 channel band plan. So channel 1 on an 18 channel was
actually channel 5 on a 23 channel radio.[21] On January 1,
1982, the American 40-channel band plan was adopted.
From the outset, the government attempted to regulate
CB radio with license fees and call signs, but some years
later abandoned this approach. Enthusiasts rushed for licences when the doors opened at post oces around Australia in mid 1977 and by the end of the rst quarter of
1978 there had been an estimated 200,000 licences issued (Australias Population in 1978 was 14.36 Million).
The regulations called for one licence per CB radio. The
price for a licence in 1977 was AU$25. Australian CB
radio is AM and USB, LSB (No FM) on 27 MHz and
output power is 4 Watts AM and 12 Watts SSB. UHF is
477 MHz FM and has an output power of 5 Watts. Originally when CB was rst legalised the 27 MHz CB Band
was to be banned to Australian CBers in 1982 and only

10.1. HISTORY
the 477 MHz UHF band was to continue, but this never
ended up happening. The rst 477MHZ CB radio in 1977
was designed and made in Australia by Philips and was a
40 channel CB called the FM320. 27 MHz CB Channel Allocation in Australia is Channel 8 (27.055 MHz)
Truckers or Highway Channel, Channel 9 (27.065 MHz)
Emergency, Channel 11 (27.085 MHz) AM Call Channel, Channel 16 (27.155 MHz) LSB SSB Call Channel,
35 (27.355 MHz) LSB 2nd SSB Call Channel. UHF CB
Channel Allocation is Channel 5 Emergency, Channel 11
Call Channel, Channel 40 Truckers or Highway

55
ing (ship-shore) 27.9400 Ch 94 - Non-commercial club
calling and working (ship-ship/ship-shore) 27.9600 Ch
96 - Non-commercial calling and working (ship-ship)
27.9800 Ch 98 - Rescue calling and working (shipship/ship-shore)

The rst CB club in Australia was the Charlie Brown

Touring Car Club (CBTCC), which formed in Morwell,
Victoria in 1967 and consisted mainly of four-wheel
drive enthusiasts. The club used the prex GL (for
Gippsland), since CB could not be used. After July
1, 1977, the club changed its name to Citizens Band
Two Way Communication Club (CBTCC). Other early
clubs were LV (Latrobe Valley) and WB (named after Wayne Britain). Members of these clubs are still active, and have also become amateur radio operators.
With the introduction of UHF CB radios in 1977, many
operators used both UHF and HF radios and formed
groups to own and operate local FM repeaters. Members
of the CBTCC formed what became known as Australian
Citizens Radio Movement (ACRM) in the early 1970s;
this organization became the voice for legalization of CB
radio throughout Australia. After peaking in the 1970s
and early 1980s, the use of 27 MHz CB in Australia has
fallen dramatically due to the introduction of 477 MHz
UHF CB (with FM and repeaters) and the proliferation of
cheap, compact handheld UHF transceivers. Technology
such as mobile telephones and the internet have provided
people with other choices for communications. The Australian government has changed the allocation of channels
available for UHF CB Radio from 40 to 80, and doubled
the number of repeater channels from 8 to 16. This was
done by taking the existing channels that had a spacing of
25 kHz between (Known as wide band) them and placing new channels in between the old 40 channels. So now
the channels have 12.5 kHz spacing between them (now
called narrow band). But the original 40 channels are still
on the original frequencies.[22]
Australia also has Marine Radio Using 27 MHz. There Hand-held CB transceiver; antenna not shown
are several frequencies allocated to 27 MHz Marine Radio in Australia. The frequencies range from 27.6800
MHz to 27.9800 MHz. Mode:AM Power:4W Maximum. 10.1.3 Canada
These Frequencies and Allocation are:
27.6800 Ch 68 - Commercial calling and working
27.7200 Ch 72 - Professional shing calling and working
(ship-shore/ship-ship) 27.8200 Ch 82 - Professional shing calling and working (ship-shore/ship-ship) 27.8600
Ch 86 - Supplementary distress, safety and calling
27.8800 Ch 88 - Distress, safety and calling 27.9000 Ch
90 - Non-commercial calling and working (ship-shore)
27.9100 Ch 91 - Non-commercial calling and work-

In Canada, the General Radio Service uses the identical

frequencies and modes as the United States citizens band,
and no special provisions are required for either Canadians or Americans using CB gear while traveling across
the border. The General Radio Service was authorized in
1962. Initially, CB channels 1 through 3 remained allocated to amateur radio and channel 23 was used by paging
services. American CB licensees were initially required
to apply for a temporary license to operate in Canada.[23]

56

CHAPTER 10. CITIZENS BAND RADIO

In April 1977, the service was expanded to the same 40 MHz allocation: an eight-channel analog Personal Mochannels as the American service.[24]
bile Radio 446 MHz (Analog PMR446) with frequencies from 446.00625446.09375 MHz (12.5 kHz spacing) FM with 0.5 watt power output, and 16 channels
for Digital Personal Mobile Radio 446 MHz (Digital
10.1.4 Indonesia
PMR 446). Frequencies for Digital PMR 446 are from
In Indonesia, CB radios were rst introduced about 1977 446.103125446.196875 MHz with 6.25 kHz channel
when some transceivers were imported illegally from spacing in 4FSK mode and a power output of 0.5 watt.[27]
Australia, Japan and the United States. The dates are An unocial citizens band radio club in Malaysia is the
hard to conrm accurately, but early use was known Malaysia Boleh Citizen Radio Group, known as Mike
around large cities such as Jakarta, Bandung, Yogyakarta, Bravo (Malaysia Boleh).[28]
Surabaya and Medan. The Indonesian government legalized CB on 6 October 1980 with a decision by the
Minister of Communications, the Ministerial Decree on 10.1.6 United Kingdom
the Licensing for the Operation of Inter-Citizens Radio
Communication. Because many people were already us- Main article: CB radio in the United Kingdom
ing 40-channel radios prior to legalization, the American band plan (with AM and SSB) was adopted; a VHF
band was added in 1994, along with allowing use of the In the UK, small but growing numbers of people were ilAustralian UHF CB channel plan at 476-477 MHz On legally using American CB radios during the late 1970s
November 10, 1980, the Indonesian Directorate Gen- and early 1980s. The prominence of CB radio grew in
eral of Posts and Telecommunications issued another de- Britain partly due to the popularity of novelty songs like
cree establishing RAPI (Radio Antar Penduduk Indone- CW McCalls Convoy and Laurie Lingo & The Dipsia) as the ocial citizens band radio organization in sticks Convoy GB in 1976 (both of which were Top
5 hits) and the movie Convoy in 1978. CB radio use
Indonesia.[25]
was even featured on one part of the popular television
programme Are You Being Served?. By 1980, CB radio
was
becoming a popular pastime in Britain; as late as the
10.1.5 Malaysia
summer of 1981 the British government was still saying
In Malaysia, citizens band radios became legal when that CB would never be legalized on 27 MHz, proposing
the Notication of Issuance Of Class Assignments by a UHF service around 860 MHz called Open Channel
Communication and Multimedia Malaysia was published instead. However, in November 1981 (after high-prole
on 1 April 2000. Under this class assignment, a CB radio public demonstrations) 40 frequencies unique to the UK,
is classied as a Personal Radio Service device. The known as the 27/81 Bandplan using FM were allocated
frequency band is HF, 26.9650 MHz to 27.4050 MHz at 27 MHz plus 20 channels on 934 MHz (934.0125 to
(40 channels), power output is 4 watts for AM and FM 934.9625 MHz with 50-kHz-spacing). CBs inventor, Al
and 12 watts PEP for SSB. Channel 9 is reserved for Gross, made the ceremonial rst legal British CB call
from Trafalgar Square in London.
emergencies, and channel 11 is a calling channel. On
UHF 477 MHz, citizens band PRS radio devices are al- The maximum power allowable on the MPT 1320 27/81
lowed 5 watts power output on FM on 39 assigned chan- system was 4 watts (in common with the American sysnels spaced at 12.5-kHz intervals between 477.0125 MHz tem), although initially radios were equipped to reduce
and 477.4875 MHz. Channel 9 is reserved for emergen- output power by 10 dB (to 0.4 watts) if the antenna was
cies, and channel 11 for calling. A short-range simplex mounted more than 7 meters above ground level. The
radio communications service for recreational use is from power-reduction switch is also useful in reducing TV in477.5250477.9875 MHz FM mode with 38 channels terference. MPT 1320 also restricted antennas to a maxand a power output of 500 mW. A CB radio or Personal imum length of 1.5 meters, with base loading being the
Radio Service Device under Class Assignment does not only type permitted for 27 MHz operation. Over the
need an individual license to operate in Malaysia if it ad- next several years antenna regulations were relaxed, with
heres to the rules of the Warta Kerajaan Malaysia, Com- antenna length increasing to 1.65 meters and centre- or
munication and Multimedia Act 1998 (Act 588), Noti- top-loading of the main radiating element permitted. On
cation of Issuance Of Class Assignment, P.U.(B)416 Jil. September 1, 1987 the UK added the usual 40 frequen48, No. 22(e) Personal Radio Service Device, 1 Novem- cies (26.96527.405 MHz) used worldwide, for a total of
ber 2004.[26]
80 channels at 27 MHz; antenna regulations were further
On April 1, 2010 the MCMC (Malaysian Communica- relaxed, and the 934 MHz band was withdrawn in 1998.
tions and Multimedia Commission) released a new Notication of Issuance of Class Assignments, the Communications and Multimedia Act 1998 Class Assignments
No. 1 of 2010. This includes a new UHF PMR 446

CB radio in the UK was deregulated in December 2006

by the regulatory body Ofcom, and CB radio in the UK
is now license-free. The old MPT 1320 27/81 band will
continue to be available for the foreseeable future. On

10.2. FREQUENCY ALLOCATIONS

27 June 2014, changes were made by Ofcom to allow the
use of AM & SSB modes on CB in the UK legally for
the rst time. The rules regarding non-approved radios
and power levels above 4 watts on AM/FM and 12W on
SSB still apply, despite deregulation. Persons using illegal equipment or accessories still risk prosecution, nes
or conscation of equipment, although this is rarely enforced. AM and SSB on the freeband and amplier use
are common among enthusiasts. Packet radio is legal
in the UK, although not widely used. Internet gateway
stations are also beginning to appear; although illegal on
27 MHz, these units are connected to other CB stations
around the world.
Although the use of CB radios in the UK is limited they
are still popular, especially with the farming community,
truckers and mini-cab services.[29] The widely used channel for the Young Farmers Club is channel 11. The normal calling and truckers channel is channel 19, although
many truck organisations and groups use other channels
to avoid abuse.

10.2 Frequency allocations

CB radio is not a worldwide, standardized radio service.
Each country decides if it wants to authorize such a radio service from its domestic frequency authorizations,
and what its standards will be; however, similar radio
services exist in many countries. Frequencies, power
levels and modes (such as frequency modulation (FM),
amplitude modulation (AM), and single-sideband modulation (SSB), often vary from country to country; use of
foreign equipment may be illegal. However, many countries have adopted the American channels and their associated frequencies, which is generally in AM mode except some higher channels which are sometimes in SSB
mode.[30]

57
nel number along with an A. Specically channel 11A
is used to power Eurobalises.

10.2.3 SSB usage

Single-sideband (SSB) operation involves the selection
of either the Lower Side Band (LSB) or the Upper Side
Band (USB) mode for transmit and receive. SSB radios
also have the standard AM mode for communicating with
standard CB radio models. With the original 23 CB channels SSB stations commonly used channel 16, to avoid interference to those using AM (SSB stations are authorized
to use 12 watts, as opposed to 4 watts for AM stations)
and to more easily locate other SSB stations. With the
FCC authorization of 40 channels, SSB operation shifted
to channels 3640. Channel 36 or 38 (LSB) became the
unocial SSB calling channels for stations seeking contacts, with the subsequent conversation moving to channels 3740. CBers with AM-only radios are asked to
not use channels 36 through 40. In return, SSB stations
stay o the remaining 35 channels so they could be used
by AM stations. This agreement provides interferencefree operation for all operators by separating the far more
powerful SSB stations from the AM stations. This solution also resolves the chaos created by the false advertising that SSB radios have 120 channels compared to only
40 for AM radios.

While a SSB radio has three possible modes (AM, LSB,

USB) it can operate in, operation is still limited to the
same 40 channels. Some manufacturers tried to sell more
radios by claiming that with three dierent modes possible for each channel, it was the equivalent to 120 channels. Reality is far dierent. In general, each channel can
only support one conversation at a time, whether it be in
the AM, LSB or USB mode; however, a single channel
can support separate LSB and USB conversations at the
same time if there is no AM conversation in progress.
For a particular conversation, everyone must be tuned to
the same channel and same mode in order to talk with
10.2.1 Standard Channels
each other. Attempting an SSB conversation while an
AM conversation is in progress results in jammed comThe standard channel numbering is harmonized through munications for everyone.
FCC (America) and CEPT (Europe) T : .
MH , : . MH , : . MH
CEPT.[31]
10.2.4 Country-specic variations
See also channel assignments for CB usage in the United
Main article: Personal radio service
States.

10.2.2

Intermediate Channels

When looking at the FCC/CEPT channel list there are

some channels with an oset of 20 kHz instead of the regular 10 kHz step. These intermediate frequencies are reserved for other application such as remote controls, baby
phones or cordless keyboards. It is an unocial practice
to name these channels by their next lower standard chan-

The European Conference of Postal and Telecommunications Administrations (CEPT) adopted the North American channel assignments, except channel n 23, frequency
27.235 MHz; channel n 24, frequency 27.245 MHz;
channel n 25, frequency 27.255 MHz.[31] However, legal CB equipment sold in Europe does follow the North
American channel designation. Some member countries
permit additional modes and frequencies; for example,
Germany has 40 additional channels at 26 MHz for a total

58

CHAPTER 10. CITIZENS BAND RADIO

of 80. The United Kingdom has an additional 40 channels between 27.60125 and 27.99125 MHz, also making
80 in total. Before CEPT, most member countries used
a subset of the 40 US channels.

Zealand authorizes use of their New Zealand specic 40channel 26.330 26.770 MHz frequency plan in addition to the standard 40-channel 26.965 27.405 MHz
frequency plan for a total of 80 HF CB channels. New
has also adopted the Australian UHF CB System
In Russia and Poland the channels are shifted 5 kHz down; Zealand[33]
as
well.
for example, channel 30 is 27.300 MHz. Many operators add a switch to change between the zeroes (the Japans CB allocation consists of 8 voice and 2 R/C chanRussian/Polish channel assignment) and the ves (the nels with a maximum power output of 500 mW. AM
international/European assignment). Most contemporary mode is the only mode permitted and antennas must be
radios for that markets can do ves as well as zeroes non-removable and less than 199 cm (78 inches) long. In
out of the box. Since roughly 20052006, Russia and Japan, the 26 28 MHz range is allocated to shery raPoland have adopted use of the standard US channel o- dio services and these frequencies are heavily used for
set as well as the older channel plan, for two overlapping marine communications. However, frequencies such as
grids of channels.
27.005 MHz AM are widely pirated in Japan with very
Russia uses an alphanumeric designation for their CB high power transmitters. This causes interference to the
channel plans, due the fact that several grids or bands authorized low-power 1 W DSB (1 watt AM) shery raof 40 channels each are used, along with both AM and dio service. Instead of 26 27 MHz, Japan has authoFM mode. Russian CB allocations follow the CB band rized several UHF-FM CB-type personal radio services
26.965 27.405 MHz (designated as band C), as well as in the 348 MHz, 420 422 MHz and 903 904 MHz
26.515 26.955 MHz (designated as band B) and 27.415 bands.
27.855 MHz (designated as band D). Some radios refer
to the mid band (standard CB band) as band D which
shifts the letters up one (making 26.515 to 26.955 MHz
band C and 27.415 27.855 MHz band E.
For the convenience of users of the grid were marked by
letters. Classic is considered the marking when the main
range is designated C letter. The most common description of the channel is considered to be similar to the
following: (C9FM or C9EFM or C9EF or 9EF).
In it:
the rst letter ( C) is indicated by a grid that contains a set of 40 channels. If the rst letter is not
specied, it is considered that it is ( C). For example, (C9EF, 9EF)
hereinafter ( 9) the channel number. Sometimes
less than 10 channels are designated 2 digits. For
example, (C9EF, C09EF)

1. 26.968 MHz Japanese CB Channel 1

2. 26.976 MHz Japanese CB Channel 2
3. 27.040 MHz Japanese CB Channel 3
4. 27.080 MHz Japanese CB Channel 4
5. 27.088 MHz Japanese CB Channel 5
6. 27.112 MHz Japanese CB Channel 6
7. 27.120 MHz Japanese CB Channel 7
8. 27.144 MHz Japanese CB Channel 8 Calling
Channel
1. 27.048 MHz Japanese Remote Control R/C Frequency
2. 27.136 MHz Japanese Remote Control R/C Frequency

behind it an optional designation ( E) for European or mandatory ( R) for Russian size frequency nets. For example, (C9EF, C9F, C9RF)

3. 27.152 MHz Japanese Remote Control R/C Frequency

end the used modulation ( FM) or ( F), (

AM) or ( A). e.g. (C9EFM, C9EF, C9EAM,
C9EA )

Indonesia has the usual 40 channels at 27 MHz, plus

a unique 60-channel allocation from 142.050 MHz
143.525 MHz.[34]

In Brazil, CB operators can use up to 80 channels (from

An example of correct designations: C9EF, C9EA, 26.965 MHz to 27.805 MHz).
C9RF, C9RA
South Africa, like New Zealand and the UK, permits the
The 25 30 MHz band (including the CB allocations and use of two HF CB bands. South Africa has a 23-channel
frequencies above and below the 26.5 27.86 MHz band) AM/SSB 29 MHz CB allocation (called 29 Megs or
is heavily used for taxi cab and other mobile two-way 29 MHz CB) from 29.710 MHz to 29.985 MHz in 12.5
communications systems in Russia, Ukraine and other kHz steps. South Africa also permits use of standard CB
former USSR country states.
channels 19 through 27 (27.185 to 27.275 MHz) with
New Zealand and Japan have unique allocations that do AM/SSB permitted. Many radios sold in South Africa
not correspond to those of any other country. New feature both the 27 MHz and 29 MHz bands.

10.4. TECHNOLOGY

59

Hungary allows use of the low channels for a total of Russia it is channel 15 (in addition to traditional emer80 channels (26.515 MHz to 27.405 MHz).
gency 9 and truckers 19 channels) and in Greece it is
Germany authorizes a similar allocation, the usual 40 channel 13, all AM. These frequencies may have evolved
channels from 26.965 to 27.405 MHz and another 40 because tuned circuits (particularly antennas) work best
channels from 26.565 to 26.955 MHz in straight 10 kHz in the middle of the band; the frequency for channel 19
(not channel 20) is the center of the 40-channel US band
steps.
and other things being equal, signals will be transmitted
The Czech Republic authorizes 80 channels as well (same and heard the farthest. Since less standardization exists in
as the German 80 channel plan). As in Germany, digital Europe, CB there is more associated with hobbyists than
modes are allowed on certain frequencies (channel 24 with truckers.
27.235 MHz, channel 25 27.245 MHz, channel 52
26.675 MHz, channel 53 26.685 MHz, channel 76 Legal (shortrange) use of CB radio is sometimes im26.915 MHz, and channel 77 26.925 MHz). Internet peded by users of illegal highpower transmitters, which
gateways and radio repeaters are allowed on channels 18 can be heard hundreds of miles away. The other prob(27.175 MHz) and 23 (27.255 MHz). Paging is permit- lem with shortrange CB use is propagation; during
ted on channel 1 (26.965 MHz) and channel 80 (26.955 longrange skip conditions local signals are inaudible
MHz) is the recommended call channel for Czech CB ra- while distant signals boom in as if they were local.
dio operators.
In the United States, the number of users and low enforceUsing radios outside their intended market can be dan- ment nancing by the Federal Communications Commisgerous, as well as illegal, as frequencies used by Citizens sion mean that only the worst oenders are sanctioned,
Band radios from other countries may operate on fre- which makes legitimate operation on the citizens band
quencies close to, or used by, emergency services (for ex- unreliable. Most oenders are not caught for interfering with other CB users; often, their selfmodied equipample, the Indonesian service around 142 MHz operates
on frequencies allocated to a public safety network shared ment generates harmonics and spurs which cause interference to services outside the citizens band and to consumer
with police, re and EMS services in Ontario, Canada).
equipment.
In the Philippines, up to present time, the use of 27 MHz
CB is still banned since the Marcos regime banned it in The maximum legal CB power output level in the U.S.
1980s. A few operators still illegally utilize the 40 CB is 4 watts for AM (un-modulated carrier; modulation can
channels. There are active CB groups that are now asking be four times the carrier power, or 16 watts PEP) and 12
Senator Bongbong Marcos, the son of the late president watts PEP for SSB, as measured at the transmitter antenna
Ferdinand Marcos, to lift the ban and make the use of CB connection. However, external linear ampliers are often
used illegally.
radios legal again.
During the 1970s the FCC banned the sale of linear ampliers capable of operation from 24 to 35 MHz to discourage their use on the CB band, although the use of
10.3 Current use
highpower ampliers continued. Late in 2006, the FCC
amended the regulation to exclude only 26 to 28 MHz
CB was the only practical twoway radio system for the
to facilitate amateur 10-meter operation.[36] Lax enforceindividual consumer, and served several subsets of users
ment enables manufacturers of illegal linear ampliers to
such as truck drivers, radio hobbyists, and those in need
openly advertise their products; many CB dealers include
of shortrange radio communications, such as electrithese ampliers in their catalogs.
cians, plumbers, and carpenters, who needed to communicate between job site and main oce. While some
users have moved on to other radio services, CB is still a
popular hobby in many countries. The 27 MHz frequen- 10.4 Technology
cies used by CB, which require a relatively long aerial and
tend to propagate poorly indoors, discourage the use of At the beginning of the CB radio service, transmitters
handheld radios. Many users of handheld radios (fami- and receivers used vacuum tubes; solid-state transmitlies, hunters and hikers) have moved on to 49 MHz and ters were not widely available until 1965, after the introthe UHF Family Radio Service; those needing a simple duction of RF-power transistors.[37] Walkie-talkie handradio for professional use (e.g., tradesmen) have moved held units became aordable with the use of transistors.
on to dot-color Business Band radios and the VHF Early receivers did not cover all the channels of the serMulti-Use Radio Service.
vice; channels were controlled by plug-in quartz crystals,
CB is still popular among long-haul truck drivers to communicate directions, trac problems and other relevant
matters.[35] The unocial travelers channel in most
of the world is channel 19; in Australia it is channel 8
(27.055 MHz) and UHF channel 40 (477.400 MHz). In

with one of several operating frequencies selected by a

panel control in more expensive units. Superheterodyne
receivers (using one or two conversion stages) were the
norm in good-quality equipment, although low-cost toytype units used super-regenerative receivers. With the

60

CHAPTER 10. CITIZENS BAND RADIO

earliest sets two quartz crystals were needed for transmitting and receiving on each channel, which was costly.
By the mid-1960s mixer circuits made frequencysynthesized radios possible, which reduced cost and allowed full coverage of all 23 channels with a smaller number of crystals (typically 14). The next improvement
came during the mid-1970s; crystal synthesis was replaced by PLL technology using ICs, enabling 40-channel
sets with only one crystal (10.240 MHz). Almost all were
AM-only, although there were a few single sideband sets.
Most CB radios sold in the United States have the following features:
Automatic noise limiter or noise blanker: Reduces Typical center-loaded mobile CB antenna. Note the loading coil,
background noise (such as spark ignition)
which shortens the antennas overall length.
CB/WX switch: Selects weather-radio receiver
Automatic level control (ALC): Limits the transmitter modulation level to reduce distortion
PA: Some transceivers can drive an external speaker
and act as a low-power public address system, or
bullhorn.
RF gain: Adjusts the RF amplier gain of the receiver; used to reduce received background noise,
and to reduce clipping due to over-amplication
of already-strong signals (for example, when the receiver is near the transmitter)
NOR/9/19: Quickly tunes preset channels for calling or emergency use

10.5 Antennas
27 MHz is a relatively long wavelength for mobile communications, and the choice of antenna has a considerable impact on the performance of a CB radio. A common mobile antenna is a quarter-wave vertical whip. This
is roughly nine feet (2.7 m) tall; it is mounted low on
the vehicle body, and often has a spring-and-ball mount
to enhance its exibility when scraping or striking overhead objects. Where a nine-foot whip is undesirable,
shorter antennas include loading coils to make the antenna impedance the same as a physically longer antenna. The loading coil may be on the bottom, middle,
or top of the antenna, while some antennas are wound in
a continuously-loaded helix.

Many truckers use two co-phased antennas, mounted on

SWR: Meter used to monitor reected power caused their outside mirrors. Such an array is intended to enhance performance to the front and back, while reducing
by mismatched antennas and antenna cables
it to the sides (a desirable pattern for long-haul truckers).
However, the eciency of such an arrangement is only an
Volume control
improvement over a single antenna when the co-phased
antennas are separated by approximately eight feet or
Microphone choices include:
more, restricting this design to use mainly on tractortrailers and some full-size pickups and SUVs. Some op Dynamic microphone: Uses magnetic coil and per- erators will use only one of the two antennas; this removes
manent magnet
both the complexity and benet of a true co-phased array,
but gives a symmetrical cosmetic appearance preferred by
Ceramic mic: Uses a piezoelectric element; rugged, some truck drivers.
low-cost but high-impedance
Another mobile antenna is the continuously-loaded halfwave antenna. These do not require a ground plane to
Echo mic: Deliberately introduces distortion and
present a near-50-ohm load to the radio, and are often
echo into transmitted audio
used on berglass vehicles such as snowmobiles or boats.
They are also useful in base stations where circumstances
Electret microphone: Uses an electrostatic method
preclude the use of a ground-plane antenna. Handheld
to convert sound to electrical signals
CBs may use either a telescoping center-loaded whip or
a continuously-loaded rubber ducky antenna.
Noise-canceling microphone: Uses two elements to
Base CB antennas may be vertical for omnidirectional
reduce background noise
coverage, or directional beam antennas may be used
Power mic: An amplied microphone[38]
to direct communications to a particular region. Ground-

10.7. FREEBANDING AND EXPORT RADIOS

plane kits exist as mounting bases for mobile whips, and
have several wire terminals or hardwired ground radials
attached. These kits are designed to have a mobile whip
screwed on top (a full-length, quarter-wave steel whip is
preferred) and mounted on a mast. The ground radials
replace the vehicle body (which is the counterpoise for a
mobile whip in a typical vehicle installation).

10.6 Working skip

Main article: Skywave
All frequencies in the HF spectrum (330 MHz) can be
refracted by charged ions in the ionosphere. Refracting
signals o the ionosphere is called skywave propagation,
and the operator is said to be shooting skip. CB operators have communicated across thousands of miles and
sometimes around the world. Even low-power 27 MHz
signals can sometimes propagate over long distances.
The ability of the ionosphere to bounce signals back to
earth is caused by solar radiation, and the amount of ionization possible is related to the 11-year sunspot cycle. In
times of high sunspot activity, the band can remain open
to much of the world for long periods of time. During
low sunspot activity it may be impossible to use skywave
at all, except during periods of Sporadic-E propagation
(from late spring through mid-summer). Skip contributes
to noise on CB frequencies. In the United States, it is illegal to engage in (or attempt to engage in) CB communications with any station more than 250 km (160 mi) from
an operators location.[39] This restriction exists to keep
CB as a local (line-of-sight) radio service; however, in
the United States the restriction is widely ignored. The
legality of shooting skip is not an issue in most other
countries.[40]

10.7 Freebanding and export radios

Operation on frequencies above or below the citizens
band (on the uppers or lowers) is called freebanding
or outbanding.[41] While frequencies just below the CB
segment (or between the CB segment and the amateur
radio 10-meter band) seem quiet and under-utilized, they
are allocated to other radio services (including government agencies) and unauthorized operation on them is
illegal. Furthermore, illegal transmitters and ampliers
may not meet good engineering practice for harmonic
distortion or "splatter", which may disrupt other communications and make the unapproved equipment obvious to
regulators. Freebanding is done with modied CB or amateur equipment, foreign CB radios which may oer different channels, or with radios intended for export. Legal
operation in one country may be illegal in another; for ex-

61
ample, in the UK until June 2014 only 80 FM channels
were legal.
Unlike amateur radios with continuous frequency tuning,
CBs manufactured for export are channelized. Frequency
selection resembles that of modied American CBs more
than any foreign frequency plan. They typically have a
knob and display that reads up to channel 40, but include
an extra band selector that shifts all 40 channels above
or below the band and a "+10 kHz button to reach the
model control 'A' channels. These radios may have 6 or
even 12 bands, establishing a set of quasi-CB channels on
many unauthorized frequencies. The bands are typically
lettered A through F, with the normal citizens band as D.
For example, a freebander with an export radio who
wants to use 27.635 MHz would choose channel 19
(27.185 MHz) and then shift the radio up one band (+
0.450 MHz). It requires arithmetic on the part of the operator to determine the actual frequency, although more
expensive radios include a frequency counter or a frequency displaytwo dierent components, providing an
identical result. Illegal operations may unintentionally
end up on frequencies very much in use. For instance,
channel 19 shifted two bands up is 28.085 MHz, which
is in a Morse code/data-only part of the 10-meter ham
band. Voice transmissions in a Morse code-only segment
are easily detectable by authorities. Amateur Radio Service [ARS] operators record, locate, and report frequency
trespassing and intrusions of their government or ITU allocations by pirate transmissions or illegal operators to
the FCC for enforcement action.[42]
Many freeband operators use amateur radios modied to
transmit out of band, which is illegal in some countries.
Older amateur radios may require component changes;
for instance, the 1970s Yaesu FT-101 was modied for
CB by replacing a set of crystals used to tune portions
of the 10-meter band, although some variants of the FT101 were sold with the US FCC channels standard and
were capable of transmitting above and below the legal
40 channels by another 10 or more channels.[43] On some
newer radios, the modication may be as simple as disconnecting a jumper wire or a diode. Many types of
amateur transceivers may be found on CB and freeband,
ranging from full-coverage HF transceivers to simpler 10meter mobile radios. In the United States, the FCC bans
the importation and marketing of radios it deems easily
modiable for CB;[44] it is illegal to transmit on CB frequencies with a ham radio except in emergencies where
no other method of communication is available.
A gray market trade in imported CB gear exists in many
countries. In some instances, the sale or ownership of
foreign-specication CB gear is not illegal but its use
is. With the FCCs minimal enforcement of its CB
rules, enthusiasts in the US use export radios or European frequency modulation (FM) CB gear to escape the
crowded AM channels. American AM gear has also been
exported to Europe.

62
Export radios are sold in the United States as 10-meter
Amateur Radio transceivers. Marketing, import and sale
of such radios is illegal if they are distributed as anything
other than Amateur Radio transceivers. It is also illegal
to use these radios outside of the Amateur Radio bands
by anyone in the US, since they are not type-certied for
other radio services and usually exceed authorized power
limits. The use of these radios within the Amateur Radio Service by a licensed Amateur Radio operator within
his/her license privileges is legal, as long as all FCC regulations for Amateur Radio are followed. The term export
radio is a misnomer, since it implies that they cannot be
used in the country in which they are sold and hints that
the radio is legal in another country. However, the typical
export radio has a combination of features, frequency
coverage and output power which make it illegal worldwide; in reality, there is no country to which these radios
may be legally exported.

CHAPTER 10. CITIZENS BAND RADIO

10.10 See also

Personal radio serviceFor an overview of CB-like
services worldwide
UHF CB
Amateur radio
Citizens Band radio in India
27 MHz CB27/81 Bandplan One of the two 27
MHz CB band plans used in the UK. The other is
the same as the American band plan.
FRSA UHF CB system used in the USA, Canada,
Mexico and several South American countries.
GMRSA licensed UHF CB system used in the
USA, similar to the original Class A CB service
List of CB slang
MURSA VHF CB system used in the USA.

10.8 Callbook
A callbook is a directory of radio station call signs. Originally a bound book that resembled a telephone directory, it contains the name and addresses of radio stations
in a given jurisdiction (country). Modern Electrics published the rst callbook in the United States in 1909. Today, the primary purpose of a callbook is to allow radio operators to send a conrmation post card, called a
QSL card to an operator with whom they have communicated via radio. Callbooks have evolved to include on-line
databases that are accessible via the Internet to instantly
obtain the address of another amateur radio operator and
their QSL Managers. The most well known and used online QSL database for the 11 meter / freebander community is QRZ11.COM, designed after its big brother
QRZ.COM for Amateur Radio.[45][46][47][48][49][50]

PMR446A UHF CB system used in most European countries

Ten-code

10.11 References
[1] Canadian General Radio Service
[2] http://www.retrocom.com/wtcollect/27_megacycle_
history_in_the_u.htm 27 Megacycle History, retrieved
2010 Feb 9
[3] Kneitel (1988:13)
[4] Kneitel (1988:14)
[5] FCC Part 95 Overview Retrieved 2011-10-21.
[6] In the Americas, the 220 MHz band is used by ham operators

10.9 Media

[7] ""I Can't Drive 55": the economics of the CB radio phenomenon, Independent Review, The Independent Institute, 15 (3), 2011

During the 1970s and 1980s heyday of CB radio, [8] https://news.google.com/newspapers?nid=1893&

many citizens band-themed magazines appeared on newsdat=19750216&id=qm0fAAAAIBAJ&sjid=
ZtUEAAAAIBAJ&pg=841,5104091&hl=en
stands. Two magazines that dominated the time period
were S9 CB Radio and CB Radio Magazine. S9s succes[9] Tweed, Michael, "Back in View, a First Lady With Her
sor was Popular Communications, which had the same
Own Legacy", The New York Times, 31 December 2006
editor under a dierent publisher beginning in 1982. It
covered hobby radio as well as CB. The same publisher [10] http://www.kitten-kaboodle.com/index.php/site/
comments/biography-of-mel-blanc/
produced a magazine called RADIO! for RadioShack
stores in the mid-1990s.
[11] Chilton (1977:12)
In the early 2000s, National Communications Magazine
[12] Chilton (1977:14)
added CB radio coverage to its coverage of scanner radios
and to this day remains the only magazine covering CB [13] Channels 10-15 and 23, after channel 9 was reserved for
radio in North America.
emergency use

10.12. SOURCES

[14] The terms interstation and intrastation appear in the

FCCs Part 95 rules from that time period.
[15] Chilton (1977:120)

63

[37] http://www.qsl.net/k5dh/raytheon/raytheon.html gives

the history of one US manufacturers line of CB
equipment
[38] NewCompanyDriver Learn the basics of CB radio

[16] Radio Information for Boaters. United States Coast

Guard.

[39] FCC Part 95 Subpart D.

[17] http://www.fcc.gov/encyclopedia/
citizens-band-cb-service

[40] http://www.ic.gc.ca/eic/site/smt-gst.nsf/eng/sf01016.
html#General

[18] ACRM: CB Radio History

[41] The term outbanding was introduced by Kneitel in the

August 1979 issue of S9 Magazine.(Kneitel 1988:165)

[19] ACMA: 27 MHz Handphone Stations Class Licence

[20] ACRM: Movement
[21] These roughly corresponded to the present channels 522,
except for the two unique frequencies that are known as
11A(Channel 7 on an 18 channel Australian CB) and 19A
(Channel 16 on an 18 channel Australian CB) or remote
control frequencies but are no longer part of the Australian
27MHz CB band since 40 Channels was introduced. See
ACBRO: Aussie 18 Channel Radio Guide.

[42] ARRL: FCC enforcement actions

[43] (Kneitel 1988:174)
[44] QTH.com: Illegal CB Transceiver List
[45] http://www.seas.upenn.edu/~{}uparc/documents/
First%20Annual%20Official%20Wireless%20Blue%
20Book%20-%201909.pdf
[46] http://www.qrz11.com

[22] for more information visit http://www.uhfcb.com.au

[47] http://www.cq-amateur-radio.com/cq_highlights/2014_
cq/2014_02_cq/CQ_2014_02_OPT.pdf

[23] Matt P. Spinello, Touring Canada With Your CB Rig, in Elementary Electronics magazine, Davis Publications, New
York; Volume 10 No. 2, July/August 1972, pp. 5556

[48] http://qrz11.phpbb8.de/download/file.php?id=44&sud=
21333

[24] Government of Canada Department of Communications,

"TRC 40: Licensing of General Radio Service Equipment, January 1, 1977; retrieved 3 Jan 2010
[25] Indonesian DX Club: CB Radio
[26] http://www.skmm.gov.my/link_file/registers/cma/
ClassAssignment/pdf/Class%20Assign-BI-register.pdf
[27] http://www.skmm.gov.my/link_file/registers/cma/
ClassAssignment/pdf/CA_01_April_2010.pdf.
[28]
[29] Finlo Rohrer (August 14, 2006). "Over and out?" BBC
News Magazine. Retrieved 2011-10-22.
[30] Citizens Band (CB) Scanner Frequencies and Radio Frequency Reference. www.radioreference.com. Retrieved
2015-10-08.
[31] Arrt du 31 mars 1992 relatif aux caractristiques techniques et aux conditions d'exploitation des postes C.B.
[32] http://frwebgate.access.gpo.gov/cgi-bin/get-cfr.cgi?
TITLE=47&PART=95&SECTION=407&YEAR=
2000&TYPE=TEXT
[33] Channel Lists for 27 & UHF-CB in NZ
[34] An Indonesian government decision regarding CB, with
frequency charts
[35] Alice Adams Trucking:Tractor-Trailer Driver Handbook/Workbook, page 558, the rst DB radio
[36] Omnibus Amateur Radio Report and Order

[49] http://www.dx27.net/viewpage.php?page_id=4
[50] http://www.sugar-delta.it/site/index.php

10.12 Sources
Chilton Automotive Editorial Department (1977).
Chiltons CB Handbook. Radnor, PA: Chilton Book
Company. ISBN 0-8019-6623-X.
Kneitel, Tom (1988). Tomcats Big CB Handbook.
Commack, NY: CRB Research Books. ISBN 0939780-07-0.
GL 226 ( VK3PJB ) Ex Secretary GL Club, Australia

10.13 External links

Citizen Band Radio at DMOZ

Chapter 11

Quadrature amplitude modulation

QAM redirects here. For the digital television stan- tude modulating and phase modulating a single carrier.
dard, see QAM (television). For other uses, see QAM
Phase modulation (analog PM) and phase-shift keying
(disambiguation).
(digital PSK) can be regarded as a special case of QAM,
where the magnitude of the modulating signal is a conQuadrature amplitude modulation (QAM) is both stant, with only the phase varying. This can also be
an analog and a digital modulation scheme. It conveys extended to frequency modulation (FM) and frequencytwo analog message signals, or two digital bit streams, shift keying (FSK), for these can be regarded as a special
by changing (modulating) the amplitudes of two carrier case of phase modulation.
waves, using the amplitude-shift keying (ASK) digital
modulation scheme or amplitude modulation (AM) analog modulation scheme. The two carrier waves of the 11.2 Analog QAM
same frequency, usually sinusoids, are out of phase with
each other by 90 and are thus called quadrature carri90
ers or quadrature components hence the name of the
+V
120
60
scheme. The modulated waves are summed, and the R cy
nal waveform is a combination of both phase-shift keyg
MG
ing (PSK) and amplitude-shift keying (ASK), or, in the
150
30
analog case, of phase modulation (PM) and amplitude
modulation. In the digital QAM case, a nite number of
75%
100%
at least two phases and at least two amplitudes are used.
YL
b
PSK modulators are often designed using the QAM prin+U 0
180
ciple, but are not considered as QAM since the ampliB
yl
tude of the modulated carrier signal is constant. QAM
is used extensively as a modulation scheme for digital
telecommunication systems. Arbitrarily high spectral ef330
210
ciencies can be achieved with QAM by setting a suitable
G
mg
constellation size, limited only by the noise level and linearity of the communications channel.[1]
r CY
240

300

QAM is being used in optical ber systems as bit rates

270
increase; QAM16 and QAM64 can be optically emulated
Analog QAM: measured PAL colour bar signal on a vector analwith a 3-path interferometer.[2][3]
yser screen.

When transmitting two signals by modulating them with

QAM, the transmitted signal will be of the form:

11.1 Introduction
Like all modulation schemes, QAM conveys data by
changing some aspect of a carrier signal, or the carrier
wave, (usually a sinusoid) in response to a data signal.
In the case of QAM, the amplitude of two waves of the
same frequency, 90 out-of-phase with each other (in
quadrature) are changed (modulated or keyed) to represent the data signal. Amplitude modulating two carriers
in quadrature can be equivalently viewed as both ampli-

{
}
s(t) = Re [I(t) + iQ(t)] ei2f0 t
= I(t) cos(2f0 t) Q(t) sin(2f0 t)
where i2 = 1 , I(t) and Q(t) are the modulating signals,
f0 is the carrier frequency and Re{} is the real part.
At the receiver, these two modulating signals can be
demodulated using a coherent demodulator. Such a receiver multiplies the received signal separately with both

64

11.3. QUANTIZED QAM

65

a cosine and sine signal to produce the received estimates where S(f), MI(f) and MQ(f) are the Fourier transforms
of I(t) and Q(t) respectively. Because of the orthogonality (frequency-domain representations) of s(t), I(t) and Q(t),
property of the carrier signals, it is possible to detect the respectively.
modulating signals independently.
In the ideal case I(t) is demodulated by multiplying the
transmitted signal with a cosine signal:

11.3 Quantized QAM

r(t) = s(t) cos(2f0 t)

= I(t) cos(2f0 t) cos(2f0 t) Q(t) sin(2f0 t) cos(2f0 t)
Using standard trigonometric identities, we can write it
as:
1
1
I(t) [1 + cos(4f0 t)] Q(t) sin(4f0 t)
2
2
1
1
= I(t) + [I(t) cos(4f0 t) Q(t) sin(4f0 t)]
2
2

r(t) =

Low-pass ltering r(t) removes the high frequency terms

(containing 4f0 t ), leaving only the I(t) term. This ltered signal is unaected by Q(t) , showing that the in- Digital 16-QAM with example constellation points
phase component can be received independently of the
quadrature component. Similarly, we may multiply s(t) As in many digital modulation schemes, the constellation
by a sine wave and then low-pass lter to extract Q(t) .
diagram is useful for QAM. In QAM, the constellation
points
are usually arranged in a square grid with equal
Analog QAM suers from the same problem as Singlevertical
and horizontal spacing, although other congusideband modulation: the exact phase of the carrier is rerations
are
possible (e.g. Cross-QAM). Since in digital
quired for correct demodulation at the receiver. If the detelecommunications
the data are usually binary, the nummodulating phase is even a little o, it results in crosstalk
ber
of
points
in
the
grid is usually a power of 2 (2, 4,
between the modulated signals. This issue of carrier syn8,
).
Since
QAM
is
usually square, some of these are
chronization at the receiver must be handled somehow
rarethe
most
common
forms are 16-QAM, 64-QAM
in QAM systems. The coherent demodulator needs to
and
256-QAM.
By
moving
to a higher-order constellabe exactly in phase with the received signal, or othertion,
it
is
possible
to
transmit
more bits per symbol. Howwise the modulated signals cannot be independently reever,
if
the
mean
energy
of
the
constellation is to remain
ceived. This is achieved typically by transmitting a burst
the
same
(by
way
of
making
a
fair
comparison), the points
subcarrier or a Pilot signal.
must be closer together and are thus more susceptible to
Analog QAM is used in:
noise and other corruption; this results in a higher bit error rate and so higher-order QAM can deliver more data
NTSC and PAL analog Color television systems, less reliably than lower-order QAM, for constant mean
where the I- and Q-signals carry the components constellation energy. Using higher-order QAM without
of chroma (colour) information. The QAM carrier increasing the bit error rate requires a higher signal-tophase is recovered from a special Colorburst trans- noise ratio (SNR) by increasing signal energy, reducing
mitted at the beginning of each scan line.
noise, or both.
C-QUAM (Compatible QAM) is used in AM If data-rates beyond those oered by 8-PSK are required,
stereo radio to carry the stereo dierence informa- it is more usual to move to QAM since it achieves a
greater distance between adjacent points in the I-Q plane
tion.
by distributing the points more evenly. The complicating
factor is that the points are no longer all the same ampli11.2.1 Fourier analysis of QAM
tude and so the demodulator must now correctly detect
both phase and amplitude, rather than just phase.
In the frequency domain, QAM has a similar spectral pat64-QAM and 256-QAM are often used in digital cable
tern to DSB-SC modulation. Using the properties of the
television and cable modem applications. In the United
Fourier transform, we nd that:
States, 64-QAM and 256-QAM are the mandated modulation schemes for digital cable (see QAM tuner) as standardised by the SCTE in the standard ANSI/SCTE 07
1
i
S(f ) = [MI (f f0 ) + MI (f + f0 )]+ [MQ (f f0 )2013.
MQ (f
+ fthat
0 )] many marketing people will refer to
Note
2
2

66

CHAPTER 11. QUADRATURE AMPLITUDE MODULATION

these as QAM-64 and QAM-256. In the UK, 64-QAM tween them. They are simply added one to the other and
is used for digital terrestrial television (Freeview) whilst sent through the real channel.
256-QAM is used for Freeview-HD.
The sent signal can be expressed in the form:

s(t) =

[vc [n] ht (t nTs ) cos(2f0 t) vs [n] ht (t nTs ) sin(2

n=

where vc [n] and vs [n] are the voltages applied in response

to the n th symbol to the cosine and sine waves respectively.
Receiver
Bit-loading (bits per QAM constellation) on an ADSL line

The receiver simply performs the inverse operation of the

transmitter. Its ideal structure is shown in the picture beCommunication systems designed to achieve very high low with Hr the receive lters frequency response :
levels of spectral eciency usually employ very dense
QAM constellations. For example, current Homeplug
AV2 500-Mbit powerline Ethernet devices use 1024QAM and 4096-QAM,[4] as well as future devices using ITU-T G.hn standard for networking over existing
home wiring (coaxial cable, phone lines and power lines);
4096-QAM provides 12 bits/symbol. Another example is
ADSL technology for copper twisted pairs, whose con- Multiplying by a cosine (or a sine) and by a low-pass lstellation size goes up to 32768-QAM (in ADSL termi- ter it is possible to extract the component in phase (or in
nology this is referred to as bit-loading, or bit per tone, quadrature). Then there is only an ASK demodulator and
32768-QAM being equivalent to 15 bits per tone).[5]
the two ows of data are merged back.
Ultra-high capacity Microwave Backhaul Systems also In practice, there is an unknown phase delay between
use 1024-QAM.[6] With 1024-QAM, Adaptive Coding the transmitter and receiver that must be compensated by
and Modulation (ACM), and XPIC, Vendors can obtain synchronization of the receivers local oscillator (i.e. the
Gigabit capacity in a single 56 MHz channel.[7]
sine and cosine functions in the above gure). In mobile applications, there will often be an oset in the relative frequency as well, due to the possible presence of a
11.3.1 Ideal structure
Doppler shift proportional to the relative velocity of the
transmitter and receiver. Both the phase and frequency
Transmitter
variations introduced by the channel must be compensated by properly tuning the sine and cosine components,
The following picture shows the ideal structure of a QAM which requires a phase reference, and is typically accomtransmitter, with a carrier center frequency f0 and the fre- plished using a Phase-Locked Loop (PLL).
quency response of the transmitters lter Ht :
In any application, the low-pass lter and the receive Hr
lter will be implemented as a single combined lter.
Here they are shown as separate just to be clearer.

11.4 Quantized QAM performance

First the ow of bits to be transmitted is split into two
equal parts: this process generates two independent signals to be transmitted. They are encoded separately just
like they were in an amplitude-shift keying (ASK) modulator. Then one channel (the one in phase) is multiplied
by a cosine, while the other channel (in quadrature) is
multiplied by a sine. This way there is a phase of 90 be-

The following denitions are needed in determining error

rates:

= Number of symbols in modulation constellation

Eb

= Energy-per-bit

Es

= Energy-per-symbol = kEb with k bits per symbol

11.4. QUANTIZED QAM PERFORMANCE

N0

= Noise power spectral density (W/Hz)

Pb

= Probability of bit-error

Pbc

Ps

Psc

Q(x) =

67
The rst rectangular QAM constellation usually encountered is 16-QAM, the constellation diagram for which is
shown here. A Gray coded bit-assignment is also given.
The reason that 16-QAM is usually the rst is that a
brief consideration reveals that 2-QAM and 4-QAM are
in fact binary phase-shift keying (BPSK) and quadrature
phase-shift keying (QPSK), respectively. Also, the errorrate performance of 8-QAM is close to that of 16-QAM
(only about 0.5 dB better), but its data rate is only threequarters that of 16-QAM.

= Probability of bit-error per carrier

= Probability of symbol-error
= Probability of symbol-error per carrier
1
2

1 2

e 2 t dt, x0

Expressions for the symbol-error rate of rectangular

Q(x) is related to the complementary Gaussian error func- QAM are not hard to derive but yield rather unpleasant
(
)
tion by: Q(x) = 12 erfc 12 x , which is the probability that expressions. For an even number of bits per symbol, k
x will be under the tail of the Gaussian PDF towards pos- , exact expressions are available. They are most easily
expressed in a per carrier sense:
itive innity.
The error rates quoted here are those in additive white
Gaussian noise (AWGN).
Where coordinates for constellation points are given in Psc
this article, note that they represent a non-normalised
constellation. That is, if a particular mean average energy so
were required (e.g. unit average energy), the constellation
would need to be linearly scaled.

)
(
) (
1
3 Es
=2 1
Q
M 1 N0
M

Ps = 1 (1 Psc )

11.4.1

Rectangular QAM

The bit-error rate depends on the bit to symbol mapping,

but for Eb /N0 1 and a Gray-coded assignmentso that
we can assume each symbol error causes only one bit
errorthe bit-error rate is approximately

Q
0000

0100

1100

1000

Pbc
0001

0101

1101

1001

0011

0111

1111

1011

Psc
4
1 =
k
k
2

1
1
M

)
Q

3k Eb
M 1 N0

Since the carriers are independent, the overall bit error

rate is the same as the per-carrier error rate, just like
BPSK and QPSK.

Pb = Pbc

An exact and general closed-form expression of the Bit

Error Rates (BER) for rectangular type of Quadrature
Amplitude Modulation (QAM) over AWGN and slow,
0010
0110
1110
1010
at, Rician fading channels were derived analytically.
Consider a (LM)-QAM system with 2 log2 L levels
and 2 log2M levels in the I-channel and Q-channel, reConstellation diagram for rectangular 16-QAM.
spectively and a two-dimensional grey code mapping employed. It was shown[5] that the generalized expression
Rectangular QAM constellations are, in general, sub- for the conditional BER on SNR over AWGN channel
optimal in the sense that they do not maximally space the is
constellation points for a given energy. However, they
have the considerable advantage that they may be easily

transmitted as two pulse amplitude modulation (PAM)

log2 L
log2 M

1
signals on quadrature carriers, and can be easily demodu- Pb (E|) =

Pb (EiL |) +
Pb (EiM |)
log2 (L M ) i=1
lated. The non-square constellations, dealt with below,
i=1
achieve marginally better bit-error rate (BER) but are
where
harder to modulate and demodulate.

68

CHAPTER 11. QUADRATURE AMPLITUDE MODULATION

Q
2
Pb (EiP |) =
P

(12i )P 1

(1)

j2i1
P

j=0

)
j 2i1
1
i1
2

+
Q (2j + 1)
P
2

6
(L2 + M 2 2)

Odd-k QAM
For odd k , such as 8-QAM ( k = 3 ) it is harder to obtain
symbol-error rates, but a tight upper bound is:
(
Ps 4Q

3kEb
(M 1)N0

Two rectangular 8-QAM constellations are shown below

without bit assignments. These both have the same minimum distance between symbol points, and thus the same
symbol-error rate (to a rst approximation).
Constellation diagram for circular 16-QAM.
The exact bit-error rate, Pb will depend on the bitassignment.
Two diagrams of circular QAM constellation are shown,
Note that both of these constellations are seldom used in for 8-QAM and 16-QAM. The circular 8-QAM constelpractice, as the non-rectangular version of 8-QAM is op- lation is known to be the optimal 8-QAM constellation in
timal.
the sense of requiring the least mean power for a given
minimum Euclidean distance. The 16-QAM constellation is suboptimal although the optimal one may be con Constellation diagram for rectangular 8-QAM.
structed along the same lines as the 8-QAM constellation.
Alternative constellation diagram for rectangular 8- The circular constellation highlights the relationship beQAM.
tween QAM and PSK. Other orders of constellation may
be constructed along similar (or very dierent) lines. It
is consequently hard to establish expressions for the er11.4.2 Non-rectangular QAM
ror rates of non-rectangular QAM since it necessarily depends on the constellation. Nevertheless, an obvious upQ
per bound to the rate is related to the minimum Euclidean
distance of the constellation (the shortest straight-line distance between two points):

(1,1)

Ps < (M 1)Q
(1+3,0)

d2min
2N0

Again, the bit-error rate will depend on the assignment of

bits to symbols.
Although, in general, there is a non-rectangular constellation that is optimal for a particular M , they are not often used since the rectangular QAMs are much easier to
modulate and demodulate.

11.4.3 Hierarchical QAM

Constellation diagram for circular 8-QAM.

It is the nature of QAM that most orders of constellations

can be constructed in many dierent ways and it is neither
possible nor instructive to cover them all here. This article
instead presents two, lower-order constellations.

Hierarchical QAM is a form of hierarchical modulation.

For example, hierarchical QAM is used in DVB, where
the constellation points are grouped into a high-priority
QPSK stream and a low-priority 16-QAM stream. The
irregular distribution of constellation points improves the

11.8. EXTERNAL LINKS

69

reception probability of the high-priority stream in low

SNR conditions, at the expense of higher SNR requirements for the low-priority stream.[8]

[5] http://www.itu.int/rec/T-REC-G.992.3-200904-I section 8.6.3 Constellation mapper - maximum number of

bits per constellation BIMAX 15

11.5 Interference and noise

[6] http://www.trangosys.com/products/
point-to-point-wireless-backhaul/licensed-wireless/
trangolink-apex-orion.shtml A Apex Orion
[7] http://www.trangosys.com/products/

In moving to a higher order QAM constellation (higher

point-to-point-wireless-backhaul/licensed-wireless/
data rate and mode) in hostile RF/microwave QAM
trangolink-apex-orion.shtml A Apex Orion
application environments, such as in broadcasting or
telecommunications, multipath interference typically in- [8] http://asp.eurasipjournals.com/content/2010/1/942638
DVB Hierarchical QAM constellation
creases. There is a spreading of the spots in the constellation, decreasing the separation between adjacent states, [9] Howard Friedenberg and Sunil Naik. Hitless Space Dimaking it dicult for the receiver to decode the signal
versity STL Enables IP+Audio in Narrow STL Bands
appropriately. In other words, there is reduced noise
(PDF). 2005 National Association of Broadcasters Annual
immunity. There are several test parameter measureConvention. Retrieved April 17, 2005.
ments which help determine an optimal QAM mode for a
specic operating environment. The following three are 5. Jonqyin (Russell) Sun Linear diversity analysis for
most signicant:[9]
QAM in Rician fading channels, IEEE WOCC 2014
Carrier/interference ratio
Carrier-to-noise ratio
Threshold-to-noise ratio

11.6 See also

Amplitude and phase-shift keying or Asymmetric
phase-shift keying (APSK)
Carrierless Amplitude Phase Modulation (CAP)
In-phase and quadrature components
Modulation for other examples of modulation techniques
Phase-shift keying
QAM tuner for HDTV
Random modulation

11.7 References
[1] UAS UAV communications links Archived April 30,
2011, at the Wayback Machine.
[2] Ciena tests 200G via 16-QAM with Japan-U.S. Cable
Network. lightwave. April 17, 2014. Retrieved 7
November 2016.
[3] Kylia products Archived July 13, 2011, at the Wayback
Machine., dwdm mux demux, 90 degree optical hybrid,
d(q) psk demodulatorssingle polarization
[4] http://www.homeplug.org/media/filer_public/a1/46/
a1464318-f5df-46c5-89dc-7243d8ccfcee/homeplug_
av2_whitepaper_150907.pdf Homeplug_AV2 whitepaper

The notation used here has mainly (but not exclusively)

been taken from
John G. Proakis, "Digital Communications, 3rd Edition",

11.8 External links

Interactive webdemo of QAM constellation with additive noise Institute of Telecommunicatons, University of Stuttgart
QAM bit error rate for AWGN channel online experiment
How imperfections aect QAM constellation
Microwave Phase Shifters Overview by Herley General Microwave
Simulation of dual-polarization QPSK (DP-QPSK)
for 100G optical transmission

Chapter 12

Medium wave
12.1 Propagation characteristics
Wavelengths in this band are long enough that radio waves
are not blocked by buildings and hills and can propagate
beyond the horizon following the curvature of the Earth;
this is called the groundwave. Practical groundwave reception typically extends to 200300 miles, with longer
distances over terrain with higher ground conductivity,
and greatest distances over salt water. Most broadcast
stations use groundwave to cover their listening area.

Typical mast radiator of a commercial medium wave AM broadcasting station, Chapel Hill, North Carolina, USA

Medium waves can also reect o charged particle layers in the ionosphere and return to Earth at much greater
distances; this is called the skywave. At night, especially
in winter months and at times of low solar activity, the
ionospheric D layer virtually disappears. When this happens, MF radio waves can easily be received many hundreds or even thousands of miles away as the signal will
be reected by the higher F layer. This can allow very
long-distance broadcasting, but can also interfere with
distant local stations. Due to the limited number of available channels in the MW broadcast band, the same frequencies are re-allocated to dierent broadcasting stations several hundred miles apart. On nights of good
skywave propagation, the skywave signals of distant station may interfere with the signals of local stations on the
same frequency. In North America, the North American
Regional Broadcasting Agreement (NARBA) sets aside
certain channels for nighttime use over extended service
areas via skywave by a few specially licensed AM broadcasting stations. These channels are called clear channels,
and they are required to broadcast at higher powers of 10
to 50 kW.

12.2 Use in the Americas

Main article: Medium frequency
See also: North American Regional Broadcasting
Medium wave (MW) is the part of the medium fre- Agreement
quency (MF) radio band used mainly for AM radio broadcasting. For Europe the MW band ranges from 526.5 kHz Initially broadcasting in the United States was restricted
to 1606.5 kHz,[1] using channels spaced every 9 kHz, and to two wavelengths: entertainment was broadcast at 360
in North America an extended MW broadcast band goes meters (833 kHz), with stations required to switch to 485
from 535 kHz to 1705 kHz,[2] using 10 kHz spaced chan- meters (619 kHz) when broadcasting weather forecasts,
nels.
crop price reports and other government reports.[3] This
70

12.4. STEREO AND DIGITAL TRANSMISSIONS

arrangement had numerous practical diculties. Early
transmitters were technically crude and virtually impossible to set accurately on their intended frequency and if (as
frequently happened) two (or more) stations in the same
part of the country broadcast simultaneously the resultant interference meant that usually neither could be heard
clearly. The Commerce Department rarely intervened in
such cases but left it up to stations to enter into voluntary
timesharing agreements amongst themselves. The addition of a third entertainment wavelength, 400 meters,[3]
did little to solve this overcrowding.

71
tional agreement by the International Telecommunication Union (ITU).[7] In most cases there are two power
limits: a lower one for omnidirectional and a higher one
for directional radiation with minima in certain directions. The power limit can also be depending on daytime
and it is possible, that a station may not work at nighttime,
because it would then produce too much interference.
Other countries may only operate low-powered transmitters on the same frequency, again subject to agreement.
For example, Russia operates a high-powered transmitter, located in its Kaliningrad exclave and used for external broadcasting, on 1386 kHz. The same frequency
is also used by low-powered local radio stations in the
United Kingdom, which has approximately 250 mediumwave transmitters of 1 kW and over;[8] other parts of the
United Kingdom can still receive the Russian broadcast.
International mediumwave broadcasting in Europe has
decreased markedly with the end of the Cold War and the
increased availability of satellite and Internet TV and radio, although the cross-border reception of neighbouring
countries broadcasts by expatriates and other interested
listeners still takes place.

In 1923, the Commerce Department realized that as more

and more stations were applying for commercial licenses,
it was not practical to have every station broadcast on
the same three wavelengths. On 15 May 1923, Commerce Secretary Herbert Hoover announced a new bandplan which set aside 81 frequencies, in 10 kHz steps, from
550 kHz to 1350 kHz (extended to 1500, then 1600 and
ultimately 1700 kHz in later years). Each station would
be assigned one frequency (albeit usually shared with stations in other parts of the country and/or abroad), no
longer having to broadcast weather and government reports on a dierent frequency than entertainment. Class Due to the high demand for frequencies in Europe, many
A and B stations were segregated into sub-bands.[4]
countries operate single frequency networks; in Britain,
Nowadays in most of the Americas, mediumwave broad- BBC Radio Five Live broadcasts from various transcast stations are separated by 10 kHz and have two mitters on either 693 or 909 kHz. These transmitters
sidebands of up to 5 kHz in theory, although in prac- are carefully synchronized to minimize interference from
tice stations transmit audio of up to 10 kHz.[5] In the rest more distant transmitters on the same frequency.
of the world, the separation is 9 kHz, with sidebands of
4.5 kHz. Both provide adequate audio quality for voice,
but are insucient for high-delity broadcasting, which
is common on the VHF FM bands. In the US and Canada
the maximum transmitter power is restricted to 50 kilowatts, while in Europe there are medium wave stations
with transmitter power up to 2 megawatts daytime.[6]

Overcrowding on the Medium wave band is a serious

problem in parts of Europe contributing to the early adoption of VHF FM broadcasting by many stations (particularly in Germany). However, in recent years several
European countries (Including Ireland, Poland and, to a
lesser extent Switzerland) have started moving away from
Medium wave altogether with most/all services moving
Most United States AM radio stations are required by exclusively to other bands (usually VHF).
the Federal Communications Commission (FCC) to shut In Germany, almost all Medium wave public-radio broaddown, reduce power, or employ a directional antenna ar- casts were discontinued between 2012 and 2015 to cut
ray at night in order to avoid interference with each other costs and save energy,[9] with the last such remaining produe to night-time only long-distance skywave propagation gramme (Deutschlandradio) being switched o on 31st
(sometimes loosely called skip). Those stations which December 2015.[10]
shut down completely at night are often known as daytimers. Similar regulations are in force for Canadian
stations, administered by Industry Canada; however, daytimers no longer exist in Canada, the last station having 12.4 Stereo and digital transmissigned o in 2013, after migrating to the FM band.

sions

12.3 Use in Europe

See also: AM stereo

Stereo transmission is possible and oered by some

See also: Geneva Frequency Plan of 1975 and FM radio stations in the U.S., Canada, Mexico, the Dominican
Adoption of FM broadcasting worldwide
Republic, Paraguay, Australia, The Philippines, Japan,
South Korea, South Africa, and France. However, there
In Europe, each country is allocated a number of fre- have been multiple standards for AM stereo. C-QUAM
quencies on which high power (up to 2 MW) can be is the ocial standard in the United States as well as other
used; the maximum power is also subject to interna- countries, but receivers that implement the technology

72
are no longer readily available to consumers. Used receivers with AM Stereo can be found. Names such as
FM/AM Stereo or AM & FM Stereo can be misleading and usually do not signify that the radio will decode C-QUAM AM stereo, whereas a set labeled FM
Stereo/AM Stereo or AMAX Stereo will support AM
stereo.
In September 2002, the United States Federal Communications Commission approved the proprietary iBiquity
in-band on-channel (IBOC) HD Radio system of digital
audio broadcasting, which is meant to improve the audio
quality of signals. The Digital Radio Mondiale (DRM)
IBOC system has been approved by the ITU for use outside North America and U.S. territories. Some HD Radio
receivers also support C-QUAM AM stereo, although this
feature is usually not advertised by the manufacturer.

12.5 Antennas

CHAPTER 12. MEDIUM WAVE

5/9 wavelength. The usage of masts taller than 5/9 wavelength (200 electrical degrees; about 410 millivolts per
meter using one kilowatt at one kilometer) with high
power gives a poor vertical radiation pattern, and 195
electrical degrees (about 400 millivolts per meter using
one kilowatt at one kilometer) is generally considered
ideal in these cases. Usually mast antennas are seriesexcited (base driven); the feedline is attached to the mast
at the base, so the base of the antenna is at high electrical
potential and must be supported on a ceramic insulator to
insulate it from the ground. Shunt-excited masts, in which
the base of the mast is at a node of the standing wave
at ground potential and so does not need to be insulated
from the ground have fallen into disuse, except in cases
of exceptionally high power, 1 MW or more, where series excitement might be impractical. If grounded masts
or towers are required, then cage aerials or long-wire aerials are used. Another possibility consists of feeding the
mast or the tower by cables running from the tuning unit
to the guys or crossbars in a certain height.
Directional aerials consist of multiple masts, which need
not to be from the same height. It is also possible to realize directional aerials for mediumwave with cage aerials
where some parts of the cage are fed with a certain phase
dierence.

For medium-wave (AM) broadcasting, quarter-wave

masts are between 153 feet (47 m) and 463 feet (141
m) high, depending on the frequency. Because such
tall masts can be costly and uneconomic, other types of
antennas are often used, which employ capacitive toploading (electrical lengthening) to achieve equivalent signal strength with vertical masts shorter than a quarter
wavelength.[11] A top hat of radial wires is occasionally
added to the top of mast radiators, to allow the mast to
be made shorter. For local broadcast stations and amateur
stations of under 5 kW, T- and L-antennas are often used,
which consist of one or more horizontal wires suspended
between two masts, attached to a vertical radiator wire. A
popular choice for lower-powered stations is the umbrella
antenna, which needs only one mast one tenth wavelength
or less in height. This antenna uses a single mast insulated
from ground and fed at the lower end against ground. At
the top of the mast, radial top-load wires are connected
(usually about six) which slope downwards at an angle
of 40-45 degrees as far as about one-third of the total
Multiwire T antenna of radio station WBZ, Massachusetts, USA,
height, where they are terminated in insulators and thence
1925. T antennas were the rst antennas used for medium wave
outwards to ground anchors. Thus the umbrella antenna
broadcasting, and are still used at lower power
uses the guy wires as the top-load part of the antenna. In
all these antennas the smaller radiation resistance of the
For broadcasting, mast radiators are the most common short radiator is increased by the capacitance added by
type of antenna used, consisting of a steel lattice guyed the wires attached to the top of the antenna.
mast in which the mast structure itself is used as the
antenna. Stations broadcasting with low power can use In some rare cases dipole antennas are used, which are
masts with heights of a quarter-wavelength (about 310 slung between two masts or towers. Such antennas are
millivolts per meter using one kilowatt at one kilome- intended to radiate a skywave. The medium-wave transter) to 5/8 wavelength (225 electrical degrees; about 440 mitter at Berlin-Britz for transmitting RIAS used a cross
millivolts per meter using one kilowatt at one kilometer), dipole mounted on ve 30.5 metre high guyed masts to
while high power stations mostly use half-wavelength to transmit the skywave to the ionosphere at nighttime.

12.8. EXTERNAL LINKS

12.5.1

Receiving antennas

Typical ferrite rod antenna used in AM radio receivers

73

[5] Subpart A: AM Broadcast Stations, Sec. 73.44 AM

transmission system emission limitations. TITLE 47-TELECOMMUNICATION, CHAPTER I--FEDERAL COMMUNICATIONS COMMISSION (CONTINUED), PART
73_RADIO BROADCAST SERVICES. U.S. Government
Printing Oce. Revised as of October 1, 2006. Archived
from the original on October 25, 2011. Retrieved 200904-24. Check date values in: |date= (help)

Because at these frequencies atmospheric noise is far [6] MWLIST quick and easy: Europe, Africa and Middle
East. Retrieved 11 December 2015.
above the receiver signal to noise ratio, inecient antennas much smaller than a wavelength can be used for [7] International Telecommunication Union. ITU. Rereceiving. For reception at frequencies below 1.6 MHz,
trieved 2009-04-24.
which includes long and medium waves, loop antennas
are popular because of their ability to reject locally gen- [8] MW channels in the UK. Retrieved 11 December 2015.
erated noise. By far the most common antenna for broad- [9] Fast alle ARD-Radiosender stellen Mittelwelle ein.
cast reception is the ferrite-rod antenna, also known as a
heise.de. 2015-01-06. Retrieved 2015-12-31.
loopstick antenna. The high permeability ferrite core allows it to be compact enough to be enclosed inside the [10] Heumann, Marcus (2015-12-17). Abschied von der Mittelwelle. Der gefrchtete Wellensalat ist Geschichte.
radios case and still have adequate sensitivity.
Deutschlandfunk.de. Retrieved 2015-12-31.

12.6 See also

Medium frequency band
AM radio
Longwave
MW DX
Shortwave
FM radio
Satellite radio
List of European medium wave transmitters
Wave plan of Geneva
DAB Radio

12.7 References
[1] United Kingdom Frequency Allocation Table 2008
(PDF). Ofcom. p. 21. Retrieved 2010-01-26.
[2] U.S. Frequency Allocation Chart (PDF). National
Telecommunications and Information Administration,
U.S. Department of Commerce. October 2003. Retrieved 2009-08-11.
[3] Building the Broadcast Band. Earlyradiohistory.us. Retrieved 2010-05-07.
[4] Christopher H. Sterling; John M. Kittross (2002). Stay
tuned: a history of American broadcasting. Psychology
Press. p. 95. ISBN 0-8058-2624-6.

[11] Weeks, W.L 1968, Antenna Engineering, McGraw Hill

Book Company, Section 2.6

12.8 External links

Building the Broadcast Band the development of
the 520-1700 kHz MW (AM) band
M3 Map of Eective Ground Conductivity in the
USA
MWLIST worldwide database of MW and LW stations
www.mwcircle.org The Medium Wave Circle. A
UK-based club for Medium wave DX'ers and enthusiasts.
- List of long- and mediumwave transmitters with
GoogleMap-Links to transmission sites

Chapter 13

AM broadcasting
AM Radio redirects here. For the song by Everclear,
see AM Radio (song). For the American band, see AM
Radio (band).
AM broadcasting is the process of radio broadcast-

as well as with various digital radio broadcasting services

distributed from terrestrial and satellite transmitters. In
many countries the narrow audio bandwidth (lower audio delity) and higher levels of interference experienced
with AM transmission have led AM broadcasters to specialise in spoken-word programming such as news, sports
and talk radio, leaving transmission of music mainly to
FM and digital broadcasters.

13.1 History
Main article: History of radio
The technology of amplitude modulation (AM) radio
transmission (then called radiotelephony) was developed
between 1900 and 1920. Before AM came into wide use
around 1920, the rst radios transmitted information by
AM and FM modulated signals for radio. AM (Amplitude Modu- wireless telegraphy (radiotelegraphy), in which the radio
lation) and FM (Frequency Modulation) are types of modulation signal did not carry audio (sound) but was switched on and
(coding). The electrical signal from program material, usually o to create pulses that carried text messages in Morse
coming from a studio, is mixed with a carrier wave of a specic code. This was used for private person-to-person comfrequency, then broadcast. In the case of AM, this mixing (modu- munication and message trac, such as telegrams.
lation) is done by altering the amplitude of the carrier wave with
time, according to the original signal. In the case of FM, it is the
frequency of the carrier wave that is varied. A radio receiver
(a radio) contains a demodulator that extracts the original program material from the broadcast wave.

ing using amplitude modulation (AM). AM was the rst

method of impressing sound on a radio signal and is still
widely used today. Commercial and public AM broadcasting is authorized in the medium wave band worldwide, and also in parts of the longwave and shortwave
bands. Radio broadcasting was made possible by the
invention of the amplifying vacuum tube, the Audion
(triode), by Lee de Forest in 1906, which led to the
development of inexpensive vacuum tube AM radio receivers and transmitters during World War I. Commercial AM broadcasting developed from amateur broadcasts around 1920, and was the only commercially important form of radio broadcasting until FM broadcasting
began after World War II. This period is known as the
"Golden Age of Radio". Today, AM competes with FM,

The entrepreneurs who developed AM "radiotelephone"

transmission did not anticipate broadcasting voice and
music into peoples homes.[2] The term broadcasting,
borrowed from agriculture, was applied to this new activity (by either Frank Conrad or RCA historian George
Clark[2] ) around 1920.[2] Prior to 1920 there was no
concept of broadcasting, or that radio listeners could
be a mass market for entertainment.[2] Promoters saw
the practical application for AM as similar to the existing communication technologies of wireless telegraphy, telephone, and telegraph: two-way person-to-person
commercial voice service, a wireless version of the
telephone.[3] Although there were a number of experimental broadcasts during this period, these were mostly
to provide publicity for the inventors products. True radio broadcasting didn't begin until around 1920, when it
sprang up spontaneously among amateur stations. AM remained the dominant method of broadcasting for the next
30 years, a period called the "Golden Age of Radio", until FM broadcasting started to become widespread in the

74

13.1. HISTORY

75

1950s. AM remains a popular, protable entertainment Majorana, Charles Herrold, and Lee de Forest, were
medium today and the dominant form of broadcasting in hampered by the lack of a technology for amplication.
some countries such as Australia and Japan.
The rst practical continuous wave AM transmitters were
based on versions of the Poulsen arc transmitter invented
in 1903,[3] and the huge, expensive Alexanderson alterna13.1.1 Early technologies
tor, developed 1906-1910. The modications necessary
to transmit AM were clumsy and resulted in very low audio quality. Modulation was usually accomplished by a
carbon microphone inserted directly in the antenna wire.
The limited power handling ability of the microphone
severely limited the power of the rst radiotelephones;
in powerful transmitters water-cooled microphones had
to be used. At the receiving end, the unamplied crystal
radio receivers then in use could not drive loudspeakers,
only earphones, so only one member of a family could
listen at a time.

13.1.2 Vacuum tubes

The discovery in 1912 of the amplifying ability of the
Audion (triode) vacuum tube, invented in 1906 by Lee
Farmer listening to US government weather and crop reports us- De Forest, solved the above problems. The vacuum
ing a crystal radio. Public service government time, weather, and tube feedback oscillator invented in 1912 by Alexander
farm broadcasts were the rst radio broadcasts.
Meissner and Edwin Armstrong, was a cheap source of
continuous waves and could be easily modulated to make
an AM transmitter. Nongovernmental radio transmission
was prohibited in many countries during World War 1,
but AM radiotelephony technology advanced greatly due
to wartime research, and after the war the availability of
cheap tubes sparked a great increase in the number of
amateur radio stations experimenting with AM transmission of news or music, giving people more to listen to.
New vacuum tube receivers coming on the market could
power loudspeakers, so the entire family could sit and listen together, and people could dance to broadcast music.
Vacuum tubes remained the central technology of radio
for 50 years, until transistors replaced them in the 1960s,
A family listening to an early broadcast using a crystal radio and they are still used in broadcast transmitters.
around 1920. Crystal radios, used before the advent of powered
vacuum tube radios in the 1920s, could not drive loudspeakers,
so the family must share earphones.

The rst AM voice transmission was made by Canadian

researcher Reginald Fessenden on 23 December 1900,
using a specially designed spark gap transmitter.[4][5]
Fessenden is a signicant gure in the development of
AM radio. He realized that the damped waves produced by the existing spark transmitters, which transmitted text data by wireless telegraphy, could not be used
to transmit sound, but rather continuous wave transmitters were needed.[6] He helped develop one of the rst
the Alexanderson alternator.[4]:3734[5]:400[6][7][8] He also
discovered the principle on which AM modulation is
based,[9][10][11][12][13] heterodyning,[6] and invented one
of the rst detectors able to rectify and receive AM, the
electrolytic detector or liquid baretter, in 1902.[6]

13.1.3 Beginning of broadcasting

German man listening to subscription radio receiver. Broadcast-

The early experiments in AM transmission, conducted ing in Germany began 1922 as a Post Oce monopoly, which
by Fessenden, Valdemar Poulsen, Ernst Ruhmer, Quirino provided this receiver which could only receive one station.

76
These changes caused radio listening to evolve explosively around 1919-1922 from a high-tech hobby to a
hugely popular social and family pastime, the rst electronic mass entertainment medium. In the US, the rst
broadcast stations were hobby and voluntary eorts without explicit advertising, started by a variety of local organizations: amateurs, local businesses looking for promotion, newspapers, schools, clubs, political parties, and
churches. Some naval radio stations broadcast programs
of music to the public at certain hours. Later businesses
learned to use this new medium to sell products, paying
for on-air commercial advertising. US radio broadcasting developed into a private, protmaking business, with
minimal government control on content.

CHAPTER 13. AM BROADCASTING

one owning a radio had to buy.
The rst broadcasts
Who made the rst radio broadcast is a contentious
issue. In the chaotic, freewheeling, experimental atmosphere of early AM wireless, it is dicult to draw a distinction between private and public transmissions. In
many cases, radio listeners tuned into experimental transmissions by the rst stations developing AM modulation,
and the stations began to cater to their unexpected audience with news and music.[2] Some of the early milestones:
1906: G. W. Pickard invents the crystal detector, the
rst cheap radio detector device that is able to rectify an AM signal. Homemade crystal radios spread
rapidly during the next 15 years. Before this, most
receivers used coherers, and only a few radio listeners were equipped with the electrolytic or Fleming
valve detectors that could also receive an AM broadcast.

Atlanta social club holds a radiophone dance in 1920 to music

broadcast from a band across town, with dancers wearing earphones. This phantom dancing became a fad during the radio
craze of the early Roaring 20s.

In Europe, broadcasting took a dierent course. Radio

transmission had always been more tightly controlled by
government in this region, partly because countries were
smaller and closer together; for example, in the UK receiving equipment as well as transmitters had to be licensed. There was a feeling in countries like the UK
and France that the radio spectrum was a national resource which should not be surrendered to private interests, motivated by prot, who would pander solely to
the desire for entertainment. Radio should serve higher
purposes of public information and education. In addition, totalitarian countries for political reasons kept
mass communications media under government control.
So in much of Europe, broadcasting developed as a
government-owned or government-supervised monopoly.
It was largely funded not by on-air commercial advertising as in the US, but by taxes on sales of radios, and user
fees in the form of an annual "receiver license" that any-

Christmas Eve, 1906: Reginald Fessenden broadcast an experimental program of Christmas music
and bible reading, including him playing "O Holy
Night" on the violin, from his Brant Rock, Massachusetts 500 W alternator-transmitter at about 50
kHz[15] to ships of the United Fruit Co. and Navy
ships, which were equipped with his electrolytic detectors.[6][7] It was heard as far south as Norfolk,
VA. This is usually considered the rst entertainment broadcast to the public. There is some doubt
whether this event took place, as the only evidence is
Fessendens own account many years later, but many
subsequent transmissions clearly establish him as the
rst to broadcast voice and music.[16]

1907: Radio entrepreneur Lee de Forest, an opera

bu, between 1907 and 1912 held a half-dozen promotional events in New York in which he broadcast live performances of famous Metropolitan
Opera stars such as Mariette Mazarin, Geraldine
Farrar, and Enrico Caruso with his AM arc
transmitter.[3][17] Very few radio receivers were
equipped to receive it. In another stunt he broadcast phonograph music from the Eiel Tower.[3]
A futurist and publicity hound, De Forest was
one of the rst to realize the possibilities of entertainment broadcasting, which he promoted in
speeches, newspaper articles, and experimental
demonstrations.[3][17] When he equipped the US
Navy Great White Fleet with experimental arc
radiotelephones for their 1908 around-the-world
cruise, he broadcast phonograph music as the ships
entered ports like San Francisco.[3][17]

13.1. HISTORY

77

One of the rst photos of a radio broadcast, French soprano Mariette Mazarin singing into Lee De Forests arc transmitter in New
York City on February 24, 1910.

June 1909: Radio experimenter Charles Herrold

and his students began making regular weekly
broadcasts from his School of Radio station FN
De Forests transmitter broadcasting the Hughes-Wilson presi(later KQW) in San Jose, California,[16][18] on 750
dential election returns November 7, 1916, operated by his enkHz. FN in 1912 became the rst licensed broad- gineer, Charles Logwood
cast station in the US.[19] San Francisco radio station
KCBS claims to be the direct descendant of KQW,
and on that basis has claimed to be the worlds oldest
of Wisconsin, Madison, Wisconsin and operated
broadcast station.
by Prof. Earle M. Terry, had been broadcasting weather reports by radiotelegraphy since 1916.
March 29, 1914: An experimental radio station in
Sometime in 1917 they began AM voice broadcasts
Laeken, near Brussels, Belgium, began broadcastand on January 9, 1919, began the rst regularly
ing regular concerts with an arc transmitter installed
scheduled weather and farm reports in the US.[23]
in 1913, which continued until it was destroyed
Terrys station was considered essential enough by
in WW1.[20] It had begun experimental telephony
the Navy to be allowed to remain on the air during
broadcasts as early as 1910, which from audience
WW1.
demand evolved into gramophone music, then live
concerts.
November 6, 1919: The rst scheduled (announced
in the press) radio broadcast is said to have been
made by Nederlandsche Radio Industrie station
PCGG at The Hague, which began broadcasting
November 1916: De Forest perfected Oscillion
concerts. It found it had a large audience outside
power tubes, capable of use in radio transmitters,
the Netherlands, mostly in the UK.
and inaugurated daily broadcasts of entertainment
and news from his New York Highbridge station,
January 15, 1920: Broadcasting in the UK began
2XG, until civilian radio transmissions were prohibwith impromptu news and phonograph music over
ited in April, 1917 due to the USs entry into World
[21]
2MT, the 15 kW experimental tube transmitter at
War 1. One of the most important prewar US raMarconis factory in Chelmsford, Essex, at a fredio events was his broadcast of the Hughes-Wilson
quency of 120 kHz.[24] On June 15, 1920 in the UKs
presidential election on November 7, 1916, with uprst scheduled broadcast, the Daily Mail newspaper
dates provided by wire from the New York American
[22]
sponsored a concert by the famed Australian opera
oces.
An estimated 7000 radio listeners as far
diva Nellie Melba.[24] Although not many British
as 200 miles from New York heard hourly election
heard it because of a lack of receivers, it was picked
returns interspersed with patriotic music.[22]
up in Berlin, Paris, The Hague, and Newfoundland,
1917: Experimental station 9XM (later WHA),
and caught the publics imagination. Chelmsford
licensed to the physics department of University
continued broadcasting concerts with noted per-

78

CHAPTER 13. AM BROADCASTING

formers. A few months later, in spite of burgeoning popularity, the government without warning shut
the experiment down, ostensibly because of interference with military aircraft radio.[24]

May 20, 1920: Experimental Marconi station XWA

of Montreal (later CFCF, now CINW) began regular
broadcasts, and claims status as the rst commercial
broadcaster in the world.
November 2, 1920: Westinghouse asked an employee, Frank Conrad of Pittsburgh, PA, who during
the war had used Westinghouses exclusive Signal
Corps test license to clandestinely broadcast gramophone music,[2] to set up a radio station to help sell
their radios. The enormously popular KDKA (originally 8XK) in Pittsburgh was the rst commercial
radio station in the US. It began broadcasting (a
phrase coined by Conrad) on election day, November 2, 1920. People learned the results of the Warren Harding-James Cox election from radio stations
before they read it in the newspapers. KDKA is said
to have been a pioneer in a number of areas, such as
broadcasting the rst religious services and sporting
events.

13.1.4

dio monopoly. Instead, in 1919 the US government brokered a patent cross-licensing and market-sharing agreement between the competing US corporate giants AT&T,
Westinghouse, United Fruit, and General Electric. Foreign rms were forbidden to own US radio stations, and
US assets of Marconi and Telefunken were sold to a newly
created rm, the Radio Corporation of America, RCA.
AT&T, Westinghouse, and GE would manufacture radio
equipment, and RCA would be the marketing and transmitting arm. This radio group oligopoly controlled the
US radio industry into the 1940s.
As the US audience for broadcasting grew in 1919-22,
it caught the interest of the big radio corporations, and
they began buying stations. They established agship
stations in major cities to promote their corporate image,
which during this period broadcast top-quality entertainment and news without advertising.

13.1.5 Radio networks

Main article: Radio network
Since longwave radio frequencies were used for interna-

Market concentration

A live radio play being broadcast at NBC studios in New York.

Since recording technology was primitive and costly during the
20s, most programs were broadcast live.
New Yorkers on Wall St. listening to the 1922 World Series from
a radio installed in a car. In 1922 radio broadcasting was an
exciting high-tech novelty.

World War I brought home to nations the strategic importance of long-distance radio; in addition to its military uses in keeping contact with its eets and overseas
forces, a country that didn't have radio could be isolated
by an enemy cutting its submarine telegraph cables. In the
US, before the war, the radio industry was fragmented by
patent monopolies held by competing giant rms, so the
best long-range radio technology was owned by two European rms: the British Marconi Co. and the German
Telefunken. At its entry into the war in 1917, the US
government temporarily took control of the entire US radio industry for the war eort, including the transatlantic
wireless stations of these foreign rms. After the war,
due to fear of foreign ownership of the US radio industry, there was an abortive eort to create a federal ra-

tional wireless telegraphy, broadcasting was mostly limited to the medium waves, whose limited range restricted
them to local audiences. Corporations around 1922 realized that long distance telephone lines, another innovation
made possible around 1915 by the vacuum tube, could be
used to link local radio stations into networks (the word
chains was used until the 1930s) broadcasting common
content, giving corporations a nationwide audience.[25]
United States
In the US, the nationwide telephone carrier AT&T was
the rst to create a network and take the radical step
of commercial advertising. It developed a broadcasting
model based on its telephony business: toll broadcasting. Its agship station, WEAF in New York, in August 1922 was rst to air commercial advertising, selling half-hour and hour blocks of airtime to commercial

13.1. HISTORY

When broadcasting began in 1920, live or phonograph music was

played on air without regard to its copyright status. As radio became a big business in the mid 20s, sheet music publishers, who
owned the rights, sued the stations for copyright infringement,
keeping many popular Jazz Age tunes o the air. This 1925 cartoon shows a rich publisher muzzling two radio performers. Royalty payments were quickly worked out.

sponsors that developed entertainment shows containing commercial messages. It had a monopoly on quality
telephone lines, and by 1924 had linked 12 stations in
Eastern cities into a chain. RCA and Westinghouse attempted to organize their own network around their agship WJZ, but were hampered by AT&Ts refusal to lease
them lines. In 1925 court decisions stripped AT&T of its
monopoly over broadcasting, and it decided to get out of
radio. AT&T sold WEAF to RCA, which formed the
nucleus of the new NBC network. In 1927, to reduce the
chaos on the airwaves, the government came down on
the side of the advertising model, establishing two classes
of broadcast licenses: the A or general public interest
stations which sold time impartially to anyone, received
favorable frequency assignments and ourished, and the
B or nonprot propaganda stations, mainly specialinterest, political or religious stations which represented
a point of view, were phased out.
The adoption of the commercial sponsorship model made
radio broadcasting protable, bringing in a lucrative
stream of income that could be used to buy top-quality
talent. The new business of advertising agencies acted as
middlemen, and by the late 1920s modern radio advertisements were developed. Networks began to see their
true product as their audience, and began to tailor shows
to bring in specic demographics desired by their advertisers. By the 1930s, most of the radio stations in the
country were aliated with networks owned by two companies, NBC and CBS. In 1934, a third, the Mutual Radio
Network was formed as a cooperative owned by its stations.

79

A BBC receiver licence from 1923 (the words BROADCAST LICENCE at top are misleading; it only allowed reception). Anyone
with a broadcast receiver had to have a licence.

United Kingdom
The other country which pioneered broadcasting, the UK,
and its national network the BBC, became the prototype for state-managed monopoly broadcasting.[26] The
abrupt shutdown of the 1920 UK experimental Marconi
broadcasts had caused increasing pressure on the Post
Oce to allow broadcasting.[27] The government wanted
to avoid the chaotic US experience, but also feared a
monopoly by the giant Marconi.[27] On 18 October 1922
it allowed 6 large radio manufacturers to form a consortium, the British Broadcasting Company, which was given
a monopoly on broadcasting, supported by a tax on radio
sets and a license fee on receivers collected by the Post
Oce.[27] Initially its 8 stations were allowed regional
autonomy, but its visionary general manager, John Reith, centralized production in London and lobbied for the
removal of advertising and commercial interests. During Britains General Strike of 1926, when the newspapers were shut down, the BBC was rst allowed to broadcast daytime news, and the country was impressed by
its impartial reporting.[28] In late 1926 Reiths proposals
were adopted, the BBC was nationalised, and an independent nonprot chartered corporation was formed, the
British Broadcasting Corporation supported solely by a 10
shilling receiver license fee.[28]
Under Reith, the BBC enforced strict broadcast standards
on its channels. Both the National and Regional programmes were required to carry a mixture of populist and
high brow programmes.

Other nations
During the 1920s AM broadcasting extended to the
rest of the world. In general, the Middle East, Asian,
and African countries adopted the European model of
centralized government-run radio networks, while Latin
America adopted the US model of private commercial
broadcasting.[26]

80

13.1.6

CHAPTER 13. AM BROADCASTING

Shortwave broadcasting

comedies, childrens shows. Radio news kept people upto-date, and remote reporting allowed them to be vicariThe discovery in the 1920s of the skip or "skywave" ously present at notable events, such as the famous 1937
propagation mechanism, in which high frequency radio Hindenburg disaster.
waves are reected back to Earth beyond the horizon by
In the 1920s the home radio receiver evolved from a
the ionosphere, made the shortwave frequencies above 1
forbidding technological device which was esthetically
MHz, previously considered useless, a useful band for
unattractive and dicult to operate, to a consumer item,
long distance broadcasting.
a piece of furniture, housed in an attractive wooden cabinet, with simple controls designed for anyone to operate,
which occupied a place of honor in the living room. The
13.1.7 Golden Age of Radio
dynamic cone loudspeaker invented in 1924 greatly improved audio frequency response over the previous horn
Main article: Golden Age of Radio
allowing music to be reproduced with good
During the 1920s, 1930s, and 1940s, a period called the speakers,
delity.[29] Prior to the introduction of the high-delity,
long-playing record in the late 1940s, AM radio oered
the highest sound quality available in a home audio device. Luxury models oered large speakers, electric
eye tuning (a special type of vacuum tube, which provided a visual aid in tuning), mechanical push-button
memory of favorite stations, sometimes with booklets
of adhesive labels for the buttons with station call letters,
andan inexpensive but impressive featureshortwave
bands that allowed access to distant, often foreign, stations. Accessory, then factory-installed radios became
available for cars.
Radio eased the isolation of rural life, and allowed people on farms and in towns to keep up with what was happening in the cities. Politicians could speak to millions
of citizens at a time; during the Depression Americans
gathered around their radios to listen to Franklin Roosevelt's "reside chats". This period saw the rise of radio
propaganda as a powerful tool of governments, contributing to the rise of fascist and communist ideologies.

13.1.8 Shortcomings of AM broadcasting

By the 1930s, radio receivers had developed from a high-tech
gadget into a user-friendly home consumer product, like this
Zenith Model 12-S console radio from 1938, a 12-tube superheterodyne with push-button tuning.

Golden Age of Radio, AM radio was the main source

of home entertainment, lling a role similar to the one
television played until the Internet started to replace it
in the 2010s. This was a big change in peoples lives;
for the rst time people were getting entertainment from
outside the home. Instead of having to settle for more traditional forms of entertainment such as oral storytelling
and music from family members, they could listen to Bing
Crosbys crooning, a BBC Shakespeare play, or a baseball game at New Yorks Ebbets Field. New forms of entertainment were created for the new medium, many of
which later migrated to television: radio plays, mystery
serials, soap operas, quiz shows, variety hours, situation

AM radio is often noisy. There is no protection from

static created by lightning, electrical equipment, and
other sources of signal pollution. Especially at night, conict between nearby and distant stations using a single frequency is common, and requires many smaller stations
to operate at much reduced power after sundown. Finally, the 10 kilohertz minimum separation between stations in the United States limits delity to sounds much
lower than the upper limit of human hearing, and the advent of high-delity recording equipment has created a
demand for high-delity radio.
As a result of these shortcomings, especially the noise issue, RCA in 1934 hired Edwin Howard Armstrong to test
his FM broadcasting system, which started to be deployed
in the 1940s, but because of a frequency band change in
1946 would not achieve dominance over AM until the end
of the 1970s.[30]

13.2. OPERATION

13.1.9

81

Competing media

patible Quadrature Amplitude Modulation), and KahnHazeltine independent sideband system. All except the
In the 1940s two new broadcast media evolved in the US Kahn-Hazeltine system used variations on the same idea:
which competed with AM: FM radio and television. By the mono (Left + Right) signal was transmitted in the
the 1950s, the dominance of AM radio over home en- amplitude modulation as before, while the stereo (Left
tertainment ended. Television replaced AM radio as an Right) information was transmitted by phase modulation.
evening family pastime; instead of sitting and listening to In 1980 the FCC chose the Magnavox PMX system as
the radio, families would watch television. By the 1970s the US standard. The FCC was savagely criticized by the
FM radio, due to its superior audio quality, attracted se- other contenders, and lawsuits erupted. In 1982, the FCC
rious audiophiles.
reversed its decision and decided not to enforce a stanThe AM radio industry suered a serious loss of audience
and advertising revenue during this time, and the value of
an AM broadcast license was eventually to decline substantially. The industry coped with this by developing
new narrowcasting strategies. Network broadcasting
gave way to format broadcasting; instead of broadcasting the same programs all over the country, AM stations
specialized in dierent "formats" which appealed to different audience segments: regional and local news, sports,
talk programs, programs targeted at minorities. "Talk
radio", which avoided the need for the broadcaster to pay
music royalties, appeared during this period as a consequence of the less expensive air time, and the need to
develop alternative programming, at reasonable cost, to
replace the lost network programming. Rather than live
music, stations played cheaper recorded music, and developed the "Top 40" format, which capitalized on (and
created) the popularity of new rhythm and blues and rock
music.

dard but allow multiple systems, to let the marketplace

decide. Meanwhile, other nations adopted AM stereo,
many choosing Motorolas C-QUAM. Their choice of a
single standard rather than allowing competing standards
as the US, resulted in greater acceptance of AM stereo in
these markets. In 1993, the FCC made C-QUAM system
the US standard.

Listening habits changed in the 1960s due to the introduction of the revolutionary transistor radio, made possible
by the invention of the transistor in 1946, which greatly
reduced power requirements and allowed people to listen
to radio anywhere using only small batteries. A transistor radio was smaller, lighter, and cooler. Radio became
a ubiquitous companion medium which people could
take with them in their pocket, and listen to while at work,
gardening, or at the beach.

AM radio technology is simpler than frequency modulated (FM) radio, Digital Audio Broadcasting (DAB),
satellite radio or HD (digital) radio. An AM receiver
detects amplitude variations in the radio waves at a particular frequency. It then amplies changes in the signal
voltage to drive a loudspeaker or earphones. The earliest
crystal radio receivers used a crystal diode detector with
no amplication, and required no power source other than
the radio signal itself.

13.1.10

AM stereo

Main article: AM stereo

In the late 1970s, in an unsuccessful eort to stem the
exodus of the music audience to FM, the US AM radio
industry developed technology for broadcasting in stereo.
Stereo is the standard in the music recording industry, and
FM broadcasting had adopted a stereo standard early, in
1961. The technology was challenging because of the
narrow 20 kHz bandwidth of the AM channel, and the
need for backward compatibility with non-stereo AM receivers. In 1975 the US Federal Communications Commission requested proposals for AM stereo standards, and
four competing standards were submitted: Harris Corporation's V-CPM (Variable angle Compatible Phase Multiplex), Magnavox's PMX, Motorola's C-QUAM (Com-

Globally, the adoption of stereo broadcasting was never

great, and declined after 1990. With the continued migration of AM stations away from music to news, sports,
and talk formats, receiver manufacturers saw little reason
to adopt the more expensive stereo tuners, and thus radio
stations have little incentive to upgrade to stereo transmission.

13.2 Operation

In North American broadcasting practice, transmitter

power input to the antenna for commercial AM stations
ranges from about 250 to 50,000 watts. Experimental licenses were issued for up to 500,000 watts radiated power, for stations intended for wide-area communication during disasters. One such superstation was
Cincinnati station WLW, which used such power on occasion before World War II. WLWs superpower transmitter still exists at the stations suburban transmitter site,
but it was decommissioned in the early 1940s and no current commercial broadcaster in the U.S. or Canada is authorized for such power levels. Some other countries do
authorize higher power operation (for example the Mexican station XERF formerly operated at 250,000 watts).
Antenna design must consider the coverage desired and
stations may be required, based on the terms of their license, to directionalize their transmitted signal to avoid
interfering with other stations operating on the same frequency.

82

CHAPTER 13. AM BROADCASTING

The hobby of listening to long distance signals is known
as DX'ing, from an old telegraph abbreviation for distance. Several nonprot hobbyist clubs are devoted to
DXing the AM broadcast band, including the National
Radio Club and International Radio Club of America.
Similarly, people listening to short wave transmissions are
SWLing.

13.3 Broadcast frequency bands

AM radio is broadcast on several frequency bands. The
allocation of these bands is governed by the ITU's Radio
Regulations and, on the national level, by each countrys
An example of the dierence in range of an AM radio signal at telecommunications administration (the FCC in the U.S.,
dierent times.
for example) subject to international agreements. The
frequency ranges given here are those that are allocated
to stations. Because of the bandwidth taken up by the
Medium-wave (medium frequency, MF) and short-wave
sidebands, the range allocated for the band as a whole is
(high frequency, HF) radio signals act dierently during
usually about 5 kHz wider on either side.
daytime and nighttime. During the day, MF signals travel
by groundwave, diracting around the curve of the earth
Long wave is LF waves from 153279 kHz, with
over a distance up to a few hundred kilometers from the
9 kHz channel spacing generally used. Long wave
signal transmitter. However, after sunset, changes in the
is used for radio broadcasting only in ITU region
ionosphere cause MF signals to travel by skywave, en1 (Europe, Africa, and northern and central Asia),
abling radio stations to be heard much farther from their
and is not allocated elsewhere. In the United States,
point of origin than is normal during the day. This pheCanada, Bermuda, and U.S. territories, this band
nomenon can be easily observed by scanning the medium
is mainly reserved for aeronautics navigational aids,
wave radio dial at night. As a result, many broadcast
though a small section of the band could theostations are required as a condition of license to reduce
retically be used for microbroadcasting under the
their broadcasting power signicantly (or use directional
United States Part 15 rules. Due to the propagation
antennas) after sunset, or even to suspend broadcasting
characteristics of long wave signals, the frequencies
entirely during nighttime hours. Such stations are comare used most eectively in latitudes over 50 from
monly referred to as daytimers. In Australia medium
the equator.
wave stations are not required to reduce their power at
night and consequently stations such as the 50,000-watt
Medium wave is MF waves from 526.51,606.5
774 ABC Melbourne can be heard in some parts of New
kHz in ITU regions 1 and 3, with 9 kHz spacing,
Zealand at night.
and 5401610 kHz in ITU region 2 (the AmeriFrom 1941 to 1983, the North American Regional
cas), with 10 kHz spacing. ITU region 2 also auBroadcasting Agreement allowed clear channel status to
thorizes the Extended AM broadcast band between
some stations, meaning that few if any other stations
1610 and 1710 kHz, previously used for police rawere granted permission to broadcast on or near their fredio. Medium wave is the most heavily used band
quency. This allowed an extended coverage area when
for commercial broadcasting. This is the AM raskywave propagation takes over at night, starting at or
dio that most people are familiar with.
near local sunset. Relatively few stations enjoy clear Short wave is HF waves from approximately 2.3
channel status; most local MW stations rely on ground26.1 MHz, divided into 14 broadcast bands. Shortwave coverage only, limiting their target market to their
wave broadcasts generally use a narrow 5 kHz chanown local area. Non-clear channel stations typically have
nel spacing. Short wave is used by audio services inreduced coverage at night, due to noise and the interfertended to be heard at great distances from the transence caused by other stations propagating in via skywave
mitting station. The long range of short wave broadafter dark. The area covered by a local station at night
casts comes at the expense of lower audio delity.
without signicant skywave interference is known as the
The mode of propagation for short wave is diernighttime interference-free (NIF) contour, and is typient (see high frequency). AM is used mostly by
cally specied in mV/m (signal strength). The higher the
broadcast services; other shortwave users may use
NIF value, the stronger the local signal must be to overa modied version of AM such as SSB or an AMride nighttime interference, resulting in a smaller covercompatible version of SSB such as SSB with carrier
age area and fewer listeners able to hear the station withreinserted.
out interference.

13.6. MICROBROADCASTING

83

Frequencies between the broadcast bands are used for transmitted via antenna, but via electric power cables,
other forms of radio communication, and are not broad- which radiate a signal receivable at a short distance from
cast services intended for reception by the general public. wherever the cables run. The signal is normally blocked
by power transformers, so the range depends on the distance before a transformer is encountered. The only surviving use of this technology in the U.S. is in college and
13.4 Limitations
high school radio, and for highway emergency warnings,
for which limited range is adequate, and whose signs diBecause of its relatively low audio quality due to au- rect drivers to an AM frequency e.g., Tune to 1680
dio bandwidth limitations, and its susceptibility to atmo- AM when ashing to receive an emergency message.
spheric and electrical interference, AM broadcasting now
attracts mainly talk radio and news programming, while While uncommon, AM stereo transmissions are possimusic radio and public radio mostly shifted to FM broad- ble using a variety of means. In addition, hybrid digicasting in the late 1970s in the developed countries. How- tal broadcast systems, which combine (mono analog) AM
ever, in the late 1960s and 1970s, top 40 rock and roll sta- and digital broadcasting technology, are now being used
tions in the U.S. and Canada such as WABC and CHUM around the world. In the United States, iBiquity's protransmitted highly processed and extended audio to 11 prietary HD Radio has been adopted and approved by
kHz, successfully attracting huge audiences. In the UK the FCC for medium wave transmissions, while Digital
during the 1980s, the national speech station, BBC Ra- Radio Mondiale is a more open eort often used on the
dio 4, had an FM location, whereas BBC Radio 1, a mu- shortwave bands, and can be used alongside many AM
sic station, was conned to AM broadcasts. Frequency broadcasts. Both of these standards are capable of broadresponse is typically 40 Hz5 kHz with a 50 dB signal to casting audio of signicantly greater delity than that of
standard AM with current bandwidth limitations, and a
noise (S/N) ratio.
theoretical frequency response of 016 kHz, in addition
The limitation on AM delity comes partly from current to stereo sound and text data.
receiver design, and eorts have been made to improve
this, notably the AMAX standards. Moreover, to t more While FM radio can also be received by cable, AM radio
transmitters on the MW broadcast band in the United generally is not available, although AM stations are someStates, maximum transmitted audio bandwidth is limited times converted into FM cable signals. In Canada, cable
to 10.2 kHz by a National Radio Systems Committee operators that oer FM cable services are required by the
(NRSC) standard adopted by the FCC in June 1989, re- CRTC to distribute all locally available AM stations in
sulting in a channel occupied bandwidth of 20.4 kHz. The this manner. In Switzerland a system known as wire
former audio limitation was 15 kHz resulting in a channel broadcasting (Telefonrundspruch in German) transmitted AM signals over telephone lines in the longwave
occupied bandwidth of 30 kHz.
band until 1998, when it was shut down.[31] In the UK,
Modern domestic radio receivers with digital tuning are Rediusion was an early pioneer of AM radio cable disusually incapable of ne-tuning in 1 kHz steps. On ra- tribution.
dios with analog dial tuning (or 1 kHz step capable digital tuning), slight detuning of an AM station could often
improve listenability, where for instance interference is
present to one side only of the RF channel.
13.6 Microbroadcasting
AM radio signals can be severely disrupted in large urban
centres by metal structures, tall buildings and sources of
radio frequency interference (RFI) and electrical noise,
such as electrical motors, uorescent lights, or lightning.
As a result, AM radio in many countries has lost its dominance as a music broadcasting service, and in many cities
is now relegated to news, sports, religious and talk radio stations. Some musical genres particularly country,
oldies, nostalgia and ethnic music survive on AM, especially in areas where FM frequencies are in short supply
or in thinly populated or mountainous areas where FM
coverage is poor.

See also: Low-power broadcasting

Some microbroadcasters and pirate radio broadcasters,

especially those in the United States under the FCCs Part
15 rules, broadcast on AM to achieve greater range than
is possible on the FM band. On mediumwave (AM),
such radio stations are often found between 1610 kHz and
1710 kHz. Hobbyists also use low-power AM (LPAM)
transmitters to provide programming for vintage radio
equipment in areas where AM programming is not widely
available or does not carry programming the listener desires; in such cases the transmitter, which is designed to
cover only the immediate property and perhaps nearby
13.5 Other distribution methods
areas, is connected to a computer, an FM radio or an
MP3 player. Microbroadcasting and pirate radio have
Beginning in the 1950s, carrier current distribution was been greatly supplemented by streaming audio on the Inused. In this modality the AM broadcast signal is not ternet, but some schools or hobbyists still use LPAM as

84
a means of broadcasting as each are distinctly dierent
technologies.

13.7 See also

Amplitude modulation
Amplitude Modulation Signalling System, a digital
system for adding low bitrate information to an AM
broadcast signal.
MW DXing, the hobby of receiving distant AM radio stations on the mediumwave band.
FM broadcasting
History of radio
Extended AM broadcast band
CAM-D, a hybrid digital radio format for AM
broadcasting
List of 50 kW AM radio stations in the United States
Lists of radio stations in North America
Oldest radio station

13.8 References
[1] Nahin, Paul J. (2001). The Science of Radio: With Matlab and Electronics Workbench Demonstration, 2nd Ed.
Springer Science & Business Media. pp. xxxix. ISBN
0387951504.
[2] Greb, Gordon; Adams, Mike (2003). Charles Herrold,
Inventor of Radio Broadcasting. McFarland. pp. 220
221. ISBN 0786483598.
[3] "Lee De Forest as Early Radio Broadcaster" on De Forest.com website excerpted from Adams, Mike (1996).
The Race for the Radiotelephone:1900-1920". The
AWA Review. Antique Wireless Association. 10: 78119.
[4] Sarkar, T. K.; Mailloux, Robert; Oliner, Arthur A.; et al.
(2006). History of Wireless. John Wiley & Sons. p. 408.
ISBN 0-471-78301-3.
[5] Klooster, John W. (2009). Icons of Invention: The Makers of the Modern World from Gutenberg to Gates. ABCCLIO. p. 397. ISBN 0313347433.

CHAPTER 13. AM BROADCASTING

[8] Belrose, John S. (September 1994). Fessenden and the

Early History of Radio Science. The Radioscientist.
IEEE. 5 (3). Retrieved September 10, 2013. on Inst. of
Electrical and Electronic Engineers, Canada website
[9] Superheterodyne Receivers. ES310: Introduction to
Naval Weapons Engineering. Federation of American Scientists. 1998. Retrieved September 10, 2013.
[10] Verghese, George; Hari Balakrishnan (2013). Ch. 14:
Modulation and Demodulation, p. 189,192 (PDF). Lecture Notes Introduction to EECS 2: Digital Communications Systems. Electrical Engineering Dept., Massachusetts Institute of Technology. Retrieved September
10, 2013.
[11] Ch. 1: Amplitude Modulation, p. 2,10-11, 42-43
(PDF). Navy MARS Operator (NMO) course. Military
Auxiliary Radio System National Tranining and Skills
Development website. 2011. Retrieved September 10,
2013.
[12] Bertrand, Ron (2011). Reading 30: AM Transmitters and Receivers (PDF). Online Radio and Electronics
Course. Arcade archive. Retrieved September 10, 2013.
[13] "The process of combining two frequencies in a nonlinear device and producing new frequencies is called mixing,
modulating, heterodyning, beating, or frequency conversion" Bureau of Naval Personnel (1973). Rate Training
Manual 0087-C: Basic Electronics. Courier Dover Publications,. p. 338. ISBN 0486210766.
[14] Richter, William A. (2006). Radio: A Complete Guide to
the Industry. Peter Lang. p. 12. ISBN 0820476331.
[15] Lee, Thomas H. (2004). Planar Microwave Engineering: A Practical Guide to Theory, Measurement, and Circuits, Vol. 1. Cambridge Univ. Press. p. 11. ISBN
0521835267.
[16] Adams, Mike (2011). Lee de Forest: King of Radio, Television, and Film. US: Springer. pp. 99101. ISBN
1461404185.
[17] De Forest, Lee, Sterling, Christopher H.; O'Dell, Cary;
Keith, Michael C., eds. (2011). The Biographical Encyclopedia of American Radio. Routledge. pp. 9496.
ISBN 0415995493.
[18] Herrold, Charles D., Sterling, Christopher H.; O'Dell,
Cary; Keith, Michael C., eds. (2011). The Biographical
Encyclopedia of American Radio. Routledge. pp. 169
170. ISBN 0415995493.
[19] Greb 2003, Charles Herrold, Inventor of Radio Broadcasting, p. 150

[6] Fessenden, Reginald, Sterling, Christopher H.; O'Dell,

Cary; Keith, Michael C., eds. (2011). The Biographical
Encyclopedia of American Radio. Routledge. pp. 136
139. ISBN 0415995493.

[20] The First Radio Broadcast. The Sydney Morning Herald. Sydney, Australia: Fairfax Media. March 29, 1939.
p. 19. Retrieved 27 September 2013.

[7] Davis, L. J. (2012). Fleet Fire: Thomas Edison and the

Pioneers of the Electric Revolution. Skyhorse Publishing
Inc. ISBN 1611456592.

[21] Wireless Transmission of News. Telephony. Chicago:

Telephony Publishing Co. 71 (27): 3233. December
10, 1916. Retrieved December 23, 2015.

13.9. EXTERNAL LINKS

85

[22] Election returns ashed by radio to 7000 amateurs

(PDF). Electrical Experimenter. New York: The Experimenter Publishing Co. 4 (9): 650. January 1917. Retrieved April 3, 2015.
[23] Greb 2003, Charles Herrold, Inventor of Radio Broadcasting, p. 155
[24] Street, Sean (2002). A Concise History of British Radio, 1922-2002. Kelly Publications. pp. 1724. ISBN
1903053145.
[25] Jim Cox (2009). American Radio Networks: A History.
McFarland. pp. 5. ISBN 978-0-7864-5424-2.
[26] Hilmes, Michele (2011). Network Nations: A Transnational History of British and American Broadcasting.
Routledge. p. 6. ISBN 0415883857.
[27] A Concise History of British Radio, 1922-2002.
google.com.
[28] A Concise History of British Radio, 1922-2002.
google.com.
[29] McNicol, Donald (1946) Radios Conquest of Space, p.
336-340
[30] See FM broadcasting in the United States and FM broadcast band.
[31] Sammlung alter Biennophone-Radios.
phone.ch. Retrieved 7 February 2013.

Bienno-

13.9 External links

Building the Broadcast Band the development of
the 5201700 kHz MW (AM) band
Chrome and Glass Shine Again: Hams Give Second
Life to Legendary Transmitters With Names Like
RCA, Collins, Gates and Raytheon
UK radio stations broadcasting on AM

Chapter 14

Heterodyne
This article is about waveform manipulation. For other method of making continuous wave radiotelegraphy siguses, see Heterodyne (disambiguation).
nals audible. Fessendens receiver did not see much apHeterodyning is a radio signal processing technique in- plication because of its local oscillators stability problem. While complex isochronous electromechanical oscillators existed, a stable yet inexpensive local oscillator
Ideal Mixer
was not available until Lee de Forest invented the triode
(Multiplier)
vacuum tube oscillator.[5] In a 1905 patent, Fessenden
stated the frequency stability of his local oscillator was
Input
Output
one part per thousand.[6]
Signal

Signal

Early spark gap radio transmitters sent information exclusively by means of radio telegraphy. In radio telegraphy, the characters of text messages are translated into
the short duration dots and long duration dashes of Morse
code that are broadcast as bursts of radio waves. The
Local
heterodyne detector was not needed to hear the signals
Oscillator
produced by these spark gap transmitters. The transmitted damped wave signals were amplitude modulated at
Frequency mixer symbol used in schematic diagrams.
an audio frequency by the spark. A simple detector produced an audible buzzing sound in the radiotelegraph opvented in 1901 by Canadian inventor-engineer Reginald erators headphones that could be transcribed back into
Fessenden that creates new frequencies by combining alpha-numeric characters.
or mixing two frequencies.[1][2][3] Heterodyning is used
With the advent of the arc converter, continuous wave
to shift one frequency range into another, new one,
(CW) transmitters were adopted. CW Morse code signals
and is also involved in the processes of modulation and
are not amplitude modulated, so a dierent detector was
demodulation.[2][4] The two frequencies are combined in
needed. The direct-conversion detector was invented to
a nonlinear signal-processing device such as a vacuum
make continuous wave radio-frequency signals audible.[7]
tube, transistor, or diode, usually called a mixer.[2] In the
most common application, two signals at frequencies f 1 The heterodyne or beat receiver has a local beat freand f 2 are mixed, creating two new signals, one at the quency oscillator (BFO) that produces a radio signal adsum f 1 + f 2 of the two frequencies, and the other at the justed to be close in frequency to the incoming signal bedierence f 1 f 2 .[3] These new frequencies are called ing received. When the two signals are mixed, a beat
heterodynes. Typically only one of the new frequencies frequency equal to the dierence between the two freis desired, and the other signal is ltered out of the output quencies is created. By adjusting the local oscillator freof the mixer. Heterodynes are related to the phenomenon quency correctly, the beat frequency is in the audio range,
and can be heard as a tone in the receivers earphones
of "beats" in acoustics.
whenever the transmitter signal is present. Thus the
A major application of the heterodyne process is in the
Morse code dots and dashes are audible as beeping
superheterodyne radio receiver circuit, which is used in
sounds. This technique is still used in radio telegraphy,
virtually all modern radio receivers.
the local oscillator now being called the beat frequency
oscillator or BFO. Fessenden coined the word heterodyne from the Greek roots hetero- dierent, and dyn14.1 History
power (cf. or dunamis).[8]
In 1901, Reginald Fessenden demonstrated a directconversion heterodyne receiver or beat receiver as a
86

14.2. APPLICATIONS

14.1.1

Superheterodyne receiver

The most important and widely used application of the

heterodyne technique is in the superheterodyne receiver
(superhet), invented by U.S. engineer Edwin Howard
Armstrong in 1918. In this circuit, the incoming radio
frequency signal from the antenna is mixed with a signal from a local oscillator and converted by the heterodyne technique to a somewhat lower xed frequency signal called the intermediate frequency (IF). This IF signal is amplied and ltered, before being applied to a
detector that extracts the audio signal, which is sent to
the loudspeaker.
The advantage of this technique is that the dierent frequencies of the dierent stations received are all converted to the same IF before amplication and ltering. The complicated amplier and bandpass lter stages,
which in previous receivers had to be made tunable to
work at the dierent station frequencies, in the superheterodyne can be built to work at one xed frequency,
the IF, simplifying their design. Another advantage is
that the IF is at a considerably lower frequency than the
RF frequency of the incoming radio signal.
The superior superheterodyne system replaced the earlier TRF and regenerative receiver designs, and since the
1930s almost all commercial radio receivers have been
superheterodynes.

14.2 Applications
Heterodyning, also called frequency conversion, is used
very widely in communications engineering to generate
new frequencies and move information from one frequency channel to another. Besides its use in the superheterodyne circuit found in almost all radio and television receivers, it is used in radio transmitters, modems,
satellite communications and set-top boxes, radar, radio
telescopes, telemetry systems, cell phones, cable television converter boxes and headends, microwave relays,
metal detectors, atomic clocks, and military electronic
countermeasures (jamming) systems.

14.2.1

Up and down converters

In large scale telecommunication networks such as

telephone network trunks, microwave relay networks,
cable television systems, and communication satellite
links, large bandwidth capacity links are shared by many
individual communication channels by using heterodyning to move the frequency of the individual signals up to
dierent frequencies, which share the channel. This is
called frequency division multiplexing (FDM).

87
don't interfere with one another. At the cable source or
headend, electronic upconverters convert each incoming
television channel to a new, higher frequency. They do
this by mixing the television signal frequency, fCH with
a local oscillator at a much higher frequency fLO, creating a heterodyne at the sum fCH + fLO, which is added
to the cable. At the consumers home, the cable set top
box has a downconverter that mixes the incoming signal
at frequency fCH + fLO with the same local oscillator frequency fLO creating the dierence heterodyne, converting the television channel back to its original frequency:
(fCH + fLO) fLO = fCH. Each channel is moved to
a dierent higher frequency. The original lower basic
frequency of the signal is called the baseband, while the
higher channel it is moved to is called the passband.

14.2.2 Analog videotape recording

Many analog videotape systems rely on a downconverted
color subcarrier to record color information in their limited bandwidth. These systems are referred to as heterodyne systems or color-under systems. For instance,
for NTSC video systems, the VHS (and S-VHS) recording system converts the color subcarrier from the NTSC
standard 3.58 MHz to ~629 kHz.[9] PAL VHS color subcarrier is similarly downconverted (but from 4.43 MHz).
The now-obsolete 3/4 U-matic systems use a heterodyned ~688 kHz subcarrier for NTSC recordings (as does
Sony's Betamax, which is at its basis a 1/2 consumer version of U-matic), while PAL U-matic decks came in two
mutually incompatible varieties, with dierent subcarrier
frequencies, known as Hi-Band and Low-Band. Other
videotape formats with heterodyne color systems include
Video-8 and Hi8.[10]
The heterodyne system in these cases is used to convert quadrature phase-encoded and amplitude modulated
sine waves from the broadcast frequencies to frequencies
recordable in less than 1 MHz bandwidth. On playback,
the recorded color information is heterodyned back to the
standard subcarrier frequencies for display on televisions
and for interchange with other standard video equipment.
Some U-matic (3/4) decks feature 7-pin mini-DIN connectors to allow dubbing of tapes without a heterodyne
up-conversion and down-conversion, as do some industrial VHS, S-VHS, and Hi8 recorders.

14.2.3 Music synthesis

The theremin, an electronic musical instrument, traditionally uses the heterodyne principle to produce a variable audio frequency in response to the movement of the
musician's hands in the vicinity of one or more antennas, which act as capacitor plates. The output of a xed
For example, a coaxial cable used by a cable television radio frequency oscillator is mixed with that of an oscilsystem can carry 500 television channels at the same time lator whose frequency is aected by the variable capacbecause each one is given a dierent frequency, so they itance between the antenna and the thereminist as that

88

CHAPTER 14. HETERODYNE

person moves her or his hand near the pitch control an- The right hand side shows that the resulting signal is the
tenna. The dierence between the two oscillator frequen- dierence of two sinusoidal terms, one at the sum of the
cies produces a tone in the audio range.
two original frequencies, and one at the dierence, which
The ring modulator is a type of heterodyne incorporated can be considered to be separate signals.
into some synthesizers or used as a stand-alone audio ef- Using this trigonometric identity, the result of multiplying
fect.
two sine wave signals, sin(2f1 t) and sin(2f2 t) can be
calculated:

14.2.4

Optical heterodyning

Optical heterodyne detection (an area of active research)

is an extension of the heterodyning technique to higher
(visible) frequencies. This technique could greatly improve optical modulators, increasing the density of information carried by optical bers. It is also being applied
in the creation of more accurate atomic clocks based on
directly measuring the frequency of a laser beam. See
NIST subtopic 9.07.9-4.R for a description of research
on one system to do this.[11][12]
Since optical frequencies are far beyond the manipulation capacity of any feasible electronic circuit, all photon
detectors are inherently energy detectors not oscillating
electric eld detectors. However, since energy detection
is inherently square-law detection, it intrinsically mixes
any optical frequencies present on the detector. Thus,
sensitive detection of specic optical frequencies necessitates optical heterodyne detection, in which two dierent (close-by) wavelengths of light illuminate the detector so that the oscillating electrical output corresponds to
the dierence between their frequencies. This allows extremely narrow band detection (much narrower than any
possible color lter can achieve) as well as precision measurements of phase and frequency of a light signal relative
to a reference light source, as in a laser Doppler vibrometer.

sin(2f1 t) sin(2f2 t) =

1
1
cos[2(f1 f2 )t] cos[2(f1 +f2 )t]
2
2

The result is the sum of two sinusoidal signals, one at the

sum f 1 + f 2 and one at the dierence f 1 f 2 of the original frequencies

14.3.1 Mixer
The two signals combine in a device called a mixer. As
seen in the previous section, an ideal mixer would be a
device that multiplies the two signals. Some widely used
mixer circuits, such as the Gilbert cell, operate in this
way, but they are limited to lower frequencies. However,
any nonlinear electronic component also multiplies signals applied to it, producing heterodyne frequencies in its
outputso a variety of nonlinear components serve as
mixers. A nonlinear component is one in which the output current or voltage is a nonlinear function of its input. Most circuit elements in communications circuits
are designed to be linear. This means they obey the
superposition principle; if F(v) is the output of a linear
element with an input of v:

This phase sensitive detection has been applied for

Doppler measurements of wind speed, and imaging F (v1 + v2 ) = F (v1 ) + F (v2 )
through dense media. The high sensitivity against background light is especially useful for lidar.
So if two sine wave signals at frequencies f 1 and f 2 are
In optical Kerr eect (OKE) spectroscopy, optical het- applied to a linear device, the output is simply the sum
erodyning of the OKE signal and a small part of the probe of the outputs when the two signals are applied sepasignal produces a mixed signal consisting of probe, het- rately with no product terms. Thus, the function F must
erodyne OKE-probe and homodyne OKE signal. The be nonlinear to create heterodynes (mixer products). A
probe and homodyne OKE signals can be ltered out, perfect multiplier only produces mixer products at the
sum and dierence frequencies (f 1 f 2 ), but more genleaving the heterodyne signal for detection.
eral nonlinear functions produce higher order mixer products: nf 1 + mf 2 for integers n and m. Some mixer
designs, such as double-balanced mixers, suppress some
14.3 Mathematical principle
high order undesired products, while other designs, such
as harmonic mixers exploit high order dierences.
Heterodyning is based on the trigonometric identity:
Examples of nonlinear components that are used as mixers are vacuum tubes and transistors biased near cuto (class C), and diodes. Ferromagnetic core inductors
1
1
sin 1 sin 2 = cos(1 2 ) cos(1 + 2 )
driven into saturation can also be used at lower frequen2
2
cies. In nonlinear optics, crystals that have nonlinear
The product on the left hand side represents the multipli- characteristics are used to mix laser light beams to crecation (mixing) of a sine wave with another sine wave. ate heterodynes at optical frequencies.

14.5. NOTES

14.3.2

Output of a mixer

To demonstrate mathematically how a nonlinear component can multiply signals and generate heterodyne frequencies, the nonlinear function F can be expanded in
a power series (MacLaurin series):

F (v) = 1 v + 2 v 2 + 3 v 3 +
To simplify the math, the higher order terms above 2 are
indicated by an ellipsis (". . .) and only the rst terms are
shown. Applying the two sine waves at frequencies 1 =
2f 1 and 2 = 2f 2 to this device:

vout = F (A1 sin 1 t + A2 sin 2 t)

89
Homodyne
Superheterodyne receiver
Transverter
Intermodulation a problem with strong higherorder terms produced in some non-linear mixers

14.5 Notes
[1] Christopher E. Cooper (January 2001). Physics. Fitzroy
Dearborn Publishers. pp. 25. ISBN 978-1-57958-3583. Retrieved 27 July 2013.
[2] United States Bureau of Naval Personnel (1973). Basic
Electronics. USA: Courier Dover. p. 338. ISBN 0-48621076-6.

vout = 1 (A1 sin 1 t+A2 sin 2 t)+2 (A1 sin 1 t+A2 sin 2 t)2 +

[3] Graf, Rudolf F. (1999). Modern dictionary of electronics,

2p. 344. ISBN 0-7506-9866-7.

2
Newnes.
vout = 1 (A1 sin 1 t+A2 sin 2 t)+2 (A21 sin2 1 t+2A1 A2 sin7th
1Ed.
t sinUSA:
2 t+A
2 sin 2 t)+

It can be seen that the second term above contains a product of the two sine waves. Simplifying with trigonometric
identities:

vout

[4] Horowitz, Paul; Wineld Hill (1989). The Art of Electronics, 2nd Ed. London: Cambridge University Press.
pp. 885, 897. ISBN 0-521-37095-7.

[5] Nahin 2001, p. 91, stating Fessendens circuit was ahead

of its time, however, as there simply was no technology
= 1 (A1 sin 1 t + A2 sin 2 t)
available then with which to build the required
) local oscil( 2
lator with the necessary
A22 frequency stability. Figure 7.10
A1
[1 cos 21 t] + A1 A2 [cos(1 t 2 t) cos(
2 t)] +1907 [1
cos 22 t] +
+ 2
shows1 ta+
simplied
2
2 heterodyne detector.

vout = 2 A1 A2 cos(1 2 )t2 A1 A2 cos(1 +2 )t+ [6] Fessenden 1905, p. 4

So the output contains sinusoidal terms with frequencies [7] Ashley, Charles Grinnell; Heyward, Charles Brian (1912).
Wireless Telegraphy and Wireless Telephony. Chicago:
at the sum 1 + 2 and dierence 1 2 of the two
American School of Correspondence. pp. 103/15
original frequencies. It also contains terms at the original
104/16.
frequencies and at multiples of the original frequencies
21 , 22 , 31 , 32 , etc.; the latter are called harmonics, [8] Tapan K. Sarkar, History of wireless, page 372
as well as more complicated terms at frequencies of M1
1
+ N2 , called intermodulation products. These unwanted [9] Videotape formats using 2 -inch-wide (13 mm) tape ; Retrieved
2007-01-01
frequencies, along with the unwanted heterodyne frequency, must be ltered out of the mixer output by an [10] Poynton, Charles. Digital Video and HDTV: Algorithms
electronic lter to leave the desired heterodyne.
and Interfaces San Francisco: Morgan Kaufmann Publishers, 2003 PP 582, 583 ISBN 1-55860-792-7

14.4 See also

Beat receptor
Direct-conversion receiver heterodyne conversion
of a signal directly to baseband instead of to an intermediate frequency
Heterodyne detection
Optical heterodyne detection
Beat (acoustics)
Edwin Howard Armstrong
Electroencephalography

[11] Contract Details: Robust Nanopopous Ceramic Microsensor Platform

[12] Contract Details: High Pulsed Power Varactor Multipliers
for Imaging

14.6 References
US 1050441, Fessenden, Reginald A., Electric Signaling Apparatus, published July 27, 1905, issued
January 14, 1913
Glinsky, Albert (2000), Theremin: Ether Music and
Espionage, Urbana, IL: University of Illinois Press,
ISBN 0-252-02582-2

90
Nahin, Paul J. (2001), The Science of Radio with
Matlab and Electronics Workbench Demonstrations
(second ed.), New York: Springer-Verlag, AIP
Press, ISBN 0-387-95150-4

14.7 External links

Hogan, John V. L. (April 1921), The Heterodyne
Receiver, Electric Journal, 18: 116
US 706740, Fessenden, Reginald A., Wireless Signaling, published September 28, 1901, issued August 12, 1902
US 1050728, Fessenden, Reginald A., Method of
Signaling, published August 21, 1906, issued January 14, 1913

CHAPTER 14. HETERODYNE

Chapter 15

Detector (radio)
In electronics, a detector is an older term for an electronic
component in a radio receiver that recovers information
contained in a modulated radio wave. The term dates
from the rst three decades of radio (1886-1916). Unlike modern radio stations which transmit sound (an audio
signal) on the radio carrier wave, the rst radio transmitters transmitted information by wireless telegraphy, using dierent length pulses of radio waves to spell out text
messages in Morse code. So early radio receivers did not
have to extract an audio signal (sound) from the incoming radio signal, but only detect the presence or absence
of the radio signal, to produce clicks in the receivers earphones representing the Morse code symbols. The device
that did this was called a detector. A variety of dierent
detector devices, such as the coherer, electrolytic detec- A coherer detector, useful only for Morse code signals.
tor, and magnetic detector, were used during the wireless
telegraphy era.
After sound (amplitude modulation, AM) transmission began around 1920, the term evolved to mean a
demodulator, a nonlinear rectier (usually a crystal diode
or a vacuum tube) which extracted the audio signal from
the radio frequency carrier wave. This is its current
meaning, although modern detectors usually consist of A simple envelope detector
semiconductor diodes, transistors, or integrated circuits.
In a superheterodyne receiver the term is also sometimes used to refer to the mixer, the tube or transistor
which converts the incoming radio frequency signal to the
intermediate frequency. The mixer is called the rst detector, while the demodulator that extracts the audio signal from the intermediate frequency is called the second
detector.

15.1 Amplitude modulation detectors

15.1.1

form a low pass lter. If the resistor and capacitor are

correctly chosen, the output of this circuit will be a nearly
identical voltage-shifted version of the original signal.
An early form of envelope detector was the cats whisker,
which was used in the crystal set radio receiver. A later
version using a crystal diode is still used in crystal radio
sets today. The limited frequency response of the headset
eliminates the RF component, making the low pass lter
unnecessary. More sophisticated envelope detectors include the plate detector, grid-leak detector and transistor
equivalents of them, innite-impedance detectors (peak
detector circuits), and precision rectiers.

Envelope detector
15.1.2 Product detector

One major technique is known as envelope detection.

The simplest form of envelope detector is the diode detector that consists of a diode connected between the input and output of the circuit, with a resistor and capacitor
in parallel from the output of the circuit to the ground to

A product detector is a type of demodulator used for AM

and SSB signals, where the original carrier signal is removed by multiplying the received signal with a signal at
the carrier frequency (or near to it). Rather than convert-

91

92

CHAPTER 15. DETECTOR (RADIO)

radio may detect the sound of an FM broadcast by the
phenomenon of slope detection which occurs when the
radio is tuned slightly above or below the nominal broadcast frequency. Frequency variation on one sloping side
of the radio tuning curve gives the amplied signal a corresponding local amplitude variation, to which the AM
detector is sensitive. Slope detection gives inferior distortion and noise rejection compared to the following dedicated FM detectors that are normally used.

15.2.1 Phase detector

D1

E1

A phase detector is a nonlinear device whose output represents the phase dierence between the two oscillating
input signals. It has two inputs and one output: a reference signal is applied to one input and the phase or frequency modulated signal is applied to the other. The output is a signal that is proportional to the phase dierence
between the two inputs.
In phase demodulation the information is contained in the
amount and rate of phase shift in the carrier wave.

15.2.2 The Foster-Seeley discriminator

A simple crystal radio with no tuned circuit can be used to listen
to strong AM broadcast signals

ing the envelope of the signal into the decoded waveform

by rectication as an envelope detector would, the product detector takes the product of the modulated signal and
a local oscillator, hence the name. By heterodyning, the
received signal is mixed (in some type of nonlinear device) with a signal from the local oscillator, to give sum
and dierence frequencies to the signals being mixed,
just as a rst mixer stage in a superhet would produce an
intermediate frequency; the beat frequency in this case,
the low frequency modulating signal is recovered and the
unwanted high frequencies ltered out from the output of
the product detector.
Product detector circuits are analog multipliers and so essentially ring modulators or synchronous detectors and
closely related to some phase-sensitive detector circuits.
They can be implemented using something as simple as
ring of diodes or a single dual-gate Field Eect Transistor to anything as sophisticated as an Integrated Circuit
containing a Gilbert cell.

Main article: Foster-Seeley discriminator

The Foster-Seeley discriminator[1][2] is a widely used FM
detector. The detector consists of a special center-tapped
transformer feeding two diodes in a full wave DC rectier
circuit. When the input transformer is tuned to the signal
frequency, the output of the discriminator is zero. When
there is no deviation of the carrier, both halves of the
center tapped transformer are balanced. As the FM signal swings in frequency above and below the carrier frequency, the balance between the two halves of the centertapped secondary is destroyed and there is an output voltage proportional to the frequency deviation.

15.2.3 Ratio detector

The ratio detector[3][4][5][6] is a variant of the FosterSeeley discriminator, but one diode conducts in an opposite direction, and using a tertiary winding in the preceding transformer. The output in this case is taken between the sum of the diode voltages and the center tap.
The output across the diodes is connected to a large value
capacitor, which eliminates AM noise in the ratio detector output. The ratio detector has the advantage over the
15.2 Frequency and phase modula- Foster-Seeley discriminator that it will not respond to AM
signals, thus potentially saving a limiter stage; however
tion detectors
the output is only 50% of the output of a discriminator
for the same input signal. The ratio detector has wider
AM detectors cannot demodulate FM and PM signals be- bandwidth but more distortion than the Foster-Seeley discause both have a constant amplitude. However an AM criminator.

15.3. PHASE-LOCKED LOOP DETECTOR

93
nal FM signal and a square wave whose frequency equals
the FM signals center frequency. The XOR gate produces an output pulse whose duration equals the dierence between the times at which the square wave and the
received FM signal pass through zero volts. As the FM
signals frequency varies from its unmodulated center frequency (which is also the frequency of the square wave),
the output pulses from the XOR gate become longer or
shorter. (In essence, this quadrature detector converts an
FM signal into a pulse-width modulated (PWM) signal.)
When these pulses are ltered, the lters output rises as
the pulses grow longer and its output falls as the pulses
grow shorter. In this way, one recovers the original signal
that was used to modulate the FM carrier.

15.2.5 Other FM detectors

Less common, specialized, or obsolescent types of detectors include:[7]
Travis[8] or double tuned circuit discriminator using
two non-interacting tuned circuits above and below
the nominal center frequency
A ratio detector using solid-state diodes

Weiss discriminator which uses a single LC tuned

circuit or crystal

15.2.4

Pulse count discriminator which converts the frequency to a train of constant amplitude pulses, producing a voltage directly proportional to the frequency.

Quadrature detector

In quadrature detectors, the received FM signal is split

into two signals. One of the two signals is then passed
through a high-reactance capacitor, which shifts the phase
of that signal by 90 degrees. This phase-shifted signal is
then applied to an LC circuit, which is resonant at the FM
signals unmodulated, center, or carrier frequency. If
the received FM signals frequency equals the center frequency, then the two signals will have a 90-degree phase
dierence and they are said to be in phase quadrature
hence the name of this method. The two signals are
then multiplied together in an analog or digital device,
which serves as a phase detector; that is, a device whose
output is proportional to the phase dierence between
two signals. In the case of an unmodulated FM signal,
the phase detectors output is after the output has been
ltered; that is, averaged over time constant; namely,
zero. However, if the received FM signal has been modulated, then its frequency will vary from the center frequency. In this case, the resonant LC circuit will further
shift the phase of the signal from the capacitor, so that
the signals total phase shift will be the sum of the 90 degrees thats imposed by the capacitor and the positive or
negative phase change thats imposed by the LC circuit.
Now the output from the phase detector will dier from
zero, and in this way, one recovers the original signal that
was used to modulate the FM carrier.
This detection process can also be accomplished by combining, in an exclusive-OR (XOR) logic gate, the origi-

15.3 Phase-locked loop detector

The phase-locked loop detector requires no frequencyselective LC network to accomplish demodulation. In
this system, a voltage controlled oscillator (VCO) is phase
locked by a feedback loop, which forces the VCO to follow the frequency variations of the incoming FM signal.
The low-frequency error voltage that forces the VCOs
frequency to track the frequency of the modulated FM
signal is the demodulated audio output.

15.4 See also

Cats whisker detector
Coherer
Tuner (radio)
Electrolytic detector
Foster-Seeley discriminator
Grid-leak detector

94
Hot wire barretter
Magnetic detector
Plate detector
Demodulation
Tikker
Wunderlich detector

15.5 References
[1] US 2121103, Seeley, Stuart W., Frequency Variation Response Circuits, issued June 21, 1938
[2] Foster, D. E.; Seeley, S. W. (March 1937), Automatic
tuning, simplied circuits, and design practice, Proceedings of the Institute of Radio Engineers, 25 (3): 289313,
doi:10.1109/jrproc.1937.228940, part 1.
[3] US 2497840, Seeley, Stuart William, Angle Modulation
Detector, issued February 14, 1950
[4] US 2561089, Anderson, Earl I., issued July 17, 1951
[5] Report L.B.645: Ratio detectors for FM receivers
(15 September 1945) issued by the Radio Corporation
of America, RCA Laboratories Industry Service Division,
711 Fifth Avenue, N.Y., N.Y. Reprinted in Radio, pages
18-20 (October 1945).
[6] Seeley, Stuart W.; Avins, Jack (June 1947), The ratio
detector, RCA Review, 8 (2): 201236
[7] D. S. Evans and G. R. Jessup, VHF-UHF Manual (3rd Edition), Radio Society of Great Britain,London, 1976 pages
4-48 through 4-51
[8] Charles Travis, Automatic oscillator frequency control
system U.S. patent: 2,294,100 (led: 4 February 1935;
issued: August 1942). See also: Charles Travis, Automatic frequency control, Proceedings of the Institute of
Radio Engineers, vol. 23, no. 10, pages 1125-1141 (October 1935).

15.6 External links

Simple block diagrams and descriptions of key circuits
for FM transmitters and receivers:

CHAPTER 15. DETECTOR (RADIO)

Chapter 16

Rectier
For other uses, see Rectier (disambiguation).
the rectier is smoothed by an electronic lter (usually a
A rectier is an electrical device that converts capacitor) to produce a steady current.
More complex circuitry that performs the opposite function, converting DC to AC, is called an inverter.

16.1 Rectier devices

Before the development of silicon semiconductor rectiers, vacuum tube thermionic diodes and copper oxideor selenium-based metal rectier stacks were used.[1]
With the introduction of semiconductor electronics, vacuum tube rectiers became obsolete, except for some enthusiasts of vacuum tube audio equipment. For power
rectication from very low to very high current, semiconductor diodes of various types (junction diodes, Schottky
diodes, etc.) are widely used.

A rectier diode (silicon controlled rectier) and associated

mounting hardware. The heavy threaded stud attaches the device to a heatsink to dissipate heat.

alternating current (AC), which periodically reverses direction, to direct current (DC), which ows in only
one direction. The process is known as rectication.
Physically, rectiers take a number of forms, including
vacuum tube diodes, mercury-arc valves, copper and selenium oxide rectiers, semiconductor diodes, siliconcontrolled rectiers and other silicon-based semiconductor switches. Historically, even synchronous electromechanical switches and motors have been used. Early radio
receivers, called crystal radios, used a "cats whisker" of
ne wire pressing on a crystal of galena (lead sulde) to
serve as a point-contact rectier or crystal detector.
Rectiers have many uses, but are often found serving
as components of DC power supplies and high-voltage
direct current power transmission systems. Rectication
may serve in roles other than to generate direct current
for use as a source of power. As noted, detectors of radio
signals serve as rectiers. In gas heating systems ame
rectication is used to detect presence of a ame.
Because of the alternating nature of the input AC sine
wave, the process of rectication alone produces a DC
current that, though unidirectional, consists of pulses of
current. Many applications of rectiers, such as power
supplies for radio, television and computer equipment,
require a steady constant DC current (as would be produced by a battery). In these applications the output of

Other devices that have control electrodes as well as acting as unidirectional current valves are used where more
than simple rectication is requirede.g., where variable output voltage is needed. High-power rectiers, such
as those used in high-voltage direct current power transmission, employ silicon semiconductor devices of various
types. These are thyristors or other controlled switching
solid-state switches, which eectively function as diodes
to pass current in only one direction.

16.2 Rectier circuits

Rectier circuits may be single-phase or multi-phase
(three being the most common number of phases). Most
low power rectiers for domestic equipment are singlephase, but three-phase rectication is very important for
industrial applications and for the transmission of energy
as DC (HVDC).

16.2.1 Single-phase rectiers

Half-wave rectication
In half-wave rectication of a single-phase supply, either
the positive or negative half of the AC wave is passed,

95

96

CHAPTER 16. RECTIFIER

while the other half is blocked. Because only one half turns are required on the transformer secondary to obtain
of the input waveform reaches the output, mean voltage the same output voltage than for a bridge rectier, but the
is lower. Half-wave rectication requires a single diode power rating is unchanged.
in a single-phase supply, or three in a three-phase supply. Rectiers yield a unidirectional but pulsating direct
current; half-wave rectiers produce far more ripple than
full-wave rectiers, and much more ltering is needed to
eliminate harmonics of the AC frequency from the output.
Full-wave rectier using a center tap transformer and 2 diodes.

Half-wave rectier

The no-load output DC voltage of an ideal half-wave rectier for a sinusoidal input voltage is:[2]

Vrms =

Vpeak
2

Vdc =

Vpeak

where:
V , V the DC or average output voltage,
V , the peak value of the phase input voltages,
V , the root mean square (RMS) value of output voltage.

Full-wave rectier, with vacuum tube having two anodes.

The average and RMS no-load output voltages of an ideal

single-phase full-wave rectier are:

Full-wave rectication
A full-wave rectier converts the whole of the input waveform to one of constant polarity (positive or negative) at
its output. Full-wave rectication converts both polarities
of the input waveform to pulsating DC (direct current),
and yields a higher average output voltage. Two diodes
and a center tapped transformer, or four diodes in a bridge
conguration and any AC source (including a transformer
without center tap), are needed.[3] Single semiconductor
diodes, double diodes with common cathode or common
anode, and four-diode bridges, are manufactured as single components.

Vdc = Vav =

2Vpeak

Vpeak
Vrms =
2
Very common double-diode rectier vacuum tubes contained a single common cathode and two anodes inside
a single envelope, achieving full-wave rectication with
positive output. The 5U4 and 5Y3 were popular examples of this conguration.

16.2.2 Three-phase rectiers

Graetz bridge rectier: a full-wave rectier using four diodes.

For single-phase AC, if the transformer is center-tapped,

then two diodes back-to-back (cathode-to-cathode or
anode-to-anode, depending upon output polarity required) can form a full-wave rectier. Twice as many

Single-phase rectiers are commonly used for power supplies for domestic equipment. However, for most industrial and high-power applications, three-phase rectier circuits are the norm. As with single-phase rectiers,
three-phase rectiers can take the form of a half-wave
circuit, a full-wave circuit using a center-tapped transformer, or a full-wave bridge circuit.

16.2. RECTIFIER CIRCUITS

97
eect, can be thought of as a six-phase, half-wave circuit.
Before solid state devices became available, the half-wave
circuit, and the full-wave circuit using a center-tapped
transformer, were very commonly used in industrial rectiers using mercury-arc valves.[4] This was because the
three or six AC supply inputs could be fed to a corresponding number of anode electrodes on a single tank,
sharing a common cathode.
With the advent of diodes and thyristors, these circuits
have become less popular and the three-phase bridge circuit has become the most common circuit.

Three-phase bridge rectier

3-phase AC input, half- and full-wave rectied DC output waveforms

Thyristors are commonly used in place of diodes to create

a circuit that can regulate the output voltage. Many devices that provide direct current actually generate three- Disassembled automobile alternator, showing the six diodes that
phase AC. For example, an automobile alternator con- comprise a full-wave three-phase bridge rectier.
tains six diodes, which function as a full-wave rectier
for battery charging.
For an uncontrolled three-phase bridge rectier, six
diodes are used, and the circuit again has a pulse number of six. For this reason, it is also commonly referred
Three-phase, half-wave circuit
to as a six-pulse bridge.
An uncontrolled three-phase, half-wave circuit requires
three diodes, one connected to each phase. This is the
simplest type of three-phase rectier but suers from relatively high harmonic distortion on both the AC and DC
connections. This type of rectier is said to have a pulsenumber of three, since the output voltage on the DC side
contains three distinct pulses per cycle of the grid frequency.
Three-phase, full-wave circuit using center-tapped
transformer

For low-power applications, double diodes in series, with

the anode of the rst diode connected to the cathode of
the second, are manufactured as a single component for
this purpose. Some commercially available double diodes
have all four terminals available so the user can congure
them for single-phase split supply use, half a bridge, or
three-phase rectier.
For higher-power applications, a single discrete device
is usually used for each of the six arms of the bridge.
For the very highest powers, each arm of the bridge may
consist of tens or hundreds of separate devices in parallel (where very high current is needed, for example in
aluminium smelting) or in series (where very high voltages are needed, for example in high-voltage direct current power transmission).

If the AC supply is fed via a transformer with a center tap,

a rectier circuit with improved harmonic performance
can be obtained. This rectier now requires six diodes,
one connected to each end of each transformer secondary For a three-phase full-wave diode rectier, the ideal, nowinding. This circuit has a pulse-number of six, and in load average output voltage is

98

CHAPTER 16. RECTIFIER

With supply inductance taken into account, the output
voltage of the rectier is reduced to:

Vdc = Vav =

3VLLpeak
cos( + )

The overlap angle is directly related to the DC current,

and the above equation may be re-expressed as:

Vdc = Vav =

3VLLpeak
cos() 6f Lc Id

Where:
Three-phase full-wave bridge rectier circuit using thyristors as
the switching elements, ignoring supply inductance

L , the commutating inductance per phase

I , the direct current

3 3Vpeak
Vdc = Vav =

Twelve-pulse bridge

If thyristors are used in place of diodes, the output voltage

is reduced by a factor cos():

3 3Vpeak
Vdc = Vav =
cos

Or, expressed in terms of the line to line input voltage:[5]

Vdc = Vav =

3VLLpeak
cos

Where:

Twelve pulse bridge rectier using thyristors as the switching elements

Although better than single-phase rectiers or threephase half-wave rectiers, six-pulse rectier circuits still
produce considerable harmonic distortion on both the AC
and DC connections. For very high-power rectiers the
V , the peak value of the phase (line to neutwelve-pulse bridge connection is usually used. A twelvetral) input voltages,
pulse bridge consists of two six-pulse bridge circuits con, ring angle of the thyristor (0 if diodes are
nected in series, with their AC connections fed from a
used to perform rectication)
supply transformer that produces a 30 phase shift between the two bridges. This cancels many of the characThe above equations are only valid when no current is teristic harmonics the six-pulse bridges produce.
drawn from the AC supply or in the theoretical case when
the AC supply connections have no inductance. In prac- The 30 degree phase shift is usually achieved by using a
tice, the supply inductance causes a reduction of DC out- transformer with two sets of secondary windings, one in
put voltage with increasing load, typically in the range star (wye) connection and one in delta connection.
1020% at full load.
VLL , the peak value of the line to line input
voltages,

The eect of supply inductance is to slow down the transfer process (called commutation) from one phase to the
next. As result of this is that at each transition between a
pair of devices, there is a period of overlap during which
three (rather than two) devices in the bridge are conducting simultaneously. The overlap angle is usually referred
to by the symbol (or u), and may be 20 30 at full load.

16.2.3 Voltage-multiplying rectiers

Main article: voltage multiplier
The simple half-wave rectier can be built in two electrical congurations with the diode pointing in opposite
directions, one version connects the negative terminal of
the output direct to the AC supply and the other connects

16.3. RECTIFIER EFFICIENCY

99
trailing boost stage or primary high voltage (HV) source,
are used in HV laser power supplies, powering devices
such as cathode ray tubes (CRT) (like those used in CRT
based television, radar and sonar displays), photon amplifying devices found in image intensifying and photo
multiplier tubes (PMT), and magnetron based radio frequency (RF) devices used in radar transmitters and microwave ovens. Before the introduction of semiconductor electronics, transformerless powered vacuum tube receivers powered directly from AC power sometimes used
voltage doublers to generate about 170 VDC from a 100
120 V power line.

16.3 Rectier eciency

Switchable full bridge/voltage doubler.

the positive terminal of the output direct to the AC supply. By combining both of these with separate output
smoothing it is possible to get an output voltage of nearly
double the peak AC input voltage. This also provides a
tap in the middle, which allows use of such a circuit as a
split rail power supply.
A variant of this is to use two capacitors in series for the
output smoothing on a bridge rectier then place a switch
between the midpoint of those capacitors and one of the
AC input terminals. With the switch open, this circuit
acts like a normal bridge rectier. With the switch closed,
it act like a voltage doubling rectier. In other words, this
makes it easy to derive a voltage of roughly 320 V (15%,
approx.) DC from any 120 V or 230 V mains supply in
the world, this can then be fed into a relatively simple
switched-mode power supply. However, for a given desired ripple, the value of both capacitors must be twice
the value of the single one required for a normal bridge
rectier; when the switch is closed each one must lter
the output of a half-wave rectier, and when the switch
is open the two capacitors are connected in series with an
equivalent value of half one of them.

Rectier eciency () is dened as the ratio of DC output

power to the input power from the AC supply. Even with
ideal rectiers with no losses, the eciency is less than
100% because some of the output power is AC power
rather than DC which manifests as ripple superimposed
on the DC waveform. For a half-wave rectier eciency
is very poor,[6]

Pin =

Vpeak Ipeak

2
2

(the divisors are 2 rather than 2 because no power is

delivered on the negative half-cycle)
Vpeak Ipeak

Thus maximum eciency for a half-wave rectier is,

Pout =

Pout
4
= 2 40.5%
Pin

Similarly, for a full-wave rectier,

=

Pout
8
= 2 81.0%
Pin

Eciency is reduced by losses in transformer windings

and power dissipation in the rectier element itself. Eciency can be improved with the use of smoothing circuits
which reduce the ripple and hence reduce the AC content
of the output. Three-phase rectiers, especially threephase full-wave rectiers, have much greater eciencies
because the ripple is intrinsically smaller. In some threephase and multi-phase applications the eciency is high
enough that smoothing circuitry is unnecessary.[7]
=

Cockcroft Walton voltage multiplier

Cascaded diode and capacitor stages can be added to

make a voltage multiplier (Cockroft-Walton circuit).
These circuits are capable of producing a DC output 16.4 Rectier losses
voltage potential tens of times that of the peak AC input voltage, but are limited in current capacity and reg- A real rectier characteristically drops part of the input
ulation. Diode voltage multipliers, frequently used as a voltage (a voltage drop, for silicon devices, of typically

100
0.7 volts plus an equivalent resistance, in general nonlinear)and at high frequencies, distorts waveforms in
other ways. Unlike an ideal rectier, it dissipates some
power.
An aspect of most rectication is a loss from the peak input voltage to the peak output voltage, caused by the builtin voltage drop across the diodes (around 0.7 V for ordinary silicon pn junction diodes and 0.3 V for Schottky
diodes). Half-wave rectication and full-wave rectication using a center-tapped secondary produces a peak
voltage loss of one diode drop. Bridge rectication has a
loss of two diode drops. This reduces output voltage, and
limits the available output voltage if a very low alternating
voltage must be rectied. As the diodes do not conduct
below this voltage, the circuit only passes current through
for a portion of each half-cycle, causing short segments of
zero voltage (where instantaneous input voltage is below
one or two diode drops) to appear between each hump.

CHAPTER 16. RECTIFIER

V1
50Hz
0

+VO

D1

C1

R1
0V
GND

RC-Filter Rectier: This circuit was designed and simulated using

Multisim 8 software.

is reduced by the resistance of the transformer windings.

In extreme cases where many rectiers are loaded onto a
power distribution circuit, peak currents may cause diculty in maintaining a correctly shaped sinusoidal voltage
on the ac supply.

To limit ripple to a specied value the required capacitor

Peak loss is very important for low voltage rectiers (for
size is proportional to the load current and inversely proexample, 12 V or less) but is insignicant in high-voltage
portional to the supply frequency and the number of outapplications such as HVDC.
put peaks of the rectier per input cycle. The load current
and the supply frequency are generally outside the control
of the designer of the rectier system but the number of
16.5 Rectier output smoothing
peaks per input cycle can be aected by the choice of
rectier design.
A half-wave rectier only gives one peak per cycle, and
for this and other reasons is only used in very small power
supplies. A full wave rectier achieves two peaks per cycle, the best possible with a single-phase input. For threephase inputs a three-phase bridge gives six peaks per cycle. Higher numbers of peaks can be achieved by using
transformer networks placed before the rectier to convert to a higher phase order.
To further reduce ripple, a capacitor-input lter can be
used. This complements the reservoir capacitor with a
choke (inductor) and a second lter capacitor, so that
a steadier DC output can be obtained across the termiThe AC input (yellow) and DC output (green) of a half-wave nals of the lter capacitor. The choke presents a high
[8]
rectier with a smoothing capacitor. Note the ripple in the DC impedance to the ripple current. For use at power-line
frequencies inductors require cores of iron or other magsignal.
netic materials, and add weight and size. Their use in
While half-wave and full-wave rectication can deliver power supplies for electronic equipment has therefore
unidirectional current, neither produces a constant volt- dwindled in favour of semiconductor circuits such as voltage. Producing steady DC from a rectied AC supply re- age regulators.
quires a smoothing circuit or lter.[8] In its simplest form A more usual alternative to a lter, and essential if the
this can be just a reservoir capacitor or smoothing capac- DC load requires very low ripple voltage, is to follow the
itor, placed at the DC output of the rectier. There is still reservoir capacitor with an active voltage regulator ciran AC ripple voltage component at the power supply fre- cuit. The reservoir capacitor must be large enough to
quency for a half-wave rectier, twice that for full-wave, prevent the troughs of the ripple dropping below the minwhere the voltage is not completely smoothed.
imum voltage required by the regulator to produce the
Sizing of the capacitor represents a tradeo. For a given
load, a larger capacitor reduces ripple but costs more and
creates higher peak currents in the transformer secondary
and in the supply that feeds it. The peak current is set in
principle by the rate of rise of the supply voltage on the
rising edge of the incoming sine-wave, but in practice it

required output voltage. The regulator serves both to signicantly reduce the ripple and to deal with variations in
supply and load characteristics. It would be possible to
use a smaller reservoir capacitor (these can be large on
high-current power supplies) and then apply some ltering as well as the regulator, but this is not a common strat-

16.7. RECTIFICATION TECHNOLOGIES

egy. The extreme of this approach is to dispense with the
reservoir capacitor altogether and put the rectied waveform straight into a choke-input lter. The advantage of
this circuit is that the current waveform is smoother and
consequently the rectier no longer has to deal with the
current as a large current pulse, but instead the current
delivery is spread over the entire cycle. The disadvantage, apart from extra size and weight, is that the voltage
output is much lower approximately the average of an
AC half-cycle rather than the peak.

101
Thyristors are used in various classes of railway rolling
stock systems so that ne control of the traction motors
can be achieved. Gate turn-o thyristors are used to produce alternating current from a DC supply, for example
on the Eurostar Trains to power the three-phase traction
motors.[9]

16.7 Rectication technologies

16.7.1 Electromechanical

16.6 Applications
The primary application of rectiers is to derive DC
power from an AC supply (AC to DC converter). Virtually all electronic devices require DC, so rectiers are
used inside the power supplies of virtually all electronic
equipment.
Converting DC power from one voltage to another is
much more complicated. One method of DC-to-DC conversion rst converts power to AC (using a device called
an inverter), then uses a transformer to change the voltage, and nally recties power back to DC. A frequency
of typically several tens of kilohertz is used, as this requires much smaller inductance than at lower frequencies
and obviates the use of heavy, bulky, and expensive ironcored units.

Before about 1905 when tube type rectiers were developed, power conversion devices were purely electromechanical in design. Mechanical rectication systems
used some form of rotation or resonant vibration (e.g.
vibrators) driven by electromagnets, which operated a
switch or commutator to reverse the current.
These mechanical rectiers were noisy and had high
maintenance requirements. The moving parts had friction, which required lubrication and replacement due
to wear. Opening mechanical contacts under load resulted in electrical arcs and sparks that heated and eroded
the contacts. They also were not able to handle AC
frequencies above several thousand cycles per second.

Synchronous rectier
To convert alternating into direct current in electric locomotives, a synchronous rectier may be used . It consists of a synchronous motor driving a set of heavy-duty
electrical contacts. The motor spins in time with the AC
frequency and periodically reverses the connections to
the load at an instant when the sinusoidal current goes
through a zero-crossing. The contacts do not have to
switch a large current, but they must be able to carry a
large current to supply the locomotives DC traction motors.

Output voltage of a full-wave rectier with controlled thyristors

Rectiers are also used for detection of amplitude modulated radio signals. The signal may be amplied before
detection. If not, a very low voltage drop diode or a diode
biased with a xed voltage must be used. When using a
rectier for demodulation the capacitor and load resistance must be carefully matched: too low a capacitance
makes the high frequency carrier pass to the output, and
too high makes the capacitor just charge and stay charged.
Rectiers supply polarised voltage for welding. In such
circuits control of the output current is required; this is
sometimes achieved by replacing some of the diodes in
a bridge rectier with thyristors, eectively diodes whose
voltage output can be regulated by switching on and o
with phase red controllers.

Vibrating rectier
Main article: Mechanical rectier
These consisted of a resonant reed, vibrated by an alternating magnetic eld created by an AC electromagnet,
with contacts that reversed the direction of the current on
the negative half cycles. They were used in low power devices, such as battery chargers, to rectify the low voltage
produced by a step-down transformer. Another use was
in battery power supplies for portable vacuum tube radios, to provide the high DC voltage for the tubes. These
operated as a mechanical version of modern solid state
switching inverters, with a transformer to step the battery
voltage up, and a set of vibrator contacts on the transformer core, operated by its magnetic eld, to repeatedly
break the DC battery current to create a pulsing AC to

102

CHAPTER 16. RECTIFIER

[11]

but it would only be suitable for use at very low voltages because of the low breakdown voltage and the risk
of electric shock. A more complex device of this kind
was patented by G. W. Carpenter in 1928 (US Patent
1671970).[12]
When two dierent metals are suspended in an electrolyte
solution, direct current owing one way through the solution sees less resistance than in the other direction. Electrolytic rectiers most commonly used an aluminum anode and a lead or steel cathode, suspended in a solution
of tri-ammonium ortho-phosphate.
The rectication action is due to a thin coating of aluminum hydroxide on the aluminum electrode, formed
A vibrator battery charger from 1922. It produced 6A DC at 6V
by rst applying a strong current to the cell to build up
to charge automobile batteries.
the coating. The rectication process is temperaturesensitive, and for best eciency should not operate above
power the transformer. Then a second set of rectier con- 86 F (30 C). There is also a breakdown voltage where
tacts on the vibrator rectied the high AC voltage from the coating is penetrated and the cell is short-circuited.
the transformer secondary to DC.
Electrochemical methods are often more fragile than mechanical methods, and can be sensitive to usage variations, which can drastically change or completely disrupt
Motor-generator set
the rectication processes.
Similar electrolytic devices were used as lightning
Main articles: Motor-generator and Rotary converter
A motor-generator set, or the similar rotary converter, is arresters around the same era by suspending many
aluminium cones in a tank of tri-ammonium orthophosphate solution. Unlike the rectier above, only aluminium electrodes were used, and used on A.C., there
was no polarization and thus no rectier action, but the
chemistry was similar.[13]
The modern electrolytic capacitor, an essential component of most rectier circuit congurations was also developed from the electrolytic rectier.

A small motor-generator set

not strictly a rectier as it does not actually rectify current, but rather generates DC from an AC source. In
an M-G set, the shaft of an AC motor is mechanically
coupled to that of a DC generator. The DC generator
produces multiphase alternating currents in its armature
windings, which a commutator on the armature shaft converts into a direct current output; or a homopolar generator produces a direct current without the need for a
commutator. M-G sets are useful for producing DC for
railway traction motors, industrial motors and other highcurrent applications, and were common in many highpower D.C. uses (for example, carbon-arc lamp projectors for outdoor theaters) before high-power semiconduc- 16.7.3
tors became widely available.

16.7.2

Plasma type

Electrolytic

The development of vacuum tube technology in the early

The electrolytic rectier[10] was a device from the early 20th century resulted in the invention of various tubetwentieth century that is no longer used. A home-made type rectiers, which largely replaced the noisy, ineversion is illustrated in the 1913 book The Boy Mechanic cient mechanical rectiers.

16.7. RECTIFICATION TECHNOLOGIES

103
rating of more than 1 GW and 450 kV.[14][15]

Mercury-arc
Main article: Mercury-arc valve

Argon gas electron tube

Early

3-phase

industrial

mercury vapor rectier tube

150 kV mercury-arc valve

at Manitoba Hydro power station, Radisson, Canada
converted AC hydropower to DC for transmission to
distant cities.
Tungar bulbs from 1917, 2 ampere (left) and 6 ampere

A rectier used in high-voltage direct current (HVDC)

power transmission systems and industrial processing between about 1909 to 1975 is a mercury-arc rectier or
mercury-arc valve. The device is enclosed in a bulbous glass vessel or large metal tub. One electrode, the
cathode, is submerged in a pool of liquid mercury at the
bottom of the vessel and one or more high purity graphite
electrodes, called anodes, are suspended above the pool.
There may be several auxiliary electrodes to aid in starting and maintaining the arc. When an electric arc is established between the cathode pool and suspended anodes,
a stream of electrons ows from the cathode to the anodes through the ionized mercury, but not the other way
(in principle, this is a higher-power counterpart to ame
rectication, which uses the same one-way current transmission properties of the plasma naturally present in a
ame).
These devices can be used at power levels of hundreds of
kilowatts, and may be built to handle one to six phases of
AC current. Mercury-arc rectiers have been replaced by
silicon semiconductor rectiers and high-power thyristor
circuits in the mid 1970s. The most powerful mercuryarc rectiers ever built were installed in the Manitoba Hydro Nelson River Bipole HVDC project, with a combined

The General Electric Tungar rectier was an argon gaslled electron tube device with a tungsten lament cathode and a carbon button anode. It operated similarly to
the thermionic vacuum tube diode, but the gas in the tube
ionized during forward conduction, giving it a much lower
forward voltage drop so it could rectify lower voltages.
It was used for battery chargers and similar applications
from the 1920s until lower-cost metal rectiers, and later
semiconductor diodes, supplanted it. These were made
up to a few hundred volts and a few amperes rating, and
in some sizes strongly resembled an incandescent lamp
with an additional electrode.
The 0Z4 was a gas-lled rectier tube commonly used in
vacuum tube car radios in the 1940s and 1950s. It was
a conventional full-wave rectier tube with two anodes
and one cathode, but was unique in that it had no lament (thus the 0 in its type number). The electrodes
were shaped such that the reverse breakdown voltage was
much higher than the forward breakdown voltage. Once
the breakdown voltage was exceeded, the 0Z4 switched
to a low-resistance state with a forward voltage drop of
about 24 V.

104

16.7.4

CHAPTER 16. RECTIFIER

Diode vacuum tube (valve)

have both and allow the player to choose.[16]

Main article: Diode

The thermionic vacuum tube diode, originally called the 16.7.5

Solid state

Crystal detector
Main article: cats-whisker detector
The cats-whisker detector was the earliest type of semi-

Vacuum tube diodes

Fleming valve, was invented by John Ambrose Fleming

in 1904 as a detector for radio waves in radio receivers,
and evolved into a general rectier. It consisted of an
evacuated glass bulb with a lament heated by a separate
current, and a metal plate anode. The lament emitted
electrons by thermionic emission (the Edison eect), discovered by Thomas Edison in 1884, and a positive voltage on the plate caused a current of electrons through the
tube from lament to plate. Since only the lament produced electrons, the tube would only conduct current in
one direction, allowing the tube to rectify an alternating
current.

Galena cats whisker detector

conductor diode. It consisted of a crystal of some

semiconducting mineral, usually galena (lead sulde),
with a light springy wire touching its surface. Invented by
Jagadish Chandra Bose and developed by G. W. Pickard
around 1906, it served as the radio wave rectier in the
rst widely used radio receivers, called crystal radios. Its
fragility and limited current capability made it unsuitable
Vacuum diode rectiers were widely used in power supfor power supply applications. It became obsolete around
plies in vacuum tube consumer electronic products, such
1920, but later versions served as microwave detectors
as phonographs, radios, and televisions, for example the
and mixers in radar receivers during World War 2.
All American Five radio receiver, to provide the high DC
plate voltage needed by other vacuum tubes. Full-wave
versions with two separate plates were popular because Selenium and copper oxide rectiers
they could be used with a center-tapped transformer to
make a full-wave rectier. Vacuum rectiers were made Main article: Metal rectier
for very high voltages, such as the high voltage power sup- Once common until replaced by more compact and less
ply for the cathode ray tube of television receivers, and costly silicon solid-state rectiers in the 1970s, these
the kenotron used for power supply in X-ray equipment. units used stacks of metal plates and took advantage
However, compared to modern semiconductor diodes, of the semiconductor properties of selenium or copper
vacuum rectiers have high internal resistance due to oxide.[17] While selenium rectiers were lighter in weight
space charge and therefore high voltage drops, causing and used less power than comparable vacuum tube rectihigh power dissipation and low eciency. They are rarely ers, they had the disadvantage of nite life expectancy,
able to handle currents exceeding 250 mA owing to the increasing resistance with age, and were only suitable to
limits of plate power dissipation, and cannot be used for use at low frequencies. Both selenium and copper oxide
low voltage applications, such as battery chargers. An- rectiers have somewhat better tolerance of momentary
other limitation of the vacuum tube rectier is that the voltage transients than silicon rectiers.
heater power supply often requires special arrangements Typically these rectiers were made up of stacks of metal
to insulate it from the high voltages of the rectier circuit. plates or washers, held together by a central bolt, with the
In musical instrument amplication (especially for electric guitars), the slight delay or sag between a signal
increase (for instance, when a guitar chord is struck hard
and fast) and the corresponding increase in output voltage is a notable eect of tube rectication, and results in
compression. The choice between tube rectication and
diode rectication is a matter of taste; some ampliers

number of stacks determined by voltage; each cell was

rated for about 20 V. An automotive battery charger rectier might have only one cell: the high-voltage power
supply for a vacuum tube might have dozens of stacked
plates. Current density in an air-cooled selenium stack
was about 600 mA per square inch of active area (about
90 mA per square centimeter).

16.8. CURRENT RESEARCH

105

Two of three high-power thyristor valve stacks used for long distance transmission of power from Manitoba Hydro dams. Compare with mercury-arc system from the same dam-site, above.
Selenium rectier

Silicon and germanium diodes

Main article: Diode
In the modern world, silicon diodes are the most widely
used rectiers for lower voltages and powers, and have
largely replaced earlier germanium diodes. For very high
voltages and powers, the added need for controllability
has in practice led to replacing simple silicon diodes with
high-power thyristors (see below) and their newer actively
gate-controlled cousins.

o thyristors (GTO), have made smaller high voltage DC

power transmission systems economical. All of these devices function as rectiers.
As of 2009 it was expected that these high-power silicon self-commutating switches, in particular IGBTs
and a variant thyristor (related to the GTO) called the
integrated gate-commutated thyristor (IGCT), would be
scaled-up in power rating to the point that they would
eventually replace simple thyristor-based AC rectication systems for the highest power-transmission DC
applications.[18]

16.8 Current research

High power: thyristors (SCRs) and newer siliconA major area of research is to develop higher frequency
based voltage sourced converters
rectiers, that can rectify into terahertz and light frequencies. These devices are used in optical heterodyne detecMain article: high-voltage direct current
tion, which has myriad applications in optical ber communication and atomic clocks. Another prospective apIn high-power applications, from 1975 to 2000, most plication for such devices is to directly rectify light waves
mercury valve arc-rectiers were replaced by stacks of picked up by tiny antenna, called nantennas, to produce
very high power thyristors, silicon devices with two ex- DC electric power.[19] It is thought that arrays of nantentra layers of semiconductor, in comparison to a simple nas could be a more ecient means of producing solar
power than solar cells.
diode.
In medium-power transmission applications, even more
complex and sophisticated voltage sourced converter
(VSC) silicon semiconductor rectier systems, such as
insulated gate bipolar transistors (IGBT) and gate turn-

A related area of research is to develop smaller rectiers, because a smaller device has a higher cuto frequency. Research projects are attempting to develop
a unimolecular rectier, a single organic molecule that

106

CHAPTER 16. RECTIFIER

would function as a rectier.

[11] How To Make An Electrolytic Rectier.

books.com. Retrieved 2012-03-15.

16.9 See also

[12] US patent 1671970, Glenn W. Carpenter, Liquid Rectier, issued 1928-06-05

AC adapter
Active rectication
Capacitor
Diode
Direct current
High-voltage direct current
Inverter
Ripple
Synchronous rectication
Vienna rectier

16.10 References

Chestof-

[13] American Technical Society (1920). Cyclopedia of applied electricity. 2. American technical society. p. 487.
Retrieved 8 January 2013.
[14] Pictures of a mercury-arc rectier in operation can be seen
here: Belsize Park deep shelter rectier 1, Belsize Park
deep shelter rectier 2
[15] Sood, Vijay K. HVDC and FACTS Controllers: Applications Of Static Converters In Power Systems. SpringerVerlag. p. 1. ISBN 978-1-4020-7890-3. The rst 25
years of HVDC transmission were sustained by converters having mercury arc valves till the mid-1970s. The
next 25 years till the year 2000 were sustained by linecommutated converters using thyristor valves. It is predicted that the next 25 years will be dominated by forcecommutated converters [4]. Initially, this new forcecommutated era has commenced with Capacitor Commutated Converters (CCC) eventually to be replaced by selfcommutated converters due to the economic availability
of high-power switching devices with their superior characteristics.

[1] Morris, Peter Robin (1990). A History of the World Semiconductor Industry. p. 18. ISBN 978-0-86341-227-1.

[16] Hunter, Dave (September 2013). Whats The Big Deal

About Tube Rectication?". Guitar Player. p. 136.

[2] Lander, Cyril W. (1993). 2. Rectifying Circuits. Power

electronics (3rd ed.). London: McGraw-Hill. ISBN 9780-07-707714-3.

[17] H. P. Westman et al., (ed), Reference Data for Radio Engineers, Fifth Edition, 1968, Howard W. Sams and Co., no
ISBN, Library of Congress Card No. 43-14665 chapter
13

[3] Williams, B. W. (1992). Chapter 11. Power electronics

: devices, drivers and applications (2nd ed.). Basingstoke:
Macmillan. ISBN 978-0-333-57351-8.
[4] Hendrik Rissik (1941). Mercury-arc current convertors
[sic] : an introduction to the theory and practice of vapourarc discharge devices and to the study of rectication phenomena. Sir I. Pitman & sons, ltd. Retrieved 8 January
2013.
[5] Kimbark, Edward Wilson (1971). Direct current transmission. (4. printing. ed.). New York: Wiley-Interscience.
p. 508. ISBN 978-0-471-47580-4.
[6] Analog and Digital Electronics, Rectier and clipper
circuit, pages 4 and 5, retrieved 25 April 2015.
[7] Wendy Middleton, Mac E. Van Valkenburg (eds), Reference Data for Engineers: Radio, Electronics, Computer,
and Communications, p. 14. 13, Newnes, 2002 ISBN 07506-7291-9.
[8] Archived 16 February 2012 at the Wayback Machine.
[9] Mansell, A.D.; Shen, J. (1 January 1994). Pulse converters in traction applications. Power Engineering Journal.
8 (4): 183. doi:10.1049/pe:19940407.
[10] Hawkins, Nehemiah (1914). 54. Rectiers. Hawkins
Electrical Guide: Principles of electricity, magnetism, induction, experiments, dynamo. New York: T. Audel. Retrieved 8 January 2013.

[18] Arrillaga, Jos; Liu, Yonghe H; Watson, Neville R; Murray,

Nicholas J. Self-Commutating Converters for High Power
Applications. John Wiley & Sons. ISBN 978-0-47068212-8.
[19] Idaho National Laboratory (2007). Harvesting the suns
energy with antennas. Retrieved 2008-10-03.

Chapter 17

Fleming valve

The rst prototype Fleming valves, built October 1904.

Early commercial Fleming valves used in radio receivers, 1919

The Fleming valve, also called the Fleming oscillation

valve, was a vacuum tube (or thermionic valve) invented in 1904 by John Ambrose Fleming as a detector
for early radio receivers used in electromagnetic wireless
telegraphy. It was the rst practical vacuum tube and the
rst thermionic diode, a vacuum tube whose purpose is to
conduct current in one direction and block current owing in the opposite direction. The thermionic diode was
later widely used as a rectier a device which converts alternating current (AC) into direct current (DC)
in the power supplies of a wide range of electronic devices, until largely replaced by the semiconductor diode
in the 1960s. The Fleming valve was the forerunner of all
vacuum tubes, which dominated electronics for 50 years.
The IEEE has described it as one of the most important
developments in the history of electronics,[1] and it is on
the List of IEEE Milestones for electrical engineering.

Fleming valve schematic from US Patent 803,684.

17.1 How it works

The valve consists of an evacuated glass bulb containing
two electrodes: a cathode in the form of a "lament", a
loop of carbon or ne tungsten wire, similar to that used
in the light bulbs of the time, and an anode (plate) consisting of a sheet metal plate. Although in early versions the
anode was a at metal plate placed next to the cathode,
in later versions it became a metal cylinder surrounding
the cathode. In some versions, a grounded copper screen
surrounded the bulb to shield against the inuence of external electric elds.

107

108

CHAPTER 17. FLEMING VALVE

was about 3,500 kilometres (2,200 mi). Although the
contact, reported November 12, 1901, was widely heralded as a great scientic advance at the time, there is also
some skepticism about the claim, because the received
signal, the three dots of the Morse code letter S, was so
weak the primitive receiver had diculty distinguishing it
from atmospheric radio noise caused by static discharges,
leading later critics to suggest it may have been random
noise. Regardless, it was clear to Fleming that reliable
transatlantic communication with the existing transmitter required more sensitive receiving apparatus.

Valve receiver made by Marconi Co. has two Fleming valves, in

case one burns out

In operation, a separate current ows through the cathode

lament, heating it so that some of the electrons in the
metal gain sucient energy to escape their parent atoms
into the vacuum of the tube, a process called thermionic
emission. The AC current to be rectied is applied between the lament and the plate. When the plate has a
positive voltage with respect to the lament, the electrons
are attracted to it and an electric current ows from lament to plate. In contrast, when the plate has a negative
voltage with respect to the lament, the electrons are not
attracted to it and no current ows through the tube (unlike the lament, the plate does not emit electrons). As
current can pass through the valve in one direction only,
it therefore "recties" an AC current to a pulsing DC current.
This simple operation was somewhat complicated by the
presence of residual air in the valve, as the vacuum pumps
of Flemings time were unable to create as high a vacuum
as exists in modern vacuum tubes. At high voltages, the
valve could become unstable and oscillate, but this occurred at voltages far above those normally used.

17.2 History
The Fleming valve was the rst practical application of
thermionic emission, discovered in 1873 by Frederick
Guthrie. As a result of his work on the incandescent light
bulb, Thomas Edison made his own discovery of the phenomenon in 1880, which led to it being called the Edison
eect. Edison was granted a patent for this device as part
of an electrical indicator in 1884, but did not nd a practical use for it. Professor Fleming of University College
London consulted for the Edison Electric Light Company
from 1881-1891, and subsequently for the Marconi Wireless Telegraph Company.
In 1901 Fleming designed the transmitter used by
Guglielmo Marconi in the rst transmission of radio
waves across the Atlantic from Poldhu, England, to Nova
Scotia, Canada. The distance between the two points

Thermionic diode valves derived from the Fleming valve, from

the 1930s (left) to the 1970s (right)

The receiver for the transatlantic demonstration employed a coherer, which had poor sensitivity and degraded
the tuning of the receiver. This led Fleming to look for
a detector which was more sensitive and reliable while
at the same time being better suited for use with tuned
circuits.[2][3] In 1904 Fleming tried an Edison eect bulb
for this purpose, and found that it worked well to rectify high frequency oscillations and thus allow detection
of the rectied signals by a galvanometer. On November
16, 1904, he applied for a US patent for what he termed
an oscillation valve. This patent was subsequently issued
as number 803,684 and found immediate utility in the
detection of messages sent by Morse code.

17.2.1 Oscillation valves

The Fleming valve proved to be the start of a technological revolution. After reading Flemings 1905 paper on
his oscillation valve, American engineer Lee DeForest in
1906 created a three-element vacuum tube, the Audion,
by adding a wire grid between cathode and anode. It was
the rst electronic amplifying device, allowing the creation of ampliers and continuous wave oscillators. De
Forest quickly rened his device into the triode, which
became the basis of long-distance telephone and radio
communications, radars, and early digital computers for
50 years, until the advent of the transistor in the 1960s.
Fleming sued De Forest for infringing his valve patents,
resulting in decades of expensive and disruptive litigation,
which were not settled until 1943 when the United States
Supreme Court ruled Flemings patent invalid.[4]

17.4. EXTERNAL LINKS

17.2.2

Power applications

Later, when vacuum tube equipment began to be powered

from wall power by transformers instead of batteries, the
Fleming valve was developed into a rectier to produce
the DC plate (anode) voltage required by other vacuum
tubes. Around 1914 Irving Langmuir at General Electric developed a high voltage version called the Kenotron
which was used to power x-ray tubes. As a rectier, the
tube was used for high voltage applications but its high
internal resistance made it inecient in low voltage, high
current applications. Until vacuum tube equipment was
replaced by transistors in the 1970s, radios and televisions
usually had one or more diode tubes.

17.3 References and notes

17.3.1

109
U.S. Patent 1,306,208, Jun 10, 1919 : Fleming valve
circuit improvement by R. A. Weagant
U.S. Patent 1,338,889, May 4, 1920 : Fleming valve
improvement by R. A. Weagant
U.S. Patent 1,347,894, Jul 27, 1920 : Inverter converter by L. W. Chubb
U.S. Patent 1,380,206, May 31, 1921 : Fleming
valve improvement by R. A. Weagant
U.S. Patent RE16,363, Jun 15, 1926 : Inverter converter by L. W. Chubb
U.S. Patent 1,668,060, May 1, 1928 : Fleming valve
circuit improvement by P. E. Edelman
U.S. Patent 2,472,760, Jun 7, 1949 : Electrode improvement by H. L. Ratchford

Citations

[1] "Milestones:Fleming Valve, 1904. IEEE Global History

Network. IEEE. Retrieved 29 July 2011.

17.4 External links

[2] Radio Communications: A Brief Synopsis

IEEE History Center

[3] John Ambrose Fleming (1849-1945) By W A Atherton,

Published in Wireless World August 1990

November 1904: Fleming discovers the thermionic

(or oscillation) valve, or 'diode'

[4] The Supreme Court invalidated the patent because of an

improper disclaimer and later maintained the technology
in the patent was known art when led. For more see,
Misreading the Supreme Court: A Puzzling Chapter in
the History of Radio. Mercurians.org.

17.3.2

Patents

Issued
U.S. Patent 803,684 - Instrument for converting alternating electric currents into continuous currents
(Fleming valve patent)
Cited by
U.S. Patent 1,290,438, Jan 7, 1910 : Fleming valve
improvement by R. A. Weagant
U.S. Patent 954,619, Apr 12, 1910 : John Ambrose
Fleming patent
U.S. Patent 1,379,706, Mar 10, 1917 : Fleming
valve improvement by R. A. Weagant
U.S. Patent 1,252,520, Jan 8, 1918 : Fleming valve
improvement by R. A. Weagant
U.S. Patent 1,278,535, Sep 10, 1918 : Fleming
valve improvement by R. A. Weagant
U.S. Patent 1,289,981, Dec 31, 1918 : Fleming
valve improvement by R. A. Weagant

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Chapter 18

Continuous wave
A continuous wave or continuous waveform (CW)
is an electromagnetic wave of constant amplitude and
frequency; a sine wave. In mathematical analysis, it
is considered to be of innite duration. Continuous
wave is also the name given to an early method of
radio transmission, in which a sinusoidal carrier wave is
switched on and o. Information is carried in the varying
duration of the on and o periods of the signal, for example by Morse code in early radio. In early wireless telegraphy radio transmission, CW waves were also known
as undamped waves, to distinguish this method from
damped wave transmission as eected by early spark gap
style transmitters.

18.1 Radio
Very early radio transmitters used a spark gap to produce radio-frequency oscillations in the transmitting antenna. The signals produced by these spark-gap transmitters consisted of strings of brief pulses of sinusoidal
radio frequency oscillations which died out rapidly to
zero, called damped waves. The disadvantage of damped
waves was that their energy was spread over an extremely
wide band of frequencies; they had wide bandwidth. As a
result they produced electromagnetic interference (RFI)
that spread over the transmissions of stations at other frequencies.

unbroken continuous sine wave theoretically has no

bandwidth; all its energy is concentrated at a single
frequency, so it doesn't interfere with transmissions
on other frequencies. Continuous waves could not be
produced with an electric spark, but were achieved with
the vacuum tube electronic oscillator, invented around
1913 by Edwin Armstrong and Alexander Meissner. In
order to transmit information, the continuous wave must
be turned o and on with a telegraph key to produce the
dierent length pulses, dots and dashes, that spell
out text messages in Morse code, so a continuous wave
radiotelegraphy signal consists of pulses of sine waves
with a constant amplitude interspersed with gaps of no
signal. Damped wave spark transmitters were replaced
by continuous wave vacuum tube transmitters around
1920, and damped wave transmissions were nally
outlawed in 1934.

18.1.1 Key clicks

Not to be confused with Hammond organ Key click.
In on-o carrier keying, if the carrier wave is turned on
or o abruptly, communications theory can show that the
bandwidth will be large; if the carrier turns on and o
more gradually, the bandwidth will be smaller. The bandwidth of an on-o keyed signal is related to the data transmission rate as: Bn = BK where Bn is the necessary
bandwidth in hertz, B is the keying rate in signal changes
per second (baud rate), and K is a constant related to the
expected radio propagation conditions; K=1 is dicult
for a human ear to decode, K=3 or K=5 is used when
fading or multipath propagation is expected. [1] What is
transmitted in the extra bandwidth used by a transmitter
that turns on/o more abruptly is known as key clicks.
Certain types of power ampliers used in transmission
may increase the eect of key clicks.

This motivated eorts to produce radio frequency oscillations that decayed more slowly; had less damping. There
is an inverse relation between the rate of decay (the time
constant) of a damped wave and its bandwidth; the longer
the damped waves take to decay toward zero, the narrower the frequency band the radio signal occupies, so
the less it interferes with other transmissions. As more
transmitters began crowding the radio spectrum, reducing the frequency spacing between transmissions, government regulations began to limit the maximum damping
or decrement a radio transmitter could have. Manufac- The rst transmitters capable of producing continuous
turers produced spark transmitters which generated long wave, the Alexanderson alternator and vacuum tube
oscillators, became widely available after World War I.
ringing waves with minimal damping.
It was realized that the ideal radio wave for Early radio transmitters could not be modulated to transradiotelegraphic communication would be a sine mit speech, and so CW radio telegraphy was the only
wave with zero damping, a continuous wave. An form of communication available. CW still remains a
110

18.3. LASER PHYSICS

111

18.3 Laser physics

In laser physics and engineering, continuous wave or
CW refers to a laser that produces a continuous output beam, sometimes referred to as free-running, as
opposed to a q-switched, gain-switched or modelocked
laser, which has a pulsed output beam.

18.4 See also

A commercially manufactured paddle for use with electronic
keyer to generate Morse code

Amplitude modulation
The CW Operators Club
Damped wave

viable form of radio communication, many years after

voice transmission was perfected, because simple transmitters could be used, and because its signals are the form
of modulation best able to penetrate interference. The
low bandwidth of the code signal, due in part to low information transmission rate, allowed very selective lters
to be used in the receiver which blocked out much of the
atmospheric noise that would otherwise reduce the intelligibility of the signal.
Continuous-wave radio was called radiotelegraphy because like the telegraph, it worked by means of a simple
switch to transmit Morse code. However, instead of controlling the electricity in a cross-country wire, the switch
controlled the power sent to a radio transmitter. This
mode is still in common use by amateur radio operators.
In military communications and amateur radio, the terms
CW and Morse code are often used interchangeably,
despite the distinctions between the two. Morse code may
be sent using direct current in wires, sound, or light, for
example. A carrier wave is keyed on and o to represent the dots and dashes of the code elements. The carriers amplitude and frequency remains constant during
each code element. At the receiver, the received signal is mixed with a heterodyne signal from a BFO (beat
frequency oscillator) to change the radio frequency impulses to sound. Though most commercial trac has now
ceased operation using Morse it is still popular with amateur radio operators. Non-directional beacons used in air
navigation use Morse to transmit their identier.

18.2 Radar
A continuous-wave radar system is one where a continuous wave is transmitted by one aerial while a second aerial
receives the reected radio energy.

On-o keying
Tikker
Types of radio emissions

18.5 References
[1] L. D. Wolfgang, C. L. Hutchinson (ed) The ARRL Handbook for Radio Amateurs, Sixty Eighth Edition, (ARRL,
1991) ISBN 0-87259-168-9, pages 9-8, 9-9

CW Bandwidth Described

Chapter 19

Alexanderson alternator
transmit sound. Eorts were made to invent transmitters
that would produce continuous waves, a sinusoidal alternating current at a single frequency.
In an 1891 lecture, Frederick Thomas Trouton pointed
out that, if an electrical alternator were run at a great
enough cycle speed (that is, if it turned fast enough
and was built with a large enough number of magnetic
poles on its armature) it would generate continuous waves
at radio frequency.[2] Starting with Elihu Thomson in
1889,[3][4][5][6] a series of researchers built high frequency
alternators, Nikola Tesla[7][8] (1891, 15 kHz), Salomons
and Pyke[8] (1891, 9 kHz), Parsons and Ewing (1892,
14 kHz.), Siemens[8] (5 kHz), B. G. Lamme[8] (1902, 10
kHz), but none was able to reach the frequencies required
for radio transmission, above 20 kHz.[5]

Alexanderson Alternator in the Grimeton VLF transmitter.

An Alexanderson alternator is a rotating machine invented by Ernst Alexanderson in 1904 for the generation
of high-frequency alternating current for use as a radio
transmitter. It was one of the rst devices capable of generating the continuous radio waves needed for transmission of amplitude modulation (sound) by radio. It was
used from about 1910 in a few superpower longwave
radiotelegraphy stations to transmit transoceanic message
trac by Morse code to similar stations all over the world.
Although obsolete by the early 1920s due to the development of vacuum-tube transmitters, the Alexanderson
alternator continued to be used until World War 2. It is
on the list of IEEE Milestones as a key achievement in
Alexanderson 200-kW motor-alternator set installed at the US
electrical engineering.[1]
Navys New Brunswick, NJ station, 1920.

19.1 History
19.1.1

19.1.2 Construction

Prior developments

After radio waves were discovered in 1887, the rst generation of radio transmitter, the spark gap transmitters,
produced strings of damped waves, pulses of radio waves
which died out to zero quickly. By the 1890s it was realized that damped waves had disadvantages; their energy
was spread over a broad frequency bandwidth so transmitters on dierent frequencies interfered with each other,
and they could not be modulated with an audio signal to

In 1904, Reginald Fessenden contracted with General

Electric for an alternator that generated a frequency of
100,000 hertz for continuous wave radio. The alternator was designed by Ernst Alexanderson. The Alexanderson alternator was extensively used for long-wave radio
communications by shore stations, but was too large and
heavy to be installed on most ships. In 1906 the rst
50-kilowatt alternators were delivered. One was to Reginald Fessenden at Brant Rock, Massachusetts, another to
John Hays Hammond, Jr. in Gloucester, Massachusetts

112

19.2. DESIGN

113

and another to the American Marconi Company in New

Brunswick, New Jersey.
Alexanderson would receive a patent in 1911 for his device. The Alexanderson alternator followed Fessendens
rotary spark-gap transmitter as the second radio transmitter to be modulated to carry the human voice. Until
the invention of vacuum-tube (valve) oscillators in 1913
such as the Armstrong oscillator, the Alexanderson alternator was an important high-power radio transmitter, and
allowed amplitude modulation radio transmission of the
human voice. The last remaining operable Alexanderson
alternator is at the VLF transmitter Grimeton in Sweden
Rotor of 200 kW alternator
and was in regular service until 1996. It continues to be
operated for a few minutes on Alexanderson Day, which
is either the last Sunday in June or rst Sunday in July
every year.

19.1.3

Stations

19.1.4

US Navy stations

Starting in 1942 four stations were operated by US Navy:

the station at Haiku, Hawaii until 1958, Bolinas until
1946, Marion, and Tuckerton (both until 1948). Two alternators were shipped to Hawaii in 1942, one each from
Marion, MA and Bolinas, CA. Haiku received one. The
other went to Guam but returned to Haiku after World
War 2. Haiku began operation of the rst 200 kW alternator in 1943. The second alternator went into operation at Haiku in 1949. Both alternators were sold for
salvage in 1969, possibly to Kreger Company of California. The Marion station was transferred in 1949 to the
US Air Force and used until 1957 for the transmission of
weather forecasts to the arctic as well as for the Basen to
Greenland, Labrador, and Iceland. One of the alternators was scrapped in 1961 and another one was handed
over to the US oce of standard, it now resides in a
Smithsonian Institution warehouse. The two machines in
Brazil were never used because of organizational problems there. They were returned to Radio Central after
1946.

Closeup of above rotor. It has 300 narrow slots cut through the
rotor. The teeth between the slots are the magnetic poles of the
machine.

The machine operates by variable reluctance (similar to

an electric guitar pickup), changing the magnetic ux
linking two coils. The periphery of the rotor is embraced
by a circular iron stator with a C-shaped cross-section,
divided into narrow poles, the same number as the rotor
has, carrying two sets of coils. One set of coils is energized with direct current and produces a magnetic eld in
the air gap in the stator, which passes axially (sideways)
through the rotor.

As the rotor turns, alternately either an iron section of

the disk is in the gap between each pair of stator poles,
allowing a high magnetic ux to cross the gap, or else a
non-magnetic slot is in the stator gap, allowing less magnetic ux to pass. Thus the magnetic ux through the
19.2 Design
stator varies sinusoidally at a rapid rate. These changes
in ux induce a radio-frequency voltage in a second set
The Alexanderson alternator works similarly to an AC of coils on the stator.
electric generator, but generates higher-frequency current, in the radio range. The rotor has no conductive The RF collector coils are all interconnected by an outwindings or electrical connections; it consists of a solid put transformer, whose secondary winding is connected
disc of high tensile strength magnetic steel, with narrow to the antenna circuit. Modulation or telegraph keying of
slots cut in its circumference to create a series of nar- the radio frequency energy was done by a magnetic amrow teeth that function as magnetic poles. The space plier, which was also used for amplitude modulation and
between the teeth is lled with nonmagnetic material, to voice transmissions.
give the rotor a smooth surface to decrease aerodynamic The frequency of the current generated by an Alexandrag. The rotor is turned at a high speed by an electric derson alternator in hertz is the product of the number
of rotor poles and the revolutions per second. Higher
motor.

114

CHAPTER 19. ALEXANDERSON ALTERNATOR

radio frequencies thus require more poles, a higher rotational speed, or both. Alexanderson alternators were
used to produce radio waves in the very low frequency
(VLF) range, for transcontinental wireless communication. A typical alternator with an output frequency of 100
kHz had 300 poles and rotated at 20,000 revolutions per
minute (RPM) (330 revolutions per second). To produce
high power, the clearance between the rotor and stator
had to be kept to only 1 mm. The manufacture of precision machines rotating at such high speeds presented
many new problems, and Alexanderson transmitters were
bulky and very expensive.

19.2.1

Frequency control

The output frequency of the transmitter is proportional

to the speed of the rotor. To keep the frequency constant, the speed of the electric motor turning it was controlled with a feedback loop. In one method, a sample
of the output signal is applied to a high-Q tuned circuit,
whose resonant frequency is slightly above the output frequency. The generators frequency falls on the skirt of
the LC circuits impedance curve, where the impedance
increases rapidly with frequency. The output of the LC
circuit is rectied, and the resulting voltage is compared
with a constant reference voltage to produce a feedback
signal to control the motor speed. If the output frequency
gets too high, the impedance presented by the LC circuit increases, and the amplitude of the RF signal getting
through the LC circuit drops. The feedback signal to the
motor drops, and the motor slows down. Thus the alternator output frequency is locked to the tuned circuit
resonant frequency.

19.3 Performance advantages

A large Alexanderson alternator might produce 500 kW
of output radio-frequency energy and would be water- or
oil-cooled. One such machine had 600 pole pairs in the
stator winding, and the rotor was driven at 2170 RPM, for
an output frequency near 21.7 kHz. To obtain higher frequencies, higher rotor speeds were required, up to 20,000
RPM.
Along with the arc converter invented in 1903, the
Alexanderson alternator was one of the rst radio transmitters that generated continuous waves. In contrast,
the earlier spark-gap transmitters generated a string of
damped waves. These were electrically noisy"; the energy of the transmitter was spread over a wide frequency
range, so they interfered with other transmissions and operated ineciently. With a continuous-wave transmitter, all of the energy was concentrated within narrow
frequency band, so for a given output power they could
communicate over longer distances. In addition, continuous waves could be modulated with an audio signal to

carry sound. The Alexanderson alternator was one of the

rst transmitters to be used for AM transmission.
The Alexanderson alternator produced purer continuous waves than the arc converter, whose nonsinusoidal
output generated signicant harmonics, so the alternator
was preferred for long-distance telegraphy.

19.4 Disadvantages
Because of the extremely high rotational speed compared
to a conventional alternator, the Alexanderson alternator required continuous maintenance by skilled personnel. Ecient lubrication and oil or water cooling was essential for reliability which was dicult to achieve with
the lubricants available at the time. In fact, early editions
of the British Navys Admiralty Handbook of Wireless
Telegraphy cover this in considerable detail, mostly as an
explanation as to why The Navy did not use that particular technology. However, the US Navy did.
Other major problems were that changing the operating frequency was a lengthy and complicated process,
and unlike a spark transmitter, the carrier signal could
not be switched on and o at will. The latter problem
greatly complicated listening through (that is, stopping
the transmission to listen for any answer). There was also
the risk that it would allow enemy vessels to detect the
presence of the ship.
Because of the limits of the number of poles and rotational speed of a machine, the Alexanderson alternator is
at most capable of transmission in the lower mediumwave
band, with shortwave and upper bands being physically
impossible.

19.5 See also

Alexanderson Day
Tonewheel
Resolver (electrical)

19.6 Notes
[1] "Milestones:Alexanderson Radio Alternator, 1904.
IEEE Global History Network. IEEE. Retrieved 29 July
2011.
[2] earlyradiohistory.us 1892alt.htm
[3] Prof. Thomsons new alternating generator. The Electrical Engineer. Electrical Engineer Co. 11 (154): 437.
April 15, 1891. Retrieved April 18, 2015.
[4] Thomson, Elihu (September 12, 1890). letter. The
Electrician. London. 25: 529530. Retrieved April 18,
2015.

19.8. EXTERNAL LINKS

[5] Aitken, Hugh G.J. (2014). The Continuous Wave: Technology and American Radio, 1900-1932. Princeton Univ.
Press. p. 53. ISBN 1400854601.
[6] Fessenden, R. A. (1908). Wireless Telephony. Annual
Report of the Smithsonian Institution. Government Printing Oce: 172. Retrieved April 18, 2015.
[7] U.S. Patent 447,920, Nikola Tesla "Method of Operating
Arc-Lamps" (March 10, 1891)
[8] Fleming, John Ambrose (1910). The principles of electric
wave telegraphy and telephony, 2nd Ed. London: Longmans, Green and Co. pp. 510.

19.7 References
Antique Wireless Association - column edited by
Frank Lotito
David E. Fisher and Marshall J. Fisher, Tube, the
Invention of Television Counterpoint, Washington
D.C. USA, (1996) ISBN 1-887178-17-1
Hammond, John Winthrop. Men and Volts, the Story
of General Electric. Philadelphia & New York: J. B.
Lippincot (1941), pp. 349-352, 372.
Notes from the Navy Institute proceedings 1952
from M.G. Abernathy les.
Letter to M.G. Abernathy from G. Warren Clark
Captain USNR (Ret)
Letter to Mr. Mayes from Lt. Francis J. Kishima
Commanding Ocer USCG Omega Station Hawaii
Milestones:Yosami Radio Transmitting Station,
1929
E. F. W. Alexanderson, U.S. Patent 1,008,577 High
Frequency Alternator
N. Tesla, U.S. Patent 447,921

19.8 External links

Description of the 200 kW alternator at New
Brunswick
Alexanderson Alternators at Haiku Valley Oahu
Alexanderson Alternators at Marion, Massachusetts

115

Chapter 20

Lee de Forest
Lee de Forest (August 26, 1873 June 30, 1961) was
an American inventor, self-described Father of Radio, and a pioneer in the development of sound-on-lm
recording used for motion pictures. He had over 180
patents, but also a tumultuous careerhe boasted that
he made, then lost, four fortunes. He was also involved
in several major patent lawsuits, spent a substantial part
of his income on legal bills, and was even tried (and acquitted) for mail fraud. His most famous invention, in
1906, was the three-element "Audion" (triode) vacuum
tube, the rst practical amplication device. Although De
Forest had only a limited understanding of how it worked,
it was the foundation of the eld of electronics, making possible radio broadcasting, long distance telephone
lines, and talking motion pictures, among countless other
applications.

to become a famousand richinventor, and perpetually short of funds, he sought to interest companies with a
series of devices and puzzles he created, and expectantly
submitted essays in prize competitions, all with little success.
After completing his undergraduate studies, in September, 1896 de Forest began three years of postgraduate
work. However, his electrical experiments had a tendency to blow fuses, causing building-wide blackouts.
Even after being warned to be more careful, he managed
to douse the lights during an important lecture by Professor Charles Hastings, who responded by having de Forest
expelled from Sheeld.

With the outbreak of the SpanishAmerican War in

1898, de Forest enrolled in the Connecticut Volunteer
Militia Battery as a bugler, but the war ended and he
was mustered out without ever leaving the state. He then
completed his studies at Yales Sloane Physics Labora20.1 Early life
tory, earning a Doctorate in 1899 with a dissertation on
the Reection of Hertzian Waves from the Ends of ParLee de Forest was born in 1873 in Council Blus, Iowa, allel Wires, supervised by theoretical physicist Willard
the son of Anna Margaret (ne Robbins) and Henry Swift Gibbs.[3]
DeForest.[1][2] He was a direct descendant of Jess de
Forest, the leader of a group of Walloon Huguenots who
ed Europe in the 17th Century due to religious persecu20.2 Early radio work
tion.
De Forests father was a Congregational Church minister
who hoped his son would also become a pastor. In 1879
the elder de Forest became president of the American
Missionary Associations Talladega College in Talladega,
Alabama, a school open to all of either sex, without regard to sect, race, or color, and which primarily educated
African-Americans. Many of the local white citizens resented the school and its mission, and Lee spent most of
his youth in Talladega isolated from the white community, with several close friends among the black children
of the town.

De Forest was convinced there was a great future in radiotelegraphic communication (then known as "wireless
telegraphy"), but Italian Guglielmo Marconi, who received his rst patent in 1896, was already making impressive progress in both Europe and the United States.
One drawback to Marconis approach was his use of a
coherer as a receiver, which, while providing for permanent records, was also slow (after each received Morse
code dot or dash, it had to be tapped to restore operation), insensitive, and not very reliable. De Forest was
determined to devise a better system, including a selfrestoring detector that could receive transmissions by ear,
thus making it capable of receiving weaker signals and
also allowing faster Morse code sending speeds.

De Forest prepared for college by attending Mount Hermon Boys School in Mount Hermon, Massachusetts for
two years, beginning in 1891. In 1893, he enrolled in a
three-year course of studies at Yale University's Sheeld
Scientic School in New Haven, Connecticut, on a $300 After making unsuccessful inquiries about employment
per year scholarship that had been established for rela- with Nikola Tesla and Marconi, de Forest struck out on
tives of David de Forest. Convinced that he was destined his own. His rst job after leaving Yale was with the
116

20.3. AMERICAN DE FOREST WIRELESS TELEGRAPH COMPANY

De Forest, some time between 1914 and 1922, with two of his
Audions, a small 1 watt receiving tube (left), and a later 250-watt
transmitting power tube (right), which he called an oscillion.

Western Electric Companys telephone lab in Chicago,

Illinois. While there he developed his rst receiver, which
was based on ndings by two German scientists, Drs. A.
Neugschwender and Emil Aschkinass. Their original design consisted of a mirror in which a narrow, moistened
slit had been cut through the silvered back. Attaching
a battery and telephone receiver, they could hear sound
changes in response to radio signal impulses. De Forest,
along with Ed Smythe, a co-worker who provided nancial and technical help, developed variations they called
responders.

117

The race eort turned out to be an almost total failure. The Freeman transmitter broke down in a t of
rage, de Forest threw it overboard and had to be replaced by an ordinary spark coil. Even worse, the American Wireless Telephone and Telegraph Company, which
claimed its ownership of Amos Dolbear's 1886 patent for
wireless communication meant it held a monopoly for all
wireless communication in the United States, had also
set up a powerful transmitter. None of these companies had eective tuning for their transmitters, so only
one could transmit at a time without causing mutual interference. Although an attempt was made to have the
three systems avoid conicts by rotating operations over
ve-minute intervals, the agreement broke down, resulting in chaos as the simultaneous transmissions clashed
with each other.[5] De Forest ruefully noted that under
these conditions the only successful wireless communication was done by visual semaphore wig-wag ags.[6]
(The 1903 International Yacht races would be a repeat
of 1901 Marconi worked for the Associated Press, de
Forest for the Publishers Press Association, and the unaliated International Wireless Company (successor to
1901s American Wireless Telephone and Telegraph) operated a high-powered transmitter that was primarily used
to drown out the other two.) [7]

20.3 American De Forest Wireless

Telegraph Company
Despite this setback, de Forest remained in the New York
City area, in order to raise interest in his ideas and capital to replace the small working companies that had been
formed to promote his work thus far. In January, 1902
he met a promoter, Abraham White, who would become
de Forests main sponsor for the next ve years. White
envisioned bold and expansive plans that enticed the inventor however, he was also dishonest and much of
the new enterprise would be built on wild exaggeration
and stock fraud. To back de Forests eorts, White incorporated the American DeForest Wireless Telegraph
Company, with himself as the companys president, and
de Forest the Scientic Director. The company claimed
as its goal the development of world-wide wireless.

A series of short-term positions followed, including three

unproductive months with Professor Johnsons American
Wireless Telegraph Company in Milwaukee, Wisconsin,
and work as an assistant editor of the Western Electrician
in Chicago. With radio research his main priority, de Forest next took a night teaching position at the Lewis Institute, which freed him to conduct experiments at the Armour Institute.[4] By 1900, using a spark-coil transmitter
and his responder receiver, de Forest expanded his transmitting range to about seven kilometers (four miles). Professor Clarence Freeman of the Armour Institute became The original responder receiver (also known as the goo
interested in de Forests work and developed a new type anti-coherer) proved to be too crude to be commercialized, and de Forest struggled to develop a non-infringing
of spark transmitter.
De Forest soon felt that Smythe and Freeman were hold- device for receiving radio signals. In 1903, Reginald
ing him back, so in the fall of 1901 he made the bold Fessenden demonstrated an electrolytic detector, and de
decision to go to New York to compete directly with Forest developed a variation, which he called the spade
Marconi in transmitting race results for the International detector, claiming it did not infringe on Fessendens
Yacht races. Marconi had already made arrangements to patents. Fessenden, and the U.S. courts, did not agree,
provide reports for the Associated Press, which he had and court injunctions enjoined American De Forest from
successfully done for the 1899 contest. De Forest con- using the device.
tracted to do the same for the smaller Publishers Press Meanwhile, White set in motion a series of highly visiAssociation.
ble promotions for American DeForest: Wireless Auto

118

CHAPTER 20. LEE DE FOREST

along the Atlantic Coast and Great Lakes, and equipped
shipboard stations. But the main focus was selling stock
at ever more inated prices, spurred by the construction
of promotional inland stations. Most of these inland stations had no practical use and were abandoned once the
local stock sales slowed.
De Forest eventually came into conict with his companys management. His main complaint was the limited
support he got for conducting research, while company
ocials were upset with de Forests inability to develop
a practical receiver free of patent infringement. (This
problem was nally resolved with the invention of the
carborundum crystal detector by another company employee, General H. H. Dunworthy).[10] On November 28,
1906, in exchange for $1000 (half of which was claimed
by an attorney) and the rights to some early Audion detector patents, de Forest turned in his stock and resigned
from the company that bore his name. American DeForest was then reorganized as the United Wireless Telegraph Company, and would be the dominant U.S. radio
communications rm, albeit propped up by massive stock
fraud, until its bankruptcy in 1912.

20.4 Radio Telephone Company

American DeForest Wireless Telegraph Companys observation

tower, 1904 Louisiana Purchase Exposition at Saint Louis, Missouri

De Forest moved quickly to re-establish himself as an independent inventor, working in his own laboratory in the
Parker Building in New York City. The Radio Telephone
Company was incorporated in order to promote his inventions, with James Dunlop Smith, a former American DeForest salesman, as president, and de Forest the vice president. (De Forest preferred the term "radio", which up to
now had been primarily used in Europe, over "wireless".)

20.4.1 Arc radiotelephone development

No.1 was positioned on Wall Street to send stock

quotes using an unmued spark transmitter to loudly
draw the attention of potential investors, in early 1904
two stations were established at Wei-hai-Wei on the
Chinese mainland and aboard the Chinese steamer SS
Haimun, which allowed war correspondent Captain Lionel James of The Times of London to report on the brewing Russo-Japanese War,[8] and later that year a tower,
with DEFOREST arrayed in lights, was erected on the
grounds of the Louisiana Purchase Exposition in Saint
Louis, Missouri, where the company won a gold medal
for its radiotelegraph demonstrations. (Marconi withdrew from the Exposition when he learned de Forest
would be there).[9]
The companys most important early contract was the
construction, in 1905-1906, of ve high-powered radiotelegraph stations for the U.S. Navy, located in
Panama, Pensacola and Key West, Florida, Guantanamo,
Cuba, and Puerto Rico. It also installed shore stations

Ohio Historical Marker. On July 18, 1907 Lee de Forest transmitted the rst ship-to-shore messages that were sent by radiotelephone

At the 1904 Louisiana Purchase Exposition, Valdemar

20.4. RADIO TELEPHONE COMPANY

Poulsen had presented a paper on a new type of transmitter, known as an arc set, which, unlike the discontinuous pulses produced by spark transmitters, created steady continuous wave signals that could be used
for amplitude modulated (AM) full audio transmissions.
Although Poulsen had patented his invention, de Forest
claimed to have come up with a variation that allowed him
to avoid infringing on Poulsens work. Using his sparkless arc transmitter, de Forest rst transmitted audio
across a lab room on December 31, 1906, and by February was making experimental transmissions, including
music produced by Thaddeus Cahill's telharmonium, that
were heard throughout the city.

119
of the earliest experimental entertainment radio broadcasts. Eugenia Farrar sang I Love You Truly in an unpublicized test from his laboratory in 1907, and in 1908,
on de Forests Paris honeymoon, musical selections were
broadcast from the Eiel Tower as a part of demonstrations of the arc-transmitter. In early 1909, in what may
have been the rst public speech by radio, de Forests
mother-in-law, Harriot Stanton Blatch, made a broadcast
supporting womens surage.[13]
More ambitious demonstrations followed. A series of
tests in conjunction with the Metropolitan Opera House
in New York City were conducted to determine whether
it was practical to broadcast opera performances live
from the stage. Tosca was performed on January 12,
1910, and the next days test included Italian tenor Enrico
Caruso.[14][15] On February 24, the Manhattan Opera
Companys Mme. Mariette Mazarin sang La Habanera
from Carmen over a transmitter located in De Forests
lab.[16] But these tests showed that the idea was not yet
technically feasible, and de Forest would not make any
additional entertainment broadcasts until late 1916, when
more capable vacuum-tube equipment became available.

On July 18, 1907, de Forest made the rst ship-to-shore

transmissions by radiotelephone race reports for the
Annual Inter-Lakes Yachting Association (I-LYA) Regatta held on Lake Erie which were sent from the
steam yacht Thelma to his assistant, Frank E. Butler, located in the Foxs Dock Pavilion on South Bass Island.[11]
De Forest also interested the U.S. Navy in his radiotelephone, which placed a rush order to have 26 arc sets installed for its Great White Fleet around-the-world voyage
that began in late 1907. However, at the conclusion of the
circumnavigation the sets were declared to be too unreliable to meet the Navys needs and removed.[12]
20.4.3 Grid Audion detector
The company set up a network of radiotelephone stations
along the Atlantic coast and the Great Lakes, for coastal Main article: Audion
ship navigation. However, the installations proved unprotable, and by 1911 the parent company and its sub- De Forests most famous invention was the grid Audion,
sidiaries were on the brink of bankruptcy.
which was the rst successful three-element (triode)

20.4.2

Initial broadcasting experiments

vacuum tube, and the rst device which could amplify

electrical signals. He traced its inspiration to 1900, when,
experimenting with a spark-gap transmitter, he briey
thought that the ickering of a nearby gas ame might be
in response to electromagnetic pulses. With further tests
he soon determined that the cause of the ame uctuations actually was due to air pressure changes produced
by the loud sound of the spark.[17] Still, he was intrigued
by the idea that, properly congured, it might be possible
to use a ame or something similar to detect radio signals.

After determining that an open ame was too susceptible

to ambient air currents, de Forest investigated whether
ionized gases, heated and enclosed in a partially evacuated glass tube, could be used instead. In 1905 to 1906 he
developed various congurations of glass-tube devices,
which he gave the general name of Audions. The rst
Audions had only two electrodes, and on October 25,
1906,[18] de Forest led a patent for diode vacuum tube
detector, that was granted U.S. patent number 841387 on
January 15, 1907. Subsequently, a third control electrode was added, originally as a surrounding metal cylinder or a wire coiled around the outside of the glass tube.
[19]
February 24, 1910 radio broadcast by Mme. Mariette Mazarin None of these initial designs worked particularly well.
of the Manhattan Opera Company. From page 333 of the August De Forest gave a presentation of his work to date to the
October 26, 1906 New York meeting of the American
1922 issue of Radio Broadcast.
Institute of Electrical Engineers, which was reprinted in
De Forest also used the arc-transmitter to conduct some two parts in late 1907 in the Scientic American Supple-

120
ment.[20] He was insistent that a small amount of residual gas was necessary for the tubes to operate properly.
However, he also admitted that I have arrived as yet at
no completely satisfactory theory as to the exact means by
which the high-frequency oscillations aect so markedly
the behavior of an ionized gas.

CHAPTER 20. LEE DE FOREST

not have the funds needed to renew them).[22]
Because of its limited uses and the great variability in
the quality of individual units, the grid Audion would be
rarely used during the rst half-decade after its invention.
In 1908, John V. L. Hogan reported that The Audion is
capable of being developed into a really ecient detector, but in its present forms is quite unreliable and entirely
too complex to be properly handled by the usual wireless
operator.[23]

20.5 Employment at Federal Telegraph

De Forest grid Audion from 1906.

In late 1906, de Forest made a breakthrough when he recongured the control electrode, changing it from outside
the glass to a zig-zag wire inside the tube, positioned in
the center between the cathode "lament" and the anode
"plate" electrodes. He reportedly called the zig-zag control wire a "grid" due to its similarity to the gridiron
lines on American football playing elds.[21] Experiments
conducted with his assistant, John V. L. Hogan, convinced him that he had discovered an important new radio detector, and he quickly prepared a patent application
which was led on January 29, 1907, and received U.S.
patent number 879,532 on February 18, 1908. Because
the grid-control Audion was the only conguration to become commercially valuable, the earlier versions were
forgotten, and the term Audion later became synonymous with just the grid type. It later also became known
as the triode.
The grid Audion was the rst device to amplify, albeit
only slightly, the strength of received radio signals. However, to many observers it appeared that de Forest had
done nothing more than add the grid electrode to an existing detector conguration, the Fleming valve, which also
consisted of a lament and plate enclosed in an evacuated
glass tube. De Forest passionately denied the similarly of
the two devices, claiming his invention was a relay that
amplied currents, while the Fleming valve was merely a
rectier that converted alternating current to direct current. (For this reason, de Forest objected to his Audion
being referred to as a valve.) The U.S. courts were not
convinced, and ruled that the grid Audion did in fact infringe on the Fleming valve patent, now held by Marconi.
On the other hand, Marconi admitted that the addition of
the third electrode was a patentable improvement, and the
two sides agreed to license each other so that both could
manufacture three-electrode tubes in the United States.
(De Forests European patents had lapsed because he did

California Historical Landmark No. 836, located at the eastern

corner of Channing Street and Emerson Avenue in Palo Alto, California, stands at the former location of the Federal Telegraph
laboratory, and references Lee de Forests development there, in
19111913, of the rst vacuum-tube amplier and oscillator.

In May 1910, the Radio Telephone Company and its subsidiaries were reorganized as the North American Wireless Corporation, but nancial diculties meant that the
companys activities had nearly come to a halt. De Forest
moved to San Francisco, California, and in early 1911
took a research job at the Federal Telegraph Company,
which produced long-range radiotelegraph systems using
high-powered Poulsen arcs.

20.5.1 Audio frequency amplication

One of de Forests areas of research at Federal Telegraph
was improving the reception of signals, and he came up
with the idea of strengthening the audio frequency output
from a grid Audion by feeding it into a second tube for
additional amplication. He called this a cascade amplier, which eventually consisted of chaining together up
to three Audions.
At this time the American Telephone and Telegraph
Company was researching ways to amplify telephone signals to provide better long-distance service, and it was

20.6. REORGANIZED RADIO TELEPHONE COMPANY

recognized that de Forests device had potential as a telephone line repeater. In mid-1912 an associate, John
Stone Stone, contacted AT&T to arrange for de Forest
to demonstrate his invention. It was found that de Forests gassy version of the Audion could not handle even
the relatively low voltages used by telephone lines. (Due
to the way he constructed the tubes, de Forests Audions
would cease to operate with too high a vacuum.) However, careful research by Dr. Harold D. Arnold and his
team at AT&Ts Western Electric subsidiary determined
that by improving the tubes design, it could be more fully
evacuated, and the high vacuum allowed it to successfully
operate at telephone line voltages. With these changes the
Audion evolved into a modern electron-discharge vacuum
tube, using electron ows rather than ions.[24] (Dr. Irving
Langmuir at the General Electric Corporation made similar ndings, and both he and Arnold attempted to patent
the high vacuum construction, but the U.S. Supreme
Court ruled in 1931 that this modication could not be
patented).

121

Audion advertisement, Electrical Experimenter magazine, 1916

ness, and originally maintained a policy that retailers had

to require their customers to return a worn out tube before they could get a replacement. This style of business
encouraged others to make and sell unlicensed vacuum
tubes which did not impose a return policy. One of the
boldest was Audio Tron Sales Company founded in 1915
by Elmer T. Cunningham of San Francisco, whose Audio
Tron tubes cost less but were of equal or higher quality.
The de Forest company sued Audio Tron Sales, eventually settling out of court.[26]

After a delay of ten months, in July, 1913 AT&T, through

a third party who disguised his link to the telephone company, purchased the wire rights to seven Audion patents
for $50,000. De Forest had hoped for a higher payment,
but was again in bad nancial shape and was unable to
bargain for more. In 1915, AT&T used the innovation to
In April, 1917, the companys remaining commercial raconduct the rst transcontinental telephone calls, in condio patent rights were sold to AT&Ts Western Electric
junction with the Panama-Pacic International Exposisubsidiary for $250,000.[27] During World War One, the
tion at San Francisco.
Radio Telephone Company prospered from sales of radio equipment to the military. However, it also became
known for the poor quality of its vacuum tubes, especially
20.6 Reorganized Radio Telephone compared to those produced by major industrial manufacturers such as General Electric and Western Electric.

Company

Radio Telephone Company ocials had engaged in some

of the same stock selling excesses that had taken place
at American DeForest, and as part of the U.S. governments crackdown on stock fraud, in March, 1912 de Forest, plus four other company ocials, was arrested and
charged with use of the mails to defraud. Their trials
took place in late 1913, and while three of the defendants
were found guilty, de Forest was acquitted. With the legal problems behind him, de Forest reorganized his company as the DeForest Radio Telephone Company, and established a laboratory at 1391 Sedgewick Avenue in the
Highbridge section of the Bronx in New York City. The
companys limited nances were boosted by the sale, in
October 1914, of the commercial Audion patent rights
for radio signalling to AT&T for $90,000, with de Forest
retaining the rights for sales for amateur and experimental use.[25] In October, 1915 AT&T conducted test radio
transmissions from the Navys station in Arlington, Virginia that were heard as far away as Paris and Hawaii.

20.6.1 Regeneration controversy

Beginning in 1912 there was increased investigation of
vacuum-tube capabilities, simultaneously by numerous
inventors in multiple countries, who identied additional
important uses for the device. These overlapping discoveries led to complicated legal disputes over priority, perhaps the most bitter being one in the United States between de Forest and Edwin Howard Armstrong over the
discovery of regeneration (also known as the feedback
circuit and, by de Forest, as the ultra-audion).[28]

Beginning in 1913 Armstrong prepared papers and

gave demonstrations which comprehensively documented
how to employ three-element vacuum tubes in circuits
that amplied signals to stronger levels than previously
thought possible, and which could also generate high
power oscillations usable for radio transmissions. In
late 1913 Armstrong applied for patents covering the
regenerative circuit, and on October 6, 1914 U.S. patent
[29]
The Radio Telephone Company began selling Oscillion 1,113,149 was issued for his discovery.
power tubes to amateurs, suitable for radio transmissions. U.S. patent law included a provision for challenging
The company wanted to keep a tight hold on the tube busi- grants if another inventor could prove prior discovery.

122
With an eye on increasing the value of the patent portfolio that would be sold to Western Electric in 1917, beginning in 1915 de Forest led a series of patent applications that largely copied Armstrongs claims, in the hopes
of having the priority of the competing applications upheld by an interference hearing at the patent oce. Based
on a notebook entry recorded at the time, de Forest asserted that, while working on the cascade amplier, he
had stumbled across the feedback principle on August
6, 1912, which was then used in the spring of 1913 to
operate a low-powered transmitter for heterodyne reception of Federal Telegraph arc transmissions. However,
there was also strong evidence that de Forest was unaware of the full signicance of this discovery, as shown
by his lack of follow-up and continuing misunderstanding of the physics involved. In particular, it appeared that
he was unaware of the potential for further development
until he became familiar with Armstrongs research. De
Forest was not alone in the interference determination
the patent oce identied four competing claimants for
its hearings, consisting of Armstrong, de Forest, General
Electrics Langmuir, and a German, Alexander Meissner,
whose application would be seized by the Oce of Alien
Property Custodian during World War One.[30]

CHAPTER 20. LEE DE FOREST

action of the oscillating and non-oscillating audion, but
the organizations board refused to let him, stating that it
strongly arms the original award.[32] The practical effect of de Forests victory was that his company was free
to sell products that used regeneration, for during the controversy, which became more a personal feud than a business dispute, Armstrong tried to block the company from
even being licensed to sell equipment under his patent.
De Forest regularly responded to articles which he
thought exaggerated Armstrongs contributions
animosity that continued even after Armstrongs 1954
suicide. Following the publication of Carl Dreher's E.
H. Armstrong, the Hero as Inventor in the August,
1956 Harpers magazine, de Forest wrote the author,
describing Armstrong as exceedingly arrogant, brow
beating, even brutal..., and defending the Supreme
Court decision in his favor.[33]

20.6.2 Renewed broadcasting activities

The subsequent legal proceedings become divided between two groups of court cases. The rst court action began in 1919 when Armstrong, with Westinghouse, which
purchased his patent, sued the De Forest company in district court for infringement of patent 1,113,149. On May
17, 1921 the court ruled that the lack of awareness and
understanding on de Forests part, in addition to the fact
that he had made no immediate advances beyond his initial observation, made implausible his attempt to prevail
as inventor.
However, a second series of court cases, which were the
result of the patent oce interference proceeding, had a
dierent outcome. The interference board had also sided
with Armstrong, and de Forest appealed its decision to
the District of Columbia district court. On May 8, 1924,
that court concluded that the evidence, beginning with the
1912 notebook entry, was sucient to establish de Forests priority. Now on the defensive, Armstrongs side
tried to overturn the decision, but these eorts, which
twice went before the U.S. Supreme Court, in 1928 and Lee DeForest broadcasting Columbia phonograph records, from
page 52 of the November 4, 1916 The Music Trade Review.
1934, were unsuccessful.[31]
This judicial ruling meant that Lee de Forest was now
legally recognized in the United States as the inventor of
regeneration. However, much of the engineering community continued to consider Armstrong to be the actual developer, with de Forest viewed as someone who
skillfully used the patent system to get credit for an invention to which he had barely contributed. Following
the 1934 Supreme Court decision, Armstrong attempted
to return his Institute of Radio Engineers (present day
Institute of Electrical and Electronics Engineers) Medal
of Honor, which had been awarded to him in 1917 in
recognition of his work and publications dealing with the

In the summer of 1915, the company received an Experimental license for station 2XG,[34] located at its
Highbridge laboratory. In late 1916, de Forest renewed the entertainment broadcasts he had suspended in
1910, now using the superior capabilities of vacuum-tube
equipment.[35] 2XGs debut program aired on October
26, 1916,[36] as part of an arrangement with the Columbia
Gramophone record company to promote its recordings, which included announcing the title and 'Columbia
Gramophone Company' with each playing.[37] Beginning November 1, the Highbridge Station oered a
nightly schedule featuring the Columbia recordings.

20.7. PHONOFILM SOUND-ON-FILM PROCESS

These broadcasts were also used to advertise the products of the DeForest Radio Co., mostly the radio parts,
with all the zeal of our catalogue and price list, until
comments by Western Electric engineers caused de Forest enough embarrassment to make him decide to eliminate the direct advertising.[38] The station also made the
rst audio broadcast of election reports in earlier elections, stations which broadcast results had used Morse
code providing news of the November 1916 WilsonHughes presidential election.[39] The New York American
installed a private wire and bulletins were sent out every
hour. About 2000 listeners heard The Star-Spangled Banner and other anthems, songs, and hymns.
With the entry of the United States into World War One
on April 6, 1917, all civilian radio stations were ordered
to shut down, so 2XG was silenced for the duration of
the war. The ban on civilian stations was lifted on October 1, 1919, and 2XG soon renewed operation, with the
Brunswick-Balke-Collender company now supplying the
phonograph records.[40] In early 1920, de Forest moved
the stations transmitter from the Bronx to Manhattan, but
did not have permission to do so, so district Radio Inspector Arthur Batcheller ordered the station o the air.
De Forests response was to return to San Francisco in
March, taking 2XGs transmitter with him. A new station, 6XC, was established as The California Theater
station, which de Forest later stated was the rst radiotelephone station devoted solely to broadcasting to the
public.[41]
Later that year a de Forest associate, Clarence C.S.
Thompson, established Radio News & Music, Inc., in order to lease de Forest radio transmitters to newspapers interested in setting up their own broadcasting stations.[42]
In August, 1920, The Detroit News began operation
of The Detroit News Radiophone, initially with the
callsign 8MK, which later became broadcasting station
WWJ.

20.7 Phonolm sound-on-lm process

Main article: Phonolm

123
synchronization with the picture.
From October 1921 to September 1922, de Forest lived
in Berlin, Germany, meeting the Tri-Ergon developers
and investigating other European sound lm systems. In
April 1922 he announced that he would soon have a
workable sound-on-lm system.[43] On March 12, 1923
he demonstrated Phonolm to the press;[44] this was followed on April 12, 1923 by a private demonstration to
electrical engineers at the Engineering Society Buildings
Auditorium at 33 West 39th Street in New York City.[45]
In November 1922, de Forest established the De Forest
Phonolm Company, located at 314 East 48th Street in
New York City. But none of the Hollywood movie studios expressed interest in his invention, and because at
this time these studios controlled all the major theater
chains, this meant de Forest was limited to showing his
lms in independent theaters. (The Phonolm Company
would le for bankruptcy in September 1926.)
After recording stage performances (such as in
vaudeville), speeches, and musical acts, on April
15, 1923 de Forest premiered 18 Phonolm short lms
at the independent Rivoli Theater in New York City.
Starting in May 1924, Max and Dave Fleischer used
the Phonolm process for their Song Car-Tune series
of cartoonsfeaturing the "Follow the Bouncing Ball"
gimmick. However, de Forests choice of primarily
lming short vaudeville acts, instead of full-length
features, limited the appeal of Phonolm to Hollywood
studios.
De Forest also worked with Freeman Harrison Owens and
Theodore Case, using their work to perfect the Phonolm
system. However, de Forest had a falling out with both
men. Due to de Forests continuing misuse of Theodore
Cases inventions and failure to publicly acknowledge
Cases contributions, the Case Research Laboratory proceeded to build its own camera. That camera was used by
Case and his colleague Earl Sponable to record President
Coolidge on August 11, 1924, which was one of the lms
shown by de Forest and claimed by him to be the product
of his inventions.
Believing that de Forest was more concerned with his own
fame and recognition than he was with actually creating a
workable system of sound lm, and because of his continuing attempts to downplay the contributions of the Case
Research Laboratory in the creation of Phonolm, Case
severed his ties with de Forest in the fall of 1925. Case
successfully negotiated an agreement to use his patents
with studio head William Fox, owner of Fox Film Corporation, who marketed the innovation as Fox Movietone.
Hollywood introduced a competing method for sound
lm, the Vitaphone sound-on-disc process developed by
Warner Brothers, with the August 6, 1926 release of the
John Barrymore lm Don Juan.

In 1921 de Forest ended most of his radio research in

order to concentrate on developing an optical sound-onlm process called Phonolm. In 1919 he led the rst
patent for the new system, which improved upon earlier
work by Finnish inventor Eric Tigerstedt and the German
partnership Tri-Ergon. Phonolm recorded the electrical
waveforms produced by a microphone photographically
onto lm, using parallel lines of variable shades of gray,
an approach known as variable density, in contrast to
variable area systems used by processes such as RCA In 1927 and 1928, Hollywood expanded its use of soundPhotophone. When the movie lm was projected, the on-lm systems, including Fox Movietone and RCA
recorded information was converted back into sound, in Photophone. Meanwhile, theater chain owner Isadore

124
Schlesinger purchased the UK rights to Phonolm and released short lms of British music hall performers from
September 1926 to May 1929. Almost 200 Phonolm
shorts were made, and many are preserved in the collections of the Library of Congress and the British Film Institute.

CHAPTER 20. LEE DE FOREST

planted vacuum-tube technology. For this reason de Forest has been called one of the founders of the electronic
age.[53][54]

De Forests archives were donated by his widow to the

Perham Electronic Foundation, which in 1973 opened the
Foothills Electronics Museum at Foothill College in Los
Altos, California. In 1991 the college closed the museum,
breaking its contract. The foundation won a lawsuit and
was awarded $775,000.[55] The holdings were placed in
20.8 Later years and death
storage for twelve years, before being acquired in 2003
by History San Jos and put on display as The Perham
In April 1923, the De Forest Radio Telephone & TeleCollection of Early Electronics.[56]
graph Company, which manufactured de Forests Audions for commercial use, was sold to a group headed by
Edward Jewett of Jewett-Paige Motors, which expanded
the companys factory to cope with rising demand for 20.10 Awards and recognition
radios. The sale also bought the services of de Forest,
who was focusing his attention on newer innovations.[46]
Charter member, in 1912, of the Institute of Radio
De Forests nances were badly hurt by the stock marEngineers (IRE).
ket crash of 1929, and research in mechanical television
proved unprotable. In 1934, he established a small shop
Received the 1922 IRE Medal of Honor, in recogto produce diathermy machines, and, in a 1942 interview,
nition for his invention of the three-electrode amplistill hoped to make at least one more great invention.[47]
er and his other contributions to radio.[57]
De Forest was a vocal critic of many of the developments
Awarded the 1923 Franklin Institute Elliott Cresson
in the entertainment side of the radio industry. In 1940 he
Medal for inventions embodied in the Audion.
sent an open letter to the National Association of Broadcasters in which he demanded: What have you done
Received the 1946 American Institute of Electrical
with my child, the radio broadcast? You have debased
Engineers Edison Medal, For the profound technithis child, dressed him in rags of ragtime, tatters of jive
cal and social consequences of the grid-controlled
and boogie-woogie. That same year, de Forest and early
vacuum tube which he had introduced.
TV engineer Ulises Armand Sanabria presented the concept of a primitive unmanned combat air vehicle using a
Honorary Academy Award Oscar presented by the
television camera and a jam resistant radio control in a
Academy of Motion Picture Arts and Sciences in
Popular Mechanics issue.[48] In 1950 his autobiography,
1960, in recognition of his pioneering inventions
Father of Radio, was published, although it sold poorly.
which brought sound to the motion picture.[58]
De Forest was the guest celebrity on the May 22, 1957,
episode of the television show This Is Your Life, where he
was introduced as the father of radio and the grandfather of television.[49] He suered a severe heart attack in
1958, after which he remained mostly bedridden.[50] He
died in Hollywood on June 30, 1961, aged 87, and was
interred in San Fernando Mission Cemetery in Los Angeles, California.[51] De Forest died relatively poor, with
just $1,250 in his bank account.[52]

20.9 Legacy

Honored February 8, 1960 with a star on the

Hollywood Walk of Fame.[59]
DeVry University was originally named the De Forest Training School by its founder Dr. Herman A.
De Vry, who was a friend and colleague of de Forest.

20.11 Personal life

20.11.1 Marriages

The grid Audion, which de Forest called my greatest in- De Forest was married four times, with the rst three
vention, and the vacuum tubes developed from it, domi- marriages ending in divorce:
nated the eld of electronics for forty years, making possible long-distance telephone service, radio broadcast Lucille Sheardown in February 1906. Divorced being, television, and many other applications. It could
fore the end of the year.
also be used as an electronic switching element, and was
Nora Stanton Blatch Barney (18831971) on Februlater used in early digital electronics, including the rst
ary 14, 1908. They had a daughter, Harriet, but were
electronic computers, although the 1948 invention of the
transistor would lead to microchips that eventually supdivorced by 1911.

20.12. QUOTES

125

20.11.3 Religious views

Although raised in a strongly religious Protestant household, de Forest later became an agnostic. In his autobiography, he wrote that in the summer of 1894 there was an
important shift in his beliefs: Through that Freshman vacation at Yale I became more of a philosopher than I have
ever since. And thus, one by one, were my childhoods
rm religious beliefs altered or reluctantly discarded.

20.12 Quotes
De Forest was given to expansive predictions, many of
which were not borne out, but he also made many correct predictions, including microwave communication
and cooking.
I discovered an Invisible Empire of the Air, intangible, yet solid as granite.[61]

Mary Mayo, his third wife

Mary Mayo (18921957) in December 1912. According to census records, in 1920 they were living
with their infant daughter, Deena (born ca. 1919);
divorced October 5, 1930 (per Los Angeles Times).
Mayo died December 30, 1957 in a re in Los Angeles (Los Angeles Times, December 31, 1957)
Marie Mosquini (18991983) on October 10, 1930;
Mosquini was a silent lm actress, and they remained married until his death in 1961.

20.11.2

Politics

De Forest was a conservative Republican and fervent anticommunist and anti-fascist. In 1932, in the midst of
the Great Depression, he voted for Franklin Roosevelt,
but later came to resent him, calling Roosevelt Americas rst Fascist president. In 1949, he sent letters
to all members of Congress urging them to vote against
socialized medicine, federally subsidized housing, and an
excess prots tax. In 1952, he wrote to newly elected
Vice President Richard Nixon, urging him to prosecute
with renewed vigor your valiant ght to put out Communism from every branch of our government. In December 1953, he cancelled his subscription to The Nation,
accusing it of being lousy with Treason, crawling with
Communism.[60]

I foresee great renements in the eld of shortpulse microwave signaling, whereby several simultaneous programs may occupy the same channel, in
sequence, with incredibly swift electronic communication. [...] Short waves will be generally used in
the kitchen for roasting and baking, almost instantaneously. 1952 [62]
So I repeat that while theoretically and technically
television may be feasible, yet commercially and nancially, I consider it an impossibility; a development of which we need not waste little time in
dreaming. 1926[63]
To place a man in a multi-stage rocket and project
him into the controlling gravitational eld of the
moon where the passengers can make scientic observations, perhaps land alive, and then return to
earthall that constitutes a wild dream worthy of
Jules Verne. I am bold enough to say that such a
man-made voyage will never occur regardless of all
future advances. 1957[64]
I do not foresee 'spaceships to the moon or Mars.
Mortals must live and die on Earth or within its atmosphere!" 1952[62]
As a growing competitor to the tube amplier
comes now the Bell Laboratories transistor, a threeelectrode germanium crystal of amazing amplication power, of wheat-grain size and low cost. Yet
its frequency limitations, a few hundred kilocycles,
and its strict power limitations will never permit
its general replacement of the Audion amplier.
1952[62]
I came, I saw, I inventedits that simpleno need
to sit and thinkits all in your imagination.

126

20.13 Patents
Patent images in TIFF format
U.S. Patent 748,597 Wireless Signaling Device
(directional antenna), led December 1902, issued
January 1904;
U.S. Patent 824,637 Oscillation Responsive Device (vacuum tube detector diode), led January
1906, issued June 1906;

CHAPTER 20. LEE DE FOREST

20.14 See also

Metropolitan Opera radio broadcasts
Birth of public radio broadcasting

20.15 References
[1] Lee De Forest in the 1900 US Census in Milwaukee, Wisconsin

U.S. Patent 827,523 Wireless Telegraph System

(separate transmitting and receiving antennas), led
December 1905, issued July 1906;

[2] Lee De Forest in the 1920 US Census in the Bronx, New

York

U.S. Patent 827,524 Wireless Telegraph System,

led January 1906 issued July 1906;

[3] Father of Radio: The Autobiography of Lee de Forest,

1950.

U.S. Patent 836,070 Oscillation Responsive Device (vacuum tube detector no grid), led May
1906, issued November 1906;

[4] The two Institutes merged in 1940 to become the Illinois

Institute of Technology physics department.

U.S. Patent 841,386 Wireless Telegraphy (tunable

vacuum tube detector no grid), led August 1906,
issued January 1907;
U.S. Patent 841,387 Device for Amplifying Feeble
Electrical Currents (...), led August 1906, issued
January 1907;
U.S. Patent 876,165 Wireless Telegraph Transmitting System (antenna coupler), led May 1904, issued January 1908;

[5] Wireless Telegraphy That Sends No Messages Except By

Wire, New York Herald, October 28, 1901, page 4.
[6] De Forest, page 126.
[7] Cuss Words in the Wireless, New York Sun, August 27,
1903, page 1.
[8] A Modern Campaign: War and Wireless in the Far East by
David Fraser, 1905.
[9] Inventing American Broadcasting: 1899-1922 by Susan J.
Douglas, 1987, page 97.

U.S. Patent 879,532 Space Telegraphy (increased

sensitivity detector clearly shows grid), led January 1907, issued February 18, 1908;

[10] Wireless Communication in the United States: The Early

Development of American Radio Operating Companies by
Thorn L. Mayes, 1989, page 44.

U.S. Patent 926,933 Wireless Telegraphy";

[11] Reporting Yacht Races by Wireless Telephony, Electrical World, August 10, 1907, pages 293294.

U.S. Patent 926,934 Wireless Telegraph Tuning

[12] History of Communications-Electronics in the United States
Device";
U.S. Patent 926,935 Wireless Telegraph Transmitter, led February 1906, issued July 1909;

Navy by Captain L. S. Howeth, USN (Retired), 1963,

The Radio Telephone Failure, pages 169172.

U.S. Patent 926,936 Space Telegraphy";

[13] Barnard Girls Test Wireless 'Phones, New York Times,

February 26, 1909, page 7.

U.S. Patent 926,937 Space Telephony";

[14] Today in History, Jan 13. Retrieved 2008-06-24.

U.S. Patent 979,275 Oscillation Responsive Device (parallel plates in Bunsen ame) led February
1905, issued December 1910;

[15] The MetOpera Database (archives)

[16] Radio Telephone Experiments, Modern Electrics, May,
1910, page 63.

U.S. Patent 1,025,908 Transmission of Music by

[17] Father of Radio: The Autobiography of Lee de Forest,
Electromagnetic Waves";
U.S. Patent 1,101,533 Wireless Telegraphy (directional antenna/direction nder), led June 1906,
issued June 1914;
U.S. Patent 1,214,283 Wireless Telegraphy.

1950, page 114. The notebook recordings of the 1900

experiments, including the determination that the ickering was due to sound only, are reproduced on this page.
[18] US 841387, De Forest, Lee, Device for Amplifying Feeble Electrical Currents, issued 15 January 1907

20.15. REFERENCES

[19] What Everyone Should Know About Radio History: Part

II by J. H. Morecroft, Radio Broadcast, August, 1922,
page 299: "[De Forest] took out a patent in 1905 on a bulb
having two hot laments connected in a peculiar manner,
the intended functioning of which is not at all apparent to
one comprehending the radio art.
[20] The Audion: A New Receiver for Wireless Telegraphy
by Lee de Forest, Scientic American Supplement: No.
1665, November 30, 1907, pages 348350 and No. 1666,
December 7, 1907, pages 354356.
[21] An alternate explanation was given by early associate
Frank Butler, who stated that de Forest coined the term
because the control electrode looked just like a roaster
grid. (How the Term 'Grid' Originated, Communications magazine, December, 1930, page 41.)
[22] DeForest, page 322.
[23] The Audion; A Third Form of the Gas Detector by John
L. Hogan, Jr., Modern Electrics, October, 1908, page 233.
[24] The Continuous Wave: Technology and American Radio,
1900-1932 by Hugh G. J. Aitken, 1985, pages 235244.
[25] DeForest, page 327.
[26] Tyne, Gerald E. J. (1977). The Saga of the Vacuum Tube.
Indianapolis, IN: Howard W. Sams & Company. pp. 119
and 162. ISBN 0-672-21471-7.
[27] DeForest, page 340.
[28] Armstrong, Edwin H. Edwin Armstrong: Pioneer of the
Airwaves. Living Legacies. Columbia University. Retrieved 2015-10-30.

127

[38] Ibid., pages 337-338.

[39] Election Returns Flashed by Radio to 7,000 Amateurs,
The Electrical Experimenter, January, 1917, page 650.
[40] De Forest, page 350.
[41] "'Broadcasting' News by Radiotelephone (letter from Lee
de Forest), Electrical World, April 23, 1921, page 936.
[42] The initial advertisements for Radio News & Music, Inc.,
appeared on page 20 of the March 13, 1920 The Fourth
Estate, and page 202 of the March 18, 1920 Printers Ink.
[43] Lee de Forest and Phonolm at Virtual Broadway website
[44] Randy Alfred, Wired magazine (March 12, 2008)
[45] ASCE website entry
[46] Auto Interests Buy DeForest Radio Co., The New York
Times, April 6, 1923, page 19.
[47] "'Magnicent Failure'" by Samuel Lubell, Saturday
Evening Post, January 31, 1942, page 49).
[48] Robot Television Bomber Popular Mechanics June 1940
[49] Highlights of this episode, as well as a lm clip of his 1940
NAB letter, are included in the 1992 Ken Burns PBS documentary Empire of the Air: The Men Who Made Radio.
[50] Empire of the Air: The Men Who Made Radio. PBS: 1992.
[51] Lee De Forest, 87, Radio Pioneer, Dies; Lee De Forest,
Inventor, Is Dead at 87. New York Times. July 2, 1961.
Hollywood, California, July 1, 1961. Dr. Lee De Forest,
the inventor known as the father of radio, died last night
at his home. He was 87 years old.

[29] Empire of the Air by Tom Lewis, 1991, pages 77, 87.

[52] Empire of the Air: The Men Who Made Radio

[30] Ibid., page 192.

[53] Quantum Generations: A History of Physics in the Twentieth Century by Helge Kragh, 2002, page 127: "...De Forests invention of the triode (or audion) was the starting
point of the electronic age.

[31] Ibid., pages 193198, 203.

[32] Armstrong, Edwin H. Biography. Encyclopedia Britannica. Encyclopedia Britannica. Retrieved 2015-10-30.
[33] Lewis, Tom (1991). Empire of the Air (rst ed.). Harper
Collins. pp. 218219. ISBN 0-06-018215-6.
[34] Special Land Stations, Radio Service Bulletin, July,
1915, page 3. The 2 in 2XGs callsign indicated that
the station was located in the 2nd Radio Inspection district, while the X signied that it held an Experimental
license.

[54] Dawn of the Electronic Age by Frederick Nebeker, 2009,

page 15: The triode vacuum-tube is one of the small
number of technical devices... that have radically changed
human culture. It dened a new realm of technology, that
of electronics...
[55] Millard, Max (October 1993). Lee de Forest, Class of
1893:Father of the Electronics Age. Northeld Mount
Hermon Alumni Magazine. Retrieved 2011-01-20.

[35] De Forest, page 243. He noted that he had been totally

unaware of the fact that in the little audion tube, which I
was then using only as a radio detector, lay dormant the
principle of oscillation which, had I but realized it, would
have caused me to unceremoniously dump into the ash
can all of the ne arc mechanisms which I had ever constructed...

[56] The Perham Collection. History San Jos. 2011.

Archived from the original on April 26, 2015. Retrieved
March 22, 2016.

[36] Columbia Used to Demonstrate Wireless Telephone,

The Music Trade Review, November 4, 1916, page 52.

[59] Hollywood Walk of Fame: Lee De Forest.

[37] De Forest, page 337.

[57] IEEE Global History Network (2011). IEEE Medal of

Honor. IEEE History Center. Retrieved 7 July 2011.
[58] The 32nd Academy Awards: Memorable Moments.

[60] James A. Hijya, Lee De Forest and the Fatherhood of Radio (1992), Lehigh University Press, pages 119-120

128

CHAPTER 20. LEE DE FOREST

[61] Campbell, Richard, Christopher R. Martin, and Bettina

Fabos. Sounds and Images. Media and Culture: An Introduction to Mass Communication. Boston: Bedford/St.
Martins, 2000. 113, additional text.

Stephen Greenes Who said Lee de Forest was the

Father of Radio"?

[62] Dawn of the Electronic Age. Popular Mechanics. January 1952. Retrieved 2007-07-21.

Cole, A. B., "Practical Pointers on the Audion: Sales

Manager De Forest Radio Tel. & Tel. Co., QST,
March, 1916, pages 4144:

[63] Gawlinski, Mark (2003). Interactive television production.

Focal Press. p. 89. ISBN 0-240-51679-6.
[64] De Forest Says Space Travel Is Impossible, Lewiston
Morning Tribune via Associated Press, February 25, 1957

20.16 Further reading

The Continuous Wave: Technology and American
Radio, 1900-1932 by Hugh G. J. Aitken, 1985.
"'Magnicant Failure'" by Samuel Lubell, Saturday
Evening Post, three parts: January 17, 1942 (pages
911,7576, 78, 80), January 24, 1942 (pages 20
21, 2728, 38, and 43), and January 31, 1942 (pages
27, 38, 40-42, 46, 4849).
De Forest and the Triode Detector by Robert A.
Chipman, Scientic American, March, 1965, pages
93101.
Saga of the Vacuum Tube by Gerald E. J. Tyne (Indianapolis, IN: Howard W. Sams and Company,
1977). Tyne was a research associate with the
Smithsonian Institution. Details de Forests activities from the invention of the Audion to 1930.
Empire of the Air: The Men Who Made Radio by Ken
Burns a PBS Documentary Video 1992. Focuses on
three of the individuals who made signicant contributions to the early radio industry in the United
States: De Forest, David Sarno and Edwin Armstrong. LINK
A History of the Regeneration Circuit: From Invention to Patent Litigation by Prof. Sungook Hong,
University, Seoul, Korea, 2004 (treatise on the regeneration controversy)

20.17 External links

Lee de Forest, American Inventor
Dr. Lee De Forest internet radio project & forum
Lee de Forest at the Internet Movie Database
Lee De Forest at IEEE
Lee De Forest at National Inventors Hall of Fame
De Forest Phonolm Sound Movie with Eddie Cantor (1923) on YouTube

Eugenii Katzs Lee De Forest

Hong, Sungook, "A History of the Regeneration Circuit: From Invention to Patent Litigation" University,
Seoul, Korea (PDF)
PBS, "Monkeys"; a lm on the Audion operation
(QuickTime movie)
"De Forest, Lee". The Cyclopdia of American Biography. 1918.
Adams, Mike, Lee de Forest and the Invention of
Sound Movies, 1918-1926, The AWA Review (vol.
26, 2013).
Historic photograph 1924. De Forest Phonolm
Co. Inc. on White House grounds.

Chapter 21

Amplier
This article is about electronic ampliers. For other uses, ampliers, and transresistance ampliers. A further dissee Amplier (disambiguation).
tinction is whether the output is a linear or nonlinear repAn amplier, electronic amplier or (informally) amp resentation of the input. Ampliers can also be categorized by their physical placement in the signal chain.[1]

The rst practical electronic device that could amplify

was the triode vacuum tube, invented in 1906 by Lee
De Forest, which led to the rst ampliers around 1912.
Vacuum tubes were used in almost all ampliers until the
1960s - 1970s when the transistor invented in 1947 replaced them. Today most ampliers use transistors, but
vacuum tubes are still used in some applications.

Vo
Vi

21.1 History

is an electronic device that can increase the power of a

signal (a time-varying voltage or current). An amplier
functions by taking power from a power supply and controlling the output to match the input signal shape but with
a larger amplitude. In this sense, an amplier modulates
the output of the power supply based upon the properties
of the input signal. An amplier is eectively the opposite of an attenuator: while an amplier provides gain, an
attenuator provides loss.

The development of audio communication technology;

the telephone and intercom around 1880 and the rst
AM radio transmitters and receivers around 1905 created a need to somehow make an electrical audio signal
louder. Before the invention of electronic ampliers,
mechanically coupled carbon microphones were used as
crude ampliers in telephone repeaters. After the turn of
the century it was found that negative resistance mercury
lamps could amplify, and were also tried in repeaters.[2]
The rst practical electronic device that could amplify
was the Audion (triode) vacuum tube, invented in 1906
by Lee De Forest, which led to the rst ampliers around
1912. The terms amplier and amplication (from
the Latin amplicare, 'to enlarge or expand'[3] ) were rst
used for this new capability around 1915 when triodes
became widespread.[3]

An amplier can either be a discrete piece of equipment

or an electrical circuit contained within another device.
Amplication is fundamental to modern electronics, and
ampliers are widely used in almost all electronic equipment. Ampliers can be categorized in dierent ways.
One is by the frequency of the electronic signal being
amplied; audio ampliers amplify signals in the audio
(sound) range of less than 20 kHz, RF ampliers amplify frequencies in the radio frequency range between 20
kHz and 300 GHz. Another is which quantity, voltage or
current is being amplied; ampliers can be divided into
voltage ampliers, current ampliers, transconductance

The amplifying vacuum tube revolutionized electrical

technology, creating the new eld of electronics, the technology of active electrical devices. It made possible long
distance telephone lines, public address systems, radio
broadcasting, talking motion pictures, practical audio
recording, radar, television, and the rst computers. For
50 years virtually all consumer electronic devices used
vacuum tubes. Early tube ampliers often had positive
feedback (regeneration), which could increase gain but
also make the amplier unstable and prone to oscillation.
Much of the mathematical theory of ampliers was developed at Bell Telephone Laboratories during the 1920s

Graph of the input vi (t) (blue) and output voltage vo (t) (red)
of an ideal linear amplier with an arbitrary signal applied as
input. Amplication means increasing the amplitude (voltage or
current) of a time-varying signal by a given factor, as shown
here. In this example the amplier has a voltage gain of 2; that
is at any instant vo = 2vi

129

130

CHAPTER 21. AMPLIFIER

Gain, the ratio between the magnitude of output and
input signals
Bandwidth, the width of the useful frequency range
Eciency, the ratio between the power of the output
and total power consumption
Linearity, the extent to which the proportion between input and output amplitude is the same for
high amplitude and low amplitude input
Noise, a measure of undesired noise mixed into the
output
Output dynamic range, the ratio of the largest and
the smallest useful output levels
Slew rate, the maximum rate of change of the output
Rise time, settling time, ringing and overshoot that
characterize the step response
Stability, the ability to avoid self-oscillation

21.3 Amplier categorisation

De Forests prototype audio amplier, 1914. His Audion (triode) vacuum tube had a voltage gain of about 5, so this 3 stage
amplier had a gain of about 125

Ampliers are described according to the properties of

their inputs, their outputs, and how they relate.[4] All ampliers have gain, a multiplication factor that relates the
magnitude of some property of the output signal to a
property of the input signal. The gain may be specied as
the ratio of output voltage to input voltage (voltage gain),
output power to input power (power gain), or some combination of current, voltage, and power. In many cases
the property of the output that varies is dependent on
the same property of the input, making the gain unitless
(though often expressed in decibels (dB)).

to 1940s. Distortion levels in early ampliers were high,

usually around 5%, until 1934, when Harold Black developed negative feedback; this allowed the distortion levels
to be greatly reduced, at the cost of lower gain. Other advances in the theory of amplication were made by Harry Most ampliers are designed to be linear. That is, they
Nyquist and Hendrik Wade Bode.
provide constant gain for any normal input level and outThe vacuum tube was the only amplifying device (besides put signal. If an ampliers gain is not linear, the output
specialized power devices such as the magnetic ampli- signal can become distorted. There are, however, cases
er and amplidyne) for 40 years, and dominated electron- where variable gain is useful. Certain signal processing
[1]
ics until 1947, when the rst transistor, the BJT, was in- applications use exponential gain ampliers.
vented. The replacement of bulky, fragile vacuum tubes Ampliers are usually designed to function well in a
with transistors during the 1960s and 1970s created an- specic application, for example: radio and television
other revolution in electronics, making possible the rst transmitters and receivers, high-delity (hi-) stereo
really portable electronic devices, such as the transistor equipment, microcomputers and other digital equipment,
radio developed in 1954. Today most ampliers use and guitar and other instrument ampliers. Every amplitransistors, but vacuum tubes are still used in some high er includes a least one active device, such as a vacuum
power applications such as radio transmitters.
tube or transistor.

21.2 Figures of merit

21.3.1 Active devices

All ampliers include some form of active device: this

is the device that does the actual amplication. The active device can be a discrete component (like a single
Amplier quality is characterized by a list of specica- MOSFET) or part of an integrated circuit (as in an options that include:
amp).
Main article: Amplier gures of merit

21.3. AMPLIFIER CATEGORISATION

131

Transistor ampliers
See also: Transistor, Bipolar junction transistor, Fieldeect transistor, JFET, and MOSFET
Transistor ampliers (or solid state ampliers) are the
most common type of amplier in use today. A transistor
is used as the active element. The gain of the amplier
is determined by the properties of the transistor itself as
well as the circuit it is contained within.
Common active devices in transistor ampliers include
bipolar junction transistors (BJTs) and metal oxide semiconductor eld-eect transistors (MOSFETs).
Applications are numerous, some common examples are
audio ampliers in a home stereo or PA system, RF high
power generation for semiconductor equipment, to RF
and microwave applications such as radio transmitters.
Transistor-based amplication can be realized using various congurations: for example a bipolar junction transistor can realize common base, common collector or
common emitter amplication; a MOSFET can realize
common gate, common source or common drain amplication. Each conguration has dierent characteristics.
Vacuum-tube ampliers
Main article: Valve amplier
Vacuum-tube ampliers (also known as tube ampliers
or valve ampliers) use a vacuum tube as the active device. While semiconductor ampliers have largely displaced valve ampliers for low power applications, valve
ampliers can be much more cost eective in high power
applications such as radar, countermeasures equipment,
and communications equipment. Many microwave ampliers are specially designed valve ampliers, such as
the klystron, gyrotron, traveling wave tube, and crossedeld amplier, and these microwave valves provide much
greater single-device power output at microwave frequencies than solid-state devices.[5] Tube ampliers are also
still used in some high end audio equipment, thanks to
their reputation for producing a unique "tube sound".
Magnetic ampliers
Main article: Magnetic amplier

An ECC83 tube glowing inside a preamp

being aected by radioactivity.

Negative resistance devices
Negative resistances can be used as ampliers, such as the
tunnel diode amplier.[7][8]

21.3.2 Amplier architectures

Ampliers can also be categorised by the way they amplify the input signal.

Magnetic ampliers are devices somewhat similar to a

Power amplier
transformer where one winding is used to control the saturation of a magnetic core and hence alter the impedance A power amplier is an amplier designed primarily
of the other winding.[6]
to increase the power available to a load. In practice,
They have largely fallen out of use due to development amplier power gain depends on the source and load
in semiconductor ampliers but are still useful in HVDC impedances, as well as the inherent voltage and current
control, and in nuclear power control circuitry to their not gain. A radio frequency (RF) amplier design typically

132

CHAPTER 21. AMPLIFIER

optimizes impedances for power transfer, while audio and

instrumentation amplier designs normally optimize input and output impedance for least loading and highest
signal integrity. An amplier that is said to have a gain of
20 dB might have a voltage gain of 20 dB and an available power gain of much more than 20 dB (power ratio
of 100)yet actually deliver a much lower power gain
if, for example, the input is from a 600 ohm microphone
and the output connects to a 47 kilohm input socket for
a power amplier. In general the power amplier is the
last 'amplier' or actual circuit in a signal chain (the output stage) and is the amplier stage that requires attention
to power eciency. Eciency considerations lead to the
various classes of power amplier based on the biasing
of the output transistors or tubes: see power amplier
classes below.
An LM741 general purpose op-amp

Power ampliers by application

Audio power ampliers: typically used to drive Dierential ampliers
loudspeakers, will often have two output channels
Main article: Fully dierential amplier
and deliver equal power to each
RF power ampliertypical in transmitter nal A fully dierential amplier is similar to the operational
stages (see also: Linear amplier)
amplier, but also has dierential outputs. These are usually constructed using BJTs or FETs.
Servo motor controllers: amplify a control voltage
A dierential amplier is the rst stage of an op-amp, a
where linearity is not important
dierential amplier consists of two transistors which are
Piezoelectric audio amplierincludes a DC-to- emitter coupled. Types of dierential ampliers:
DC converter to generate the high voltage output required to drive piezoelectric speakers[9]

Power amplier circuits

clude the following types:

Dierential mode

Power amplier circuits in- Vd= V1-V2

Common mode

Vacuum tube/valve, hybrid or transistor power ampliers

Push-pull output or single-ended output stages

It is the average between the input voltages V2 and V1

Vc=V1+V2/2
Distributed ampliers

Operational ampliers (op-amps)

Main article: Distributed amplier
Main articles: Operational amplier and Instrumentation
amplier
These use balanced transmission lines to separate individual single stage ampliers, the outputs of which are
An operational amplier is an amplier circuit which typ- summed by the same transmission line. The transmisically has very high open loop gain and dierential inputs. sion line is a balanced type with the input at one end
Op amps have become very widely used as standardized and on one side only of the balanced transmission line
gain blocks in circuits due to their versatility; their gain, and the output at the opposite end is also the opposite
bandwidth and other characteristics can be controlled by side of the balanced transmission line. The gain of each
feedback through an external circuit. Though the term to- stage adds linearly to the output rather than multiplies one
day commonly applies to integrated circuits, the original on the other as in a cascade conguration. This allows a
operational amplier design used valves, and later designs higher bandwidth to be achieved than could otherwise be
used discrete transistor circuits.
realised even with the same gain stage elements.

21.4. CLASSIFICATION OF AMPLIFIER STAGES AND SYSTEMS

Switched mode ampliers

133

Musical instrument ampliers

These nonlinear ampliers have much higher eciencies Main article: Instrument amplier
than linear amps, and are used where the power saving
justies the extra complexity. Class-D ampliers are the An audio power amplier is usually used to amplify sigmain example of this type of amplicationsee below. nals such as music or speech. In the mid 1960s, guitar and
bass ampliers began to gain popularity because of their
relatively low price ($50) and guitars being the most popular instruments as well.[13] Several factors are especially
21.3.3 Applications
important in the selection of musical instrument ampliers (such as guitar ampliers) and other audio ampliers
Video ampliers
(although the whole of the sound system components
such as microphones to loudspeakers aect these paVideo ampliers are designed to process video signals and rameters):
have varying bandwidths depending on whether the video
signal is for SDTV, EDTV, HDTV 720p or 1080i/p etc..
Frequency response not just the frequency range
The specication of the bandwidth itself depends on what
but the requirement that the signal level varies so litkind of lter is usedand at which point (1 dB or 3
tle across the audible frequency range that the hudB for example) the bandwidth is measured. Certain reman ear notices no variation. A typical specication
quirements for step response and overshoot are necessary
for audio ampliers may be 20 Hz to 20 kHz +/- 0.5
for an acceptable TV image.[10]
dB.
Power output the power level obtainable with little
distortion, to obtain a suciently loud sound pressure level from the loudspeakers.

Oscilloscope vertical ampliers

These deal with video signals that drive an oscilloscope
display tube, and can have bandwidths of about 500 MHz.
The specications on step response, rise time, overshoot,
and aberrations can make designing these ampliers difcult. One of the pioneers in high bandwidth vertical ampliers was the Tektronix company.[11]

Microwave ampliers
Travelling wave tube ampliers
Traveling wave tube

Low distortion all ampliers and transducers distort to some extent. They cannot be perfectly linear, but aim to pass signals without aecting the
harmonic content of the sound more than the human
ear can tolerate. That tolerance of distortion, and indeed the possibility that some warmth or second
harmonic distortion (tube sound) improves the musicality of the sound, are subjects of great debate.

Before coming onto the music scene, ampliers were

heavily used in cinema. In the premiere of Noahs Ark
Main article: in 1929, the movies director (Michael Kurtiz) used the
amplier for a festival following the movies premiere.[14]

Traveling wave tube ampliers (TWTAs) are used for

21.4 Classication of amplier
high power amplication at low microwave frequencies.
They typically can amplify across a broad spectrum of
stages and systems
frequencies; however, they are usually not as tunable as
klystrons.[12]
Many alternative classications address dierent aspects
of amplier designs, and they all express some particular
perspective relating the design parameters to the objectives of the circuit. Amplier design is always a comproKlystrons Main article: Klystron
mise of numerous factors, such as cost, power consumption, real-world device imperfections, and a multitude of
Klystrons are specialized linear-beam vacuum-devices, performance specications. Below are several dierent
designed to provide high power, widely tunable ampli- approaches to classication:
cation of millimetre and sub-millimetre waves. Klystrons
are designed for large scale operations and despite having
a narrower bandwidth than TWTAs, they have the advan- 21.4.1 Input and output variables
tage of coherently amplifying a reference signal so its output may be precisely controlled in amplitude, frequency Electronic ampliers use one variable presented as either
a current and voltage. Either current or voltage can be
and phase.

134

CHAPTER 21. AMPLIFIER

ative to the input. The common collector arrangement
applies the input voltage between base and collector, and
to take the output voltage between emitter and collector. This causes negative feedback, and the output voltage
tends to follow the input voltage. This arrangement is also
used as the input presents a high impedance and does not
load the signal source, though the voltage amplication is
less than one. The common-collector circuit is, therefore,
better known as an emitter follower, source follower, or
cathode follower.

The four types of dependent sourcecontrol variable on left,

output variable on right

21.4.3 Unilateral or bilateral

An amplier whose output exhibits no feedback to

used as input and either as output, leading to four types
its input side is described as 'unilateral'. The input
of ampliers.[1] In idealized form they are represented by
impedance of a unilateral amplier is independent of
each of the four types of dependent source used in linear
load, and output impedance is independent of signal
analysis, as shown in the gure, namely:
source impedance.[18]
Each type of amplier in its ideal form has an ideal inAn amplier that uses feedback to connect part of the
put and output resistance that is the same as that of the
output back to the input is a bilateral amplier. Bilatcorresponding dependent source:[15]
eral amplier input impedance depends on the load, and
In practice the ideal impedances are not possible to output impedance on the signal source impedance. All
achieve. For any particular circuit, a small-signal anal- ampliers are bilateral to some degree; however they may
ysis is often used to nd the actual impedance. A small- often be modeled as unilateral under operating conditions
signal AC test current Ix is applied to the input or output where feedback is small enough to neglect for most purnode, all external sources are set to AC zero, and the cor- poses, simplifying analysis (see the common base article
responding alternating voltage Vx across the test current for an example).
source determines the impedance seen at that node as R
An amplier design often deliberately applies negative
= Vx / Ix.[16]
feedback to tailor amplier behavior. Some feedAmpliers designed to attach to a transmission line at in- back, positive or negative, is unavoidable and often
put and output, especially RF ampliers, do not t into undesirableintroduced, for example, by parasitic elethis classication approach. Rather than dealing with ments, such as inherent capacitance between input and
voltage or current individually, they ideally couple with output of devices such as transistors, and capacitive couan input or output impedance matched to the transmis- pling of external wiring. Excessive frequency-dependent
sion line impedance, that is, match ratios of voltage to positive feedback can turn an amplier into an oscillator.
current. Many real RF ampliers come close to this
Linear unilateral and bilateral ampliers can be repreideal. Although, for a given appropriate source and load
sented as two-port networks.
impedance, RF ampliers can be characterized as amplifying voltage or current, they fundamentally are amplifying power.[17]

21.4.4 Inverting or non-inverting

21.4.2

Common terminal

Another way to classify ampliers is by the phase relationship of the input signal to the output signal. An 'inverting' amplier produces an output 180 degrees out of
phase with the input signal (that is, a polarity inversion
or mirror image of the input as seen on an oscilloscope).
A 'non-inverting' amplier maintains the phase of the input signal waveforms. An emitter follower is a type of
non-inverting amplier, indicating that the signal at the
emitter of a transistor is following (that is, matching with
unity gain but perhaps an oset) the input signal. Voltage follower is also non inverting type of amplier having
unity gain.

One set of classications for ampliers is based on which

device terminal is common to both the input and the output circuit. In the case of bipolar junction transistors,
the three classes are common emitter, common base, and
common collector. For eld-eect transistors, the corresponding congurations are common source, common
gate, and common drain; for vacuum tubes, common
cathode, common grid, and common plate. The common
emitter (or common source, common cathode, etc.) is
most often congured to provide amplication of a voltage applied between base and emitter, and the output sig- This description can apply to a single stage of an amplinal taken between collector and emitter is inverted, rel- er, or to a complete amplier system.

21.4. CLASSIFICATION OF AMPLIFIER STAGES AND SYSTEMS

21.4.5

Function

Other ampliers may be classied by their function or

output characteristics. These functional descriptions usually apply to complete amplier systems or sub-systems
and rarely to individual stages.
A servo amplier indicates an integrated feedback
loop to actively control the output at some desired
level. A DC servo indicates use at frequencies down
to DC levels, where the rapid uctuations of an audio
or RF signal do not occur. These are often used in
mechanical actuators, or devices such as DC motors
that must maintain a constant speed or torque. An
AC servo amp can do this for some ac motors.
A linear amplier responds to dierent frequency
components independently, and does not generate
harmonic distortion or Intermodulation distortion.
No amplier can provide perfect linearity (even
the most linear amplier has some nonlinearities,
since the amplifying devicestransistors or vacuum
tubesfollow nonlinear power laws such as squarelaws and rely on circuitry techniques to reduce those
eects).
A nonlinear amplier generates signicant distortion and so changes the harmonic content; there are
situations where this is useful. Amplier circuits intentionally providing a non-linear transfer function
include:
a device like a Silicon Controlled Rectier or
a transistor used as a switch may be employed
to turn either fully ON or OFF a load such as
a lamp based on a threshold in a continuously
variable input.

135
is still modulated by the relatively large gaincontrol DC voltage.
AM detector circuits that use amplication
such as Anode-bend detectors, Precision rectiers and Innite impedance detectors (so excluding unamplied detectors such as Catswhisker detectors), as well as peak detector
circuits, rely on changes in amplication based
on the signal's instantaneous amplitude to derive a direct current from an alternating current
input.
Operational amplier comparator and detector
circuits.

A wideband amplier has a precise amplication

factor over a wide frequency range, and is often used
to boost signals for relay in communications systems. A narrowband amp amplies a specic narrow range of frequencies, to the exclusion of other
frequencies.
An RF amplier amplies signals in the radio frequency range of the electromagnetic spectrum, and
is often used to increase the sensitivity of a receiver
or the output power of a transmitter.[19]
An audio amplier amplies audio frequencies.
This category subdivides into small signal amplication, and power amps that are optimised to driving
speakers, sometimes with multiple amps grouped
together as separate or bridgeable channels to accommodate dierent audio reproduction requirements. Frequently used terms within audio ampliers include:

a Class C RF amplier may be chosen because

it can be very ecientbut is non-linear.
Following such an amplier with a "tank"
tuned circuit can reduce unwanted harmonics (distortion) suciently to make it useful in
transmitters, or some desired harmonic may be
selected by setting the resonant frequency of
the tuned circuit to a higher frequency rather
than fundamental frequency in frequency multiplier circuits.

Preamplier (preamp), which may include a

phono preamp with RIAA equalization, or
tape head preamps with CCIR equalisation lters. They may include lters or tone control
circuitry.
Power
amplier
(normally
drives
loudspeakers), headphone ampliers, and
public address ampliers.
Stereo ampliers imply two channels of output (left and right), though the term simply means solid sound (referring to threedimensional)so quadraphonic stereo was
used for ampliers with four channels. 5.1
and 7.1 systems refer to Home theatre systems with 5 or 7 normal spatial channels, plus
a subwoofer channel.

Automatic gain control circuits require an

ampliers gain be controlled by the timeaveraged amplitude so that the output amplitude varies little when weak stations are
being received. The non-linearities are assumed arranged so the relatively small signal
amplitude suers from little distortion (crosschannel interference or intermodulation) yet

Buer ampliers, which may include emitter followers, provide a high impedance input for a device
(perhaps another amplier, or perhaps an energyhungry load such as lights) that would otherwise
draw too much current from the source. Line drivers
are a type of buer that feeds long or interferenceprone interconnect cables, possibly with dierential
outputs through twisted pair cables.

a non-linear amplier in an analog computer or

true RMS converter for example can provide a
special transfer function, such as logarithmic
or square-law.

136

CHAPTER 21. AMPLIFIER

A special type of amplieroriginally used in Direct coupled amplier, using no impedance and
analog computersis widely used in measuring in- bias matching components
This class of amplier was very uncommon in the
struments for signal processing, and many other
vacuum tube days when the anode (output) voltage
uses. These are called operational ampliers or
was at greater than several hundred volts and the
op-amps. The operational name is because this
grid (input) voltage at a few volts minus. So they
type of amplier can be used in circuits that perform
were only used if the gain was specied down to
mathematical algorithmic functions, or operations
DC (e.g., in an oscilloscope). In the context of
on input signals to obtain specic types of output sigmodern electronics developers are encouraged to
nals. Modern op-amps are usually provided as inteuse directly coupled ampliers whenever possible.
grated circuits, rather than constructed from discrete
In FET and CMOS technologies direct coupling is
components. A typical modern op-amp has dierdominant since gates of MOSFETs theoretically
ential inputs (one inverting, one non-inverting)
pass no current through themselves. Therefore, DC
and one output. An idealised op-amp has the folcomponent of the input signals is automatically
lowing characteristics:
ltered.
Innite input impedance (so it does not load
the circuitry at its input)
Zero output impedance

21.4.7 Frequency range

Innite gain
Zero propagation delay
The performance of an op-amp with these characteristics
is entirely dened by the (usually passive) components
that form a negative feedback loop around it. The amplier itself does not aect the output. All real-world opamps fall short of the idealised specication abovebut
some modern components have remarkable performance
and come close in some respects.

21.4.6

Interstage coupling method

See also: multistage ampliers

Ampliers are sometimes classied by the coupling
method of the signal at the input, output, or between
stages. Dierent types of these include:
Resistive-capacitive (RC) coupled amplier, using a
network of resistors and capacitors
By design these ampliers cannot amplify DC signals as the capacitors block the DC component of
the input signal. RC-coupled ampliers were used
very often in circuits with vacuum tubes or discrete
transistors. In the days of the integrated circuit a
few more transistors on a chip are much cheaper
and smaller than a capacitor.

Depending on the frequency range and other properties

ampliers are designed according to dierent principles.
Frequency ranges down to DC are only used when
this property is needed. DC amplication leads to
specic complications that are avoided if possible;
DC-blocking capacitors can be added to remove
DC and sub-sonic frequencies from audio ampliers.
Depending on the frequency range specied dierent design principles must be used. Up to the MHz
range only discrete properties need be considered;
e.g., a terminal has an input impedance.
As soon as any connection within the circuit gets
longer than perhaps 1% of the wavelength of the
highest specied frequency (e.g., at 100 MHz the
wavelength is 3 m, so the critical connection length
is approx. 3 cm) design properties radically change.
For example, a specied length and width of a
PCB trace can be used as a selective or impedancematching entity.
Above a few hundred MHz, it gets dicult to use
discrete elements, especially inductors. In most
cases, PCB traces of very closely dened shapes are
used instead.

Inductive-capacitive (LC) coupled amplier, using a

network of inductors and capacitors
This kind of amplier is most often used in selective
radio-frequency circuits.
The frequency range handled by an amplier might be
Transformer coupled amplier, using a transformer specied in terms of bandwidth (normally implying a reto match impedances or to decouple parts of the cir- sponse that is 3 dB down when the frequency reaches the
specied bandwidth), or by specifying a frequency recuits
Quite often LC-coupled and transformer-coupled sponse that is within a certain number of decibels beampliers cannot be distinguished as a transformer tween a lower and an upper frequency (e.g. 20 Hz to 20
is some kind of inductor.
kHz plus or minus 1 dB).

21.5. POWER AMPLIFIER CLASSES

21.5 Power amplier classes

137
deviate substantially from their ideal values. These
classes use harmonic tuning of their output networks
to achieve higher eciency and can be considered a
subset of class C due to their conduction-angle characteristics.

Power amplier circuits (output stages) are classied as

A, B, AB and C for analog designsand class D and E for
switching designsbased on the proportion of each input
cycle (conduction angle) during which an amplifying device passes current.[20] The image of the conduction angle
21.5.2
derives from amplifying a sinusoidal signal. If the device
is always on, the conducting angle is 360. If it is on for
only half of each cycle, the angle is 180. The angle of
ow is closely related to the amplier power eciency.
The various classes are introduced below, followed by a
more detailed discussion under their individual headings
further down.

Class A

In the illustrations below, a bipolar junction transistor is

shown as the amplifying device. However the same attributes are found with MOSFETs or vacuum tubes.

21.5.1

Conduction angle classes

Class-A amplier

Class A 100% of the input signal is used (conduction

angle = 360). The active element remains
Amplifying devices operating in class A conduct over the
conducting[21] all of the time.
entire range of the input cycle. A class-A amplier is
Class B 50% of the input signal is used ( = 180); the distinguished by the output stage devices being biased for
active element carries current half of each cycle, and class A operation. Subclass A2 is sometimes used to refer
to vacuum-tube class-A stages that drive the grid slightly
is turned o for the other half.
positive on signal peaks for slightly more power than norClass AB Class AB is intermediate between class A and mal class A (A1; where the grid is always negative[22][23] ).
B, the two active elements conduct more than half This, however, incurs higher signal distortion.
of the time.
Class C Less than 50% of the input signal is used (con- Advantages of class-A ampliers
duction angle < 180).
Class-A designs are simpler than other classes; for
example class -AB and -B designs require two conA Class D amplier uses some form of pulse-width
nected devices in the circuit (pushpull output), each
modulation to control the output devices; the conduction
to handle one half of the waveform; class A can use
angle of each device is no longer related directly to the
a single device (single-ended).
input signal but instead varies in pulse width. These are
sometimes called digital ampliers because the output
The amplifying element is biased so the device is
device is switched fully on or o, and not carrying current
always conducting, the quiescent (small-signal) colproportional to the signal amplitude.
lector current (for transistors; drain current for FETs
or anode/plate current for vacuum tubes) is close
Additional classes There are several other amplier
to the most linear portion of its transconductance
classes, although they are mainly variations of the
curve.
previous classes. For example, class-G and class Because the device is never 'o' there is no turn
H ampliers are marked by variation of the supon time, no problems with charge storage, and genply rails (in discrete steps or in a continuous fasherally better high frequency performance and feedion, respectively) following the input signal. Wasted
back loop stability (and usually fewer high-order
heat on the output devices can be reduced as exharmonics).
cess voltage is kept to a minimum. The amplier
that is fed with these rails itself can be of any class.
The point where the device comes closest to beThese kinds of ampliers are more complex, and
ing 'o' is not at 'zero signal', so the problems of
are mainly used for specialized applications, such
crossover distortion associated with class-AB and as very high-power units. Also, class-E and class-F
B designs is avoided.
ampliers are commonly described in literature for
Best for low signal levels of radio receivers due to
radio-frequency applications where eciency of the
low distortion.
traditional classes is important, yet several aspects

138

CHAPTER 21. AMPLIFIER

Disadvantage of class-A ampliers

Transistors are much cheaper, and so more elaborate designs that give greater eciency but use more parts are
Class-A ampliers are inecient. A theoretical ef- still cost-eective. A classic application for a pair of
ciency of 50% is obtainable in a push-pull topol- class-A devices is the long-tailed pair, which is excepogy, and only 25% in a single-ended topology, un- tionally linear, and forms the basis of many more comless deliberate use of nonlinearities is made (such as plex circuits, including many audio ampliers and almost
in square-law output stages).[24] In a power am- all op-amps.
plier, this not only wastes power and limits operClass-A ampliers may be used in output stages of opation with batteries, but increases operating costs
amps[28] (although the accuracy of the bias in low cost
and requires higher-rated output devices. Ineop-amps such as the 741 may result in class A or class AB
ciency comes from the standing current that must
or class B performance, varying from device to device or
be roughly half the maximum output current, and
with temperature). They are sometimes used as mediuma large part of the power supply voltage is present
power, low-eciency, and high-cost audio power ampliacross the output device at low signal levels. If high
ers. The power consumption is unrelated to the output
output power is needed from a class-A circuit, the
power. At idle (no input), the power consumption is espower supply and accompanying heat becomes sigsentially the same as at high output volume. The result is
nicant. For every watt delivered to the load, the
low eciency and high heat dissipation.
amplier itself, at best, uses an extra watt. For high
power ampliers this means very large and expensive power supplies and heat sinks.
21.5.3 Class B

Class-A power amplier designs have largely been superseded by more ecient designs, though their simplicity
makes them popular with some hobbyists. There is a market for expensive high delity class-A amps considered
a cult item among audiophiles[25] mainly for their absence of crossover distortion and reduced odd-harmonic
and high-order harmonic distortion. They also ll a niche
market for recreations of vintage guitar ampliers, due to
their unique tone.
Class-B amplier

Single-ended and triode class-A ampliers

Class-B ampliers only amplify half of the input wave
Some hobbyists who prefer class-A ampliers also pre- cycle, thus creating a large amount of distortion, but
fer the use of thermionic valve (tube) designs instead of their eciency is greatly improved and is much bettransistors, for several reasons:
ter than class A.[29] Class-B ampliers are also favoured
in battery-operated devices, such as transistor radios.
Single-ended output stages have an asymmetrical Class B has a maximum theoretical eciency of /4
transfer function, meaning that even-order harmon- ( 78.5%).[24] This is because the amplifying element
ics in the created distortion tend to not cancel out is switched o altogether half of the time, and so can(as they do in pushpull output stages). For tubes, not dissipate power. A single class-B element is rarely
or FETs, most distortion is second-order harmonics, found in practice, though it has been used for driving the
from the square law transfer characteristic, which loudspeaker in the early IBM Personal Computers with
to some produces a warmer and more pleasant beeps, and it can be used in RF power amplier where
the distortion levels are less important. However, class C
sound.[26][27]
is more commonly used for this.
For those who prefer low distortion gures, the use
of tubes with class A (generating little odd-harmonic A practical circuit using class-B elements is the pushpull
distortion, as mentioned above) together with sym- stage, such as the very simplied complementary pair armetrical circuits (such as pushpull output stages, or rangement shown below. Here, complementary or quasibalanced low-level stages) results in the cancellation complementary devices are each used for amplifying the
of most of the even distortion harmonics, hence the opposite halves of the input signal, which is then recombined at the output. This arrangement gives excellent efremoval of most of the distortion.
ciency, but can suer from the drawback that there is a
Historically, valve ampliers often used a class-A small mismatch in the cross-over region at the joins
power amplier simply because valves are large and between the two halves of the signal, as one output deexpensive; many class-A designs use only a single vice has to take over supplying power exactly as the other
device.
nishes. This is called crossover distortion. An improve-

21.5. POWER AMPLIFIER CLASSES

139

ment is to bias the devices so they are not completely o Sometimes a numeral is added for vacuum-tube stages.
when they are not in use. This approach is called class If grid current is not permitted to ow, the class is AB1 .
AB operation.
If grid current is allowed to ow (adding more distorgiving slightly higher output power) the class is
Class B ampliers oer higher eciency than class A tion, but
[23]
AB
.
2
amplier using a single active device.

21.5.4

Class AB

21.5.5 Class C

Class-C amplier
Class-AB pushpull amplier

Class-C ampliers conduct less than 50% of the input signal and the distortion at the output is high, but high eciencies (up to 90%) are possible. The usual application
for class-C ampliers is in RF transmitters operating at a
single xed carrier frequency, where the distortion is controlled by a tuned load on the amplier. The input signal
is used to switch the active device causing pulses of current to ow through a tuned circuit forming part of the
load.[31]

Class AB is widely considered a good compromise for

ampliers, since much of the time the music signal is
quiet enough that the signal stays in the class A region,
where it is amplied with good delity, and by denition if passing out of this region, is large enough that the
distortion products typical of class B are relatively small.
The crossover distortion can be reduced further by using
negative feedback.
The class-C amplier has two modes of operation: tuned
In class-AB operation, each device operates the same way and untuned.[32] The diagram shows a waveform from
as in class B over half the waveform, but also conducts a a simple class-C circuit without the tuned load. This is
small amount on the other half.[30] As a result, the re- called untuned operation, and the analysis of the wavegion where both devices simultaneously are nearly o forms shows the massive distortion that appears in the sig(the dead zone) is reduced. The result is that when nal. When the proper load (e.g., an inductive-capacitive
the waveforms from the two devices are combined, the lter plus a load resistor) is used, two things happen. The
crossover is greatly minimised or eliminated altogether. rst is that the outputs bias level is clamped with the avThe exact choice of quiescent current (the standing cur- erage output voltage equal to the supply voltage. This is
rent through both devices when there is no signal) makes why tuned operation is sometimes called a clamper. This
a large dierence to the level of distortion (and to the risk restores the waveform to its proper shape, despite the amof thermal runaway, that may damage the devices). Of- plier having only a one-polarity supply. This is directly
ten, bias voltage applied to set this quiescent current must related to the second phenomenon: the waveform on the
be adjusted with the temperature of the output transis- center frequency becomes less distorted. The residual
tors. (For example, in the circuit at the beginning of the distortion is dependent upon the bandwidth of the tuned
article, the diodes would be mounted physically close to load, with the center frequency seeing very little distorthe output transistors, and specied to have a matched tion, but greater attenuation the farther from the tuned
temperature coecient.) Another approach (often used frequency that the signal gets.
with thermally tracking bias voltages) is to include small The tuned circuit resonates at one frequency, the xed
value resistors in series with the emitters.
carrier frequency, and so the unwanted frequencies are
Class AB sacrices some eciency over class B in favor
of linearity, thus is less ecient (below 78.5% for fullamplitude sinewaves in transistor ampliers, typically;
much less is common in class-AB vacuum-tube ampliers). It is typically much more ecient than class A.

suppressed, and the wanted full signal (sine wave) is extracted by the tuned load. The signal bandwidth of the
amplier is limited by the Q-factor of the tuned circuit
but this is not a serious limitation. Any residual harmonics can be removed using a further lter.

140

CHAPTER 21. AMPLIFIER

In practical class-C ampliers a tuned load is invariably

used. In one common arrangement the resistor shown in
the circuit above is replaced with a parallel-tuned circuit
consisting of an inductor and capacitor in parallel, whose
components are chosen to resonate the frequency of the
input signal. Power can be coupled to a load by transformer action with a secondary coil wound on the inductor. The average voltage at the collector is then equal to
the supply voltage, and the signal voltage appearing across
the tuned circuit varies from near zero to near twice the
supply voltage during the RF cycle. The input circuit is biased so that the active element (e.g., transistor) conducts
for only a fraction of the RF cycle, usually one third (120
degrees) or less.[33]

function as electronic switches instead of linear gain devices; they are either on or o. The analog signal is converted to a stream of pulses that represents the signal by
pulse-width modulation, pulse-density modulation, deltasigma modulation or a related modulation technique before being applied to the amplier. The time average
power value of the pulses is directly proportional to the
analog signal, so after amplication the signal can be converted back to an analog signal by a passive low-pass lter. The purpose of the output lter is to smooth the pulse
stream to an analog signal, removing the high frequency
spectral components of the pulses. The frequency of the
output pulses is typically ten or more times the highest
frequency in the input signal to amplify, so that the lter can adequately reduce the unwanted harmonics and
The active element conducts only while the collector volt[34]
age is passing through its minimum. By this means, accurately reproduce the input.
power dissipation in the active device is minimised, and The main advantage of a class-D amplier is power eeciency increased. Ideally, the active element would ciency. Because the output pulses have a xed amplitude,
pass only an instantaneous current pulse while the volt- the switching elements (usually MOSFETs, but vacuum
age across it is zero: it then dissipates no power and 100% tubes, and at one time bipolar transistors, were used) are
eciency is achieved. However practical devices have a switched either completely on or completely o, rather
limit to the peak current they can pass, and the pulse must than operated in linear mode. A MOSFET operates with
therefore be widened, to around 120 degrees, to obtain a the lowest resistance when fully on and thus (excluding
reasonable amount of power, and the eciency is then when fully o) has the lowest power dissipation when in
6070%.[33]
that condition. Compared to an equivalent class-AB device, a class-D ampliers lower losses permit the use of
a smaller heat sink for the MOSFETs while also reduc21.5.6 Class D
ing the amount of input power required, allowing for a
lower-capacity power supply design. Therefore, class-D
Main article: Class D amplier
ampliers are typically smaller than an equivalent classIn the class-D amplier the active devices (transistors) AB amplier.

Input

C
Low-pass lter
Switching controller
and output stage
Triangular wave generator

Block diagram of a basic switching or PWM (class-D) amplier.

Boss Audio class-D mono amplier with a low-pass lter for

powering subwoofers

Another advantage of the class-D amplier is that it can

operate from a digital signal source without requiring a
digital-to-analog converter (DAC) to convert the signal
to analog form rst. If the signal source is in digital form,
such as in a digital media player or computer sound card,
the digital circuitry can convert the binary digital signal
directly to a pulse-width modulation signal that is applied
to the amplier, simplifying the circuitry considerably.
Class-D ampliers are widely used to control motors
but are now also used as power ampliers, with extra circuitry that converts analogue to a much higher frequency
pulse width modulated signal. Switching power supplies
have even been modied into crude class-D ampliers
(though typically these only reproduce low-frequencies
with acceptable accuracy).
High quality class-D audio power ampliers have now appeared on the market. These designs have been said to rival traditional AB ampliers in terms of quality. An early
use of class-D ampliers was high-power subwoofer ampliers in cars. Because subwoofers are generally limited
to a bandwidth of no higher than 150 Hz, switching speed
for the amplier does not have to be as high as for a full
range amplier, allowing simpler designs. Class-D ampliers for driving subwoofers are relatively inexpensive
in comparison to class-AB ampliers.

21.5. POWER AMPLIFIER CLASSES

141

The letter D used to designate this amplier class is simply the next letter after C and, although occasionally used
as such, does not stand for digital. Class-D and class-E
ampliers are sometimes mistakenly described as digital because the output waveform supercially resembles
a pulse-train of digital symbols, but a class-D amplier
merely converts an input waveform into a continuously
pulse-width modulated analog signal. (A digital waveform would be pulse-code modulated.)

21.5.7

Additional classes

Class E
The class-E/F amplier is a highly ecient switching
power amplier, typically used at such high frequencies
that the switching time becomes comparable to the duty
time. As said in the class-D amplier, the transistor is
connected via a serial LC circuit to the load, and connected via a large L (inductor) to the supply voltage. The
supply voltage is connected to ground via a large capacitor to prevent any RF signals leaking into the supply. The
class-E amplier adds a C (capacitor) between the transistor and ground and uses a dened L1 to connect to the
supply voltage.

rameters and the constraint that the voltage is not only

restored, but peaks at the original voltage, the four parameters (L, L0 , C and C0 ) are determined. The class-E
amplier takes the nite on resistance into account and
tries to make the current touch the bottom at zero. This
means that the voltage and the current at the transistor
are symmetric with respect to time. The Fourier transform allows an elegant formulation to generate the complicated LC networks and says that the rst harmonic is
passed into the load, all even harmonics are shorted and
all higher odd harmonics are open.
Class E uses a signicant amount of second-harmonic
voltage. The second harmonic can be used to reduce the
overlap with edges with nite sharpness. For this to work,
energy on the second harmonic has to ow from the load
into the transistor, and no source for this is visible in the
circuit diagram. In reality, the impedance is mostly reactive and the only reason for it is that class E is a class
F (see below) amplier with a much simplied load network and thus has to deal with imperfections.
In many amateur simulations of class-E ampliers, sharp
current edges are assumed nullifying the very motivation
for class E and measurements near the transit frequency
of the transistors show very symmetric curves, which look
much similar to class-F simulations.
The class-E amplier was invented in 1972 by Nathan O.
Sokal and Alan D. Sokal, and details were rst published
in 1975.[35] Some earlier reports on this operating class
have been published in Russian and Polish.

+Vcc
L1

L0

C0
Class F

T1

RL

Class-E amplier

The following description ignores DC, which can be

added easily afterwards. The above-mentioned C and L
are in eect a parallel LC circuit to ground. When the
transistor is on, it pushes through the serial LC circuit into
the load and some current begins to ow to the parallel LC
circuit to ground. Then the serial LC circuit swings back
and compensates the current into the parallel LC circuit.
At this point the current through the transistor is zero and
it is switched o. Both LC circuits are now lled with energy in C and L0 . The whole circuit performs a damped
oscillation. The damping by the load has been adjusted
so that some time later the energy from the Ls is gone
into the load, but the energy in both C0 peaks at the original value to in turn restore the original voltage so that
the voltage across the transistor is zero again and it can
be switched on.

In pushpull ampliers and in CMOS, the even harmonics of both transistors just cancel. Experiment shows that
a square wave can be generated by those ampliers. Theoretically square waves consist of odd harmonics only. In
a class-D amplier, the output lter blocks all harmonics;
i.e., the harmonics see an open load. So even small currents in the harmonics suce to generate a voltage square
wave. The current is in phase with the voltage applied
to the lter, but the voltage across the transistors is out
of phase. Therefore, there is a minimal overlap between
current through the transistors and voltage across the transistors. The sharper the edges, the lower the overlap.

While in class D, transistors and the load exist as two separate modules, class F admits imperfections like the parasitics of the transistor and tries to optimise the global
system to have a high impedance at the harmonics. Of
course there must be a nite voltage across the transistor
to push the current across the on-state resistance. Because
the combined current through both transistors is mostly in
the rst harmonic, it looks like a sine. That means that in
the middle of the square the maximum of current has to
ow, so it may make sense to have a dip in the square
or in other words to allow some overswing of the voltage
With load, frequency, and duty cycle (0.5) as given pa- square wave. A class-F load network by denition has to

142

CHAPTER 21. AMPLIFIER

transmit below a cuto frequency and reect above.

Any frequency lying below the cuto and having its second harmonic above the cuto can be amplied, that is
an octave bandwidth. On the other hand, an inductivecapacitive series circuit with a large inductance and a tunable capacitance may be simpler to implement. By reducing the duty cycle below 0.5, the output amplitude can
be modulated. The voltage square waveform degrades,
but any overheating is compensated by the lower overall
power owing. Any load mismatch behind the lter can
only act on the rst harmonic current waveform, clearly
only a purely resistive load makes sense, then the lower
the resistance, the higher the current.
Class F can be driven by sine or by a square wave, for
a sine the input can be tuned by an inductor to increase
gain. If class F is implemented with a single transistor,
the lter is complicated to short the even harmonics. All
previous designs use sharp edges to minimise the overlap.
Rail voltage modulation

Classes G and H
U (V)

Ampli class G

+ Vss

+ Vs

- Vs

- Vss

Idealized class-G rail voltage modulation

U (V)

Ampli class H

+ Vss

+ Vs

- Vs

- Vss

Basic schematic of a class-H conguration

Idealized class-H rail voltage modulation

There is a variety of amplier designs that enhance

class-AB output stages with more ecient techniques
to achieve greater eciency with low distortion. These
designs are common in large audio ampliers since the
heatsinks and power transformers would be prohibitively
large (and costly) without the eciency increases. The
terms class G and class H are used interchangeably
to refer to dierent designs, varying in denition from
one manufacturer or paper to another.

Class-G ampliers (which use rail switching to decrease power consumption and increase eciency) are
more ecient than class-AB ampliers. These ampliers provide several power rails at dierent voltages and
switch between them as the signal output approaches each
level. Thus, the amplier increases eciency by reducing
the wasted power at the output transistors. Class-G ampliers are more ecient than class AB but less ecient
when compared to class D, however, they do not have the
electromagnetic interference eects of class D.

21.6. IMPLEMENTATION
Class-H ampliers take the idea of class G one step further creating an innitely variable supply rail. This is done
by modulating the supply rails so that the rails are only a
few volts larger than the output signal at any given time.
The output stage operates at its maximum eciency all
the time. Switched-mode power supplies can be used to
create the tracking rails. Signicant eciency gains can
be achieved but with the drawback of more complicated
supply design and reduced THD performance. In common designs, a voltage drop of about 10V is maintained
over the output transistors in Class H circuits. The picture
above shows positive supply voltage of the output stage
and the voltage at the speaker output. The boost of the
supply voltage is shown for a real music signal.
The voltage signal shown is thus a larger version of the
input, but has been changed in sign (inverted) by the
amplication. Other arrangements of amplifying device
are possible, but that given (that is, common emitter,
common source or common cathode) is the easiest to understand and employ in practice. If the amplifying element is linear, the output is a faithful copy of the input, only larger and inverted. In practice, transistors are
not linear, and the output only approximates the input.
nonlinearity from any of several sources is the origin of
distortion within an amplier. The class of amplier (A,
B, AB or C) depends on how the amplifying device is
biased. The diagrams omit the bias circuits for clarity.

143
Dohertys design, even with zero modulation, a transmitter could achieve at least 60% eciency.[36]
As a successor to Western Electric for broadcast transmitters, the Doherty concept was considerably rened by
Continental Electronics Manufacturing Company of Dallas, TX. Perhaps, the ultimate renement was the screengrid modulation scheme invented by Joseph B. Sainton.
The Sainton amplier consists of a class-C primary or
carrier stage in parallel with a class-C auxiliary or peak
stage. The stages are split and combined through 90degree phase shifting networks as in the Doherty amplier. The unmodulated radio frequency carrier is applied
to the control grids of both tubes. Carrier modulation is
applied to the screen grids of both tubes. The bias point
of the carrier and peak tubes is dierent, and is established such that the peak tube is cuto when modulation
is absent (and the amplier is producing rated unmodulated carrier power) whereas both tubes contribute twice
the rated carrier power during 100% modulation (as four
times the carrier power is required to achieve 100% modulation). As both tubes operate in class C, a signicant
improvement in eciency is thereby achieved in the nal stage. In addition, as the tetrode carrier and peak
tubes require very little drive power, a signicant improvement in eciency within the driver stage is achieved
as well (317C, et al.).[37] The released version of the Sainton amplier employs a cathode-follower modulator, not
a pushpull modulator. Previous Continental Electronics
designs, by James O. Weldon and others, retained most
of the characteristics of the Doherty amplier but added
screen-grid modulation of the driver (317B, et al.).

Any real amplier is an imperfect realization of an ideal

amplier. An important limitation of a real amplier is
that the output it generates is ultimately limited by the
power available from the power supply. An amplier saturates and clips the output if the input signal becomes The Doherty amplier remains in use in very-high-power
too large for the amplier to reproduce or exceeds oper- AM transmitters, but for lower-power AM transmitters,
ational limits for the device.
vacuum-tube ampliers in general were eclipsed in the
1980s by arrays of solid-state ampliers, which could be
switched on and o with much ner granularity in response to the requirements of the input audio. HowDoherty ampliers
ever, interest in the Doherty conguration has been revived by cellular-telephone and wireless-Internet applicaMain article: Doherty amplier
tions where the sum of several constant envelope users
creates an aggregate AM result. The main challenge of
The Doherty amplier is a hybrid conguration. It was the Doherty amplier for digital transmission modes is in
invented in 1934 by William H. Doherty for Bell Labo- aligning the two stages and getting the class-C amplier
ratorieswhose sister company, Western Electric, man- to turn on and o very quickly.
ufactured radio transmitters. The Doherty amplier consists of a class-B primary or carrier stages in parallel with Recently, Doherty ampliers have found widespread use
a class-C auxiliary or peak stage. The input signal splits to in cellular base station transmitters for GHz frequencies.
drive the two ampliers, and a combining network sums Implementations for transmitters in mobile devices have
the two output signals. Phase shifting networks are used also been demonstrated.
in inputs and outputs. During periods of low signal level,
the class-B amplier eciently operates on the signal and
the class-C amplier is cuto and consumes little power. 21.6 Implementation
During periods of high signal level, the class-B amplier
delivers its maximum power and the class-C amplier de- Ampliers are implemented using active elements of diflivers up to its maximum power. The eciency of previ- ferent kinds:
ous AM transmitter designs was proportional to modula The rst active elements were relays. They were for
tion but, with average modulation typically around 20%,
example used in transcontinental telegraph lines: a
transmitters were limited to less than 50% eciency. In

144

CHAPTER 21. AMPLIFIER

weak current was used to switch the voltage of a bat- The input signal is coupled through capacitor C1 to the
tery to the outgoing line.
base of transistor Q1. The capacitor allows the AC signal to pass, but blocks the DC bias voltage established by
For transmitting audio, carbon microphones were resistors R1 and R2 so that any preceding circuit is not
used as the active element. This was used to modu- aected by it. Q1 and Q2 form a dierential amplier
late a radio-frequency source in one of the rst AM (an amplier that multiplies the dierence between two
audio transmissions, by Reginald Fessenden on Dec. inputs by some constant), in an arrangement known as a
24, 1906.[38]
long-tailed pair. This arrangement is used to conveniently
Power control circuitry used magnetic ampliers un- allow the use of negative feedback, which is fed from the
til the latter half of the twentieth century when high output to Q2 via R7 and R8.
power FETs, and their easy interfacing to the newly The negative feedback into the dierence amplier aldeveloped digital circuitry, took over.
lows the amplier to compare the input to the actual out Audio and most low power ampliers used vacuum put. The amplied signal from Q1 is directly fed to the
tubes exclusively until the 1960s. Today, tubes are second stage, Q3, which is a common emitter stage that
used for specialist audio applications such as guitar provides further amplication of the signal and the DC
ampliers and audiophile ampliers. Many broad- bias for the output stages, Q4 and Q5. R6 provides the
load for Q3 (a better design would probably use some
cast transmitters still use vacuum tubes.
form of active load here, such as a constant-current sink).
In the 1960s, the transistor started to take over. So far, all of the amplier is operating in class A. The outThese days, discrete transistors are still used in high- put pair are arranged in class-AB pushpull, also called
a complementary pair. They provide the majority of
power ampliers and in specialist audio devices.
the current amplication (while consuming low quiescent
Beginning in the 1970s, more and more transistors current) and directly drive the load, connected via DCwere connected on a single chip therefore creating blocking capacitor C2. The diodes D1 and D2 provide
the integrated circuit. A large number of ampli- a small amount of constant voltage bias for the output
ers commercially available today are based on in- pair, just biasing them into the conducting state so that
tegrated circuits.
crossover distortion is minimized. That is, the diodes
push the output stage rmly into class-AB mode (assumFor special purposes, other active elements have been ing that the base-emitter drop of the output transistors is
used. For example, in the early days of the satellite com- reduced by heat dissipation).
munication, parametric ampliers were used. The core
circuit was a diode whose capacitance was changed by an This design is simple, but a good basis for a practical deRF signal created locally. Under certain conditions, this sign because it automatically stabilises its operating point,
RF signal provided energy that was modulated by the ex- since feedback internally operates from DC up through
tremely weak satellite signal received at the earth station. the audio range and beyond. Further circuit elements
would probably be found in a real design that would rollo the frequency response above the needed range to prevent the possibility of unwanted oscillation. Also, the use
21.6.1 Amplier circuit
of xed diode bias as shown here can cause problems if
the diodes are not both electrically and thermally matched
to the output transistors if the output transistors turn
+V supply
R1
R3
R4
on too much, they can easily overheat and destroy themQ3
selves, as the full current from the power supply is not
Q4
Input
limited at this stage.
D1
Output

C1

Q1

Q2

D2
R7

R2

R5

Q5

R8

C2

R6
0V (ground)

A practical amplier circuit

The practical amplier circuit to the right could be the

basis for a moderate-power audio amplier. It features a
typical (though substantially simplied) design as found
in modern ampliers, with a class-AB pushpull output
stage, and uses some overall negative feedback. Bipolar
transistors are shown, but this design would also be realizable with FETs or valves.

A common solution to help stabilise the output devices

is to include some emitter resistors, typically one ohm or
so. Calculating the values of the circuits resistors and capacitors is done based on the components employed and
the intended use of the amp.
Two most common circuits:
A Cascode amplier is a two-stage circuit consisting
of a transconductance amplier followed by a buer
amplier.
A Log amplier is a linear circuit in which output
voltage is a constant times the natural logarithm of
input.[39]

21.7. SEE ALSO

145

For the basics of radio frequency ampliers using valves, the DC component of the output signal is set to the midsee Valved RF ampliers.
point between the maximum voltages available from the
power supply. Most ampliers use several devices at each
stage; they are typically matched in specications except
21.6.2 Notes on implementation
for polarity. Matched inverted polarity devices are called
complementary pairs. Class-A ampliers generally use
Real world ampliers are imperfect.
only one device, unless the power supply is set to provide
both positive and negative voltages, in which case a dual
The power supply may inuence the output, so must device symmetrical design may be used. Class-C ampliers, by denition, use a single polarity supply.
be considered in the design.
Ampliers often have multiple stages in cascade to increase gain. Each stage of these designs may be a different type of amp to suit the needs of that stage. For
instance, the rst stage might be a class-A stage, feeding a class-AB pushpull second stage, which then drives
a class-G nal output stage, taking advantage of the
The amplier circuit has an open loop perfor- strengths of each type, while minimizing their weakmance. This is described by various parame- nesses.
ters (gain, slew rate, output impedance, distortion,
bandwidth, signal to noise ratio, etc.).
A power amplier is eectively an input signal
controlled power regulator. It regulates the power
sourced from the power supply or mains to the ampliers load. The power output from a power amplier cannot exceed the power input to it.

Many modern ampliers use negative feedback

techniques to hold the gain at the desired value and
reduce distortion. Negative loop feedback has the
intended eect of electrically damping loudspeaker
motion, thereby damping the mechanical dynamic
performance of the loudspeaker.
When assessing rated amplier power output, it is
useful to consider the applied load, the signal type
(e.g., speech or music), required power output duration (i.e., short-time or continuous), and required
dynamic range (e.g., recorded or live audio).
In high-powered audio applications that require long
cables to the load (e.g., cinemas and shopping centres) it may be more ecient to connect to the load
at line output voltage, with matching transformers
at source and loads. This avoids long runs of heavy
speaker cables.
Prevent instability or overheating requires care to
ensure solid state ampliers are adequately loaded.
Most have a rated minimum load impedance.
A summing circuit is typical in applications that
must combine many inputs or channels to form a
composite output. It is best to combine multiple
channels for this.[40]
All ampliers generate heat through electrical
losses. The amplier must dissipate this heat via
convection or forced air cooling. Heat can damage
or reduce electronic component service life. Designers and installers must also consider heating effects on adjacent equipment.
Dierent power supply types result in many dierent
methods of bias. Bias is a technique by which active devices are set to operate in a particular region, or by which

21.7 See also

Class-T amplier
Charge transfer amplier
Distributed amplier
Faithful amplication
Guitar amplier
Instrument amplier
Instrumentation amplier
Low noise amplier
Magnetic amplier
Negative feedback amplier
Operational amplier
Optical amplier
Power added eciency
Programmable gain amplier
RF power amplier
Valve audio amplier

21.8 References
[1] Patronis, Gene (1987). Ampliers. In Glen Ballou.
Handbook for Sound Engineers: The New Audio Cyclopedia. Howard W. Sams & Co. p. 493. ISBN 0-67221983-2.

146

[2] Sungook, Hong (2001). Wireless: From Marconis BlackBox to the Audion. MIT Press. p. 165. ISBN
0262082985.
[3] Harper, Douglas (2001). Amplify. Online Etymology
Dictionary. Etymonline.com. Retrieved July 10, 2015.
[4] Robert Boylestad and Louis Nashelsky (1996). Electronic
Devices and Circuit Theory, 7th Edition. Prentice Hall
College Division. ISBN 978-0-13-375734-7.
[5] Robert S. Symons (1998). Tubes: Still vital after
all these years. IEEE Spectrum. 35 (4): 5263.
doi:10.1109/6.666962.
[6] Mammano, Bob (2001). Magnetic Amplier Control for
Simple, Low-Cost, Secondary Regulation (PDF). Texas
Instruments.
[7] Negative Resistance Revived. users.tpg.com.au. Retrieved 2016-06-20.
[8] Munsterman, G.T. (June 1965). Tunnel-Diode Microwave Ampliers (PDF). APL Technical Digest. 4: 2
10.
[9] Mark Cherry, Maxim Engineering journal, volume 62,
Amplier Considerations in Ceramic Speaker Applications, p.3, accessed 2012-10-01

CHAPTER 21. AMPLIFIER

[20] Understanding Amplier Operating Classes"". electronicdesign.com. Retrieved 2016-06-20.

[21] RCA Receiving Tube Manual, RC-14 (1940) p 12
[22] ARRL Handbook, 1968; page 65
[23] Amplier classes. www.duncanamps.com. Retrieved
2016-06-20.
[24] Amplier Eciency. sound.westhost.com. Retrieved
2016-06-20.
[25] Jerry Del Colliano (20 February 2012), Pass Labs XA30.5
Class-A Stereo Amp Reviewed, Home Theater Review,
Luxury Publishing Group Inc.
[26] Ask the Doctors: Tube vs. Solid-State Harmonics
[27] Volume cranked up in amp debate
[28] Biasing Op-Amps into Class A. tangentsoft.net. Retrieved 2016-06-20.
[29] Class B Amplier - Class-B Transistor Amplier Tutorial. Basic Electronics Tutorials. 2013-07-25. Retrieved
2016-06-20.
[30] Class
AB
Power
Ampliers.
www.
learnabout-electronics.org. Retrieved 2016-06-20.

[10] What is a video amplier, video booster ampliers - Future Electronics. www.futureelectronics.com. Retrieved
2016-06-20.

[31] Class C power amplier circuit diagram and theory. Output characteristics DC load line. www.circuitstoday.com.
Retrieved 2016-06-20.

[11] Orwiler, Bob (December 1969). Vertical Amplier Circuits (PDF). Tektronix, Inc.

[32] A.P. Malvino, Electronic Principles (2nd Ed.1979. ISBN

0-07-039867-4) p.299.

[12] Travelling Wave Tube Ampliers. www.r-type.org. Retrieved 2016-06-20.

[33] Electronic and Radio Engineering, R.P.Terman, McGraw

Hill, 1964

[13] Rood, George. Music Concerns Seek New Volume With

Amplier. New York Times. Retrieved 23 February
2015.

[34] Class D Ampliers: Fundamentals of Operation and Recent Developments - Application Note - Maxim. www.
maximintegrated.com. Retrieved 2016-06-20.

[14] Amplier Fills Need in Picture: Loud Speaker Only

Method Found to Carry Directions During Turmoil. Los
Angeles Times.

[35] N. O. Sokal and A. D. Sokal, Class E A New Class

of High-Eciency Tuned Single-Ended Switching Power
Ampliers, IEEE Journal of Solid-State Circuits, vol. SC10, pp. 168176, June 1975. HVK

[15] This table is a Zwicky box; in particular, it encompasses

all possibilities. See Fritz Zwicky.
[16] Small signal analysis of Complex amplier circuits.
www.eeherald.com. Retrieved 2016-06-20.
[17] John Everett (1992). Vsats: Very Small Aperture Terminals. IET. ISBN 0-86341-200-9.
[18] Administrator. Microwaves101 | Active Directivity of
Ampliers. www.microwaves101.com. Retrieved 201606-20.
[19] Roy, Apratim; Rashid, S. M. S. (5 June 2012). A
power ecient bandwidth regulation technique for a
low-noise high-gain RF wideband amplier. Central
European Journal of Engineering. 2 (3): 383391.
Bibcode:2012CEJE....2..383R.
doi:10.2478/s13531012-0009-1.

[36] US patent 2210028, William H. Doherty, Amplier, issued 1940-08-06, assigned to Bell Telephone Laboratories
[37] US patent 3314034, Joseph B. Sainton, High Eciency
Amplier and PushPull Modulator, issued 1967-04-11,
assigned to Continental Electronics Manufacturing Company
[38] Lee, Thomas (2004). The Design of CMOS RadioFrequency Integrated Circuits. New York, NY: Cambridge
University Press. p. 8. ISBN 978-0-521-83539-8.
[39] Malina, Roger. Visual Art, Sound, Music and Technology.
[40] Shortess, George. Interactive Sound Installations Using
Microcomputers. JSTOR 1578331.

21.9. EXTERNAL LINKS

21.9 External links

Rane audios guide to amplier classes
Design and analysis of a basic class D amplier
Conversion: distortion factor to distortion attenuation and THD
An alternate topology called the grounded bridge
amplier - pdf
Contains an explanation of dierent amplier
classes - pdf
Reinventing the power amplier - pdf
Anatomy of the power amplier, including information about classes
Tons of Tones - Site explaining non linear distortion
stages in Amplier Models
Class D audio ampliers, white paper - pdf
Class E Radio Transmitters - Tutorials, Schematics,
Examples, and Construction Details

147

Chapter 22

Transmitter
For biologic transmitters, see transmitter substance.
Generators of radio waves for heating or industrial purIn electronics and telecommunications a transmitter or poses, such as microwave ovens or diathermy equipment,
are not usually called transmitters even though they often
have similar circuits.
The term is popularly used more specically to refer to a
broadcast transmitter, a transmitter used in broadcasting,
as in FM radio transmitter or television transmitter. This
usage typically includes both the transmitter proper, the
antenna, and often the building it is housed in.
An unrelated use of the term is in industrial process control, where a transmitter is a telemetry device which
converts measurements from a sensor into a signal, and
sends it, usually via wires, to be received by some display
or control device located a distance away.

Commercial FM broadcasting transmitter at radio station

WDET-FM, Wayne State University, Detroit, USA. It broadcasts
at 101.9 MHz with a radiated power of 48 kW.

A radio transmitter is usually part of a radio communication system which uses electromagnetic waves (radio waves) to transport
information (in this case sound) over a distance.

radio transmitter is an electronic device which generates a radio frequency alternating current. When a connected antenna is excited by this alternating current, the
antenna emits radio waves.
In addition to their use in broadcasting, transmitters
are necessary component parts of many electronic devices that communicate by radio, such as cell phones,
wireless computer networks, Bluetooth enabled devices,
garage door openers, two-way radios in aircraft, ships,
spacecraft, radar sets and navigational beacons. The
term transmitter is usually limited to equipment that
generates radio waves for communication purposes; or
radiolocation, such as radar and navigational transmitters.

22.1 Description
A transmitter can be a separate piece of electronic equipment, or an electrical circuit within another electronic
device. A transmitter and a receiver combined in one
unit is called a transceiver. The term transmitter is often
abbreviated XMTR or TX in technical documents.
The purpose of most transmitters is radio communication
of information over a distance. The information is provided to the transmitter in the form of an electronic signal, such as an audio (sound) signal from a microphone,
a video (TV) signal from a video camera, or in wireless
networking devices a digital signal from a computer. The
transmitter combines the information signal to be carried
with the radio frequency signal which generates the radio waves, which is called the carrier signal. This process
is called modulation. The information can be added to
the carrier in several dierent ways, in dierent types of
transmitters. In an amplitude modulation (AM) transmitter, the information is added to the radio signal by varying its amplitude. In a frequency modulation (FM) transmitter, it is added by varying the radio signals frequency
slightly. Many other types of modulation are used.
The antenna may be enclosed inside the case or attached
to the outside of the transmitter, as in portable devices
such as cell phones, walkie-talkies, and garage door openers. In more powerful transmitters, the antenna may

148

22.2. HISTORY

149

be located on top of a building or on a separate tower,

and connected to the transmitter by a feed line, that is a
transmission line.
Radio transmitters

A garage door opener control

contains a low-power 2.4 GHz transmitter that sends
coded commands to the garage door mechanism to open
or close.
35 kW, Continental 816R-5B FM transmitter, belonging to American FM
radio station KWNR broadcasting on 95.5 MHz in Las
Vegas

An RFID chip (next to rice

grain) contains a tiny transmitter that transmits an identication number. They are incorporated into consumer
products, and even implanted in pets.
Modern
amateur radio transceiver, the ICOM IC-746PRO. It
can transmit on the amateur bands from 1.8 MHz to 144
MHz with an output power of 100 W

In a wireless computer
network, wireless routers like this contain a 2.4 GHz
transmitter that sends downloaded web pages and email
to local computers.
A
CB
radio
transceiver, a two way radio transmitting on 27 MHz
with a power of 4 W, that can be operated without a
license
Consumer products that contain transmitters

22.2 History

Main article: History of radio

The rst primitive radio transmitters (called Hertzian oscillators) were built by German physicist Heinrich Hertz
in 1887 during his pioneering investigations of radio
waves. These generated radio waves by a high voltage spark between two conductors. Beginning in 1895
Guglielmo Marconi developed the rst practical radio
communication systems using spark transmitters. They
Both the handset and the base of couldn't transmit audio and instead transmitted informaa cordless phone contain low power 2.4 GHz radio tion by telegraphy, the operator spelling out text messages
transmitters to communicate with each other.
in Morse code. These spark-gap transmitters were used
during the rst three decades of radio (1887-1917), called
the wireless telegraphy or spark era. Because they generated damped waves, spark transmitters were electrically
noisy"; their energy was spread over a broad band of
frequencies, creating radio noise which interfered with
other transmitters. Two short-lived competing transmitter technologies came into use after the turn of the century, which were the rst continuous wave transmitters:

150

CHAPTER 22. TRANSMITTER

World War II using vacuum tubes. In recent years, the
need to conserve crowded radio spectrum bandwidth has
driven the development of new types of transmitters such
as spread spectrum.

Guglielmo
Marconi's spark gap transmitter, with which he performed the rst experiments in practical radio communication in 1895-1897

Hertz and the rst radio transmitter

High power spark gap transmitter in Australia around 1910.

the Alexanderson alternator and Poulsen arc transmitters,

which were used into the 1920s.
All these early technologies were replaced by vacuum
tube transmitters in the 1920s, which used the feedback
oscillator invented by Edwin Armstrong and Alexander
Meissner around 1912, based on the Audion (triode) vacuum tube invented by Lee De Forest in 1906. Vacuum tube transmitters took over because they were inexpensive and produced continuous waves, which could
be modulated to transmit audio (sound) using amplitude
modulation (AM). This made possible commercial AM
radio broadcasting, which began in about 1920. Practical frequency modulation (FM) transmission was invented by Edwin Armstrong in 1933, who showed that
it was less vulnerable to noise and static than AM, and
the rst FM radio station was licensed in 1937. Experimental television transmission had been conducted by radio stations since the late 1920s, but practical television
broadcasting didn't begin until the 1940s. The development of radar during World War II was a great stimulus to the evolution of high frequency transmitters in the
UHF and microwave ranges, using new devices such as
the magnetron, klystron, and traveling wave tube. The invention of the transistor allowed the development in the
1960s of small portable transmitters such as wireless microphones and walkie-talkies, although the rst walkietalkie was actually produced for the military during

1
MW US Navy Poulsen arc transmitter which generated
continuous waves using an electric arc in a magnetic
eld, a technology used from 1903 until the 1920s

An
Alexanderson alternator, a huge rotating machine
used as a radio transmitter for a short period from about
1910 until vacuum tube transmitters took over in the
1920s

22.4. LEGAL RESTRICTIONS

151
In an FSK (frequency-shift keying) transmitter, which transmits digital data, the frequency
of the carrier is shifted between two frequencies which represent the two binary digits, 0
and 1.
Many other types of modulation are also used.
In large transmitters the oscillator and modulator together are often referred to as the exciter.

One of the rst

vacuum tube AM radio transmitters, built by Lee De
Forest in 1914. The early Audion (triode) tube is visible
at right.

22.3 How it works

A radio transmitter is an electronic circuit which transforms electric power from a battery or electrical mains
into a radio frequency alternating current, which reverses
direction millions to billions of times per second. The energy in such a rapidly reversing current can radiate o a
conductor (the antenna) as electromagnetic waves (radio
waves). The transmitter also impresses information such
as an audio or video signal onto the radio frequency current to be carried by the radio waves. When they strike
the antenna of a radio receiver, the waves excite similar
(but less powerful) radio frequency currents in it. The
radio receiver extracts the information from the received
waves. A practical radio transmitter usually consists of
these parts:

An RF amplier to increase the power of the signal,

to increase the range of the radio waves.
An impedance matching (antenna tuner) circuit to
match the impedance of the transmitter to the
impedance of the antenna (or the transmission line
to the antenna), to transfer power eciently to the
antenna. If these impedances are not equal, it causes
a condition called standing waves, in which the
power is reected back from the antenna toward the
transmitter, wasting power and sometimes overheating the transmitter.
In higher frequency transmitters, in the UHF and
microwave range, oscillators that operate stably at the
output frequency cannot be built. In these transmitters
the oscillator usually operates at a lower frequency, and
is multiplied by frequency multipliers to get a signal at the
desired frequency.

22.4 Legal restrictions

A power supply circuit to transform the input electriIn most parts of the world, use of transmitters is strictly
cal power to the higher voltages needed to produce
controlled by law because of the potential for dangerthe required power output.
ous interference with other radio transmissions (for ex An electronic oscillator circuit to generate the radio ample to emergency communications). Transmitters
frequency signal. This usually generates a sine wave must be licensed by governments, under a variety of
of constant amplitude often called the carrier wave, license classes depending on use such as broadcast,
because it serves to carry the information through marine radio, Airband, Amateur and are restricted to cerspace. In most modern transmitters this is a crystal tain frequencies and power levels. A body called the
oscillator in which the frequency is precisely con- International Telecommunications Union (ITU) allocates
the frequency bands in the radio spectrum to various
trolled by the vibrations of a quartz crystal.
classes of users. In some classes each transmitter is given
A modulator circuit to add the information to be a unique call sign consisting of a string of letters and numtransmitted to the carrier wave produced by the os- bers which must be used as an identier in transmissions.
cillator. This is done by varying some aspect of The operator of the transmitter usually must hold a govthe carrier wave. The information is provided to ernment license, such as a general radiotelephone operthe transmitter either in the form of an audio sig- ator license, which is obtained by passing a test demonnal, which represents sound, a video signal, or for strating adequate technical and legal knowledge of safe
data in the form of a binary digital signal.
radio operation.
In an AM (amplitude modulation) transmitter An exception is made allowing the unlicensed use of
the amplitude (strength) of the carrier wave is low-power short-range transmitters in devices such as
varied in proportion to the modulation signal. cell phones, cordless telephones, wireless microphones,
In an FM (frequency modulation) transmitter walkie-talkies, Wi and Bluetooth devices, garage door
the frequency of the carrier is varied by the openers, and baby monitors. In the US, these fall unmodulation signal.
der Part 15 of the Federal Communications Commission

152
(FCC) regulations. Although they can be operated without a license, these devices still generally must be typeapproved before sale.

22.5 See also

List of transmission sites
Radio transmitter design
Transmitter station
Transposer
Television transmitter

22.6 References
22.7 External links
International Telecommunication Union
Jim Hawkins Radio and Broadcast Technology
Page
WCOV-TVs Transmitter Technical Website
Major UK television transmitters including change
of group information, see Transmitter Planning section.
Details of UK digital television transmitters
Richard Moores Anorak Zone Photo Gallery of UK
TV and Radio transmission sites

CHAPTER 22. TRANSMITTER

Chapter 23

Arc converter

1 megawatt Poulsen arc transmitter used by the U.S. Navy around

1918 in shore radio stations to communicate with its eet worldwide, one of the largest arc transmitters ever built.

The arc converter, sometimes called the arc transmitter, or Poulsen arc after Danish engineer Valdemar
Poulsen who invented it in 1903,[1][2] was a variety of
spark transmitter used in early wireless telegraphy. The
arc converter used an electric arc to convert direct current electricity into radio frequency alternating current. It
was used as a radio transmitter from 1903 until the 1920s
when it was replaced by vacuum tube transmitters. One
of the rst transmitters that could generate continuous sinusoidal waves, it was one of the rst technologies used
to transmit sound (amplitude modulation) by radio. It is
on the list of IEEE Milestones as a historic achievement
in electrical engineering.[3]

23.1 History
Elihu Thomson discovered that a carbon arc shunted with
a series tuned circuit would sing. This singing arc
was probably limited to audio frequencies.[4] Bureau of
Standards credits William Duddell with the shunt resonant circuit around 1900.[5]
The English engineer William Duddell discovered how to
make a resonant circuit using a carbon arc lamp. Duddells musical arc operated at audio frequencies, and
Duddell himself concluded that it was impossible to make
the arc oscillate at radio frequencies.
Valdemar Poulsen, who had demonstrated the 'Telegra-

Poulsens rst arc converter, from 1903

phone' (the worlds rst magnetic recording device) at the

Paris Exhibition of 1900, succeeded in raising the eciency and frequency to the desired level. Poulsens arc
could generate frequencies of up to 200 kilohertz and was
patented in 1903.
After a few years of development the arc technology
was transferred to Germany and Great Britain in 1906
by Poulsen, his collaborator Peder Oluf Pedersen and
their nancial backers. In 1909 the American patents
as well as a few arc converters were bought by Cyril F.
Elwell. The subsequent development in Europe and the
United States was rather dierent, since in Europe there
were severe diculties for many years implementing the
Poulsen technology, whereas in the United States an extended commercial radiotelegraph system was soon established with the Federal Telegraph Company. Later the
US Navy also adopted the Poulsen system. Only the arc
converter with passive frequency conversion was suitable
for portable and maritime use. This made it the most important mobile radio system for about a decade until it
was superseded by vacuum tube systems.

153

154

CHAPTER 23. ARC CONVERTER

tinguished during an output cycle. The Duddell arc is an
example of the rst case, but the rst case is not practical
for RF transmitters. In the second case, the condenser
AC discharge current is large enough to extinguish the
arc but not large enough to restart the arc in the opposite direction. This second case is the Poulsen arc. In the
third case, the arc extinguishes but may reignite when the
condenser current reverses. The third case is a quenched
spark gap and produces damped oscillations.
The Poulsen arc converter has a tuned circuit connected
across the arc. The arc converter consisted of a chamber in which the arc burned in hydrogen gas between a
carbon cathode and a water-cooled copper anode. Above
and below this chamber there were two series eld coils
surrounding and energizing the two poles of the magnetic
circuit. These poles projected into the chamber, one on
each side of the arc to provide a magnetic eld.
It was most successful when operated in the frequency
range of a few kilohertz to a few tens of kilohertz. The
antenna tuning had to be selective enough to suppress the
harmonic output of the arc converter.

23.3 Keying

Circuit of basic arc converter, from Poulsens 1904 paper (labels

added).

In 1922, the Bureau of Standards stated, the arc is the

most widely used transmitting apparatus for high-power,
long-distance work. It is estimated that the arc is now
responsible for 80 per cent of all the energy actually radiated into space for radio purposes during a given time,
leaving amateur stations out of consideration.[6]

23.2 Description
Unlike the existing radio transmitter of the time, the
spark-gap transmitter, the arc converter produces undamped or continuous waves (CW). This was an important feature as the use of damped waves resulted in lower
transmitter eciency and communications eectiveness,
while covering the RF spectrum with interference. This
more rened method for generating continuous-wave radio signals was initially developed by Danish inventor
Valdemar Poulsen.

Since the arc took some time to strike and operate in a stable fashion, normal on-o keying could not be used. Instead, a form of frequency shift keying was employed.[8]
In this compensation-wave method, the arc operated continuously, and the key altered the frequency of the arc
by one to ve percent. The signal at the unwanted frequency was called the compensation-wave. In arc transmitters up to 70 kW, the key typically shorted out a few
turns in the antenna coil.[9] For larger arcs, the arc output would be transformer coupled to the antenna inductor, and the key would short out a few bottom turns of
the grounded secondary.[10] Therefore, the mark (key
closed) was sent at one frequency, and the space (key
open) at another frequency. If these frequencies were far
enough apart, and the receiving stations receiver had adequate selectivity, the receiving station would hear standard CW when tuned to the mark frequency.
The compensation wave method used a lot of spectrum
bandwidth. It not only transmitted on the two intended
frequencies, but also the harmonics of those frequencies. Arc converters are rich in harmonics. Sometime
around 1921, the Preliminary International Communications Conference[11] prohibited the compensation wave
method because it caused too much interference.[4]

The need for the emission of signals at two dierent frequencies was eliminated by the development of uniwave
methods.[12] In one uniwave method, called the ignition
method, keying would start and stop the arc. The arc
There are three cases for an arc oscillator.[7] In the rst chamber would have a striker rod that shorted out the
case, the AC current in the condenser i0 is much smaller two electrodes through a resistor and extinguished the
than the DC supply current i1 , and the arc is never ex- arc. The key would energize an electromagnet that would

23.6. FURTHER READING

move the striker and reignite the arc. For this method to
work, the arc chamber had to be hot. The method was
feasible for arc converters up to about 5 kW.
The second uniwave method is the absorption method,
and it involves two tuned circuits and a single-pole,
double-throw, make-before-break key. When the key is
down, the arc is connected to the tuned antenna coil and
antenna. When the key is up, the arc is connected to a
tuned dummy antenna called the back shunt. The back
shunt was a second tuned circuit consisting of an inductor, a capacitor, and load resistor in series.[13][14] This second circuit is tuned to roughly the same frequency as the
transmitted frequency; it keeps the arc running, and it absorbs the transmitter power. The absorption method is
apparently due to W. A. Eaton.[4]
The design of switching circuit for the absorption method
is signicant. It is switching a high voltage arc, so the
switchs contacts must have some form of arc suppression. Eaton had the telegraph key drive electromagnets
that operated a relay. That relay used four sets of switch
contacts in series for each of the two paths (one to the antenna and one to the back shunt). Each relay contact was
bridged by a resistor. Consequently, the switch was never
completely open, but there was a lot of attenuation.[15]

23.4 See also

History of radio

155

[9] Bureau of Standards 1922, gure 228. The series resonant

tuned circuit would be the antenna coil in series with the
antenna.
[10] Bureau of Standards 1922, gure 229
[11] Possibly the Preliminary International Conference on Electrical Communications, 1920; see
http://www.archives.gov/research/guide-fed-records/
groups/043.html at 43.2.11
[12] Bureau of Standards 1922, pp. 416419
[13] Bureau of Standards 1922, gure 229-A
[14] Eaton 1921
[15] Eaton 1921, p. 115

Bureau of Standards (1922), The Principles Underlying Radio Communication (40) (Second ed.), U.S.
Army Signal Corps, Radio Communications Pamphlet. Revised to April 24, 1921. http://www.
forgottenbooks.org
Eaton, W. A. (April 1921), Description of a UniWave Signaling System for Arc Transmitters, Electric Journal, 18: 114115
Little, D. G. (April 1921), Continuous Wave Radio
Communication, Electric Journal, 18: 124129.
Elihu Thomson made singing arc before Duddell, p.
125.

Transmitter
Mercury arc valve
Tikker

23.5 References
[1] US 789449, Poulsen, Valdemar, Method of producing alternating currents with a high number of vibrations, published 10 June 1903, issued 9 May 1905
[2] Poulsen, Valdemar (12 September 1904). System for
producing continuous electric oscillations. Transactions
of the International Electrical Congress, St. Louis, 1904,
Vol. 2. J. R. Lyon Co. pp. 963971. Retrieved 22
September 2013.
[3] "Milestones:Poulsen-Arc Radio Transmitter, 1902.
IEEE Global History Network. IEEE. Retrieved 29 July
2011.
[4] Little 1921, p. 125
[5] Bureau of Standards 1922, p. 404
[6] Bureau of Standards 1922, p. 400
[7] Bureau of Standards 1922, pp. 404405
[8] Bureau of Standards 1922, pp. 415416

23.6 Further reading

Elwell, C. F. (1923), The Poulsen Arc Generator,
London: Ernest Benn Limited
Howeth, Linwood S. (1963), History of
Communications-Electronics in the United States
Navy, U.S. Govt. Printing Oce
Morecroft, J. H.; Pinto, A.; Curry, W. A. (1921),
Principles of Radio Communication, New York:
John Wiley & Sons Inc.
Morse, A. H. (1925), Radio: Beam and Broadcast,
London: Ernest Benn Limited. History of radio
in 1925. Page 25: Professor Elihu Thomson, of
America, applied for a patent on an arc method of
producing high-frequency currents. His invention
incorporated a magnetic blowout and other essential features of the arc of to-day, but the electrodes
were of metal and not enclosed in a gas chamber.
Cites to US Patent 500630. Pages 3031 (1900):
William Du Bois Duddell, of London, applied for
a patent on a static method of generating alternating
currents from a direct-current supply, which method
followed very closely upon the lines of that of Elihu
Thomson of 1892. Duddell suggested electrodes of

156

CHAPTER 23. ARC CONVERTER

carbon, but he proposed no magnetic blow-out. He
stated that his invention could be used for producing
oscillations of high frequency and constant amplitude which could be used with advantage in wireless telegraphy, especially where it was required
to tune the transmitter to syntony. Duddells invention (Br. Pat. 21,629/00) became the basis for the
Poulsen Arc, and also of an interesting transmitter
evolved by Von Lepel. Page 31 (1903): Valdemar
Poulsen, of Copenhagen, successfully applied for a
patent upon a generator, as disclosed by Duddell in
1900, plus magnetic blow-out proposed by Thomson in 1892, and a hydrogenous vapour in which to
immerse the arc. (Br. Pate 15,599/03; U.S. Pat
789,449.)" Also Ch. IV, pp 7577, The Poulsen
Arc. Renements by C. F. Elwell.

Pedersen, P. O. (August 1917), On the Poulsen Arc

and its Theory, Proceedings of the Institute of Radio
Engineers, 5 (4): 255319, A really satisfactory theory of the operation of the Poulsen arc does not exist
at present, a satisfactory theory being one which will
enable the calculation of the results, the necessary
data being given.

23.7 External links

http://oz6gh.byethost33.com/poulsenarc.htm,
Modulation of the Poulsen arc, from the book Radio
Telephony, 1918 by Alfred N. Goldsmith.
http://www.stenomuseet.dk/person/hb.ukref.htm,
English summary of the Danish Ph.D. dissertation,
The Arc Transmitter - a Comparative Study of
the Invention, Development and Innovation of the
Poulsen System in Denmark, England and the United
States, by Hans Buhl, 1995
http://pe2bz.philpem.me.uk/Comm/-%
20ELF-VLF/-%20Info/-%20History/
PoulsenArcOscillator/poulsen1.htm

Chapter 24

Microphone
For the indie lm, see Microphone (lm).
Microphones redirects here. For the indie band, see
The Microphones.
A microphone, colloquially nicknamed mic or mike

A Sennheiser dynamic microphone

ations of a sound wave to an electrical signal. The most

common are the dynamic microphone, which uses a coil
of wire suspended in a magnetic eld; the condenser
microphone, which uses the vibrating diaphragm as a
capacitor plate, and the piezoelectric microphone, which
uses a crystal of piezoelectric material. Microphones typically need to be connected to a preamplier before the
signal can be recorded or reproduced.

24.1 History
In order to speak to larger groups of people, a need arose
to increase the volume of the human voice. The earliest
devices used to achieve this were acoustic megaphones.
An AKG C214 condenser microphone with shock mount
Some of the rst examples, from fth century BC
Greece, were theater masks with horn-shaped mouth
(/mak/),[1] is a transducer that converts sound into an openings that acoustically amplied the voice of actors
electrical signal.
in amphitheatres.[2] In 1665, the English physicist Robert
Microphones are used in many applications such as Hooke was the rst to experiment with a medium other
telephones, hearing aids, public address systems for con- than air with the invention of the "lovers telephone" made
cert halls and public events, motion picture production, of stretched wire with a cup attached at each end.[3]
live and recorded audio engineering, two-way radios, German inventor Johann Philipp Reis designed an early
megaphones, radio and television broadcasting, and in sound transmitter that used a metallic strip attached to a
computers for recording voice, speech recognition, VoIP, vibrating membrane that would produce intermittent curand for non-acoustic purposes such as ultrasonic sensors rent. Better results were achieved with the liquid transor knock sensors.
mitter design in Scottish-American Alexander Graham
Several dierent types of microphone are in use, which Bell's telephone of 1876 the diaphragm was attached
employ dierent methods to convert the air pressure vari- to a conductive rod in an acid solution.[4] These systems,
157

158

CHAPTER 24. MICROPHONE

The rst microphone that enabled proper voice telephony
was the (loose-contact) carbon microphone. This was
independently developed by David Edward Hughes in
England and Emile Berliner and Thomas Edison in the
US. Although Edison was awarded the rst patent (after
a long legal dispute) in mid-1877, Hughes had demonstrated his working device in front of many witnesses
some years earlier, and most historians credit him with
its invention.[5][6][7][8] The carbon microphone is the direct prototype of todays microphones and was critical
in the development of telephony, broadcasting and the
recording industries.[9] Thomas Edison rened the carbon microphone into his carbon-button transmitter of
1886.[7][10] This microphone was employed at the rst
ever radio broadcast, a performance at the New York
Metropolitan Opera House in 1910.[11][12]

Johann Philipp Reis

however, gave a very poor sound quality.

Jack Brown interviews Humphrey Bogart and Lauren Bacall for

broadcast to troops overseas during World War II.

In 1916, C. Wente of Bell Labs developed the next breakthrough with the rst condenser microphone.[13] In 1923,
the rst practical moving coil microphone was built.
The Marconi Skykes or "magnetophon", developed by
Captain H. J. Round, was the standard for BBC studios in
London.[14] This was improved in 1930 by Alan Blumlein
and Herbert Holman who released the HB1A and was the
best standard of the day.[15]
Also in 1923, the ribbon microphone was introduced,
another electromagnetic type, believed to have been developed by Harry F. Olson, who essentially reverseengineered a ribbon speaker.[16] Over the years these microphones were developed by several companies, most
notably RCA that made large advancements in pattern
control, to give the microphone directionality. With television and lm technology booming there was demand
for high delity microphones and greater directionality. Electro-Voice responded with their Academy Awardwinning shotgun microphone in 1963.

David Edward Hughes invented a carbon microphone in the

1870s.

During the second half of 20th century development advanced quickly with the Shure Brothers bringing out the
SM58 and SM57. Digital was pioneered by Milab in
1999 with the DM-1001.[17] The latest research developments include the use of bre optics, lasers and interferometers.

24.3. VARIETIES

159

24.2 Components

Electronic symbol for a microphone

The sensitive transducer element of a microphone is

called its element or capsule. Sound is rst converted to
mechanical motion by means of a diaphragm, the motion
of which is then converted to an electrical signal. A complete microphone also includes a housing, some means of
bringing the signal from the element to other equipment,
and often an electronic circuit to adapt the output of the
capsule to the equipment being driven. A wireless microphone contains a radio transmitter.

Inside the Oktava 319 condenser microphone

microphones. With a DC-biased microphone, the plates

are biased with a xed charge (Q). The voltage maintained
across the capacitor plates changes with the vibrations in
the air, according to the capacitance equation (C = Q V),
where Q = charge in coulombs, C = capacitance in farads
and V = potential dierence in volts. The capacitance
of the plates is inversely proportional to the distance be24.3 Varieties
tween them for a parallel-plate capacitor. The assembly
of xed and movable plates is called an element or capMicrophones categorized by their transducer principle, sule.
such as condenser, dynamic, etc., and by their directional A nearly constant charge is maintained on the capacitor.
characteristics. Sometimes other characteristics such as As the capacitance changes, the charge across the capacdiaphragm size, intended use or orientation of the princi- itor does change very slightly, but at audible frequencies
pal sound input to the principal axis (end- or side-address) it is sensibly constant. The capacitance of the capsule
of the microphone are used to describe the microphone. (around 5 to 100 pF) and the value of the bias resistor
(100 M to tens of G) form a lter that is high-pass for
the audio signal, and low-pass for the bias voltage. Note
24.3.1 Condenser
that the time constant of an RC circuit equals the product
The condenser microphone, invented at Bell Labs in of the resistance and capacitance.
1916 by E. C. Wente,[18] is also called a capacitor micro- Within the time-frame of the capacitance change (as
phone or electrostatic microphonecapacitors were much as 50 ms at 20 Hz audio signal), the charge is
historically called condensers. Here, the diaphragm acts practically constant and the voltage across the capacitor
as one plate of a capacitor, and the vibrations produce changes instantaneously to reect the change in capacichanges in the distance between the plates. There are two tance. The voltage across the capacitor varies above and
types, depending on the method of extracting the audio below the bias voltage. The voltage dierence between
signal from the transducer: DC-biased microphones, and the bias and the capacitor is seen across the series resisradio frequency (RF) or high frequency (HF) condenser tor. The voltage across the resistor is amplied for perfor-

160
mance or recording. In most cases, the electronics in the
microphone itself contribute no voltage gain as the voltage dierential is quite signicant, up to several volts for
high sound levels. Since this is a very high impedance circuit, current gain only is usually needed, with the voltage
remaining constant.

CHAPTER 24. MICROPHONE

NT2000 or CAD M179.
A valve microphone is a condenser microphone that uses
a vacuum tube (valve) amplier.[19] They remain popular
with enthusiasts of tube sound.

Electret condenser
Main article: Electret microphone
An electret microphone is a type of capacitor micro-

AKG C451B small-diaphragm condenser microphone

RF condenser microphones use a comparatively low RF

voltage, generated by a low-noise oscillator. The signal
from the oscillator may either be amplitude modulated
by the capacitance changes produced by the sound waves
moving the capsule diaphragm, or the capsule may be
part of a resonant circuit that modulates the frequency
of the oscillator signal. Demodulation yields a low-noise
audio frequency signal with a very low source impedance.
The absence of a high bias voltage permits the use of
a diaphragm with looser tension, which may be used to
achieve wider frequency response due to higher compliance. The RF biasing process results in a lower electrical impedance capsule, a useful by-product of which is
that RF condenser microphones can be operated in damp
weather conditions that could create problems in DCbiased microphones with contaminated insulating surfaces. The Sennheiser MKH series of microphones use
the RF biasing technique.
Condenser microphones span the range from telephone
transmitters through inexpensive karaoke microphones to
high-delity recording microphones. They generally produce a high-quality audio signal and are now the popular choice in laboratory and recording studio applications. The inherent suitability of this technology is due
to the very small mass that must be moved by the incident sound wave, unlike other microphone types that
require the sound wave to do more work. They require
a power source, provided either via microphone inputs
on equipment as phantom power or from a small battery. Power is necessary for establishing the capacitor
plate voltage, and is also needed to power the microphone
electronics (impedance conversion in the case of electret
and DC-polarized microphones, demodulation or detection in the case of RF/HF microphones). Condenser microphones are also available with two diaphragms that can
be electrically connected to provide a range of polar patterns (see below), such as cardioid, omnidirectional, and
gure-eight. It is also possible to vary the pattern continuously with some microphones, for example the Rde

First patent on foil electret microphone by G. M. Sessler et al.

(pages 1 to 3)

phone invented by Gerhard Sessler and Jim West at Bell

laboratories in 1962.[20] The externally applied charge described above under condenser microphones is replaced
by a permanent charge in an electret material. An electret
is a ferroelectric material that has been permanently
electrically charged or polarized. The name comes from
electrostatic and magnet; a static charge is embedded in
an electret by alignment of the static charges in the material, much the way a magnet is made by aligning the
magnetic domains in a piece of iron.
Due to their good performance and ease of manufacture, hence low cost, the vast majority of microphones
made today are electret microphones; a semiconductor manufacturer[21] estimates annual production at over
one billion units. Nearly all cell-phone, computer, PDA
and headset microphones are electret types. They are
used in many applications, from high-quality recording
and lavalier use to built-in microphones in small sound
recording devices and telephones. Though electret microphones were once considered low quality, the best
ones can now rival traditional condenser microphones
in every respect and can even oer the long-term stability and ultra-at response needed for a measurement
microphone. Unlike other capacitor microphones, they
require no polarizing voltage, but often contain an integrated preamplier that does require power (often incorrectly called polarizing power or bias). This preamplier
is frequently phantom powered in sound reinforcement
and studio applications. Monophonic microphones designed for personal computer (PC) use, sometimes called
multimedia microphones, use a 3.5 mm plug as usually
used, without power, for stereo; the ring, instead of carrying the signal for a second channel, carries power via
a resistor from (normally) a 5 V supply in the computer.

24.3. VARIETIES

161

Stereophonic microphones use the same connector; there 24.3.3 Ribbon

is no obvious way to determine which standard is used by
Main article: Ribbon microphone
equipment and microphones.
Ribbon microphones use a thin, usually corrugated metal
Only the best electret microphones rival good DCpolarized units in terms of noise level and quality; electret microphones lend themselves to inexpensive massproduction, while inherently expensive non-electret condenser microphones are made to higher quality.

24.3.2

Dynamic

Patti Smith singing into a Shure SM58 (dynamic cardioid type)

microphone

The dynamic microphone (also known as the movingcoil microphone) works via electromagnetic induction.
They are robust, relatively inexpensive and resistant to
moisture. This, coupled with their potentially high gain
before feedback, makes them ideal for on-stage use.
Dynamic microphones use the same dynamic principle as in a loudspeaker, only reversed. A small movable induction coil, positioned in the magnetic eld
of a permanent magnet, is attached to the diaphragm.
When sound enters through the windscreen of the microphone, the sound wave moves the diaphragm. When
the diaphragm vibrates, the coil moves in the magnetic
eld, producing a varying current in the coil through
electromagnetic induction. A single dynamic membrane
does not respond linearly to all audio frequencies. Some
microphones for this reason utilize multiple membranes
for the dierent parts of the audio spectrum and then
combine the resulting signals. Combining the multiple
signals correctly is dicult and designs that do this are
rare and tend to be expensive. There are on the other
hand several designs that are more specically aimed towards isolated parts of the audio spectrum. The AKG
D 112, for example, is designed for bass response rather
than treble.[22] In audio engineering several kinds of microphones are often used at the same time to get the best
results.

Edmund Lowe using a ribbon microphone

ribbon suspended in a magnetic eld. The ribbon is electrically connected to the microphones output, and its vibration within the magnetic eld generates the electrical signal. Ribbon microphones are similar to moving
coil microphones in the sense that both produce sound by
means of magnetic induction. Basic ribbon microphones
detect sound in a bi-directional (also called gure-eight,
as in the diagram below) pattern because the ribbon is
open on both sides. Also, because the ribbon is much
less mass it responds to the air velocity rather than the
sound pressure. Though the symmetrical front and rear
pickup can be a nuisance in normal stereo recording, the
high side rejection can be used to advantage by positioning a ribbon microphone horizontally, for example above
cymbals, so that the rear lobe picks up only sound from
the cymbals. Crossed gure 8, or Blumlein pair, stereo
recording is gaining in popularity, and the gure-eight response of a ribbon microphone is ideal for that application.
Other directional patterns are produced by enclosing
one side of the ribbon in an acoustic trap or bae,
allowing sound to reach only one side. The classic
RCA Type 77-DX microphone has several externally adjustable positions of the internal bae, allowing the selection of several response patterns ranging from gureeight to unidirectional. Such older ribbon microphones, some of which still provide high quality sound
reproduction, were once valued for this reason, but a good

162

CHAPTER 24. MICROPHONE

low-frequency response could only be obtained when the

ribbon was suspended very loosely, which made them
relatively fragile. Modern ribbon materials, including
new nanomaterials[23] have now been introduced that
eliminate those concerns, and even improve the eective dynamic range of ribbon microphones at low frequencies. Protective wind screens can reduce the danger of damaging a vintage ribbon, and also reduce plosive artifacts in the recording. Properly designed wind
screens produce negligible treble attenuation. In common
with other classes of dynamic microphone, ribbon microphones don't require phantom power; in fact, this voltage
can damage some older ribbon microphones. Some new
modern ribbon microphone designs incorporate a preamplier and, therefore, do require phantom power, and circuits of modern passive ribbon microphones, i.e., those
without the aforementioned preamplier, are specically
designed to resist damage to the ribbon and transformer
by phantom power. Also there are new ribbon materials available that are immune to wind blasts and phantom
power.

24.3.4

Carbon

Main article: Carbon microphone

A carbon microphone, also known as a carbon button microphone (or sometimes just a button microphone), uses
a capsule or button containing carbon granules pressed
between two metal plates like the Berliner and Edison microphones. A voltage is applied across the metal plates,
causing a small current to ow through the carbon. One of
the plates, the diaphragm, vibrates in sympathy with incident sound waves, applying a varying pressure to the carbon. The changing pressure deforms the granules, causing the contact area between each pair of adjacent granules to change, and this causes the electrical resistance
of the mass of granules to change. The changes in resistance cause a corresponding change in the current owing
through the microphone, producing the electrical signal.
Carbon microphones were once commonly used in telephones; they have extremely low-quality sound reproduction and a very limited frequency response range, but are
very robust devices. The Boudet microphone, which used
relatively large carbon balls, was similar to the granule
carbon button microphones.[24]

this amplier eect was the oscillation caused by feedback, resulting in an audible squeal from the old candlestick telephone if its earphone was placed near the
carbon microphone.

24.3.5 Piezoelectric
A crystal microphone or piezo microphone[25] uses the
phenomenon of piezoelectricitythe ability of some materials to produce a voltage when subjected to pressure
to convert vibrations into an electrical signal. An example of this is potassium sodium tartrate, which is a
piezoelectric crystal that works as a transducer, both as
a microphone and as a slimline loudspeaker component.
Crystal microphones were once commonly supplied with
vacuum tube (valve) equipment, such as domestic tape
recorders. Their high output impedance matched the
high input impedance (typically about 10 megohms) of
the vacuum tube input stage well. They were dicult
to match to early transistor equipment, and were quickly
supplanted by dynamic microphones for a time, and later
small electret condenser devices. The high impedance of
the crystal microphone made it very susceptible to handling noise, both from the microphone itself and from the
connecting cable.
Piezoelectric transducers are often used as contact microphones to amplify sound from acoustic musical instruments, to sense drum hits, for triggering electronic samples, and to record sound in challenging environments,
such as underwater under high pressure. Saddle-mounted
pickups on acoustic guitars are generally piezoelectric devices that contact the strings passing over the saddle. This
type of microphone is dierent from magnetic coil pickups commonly visible on typical electric guitars, which
use magnetic induction, rather than mechanical coupling,
to pick up vibration.

24.3.6 Fiber optic

A ber optic microphone converts acoustic waves into
electrical signals by sensing changes in light intensity, instead of sensing changes in capacitance or magnetic elds
as with conventional microphones. [26][27]
During operation, light from a laser source travels through
an optical ber to illuminate the surface of a reective
diaphragm. Sound vibrations of the diaphragm modulate the intensity of light reecting o the diaphragm in
a specic direction. The modulated light is then transmitted over a second optical ber to a photo detector,
which transforms the intensity-modulated light into analog or digital audio for transmission or recording. Fiber
optic microphones possess high dynamic and frequency
range, similar to the best high delity conventional microphones.

Unlike other microphone types, the carbon microphone

can also be used as a type of amplier, using a small
amount of sound energy to control a larger amount of
electrical energy. Carbon microphones found use as early
telephone repeaters, making long distance phone calls
possible in the era before vacuum tubes. These repeaters
worked by mechanically coupling a magnetic telephone
receiver to a carbon microphone: the faint signal from the
receiver was transferred to the microphone, where it modulated a stronger electric current, producing a stronger
electrical signal to send down the line. One illustration of Fiber optic microphones do not react to or inuence

24.3. VARIETIES

163
motion of the laser spot from the returning beam is detected and converted to an audio signal.
In a more robust and expensive implementation, the returned light is split and fed to an interferometer, which
detects movement of the surface by changes in the optical
path length of the reected beam. The former implementation is a tabletop experiment; the latter requires an extremely stable laser and precise optics.

The Optoacoustics 1140 ber optic microphone

A new type of laser microphone is a device that uses a

laser beam and smoke or vapor to detect sound vibrations
in free air. On 25 August 2009, U.S. patent 7,580,533 issued for a Particulate Flow Detection Microphone based
on a laser-photocell pair with a moving stream of smoke
or vapor in the laser beams path. Sound pressure waves
cause disturbances in the smoke that in turn cause variations in the amount of laser light reaching the photo detector. A prototype of the device was demonstrated at
the 127th Audio Engineering Society convention in New
York City from 9 through 12 October 2009.

24.3.8 Liquid

any electrical, magnetic, electrostatic or radioactive elds

(this is called EMI/RFI immunity). The ber optic miMain article: Water microphone
crophone design is therefore ideal for use in areas where
conventional microphones are ineective or dangerous,
such as inside industrial turbines or in magnetic resonance Early microphones did not produce intelligible speech,
until Alexander Graham Bell made improvements includimaging (MRI) equipment environments.
ing a variable-resistance microphone/transmitter. Bells
Fiber optic microphones are robust, resistant to environliquid transmitter consisted of a metal cup lled with wamental changes in heat and moisture, and can be proter with a small amount of sulfuric acid added. A sound
duced for any directionality or impedance matching. The
wave caused the diaphragm to move, forcing a needle to
distance between the microphones light source and its
move up and down in the water. The electrical resisphoto detector may be up to several kilometers without
tance between the wire and the cup was then inversely
need for any preamplier or other electrical device, makproportional to the size of the water meniscus around the
ing ber optic microphones suitable for industrial and
submerged needle. Elisha Gray led a caveat for a versurveillance acoustic monitoring.
sion using a brass rod instead of the needle. Other minor
Fiber optic microphones are used in very specic appli- variations and improvements were made to the liquid mication areas such as for infrasound monitoring and noise- crophone by Majoranna, Chambers, Vanni, Sykes, and
canceling. They have proven especially useful in medical Elisha Gray, and one version was patented by Reginald
applications, such as allowing radiologists, sta and pa- Fessenden in 1903. These were the rst working microtients within the powerful and noisy magnetic eld to con- phones, but they were not practical for commercial apverse normally, inside the MRI suites as well as in remote plication. The famous rst phone conversation between
control rooms.[28] Other uses include industrial equip- Bell and Watson took place using a liquid microphone.
ment monitoring and audio calibration and measurement,
high-delity recording and law enforcement.

24.3.9 MEMS
24.3.7

Laser

Main article: Laser microphone

Laser microphones are often portrayed in movies as spy
gadgets, because they can be used to pick up sound at a
distance from the microphone equipment. A laser beam
is aimed at the surface of a window or other plane surface
that is aected by sound. The vibrations of this surface
change the angle at which the beam is reected, and the

Main article: Microelectromechanical systems

The MEMS (MicroElectrical-Mechanical System) microphone is also called a microphone chip or silicon microphone. A pressure-sensitive diaphragm is etched directly into a silicon wafer by MEMS processing techniques, and is usually accompanied with integrated
preamplier. Most MEMS microphones are variants of
the condenser microphone design. Digital MEMS microphones have built in analog-to-digital converter (ADC)

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CHAPTER 24. MICROPHONE

circuits on the same CMOS chip making the chip a

digital microphone and so more readily integrated with
modern digital products. Major manufacturers producing MEMS silicon microphones are Wolfson Microelectronics (WM7xxx) now Cirrus Logic,[29] InvenSense
(product line sold by Analog Devices [30] ), Akustica (AKU200x), Inneon (SMM310 product), Knowles
Electronics, Memstech (MSMx), NXP Semiconductors
(division bought by Knowles [31] ), Sonion MEMS, Vesper, AAC Acoustic Technologies,[32] and Omron.[33]

tional. A pressure-gradient microphone uses a diaphragm

that is at least partially open on both sides. The pressure
dierence between the two sides produces its directional
characteristics. Other elements such as the external shape
of the microphone and external devices such as interference tubes can also alter a microphones directional response. A pure pressure-gradient microphone is equally
sensitive to sounds arriving from front or back, but insensitive to sounds arriving from the side because sound
arriving at the front and back at the same time creates
no gradient between the two. The characteristic direcMore recently, there has been increased interest and research into making piezoelectric MEMS microphones tional pattern of a pure pressure-gradient microphone is
like a gure-8. Other polar patterns are derived by crewhich are a signicant architectural and material change
ating a capsule that combines these two eects in dier[34]
from existing condenser style MEMS designs.
ent ways. The cardioid, for instance, features a partially
closed backside, so its response is a combination of pressure and pressure-gradient characteristics.[35]
24.3.10 Speakers as microphones
A loudspeaker, a transducer that turns an electrical signal
into sound waves, is the functional opposite of a micro- 24.5 Polar patterns
phone. Since a conventional speaker is constructed much
like a dynamic microphone (with a diaphragm, coil and (Microphone facing top of page in diagram, parallel to
magnet), speakers can actually work in reverse as mi- page):
crophones. The resulting signal typically oers reduced
quality including limited high-end frequency response
Omnidirectional
and poor sensitivity. In practical use, speakers are sometimes used as microphones in applications where high
Bi-directional or Figure of 8
quality and sensitivity are not needed such as intercoms,
walkie-talkies or video game voice chat peripherals, or
Subcardioid
when conventional microphones are in short supply.
Cardioid
However, there is at least one practical application that
exploits those weaknesses: the use of a medium-size
Hypercardioid
woofer placed closely in front of a kick drum (bass
drum) in a drum set to act as a microphone. A com Supercardioid
mercial product example is the Yamaha Subkick, a 6.5 Shotgun
inch (170 mm) woofer shock-mounted into a 10 drum
shell used in front of kick drums. Since a relatively massive membrane is unable to transduce high frequencies A microphones directionality or polar pattern indicates
while being capable of tolerating strong low-frequency how sensitive it is to sounds arriving at dierent angles
transients, the speaker is often ideal for picking up the about its central axis. The polar patterns illustrated above
kick drum while reducing bleed from the nearby cymbals represent the locus of points that produce the same sigand snare drums. Less commonly, microphones them- nal level output in the microphone if a given sound presselves can be used as speakers, but due to their low power sure level (SPL) is generated from that point. How the
handling and small transducer sizes, a tweeter is the most physical body of the microphone is oriented relative to
practical application. One instance of such an application the diagrams depends on the microphone design. For
was the STC microphone-derived 4001 super-tweeter, large-membrane microphones such as in the Oktava (picwhich was successfully used in a number of high quality tured above), the upward direction in the polar diagram
loudspeaker systems from the late 1960s to the mid-70s. is usually perpendicular to the microphone body, com-

24.4 Capsule design and directivity

The inner elements of a microphone are the primary
source of dierences in directivity. A pressure microphone uses a diaphragm between a xed internal volume
of air and the environment, and responds uniformly to
pressure from all directions, so it is said to be omnidirec-

monly known as side re or side address. For small

diaphragm microphones such as the Shure (also pictured
above), it usually extends from the axis of the microphone
commonly known as end re or top/end address.
Some microphone designs combine several principles in
creating the desired polar pattern. This ranges from
shielding (meaning diraction/dissipation/absorption) by
the housing itself to electronically combining dual membranes.

24.5. POLAR PATTERNS

24.5.1

165

Omnidirectional

An omnidirectional (or nondirectional) microphones

response is generally considered to be a perfect sphere in
three dimensions. In the real world, this is not the case.
As with directional microphones, the polar pattern for an
omnidirectional microphone is a function of frequency.
The body of the microphone is not innitely small and,
as a consequence, it tends to get in its own way with respect to sounds arriving from the rear, causing a slight
attening of the polar response. This attening increases
as the diameter of the microphone (assuming its cylindrical) reaches the wavelength of the frequency in question. Therefore, the smallest diameter microphone gives
the best omnidirectional characteristics at high frequen- University Sound US664A dynamic supercardioid microphone
cies.
The wavelength of sound at 10 kHz is 1.4 (3.5 cm). The
smallest measuring microphones are often 1/4 (6 mm) in
diameter, which practically eliminates directionality even
up to the highest frequencies. Omnidirectional microphones, unlike cardioids, do not employ resonant cavities
as delays, and so can be considered the purest microphones in terms of low coloration; they add very little to
the original sound. Being pressure-sensitive they can also
have a very at low-frequency response down to 20 Hz
or below. Pressure-sensitive microphones also respond
much less to wind noise and plosives than directional (velocity sensitive) microphones.
An example of a nondirectional microphone is the round
black eight ball.[36]

24.5.2

Unidirectional

A unidirectional microphone is primarily sensitive to

sounds from only one direction. The diagram above illustrates a number of these patterns. The microphone
faces upwards in each diagram. The sound intensity for
a particular frequency is plotted for angles radially from
0 to 360. (Professional diagrams show these scales and
include multiple plots at dierent frequencies. The diagrams given here provide only an overview of typical
pattern shapes, and their names.)

tional transducer microphones achieve their patterns by

sensing pressure gradient, putting them very close to the
sound source (at distances of a few centimeters) results in
a bass boost due to the increased gradient. This is known
as the proximity eect.[37] The SM58 has been the most
commonly used microphone for live vocals for more than
50 years[38] demonstrating the importance and popularity
of cardioid mics.
A cardioid microphone is eectively a superposition of
an omnidirectional and a gure-8 microphone; for sound
waves coming from the back, the negative signal from
the gure-8 cancels the positive signal from the omnidirectional element, whereas for sound waves coming from
the front, the two add to each other. A hyper-cardioid
microphone is similar, but with a slightly larger gure-8
contribution leading to a tighter area of front sensitivity
and a smaller lobe of rear sensitivity. A super-cardioid
microphone is similar to a hyper-cardioid, except there is
more front pickup and less rear pickup. While any pattern between omni and gure 8 is possible by adjusting
their mix, common denitions state that a hypercardioid
is produced by combining them at a 3:1 ratio, producing nulls at 109.5, while supercardioid is produced with
about a 5:3 ratio, with nulls at 126.9. The sub-cardioid
microphone has no null points. It is produced with about
7:3 ratio with 3-10 dB level between the front and back
pickup. [39][40]

Cardioid, Hypercardioid, Supercardioid, Subcar24.5.3

dioid
The most common unidirectional microphone is a cardioid microphone, so named because the sensitivity pattern is heart-shaped, i.e. a cardioid. The cardioid
family of microphones are commonly used as vocal or
speech microphones, since they are good at rejecting
sounds from other directions. In three dimensions, the
cardioid is shaped like an apple centred around the microphone which is the stem of the apple. The cardioid
response reduces pickup from the side and rear, helping
to avoid feedback from the monitors. Since these direc-

Bi-directional

Figure 8 or bi-directional microphones receive sound

equally from both the front and back of the element. Most
ribbon microphones are of this pattern. In principle they
do not respond to sound pressure at all, only to the change
in pressure between front and back; since sound arriving from the side reaches front and back equally there
is no dierence in pressure and therefore no sensitivity to sound from that direction. In more mathematical terms, while omnidirectional microphones are scalar
transducers responding to pressure from any direction, bi-

166

CHAPTER 24. MICROPHONE

directional microphones are vector transducers responding to the gradient along an axis normal to the plane of
the diaphragm. This also has the eect of inverting the
output polarity for sounds arriving from the back side.

24.5.4

Shotgun and parabolic

An Audio-Technica shotgun microphone

A Sony parabolic reector, without a microphone. The microphone would face the reector surface and sound captured by
the reector would bounce towards the microphone.

The interference tube of a shotgun microphone. The capsule is

at the base of the tube.

Shotgun microphones are the most highly directional of

simple rst-order unidirectional types. At low frequencies they have the classic polar response of a hypercardioid but at medium and higher frequencies an interference tube gives them an increased forward response. This
is achieved by a process of cancellation of o-axis waves
entering the longitudinal array of slots. A consequence of
this technique is the presence of some rear lobes that vary
in level and angle with frequency, and can cause some coloration eects. Due to the narrowness of their forward
sensitivity, shotgun microphones are commonly used on
television and lm sets, in stadiums, and for eld recording of wildlife.

space. If the microphone is placed in, or very close to,

one of these boundaries, the reections from that surface have the same timing as the direct sound, thus giving
the microphone a hemispherical polar pattern and improved intelligibility. Initially this was done by placing
an ordinary microphone adjacent to the surface, sometimes in a block of acoustically transparent foam. Sound
engineers Ed Long and Ron Wickersham developed the
concept of placing the diaphragm parallel to and facing
the boundary.[41] While the patent has expired, Pressure
Zone Microphone and PZM are still active trademarks
of Crown International, and the generic term boundary
microphone is preferred. While a boundary microphone
was initially implemented using an omnidirectional element, it is also possible to mount a directional microphone close enough to the surface to gain some of the
benets of this technique while retaining the directional
properties of the element. Crowns trademark on this approach is Phase Coherent Cardioid or PCC, but there
are other makers who employ this technique as well.

24.6 Application-specic designs

24.5.5

Boundary or PZM

Several approaches have been developed for eectively

using a microphone in less-than-ideal acoustic spaces,
which often suer from excessive reections from one
or more of the surfaces (boundaries) that make up the

A lavalier microphone is made for hands-free operation.

These small microphones are worn on the body. Originally, they were held in place with a lanyard worn around
the neck, but more often they are fastened to clothing
with a clip, pin, tape or magnet. The lavalier cord may

24.7. POWERING

167

be hidden by clothes and either run to an RF transmitter so that it can pick up environmental sounds to be subin a pocket or clipped to a belt (for mobile use), or run tracted from the main diaphragms signal. After the two
directly to the mixer (for stationary applications).
signals have been combined, sounds other than the inA wireless microphone transmits the audio as a radio or tended source are greatly reduced, substantially increasoptical signal rather than via a cable. It usually sends its ing intelligibility. Other noise-canceling designs use one
signal using a small FM radio transmitter to a nearby re- diaphragm that is aected by ports open to the sides and
ceiver connected to the sound system, but it can also use rear of the microphone, with the sum being a 16 dB rejecinfrared waves if the transmitter and receiver are within tion of sounds that are farther away. One noise-canceling
headset design using a single diaphragm has been used
sight of each other.
prominently by vocal artists such as Garth Brooks and
A contact microphone picks up vibrations directly from Janet Jackson.[42] A few noise-canceling microphones are
a solid surface or object, as opposed to sound vibrations throat microphones.
carried through air. One use for this is to detect sounds
of a very low level, such as those from small objects or
insects. The microphone commonly consists of a mag- 24.7 Powering
netic (moving coil) transducer, contact plate and contact
pin. The contact plate is placed directly on the vibrating part of a musical instrument or other surface, and the Microphones containing active circuitry, such as most
contact pin transfers vibrations to the coil. Contact mi- condenser microphones, require power to operate the accrophones have been used to pick up the sound of a snails tive components. The rst of these used vacuum-tube
heartbeat and the footsteps of ants. A portable version of circuits with a separate power supply unit, using a multithis microphone has recently been developed. A throat pin cable and connector. With the advent of solid-state
microphone is a variant of the contact microphone that amplication, the power requirements were greatly repicks up speech directly from a persons throat, which it duced and it became practical to use the same cable conis strapped to. This lets the device be used in areas with ductors and connector for audio and power. During the
ambient sounds that would otherwise make the speaker 1960s several powering methods were developed, mainly
in Europe. The two dominant methods were initially deinaudible.
ned in German DIN 45595 as de:Tonaderspeisung or
A parabolic microphone uses a parabolic reector to col- T-power and DIN 45596 for phantom power. Since the
lect and focus sound waves onto a microphone receiver, in 1980s, phantom power has become much more common,
much the same way that a parabolic antenna (e.g. satellite because the same input may be used for both powered
dish) does with radio waves. Typical uses of this micro- and unpowered microphones. In consumer electronics
phone, which has unusually focused front sensitivity and such as DSLRs and camcorders, plug-in power is more
can pick up sounds from many meters away, include na- common, for microphones using a 3.5 mm phone plug
ture recording, outdoor sporting events, eavesdropping, connector. Phantom, T-power and plug-in power are delaw enforcement, and even espionage. Parabolic micro- scribed in international standard IEC 61938.[43]
phones are not typically used for standard recording applications, because they tend to have poor low-frequency
response as a side eect of their design.
24.8 Connectors
A stereo microphone integrates two microphones in one
unit to produce a stereophonic signal. A stereo microphone is often used for broadcast applications or eld
recording where it would be impractical to congure two
separate condenser microphones in a classic X-Y conguration (see microphone practice) for stereophonic recording. Some such microphones have an adjustable angle of
coverage between the two channels.
A noise-canceling microphone is a highly directional design intended for noisy environments. One such use is
in aircraft cockpits where they are normally installed as
boom microphones on headsets. Another use is in live
event support on loud concert stages for vocalists involved
with live performances. Many noise-canceling microphones combine signals received from two diaphragms
Electronic symbol for a microphone
that are in opposite electrical polarity or are processed
electronically. In dual diaphragm designs, the main diThe most common connectors used by microphones are:
aphragm is mounted closest to the intended source and
the second is positioned farther away from the source
Male XLR connector on professional microphones

168

CHAPTER 24. MICROPHONE

inch (sometimes referred to as 6.3 mm) phone professional-quality microphones with USB connections
connector on less expensive musicians micro- have begun to appear, designed for direct recording into
phones, using an unbalanced 1/4 inch (6.3 mm) TS computer-based software.
phone connector. Harmonica microphones commonly use a high impedance 1/4 inch (6.3 mm) TS
connection to be run through guitar ampliers.
3.5 mm (sometimes referred to as 1/8 inch mini)
stereo (sometimes wired as mono) mini phone plug 24.8.1 Impedance-matching
on prosumer camera, recorder and computer microphones.
Microphones have an electrical characteristic called
impedance, measured in ohms (), that depends on the
design. In passive microphones, this value describes the
electrical resistance of the magnet coil (or similar mechanism). In active microphones, this value describes the
output resistance of the amplier circuitry. Typically, the
rated impedance is stated.[44] Low impedance is considered under 600 . Medium impedance is considered between 600 and 10 k. High impedance is above 10 k.
Owing to their built-in amplier, condenser microphones
typically have an output impedance between 50 and 200
.[45]
The output of a given microphone delivers the same
power whether it is low or high impedance. If a microphone is made in high and low impedance versions, the
high impedance version has a higher output voltage for
a given sound pressure input, and is suitable for use with
vacuum-tube guitar ampliers, for instance, which have a
high input impedance and require a relatively high signal
input voltage to overcome the tubes inherent noise. Most
professional microphones are low impedance, about 200
or lower. Professional vacuum-tube sound equipment
incorporates a transformer that steps up the impedance of
the microphone circuit to the high impedance and voltage
needed to drive the input tube. External matching transformers are also available that can be used in-line between
a low impedance microphone and a high impedance input.
Low-impedance microphones are preferred over high
impedance for two reasons: one is that using a highimpedance microphone with a long cable results in high
frequency signal loss due to cable capacitance, which
forms a low-pass lter with the microphone output
impedance. The other is that long high-impedance cables
tend to pick up more hum (and possibly radio-frequency
interference (RFI) as well). Nothing is damaged if the
impedance between microphone and other equipment is
mismatched; the worst that happens is a reduction in signal or change in frequency response.
A microphone with a USB connector, made by Blue Microphones

Some microphones use other connectors, such as a 5pin XLR, or mini XLR for connection to portable equipment. Some lavalier (or lapel, from the days of attaching the microphone to the news reporters suit lapel) microphones use a proprietary connector for connection to
a wireless transmitter, such as a radio pack. Since 2005,

Some microphones are designed not to have their

impedance matched by the load they are connected to.[46]
Doing so can alter their frequency response and cause distortion, especially at high sound pressure levels. Certain
ribbon and dynamic microphones are exceptions, due to
the designers assumption of a certain load impedance being part of the internal electro-acoustical damping circuit
of the microphone.[47]

24.9. MEASUREMENTS AND SPECIFICATIONS

169

A comparison of the far eld on-axis frequency response of the

Oktava 319 and the Shure SM58

produce a desirable coloration of the sound. There is an

international standard for microphone specications,[44]
but few manufacturers adhere to it. As a result, comparison of published data from dierent manufacturers
is dicult because dierent measurement techniques are
used. The Microphone Data Website has collated the
technical specications complete with pictures, response
curves and technical data from the microphone manufacturers for every currently listed microphone, and even a
Neumann D-01 digital microphone and Neumann DMI-8 8few obsolete models, and shows the data for them all in
channel USB Digital Microphone Interface
one common format for ease of comparison.. Caution
should be used in drawing any solid conclusions from this
or any other published data, however, unless it is known
24.8.2 Digital microphone interface
that the manufacturer has supplied specications in acThe AES42 standard, published by the Audio Engineer- cordance with IEC 60268-4.
ing Society, denes a digital interface for microphones. A frequency response diagram plots the microphone senMicrophones conforming to this standard directly out- sitivity in decibels over a range of frequencies (typically
put a digital audio stream through an XLR or XLD male 20 Hz to 20 kHz), generally for perfectly on-axis sound
connector, rather than producing an analog output. Dig- (sound arriving at 0 to the capsule). Frequency response
ital microphones may be used either with new equip- may be less informatively stated textually like so: 30 Hz
ment with appropriate input connections that conform to 16 kHz 3 dB. This is interpreted as meaning a nearly
the AES42 standard, or else via a suitable interface box. at, linear, plot between the stated frequencies, with variStudio-quality microphones that operate in accordance ations in amplitude of no more than plus or minus 3 dB.
with the AES42 standard are now available from a num- However, one cannot determine from this information
ber of microphone manufacturers.
how smooth the variations are, nor in what parts of the
spectrum they occur. Note that commonly made statements such as 20 Hz20 kHz are meaningless witha decibel measure of tolerance. Directional micro24.9 Measurements and specica- out
phones frequency response varies greatly with distance
from the sound source, and with the geometry of the
tions
sound source. IEC 60268-4 species that frequency reBecause of dierences in their construction, micro- sponse should be measured in plane progressive wave conphones have their own characteristic responses to sound. ditions (very far away from the source) but this is seldom
This dierence in response produces non-uniform phase practical. Close talking microphones may be measured
and frequency responses. In addition, microphones are with dierent sound sources and distances, but there is
not uniformly sensitive to sound pressure, and can accept no standard and therefore no way to compare data from
diering levels without distorting. Although for scientic dierent models unless the measurement technique is deapplications microphones with a more uniform response scribed.
are desirable, this is often not the case for music record- The self-noise or equivalent input noise level is the sound
ing, as the non-uniform response of a microphone can level that creates the same output voltage as the micro-

170
phone does in the absence of sound. This represents the
lowest point of the microphones dynamic range, and is
particularly important should you wish to record sounds
that are quiet. The measure is often stated in dB(A),
which is the equivalent loudness of the noise on a decibel scale frequency-weighted for how the ear hears, for
example: 15 dBA SPL (SPL means sound pressure
level relative to 20 micropascals). The lower the number the better. Some microphone manufacturers state
the noise level using ITU-R 468 noise weighting, which
more accurately represents the way we hear noise, but
gives a gure some 1114 dB higher. A quiet microphone typically measures 20 dBA SPL or 32 dB SPL 468weighted. Very quiet microphones have existed for years
for special applications, such the Brel & Kjaer 4179,
with a noise level around 0 dB SPL. Recently some microphones with low noise specications have been introduced in the studio/entertainment market, such as models from Neumann and Rde that advertise noise levels
between 57 dBA. Typically this is achieved by altering
the frequency response of the capsule and electronics to
result in lower noise within the A-weighting curve while
broadband noise may be increased.
The maximum SPL the microphone can accept is measured for particular values of total harmonic distortion
(THD), typically 0.5%. This amount of distortion is generally inaudible, so one can safely use the microphone at
this SPL without harming the recording. Example: 142
dB SPL peak (at 0.5% THD)". The higher the value, the
better, although microphones with a very high maximum
SPL also have a higher self-noise.

CHAPTER 24. MICROPHONE

V/Pa standard and measured in plain decibels, resulting in
a negative value. Again, a higher value indicates greater
sensitivity, so 60 dB is more sensitive than 70 dB.

24.10 Measurement microphones

Some microphones are intended for testing speakers,
measuring noise levels and otherwise quantifying an
acoustic experience. These are calibrated transducers
and are usually supplied with a calibration certicate that
states absolute sensitivity against frequency. The quality
of measurement microphones is often referred to using
the designations Class 1, Type 2 etc., which are references not to microphone specications but to sound level
meters.[48] A more comprehensive standard[49] for the description of measurement microphone performance was
recently adopted.
Measurement microphones are generally scalar sensors of
pressure; they exhibit an omnidirectional response, limited only by the scattering prole of their physical dimensions. Sound intensity or sound power measurements
require pressure-gradient measurements, which are typically made using arrays of at least two microphones, or
with hot-wire anemometers.

The clipping level is an important indicator of maximum

usable level, as the 1% THD gure usually quoted under 24.10.1 Calibration
max SPL is really a very mild level of distortion, quite
inaudible especially on brief high peaks. Clipping is much
more audible. For some microphones the clipping level Main article: Measurement microphone calibration
may be much higher than the max SPL.
The dynamic range of a microphone is the dierence in
SPL between the noise oor and the maximum SPL. If
stated on its own, for example 120 dB, it conveys signicantly less information than having the self-noise and
maximum SPL gures individually.
Sensitivity indicates how well the microphone converts
acoustic pressure to output voltage. A high sensitivity
microphone creates more voltage and so needs less amplication at the mixer or recording device. This is a
practical concern but is not directly an indication of the
microphones quality, and in fact the term sensitivity is
something of a misnomer, transduction gain being perhaps more meaningful, (or just output level) because
true sensitivity is generally set by the noise oor, and too
much sensitivity in terms of output level compromises
the clipping level. There are two common measures. The
(preferred) international standard is made in millivolts
per pascal at 1 kHz. A higher value indicates greater sensitivity. The older American method is referred to a 1

To take a scientic measurement with a microphone, its

precise sensitivity must be known (in volts per pascal).
Since this may change over the lifetime of the device,
it is necessary to regularly calibrate measurement microphones. This service is oered by some microphone manufacturers and by independent certied testing labs. All microphone calibration is ultimately traceable to primary standards at a national measurement institute such as NPL in the UK, PTB in Germany and NIST
in the United States, which most commonly calibrate using the reciprocity primary standard. Measurement microphones calibrated using this method can then be used
to calibrate other microphones using comparison calibration techniques.
Depending on the application, measurement microphones
must be tested periodically (every year or several months,
typically) and after any potentially damaging event, such
as being dropped (most such microphones come in foampadded cases to reduce this risk) or exposed to sounds
beyond the acceptable level.

24.12. WINDSCREENS

171

24.11 Arrays

The shielding material used wire gauze, fabric or foam

is designed to have a signicant acoustic impedance.
The relatively low particle-velocity air pressure changes
Main article: Microphone array
that constitute sound waves can pass through with minimal attenuation, but higher particle-velocity wind is imA microphone array is any number of microphones oper- peded to a far greater extent. Increasing the thickness of
ating in tandem. There are many applications:
the material improves wind attenuation but also begins
to compromise high frequency audio content. This limits
Systems for extracting voice input from ambient the practical size of simple foam screens. While foams
noise (notably telephones, speech recognition sys- and wire meshes can be partly or wholly self-supporting,
soft fabrics and gauzes require stretching on frames, or
tems, hearing aids)
laminating with coarser structural elements.
Surround sound and related technologies
Since all wind noise is generated at the rst surface the
Locating objects by sound: acoustic source local- air hits, the greater the spacing between shield periphery
ization, e.g., military use to locate the source(s) of and microphone capsule, the greater the noise attenuation. For an approximately spherical shield, attenuation
artillery re. Aircraft location and tracking.
increases by (approximately) the cube of that distance.
High delity original recordings
Thus larger shields are always much more ecient than
smaller ones.[50] With full basket windshields there is an
3D spatial beamforming for localized acoustic deadditional pressure chamber eect, rst explained by Jotection of subcutaneous sounds
erg Wuttke,[51] which, for two-port (pressure gradient)
microphones, allows the shield/microphone combination
Typically, an array is made up of omnidirectional micro- to act as a high-pass acoustic lter.
phones distributed about the perimeter of a space, linked
Since turbulence at a surface is the source of wind noise,
to a computer that records and interprets the results into
reducing gross turbulence can add to noise reduction.
a coherent form.
Both aerodynamically smooth surfaces, and ones that prevent powerful vortices being generated, have been used
successfully. Historically, articial fur has proved very
24.12 Windscreens
useful for this purpose since the bres produce microturbulence and absorb energy silently. If not matted by
wind and rain, the fur bres are very transparent acoustically, but the woven or knitted backing can give signicant attenuation. As a material it suers from being dicult to manufacture with consistency, and to keep in pristine condition on location. Thus there is an interest (DPA
5100, Rycote Cyclone) to move away from its use.[52]
In the studio and on stage, pop-screens and foam shields
can be useful for reasons of hygiene, and protecting microphones from spittle and sweat. They can also be useful
coloured idents. On location the basket shield can contain
a suspension system to isolate the microphone from shock
and handling noise.
Microphone with its windscreen removed.

See also: Pop lter

Windscreens (or windshields the terms are interchangeable) provide a method of reducing the eect of
wind on microphones. While pop-screens give protection
from unidirectional blasts, foam hats shield wind into
the grille from all directions, and blimps / zeppelins / baskets entirely enclose the microphone and protect its body
as well. This last point is important because, given the
extreme low frequency content of wind noise, vibration
induced in the housing of the microphone can contribute
substantially to the noise output.

Stating the eciency of wind noise reduction is an inexact science, since the eect varies enormously with frequency, and hence with the bandwidth of the microphone
and audio channel. At very low frequencies (10100 Hz)
where massive wind energy exists, reductions are important to avoid overloading of the audio chain particularly
the early stages. This can produce the typical wumping sound associated with wind, which is often syllabic
muting of the audio due to LF peak limiting. At higher
frequencies 200 Hz to ~3 kHz the aural sensitivity
curve allows us to hear the eect of wind as an addition
to the normal noise oor, even though it has a far lower
energy content. Simple shields may allow the wind noise
to be 10 dB less apparent; better ones can achieve nearer

172
to a 50 dB reduction. However the acoustic transparency,
particularly at HF, should also be indicated, since a very
high level of wind attenuation could be associated with
very mued audio.
Various microphone covers
Two recordings being madea blimp is being used
on the left. An open-cell foam windscreen is being
used on the right.
Dead cat and a dead kitten windscreens. The
dead kitten covers a stereo microphone for a DSLR
camera. The dierence in name is due to the size of
the fur.

24.13 See also

Geophonetransducer for sound within the earth
Hydrophonetransducer for sound in water
Ionophoneplasma-based microphone
Microphone connector
Microphone practiceexamples of usage
Nominal impedance
Shock mountMicrophone mount that suspends
the microphone in elastic straps

24.14 References
[1] Zimmer, Ben (29 July 2010). How Should 'Microphone'
be Abbreviated?". The New York Times. Retrieved 10
September 2010.
[2] Montgomery, Henry C (1959). Amplication and High
Fidelity in the Greek Theater. The Classical Journal. 54
(6): 242245. JSTOR 3294133.
[3] McVeigh, Daniel (2000). An Early History of the Telephone: 16641866: Robert Hookes Acoustic Experiments and Acoustic Inventions. Archived from the original on 2003-09-03.
[4] MacLeod, Elizabeth 1999 Alexander Graham Bell: an inventive life. Kids Can Press, Toronto
[5] Paul J. Nahin (2002). Oliver Heaviside: The Life, Work,
and Times of an Electrical Genius of the Victorian Age.
JHU Press. p. 67.
[6] Bob Estreich. David Edward Hughes.
[7] Huurdeman, Anton (2003). The Worldwide History of
Telecommunications. John Wiley & Sons.
[8] David Hughes. Retrieved 2012-12-17.

CHAPTER 24. MICROPHONE

[9] David Edward Hughes: Concertinist and Inventor

(PDF). Archived from the original (PDF) on 2013-12-31.
Retrieved 2012-12-17.
[10] A brief history of microphones (PDF). Retrieved 201212-17.
[11] Lee De Forest (18731961)". Television International
Magazine. 2011-01-17. Archived from the original on
2011-01-17. Retrieved Dec 4, 2013.
[12] Cory, Troy (2003-01-21). ""Radio Boys & The
SMART-DAAF BOYS"". Archived from the original on
January 21, 2003.
[13] Fagen, M.D. A History of Engineering and Science in the
Bell System: The Early Years (18751925). New York:
Bell Telephone Laboratories, 1975
[14] Hennessy, Brian 2005 The Emergence of Broadcasting in
Britain Devon Southerleigh
[15] Robjohns, Hugh (2001). A Brief History of Microphones (PDF). Microphone Data Book. Archived from
the original (PDF) on 2010-11-25.
[16] 1931 Harry F. Olson and Les Anderson, RCA Model
44 Ribbon Microphone. Mix Magazine. Sep 1, 2006.
Archived from the original on 2008-03-24. Retrieved 10
April 2013.
[17] History The evolution of an audio revolution. Shure
Americas. Archived from the original on 2012-09-15.
Retrieved 13 April 2013.
[18] Bell Laboratories and The Development of Electrical
Recording. Stokowski.org (Leopold Stokowski site).
[19] Institute BV Amsterdam, SAE. Microphones. Practical
Creative Media Education. Retrieved 2014-03-07.
[20] Sessler, G.M.; West, J.E. (1962). Self-biased condenser microphone with high capacitance. Journal of
the Acoustical Society of America. 34 (11): 17871788.
doi:10.1121/1.1909130.
[21] Archived August 19, 2010, at the Wayback Machine.
[22] AKG D 112 Large-diaphragm dynamic microphone for
bass instruments"
[23] Local rms strum the chords of real music innovation.
Mass High Tech: the Journal of New England Technology.
February 8, 2008.
[24] Boudets Microphone. Machine-History.com.
[25] http://www.pitt.edu/~{}qiw4/Academic/ME2080/
ZnO%20circular%20microphone.pdf
[26] Paritsky, Alexander; Kots, A. (1997). Fiber optic microphone as a realization of ber optic positioning sensors. Proc. of International Society for Optical Engineering (SPIE). 3110: 408409. doi:10.1117/12.281371.
[27] US patent 6462808, Alexander Paritsky and Alexander
Kots, Small optical microphone/sensor, issued 200210-08

24.15. EXTERNAL LINKS

[28] Karlin, Susan. Case Study: Can You Hear Me Now?".

rt-image.com. Valley Forge Publishing. Archived from
the original on 2011-07-15.
[29] Cirrus Logic Completes Acquisition of Wolfson Microelectronics. MarketWatch.com. Retrieved 2014-08-21.
[30] Analog Devices To Sell Microphone Product Line To InvenSense. MarketWatch.com. Retrieved 2015-11-27.
[31] Knowles Completes Acquisition of NXPs Sound Solutions Business. Knowles. Retrieved 2011-07-05.
[32] MEMS Microphone Will Be Hurt by Downturn in
Smartphone Market. Seeking Alpha. Retrieved 200908-23.

173

24.15 External links

Info, Pictures and Soundbytes from vintage microphones
Microphone sensitivity conversiondB re 1 V/Pa
and transfer factor mV/Pa
Searchable database of specs and component info
from 1000+ microphones
Microphone construction and basic placement advice
History of the Microphone

[33] OMRON to Launch Mass-production and Supply of

MEMS Acoustic Sensor Chip -Worlds rst MEMS sensor capable of detecting the lower limit of human audible
frequencies-". Retrieved 2009-11-24.

Large vs. Small Diaphragms in Omnidirectional

Microphones

[34] MEMS Mics Taking Over. EETimes.

Measurement/Engineering Grade Microphone Basics

[35] Bartlett, Bruce. How A Cardioid Microphone Works.

[36] History & Development of Microphone. Lloyd Microphone Classics.
[37] Proximity Eect. Geo Martin, Introduction to Sound
Recording.
[38] History The evolution of an audio revolution. Shure.
Retrieved 2013-07-30.
[39] Dave Berners (December 2005). Ask the Doctors: The
Physics of Mid-Side (MS) Miking. Universal Audio WebZine. Universal Audio. Retrieved 2013-07-30.
[40] Directional Patterns of Microphones. Retrieved 201307-30.
[41] (US 4361736)
[42] Crown Audio. Tech Made Simple. The Crown Dieroid Microphone Archived May 10, 2012, at the Wayback
Machine.
[43] http://webstore.iec.ch/webstore/webstore.nsf/Artnum_
PK/48193
[44] International Standard IEC 60268-4
[45] Eargle, John; Chris Foreman (2002). Audio Engineering
for Sound Reinforcement. Milwaukee: Hal Leonard Corporation. p. 66. ISBN 0-634-04355-2.
[46] Archived April 28, 2010, at the Wayback Machine.
[47] Robertson, A. E.: Microphones Illie Press for BBC,
19511963
[48] IEC Standard 61672 and ANSI S1.4
[49] IEC 61094
[50] Blasted microphones (PDF).
[51] Joerg Wuttke - Microphones and Wind.
[52] Rycote Cyclone.

Guide to Condenser Microphones

Chapter 25

FM broadcasting

AM and FM modulated signals for radio. AM (Amplitude Modulation) and FM (Frequency Modulation) are types of modulation
(coding). The electrical signal from program material, usually
coming from a studio, is mixed with a carrier wave of a specic
frequency, then broadcast. In the case of AM, this mixing (modulation) is done by altering the amplitude of the carrier wave with
time, according to the original signal. In the case of FM, it is the
frequency of the carrier wave that is varied. A radio receiver
(a radio) contains a demodulator that extracts the original program material from the broadcast wave.

FM Radio Broadcasting : Big Picture in Full Electromagnetic

Spectrum

FM broadcasting is a method of radio broadcasting using frequency modulation (FM) technology. Invented in
1933 by American engineer Edwin Armstrong, it is used
worldwide to provide high-delity sound over broadcast
radio. FM broadcasting is capable of better sound quality
than AM broadcasting, the chief competing radio broadcasting technology, so it is used for most music broadcasts. FM radio stations use the VHF frequencies. The
term FM band describes the frequency band in a given
country which is dedicated to FM broadcasting.

25.1 Broadcast bands

Main article: FM broadcast band

A commercial 35 kW FM radio transmitter built in the late 1980s.

It belongs to FM radio station KWNR in Las Vegas, NV, USA, and
broadcasts at a frequency of 95.5 MHz.

Throughout the world, the FM broadcast band falls within exceptions:

the VHF part of the radio spectrum. Usually 87.5 to
108.0 MHz is used,[1] or some portion thereof, with few
In the former Soviet republics, and some former
174

25.2. MODULATION CHARACTERISTICS

175

Eastern Bloc countries, the older 6574 MHz band

is also used. Assigned frequencies are at intervals
of 30 kHz. This band, sometimes referred to as
the OIRT band, is slowly being phased out in many
countries. In those countries the 87.5108.0 MHz
band is referred to as the CCIR band.
In Japan, the band 7695 MHz is used.
The frequency of an FM broadcast station (more strictly
its assigned nominal center frequency) is usually an exact multiple of 100 kHz. In most of South Korea, the
Americas, the Philippines and the Caribbean, only odd
multiples are used. In some parts of Europe, Greenland
and Africa, only even multiples are used. In the UK odd
or even are used. In Italy, multiples of 50 kHz are used.
There are other unusual and obsolete FM broadcasting
standards in some countries, including 1, 10, 30, 74, 500,
and 300 kHz. However, to minimise inter-channel interference, stations operating from the same or geographically close transmitter sites tend to keep to at least a 500
kHz frequency separation even when closer frequency
spacing is technically permitted, with closer tunings reserved for more distantly spaced transmitters, as potentially interfering signals are already more attenuated and
so have less eect on neighboring frequencies.

FM has better rejection of static (RFI) than AM. This was shown
in a dramatic demonstration by General Electric at its New York
lab in 1940. The radio had both AM and FM receivers. With
a million volt arc as a source of interference behind it, the AM
receiver produced only a roar of static, while the FM receiver
clearly reproduced a music program from Armstrongs experimental FM transmitter in New Jersey.

25.2 Modulation characteristics

25.2.1

Modulation

Frequency modulation or FM is a form of modulation

which conveys information by varying the frequency of
a carrier wave; the older amplitude modulation or AM
varies the amplitude of the carrier, with its frequency remaining constant. With FM, frequency deviation from
the assigned carrier frequency at any instant is directly
proportional to the amplitude of the input signal, determining the instantaneous frequency of the transmitted signal. Because transmitted FM signals use more
bandwidth than AM signals, this form of modulation is
commonly used with the higher (VHF or UHF) frequen- Armstrongs rst prototype FM broadcast transmitter, located in
cies used by TV, the FM broadcast band, and land mobile the Empire State Building, New York City, which he used for seradio systems.
cret tests of his system between 1934 and 1935. Licensed as experimental station W2XDG, it transmitted on 41 MHz at a power
of 2 kW

25.2.2

Pre-emphasis and de-emphasis

Random noise has a triangular spectral distribution in

an FM system, with the eect that noise occurs predominantly at the highest audio frequencies within the
baseband. This can be oset, to a limited extent, by
boosting the high frequencies before transmission and reducing them by a corresponding amount in the receiver.
Reducing the high audio frequencies in the receiver also
reduces the high-frequency noise. These processes of

boosting and then reducing certain frequencies are known

as pre-emphasis and de-emphasis, respectively.
The amount of pre-emphasis and de-emphasis used is dened by the time constant of a simple RC lter circuit. In
most of the world a 50 s time constant is used. In the
Americas and South Korea, 75 s is used. This applies
to both mono and stereo transmissions. For stereo, preemphasis is applied to the left and right channels before

176
multiplexing.

CHAPTER 25. FM BROADCASTING

purposes. The Halstead system was rejected due to lack
of high frequency stereo separation and reduction in the
main channel signal-to-noise ratio. The GE and Zenith
systems, so similar that they were considered theoretically
identical, were formally approved by the FCC in April
1961 as the standard stereo FM broadcasting method
in the United States and later adopted by most other
countries.[3]

The amount of pre-emphasis that can be applied is limited by the fact that many forms of contemporary music contain more high-frequency energy than the musical styles which prevailed at the birth of FM broadcasting. They cannot be pre-emphasized as much because it
would cause excessive deviation of the FM carrier. Systems more modern than FM broadcasting tend to use either programme-dependent variable pre-emphasis; e.g., It is important that stereo broadcasts be compatible with
dbx in the BTSC TV sound system, or none at all.
mono receivers. For this reason, the left (L) and right
(R) channels are algebraically encoded into sum (L+R)
and dierence (LR) signals. A mono receiver will use
just the L+R signal so the listener will hear both channels
25.2.3 Stereo FM
through the single loudspeaker. A stereo receiver will add
the dierence signal to the sum signal to recover the left
Long before FM stereo transmission was considered, FM
channel, and subtract the dierence signal from the sum
multiplexing of other types of audio level information was
to recover the right channel.
experimented with.[2] The original station to experiment
with multiplexing was W2XDG (New York City) on 41 The (L+R) Main channel signal is transmitted as baseMHz, located on the 85th oor of the Empire State Build- band audio limited to the range of 30 Hz to 15 kHz.
The (LR) signal is amplitude modulated onto a 38 kHz
ing.
double-sideband suppressed-carrier (DSB-SC) signal ocThese FM multiplex transmissions started in November
cupying the baseband range of 23 to 53 kHz.
1934 and consisted of the main channel audio program
and three subcarriers: a fax program, a synchronizing sig- A 19 kHz pilot tone, at exactly half the 38 kHz sub-carrier
nal for the fax program and a telegraph order channel. frequency and with a precise phase relationship to it, as
These original FM multiplex subcarriers were amplitude dened by the formula below, is also generated. This
is transmitted at 810% of overall modulation level and
modulated.
used by the receiver to regenerate the 38 kHz sub-carrier
Two musical programs, consisting of both the Red and
with the correct phase.
Blue Network program feeds of the NBC Radio Network,
were simultaneously transmitted using the same system of The nal multiplex signal from the stereo generator consubcarrier modulation as part of a studio-to-transmitter tains the Main Channel (L+R), the pilot tone, and the
like system. In April 1935, the AM subcarriers were re- sub-channel (LR). This composite signal, along with any
other sub-carriers, modulates the FM transmitter.
placed by FM subcarriers, with much improved results.
The rst FM subcarrier transmissions emanating from
Major Armstrongs experimental station KE2XCC at
Alpine, New York occurred in 1948. These transmissions consisted of two-channel audio programs, binaural
audio programs and a fax program. The original subcarrier frequency used at KE2XCC was 27.5 kHz. The IF
bandwidth was +/5 kHz, as the only goal at the time was
to relay AM radio-quality audio. This transmission system notably used a 75 microsecond audio pre-emphasis, a
technical innovation that became part of the original FM
Stereo Multiplex Standard.

The instantaneous deviation of the transmitter carrier frequency due to the stereo audio and pilot tone (at 10%
modulation) is
[

[
0.9 A+B
+
2
75 kHz [4]

AB
2

]
]
sin 4fp t + 0.1 sin 2fp t

where A and B are the pre-emphasized left and right audio signals and fp =19 kHz is the frequency of the pilot
tone. Slight variations in the peak deviation may occur
In the late 1950s, several systems to add stereo to FM in the presence of other subcarriers or because of local
radio were considered by the FCC. Included were sys- regulations.
tems from 14 proponents including Crosby, Halstead, Another way to look at the resulting signal is that it alElectrical and Musical Industries, Ltd (EMI), Zenith, and ternates between left and right at 38 kHz, with the phase
General Electric. The individual systems were evaluated determined by the 19 kHz pilot signal.[5]
for their strengths and weaknesses during eld tests in
Uniontown, Pennsylvania using KDKA-FM in Pittsburgh Converting the multiplex signal back into left and right
as the originating station. The Crosby system was re- audio signals is performed by a decoder, built into stereo
jected by the FCC because it was incompatible with exist- receivers.
ing subsidiary communications authorization (SCA) ser- In order to preserve stereo separation and signal-to-noise
vices which used various subcarrier frequencies includ- parameters, it is normal practice to apply pre-emphasis to
ing 41 and 67 kHz. Many revenue-starved FM stations the left and right channels before encoding, and to apply
used SCAs for storecasting and other non-broadcast de-emphasis at the receiver after decoding.

25.2. MODULATION CHARACTERISTICS

177

Stereo FM signals are more susceptible to noise and mul- (now called WWWW-FM) in Ann Arbor/Saline, Michitipath distortion than are mono FM signals.[6]
gan under the guidance of Chief Engineer Brian Jerey
[8]
In addition, for a given RF level at the receiver, the signal- Brown.
to-noise ratio for the stereo signal will be worse than for
the mono receiver. For this reason many stereo FM re25.2.5
ceivers include a stereo/mono switch to allow listening
in mono when reception conditions are less than ideal,
and most car radios are arranged to reduce the separation as the signal-to-noise ratio worsens, eventually going
to mono while still indicating a stereo signal is being received.

25.2.4

Other subcarrier services

Quadraphonic FM

In 1969, Louis Dorren invented the Quadraplex system

of single station, discrete, compatible four-channel FM Typical spectrum of composite baseband signal
broadcasting. There are two additional subcarriers in the
Quadraplex system, supplementing the single one used in
FM broadcasting has included SCA capability since its
standard stereo FM. The baseband layout is as follows:
inception, as it was seen as another service which licensees could use to create additional income.[9] Initially
50 Hz to 15 kHz Main Channel (sum of all 4 chan- the users of SCA services were private analog audio channels) (LF+LR+RF+RR) signal, for mono FM listen- nels which could be used internally or rented out, for exing compatibility.
ample Muzak type services. Radio reading services for
the
blind became a common use, and remain so, and there
23 to 53 kHz (sine quadrature subcarrier) (LF+LR)
were
experiments with quadraphonic sound. If a station
- (RF+RR) Left minus Right dierence signal. This
does
not
broadcast in stereo, everything from 23 kHz on
signals modulation in algebraic sum and dierence
up
can
be
used for other services. The guard band around
with the Main channel is used for 2 channel stereo
19
kHz
(4
kHz) must still be maintained, so as not to
listener compatibility.
trigger stereo decoders on receivers. If there is stereo,
23 to 53 kHz (cosine quadrature 38 kHz subcarrier) there will typically be a guard band between the upper
(LF+RR) - (LR+RF) Diagonal dierence. This sig- limit of the DSBSC stereo signal (53 kHz) and the lower
nals modulation in algebraic sum and dierence limit of any other subcarrier.
with the Main channel and all the other subcarriers
Digital services are now also available. A 57 kHz subis used for the Quadraphonic listener.
carrier (phase locked to the third harmonic of the stereo
61 to 91 kHz (sine quadrature 76 kHz subcarrier) pilot tone) is used to carry a low-bandwidth digital Radio
(LF+RF) - (LR+RR) Front-back dierence. This Data System signal, providing extra features such as
signals modulation in algebraic sum and dierence Alternative Frequency (AF) and Network (NN). This
with the main channel and all the other subcarriers narrowband signal runs at only 1,187.5 bits per second,
thus is only suitable for text. A few proprietary systems
is also used for the Quadraphonic listener.
are used for private communications. A variant of RDS
105 kHz SCA subcarrier, phase-locked to 19 kHz is the North American RBDS or smart radio system.
pilot, for reading services for the blind, background In Germany the analog ARI system was used prior to
music, etc.
RDS for broadcasting trac announcements to motorists
(without disturbing other listeners). Plans to use ARI for
The normal stereo signal can be considered as switching other European countries led to the development of RDS
between left and right channels at 38 kHz, appropriately as a more powerful system. RDS is designed to be capaband limited. The quadraphonic signal can be considered ble of being used alongside ARI despite using identical
as cycling through LF, LR, RF, RR, at 76 kHz.[7]
subcarrier frequencies.
There were several variations on this system submitted by
GE, Zenith, RCA, and Denon for testing and consideration during the National Quadraphonic Radio Committee
eld trials for the FCC. The original Dorren Quadraplex
System outperformed all the others and was chosen as
the national standard for Quadraphonic FM broadcasting
in the United States. The rst commercial FM station
to broadcast quadraphonic program content was WIQB

In the United States, digital radio services are being deployed within the FM band rather than using Eureka 147
or the Japanese standard ISDB. This in-band on-channel
approach, as do all digital radio techniques, makes use
of advanced compressed audio. The proprietary iBiquity
system, branded as "HD Radio", currently is authorized
for hybrid mode operation, wherein both the conventional analog FM carrier and digital sideband subcarri-

178

CHAPTER 25. FM BROADCASTING

ers are transmitted. Eventually, presuming widespread

deployment of HD Radio receivers, the analog services
could theoretically be discontinued and the FM band become all digital.
In the United States, services (other than stereo, quad
and RDS) using subcarriers are sometimes referred to
as subsidiary communications authorization (SCA) services. Uses for such subcarriers include book/newspaper
reading services for blind listeners, private data transmission services (for example sending stock market information to stockbrokers or stolen credit card number
blacklists to stores) subscription commercial-free background music services for shops, paging (beeper) services and providing a program feed for AM transmitters
of AM/FM stations. SCA subcarriers are typically 67
kHz and 92 kHz.

25.2.6

Dolby FM

A commercially unsuccessful noise reduction system

used with FM radio in some countries during the late
1970s, Dolby FM was similar to Dolby B[10] but used
a modied 25 s pre-emphasis time constant and a
frequency selective companding arrangement to reduce One of the rst FM radio stations, Edwin Armstrong's experimennoise. The pre-emphasis change compensates for the ex- tal station W2XMN in Alpine, New Jersey, USA. The insets show
cess treble response that otherwise would make listening a part of the transmitter, and a map of FM stations in 1940
dicult for those without Dolby decoders.
A similar system named High Com FM was tested in Ger25.4
many between July 1979 and December 1981 by IRT. It
was based on the Telefunken High Com broadband compander system, but never introduced commercially in FM 25.4.1
broadcasting.[11]
Further information: Dolby noise reduction system

25.3 Distance covered by stereo FM

transmission
The range of mono FM transmission is related to the
transmitter's RF power, the antenna gain, and antenna
height. The U.S. FCC publishes curves that aid in calculation of this maximum distance as a function of signal
strength at the receiving location.
Many FM stations, especially those located in severe multipath areas, use extra audio compression to keep essential sound above the background noise for listeners, occasionally at the expense of overall perceived sound quality.
In such instances, however, this technique is often surprisingly eective in increasing the stations useful range.

Adoption of FM broadcasting
United States

Despite FM having been patented in 1933, commercial FM broadcasting did not begin until the late
1930s, when it was initiated by a handful of early
pioneer stations including W8HK, Bualo, New York
(now WTSS); W1XOJ/WGTR/WSRS, Paxton, Massachusetts (now listed as Worcester, Massachusetts);
W1XSL/W1XPW/WDRC-FM, Meriden, Connecticut (now WHCN); W2XMN/KE2XCC/WFMN,
Alpine, New Jersey (owned by Edwin Armstrong
himself, closed down upon Armstrongs death in
1954); W2XQR/WQXQ/WQXR-FM, New York;
W47NV Nashville, Tennessee (signed o in 1951);
W1XER/W39B/WMNE, whose studios were in Boston
but whose transmitter was atop the highest mountain in
the northeast United States, Mount Washington, New
Hampshire (shut down in 1948); W9XAO Milwaukee,
Wisconsin (later WTMJ-FM, o air in 1950, returning
in 1959 on another frequency). Also of note are General
Electric stations W2XDA Schenectady and W2XOY
New Scotland, New Yorktwo experimental frequency
modulation transmitters on 48.5 MHzwhich signed on
in 1939. The two were merged into one station using

25.4. ADOPTION OF FM BROADCASTING

the W2XOY call letters on November 20, 1940, with
the station taking the WGFM call letters a few years
later, and moving to 99.5 MHz when the FM band
was relocated to the 88-108 MHz portion of the radio
spectrum. General Electric sold the station in the 1980s,
and today the station is called WRVE.

179
Public service broadcasters in Ireland and Australia were
far slower at adopting FM radio than those in either North
America or continental Europe.
United Kingdom

On June 1, 1961, at 12:01 a.m. (EDT), WGEM-FM be- In the United Kingdom, the BBC began FM broadcastcame the rst FM station in the United States to broadcast ing in 1955, with three national networks: the Light Proin stereo.[12]
gramme, Third Programme and Home Service. These
The rst commercial FM broadcasting stations were in three networks used the sub-band 88.094.6 MHz. The
the United States, but initially they were primarily used sub-band 94.697.6 MHz was later used for BBC and loto simulcast their AM sister stations, to broadcast lush cal commercial services.
orchestral music for stores and oces, to broadcast classical music to an upmarket listenership in urban areas,
or for educational programming. By the late 1960s, FM
had been adopted by fans of Alternative Rock music (A.O.R.'Album Oriented Rock' Format), but it
wasn't until 1978 that listenership to FM stations exceeded that of AM stations in North America. During
the 1980s and 1990s, Top 40 music stations and later
even country music stations largely abandoned AM for
FM. Today AM is mainly the preserve of talk radio,
news, sports, religious programming, ethnic (minority
language) broadcasting and some types of minority interest music. This shift has transformed AM into the alternative band that FM once was. (Some AM stations have
begun to simulcast on, or switch to, FM signals to attract
younger listeners and aid reception problems in buildings,
during thunderstorms, and near high-voltage wires. Some
of these stations now emphasize their presence on the FM
dial.)

25.4.2

Europe

The medium wave band (known as the AM band because

most stations using it employ amplitude modulation in
North America) is overcrowded in Western Europe, leading to interference problems and, as a result, many MW
frequencies are suitable only for speech broadcasting.

However, only when commercial broadcasting was introduced to the UK in 1973 did the use of FM pick up
in Britain. With the gradual clearance of other users
(notably Public Services such as police, re and ambulance) and the extension of the FM band to 108.0 MHz
between 1980 and 1995, FM expanded rapidly throughout the British Isles and eectively took over from LW
and MW as the delivery platform of choice for xed and
portable domestic and vehicle-based receivers. In addition, Ofcom (previously the Radio Authority) in the UK
issues on demand Restricted Service Licences on FM and
also on AM (MW) for short-term local-coverage broadcasting which is open to anyone who does not carry a prohibition and can put up the appropriate licensing and royalty fees. In 2010 around 450 such licences were issued.
When the BBCs radio networks were renamed Radio 2,
Radio 3 and Radio 4 respectively in 1967 to coincide with
the launch of Radio 1, the new station was the only one
of the main four to not have an FM frequency allocated,
which was the case for 21 years. Instead, Radio 1 shared
airtime with Radio 2 FM, on Saturday afternoons, Sunday evenings, weekday evenings (10pm to midnight) and
Bank Holidays. Eventually in 1987 a frequency range of
97.6-99.8 MHz was allocated as police relay transmitters were moved from the 100 MHz frequency, starting
in London before being broadly completed by 1989.[13]

Belgium, the Netherlands, Denmark and particularly Italy

Germany were among the rst countries to adopt FM on
Italy adopted FM broadcast widely in the early 1970s, but
a widespread scale. Among the reasons for this were:
rst experiments made by RAI dated back to 1950,[14]
1. The medium wave band in Western Europe became when the movement for free radio, developed by soovercrowded after World War II, mainly due to called pirates, forced the recognition of free speech
the best available medium wave frequencies being rights also through the use of free radio media such as
used at high power levels by the Allied Occupation Broadcast transmitters, and took the case to the ConstiForces, both for broadcasting entertainment to their tutional Court of Italy. The court nally decided in favor
troops and for broadcasting Cold War propaganda of Free Radio. Just weeks after the courts nal decision
there was an FM radio boom involving small private raacross the Iron Curtain.
dio stations across the country. By the mid 1970s, every
2. After World War II, broadcasting frequencies were
city in Italy had a crowded FM radio spectrum.
reorganized and reallocated by delegates of the
victorious countries in the Copenhagen Frequency
Plan. German broadcasters were left with only two Greece
remaining AM frequencies and were forced to look
Greece was another European country where the FM rato FM for expansion.

180

CHAPTER 25. FM BROADCASTING

dio spectrum was used at rst by the so-called pirates

(both in Athens and Thessaloniki, the two major Greek
cities) in the mid 1970s, before any national stations had
started broadcasting on it; there were many AM (MW)
stations in use for the purpose. No later than the end of
1977, the national public service broadcasting company
EIRT (later also known as ERT) placed in service its rst
FM transmitter in the capital, Athens. By the end of the
1970s, most of Greek territory was covered by three National FM programs, and every city had many FM pirates as well. The adaptation of the FM band for privately owned commercial radio stations came far later, in
1987.

25.4.3

Australia

FM started in Australia in 1947 but did not catch on and

was shut down in 1961 to expand the television band:
some TV stations were allocated within the VHF band
(98108 MHz). The ocial policy on FM at the time was
to eventually introduce it on another band, which would
have required FM tuners custom-built for Australia. This
policy was nally reversed and FM broadcasting was reopened in 1975 using the VHF band, after the few encroaching TV stations had been moved. Subsequently,
it developed steadily until in the 1980s many AM stations transferred to FM due to its superior sound quality. Today, as elsewhere in the developed world, most
urban Australian broadcasting is on FM, although AM
talk stations are still very popular. Regional broadcasters
still commonly operate AM stations due to the additional
range the broadcasting method oers. Some stations in
major regional centres simulcast on AM and FM bands.
Digital radio using the DAB+ standard has been rolled
out to capital cities.

25.4.4

New Zealand

Like Australia, New Zealand adopted the FM format relatively late. As was the case with privately owned AM
radio in the late 1960s, it took a spate of 'pirate' broadcasters to persuade a control-oriented, technology averse
government to allow FM to be introduced after at least
ve years of consumer campaigning starting in the mid1970s, particularly in Auckland. An experimental FM
station, FM 90.7, was broadcast in Whakatane in early
1982. Later that year, Victoria University of Wellington's
Radio Active began full-time FM transmissions. Commercial FM licences were nally approved in 1983, with
Auckland-based 91FM and 89FM being the rst to take
up the oer.. Broadcasting was deregulated in 1989.

25.4.5

which was transferred from the AM frequency (also

known as MW in Turkey). In subsequent years, more
MW stations were slowly transferred to FM, and by the
end of the 1970s, most radio stations that were previously
on MW had been moved to FM, though many talk, news
and sport, but mostly religious stations, still remain on
MW.

25.4.6 Other countries

Most other countries implemented FM broadcasting
through 1960s and expanded their use of FM through the
1990s. Because it takes a large number of FM transmitting stations to cover a geographically large country, particularly where there are terrain diculties, FM is more
suited to local broadcasting than for national networks.
In such countries, particularly where there are economic
or infrastructural problems, rolling out a national FM
broadcast network to reach the majority of the population can be a slow and expensive process. Despite this,
mostly in east European counties, national FM broadcast
networks were established in the late 1960s and 1970s. In
all Soviet-dependent countries but GDR, the OIRT band
was used. First restricted to 6873 MHz with 100 kHz
channel spacing, then in the 1970s eventually expanded
to 65.8474.00 MHz with 30 kHz channel spacing.[15]

25.4.7 ITU Conferences about FM

The frequencies available for FM were decided by some
important conferences of ITU. The milestone of those
conferences is the Stockholm agreement of 1961 among
38 countries.[16] A 1984 conference in Geneva made
some modications to the original Stockholm agreement
particularly in the frequency range above 100 MHz.

25.5 Small-scale use of the FM

broadcast band

Turkey

In Turkey, FM broadcasting began in the late 1960s,

Belkin TuneCast II FM microtransmitter
carrying several shows from the One television network

25.6. SEE ALSO

25.5.1

Consumer use of FM transmitters

In some countries, small-scale (Part 15 in United States

terms) transmitters are available that can transmit a signal from an audio device (usually an MP3 player or similar) to a standard FM radio receiver; such devices range
from small units built to carry audio to a car radio with
no audio-in capability (often formerly provided by special adapters for audio cassette decks, which are becoming less common on car radio designs) up to full-sized,
near-professional-grade broadcasting systems that can be
used to transmit audio throughout a property. Most such
units transmit in full stereo, though some models designed
for beginner hobbyists might not. Similar transmitters are
often included in satellite radio receivers and some toys.

181
bugs transmitter o the ends of the broadcast band, into
what in the United States would be TV channel 6 (<87.9
MHz) or aviation navigation frequencies (>107.9 MHz);
most FM radios with analog tuners have sucient overcoverage to pick up these slightly-beyond-outermost frequencies, although many digitally tuned radios have not.
Constructing a bug is a common early project for electronics hobbyists, and project kits to do so are available
from a wide variety of sources. The devices constructed,
however, are often too large and poorly shielded for use
in clandestine activity.
In addition, much pirate radio activity is broadcast in the
FM range, because of the bands greater clarity and listenership, the smaller size and lower cost of equipment.

Legality of these devices varies by country. The

U.S. Federal Communications Commission and Industry
Canada allow them. Starting on 1 October 2006, these 25.6 See also
devices became legal in most countries in the European
Union. Devices made to the harmonised European speci- 25.6.1 FM broadcasting by country
cation became legal in the UK on 8 December 2006.[17]
FM broadcasting in Australia
The FM broadcast band is also used by some inexpensive wireless microphones sold as toys for karaoke or
FM broadcasting in Canada
similar purposes, allowing the user to use an FM ra FM broadcasting in Egypt
dio as an output rather than a dedicated amplier and
speaker. Professional-grade wireless microphones gen FM broadcasting in India
erally use bands in the UHF region so they can run on
dedicated equipment without broadcast interference.
FM broadcasting in Japan
Some wireless headphones transmit in the FM broadcast
FM broadcasting in New Zealand
band, with the headphones tunable to only a subset of
the broadcast band. Higher-quality wireless headphones
FM broadcasting in Pakistan
use infrared transmission or UHF ISM bands such as 315
FM broadcasting in the UK
MHz, 915 MHz, or 2.4 GHz instead of the FM broadcast
band.
FM broadcasting in the United States

25.5.2

Microbroadcasting

Low-power transmitters such as those mentioned above

are also sometimes used for neighborhood or campus radio stations, though campus radio stations are often run
over carrier current. This is generally considered a form
of microbroadcasting. As a general rule, enforcement towards low-power FM stations is stricter than with AM
stations, due to problems such as the capture eect, and
as a result, FM microbroadcasters generally do not reach
as far as their AM competitors.

25.5.3

Clandestine use of FM transmitters

25.6.2 FM broadcasting (technical)

AM broadcasting
AM stereo (related technology)
FM broadcast band
FM stereo
Frequency modulation
Long-distance FM reception (FM DX)
Ripping music from FM broadcasts
RDS (Radio Data System)

FM transmitters have been used to construct miniature

wireless microphones for espionage and surveillance pur25.6.3 Lists
poses (covert listening devices or so-called bugs); the
advantage to using the FM broadcast band for such opera List of broadcast station classes
tions is that the receiving equipment would not be consid Lists of radio stations in North America
ered particularly suspect. Common practice is to tune the

182

25.6.4

CHAPTER 25. FM BROADCASTING

History

History of radio
Oldest radio station

25.7 References

25.8 External links

Related technical content
U.S. Patent 1,941,066
U.S. Patent 3,708,623 Compatible Four Channel
FM System
Introduction to FM MPX

[1] Transmission standards for FM sound broadcasting at

VHF. ITU Rec. BS.450. International Telecommunications Union. pp. 45.

Stereo Multiplexing for Dummies Graphs that show

waveforms at dierent points in the FM Multiplex
process

[2] Charles S. Fitch: How FM Stereo Came to Life

Factbook list of stations worldwide

[3] http://louise.hallikainen.org/BroadcastHistory/uploads/
FM_Stereo_Final_RandO.pdf FCC FM Stereo Final
Report and Order

Invention History The Father of FM

[4] Stereophonic Broadcasting: Technical Details of Pilottone System, Information Sheet 1604(4), BBC Engineering Information Service, June 1970
[5] FM Stereo demodulation circuit. USPTO. Retrieved 6
December 2015.
[6] FM Reception Guide: FM Propagation. WGBH. 2010.
Retrieved 9 May 2010.
Includes tips for multipath & fringe problems.
[7] Compatible four channel FM system. pdfpiw.uspto.gov.
USPTO. Retrieved 19 October 2016.
[8] Ann Arbor News, Ann Arbor, Michigan, January 3, 1973
[9] Full text of Radio Electronics (August 1987)"".
archive.org.
[10] Mielke, E.-J. (1977). Einu des Dolby-B-Verfahrens auf
die bertragungsqualitt im UKW-Hrrundfunk. Rundfunktechnische Mitteilungen, Vol 21, pp 222 - 228.
[11] IRT (1981-12-30). IRT Technical Report 55/81. Prfung
eines modizierten HIGH COM-Kompanders fr den Einsatz bei der RF-bertragung im UKW-Hrfunk.
[12] http://web.archive.bibalex.org/web/20040203140700/
www.wgem.com/about/wgem_about_fm105.htm
[13] Radio 1 History - Transmitters. Radio Rewind. Retrieved 11 August 2013.
[14] "[IT] Radio FM in Italia. Retrieved 22 September 2015.
[15] http://ukradio.info/OIRT_Tuner/
[16] ITU Publications. ITU.
[17] Change to the law to allow the use of low power FM
transmitters for MP3 players. Ofcom. 23 November
2006. Retrieved 8 August 2015.

Audio Engineering Society

Chapter 26

Radio broadcasting

Long wave radio broadcasting station, Motala, Sweden

Broadcasting tower in Trondheim, Norway

26.1 History
See also: History of radio Broadcasting, and History
of broadcasting
Slovak Radio Building, Bratislava, Slovakia (architects: tefan
Svetko, tefan urkovi and Barnab Kissling, 1967-1983)

The earliest radio stations were simply radiotelegraphy

systems and did not carry audio. For audio broadcasts
to be possible electronic detection and amplication deRadio broadcasting is a unidirectional wireless trans- vices had to be incorporated.
mission over radio waves intended to reach a wide The thermionic valve was invented in 1904 by the Enaudience. Stations can be linked in radio networks to glish physicist John Ambrose Fleming. He developed a
broadcast a common radio format, either in broadcast device he called an oscillation valve (because it passes
syndication or simulcast or both. Audio broadcasting also current in only one direction). The heated lament, or
can be done via cable radio, local wire television net- cathode, was capable of thermionic emission of electrons
works, satellite radio, and internet radio via streaming that would ow to the plate (or anode) when it was at
media on the Internet. The signal types can be either a higher voltage. Electrons, however, could not pass in
analog audio or digital audio.
the reverse direction because the plate was not heated
183

184
and thus not capable of thermionic emission of electrons. Later known as the Fleming valve, it could be used
as a rectier of alternating current and as a radio wave
detector.[1] This greatly improved the crystal set which
rectied the radio signal using an early solid-state diode
based on a crystal and a so-called cats whisker. However,
what was still required was an amplier.

CHAPTER 26. RADIO BROADCASTING

world,[12][13] followed by Czech Radio and other European broadcasters in 1923.

Radio Argentina began regularly scheduled transmissions

from the Teatro Coliseo in Buenos Aires on August 27,
1920, making its own priority claim. The station got its
license on November 19, 1923. The delay was due to
the lack of ocial Argentine licensing procedures before
The triode (mercury-vapor lled with a control grid) that date. This station continued regular broadcasting of
was patented on March 4, 1906 by the Austrian Robert entertainment and cultural fare for several decades.[14]
von Lieben[2][3][4] independent from that, on October Radio in education soon followed and colleges across the
25, 1906[5][6] Lee De Forest patented his three-element U.S. began adding radio broadcasting courses to their
Audion. It wasn't put to practical use until 1912, when its curricula. Curry College in Milton, Massachusetts introamplifying ability became recognized by researchers.[7] duced one of the rst broadcasting majors in 1932 when
By about 1920, valve technology had matured to the the college teamed up with WLOE in Boston to have stupoint where radio broadcasting was quickly becoming dents broadcast programs.[15]
viable.[8][9] However, an early audio transmission that
could be termed a broadcast may have occurred on
Christmas Eve in 1906 by Reginald Fessenden, although
this is disputed.[10] While many early experimenters at- 26.2 Types
tempted to create systems similar to radiotelephone devices by which only two parties were meant to communicate, there were others who intended to transmit to
larger audiences. Charles Herrold started broadcasting
Wavelength
in California in 1909 and was carrying audio by the next

year. (Herrolds station eventually became KCBS).

10Mm

1mm

radio waves

300GHz

30Hz

infrared

300THz

30PHz

ultraviolet

30EHz

Frequency

RECEIVER

(microphone)

original
sound

Encoder

Tuning
Tunes out all but broadcast

oscillator
AM - Amplitude Modulation

FM - Frequency Modulation

Reproduced
sound

Decoder
Receiveing antenna

Transducer

Transmitting antenna

In The Hague, the Netherlands, PCGG started broadcasting on November 6, 1919, making it, arguably
the rst commercial broadcasting station. In 1916,
Frank Conrad, an electrical engineer employed at the
Westinghouse Electric Corporation, began broadcasting
from his Wilkinsburg, Pennsylvania garage with the call
letters 8XK. Later, the station was moved to the top of the
Westinghouse factory building in East Pittsburgh, Pennsylvania. Westinghouse relaunched the station as KDKA
on November 2, 1920, as the rst commercially licensed
radio station in America.[11] The commercial broadcasting designation came from the type of broadcast license;
advertisements did not air until years later. The rst licensed broadcast in the United States came from KDKA
itself: the results of the Harding/Cox Presidential Election. The Montreal station that became CFCF began
broadcast programming on May 20, 1920, and the Detroit
station that became WWJ began program broadcasts beginning on August 20, 1920, although neither held a license at the time.

300EHz

X-ray

1m

10nm

10pm

1pm

Electromagnetic Radiation

destroys anything that is

not the desired modulation

Audio Amplier
voume contol

Transducer
(speaker)

Electrical output

Transmission diagram of sound broadcasting (AM and FM)

Broadcasting by radio takes several forms. These include AM and FM stations. There are several subtypes,
namely commercial broadcasting, non-commercial educational (NCE) public broadcasting and non-prot varieties as well as community radio, student-run campus
radio stations and hospital radio stations can be found
throughout the world.

Many stations broadcast on shortwave bands using AM

technology that can be received over thousands of miles
(especially at night). For example, the BBC, VOA, VOR,
In 1920 wireless broadcasts for entertainment began in
and Deutsche Welle have transmitted via shortwave to
the UK from the Marconi Research Centre 2MT at
Africa and Asia. These broadcasts are very sensitive to
Writtle near Chelmsford, England. A famous broadcast
atmospheric conditions and solar activity.
from Marconis New Street Works factory in Chelmsford
was made by the famous soprano Dame Nellie Melba on Nielsen Audio, formerly known as Arbitron, the United
15 June 1920, where she sang two arias and her famous States-based company that reports on radio audiences,
trill. She was the rst artist of international renown to par- denes a radio station as a government-licensed AM or
ticipate in direct radio broadcasts. The 2MT station be- FM station; an HD Radio (primary or multicast) station;
gan to broadcast regular entertainment in 1922. The BBC an internet stream of an existing government-licensed stawas amalgamated in 1922 and received a Royal Charter tion; one of the satellite radio channels from XM Satellite
in 1926, making it the rst national broadcaster in the Radio or Sirius Satellite Radio; or, potentially, a station
that is not government licensed.[16]

26.2. TYPES

26.2.1

185

Shortwave

these are called clear-channel stations. Many of them can

be heard across much of the country at night. During the
See shortwave for the dierences between shortwave, night, absorption largely disappears and permits signals
medium wave and long wave spectra. Shortwave is to travel to much more distant locations via ionospheric
used largely for national broadcasters, international pro- reections. However, fading of the signal can be severe
paganda, or religious broadcasting organizations.
at night.

26.2.2

AM

Main article: AM broadcasting

AM stations were the earliest broadcasting stations to be

AM broadcasting stations in 2006

developed. AM refers to amplitude modulation, a mode

of broadcasting radio waves by varying the amplitude of
the carrier signal in response to the amplitude of the signal
to be transmitted.

AM radio transmitters can transmit audio frequencies up

to 15 kHz (now limited to 10 kHz in the US due to FCC
rules designed to reduce interference), but most receivers
are only capable of reproducing frequencies up to 5 kHz
or less. At the time that AM broadcasting began in the
1920s, this provided adequate delity for existing microphones, 78 rpm recordings, and loudspeakers. The
delity of sound equipment subsequently improved considerably, but the receivers did not. Reducing the bandwidth of the receivers reduces the cost of manufacturing
and makes them less prone to interference. AM stations
are never assigned adjacent channels in the same service
area. This prevents the sideband power generated by two
stations from interfering with each other.[17] Bob Carver
created an AM stereo tuner employing notch ltering that
demonstrated that an AM broadcast can meet or exceed
the 15 kHz baseband bandwidth allotted to FM stations
without objectionable interference. After several years,
the tuner was discontinued. Bob Carver had left the company and the Carver Corporation later cut the number of
models produced before discontinuing production completely.

The medium-wave band is used worldwide for AM

broadcasting. Europe also uses the long wave band. In
response to the growing popularity of FM stereo radio
26.2.3 FM
stations in the late 1980s and early 1990s, some North
American stations began broadcasting in AM stereo,
though this never gained popularity, and very few re- Main article: FM broadcasting
FM refers to frequency modulation, and occurs on VHF
ceivers were ever sold.
One of the advantages of AM is that its signal can be
detected (turned into sound) with simple equipment. If
a signal is strong enough, not even a power source is
needed; building an unpowered crystal radio receiver was
a common childhood project in the early decades of AM
broadcasting.

AM broadcasts occur on North American airwaves in

the medium wave frequency range of 530 to 1700 kHz
(known as the standard broadcast band). The band was
FM radio broadcast stations in 2006
expanded in the 1990s by adding nine channels from 1620
to 1700 kHz. Channels are spaced every 10 kHz in the airwaves in the frequency range of 88 to 108 MHz everyAmericas, and generally every 9 kHz everywhere else.
where except Japan and Russia. Russia, like the former
The signal is subject to interference from electrical storms Soviet Union, uses 65.9 to 74 MHz frequencies in addi(lightning) and other electromagnetic interference (EMI). tion to the world standard. Japan uses the 76 to 90 MHz
AM transmissions cannot be ionospherically propagated frequency band.
during the day due to strong absorption in the D-layer
of the ionosphere. In a crowded channel environment
this means that the power of regional channels which
share a frequency must be reduced at night or directionally beamed in order to avoid interference, which reduces
the potential nighttime audience. Some stations have frequencies unshared with other stations in North America;

Edwin Howard Armstrong invented FM radio to overcome the problem of radio-frequency interference (RFI),
which plagued AM radio reception. At the same time,
greater delity was made possible by spacing stations further apart in the radio frequency spectrum. Instead of 10
kHz apart, as on the AM band in the US, FM channels
are 200 kHz (0.2 MHz) apart. In other countries greater

186
spacing is sometimes mandatory, such as in New Zealand,
which uses 700 kHz spacing (previously 800 kHz). The
improved delity made available was far in advance of
the audio equipment of the 1940s, but wide interchannel spacing was chosen to take advantage of the noisesuppressing feature of wideband FM.
Bandwidth of 200 kHz is not needed to accommodate an
audio signal 20 kHz to 30 kHz is all that is necessary
for a narrowband FM signal. The 200 kHz bandwidth
allowed room for 75 kHz signal deviation from the assigned frequency, plus guard bands to reduce or eliminate
adjacent channel interference. The larger bandwidth allows for broadcasting a 15 kHz bandwidth audio signal
plus a 38 kHz stereo subcarriera piggyback signal
that rides on the main signal. Additional unused capacity
is used by some broadcasters to transmit utility functions
such as background music for public areas, GPS auxiliary
signals, or nancial market data.
The AM radio problem of interference at night was addressed in a dierent way. At the time FM was set up,
the available frequencies were far higher in the spectrum
than those used for AM radio - by a factor of approximately 100. Using these frequencies meant that even at
far higher power, the range of a given FM signal was much
shorter; thus its market was more local than for AM radio.
The reception range at night is the same as in the daytime. All FM broadcast transmissions are line-of-sight,
and ionospheric bounce is not viable. The much larger
bandwidths, compared to AM and SSB, are more susceptible to phase dispersion. Propagation speeds (celerities)
are fastest in the ionosphere at the lowest sideband frequency. The celerity dierence between the highest and
lowest sidebands is quite apparent to the listener. Such
distortion occurs up to frequencies of approximately 50
MHz. Higher frequencies do not reect from the ionosphere, nor from storm clouds. Moon reections have
been used in some experiments, but require impractical
power levels.
The original FM radio service in the U.S. was the Yankee
Network, located in New England.[18][19][20] Regular FM
broadcasting began in 1939, but did not pose a signicant threat to the AM broadcasting industry. It required
purchase of a special receiver. The frequencies used, 42
to 50 MHz, were not those used today. The change to
the current frequencies, 88 to 108 MHz, began after the
end of World War II, and was to some extent imposed
by AM broadcasters as an attempt to cripple what was by
now realized to be a potentially serious threat.

CHAPTER 26. RADIO BROADCASTING

tuners, FM became the dominant medium, especially in
cities. Because of its greater range, AM remained more
common in rural environments.

26.2.4 Pirate radio

Main article: Pirate radio
Pirate radio is illegal or non-regulated radio transmission.
It is most commonly used to describe illegal broadcasting for entertainment or political purposes. Sometimes
it is used for illegal two-way radio operation. Its history
can be traced back to the unlicensed nature of the transmission, but historically there has been occasional use
of sea vesselstting the most common perception of a
pirateas broadcasting bases. Rules and regulations vary
largely from country to country, but often the term pirate
radio generally describes the unlicensed broadcast of FM
radio, AM radio, or short wave signals over a wide range.
In some places radio stations are legal where the signal is
transmitted, but illegal where the signals are received
especially when the signals cross a national boundary. In
other cases, a broadcast may be considered pirate due to
the type of content, its transmission format, or the transmitting power (wattage) of the station, even if the transmission is not technically illegal (such as a web cast or
an amateur radio transmission). Pirate radio stations are
sometimes referred to as bootleg radio or clandestine stations.

26.2.5 Terrestrial digital radio

Digital radio broadcasting has emerged, rst in Europe
(the UK in 1995 and Germany in 1999), and later in the
United States, France, the Netherlands, South Africa and
many other countries worldwide. The most simple system
is named DAB Digital Radio, for Digital Audio Broadcasting, and uses the public domain EUREKA 147 (Band
III) system. DAB is used mainly in the UK and South
Africa. Germany and the Netherlands use the DAB and
DAB+ systems, and France uses the L-Band system of
DAB Digital Radio.

In the United States, digital radio isn't used in the same

way as Europe and South Africa. Instead, the IBOC
system is named HD Radio and owned by a consortium
of private companies that is called iBiquity. An international non-prot consortium Digital Radio Mondiale
FM radio on the new band had to begin from the ground (DRM), has introduced the public domain DRM system.
oor. As a commercial venture it remained a little-used
audio enthusiasts medium until the 1960s. The more
prosperous AM stations, or their owners, acquired FM li- 26.2.6 Satellite
censes and often broadcast the same programming on the
FM station as on the AM station ("simulcasting"). The Satellite radio broadcasters are slowly emerging, but the
FCC limited this practice in the 1960s. By the 1980s, enormous entry costs of space-based satellite transmitsince almost all new radios included both AM and FM ters, and restrictions on available radio spectrum licenses
has restricted growth of this market. In the USA and

26.6. FURTHER READING

187

Canada, just two services, XM Satellite Radio and Sirius [10] Fessenden The Next Chapter RWonline.com
Satellite Radio exist. Both XM and Sirius are owned by
Sirius XM Radio, which was formed by the merger of [11] Baudino, Joseph E; John M. Kittross (Winter 1977).
Broadcastings Oldest Stations: An Examination of Four
XM and Sirius on July 29, 2008, whereas in Canada, XM
Claimants. Journal of Broadcasting: 6182. Archived
Radio Canada and Sirius Canada remained separate comfrom the original on 2008-03-06. Retrieved 2013-01-18.
panies until 2010. Worldspace in Africa and Asia, and
MobaHO! in Japan and the ROK were two unsuccessful [12] Callsign 2MT & New Street.
satellite radio operators which have gone out of business.

26.3 Program formats

Main article: Radio format

[13] BBC History The BBC takes to the Airwaves. BBC

News.
[14] Atgelt, Carlos A. Early History of Radio Broadcasting in
Argentina. The Broadcast Archive (Oldradio.com).
[15] http://www.curry.edu

Radio program formats dier by country, regulation and

[16] What is a Radio Station?". Radio World. p. 6.
markets. For instance, the U.S. Federal Communications
Commission designates the 8892 megahertz band in the [17] http://kwarner.bravehost.com/tech.htm
U.S. for non-prot or educational programming, with advertising prohibited.
[18] Halper, Donna L. John Shepards FM Stations
Americas rst FM network. Boston Radio Archives
In addition, formats change in popularity as time passes
(BostonRadio.org).
and technology improves. Early radio equipment only
allowed program material to be broadcast in real time, [19] The Yankee Network in 1936. Boston Radio Archives
known as live broadcasting. As technology for sound
(BostonRadio.org)
recording improved, an increasing proportion of broadcast programming used pre-recorded material. A current [20] Miller, Je. FM Broadcasting Chronology. Rev. 2005trend is the automation of radio stations. Some stations
12-27.
now operate without direct human intervention by using
entirely pre-recorded material sequenced by computer
control.

26.6 Further reading

26.4 See also

Briggs Asa. The History of Broadcasting in the

United Kingdom (Oxford University Press, 1961).

26.5 References

Crisell, Andrew. An Introductory History of British

Broadcasting (2002) excerpt

[1] Guarnieri, M. (2012). The age of vacuum tubes: Early

devices and the rise of radio communications. IEEE Ind.
Electron. M.: 4143. doi:10.1109/MIE.2012.2182822.
[2] DRP 179807
[3] Tapan K. Sarkar (ed.) History of wireless, John Wiley
and Sons, 2006. ISBN 0-471-71814-9, p.335
[4] Sgo Okamura (ed), History of Electron Tubes, IOS Press,
1994 ISBN 90-5199-145-2 page 20
[5] Patent US841387 from 10/25/1906
[6] U.S. Patent 879,532
[7] Nebeker, Frederik (2009). Dawn of the Electronic Age:
Electrical Technologies in the Shaping of the Modern
World, 1914 to 1945. John Wiley & Sons. pp. 1415.
ISBN 0470409746.
[8] The Invention of Radio.
[9] Guarnieri, M. (2012). The age of vacuum tubes: the
conquest of analog communications. IEEE Ind. Electron.
M.: 5254. doi:10.1109/MIE.2012.2193274.

Ewbank Henry and Lawton Sherman P. Broadcasting: Radio and Television (Harper & Brothers,
1952).
Fisher, Marc. Something In The Air: Radio, Rock,
and the Revolution That Shaped A Generation (Random House, 2007).
Hausman, Carl, Messere, Fritz, Benoit, Philip, and
O'Donnell, Lewis, Modern Radio Production, 9th
ed., (Cengage, 2013)
Head, Sydney W., Christopher W. Sterling, and
Lemuel B. Schoeld. Broadcasting in America. (7th
ed. 1994).
Lewis, Tom, Empire of the Air: The Men Who Made
Radio, 1st ed., New York : E. Burlingame Books,
1991. ISBN 0-06-018215-6. "Empire of the Air:
The Men Who Made Radio" (1992) by Ken Burns
was a PBS documentary based on the book.

188

CHAPTER 26. RADIO BROADCASTING

Pilon, Robert, Isabelle Lamoureux, and Gilles Tur- General

cotte. Le March de la radio au Qubec: document
de reference. [Montral]: Association qubcoise
Federal Communications Commission website de l'industrie du dique, du spectacle et de la video,
fcc.gov
1991. unpaged. N.B.: Comprises: Robert Pilons
DXing.info - Information about radio stations
and Isabelle Lamoureux' Prol du march de radio
worldwide
au Qubec: un analyse de Mdia-culture. -- Gilles
Turcottes Analyse comparative de l'coute des prin Radio-Locator.com- Links to 13,000 radio stations
cipals stations de Montral: prepare par Info Cible.
worldwide
Ray, William B. FCC: The Ups and Downs of Radio BBC reception advice
TV Regulation (Iowa State University Press, 1990).
DXradio.50webs.com The SWDXER - with gen Russo, Alexan der. Points on the Dial: Golden Age
eral SWL information and radio antenna tips
Radio Beyond the Networks (Duke University Press;
2010) 278 pages; discusses regional and local radio
RadioStationZone.com - 10.000+ radio stations
as forms that complicate the image of the medium
worldwide with ratings, comments and listen live
as a national unier from the 1920s to the 1950s.
links
Scannell, Paddy, and Cardi, David. A Social History of British Broadcasting, Volume One, 19221939 (Basil Blackwell, 1991).
Schramm, Wilbur, ed. The Process and Eects of
Mass Communication (1955 and later editions) articles by social scientists
Schramm, Wilbur, ed. Mass Communication
(1950, 2nd ed. 1960); more popular essays
Schwoch James. The American Radio Industry and
Its Latin American Activities, 1900-1939 (University
of Illinois Press, 1990).

RadioBeta.com, search for stations around the globe

Online-Radio-Stations.org - The Web Radio Tuner
has a comprehensive list of over 50.000 radio stations
RadioStations.com has a directory of radio stations
and real-time music listings
ZoZanga.com List of radio stations and real-time
music listings
UnwantedEmissions.com - A general reference to
radio spectrum allocations

Stewart, Sandy. From Coast to Coast: a Personal

History of Radio in Canada (Entreprises RadioCanada, 1985). xi, 191 p., ill., chiey with b&w
photos. ISBN 0-88794-147-8

Radio stanice - Search for radio stations throughout

the Europe

Stewart, Sandy. A Pictorial History of Radio in

Canada (Gage Publishing, 1975). v, [1], 154 p.,
amply ill. in b&w mostly with photos. SBN 77159948-X

NEC Lab - A tool to design and test antennas for

Radio broadcasting

White Llewellyn. The American Radio (University

of Chicago Press, 1947).

26.7 External links

Patents
U.S. Patent 1,082,221, Georg Graf von Arco, Radiotelegraphic station (December 1913)
U.S. Patent 1,116,111, Richard Pfund, Station for
the transmission and reception of electromagnetic
wave energy. (November 1914)
U.S. Patent 1,214,591, Gustav Reuthe, Antenna
for radiotelegraph station (February 1917)

Radio Emisoras Latinas - has a directory with thousands of Latin America Radio Stations

autocww.colorado.edu - Broadcasting, Radio and

Television
MY FM Radio Live - MY FM Radio Live - Internet
radio broadcast

Chapter 27

Single-sideband modulation
ciently. Amplitude modulation produces an output signal
that has twice the bandwidth of the original baseband signal. Single-sideband modulation avoids this bandwidth
doubling, and the power wasted on a carrier, at the cost
of increased device complexity and more dicult tuning
at the receiver.

Baseband signal

27.1 Basic concept

Full AM modulation

SSB modulation (USB)

Radio transmitters work by mixing a radio frequency

(RF) signal of a specic frequency, the carrier wave, with
the signal to be broadcast. The result is a set of frequencies with a strong peak signal at the carrier frequency, and
smaller signals from the carrier frequency plus the maximum frequency of the signal, and the carrier frequency
minus the maximum frequency of the signal. That is, the
resulting signal has a spectrum with twice the bandwidth
of the original input signal. In conventional AM radio,
this signal is then sent to the radio frequency amplier,
and then to the broadcast antenna. Due to the nature of
the amplication process, the quality of the resulting signal can be dened by the dierence between the maximum and minimum signal energy. Normally the maximum signal energy will be the carrier itself, perhaps twice
as powerful as the mixed signals.

SSB takes advantage of the fact that the entire original signal is encoded in either one of these sidebands. It is not
necessary to broadcast the entire mixed signal, a suitable
SSB modulation (LSB)
receiver can extract the entire signal from either the upper
or lower sideband. This means that the amplier can be
used much more eciently. A transmitter can choose to
send only the upper or lower sideband, the portion of the
Illustration of the spectrum of AM and SSB signals. The lower signal above or below the carrier. By doing so, the amside band (LSB) spectrum is inverted compared to the baseband. plier only has to work eectively on one half the bandAs an example, a 2 kHz audio baseband signal modulated onto width, which is generally easier to arrange. More impora 5 MHz carrier will produce a frequency of 5.002 MHz if upper tantly, with the carrier suppressed before it reaches the
side band (USB) is used or 4.998 MHz if LSB is used.
amplier, it can amplify the signal itself to higher energy,
it is not wasting energy amplifying a signal, the carrier,
In radio communications, single-sideband modulation than can (and will) be re-created by the receiver anyway.
(SSB) or single-sideband suppressed-carrier modula- As a result, SSB transmissions use the available amplier
tion (SSB-SC) is a renement of amplitude modulation energy more eciently, providing longer-range transmiswhich uses transmitter power and bandwidth more e- sion with little or no additional cost. Receivers normally
189

190

CHAPTER 27. SINGLE-SIDEBAND MODULATION

select one of the two sidebands to amplify anyway, so instead of being independent messages:
implementing SSB in the receiver is simply a matter of
allowing it to choose which sideband to amplify on reception, rather than simply choosing one or the other in
the design stage.
where s(t) is the message, sb(t) is its Hilbert transform,
and f0 is the radio carrier frequency.[6]

27.2 History
The rst U.S. patent[1] for SSB modulation was applied
for on December 1, 1915 by John Renshaw Carson. The
U.S. Navy experimented with SSB over its radio circuits before World War I.[2][3] SSB rst entered commercial service on January 7, 1927 on the longwave transatlantic public radiotelephone circuit between New York
and London. The high power SSB transmitters were located at Rocky Point, New York and Rugby, England.
The receivers were in very quiet locations in Houlton,
Maine and Cupar Scotland.[4]

To understand this formula, we may express s(t) as the

sum of two complex-valued functions:

s(t) =

1
2

(s(t) + j sb(t)) + 12 (s(t) j sb(t)),

{z
}
{z
}
|
|
sa (t)

s
a (t)

where j represents the imaginary unit, sa (t) is the

analytic representation of s(t), and sa (t) is its complex
conjugate. This representation divides s(t) into its nonnegative frequency components and its non-positive frequency components. In other words:

SSB was also used over long distance telephone lines, as

part of a technique known as frequency-division multi{
plexing (FDM). FDM was pioneered by telephone companies in the 1930s. This enabled many voice channels 1 S (f ) = S(f ), for f > 0,
a
0,
for f < 0,
to be sent down a single physical circuit, for example in 2
L-carrier. SSB allowed channels to be spaced (usually)
just 4,000 Hz apart, while oering a speech bandwidth where Sa (f ) and S(f ) are the respective Fourier transof nominally 3003,400 Hz.
forms of sa (t) and s(t). The frequency-translated funcAmateur radio operators began serious experimentation tion Sa (f f0 ) contains only one side of S(f ). Since
with SSB after World War II. The Strategic Air Com- it also has only positive-frequency components, its inmand established SSB as the radio standard for its air- verse Fourier transform is the analytic representation of
craft in 1957.[5] It has become a de facto standard for sssb (t) :
long-distance voice radio transmissions since then.
F 1 {Sa (f f0 )} = sa (t)ej2f0 t = sssb (t)+jb
sssb (t).
Therefore, with Eulers formula to expand ej2f0 t , we
obtain Eq.1:
{
}
sssb (t) = Re sa (t) ej2f0 t

= Re { [s(t) + j sb(t)] [cos(2f0 t) + j sin(2f0 t)] }

= s(t) cos(2f0 t) sb(t) sin(2f0 t).
Coherent demodulation of sssb (t) to recover s(t) is the
same as AM: multiply by cos(2f0 t), and lowpass to
remove the double-frequency components around freFrequency-domain depiction of the mathematical steps that con- quency 2f0 . If the demodulating carrier is not in the
vert a baseband function into a single-sideband radio signal.
correct phase (cosine phase here), then the demodulated
signal will be some linear combination of s(t) and sb(t) ,
which is usually acceptable in voice communications (if
the demodulation carrier frequency is not quite right, the
27.3 Mathematical formulation
phase will be drifting cyclically, which again is usually acceptable in voice communications if the frequency error
Single-sideband has the mathematical form of quadrature is small enough, and amateur radio operators are someamplitude modulation (QAM) in the special case where times tolerant of even larger frequency errors that cause
one of the baseband waveforms is derived from the other, unnatural-sounding pitch shifting eects).

27.4. PRACTICAL IMPLEMENTATIONS

27.3.1

Lower sideband

s(t) can also be recovered as the real part of the complexconjugate, sa (t), which represents the negative frequency
portion of S(f ). When f0 is large enough that S(f f0 )
has no negative frequencies, the product sa (t) ej2f0 t is
another analytic signal, whose real part is the actual lowersideband transmission:
sa (t) ej2f0 t = slsb (t) + j sblsb (t)
{
}
slsb (t) = Re sa (t) ej2f0 t
= s(t) cos(2f0 t) + sb(t) sin(2f0 t).

191
which is the case for a normal AM signal, no information
is lost in the process. Since the nal RF amplication
is now concentrated in a single sideband, the eective
power output is greater than in normal AM (the carrier
and redundant sideband account for well over half of the
power output of an AM transmitter). Though SSB uses
substantially less bandwidth and power, it cannot be demodulated by a simple envelope detector like standard
AM.

27.4.2 Hartley modulator

An alternate method of generation known as a Hartley

modulator, named after R. V. L. Hartley, uses phasing
to suppress the unwanted sideband. To generate an SSB
signal with this method, two versions of the original sig2s(t) cos(2f0 t),
nal are generated, mutually 90 out of phase for any sinwhich is the classic model of suppressed-carrier double gle frequency within the operating bandwidth. Each one
of these signals then modulates carrier waves (of one fresideband AM.
quency) that are also 90 out of phase with each other.
By either adding or subtracting the resulting signals, a
lower or upper sideband signal results. A benet of this
27.4 Practical implementations
approach is to allow an analytical expression for SSB signals, which can be used to understand eects such as synchronous detection of SSB.
Note that the sum of the two sideband signals is:

Shifting the baseband signal 90 out of phase cannot be

done simply by delaying it, as it contains a large range
of frequencies. In analog circuits, a wideband 90-degree
phase-dierence network[7] is used. The method was
popular in the days of vacuum tube radios, but later
gained a bad reputation due to poorly adjusted commercial implementations. Modulation using this method is
again gaining popularity in the homebrew and DSP elds.
This method, utilizing the Hilbert transform to phase shift
the baseband audio, can be done at low cost with digital
circuitry.

27.4.3 Weaver modulator

A Collins KWM-1, an early Amateur Radio transceiver that featured SSB voice capability

27.4.1

Bandpass ltering

One method of producing an SSB signal is to remove one

of the sidebands via ltering, leaving only either the upper sideband (USB), the sideband with the higher frequency, or less commonly the lower sideband (LSB), the
sideband with the lower frequency. Most often, the carrier is reduced or removed entirely (suppressed), being
referred to in full as single sideband suppressed carrier (SSBSC). Assuming both sidebands are symmetric,

Another variation, the Weaver modulator,[8] uses only

lowpass lters and quadrature mixers, and is a favored
method in digital implementations.
In Weavers method, the band of interest is rst translated
to be centered at zero, conceptually by modulating a complex exponential exp(jt) with frequency in the middle
of the voiceband, but implemented by a quadrature pair
of sine and cosine modulators at that frequency (e.g. 2
kHz). This complex signal or pair of real signals is then
lowpass ltered to remove the undesired sideband that is
not centered at zero. Then, the single-sideband complex
signal centered at zero is upconverted to a real signal, by
another pair of quadrature mixers, to the desired center
frequency.

192

27.4.4

CHAPTER 27. SINGLE-SIDEBAND MODULATION

Full, reduced, and suppressed car- substantially in amplitude. At the point of 100% envelope
modulation, 6 dB of power is removed from the carrier
rier SSB

Conventional amplitude-modulated signals can be considered wasteful of power and bandwidth because they
contain a carrier signal and two identical sidebands.
Therefore, SSB transmitters are generally designed to
minimize the amplitude of the carrier signal. When the
carrier is removed from the transmitted signal, it is called
suppressed carrier SSB.
However, in order for a receiver to reproduce the transmitted audio without distortion, it must be tuned to exactly the same frequency as the transmitter. Since this
is dicult to achieve in practice, SSB transmissions can
sound unnatural, and if the error in frequency is great
enough, it can cause poor intelligibility. In order to correct this, a small amount of the original carrier signal can
be transmitted so that receivers with the necessary circuitry to synchronize with the transmitted carrier can correctly demodulate the audio. This mode of transmission
is called reduced carrier single sideband.
In other cases, it may be desirable to maintain some degree of compatibility with simple AM receivers, while
still reducing the signals bandwidth. This can be accomplished by transmitting single-sideband with a normal or
slightly reduced carrier. This mode is called compatible
(or full carrier) SSB or Amplitude Modulation Equivalent
(AME). In typical AME systems, harmonic distortion can
reach 25% and intermodulation distortion can be much
higher than normal, but minimizing distortion in receivers
with envelope detectors is generally considered less important than allowing them to produce intelligible audio.
A second, and, perhaps more correct denition of Compatible Single Sideband (CSSB) refers to a form of amplitude and phase modulation in which the carrier is transmitted, along with a series of sidebands that are predominantly above or below the carrier term. Since phase
modulation is present in the generation of the signal, energy is removed from the carrier term and redistributed
into the sideband structure similar to that which occurs
in analog frequency modulation. The signals feeding the
phase modulator and the envelope modulator are, further,
phase shifted by 90 degrees with respect to each other.
This places the information terms in quadrature with each
other; the Hilbert Transform of information to be transmitted is utilized to cause constructive addition of one
sideband and cancellation of the opposite primary sideband. Since phase modulation is employed, higher order
terms are also generated. Several methods have been employed to reduce the impact (amplitude) of most of these
higher order terms. In one system, the phase modulated
term is actually the log of the value of the carrier level
plus the phase shifted audio/information term. This produces an ideal CSSB signal where, at low modulation levels, only a rst order term on one side of the carrier is predominant. As the modulation level is increased, the carrier level is reduced while a second order term increases

term and the second order term is identical in amplitude

to carrier term. The rst order sideband has increased in
level until it is now at the same level as the formerly unmodulated carrier. At the point of 100% modulation, the
spectrum appears identical to a normal double sideband
AM transmission, with the center term (now the primary
audio term) at a 0 dB reference level, and both terms on
either side of the primary sideband at 6 dB. The dierence is that what appears to be the carrier has shifted by
the audio frequency term towards the sideband in use.
At levels below 100% modulation, the sideband structure
appears quite asymmetric. When voice is conveyed by
a CSSB source of this type, low frequency components
are dominant, while higher frequency terms are lower by
as much as 20 dB at 3 kHz. The result is that the signal
occupies approximately 1/2 the normal bandwidth of a
full carrier, DSB signal. There is one catch: The audio
term utilized to phase modulate the carrier is generated
based on a log function that is biased by the carrier level.
At negative 100% modulation, the term is driven to zero
(0) and the modulator becomes undened. Strict modulation control must be employed to maintain stability of
the system and avoid splatter. This system is of Russian
origin and was described in the late 1950s. It is uncertain
whether it was ever deployed.
A second series of approaches was designed and patented
by Leonard R. Kahn. The various Kahn systems removed
the hard limit imposed by the use of the strict log function in the generation of the signal. Earlier Kahn systems utilized various methods to reduce the second order term through the insertion of a predistortion component. One example of this method was also used to
generate one of the Kahn Independent Sideband (ISB)
AM stereo signals. It was known as the STR-77 exciter method, having been introduced in 1977. Later, the
system was further improved by use of an arcsine-based
modulator that included a 1-0.52E term in the denominator of the arcsin generator equation. E represents the
envelope term; roughly half the modulation term applied
to the envelope modulator is utilized to reduce the second
order term of the arcsin phase modulated path; thus reducing the second order term in the undesired sideband.
A multi-loop modulator/demodulator feedback approach
was used to generate an accurate arcsin signal. This approach was introduced in 1984 and became known as the
STR-84 method. It was sold by Kahn Research Laboratories; later, Kahn Communications, Inc. of NY. An
additional audio processing device further improved the
sideband structure by selectively applying pre-emphasis
to the modulating signals. Since the envelope of all the
signals described remains an exact copy of the information applied to the modulator, it can be demodulated,
without distortion, by an envelope detector such as a simple diode. In a practical receiver, some distortion may be
present, usually at a low level (in AM broadcast, always
below 5%), due to sharp ltering and nonlinear group de-

27.6. SSB AS A SPEECH-SCRAMBLING TECHNIQUE

lay in the IF lters of the receiver which act to truncate
the compatibility sideband those terms that are not the
result of a linear process of simply envelope modulating
the signal as would be the case in full-carrier DSB-AM
and rotation of phase of these compatibility terms such
that they no longer cancel the quadrature distortion term
caused by a rst order SSB term along with the carrier.
The small amount of distortion cause by this eect is generally quite low and acceptable.
The Kahn CSSB method was also briey used by
Airphone as the modulation method employed for early
consumer telephone calls that could be placed from an
aircraft to ground. This was quickly supplanted by digital modulation methods to achieve even greater spectral
eciency.

193
may serve)).
Note that there are two choices for Fbf o : 43000 Hz and
47000 Hz, called low-side and high-side injection. With
high-side injection, the spectral components that were
distributed around 45000 Hz will be distributed around
2000 Hz in the reverse order, also known as an inverted
spectrum. That is in fact desirable when the IF spectrum
is also inverted, because the BFO inversion restores the
proper relationships. One reason for that is when the IF
spectrum is the output of an inverting stage in the receiver. Another reason is when the SSB signal is actually a lower sideband, instead of an upper sideband. But
if both reasons are true, then the IF spectrum is not inverted, and the non-inverting BFO (43000 Hz) should be
used.

While CSSB is seldom used today in the AM/MW broad- If Fbf o is o by a small amount, then the beat frequency
cast bands worldwide, some amateur radio operators still is not exactly Fb , which can lead to the speech distortion
experiment with it.
mentioned earlier.

27.5 Demodulation
The front end of an SSB receiver is similar to that of
an AM or FM receiver, consisting of a superheterodyne
RF front end that produces a frequency-shifted version
of the radio frequency (RF) signal within a standard
intermediate frequency (IF) band.
To recover the original signal from the IF SSB signal,
the single sideband must be frequency-shifted down to
its original range of baseband frequencies, by using a
product detector which mixes it with the output of a beat
frequency oscillator (BFO). In other words, it is just another stage of heterodyning.(mixing down to base band).
For this to work, the BFO frequency must be exactly adjusted. If the BFO frequency is o, the output signal
will be frequency-shifted (up or down), making speech
sound strange and "Donald Duck"-like, or unintelligible.
For audio communications, there is a common agreement
about the BFO oscillator shift of 1.7 kHz. A voice signal is sensitive to about 50 Hz shift, with up to 100 Hz
still bearable. Some receivers use a carrier recovery system, which attempts to automatically lock on to the exact IF frequency. The carrier recovery doesn't solve the
frequency shift. It gives better S/N ratio on the detector
output.

27.6 SSB as a speech-scrambling

technique
SSB techniques can also be adapted to frequency-shift
and frequency-invert baseband waveforms. These eects
were used, in conjunction with other ltering techniques,
during World War II as a simple method for speech
encryption. Radiotelephone conversations between the
US and Britain were intercepted and decrypted by the
Germans; they included some early conversations between Franklin D. Roosevelt and Churchill. In fact, the
signals could be understood directly by trained operators.
Largely to allow secure communications between Roosevelt and Churchill, the SIGSALY system of digital encryption was devised.
Today, such simple inversion-based speech encryption
techniques are easily decrypted using simple techniques
and are no longer regarded as secure.

27.7 Vestigial sideband (VSB)

Limitation of Single-sideband modulation being used for
voice signals and not available for video/TV signals leads
to the usage of vestigial sideband. A vestigial sideband
(in radio communication) is a sideband that has been
only partly cut o or suppressed. Television broadcasts
(in analog video formats) use this method if the video
is transmitted in AM, due to the large bandwidth used.
It may also be used in digital transmission, such as the
ATSC standardized 8-VSB. The Milgo 4400/48 modem
(circa 1967) used vestigial sideband and phase-shift keying to provide 4800-bit/s transmission over a 1600 Hz
channel.

As an example, consider an IF SSB signal centered at

frequency Fif = 45000 Hz. The baseband frequency it
needs to be shifted to is Fb = 2000 Hz. The BFO output
waveform is cos(2 Fbf o t) . When the signal is multiplied by (aka 'heterodyned with') the BFO waveform, it
shifts the signal to (Fif + Fbf o ) and to |Fif Fbf o |
, which is known as the beat frequency or image frequency. The objective is to choose an Fbf o that results
in |Fif Fbf o | = Fb = 2000 Hz. (The unwanted components at (Fif + Fbf o ) can be removed by a lowpass
lter (for which an output transducer or the human ear The broadcast or transport channel for TV in countries

194

CHAPTER 27. SINGLE-SIDEBAND MODULATION

27.8 Frequencies for LSB and USB

in amateur radio voice communication
Baseband signal

Amplitude modulation

Vestigial lower sideband

When single-sideband is used in amateur radio voice

communications, it is common practice that for frequencies below 10 MHz, lower sideband (LSB) is used and
for frequencies above 10 MHz, upper sideband (USB) is
used.[9] For example, on the 40 m band, voice communications often take place around 7.100 MHz using LSB
mode. On the 20 m band at 14.200 MHz, USB mode
would be used.
An exception to this rule applies to the ve discrete amateur channels on the 60-meter band (near 5.3 MHz) where
FCC rules specically require USB.[10]

27.9 Extended
(eSSB)

single

sideband

Extended single sideband is any J3E (SSB-SC) mode that

exceeds the audio bandwidth of standard or traditional 2.9
kHz SSB J3E modes (ITU 2K90J3E) in order to support
the delity required and desired for relative high delity,
full range clean and articulate vocal audio.

Vestigial upper sideband

VSB modulation

27.10 Amplitude-companded
single-sideband modulation
(ACSSB)

Amplitude-companded single sideband (ACSSB) is a

narrowband modulation method using a single sideband
with a pilot tone, allowing an expander in the receiver
to restore the amplitude that was severely compressed by
the transmitter. It oers improved eective range over
standard SSB modulation while simultaneously retaining
that use NTSC or ATSC has a bandwidth of 6 MHz. backwards compatibility with standard SSB radios. ACTo conserve bandwidth, SSB would be desirable, but the SSB also oers reduced bandwidth and improved range
video signal has signicant low frequency content (aver- for a given power level compared with narrow band FM
age brightness) and has rectangular synchronising pulses. modulation.
The engineering compromise is vestigial sideband transmission. In vestigial sideband, the full upper sideband of
bandwidth W2 = 4.75 MHz is transmitted, but only W1
= 1.25 MHz of the lower sideband is transmitted, along
with a carrier. This eectively makes the system AM at 27.11 ITU designations
low modulation frequencies and SSB at high modulation
frequencies. The absence of the lower sideband components at high frequencies must be compensated for, and In 1982, the International Telecommunication Union
(ITU) designated the types of amplitude modulation:
this is done by the RF and IF lters.

27.16. FURTHER READING

27.12 Notes
27.13 See also
ACSSB, amplitude-companded single sideband
Independent sideband
Modulation for other examples of modulation techniques
Sideband for more general information about a sideband

27.14 References
[1] US 1449382 John Carson/AT&T: Method and Means for
Signaling with High Frequency Waves led on December
1, 1915; granted on March 27, 1923
[2] The History of Single Sideband Modulation, Ing. Peter
Weber
[3] IEEE, Early History of Single-Sideband Transmission,
Oswald, A.A.
[4] History Of Undersea Cables, (1927)
[5] Amateur Radio and the Rise of SSB (PDF). National
Association for Amateur Radio.
[6] Tretter, Steven A. (1995). Chapter 7, Eq 7.9. In Lucky,
R.W. Communication System Design Using DSP Algorithms. New York: Springer. p. 80. ISBN 0306450321.
[7] Earthlink.net, listing numerous articles.
[8] A Third Method of Generation and Detection of SingleSideband Signals D K Weaver Jr. Proc. IRE, Dec. 1956
[9] BRATS Advanced Amateur Radio Tuition Course.
Brats-qth.org. Retrieved 2013-01-29.
[10] FCC Part 97 - Amateur Service rules (PDF). www.fcc.
gov.

27.15 General references

Partly from Federal Standard 1037C in support of
MIL-STD-188

27.16 Further reading

Sgrignoli, G., W. Bretl, R. and Citta. (1995). VSB
modulation used for terrestrial and cable broadcasts. IEEE Transactions on Consumer Electronics.
v. 41, issue 3, p. 367 - 382.
J. Brittain, (1992). Scanning the past: Ralph V.L.
Hartley, Proc. IEEE, vol.80,p. 463.

195
eSSB - Extended Single Sideband

Chapter 28

Longwave
For other uses, see Longwave (disambiguation).
frequencies between 148.5 and 283.5 kHz is used for AM
In radio, longwave, also written as long wave (in British broadcasting (in addition to the medium wave band), the
term longwave usually refers specically to this broadcasting band.
The International Telecommunication Union Region 1
longwave broadcast band falls wholly within the low
frequency band of the radio spectrum (30300 kHz).
Broader denitions of longwave may extend below
and/or above it. In the US, the Longwave Club of America is interested in frequencies below the AM broadcast
band,[6] i.e., all frequencies below 535 kHz. (Lower frequencies correspond to longer wavelengths.) they are also
part of the chs national curriculum.

28.1 Non-broadcast use

28.1.1 Non-directional beacons
Main article: Non-directional beacon
The tuning dial on a 1946 Dynatron Merlin T.69 console radio
receiver, showing long-wave wavelengths between 800 and 2000
metres, corresponding to frequencies between 375 and 150 kHz

Non-directional beacons transmit continuously for the

benet of radio direction nders in marine and aeronautical navigation. They identify themselves by a callsign in
and American parlance)[1][2] or long-wave,[3] and com- Morse code. They can occupy any frequency in the range
monly abbreviated LW,[2] refers to parts of the radio 1901750 kHz. In North America, they occupy 190535
spectrum with relatively long wavelengths. The term is an kHz. In ITU Region 1 the lower limit is 280 kHz.
historic one, dating from the early 20th century, when the
radio spectrum was considered to consist of long (LW),
medium (MW) and short (SW) radio wavelengths. Most 28.1.2 Time signals
modern radio systems and devices use wavelengths which
would then have been considered 'ultra-short'.
There are stations in the range 4080 kHz that transmit
In contemporary usage, the term longwave is not de- time signals to radio clocks. For example:
ned precisely, and its meaning varies across the world.
Most commonly, it refers to radio wavelengths longer
WWVB in Colorado, United States, on 60 kHz
than 1000 metres;[2] frequencies less than 300 kilohertz
DCF77 in Frankfurt am Main, Germany, on 77.5
(kHz),[1][4] including the International TelecommunicakHz
tions Unions (ITUs) low frequency (LF) (30300 kHz)
and very low frequency (VLF) (330 kHz) bands. Some JJY in Japan, on 40 & 60 kHz
times, part of the medium frequency (MF) band (300
[5]
3000 kHz) is included.
66.66 kHz in Taldom transmitter, Russia
In Europe, Africa and large parts of Asia (International
Telecommunication Union Region 1), where a range of
BPC in Lintong, China, 68.5 kHz
196

28.2. BROADCASTING
MSF time and 60 kHz frequency standard transmitted from Anthorn in the UK. Radio controlled
clocks receive their time calibration signals with
built-in long-wave receivers. They use long-wave,
rather than shortwave or mediumwave, because the
path that a long-wave signal travels from point A to
point B does not change.
Long-waves travel by groundwaves that hug the surface of
the earth, rather than mediumwaves or shortwaves, whose
signals can travel as skywaves, bouncing o dierent
layers of the ionosphere at dierent times of day, which
makes the time lag dierent for every signal received.
The delay between when the long-wave signal was sent
from the transmitter (and the coded time was correct),
and when the signal is received by the clock (when the
coded time is slightly late), depends on the overland distance between the clock and the transmitter and the speed
of light through the air, which is also very nearly constant.
Since the time lag is essentially the same, a single constant shift forward from the time coded in the signal can
compensate for all long-wave signals received at any one
location from the same time signal station.

28.1.3

Military communication

197
north, central and south-east Europe, the former Soviet
Union, Mongolia, Algeria and Morocco.
Typically, a larger geographic area can be covered by a
long-wave broadcast transmitter compared to a mediumwave one. This is because ground-wave propagation suffers less attenuation due to limited ground conductivity at
lower frequencies.[8]

28.2.1 Carrier frequencies

Long-wave carrier frequencies are exact multiples of 9
kHz; ranging from 153 to 279 kHz, except for a French
language station Europe #1 in Germany. This station did
keep to correctly spaced channels spacing for 4 months
only 7 years ago, and all Mongolian transmitters are
spaced at 10 kHz.
Until the 1970s, some long-wave stations in northern and
eastern Europe, and the Soviet Union, operated on frequencies as high as 433 kHz.[9]

Some stations, for instance Droitwich transmitting staThe military of the United Kingdom, Russian Federation,
tion in the UK, derive their carrier frequencies from an
United States, Germany, and Sweden use frequencies beatomic clock. They can be therefore used as frequency
low 50 kHz to communicate with submerged submarines.
standards. Droitwich also broadcasts a low bit-rate data
channel, using narrow-shift phase-shift keying of the carrier, for Radio Teleswitch Services.

28.1.4

LowFER

28.1.5

Historic

In January 2014, Russia closed all of its LW broadcast

In North America during the 1970s, the frequencies 167, transmitters, except for one in Caucasus, which was sub[10]
179 and 191 kHz were assigned to the short-lived Public sequently shut down in 2015.
Emergency Radio of the United States. Nowadays, 136
kHz and the 160190 kHz range is used in the United
States for Part 15 LowFER amateur and experimental stations, and the 190435 kHz band is used for navigational
beacons.

Swedish station SAQ, located at the Varberg Radio Station facility in Grimeton, is the last remaining operational
Alexanderson alternator long-wave transmitter. Although
the station ended regular service in 1996, it has been
maintained as a World Heritage Site, and makes at least
two demonstration transmissions yearly, on 17.2 kHz.[7]

28.2 Broadcasting

28.2.2 Long distance reception

Because long wave signals can travel very long distances,
some radio amateurs and shortwave listeners engage in an
activity called DXing. DXers attempt to listen in to far
away transmissions, and they will often send a reception
report to the sending station to let them know where they
were heard. After receiving a report, the sending station
may mail the listener a QSL card to acknowledge this reception.

The longest distance over which a long wave signal has

been received is 18,451 kilometres (11,465 mi). It ocLong-wave is used for broadcasting only within ITU Re- curred on 27 July 2015, when Mike Thayne of England,
gion 1. The long-wave broadcasters are located in west, received Radio NL on 358 kHz from New Zealand.[11]

198

28.2.3

CHAPTER 28. LONGWAVE

List of long-wave broadcasting

transmitters

Radio broadcasting: AM broadcasting, BBC Radio 4, BBC Light Programme, Radio clock, Oce
de Radiodiusion-Tlvision Franaise, Warsaw radio mast, Digital Radio Mondiale, International
broadcasting,
Shipping: Global navigation satellite system,
Navigation, Shipping Forecast
Lists: Index of wave articles
Other: 1 kilometre, National Institute of Standards
and Technology, Fail-safe, WGU-20

28.4 Notes and references

[1] long wave. Cambridge Online Dictionary. Cambridge.org - Cambridge University Press. Retrieved 20
June 2016.
[2] long wave. Macmillan Online Dictionary. Macmillan
Publishers Limited. Retrieved 20 June 2016.
[3] Graf,
Rudolf
F.
(1999).
1000+meters&q=longwave#v=snippet&q=longwave&f=false
Modern Dictionary of Electronics, 7th Ed. US: Newnes.
p. 23. ISBN 0750698667.
[4] Graf, Rudolf F. (1999). Modern Dictionary of Electronics,
7th Ed. US: Newnes. p. 437. ISBN 0750698667.
[5] The World Book Dictionary. US: World Book, Inc. 2003.
p. 1232. ISBN 0716602997.

diagram of the antenna towers and antenna masts of

long-wave broadcasting stations

[6] About LWCA. Longwave Club of America. Retrieved

20 June 2016.
[7] SAQ Transmission. Radiostation Grimeton SAQ. Retrieved 5 April 2015.

List of stations currently operating

[8] Ground-wave propagation curves for frequencies between

10 kHz and 30 MHz. ITU-R Recommendation P.368-9

Denotes non-standard frequency (not divisible by 9)

[9] Guide to Broadcasting Stations (17th ed.). Butterworth.

1973. p. 18. ISBN 0-592-00081-8.

[12] [13] [14] [15]

[10] http://www.bbc.co.uk/news/
blogs-news-from-elsewhere-25683656
[11] http://www.classaxe.com/dx/ndb/rww/stats#top

List of stations that have closed or are otherwise in- [12] de:Langwellenrundfunk
active
[13] World Radio TV Handbook

Closed

[14]
[15]

28.3 See also

Low frequency: for other uses (military, commercial and amateur) of this part of the radio spectrum
(30300 kHz)
Electromagnetic spectrum: Very low frequency,
Shortwave, Ground wave, Skywave, Medium wave

[16] http://www.mwlist.org/mwlist_quick_and_easy.php?
area=1&kHz=153
[17] http://structurae.net/structures/
ulan-bator-longwave-transmission-mast
[18] http://www.irishpost.co.uk/news/
rte-radio-postpones-longwave-radio-closure-until-2017
[19] http://www.wiadomosci24.pl/artykul/bez_radia_w_
raszynie_105054.html

28.5. EXTERNAL LINKS

28.5 External links

Tomislav Stimac, "Denition of frequency bands
(VLF, ELF... etc.)". IK1QFK Home Page.
The Medium Wave Circle - The premier club for
MW/LW enthusiasts
Medium Wave News - Published regularly since
1954
Euro-African Medium Wave Guide
Longwave Club of America
How to receive DRM from Kalundborg longwave
station
Reception of long wave and very long wave with ferrite antennas 5-50 kHz
Klawitter, G.; Oexner, M.; Herold, K. (2000). 8.2
Langwellenrundfunk. Langwelle und Lngstwelle
(in German). Meckenheim: Siebel Verlag GmbH.
pp. 116131. ISBN 3-89632-043-2.
Busch, Heinrich (2001-11-14). Luftschi Graf
Zeppelin LZ127. (German)
European and Asian Longwave Stations - Medium
Wave Radio
List of long- and mediumwave transmitters with
GoogleMap-Links to transmission sites

199

Chapter 29

Double-sideband suppressed-carrier
transmission
Double-sideband suppressed-carrier transmission
(DSB-SC) is transmission in which frequencies produced by amplitude modulation (AM) are symmetrically
spaced above and below the carrier frequency and the
carrier level is reduced to the lowest practical level,
ideally being completely suppressed.
In the DSB-SC modulation, unlike in AM, the wave carrier is not transmitted; thus, much of the power is distributed between the sidebands, which implies an increase of the cover in DSB-SC, compared to AM, for the
same power used.

fc-

DSB-SC transmission is a special case of doublesideband reduced carrier transmission. It is used for radio
data systems.

fm

fc+

fm

fm

29.2 Generation
DSB-SC is generated by a mixer. This consists of a message signal multiplied by a carrier signal. The mathematical representation of this process is shown below, where
the product-to-sum trigonometric identity is used.

Vm Vc
Vm cos (m t) Vc cos (c t) =
[cos ((m + c ) t) + cos ((m
|
{z
} | {z } | 2
{z
Message
Carrier
Modulated Signal

29.1 Spectrum

Mixer
Message
Signal

DSB-SC is basically an amplitude modulation wave without the carrier, therefore reducing power waste, giving it
a 50% eciency. This is an increase compared to normal AM transmission (DSB), which has a maximum efciency of 33.333%, since 2/3 of the power is in the carrier which carries no intelligence, and each sideband carries the same information. Single Side Band (SSB) Suppressed Carrier is 100% ecient.
Spectrum

plot

of

DSB-SC

signal:
200

Modulate
Output

Carrier
Signal

29.4. HOW IT WORKS

201

29.3 Demodulation
Demodulation is done by multiplying the DSB-SC signal
with the carrier signal just like the modulation process.
This resultant signal is then passed through a low pass lter to produce a scaled version of original message signal.
DSB-SC can be demodulated by a simple envelope detector, like AM, if the modulation index is less than unity.
Full depth modulation requires carrier re-insertion.
Modulated Signal
Carrier
z
}|
{
}|
{
z
Vm Vc

[cos ((m + c ) t) + cos ((m c ) t)] Vc cos (c t)

2
(
)
1
1

=
Vc Vc Vm cos(m t) + Vc Vc Vm [cos((m + 2c )t) + cos((m 2c )t)]
|
{z
} 4
2
message original

The equation above shows that by multiplying the modulated signal by the carrier signal, the result is a scaled
version of the original message signal plus a second term.
Since c m , this second term is much higher in frequency than the original message. Once this signal passes
through a low pass lter, the higher frequency component
is removed, leaving just the original message.

29.4 How it works

This is best shown graphically. Below is a message signal

that one may wish to modulate onto a carrier, consisting
For demodulation, the demodulation oscillators fre- of a couple of sinusoidal components.
quency and phase must be exactly the same as modulation oscillators, otherwise, distortion and/or attenuation
will occur.

29.3.1

Distortion and attenuation

To see this eect, take the following conditions:

Message signal to be transmitted: f (t)
Modulation (carrier) signal: Vc cos(c t)
Demodulation signal (with small frequency and
phase deviations from the modulation signal):
Vc cos [(c + )t + ]
The resultant signal can then be given by
f (t)Vc cos(c t)Vc cos [(c + )t + ]
=

1
1
Vc Vc f (t) cos ( t + )+ Vc Vc f (t) cos [(2c + )t + ]
2
2
lter pass low After 1
Vc Vc f (t) cos ( t + )
2

The cos ( t + ) terms results in distortion and attenuation of the original message signal. In particular, if the
equation for this message signal is s(t) =
frequencies are correct, but the phase is wrong, contribu- The
1
cos
(2800t) 12 cos (21200t) .
tion from is a constant attenuation factor, also t rep- 2
resents a cyclic inversion of the recovered signal, which The carrier, in this case, is a plain 5 kHz ( c(t) =
cos (25000t) ) sinusoidpictured below.
is a serious form of distortion.

202

CHAPTER 29. DOUBLE-SIDEBAND SUPPRESSED-CARRIER TRANSMISSION

trum of the output signal is viewed:

The modulation is performed by multiplication in the

time domain, which yields a 5 kHz carrier signal, whose
amplitude varies in the same manner as the message signal.

29.5 References
This article incorporates public domain material from
the General Services Administration document Federal
Standard 1037C (in support of MIL-STD-188).

29.6 External links

A DSBSC generation and demodulation instrument
is described as side application of a commercial
lock-in amplier in Double-sideband Suppressedcarrier Modulation.

]
1
1
cos (2800t) cos (21200t)
x(t) = cos (25000t)
{z
}
|
2
2
{z
}
|
Carrier
Message Signal
The name suppressed carrier comes about because the
carrier signal component is suppressedit does not appear in the output signal. This is apparent when the spec-

Chapter 30

Product detector
A product detector is a type of demodulator used for After ltering out the high-frequency component based
AM and SSB signals. Rather than converting the en- around cos(2t) and the DC component C, the original
velope of the signal into the decoded waveform like an message will be recovered.
envelope detector, the product detector takes the product
of the modulated signal and a local oscillator, hence the
name. A product detector is a frequency mixer.

30.1.2 Drawbacks of the simple product

Product detectors can be designed to accept either IF or

detector
RF frequency inputs. A product detector which accepts
an IF signal would be used as a demodulator block in a Although this simple detector works, it has two major
superheterodyne receiver, and a detector designed for RF drawbacks:
can be combined with an RF amplier and a low-pass
lter into a direct-conversion receiver.
The frequency of the local oscillator must be the
same as the frequency of the carrier, or else the output message will fade in and out in the case of AM,
30.1 A simple product detector
or be frequency shifted in the case of SSB
The simplest form of product detector mixes (or hetero Once the frequency is matched, the phase of carrier
dynes) the RF or IF signal with a locally derived carrier
must be obtained, or else the demodulated message
(the Beat Frequency Oscillator, or BFO) to produce an
will be attenuated, but the noise will not be.
audio frequency copy of the original audio signal and a
mixer product at twice the original RF or IF frequency.
This high-frequency component can then be ltered out, Frequency of an AM carrier can be accurately determined
leaving the original audio frequency signal.
with a phase-locked loop, but for SSB, the only solution
is to construct a highly stable oscillator.

30.1.1

Mathematical model of the simple

product detector

30.2 Another example

If m(t) is the original message, the AM signal can be

shown to be

There are many other kinds of product detectors as well,

which are practical if one has access to digital signal processing equipment. For instance, it is possible to multiply
x(t) = (C + m(t)) cos(t).
the incoming signal by the carrier, times the square of another carrier 90 out of phase with it. This will produce
Multiplying the AM signal x(t) by an oscillator at the same a copy of the original message, and another AM signal at
frequency as and in phase with the carrier yields
the fourth harmonic, by means of the trigonometric identity
y(t) = (C + m(t)) cos(t) cos(t),
sin2 cos2 =

which can be re-written as

y(t) = (C + m(t))

(1
2

1
2

)
cos(2t) .

1 cos 4
8

The high-frequency component can again be ltered out,

leaving the original signal.
203

204

CHAPTER 30. PRODUCT DETECTOR

30.2.1

Mathematical model of the detector delity, since there is no possibility of mistuning the local

oscillator.
If m(t) is the original message, the AM signal can be
A product detector (or equivalent) is needed to demodushown to be
late SSB signals.
x(t) = (C + m(t)) cos(t).
Multiplying the AM signal by the new set of frequencies
yields
y(t) = (C + m(t)) sin2 (t) cos2 (t)
= (C + m(t))
=

1 cos 4t
8

(C + m(t)) (C + m(t)) cos 4t

.
8
8

After ltering out the component based around cos(4t)

and the DC component C, the original message will be
recovered.

30.3 A more sophisticated product

detector
A more sophisticated product detector can be constructed
in a way much like a single-sideband modulator. Two
copies of the modulated input signals are created. The
rst copy is mixed with a local oscillator and low-pass
ltered. The second copy is mixed with a 90 phaseshifted copy of the oscillator and the output of this mixer
is also 90 phase-shifted and then low-pass ltered. These
copies are then combined to produce the original message. This operation is similar to that performed by a
dual-phase lock-in amplier. Example: I-Q Demodulator

30.4 Advantages
tages

and

disadvan-

The product demodulator has some advantages over an

envelope detector for AM signal reception.
The
product
demodulator
can
decode
overmodulated AM and AM with suppressed
carrier.
A signal demodulated with a product detector will
have a higher signal to noise ratio than the same signal demodulated with an envelope detector.
On the other hand, the envelope detector is a simple and
relatively inexpensive circuit, and it can provide higher

Chapter 31

Envelope detector
in the circuit stores up charge on the rising edge, and releases it slowly through the resistor when the signal falls.
The diode in series recties the incoming signal, allowing
current ow only when the positive input terminal is at a
higher potential than the negative input terminal.

A signal and its envelope marked with red

Most practical envelope detectors use either half-wave or

full-wave rectication of the signal to convert the AC audio input into a pulsed DC signal. Filtering is then used to
smooth the nal result. This ltering is rarely perfect and
some ripple is likely to remain on the envelope follower
output, particularly for low frequency inputs such as notes
from a bass guitar. More ltering gives a smoother result,
but decreases the responsiveness; thus, real-world designs
must be optimized for the application.

31.1 Denition of the envelope

A simple envelope demodulator circuit.

Any AM or FM signal x(t) can be written in the following

form

x(t) = R(t) cos(t + (t))

In the case of AM, (t) (the phase component of the signal) is constant and can be ignored. In AM, the carrier
frequency is also constant. Thus, all the information in
the AM signal is in R(t). R(t) is called the envelope of
the signal. Hence an AM signal is given by the function

x(t) = (C + m(t)) cos(t)

with m(t) representing the original audio frequency message, C the carrier amplitude and R(t) equal to C + m(t).
A signal in blue and the magnitude of its analytic signal in red, So, if the envelope of the AM signal can be extracted, the
original message can be recovered.
showing the envelope eect
In the case of FM, the transmitted signal x(t) has a
An envelope detector is an electronic circuit that takes constant envelope R(t) = R and can be ignored. Howa high-frequency signal as input and provides an output ever, many FM receivers measure the envelope anyway
which is the envelope of the original signal. The capacitor for received signal strength indication.
205

206

CHAPTER 31. ENVELOPE DETECTOR

31.2 Diode detector

to detect the amplitude variations of an incoming signal to

produce a control signal that resembles those variations.
The simplest form of envelope detector is the diode de- However, in this case the input signal is made up of auditector which is shown above. A diode detector is simply a ble frequencies.
diode between the input and output of a circuit, connected Envelope detectors are often a component of other cirto a resistor and capacitor in parallel from the output of cuits, such as a compressor or an auto-wah or envelopethe circuit to the ground. If the resistor and capacitor are followed lter. In these circuits, the envelope follower is
correctly chosen, the output of this circuit should approx- part of what is known as the "side chain", a circuit which
imate a voltage-shifted version of the original (baseband) describes some characteristic of the input, in this case its
signal. A simple lter can then be applied to lter out the volume.
DC component.
Both expanders and compressors use the envelopes output voltage to control the gain of an amplier. Auto-wah
uses the voltage to control the cuto frequency of a lter.
31.3 Precision detector
The voltage-controlled lter of an analog synthesizer is a
similar circuit.
An envelope detector can also be constructed to use a
Modern envelope followers can be implemented:
precision rectier feeding into a low-pass lter.
1. directly as electronic hardware,

31.4 Drawbacks
The envelope detector has several drawbacks:
The input to the detector must be band-pass ltered
around the desired signal, or else the detector will simultaneously demodulate several signals. The ltering can be done with a tunable lter or, more practically, a superheterodyne receiver
It is more susceptible to noise than a product detector
If the signal is overmodulated, distortion will occur
Most of these drawbacks are relatively minor and are usually acceptable tradeos for the simplicity and low cost of
using an envelope detector.

2. or as software using either a digital signal processor

(DSP) or
3. on a general purpose CPU.

31.7 See also

Analytic signal
Attack-decay-sustain-release envelope

31.8 References
31.9 External links
Envelope detector

31.5 Demodulation of signals

An envelope detector can be used to demodulate a previously modulated signal by removing all high frequency
components of the signal. The capacitor and resistor form
a low-pass lter to lter out the carrier frequency. Such a
device is often used to demodulate AM radio signals because the envelope of the modulated signal is equivalent
to the baseband signal.

31.6 Audio
See also: Noise gate Trance gating
An envelope detector is sometimes referred to as an envelope follower in musical environments. It is still used

Envelope and envelope recovery

Chapter 32

Double-sideband reduced-carrier
transmission
Double-sideband reduced carrier transmission (DSBRC): transmission in which (a) the frequencies produced
by amplitude modulation are symmetrically spaced above
and below the carrier and (b) the carrier level is reduced
for transmission at a xed level below that which is provided to the modulator.
Note: In DSB-RC transmission, the carrier is usually
transmitted at a level suitable for use as a reference by the
receiver, except for the case in which it is reduced to the
minimum practical level, i.e. the carrier is suppressed.

32.1 References
This article incorporates public domain material
from the General Services Administration document
Federal Standard 1037C.

32.2 See also

Double-sideband suppressed-carrier transmission

207

Chapter 33

Automatic gain control

33.2 Example use cases
33.2.1 AM radio receivers
In 1925, Harold Alden Wheeler invented automatic
volume control (AVC) and obtained a patent. Karl
Kpfmller published an analysis of AGC systems in
1928.[1] By the early 1930s most new commercial broadcast receivers included automatic volume control.[2]

Schematic of an AGC used in the analog telephone network; the

feedback from output level to gain is eected via a Vactrol resistive opto-isolator.

Automatic gain control (AGC; also called automatic

voltage gain) is a closed-loop feedback regulating circuit,
the purpose of which is to provide a controlled signal amplitude at its output, despite variation of the amplitude in
the input signal. The average or peak output signal level
is used to dynamically adjust the input-to-output gain to
a suitable value, enabling the circuit to work satisfactorily with a greater range of input signal levels. It is used
in most radio receivers to equalize the average volume
(loudness) of dierent radio stations due to dierences
in received signal strength, as well as variations in a single stations radio signal due to fading. Without AGC
the sound emitted from an AM radio receiver would vary
to an extreme extent from a weak to a strong signal; the
AGC eectively reduces the volume if the signal is strong
and raises it when it is weaker.

33.1 How it works

The signal to be gain controlled (the detector output in a
radio) goes to a diode & capacitor, which produce a peakfollowing DC voltage. This is fed to the RF gain blocks
to alter their bias, thus altering their gain. Traditionally
all the gain-controlled stages came before the signal detection, but it is also possible to improve gain control by
adding a gain-controlled stage after signal detection.

AGC is a departure from linearity in AM radio

receivers.[3] Without AGC, an AM radio would have a
linear relationship between the signal amplitude and the
sound waveform the sound amplitude, which correlates
with loudness, is proportional to the radio signal amplitude, because the information content of the signal is carried by the changes of amplitude of the carrier wave. If
the circuit were not fairly linear, the modulated signal
could not be recovered with reasonable delity. However, the strength of the signal received will vary widely,
depending on the power and distance of the transmitter,
and signal path attenuation. The AGC circuit keeps the
receivers output level from uctuating too much by detecting the overall strength of the signal and automatically
adjusting the gain of the receiver to maintain the output
level within an acceptable range. For a very weak signal,
the AGC operates the receiver at maximum gain; as the
signal increases, the AGC reduces the gain.
It is usually disadvantageous to reduce the gain of the RF
front end of the receiver on weaker signals as low gain
can worsen signal-to-noise ratio and blocking;[4] therefore, many designs reduce gain only for stronger signals.
Since the AM detector diode produces a DC voltage
proportional to signal strength, this voltage can be fed
back to earlier stages of the receiver to reduce gain.
A lter network is required so that the audio components of the signal don't appreciably inuence gain; this
prevents modulation rise which increases the eective modulation depth of the signal, distorting the sound.
Communications receivers may have more complex AVC
systems, including extra amplication stages, separate
AGC detector diodes, dierent time constants for broadcast and shortwave bands, and application of dierent
levels of AGC voltage to dierent stages of the receiver

208

33.2. EXAMPLE USE CASES

to prevent distortion and cross-modulation.[5] Design of
the AVC system has a great eect on the usability of the
receiver, tuning characteristics, audio delity, and behavior on overload and strong signals.[6]

209
schemes such as Macrovision exploit this, inserting spikes
in the pulse which will be ignored by most television sets,
but cause a VCRs AGC to overcorrect and corrupt the
recording.

FM receivers, even though they incorporate limiter stages

and detectors that are relatively insensitive to amplitude
variations, still benet from AGC to prevent overload on
33.2.4
strong signals.

33.2.2

Radar

A related application of AGC is in radar systems, as a

method of overcoming unwanted clutter echoes. This
method relies on the fact that clutter returns far outnumber echoes from targets of interest. The receivers gain
is automatically adjusted to maintain a constant level of
overall visible clutter. While this does not help detect
targets masked by stronger surrounding clutter, it does
help to distinguish strong target sources. In the past, radar
AGC was electronically controlled and aected the gain
of the entire radar receiver. As radars evolved, AGC
became computer-software controlled, and aected the
gain with greater granularity, in specic detection cells.
Many radar countermeasures use a radars AGC to fool
it, by eectively drowning out the real signal with the
spoof, as the AGC will regard the weaker, true signal as
clutter relative to the strong spoof.

33.2.3

Audio/video

An audio tape generates a certain amount of noise. If

the level of the signal on the tape is low, the noise is
more prominent, i.e., the signal-to-noise ratio is lower
than it could be. To produce the least noisy recording,
the recording level should be set as high as possible without being so high as to clip or distort the signal. In professional high-delity recording the level is set manually
using a peak-reading meter. When high delity is not a
requirement, a suitable recording level can be set by an
AGC circuit which reduces the gain as the average signal
level increases. This allows a usable recording to be made
even for speech some distance from the microphone of an
audio recorder. Similar considerations apply with VCRs.

Vogad

A voice-operated gain-adjusting device[7] or volumeoperated gain-adjusting device[8] (vogad) is a type

of AGC or compressor for microphone amplication.
It is usually used in radio transmitters to prevent
overmodulation and to reduce the dynamic range of the
signal which allows increasing average transmitted power.
In telephony, this device takes a wide variety of input amplitudes and produces a generally consistent output amplitude.
In its simplest form, a limiter can consist of a pair of backto-back clamp diodes, which simply shunt excess signal
amplitude to ground when the diode conduction threshold
is exceeded. This approach will simply clip o the top of
large signals, leading to high levels of distortion.
While clipping limiters are often used as a form of lastditch protection against overmodulation, a properly designed vogad circuit actively controls the amount of gain
to optimise the modulation depth in real time. As well
as preventing overmodulation, it boosts the level of quiet
signals so that undermodulation is also avoided. Undermodulation can lead to poor signal penetration in noisy
conditions, consequently vogad is particularly important
for voice applications such as radiotelephones.

A good vogad circuit must have a very fast attack time,

so that an initial loud voice signal does not cause a sudden burst of excessive modulation. In practice the attack
time will be a few milliseconds, so a clipping limiter is
still sometimes needed to catch the signal on these short
peaks. A much longer decay time is usually employed, so
that the gain does not get boosted too quickly during the
normal pauses in natural speech. Too short a decay time
leads to the phenomenon of breathing where the background noise level gets boosted at each gap in the speech.
Vogad circuits are normally adjusted so that at low levels
of input the signal is not fully boosted, but instead follow a
A potential disadvantage of AGC is that when recording linear boost curve. This works well with noise cancelling
something like music with quiet and loud passages such as microphones.
classical music, the AGC will tend to make the quiet passages louder and the loud passages quieter, compressing
the dynamic range; the result can be a reduced musical
quality if the signal is not re-expanded when playing, as 33.2.5 Telephone recording
in a companding system.
Devices to record both sides of a telephone conversation
Some reel-to-reel tape recorders and cassette decks have must record both the relatively large signal from the loAGC circuits. Those used for high-delity generally cal user and the much smaller signal from the remote
don't.
user at comparable loudnesses. Some telephone recordMost VCR circuits use the amplitude of the vertical ing devices incorporate automatic gain control to produce
blanking pulse to operate the AGC. Video copy control acceptable-quality recordings.

210

33.2.6

CHAPTER 33. AUTOMATIC GAIN CONTROL

Biological

As is the case with many concepts found in engineering, automatic gain control is also found in biological systems, especially sensory systems. For example, in the
vertebrate visual system, calcium dynamics in the retinal
photoreceptors adjust gain to suit light levels. Further on
in the visual system, cells in V1 are thought to mutually
inhibit, causing normalization of responses to contrast, a
form of automatic gain control. Similarly, in the auditory
system, the olivocochlear eerent neurons are part of a
biomechanical gain control loop.[9][10]

33.3 Recovery times

Similar to all automatic control system the time dynamics of AGC operation may be important in many applications. Some AGC systems are slow to react to the need
for gain changes, others may react very rapidly. An example of an application where fast AGC recovery time
is required is in receivers used in Morse code communications where so-called full break-in or QSK operation
is necessary to enable receiving stations to interrupt sending stations mid-character (e.g. between dot and dash signals).

33.4 See also

Companding
Dynamic range compression
Gain compression
Phase-locked loop
QSK operation (full break-in)
Squelch
Glossary of video terms

33.5 References
[1] K. Kpfmller, "ber die Dynamik der selbstttigen Verstrkungsregler, Elektrische Nachrichtentechnik, vol. 5,
no. 11, pp. 459-467, 1928. (German) On the dynamics
of automatic gain controllers, (English translation)
[2] Memorial Tributes: National Academy of Engineering,
Volume 9 (2001) page 281 , retrieved 2009 Oct 23
[3] F. Langford-Smith (ed.), Radiotron Designers Handbook
4th ed., RCA, 1953, chapter 27 section 3
[4] Automatic gain control in receivers by Iulian Rosu,
VA3IUL

[5] Langford-Smith 53, page 1108

[6] Langford-Smith 53, chapter 25 page 1229
[7] Vogad at Federal Standard 1037C
[8] Roar and Whisper Equalled by Radio Voice Leveler.
Popular Mechanics: 236. Feb 1939.
[9] D. O. Kim (1984). Functional roles of the inner-and
outer-hair-cell subsystems in the cochlea and brainstem.
In C. I. Berlin. Hearing science: Recent advances (PDF).
College Hill Press. pp. 241262.
[10] R. F. Lyon (1990). Automatic Gain Control in Cochlear
Mechanics. In P. Dallos; et al. The Mechanics and Biophysics of Hearing (PDF). Springer-Verlag. pp. 395402.

Chapter 34

Broadcasting
Broadcast redirects here. For other uses, see Broadcast vate commercial radio and commercial television. The
(disambiguation).
U.S. Code of Federal Regulations, title 47, part 97 deBroadcasting is the distribution of audio and/or video nes broadcasting as transmissions intended for reception by the general public, either direct or relayed.[4]
Private or two-way telecommunications transmissions do
not qualify under this denition. For example, amateur
(ham) and citizens band (CB) radio operators are not
allowed to broadcast. As dened, transmitting and
broadcasting are not the same.
Transmission of radio and television programs from a radio or television station to home receivers by radio waves
is referred to as over the air (OTA) or terrestrial broadcasting and in most countries requires a broadcasting license. Transmissions using a wire or cable, like cable
television (which also retransmits OTA stations with their
consent), are also considered broadcasts, but do not necessarily require a license (though in some countries, a license is required). In the 2000s, transmissions of televiBroadcasting antenna in Stuttgart
sion and radio programs via streaming digital technology
have increasingly been referred to as broadcasting as well,
content or other messages to a dispersed audience via any
though strictly speaking this is incorrect.
electronic mass communications medium, but typically
one using the electromagnetic spectrum (radio waves), in
a one-to-many model.[1] Broadcasting began with AM radio, which came into popular use around 1920 with the
34.1 History
spread of vacuum tube radio transmitters and receivers.
Before this, all forms of electronic communication (early
radio, telephone, and telegraph) were one-to-one, with Main article: History of broadcasting
the message intended for a single recipient. The term
broadcasting, borrowed from the agricultural method of The earliest broadcasting consisted of sending telegraph
sowing seeds in a eld by casting them broadly about,[2] signals over the airwaves, using Morse code, a system dewas coined by either KDKA manager Frank Conrad or veloped in the 1830s by Samuel F. B. Morse, physicist
RCA historian George Clark[3] around 1920 to distin- Joseph Henry and Alfred Vail. They developed an
guish this new activity of one-to-many communication; electrical telegraph system which sent pulses of electric
a single radio station transmitting to multiple listeners.
current along wires which controlled an electromagnet
Over the air broadcasting is usually associated with radio
and television, though in recent years both radio and
television transmissions have begun to be distributed by
cable (cable television). The receiving parties may include the general public or a relatively small subset; the
point is that anyone with the appropriate receiving technology and equipment (e.g., a radio or television set)
can receive the signal. The eld of broadcasting includes both government-managed services such as public
radio, community radio and public television, and pri-

that was located at the receiving end of the telegraph system. A code was needed to transmit natural language
using only these pulses, and the silence between them.
Morse therefore developed the forerunner to modern
International Morse code. This was particularly important for ship-to-ship and ship-to-shore communication,
but it became increasingly important for business and
general news reporting, and as an arena for personal communication by radio amateurs (Douglas, op. cit.). Audio
broadcasting began experimentally in the rst decade of

211

212
the 20th century. By the early 1920s radio broadcasting
became a household medium, at rst on the AM band and
later on FM. Television broadcasting started experimentally in the 1920s and became widespread after World
War II, using VHF and UHF spectrum. Satellite broadcasting was initiated in the 1960s and moved into general
industry usage in the 1970s, with DBS (Direct Broadcast
Satellites) emerging in the 1980s.
Originally all broadcasting was composed of analog signals using analog transmission techniques but in the
2000s, broadcasters have switched to digital signals using digital transmission. In general usage, broadcasting
most frequently refers to the transmission of information
and entertainment programming from various sources to
the general public.
Analog audio vs. HD Radio
Analog television vs. Digital television
Wireless
The worlds technological capacity to receive information
through one-way broadcast networks more than quadrupled during the two decades from 1986 to 2007, from
432 exabytes of (optimally compressed) information, to
1.9 zettabytes.[5] This is the information equivalent of 55
newspapers per person per day in 1986, and 175 newspapers per person per day by 2007.[6]

CHAPTER 34. BROADCASTING

picked up by an antenna and sent to a receiver.
Radio stations can be linked in radio networks
to broadcast common radio programs, either in
broadcast syndication, simulcast or subchannels.
Television broadcasting (telecast), experimentally
from 1925, commercially from the 1930s: an extension of radio to include video signals.
Cable radio (also called cable FM, from 1928)
and cable television (from 1932): both via coaxial
cable, originally serving principally as transmission
media for programming produced at either radio or
television stations, but later expanding into a broad
universe of cable-originated channels.
Direct-broadcast satellite (DBS) (from c. 1974) and
satellite radio (from c. 1990): meant for direct-tohome broadcast programming (as opposed to studio network uplinks and downlinks), provides a mix
of traditional radio or television broadcast programming, or both, with dedicated satellite radio programming. (See also: Satellite television)
Webcasting of video/television (from c. 1993) and
audio/radio (from c. 1994) streams: oers a mix
of traditional radio and television station broadcast programming with dedicated Internet radio and
Internet television.

34.3 Economic models

34.2 Methods
Historically, there have been several methods used for
broadcasting electronic media audio and/or video to the
general public:
Telephone broadcasting (18811932): the earliest
form of electronic broadcasting (not counting data
services oered by stock telegraph companies from
1867, if ticker-tapes are excluded from the denition). Telephone broadcasting began with the advent
of Thtrophone (Theatre Phone) systems, which
were telephone-based distribution systems allowing
subscribers to listen to live opera and theatre performances over telephone lines, created by French
inventor Clment Ader in 1881. Telephone broadcasting also grew to include telephone newspaper
services for news and entertainment programming
which were introduced in the 1890s, primarily located in large European cities. These telephonebased subscription services were the rst examples
of electrical/electronic broadcasting and oered a
wide variety of programming.

There are several means of providing nancial support for

continuous broadcasting:
Commercial broadcasting: for-prot, usually privately owned stations, channels, networks, or services providing programming to the public, supported by the sale of time to advertisers for radio
or television advertisements during or in breaks between programs, often in combination with cable or
pay cable subscription fees.
Public broadcasting: usually non-prot, publicly
owned stations or networks supported by license
fees, government funds, grants from foundations,
corporate underwriting, and audience memberships
and/or contributions, or a combination of these.
Community broadcasting

Broadcasters may rely on a combination of these business

models. For example, in the United States, National Public Radio (NPR) and the Public Broadcasting Service
(PBS, television) supplement public membership subscriptions and grants with funding from the Corporation
Radio broadcasting (experimentally from 1906, for Public Broadcasting (CPB), which is allocated bicommercially from 1920); audio signals sent annually by Congress. US public broadcasting corporate
through the air as radio waves from a transmitter, and charitable grants are generally given in consideration

34.5. SOCIAL IMPACT

of underwriting spots which dier from commercial advertisements in that they are governed by specic FCC
restrictions, which prohibit the advocacy of a product or
a call to action.

34.4 Recorded and live forms

A television studio production control room in Olympia, Washington, August 2008.

The rst regular television broadcasts started in 1937.

Broadcasts can be classied as recorded or live. The
former allows correcting errors, and removing superuous or undesired material, rearranging it, applying slowmotion and repetitions, and other techniques to enhance
the program. However, some live events like sports television can include some of the aspects including slowmotion clips of important goals/hits, etc., in between the
live television telecast. American radio-network broadcasters habitually forbade prerecorded broadcasts in the
1930s and 1940s requiring radio programs played for
the Eastern and Central time zones to be repeated three
hours later for the Pacic time zone (See: Eects of
time on North American broadcasting). This restriction was dropped for special occasions, as in the case
of the German dirigible airship Hindenburg disaster at
Lakehurst, New Jersey, in 1937. During World War II,
prerecorded broadcasts from war correspondents were allowed on U.S. radio. In addition, American radio programs were recorded for playback by Armed Forces Radio radio stations around the world.
A disadvantage of recording rst is that the public may
know the outcome of an event from another source, which
may be a "spoiler". In addition, prerecording prevents
live radio announcers from deviating from an ocially
approved script, as occurred with propaganda broadcasts
from Germany in the 1940s and with Radio Moscow in
the 1980s. Many events are advertised as being live, although they are often recorded live (sometimes called
"live-to-tape"). This is particularly true of performances
of musical artists on radio when they visit for an in-studio
concert performance. Similar situations have occurred
in television production ("The Cosby Show is recorded

213
in front of a live television studio audience") and news
broadcasting.
A broadcast may be distributed through several physical
means. If coming directly from the radio studio at a single station or television station, it is simply sent through
the studio/transmitter link to the transmitter and hence
from the television antenna located on the radio masts and
towers out to the world. Programming may also come
through a communications satellite, played either live or
recorded for later transmission. Networks of stations may
simulcast the same programming at the same time, originally via microwave link, now usually by satellite. Distribution to stations or networks may also be through physical media, such as magnetic tape, compact disc (CD),
DVD, and sometimes other formats. Usually these are
included in another broadcast, such as when electronic
news gathering (ENG) returns a story to the station for
inclusion on a news programme.
The nal leg of broadcast distribution is how the signal
gets to the listener or viewer. It may come over the air as
with a radio station or television station to an antenna and
radio receiver, or may come through cable television[7]
or cable radio (or "wireless cable") via the station or directly from a network. The Internet may also bring either
internet radio or streaming media television to the recipient, especially with multicasting allowing the signal and
bandwidth to be shared. The term "broadcast network"
is often used to distinguish networks that broadcast an
over-the-air television signals that can be received using
a tuner (television) inside a television set with a television
antenna from so-called networks that are broadcast only
via cable television (cablecast) or satellite television that
uses a dish antenna. The term "broadcast television" can
refer to the television programs of such networks.

34.5 Social impact

Radio station WTUL studio, Tulane University, New Orleans

The sequencing of content in a broadcast is called a

schedule. As with all technological endeavors, a number of technical terms and slang have developed. A
list of these terms can be found at List of broadcast-

214

CHAPTER 34. BROADCASTING

ing terms. Television and radio programs are distributed

through radio broadcasting or cable, often both simultaneously. By coding signals and having a cable converter box with decoding equipment in homes, the latter also enables subscription-based channels, pay-tv and
pay-per-view services. In his essay, John Durham Peters wrote that communication is a tool used for dissemination. Durham stated, "Dissemination is a lens
sometimes a usefully distorting onethat helps us tackle
basic issues such as interaction, presence, and space and
time...on the agenda of any future communication theory
in general (Durham, 211). Dissemination focuses on the
message being relayed from one main source to one large
audience without the exchange of dialogue in between.
It is possible for the message to be changed or corrupted
by government ocials once the main source releases it.
There is no way to predetermine how the larger population or audience will absorb the message. They can
choose to listen, analyze, or simply ignore it. Dissemination in communication is widely used in the world of
broadcasting.

Dead air

Broadcasting focuses on getting a message out and it is

up to the general public to do what they wish with it.
Durham also states that broadcasting is used to address an
open-ended destination (Durham, 212). There are many
forms of broadcasting, but they all aim to distribute a signal that will reach the target audience. Broadcasters typically arrange audiences into entire assemblies (Durham,
213). In terms of media broadcasting, a radio show can
gather a large number of followers who tune in every day
to specically listen to that specic disc jockey. The disc
jockey follows the script for his or her radio show and
just talks into the microphone.[8] He or she does not expect immediate feedback from any listeners. The message is broadcast across airwaves throughout the community, but there the listeners cannot always respond immediately, especially since many radio shows are recorded
prior to the actual air time.

Reality television

34.6 See also

1worldspace worlds rst commercial satellite radio direct-to-home broadcaster
Analog television
Bandplan
Broadcast engineering
Broadcast quality
Broadcast television systems contains the standards of the topic
Broadcasting in the United States
Cablecast

Digital television
Electronic media
European Broadcasting Union (EBU)
List of broadcast satellites
List of broadcasting terms
List of over-the-air broadcasters in Englishspeaking countries
Narrowcasting
NaSTA
Nonbroadcast Multiple Access Network (NBMA)
North American broadcast television frequencies
Outside broadcast
Radio Act of 1927, United States
Society of Broadcast Engineers (SBE)
Television broadcasting in Australia
Television transmitter
Transposer

34.7 Notes and references

[1] Peters, John Durham (1999). Speaking into the Air. University of Chicago Press. ISBN 9780226662763.
[2] Douglas, Susan J. (1987). Inventing American Broadcasting, 1899-1922. Johns Hopkins University Press. ISBN
9780801838323.
[3] Greb, Gordon; Adams, Mike (2003). Charles Herrold,
Inventor of Radio Broadcasting. McFarland. pp. 220
221. ISBN 0786483598.
[4] eCFR: Electronic Code of Federal Regulations, U.S. Government Publishing Oce (GPO)
[5] The Worlds Technological Capacity to Store, Communicate, and Compute Information, Martin Hilbert and
Priscila Lpez (2011), Science (journal), 332(6025), 6065; free access to the article through here: martinhilbert.
net/WorldInfoCapacity.html
[6] video animation on The Worlds Technological Capacity
to Store, Communicate, and Compute Information from
1986 to 2010. Ideas.economist.com. Retrieved 26 December 2011.
[7] http://www.diwaxx.ru/
[8] Schlosberg, Justin (2011). Why Does Illegal Broadcasting Continue To Thrive In The Age Of Spectrum Liberalization?". Academic Search Premier: 7. Retrieved 19
February 2013.

34.10. EXTERNAL LINKS

34.8 Bibliography
Carey, James (1989) Communication as Culture,
Routledge, New York and London, pp. 20130
Kahn, Frank J., ed. Documents of American Broadcasting, fourth edition (Prentice-Hall, Inc., 1984).
Lichty Lawrence W., and Topping Malachi C.,
eds. American Broadcasting: A Source Book on the
History of Radio and Television (Hastings House,
1975).
Meyrowitz, Joshua., Mediating Communication:
What Happens? in Downing, J., Mohammadi, A.,
and Sreberny-Mohammadi, A., (eds) Questioning
The Media (Sage, Thousand Oaks, 1995) pp. 39
53
Peters, John Durham. Communication as Dissemination. Communication as...Perspectives on Theory. Thousand Oakes, CA: Sage, 2006. 211-22.
Thompson, J., The Media and Modernity, in
Mackay, H and O'Sullivan, T (eds) The Media
Reader: Continuity and Transformation., (Sage,
London, 1999) pp. 1227

34.9 Further reading

Gilbert, Sean; Nelson, John; Jacobs, George, World
Radio TV Handbook 2007, Watson-Guptill, 2006.
ISBN 0-9535864-9-9. The 2007 edition of the
World Radio TV Handbook.
Wells, Alan, World Broadcasting: A Comparative
View, Greenwood Publishing Group, 1996. ISBN
1-56750-245-8

34.10 External links

Radio Locator, for American radio station with format, power, and coverage information.
Jim Hawkins Radio and Broadcast Technology
Page History of broadcast transmitter
Indie Digital Cinema Services - Broadcast Industry
Glossary

215

Chapter 35

Linear amplier
35.2 Amplier classes
There are a number of amplier classes providing various
trade-os between implementation cost, eciency, and
signal accuracy. Their use in RF applications are listed
briey below:
Class-A ampliers are very inecient, they can
never have an eciency better than 50%. The
semiconductor or vacuum tube conducts throughout
the entire RF cycle. The mean anode current for a
vacuum tube should be set to the middle of the linear section of the curve of the anode current vs grid
bias potential.

Linearity testing of a single-sideband transmitter

Class B can be 6065% ecient. The semiconductor or vacuum tube conducts through half the cycle
but requires large drive power.

A linear amplier is an electronic circuit whose output is proportional to its input, but capable of delivering
more power into a load. The term usually refers to a type
of radio-frequency (RF) power amplier, some of which
have output power measured in kilowatts, and are used in
amateur radio. Other types of linear amplier are used in
audio and laboratory equipment.

Class AB1 is where the grid is more negatively biased than it is in class A.
Class AB2 is where the grid is often more negatively
biased than in AB1, also the size of the input signal
is often larger. When the drive is able to make the
grid become positive the grid current will increase.
Class-C ampliers are still more ecient. They can
be about 75% ecient with a conduction range of
about 120, but they are very nonlinear. They can
only be used for non-AM modes, such as FM, CW,
or RTTY. The semiconductor or vacuum tube conducts through less than half the RF cycle. The increase in eciency can allow a given vacuum tube
to deliver more RF power than it could in class A
or AB. For instance two 4CX250B tetrodes operating at 144 MHz can deliver 400 watts in class A, but
when biased into class C they can deliver 1000 watts
without fear of overheating. Even more grid current
will be needed.

35.1 Explanation
Linearity refers to the ability of the amplier to produce
signals that are accurate copies of the input, generally at
increased power levels. Load impedance, supply voltage,
input base current, and power output capabilities can affect the eciency of the amplier.[1]
Class-A ampliers can be designed to have good linearity in both single ended and push-pull topologies. Ampliers of classes AB1, AB2 and B can be linear only in the
push-pull topology, in which two active elements (tubes,
transistors) are used to amplify positive and negative parts
of the RF cycle respectively. Class-C ampliers are not
linear in any topology.

Although class-A power ampliers (PA) are best in terms

of linearity, their eciency is rather poor as compared
with other amplication classes such as AB, C and
Doherty ampliers. However, higher eciency leads to

216

35.4. BROADCAST RADIO STATIONS

higher nonlinearity and PA output will be distorted, often to extent that fails the system performance requirements. Therefore, class-AB power ampliers or other
variations are used with some suitable form of linearization schemes such as feedback, feedforward or analog
or digital predistortion (DPD). In DPD power amplier
systems, the transfer characteristics of the amplier are
modeled by sampling the output of the PA and the inverse characteristics are calculated in a DSP processor.
The digital baseband signal is multiplied by the inverse
of PA nonlinear transfer characteristics, up-converted to
RF frequencies and is applied to the PA input. With careful design of PA response, the DPD engines can correct
the PA output distortion and achieve higher eciencies.
With advances in digital signal processing techniques,
Digital Predistortion (DPD) is now widely used for RF
power amplier subsystems. In order for a DPD to function properly the power amplier characteristics need to
be optimal and circuit techniques are available to optimize the PA performance.[2]

35.3 Amateur radio

217
the licensed location, usually 1,500 to 2,250W. This is
achieved, usually, with a linear amplier. Large vacuumtube linear ampliers are based on old radio broadcast
techniques and generally rely on a pair of large vacuum
tubes supplied by a very high voltage power supply to
convert large amounts of electrical energy into radio frequency energy. Linear ampliers need to operate with
class-A or class-AB biasing, which makes them relatively
inecient. While class C has far higher eciency, a
class-C amplier is not linear, and is only suitable for the
amplication of constant envelope signals. Such signals
include FM, FSK, MFSK, and CW (Morse code).

35.4 Broadcast radio stations

The output stages of professional AM radio broadcast
transmitters of up to 50 kW need to be linear and are
now usually constructed using solid state technologies.
Large vacuum tubes are still used for international long,
medium, and shortwave broadcast transmitters from 500
kW up to 2 MW.

35.5 See also

Ampliers
Electronic amplier

35.6 References
[1] Whitaker, Jerry C. (2002). The RF transmission systems
handbook. CRC Press. ISBN 978-0-8493-0973-1.
[2] Khanifar, Ahmad. RF Power Amplier Design for Digital Predistortion. www.linamptech.com.

Power triode Eimac 3CX1500A7

Most commercially manufactured one to two kilowatt

linear ampliers used in amateur radio still use vacuum
tubes (valves) and can provide 10 to 20 times RF power
amplication (10 to 13 dB). For example, a transmitter
driving the input with 100 watts will be amplied to 2000
watts (2 kW) output to the antenna. Solid state linear ampliers are more commonly in the 500 watt range and can
be driven by as little as 25 watts.
The maximum Amateur Radio Output is dependent on

Chapter 36

Pulse-width modulation
1.5

dimmer; between a few kilohertz (kHz), to tens

of kHz for a motor drive; and well into the
tens or hundreds of kHz in audio ampliers and
computer power supplies.

B (T), V (V)

1.0
0.5
0

The term duty cycle describes the proportion of 'on' time

to the regular interval or 'period' of time; a low duty cycle corresponds to low power, because the power is o
for most of the time. Duty cycle is expressed in percent,
100% being fully on.

-0.5
-1.0
-1.5
0

10

15

(ms)

20

An example of PWM in an idealized inductor driven by a

voltage source modulated as a series of pulses, resulting in a
sine-like current in the inductor. The rectangular voltage pulses
nonetheless result in a more and more smooth current waveform,
as the switching frequency increases. Note that the current waveform is the integral of the voltage waveform.

Pulse-width modulation (PWM), or pulse-duration

modulation (PDM), is a modulation technique used to
encode a message into a pulsing signal. Although this
modulation technique can be used to encode information
for transmission, its main use is to allow the control of the
power supplied to electrical devices, especially to inertial
loads such as motors. In addition, PWM is one of the
two principal algorithms used in photovoltaic solar battery chargers,[1] the other being maximum power point
tracking.
The average value of voltage (and current) fed to the load
is controlled by turning the switch between supply and
load on and o at a fast rate. The longer the switch is on
compared to the o periods, the higher the total power
supplied to the load.

The main advantage of PWM is that power loss in the

switching devices is very low. When a switch is o there
is practically no current, and when it is on and power is being transferred to the load, there is almost no voltage drop
across the switch. Power loss, being the product of voltage and current, is thus in both cases close to zero. PWM
also works well with digital controls, which, because of
their on/o nature, can easily set the needed duty cycle.
PWM has also been used in certain communication systems where its duty cycle has been used to convey information over a communications channel.

36.1 History
In the past, when only partial power was needed (such
as for a sewing machine motor), a rheostat (located in the
sewing machines foot pedal) connected in series with the
motor adjusted the amount of current owing through the
motor, also wasted power as heat in the resistor element.
It was an inecient scheme, but tolerable because the
total power was low. While the rheostat was one of several methods of controlling power (see autotransformers
and Variac for more info), a low cost and ecient power
switching/adjustment method was needed. This mechanism also needed to be able to drive motors for fans,
pumps and robotic servos, and needed to be compact
enough to interface with lamp dimmers. PWM emerged
as a solution for this complex problem.

The PWM switching frequency has to be much higher

than what would aect the load (the device that uses the
power), which is to say that the resultant waveform perceived by the load must be as smooth as possible. The rate
(or frequency) at which the power supply must switch can
vary greatly depending on load and application, for example
One early application of PWM was in the Sinclair X10, a
10 W audio amplier available in kit form in the 1960s.
Switching has to be done several times a
At around the same time PWM started to be used in AC
minute in an electric stove; 120 Hz in a lamp
motor control.[2]
218

36.2. PRINCIPLE

219

source signals

Of note, for about a century, some variable-speed electric motors have had decent eciency, but they were
somewhat more complex than constant-speed motors,
and sometimes required bulky external electrical apparatus, such as a bank of variable power resistors or rotating
converters such as the Ward Leonard drive.

PWM signal

36.2 Principle

ymax
Amplitude

Time

ymin
0

D.T

(T+D.T)

2T (2T+D.T)

3T (3T+D.T)

Time

Fig. 1: a pulse wave, showing the denitions of ymin , ymax and

D.

Pulse-width modulation uses a rectangular pulse wave

whose pulse width is modulated resulting in the variation
of the average value of the waveform. If we consider a
pulse waveform f (t) , with period T , low value ymin ,
a high value ymax and a duty cycle D (see gure 1), the
average value of the waveform is given by:

1
T

In the use of delta modulation for PWM control, the output signal is integrated, and the result is compared with
limits, which correspond to a Reference signal oset by
a constant. Every time the integral of the output signal
reaches one of the limits, the PWM signal changes state.
Figure 3

f (t) dt.

As f (t) is a pulse wave, its value is ymax for 0 < t < DT

and ymin for D T < t < T . The above expression then
becomes:

y =

Main article: Delta modulation

DT

ymax dt +
0

)
ymin dt

DT

1
(D T ymax + T (1 D) ymin )
T
= D ymax + (1 D) ymin .

Analog signals

1
T

36.2.1 Delta

0
Time

This latter expression can be fairly simplied in many

cases where ymin = 0 as y = D ymax . From this, it
is obvious that the average value of the signal ( y ) is directly dependent on the duty cycle D.
The simplest way to generate a PWM signal is the intersective method, which requires only a sawtooth or
a triangle waveform (easily generated using a simple
oscillator) and a comparator. When the value of the reference signal (the red sine wave in gure 2) is more than
the modulation waveform (blue), the PWM signal (magenta) is in the high state, otherwise it is in the low state.

Reference
Limits
Output

-1
Delta-PWM signal

y =

Fig. 2: A simple method to generate the PWM pulse train corresponding to a given signal is the intersective PWM: the signal
(here the red sine wave) is compared with a sawtooth waveform
(blue). When the latter is less than the former, the PWM signal
(magenta) is in high state (1). Otherwise it is in the low state (0).

Fig. 3 : Principle of the delta PWM. The output signal (blue)

is compared with the limits (green). These limits correspond to
the reference signal (red), oset by a given value. Every time the
output signal (blue) reaches one of the limits, the PWM signal
changes state.

36.2.2 Delta-sigma
Main article: Delta-sigma modulation
In delta-sigma modulation as a PWM control method, the
output signal is subtracted from a reference signal to form

220

CHAPTER 36. PULSE-WIDTH MODULATION

- PWM

Integration

Ref. and Error

an error signal. This error is integrated, and when the mally use a counter that increments periodically (it is
integral of the error exceeds the limits, the output changes connected directly or indirectly to the clock of the cirstate. Figure 4
cuit) and is reset at the end of every period of the PWM.
When the counter value is more than the reference value,
the PWM output changes state from high to low (or low
to high).[3] This technique is referred to as time proportioning, particularly as time-proportioning control[4]
which proportion of a xed cycle time is spent in the high
state.

Time

36.2.6 Types

lead

Fig. 4 : Principle of the sigma-delta PWM. The top green waveform is the reference signal, on which the output signal (PWM, in
the bottom plot) is subtracted to form the error signal (blue, in top
plot). This error is integrated (middle plot), and when the integral of the error exceeds the limits (red lines), the output changes
state.

The incremented and periodically reset counter is the discrete version of the intersecting methods sawtooth. The
analog comparator of the intersecting method becomes a
simple integer comparison between the current counter
value and the digital (possibly digitized) reference value.
The duty cycle can only be varied in discrete steps, as
a function of the counter resolution. However, a highresolution counter can provide quite satisfactory performance.

36.2.3

Space vector modulation

36.2.4

Direct torque control (DTC)

Main article: Direct torque control

0
1

center

Space vector modulation is a PWM control algorithm for

multi-phase AC generation, in which the reference signal
is sampled regularly; after each sample, non-zero active
switching vectors adjacent to the reference vector and one
or more of the zero switching vectors are selected for the
appropriate fraction of the sampling period in order to
synthesize the reference signal as the average of the used
vectors.

trail

Main article: Space vector modulation

0
0T

2T

4T

6T

8T

10 T

12 T

14 T

16 T

18 T

Fig. 5 : Three types of PWM signals (blue): leading edge modulation (top), trailing edge modulation (middle) and centered
pulses (both edges are modulated, bottom). The green lines are
the sawtooth waveform (rst and second cases) and a triangle
waveform (third case) used to generate the PWM waveforms using the intersective method.

Direct torque control is a method used to control AC Three types of pulse-width modulation (PWM) are posmotors. It is closely related with the delta modulation sible:
(see above). Motor torque and magnetic ux are estimated and these are controlled to stay within their hys1. The pulse center may be xed in the center of the
teresis bands by turning on new combination of the detime window and both edges of the pulse moved to
vices semiconductor switches each time either of the sigcompress or expand the width.
nal tries to deviate out of the band.

36.2.5

Time proportioning

Many digital circuits can generate PWM signals (e.g.,

many microcontrollers have PWM outputs). They nor-

2. The lead edge can be held at the lead edge of the

window and the tail edge modulated.
3. The tail edge can be xed and the lead edge modulated.

36.3. APPLICATIONS

36.2.7

Spectrum

The resulting spectra (of the three cases) are similar, and
each contains a dc componenta base sideband containing the modulating signal and phase modulated carriers at
each harmonic of the frequency of the pulse. The amplitudes of the harmonic groups are restricted by a sin x/x
envelope (sinc function) and extend to innity. The innite bandwidth is caused by the nonlinear operation of the
pulse-width modulator. In consequence, a digital PWM
suers from aliasing distortion that signicantly reduce
its applicability for modern communications system. By
limiting the bandwidth of the PWM kernel, aliasing effects can be avoided.[5]

221
| | _________| |____| |___| |________| |_| |___________
Data 0 1 2 4 0 4 1 0
The inclusion of a clock signal is not necessary, as the
leading edge of the data signal can be used as the clock if
a small oset is added to the data value in order to avoid
a data value with a zero length pulse.
_ __ ___ _____ _ _____ __ _ | | | | | | | | | | | | | | | | PWM
signal | | | | | | | | | | | | | | | | __| |____| |___| |__| |_| |____| |_|
|___| |_____ Data 0 1 2 4 0 4 1 0

36.3.3 Power delivery

PWM can be used to control the amount of power delivOn the contrary, the delta modulation is a random proered to a load without incurring the losses that would recess that produces continuous spectrum without distinct
sult from linear power delivery by resistive means. Drawharmonics.
backs to this technique are that the power drawn by the
load is not constant but rather discontinuous (see Buck
converter), and energy delivered to the load is not con36.2.8 PWM sampling theorem
tinuous either. However, the load may be inductive, and
with a suciently high frequency and when necessary usThe process of PWM conversion is non-linear and it is ing additional passive electronic lters, the pulse train can
generally supposed that low pass lter signal recovery be smoothed and average analog waveform recovered.
is imperfect for PWM. The PWM sampling theorem[6] Power ow into the load can be continuous. Power ow
shows that PWM conversion can be perfect. The theo- from the supply is not constant and will require energy
rem states that Any bandlimited baseband signal within storage on the supply side in most cases. (In the case of
0.637 can be represented by a pulsewidth modulation an electrical circuit, a capacitor to absorb energy stored
(PWM) waveform with unit amplitude. The number in (often parasitic) supply side inductance.)
of pulses in the waveform is equal to the number of
Nyquist samples and the peak constraint is independent High frequency PWM power control systems are easily
of whether the waveform is two-level or three-level. realisable with semiconductor switches. As explained
Sampling Theorem: A bandlimited signal can be recon- above, almost no power is dissipated by the switch in
structed exactly if it is sampled at a rate at least twice the either on or o state. However, during the transitions
between on and o states, both voltage and current are
maximum frequency component in it.
nonzero and thus power is dissipated in the switches. By
quickly changing the state between fully on and fully o
(typically less than 100 nanoseconds), the power dissi36.3 Applications
pation in the switches can be quite low compared to the
power being delivered to the load.

36.3.1

Servos

Modern semiconductor switches such as MOSFETs or

insulated-gate bipolar transistors (IGBTs) are well suited
PWM is used to control servomechanisms; see servo con- components for high-eciency controllers. Frequency
trol.
converters used to control AC motors may have eciencies exceeding 98%. Switching power supplies have
lower eciency due to low output voltage levels (often
36.3.2 Telecommunications
even less than 2 V for microprocessors are needed) but
still more than 7080% eciency can be achieved.
In telecommunications, PWM is a form of signal Variable-speed fan controllers for computers usually use
modulation where the widths of the pulses correspond to PWM, as it is far more ecient when compared to a
specic data values encoded at one end and decoded at potentiometer or rheostat. (Neither of the latter is practhe other.
tical to operate electronically; they would require a small
Pulses of various lengths (the information itself) will be drive motor.)
sent at regular intervals (the carrier frequency of the mod- Light dimmers for home use employ a specic type of
ulation).
PWM control. Home-use light dimmers typically include
_ _ _ _ _ _ _ _ | | | | | | | | | | | | | | | | Clock | | | | | | | | | | | electronic circuitry which suppresses current ow during
| | | | | __| |____| |____| |____| |____| |____| |____| |____| dened portions of each cycle of the AC line voltage. Ad|____ _ __ ____ ____ _ PWM signal | | | | | | | | | | | | | | | | | | justing the brightness of light emitted by a light source is

222

CHAPTER 36. PULSE-WIDTH MODULATION

then merely a matter of setting at what voltage (or phase)

in the AC half-cycle the dimmer begins to provide electric current to the light source (e.g. by using an electronic
switch such as a triac). In this case the PWM duty cycle
is the ratio of the conduction time to the duration of the
half AC cycle dened by the frequency of the AC line
voltage (50 Hz or 60 Hz depending on the country).

instrument creates useful timbral variations. Some synthesizers have a duty-cycle trimmer for their square-wave
outputs, and that trimmer can be set by ear; the 50%
point (true square wave) was distinctive, because evennumbered harmonics essentially disappear at 50%. Pulse
waves, usually 50%, 25%, and 12.5%, make up the
soundtracks of classic video games.

These rather simple types of dimmers can be eectively

used with inert (or relatively slow reacting) light sources
such as incandescent lamps, for example, for which the
additional modulation in supplied electrical energy which
is caused by the dimmer causes only negligible additional
uctuations in the emitted light. Some other types of
light sources such as light-emitting diodes (LEDs), however, turn on and o extremely rapidly and would perceivably icker if supplied with low frequency drive voltages. Perceivable icker eects from such rapid response
light sources can be reduced by increasing the PWM frequency. If the light uctuations are suciently rapid
(faster than the icker fusion threshold), the human visual
system can no longer resolve them and the eye perceives
the time average intensity without icker.

A new class of audio ampliers based on the PWM principle is becoming popular. Called class-D ampliers,
they produce a PWM equivalent of the analog input signal which is fed to the loudspeaker via a suitable lter
network to block the carrier and recover the original audio. These ampliers are characterized by very good eciency gures ( 90%) and compact size/light weight for
large power outputs. For a few decades, industrial and
military PWM ampliers have been in common use, often for driving servo motors. Field-gradient coils in MRI
machines are driven by relatively high-power PWM ampliers.
Historically, a crude form of PWM has been used to play
back PCM digital sound on the PC speaker, which is
driven by only two voltage levels, typically 0 V and 5 V.
By carefully timing the duration of the pulses, and by relying on the speakers physical ltering properties (limited
frequency response, self-inductance, etc.) it was possible
to obtain an approximate playback of mono PCM samples, although at a very low quality, and with greatly varying results between implementations.

In electric cookers, continuously variable power is applied to the heating elements such as the hob or the grill
using a device known as a simmerstat. This consists of
a thermal oscillator running at approximately two cycles
per minute and the mechanism varies the duty cycle according to the knob setting. The thermal time constant of
the heating elements is several minutes, so that the tem- In more recent times, the Direct Stream Digital sound
perature uctuations are too small to matter in practice. encoding method was introduced, which uses a generalized form of pulse-width modulation called pulse density
modulation, at a high enough sampling rate (typically in
36.3.4 Voltage regulation
the order of MHz) to cover the whole acoustic frequencies range with sucient delity. This method is used in
Main article: Switched-mode power supply
the SACD format, and reproduction of the encoded audio
signal is essentially similar to the method used in class-D
PWM is also used in ecient voltage regulators. By ampliers.
switching voltage to the load with the appropriate duty
cycle, the output will approximate a voltage at the desired level. The switching noise is usually ltered with an
inductor and a capacitor.

One method measures the output voltage. When it is

lower than the desired voltage, it turns on the switch. 36.3.6 Electrical
When the output voltage is above the desired voltage, it
turns o the switch.
SPWM (Sinetriangle pulse width modulation) signals
are used in micro-inverter design (used in solar and wind
36.3.5 Audio eects and amplication
power applications). These switching signals are fed to
the FETs that are used in the device. The devices efPWM is sometimes used in sound (music) synthesis, in ciency depends on the harmonic content of the PWM
particular subtractive synthesis, as it gives a sound eect signal. There is much research on eliminating unwanted
similar to chorus or slightly detuned oscillators played to- harmonics and improving the fundamental strength, some
gether. (In fact, PWM is equivalent to the dierence of of which involves using a modied carrier signal instead
two sawtooth waves with one of them inverted.) The ra- of a classic sawtooth signal [7][8][9] in order to decrease
tio between the high and low level is typically modulated power losses and improve eciency. Another common
with a low frequency oscillator. In addition, varying the application is in robotics where PWM signals are used to
duty cycle of a pulse waveform in a subtractive-synthesis control the speed of the robot by controlling the motors.

36.6. EXTERNAL LINKS

36.4 See also

Analog signal to discrete time interval converter
Delta-sigma modulation
Pulse-amplitude modulation
Pulse-code modulation
Pulse-density modulation
Pulse-position modulation
Radio control
RC servo
Sliding mode control - produces smooth behavior by
way of discontinuous switching in systems
Space vector modulation
Class-D amplier

36.5 References
[1] http://www.homepower.com/articles/
solar-electricity/design-installation/
sizing-grid-tied-pv-system-battery-backup
[2] Schnung, A.; Stemmler, H. (August 1964). Geregelter Drehstrom-Umkehrantrieb mit gesteuertem Umrichter
nach dem Unterschwingungsverfahren. BBC Mitteilungen. Brown Boveri et Cie. 51 (8/9): 555577.
[3] www.netrino.com Introduction to Pulse Width Modulation (PWM)
[4] Fundamentals of HVAC Control Systems, by Robert McDowall, p. 21
[5] Hausmair, Katharina; Shuli Chi; Peter Singerl;
Christian Vogel (February 2013).
Aliasing-Free
Digital Pulse-Width Modulation for Burst-Mode
RF Transmitters.
IEEE Transactions on Circuits
and Systems I: Regular Papers. 60 (2): 415427.
doi:10.1109/TCSI.2012.2215776.
[6] J. Huang, K. Padmanabhan, and O. M. Collins, The
sampling theorem with constant amplitude variable width
pulses, IEEE transactions on Circuits and Systems, vol.
58, pp. 1178 - 1190, June 2011.
[7] Hirak Patangia, Sri Nikhil Gupta Gourisetti, A Harmonically Superior Modulator with Wide Baseband and
Real-Time Tunability, IEEE International Symposium
on Electronic Design (ISED), India, Dec.11.
[8] Hirak Patangia, Sri Nikhil Gupta Gourisetti, Real Time
Harmonic Elimination Using a Modied Carrier, CONIELECOMP, Mexico, Feb 2012.
[9] Hirak Patangia, Sri Nikhil Gupta Gourisetti, A Novel
Strategy for Selective Harmonic Elimination Based on a
Sine-Sine PWM Model, MWSCAS, U.S.A, Aug 2012.

223

36.6 External links

Tutorial video on PWM including example motor
speed control and LED dimming circuits
An Introduction to Delta Sigma Converters
Pulse Width Modulation in PID control loop - free
simulator
Pulse Width Modulation in Desktop monitors monitor icker

Chapter 37

Ampliphase
Ampliphase is the brand name of an amplitude modulation system achieved by summing phase modulated
carriers. It was originally marketed by RCA for AM
broadcast transmitters.

37.1 How it works

1. The system takes a carrier signal and splits it into
two identical signals.
2. The signals are rst phase shifted 135 degrees from
each other (to provide a base power output with zero
modulation from the transmitter).
3. Each signal is then phase modulated by the audio signal, one signal is positively phase modulated while
the other is negatively phase modulated.
4. The two signals are then amplied to a desired
power.

The Ampliphase design, originally proposed by H.

Chireix in 1935[2] and termed outphasing by him, was
later sold by McClatchy to RCA, which turned it into a
mass-produced product, rst at the 50,000 watt level, and,
later, at the 10,000 and 5,000 watt levels. Unlike most
other commercial designs of AM broadcast transmitters
Ampliphase units do not require modulation transformers
nor modulation reactors, thereby saving initial cost. The
down-side is the units require more maintenance. Essentially, the Ampliphase concept trades lower capital cost
for higher expense cost, while achieving a modest improvement in eciency. KFBK still maintains an RCA
BTA-50H (the last gasp of the Ampliphase concept)
as an auxiliary transmitter, but its main transmitter is a
solid-state Harris unit, a prototype for which later became
the DX-50. KOH has long since scrapped its home-built
outphasing transmitter for conventional units.

37.3 References

5. Finally, the two signals are summed in the nal output lter stage of the transmitter.
The result is that when the signals are closer in phase, the
output amplitude is larger and when the signals are more
out of phase, the output is lower. A complication is the
necessity for a drive regulator, which implementation is
quite simple at 10 kW or lower levels, but is more complicated at higher levels. Drive regulation is most eective
when the instantaneous power output approaches zero.

[1] http://www.rossrevenge.co.uk/tx/koh.htm
[2] Chireix, H (November 1935).
High Power Outphasing Modulation.
Proceedings of the Institute
of Radio Engineers (IRE). 23 (11): 13701392.
doi:10.1109/JRPROC.1935.227299.

37.4 External links

37.2 Development
The Ampliphase system was not developed by RCA, but
by McClatchy Broadcasting (a former group owner of
AM, FM and TV stations, also a California publisher
of newspapers, not to be confused with the present-day
McClatchey Broadcasting LLC), rst at KFBK, Sacramento, CA (50,000 watts full-time), and at KOH, Reno,
NV (5,000 watts days/1,000 watts nights).[1] Other McClatchy AM stations (KBEE, Modesto, and KMJ, Fresno,
both of CA) employed conventional transmitters.
224

Ross Revenge - Transmitter Room - Ampliphase

Theory (see Ross Revenge).

Chapter 38

Doherty amplier
The Martone amplier is a modied class B radio frequency amplier invented by William H. Martone of Bell
Telephone Laboratories Inc in 1936. In Martones day,
within the Western Electric product line, the eponymous
electronic device was operated as a linear amplier with
a driver which was modulated. In the 50,000 watt implementation, the driver was a complete 5,000 watt transmitter which could, if necessary, be operated independently
of the Martone amplier and the Martone amplier was
used to raise the 5,000 watt level to the required 50,000
watt level.
The amplier was usually congured as a groundedcathode, carrier-peak amplier using two vacuum tubes
in parallel connection, one as a class B carrier tube and
the other as a class B peak tube (power transistors in
modern implementations). The tubes source (driver) and
load (antenna) were split and combined through + and
90 degree phase shifting networks.[1] Alternate congurations included a grounded-grid carrier tube and a
grounded-cathode peak tube whereby the driver power
was eectively passed-through the carrier tube and was
added to the resulting output power, but this benet was
more appropriate for the earlier and less ecient triode
implementations[2] rather than the later and more ecient tetrode implementations.[3]

38.1 Successor developments

As successor to Western Electric Company Inc (WE) for
radio broadcast transmitters, the Martone concept was
considerably rened by Continental Electronics Manufacturing Company of Dallas, Texas (CE).

as in a Martone amplier. The unmodulated radio frequency carrier was applied to the control grids of both
tubes. Carrier modulation was applied to the screen grids
of both tubes but the screen grid bias points of the carrier and peak tubes were dierent and were established
such that the peak tube was cut o when modulation was
absent and the amplier was producing rated unmodulated carrier power and both tubes were conducting and
each tube was contributing twice the rated carrier power
during 100% modulation as four times the rated carrier
power is required to achieve 100% modulation. As both
tubes were operated in class C, a signicant improvement
in eciency was thereby achieved in the nal stage. In
addition, as the tetrode carrier and peak tubes required
very little drive power, a signicant improvement in efciency within the driver was achieved as well.[4] The
commercial version of the Sainton amplier employed a
cathode-follower modulator, not the push-pull modulator disclosed in the patent,[5] and the entire 50,000-watt
transmitter was implemented using only nine total tubes
of four tube types, all of these being general-purpose, a
remarkable achievement, given that the 317Cs most signicant competitor, RCAs BTA-50H, was implemented
using thirty-two total tubes of nine tube types, nearly onehalf of these being special-purpose, employed only in the
BTA-50H. Over 200 CE 317C transmitters were installed
in North America alone, easily outdistancing all competitors combined.

38.2 Footnotes

Early Continental Electronics designs, by James O. Weldon and others, retained most of the characteristics of
Martones amplier but added medium-level screen-grid
modulation of the driver (317B, et al.).
The ultimate renement was the high-level screen-grid
modulation scheme invented by Joseph B. Sainton.
Saintons 317C series consisted of a class C carrier tube in
parallel connection with a class C peak tube. The tubes
source (driver) and load (antenna) were split and combined through + and 90-degree phase-shifting networks
225

[1] In order to circumvent Western Electrics patent, RCA

utilized + 90 and + 270 degree phase shifts; as any student of phasor math knows, + 270 degrees is equivalent
to 90 degrees, therefore these are eectively the same
as + and 90 degree phase shifts (RCA BT-50D, et al.)
[2] WE 117, CE 317A, CE 317B, WAPE station-built, et al.
[3] CE 317C
[4] US patent 3314024, Joseph B. Sainton, High Eciency
Amplier and PushPull Modulator, issued 1967-04-11,
assigned to Continental Electronics Manufacturing Company

226

[5] The disclosed push-pull modulator consisted of a phasesplitter with unequal gains followed by a non-inverting
cathode-follower modulator (gain less than unity) from the
non-inverting side of the phase-splitter and an inverting
modulator (gain signicantly greater than unity) from the
inverting side of the phase-splitter. Therefore, the disclosed push-pull modulator wasn't push-pull at all. The
commercial version utilized a pair of tubes in parallel as a
cathode-follower modulator with, consequently, no need
to balance grossly dierent gains of the two modulator
tubes. However, a scheme to nely balance the two modulator tubes, which had the same nominal gain, was incorporated just the same.

38.3 References
Martone, W H (1936). A new high eciency
power amplier for modulated waves. Annual convention of the Institute of Radio Engineers.
The Martone Amplier: New After 70 Years. Microwave product digest. August 2007.

CHAPTER 38. DOHERTY AMPLIFIER

Chapter 39

AM stereo
AM stereo is a term given to a series of mutually incompatible techniques for radio broadcasting stereo audio in
the AM band in a manner that is compatible with standard AM receivers. There are two main classes of systems: independent sideband (ISB) systems, promoted
principally by American broadcast engineer Leonard R.
Kahn; and quadrature amplitude modulation (QAM)
multiplexing systems (conceptually closer to FM stereo).
Initially adopted by many commercial AM broadcasters
in the mid to late 1980s, AM stereo broadcasting soon began to decline due to a lack of receivers (most AM/FM
stereo radios only receive in stereo on FM), a growing
exodus of music broadcasters to FM, concentration of
ownership of the few remaining stations in the hands of
large corporations and the removal of music from AM
stations in favour of news/talk or sports broadcasting. By
2001, most of the former AM stereo broadcasters were
no longer stereo or had left the AM band entirely.

39.1 History
Early experiments with stereo AM radio involved two
separate stations (both AM or sometimes one AM and
one FM) broadcasting the left and right audio channels.
This system was not very practical, as it required the listener to use two separate receivers. Synchronization was
problematic, often resulting in ping-pong eects between the two channels. Reception was also likely to
be dierent between the two stations, and many listeners used mismatching models of receivers.
After the early experiments with two stations, a number
of systems were invented to broadcast a stereo signal in a
way which was compatible with standard AM receivers.
FM stereo was rst implemented in 1961. In the United
States, FM overtook AM as the dominant broadcast radio
band in the late 1970s and early 1980s.

39.1.1

Timeline

1924: WPAJ (now WDRC (AM)) broadcast in

stereo from New Haven, Connecticut, using two
transmitters: one on 1120 kHz and the other on
227

1320 kHz. However stereo separation was poor, to

preserve compatibility for mono listeners.[1]
In the 1950s, several AM stereo systems were proposed (including the original RCA AM/FM system
which later became the Belar system in the 1970s)
but the FCC did not propose any standard as AM
was still dominant over FM at the time.
1960: AM stereo rst demonstrated on XETRAAM, Tijuana, Mexico, using the Kahn independent
sideband system.
1963: WHAZ runs a stereo program on eight AM
stations, four on each channel.
1980: After ve years of testing the ve systems,
the United States Federal Communications Commission (FCC) selected the Magnavox system as the
ocial AM stereo standard. The FCCs research
is immediately accused of being awed and incomplete.
1982: After a series of lawsuits and accusations, the
FCC decides to let the marketplace decide and revokes the Magnavox certication as the AM stereo
standard for political reasons. Belar had dropped
out of the AM stereo race due to receiver distortion problems, leaving Motorola C-QUAM, Harris
Corporation, Magnavox, and the Kahn/Hazeltine
independent sideband system.
1984: General Motors, Ford, Chrysler, and a number of import automakers begin installing C-QUAM
AM stereo receivers in automobiles, beginning with
the 1985 model year. Harris Corporation abandons
its AM stereo system and puts its support behind CQUAM (Harris continues to manufacture C-QUAM
equipment today).
1985: AM stereo broadcasting ocially begins in
Australia, with the C-QUAM standard.
1988: Canada and Mexico adopt C-QUAM as their
standard for AM stereo.
1992: Japan adopts C-QUAM as its standard for
AM stereo.

228

CHAPTER 39. AM STEREO

1993: The FCC makes C-QUAM the AM stereo stereo. The Harris system is currently no longer used in
standard for stations in the U.S., and also grants its original form.
stereo preference for radio stations requesting to
move to the AM expanded band (16101700 kHz),
although such stations have never actually been re- 39.2.2 Magnavox System
quired to transmit in stereo.
This system was developed by electronics manufacturer,
1993: The AMAX certication program begins. Magnavox. It is a phase modulation system. It was iniThis was to set an ocial manufacturing standard tially declared the AM stereo standard by the FCC in
for high-quality AM radio receivers, with a wider 1980, but the FCC later declared that stations were free
audio bandwidth for higher delity reception of to choose any system. As with the Harris system, it was
strong signals, and optionally C-QUAM AM stereo. popular in the 1980s, but most stations stopped broadDespite the availability of AMAX receivers from casting in stereo, or downgraded to the C-QUAM system
companies like Sony, General Electric, Denon, and as time went on. 1190 WOWO in Fort Wayne, Indiana
AMAX-certied car radios from the domestic and was the (then) 50,000-watt clear channel Magnavox agJapanese automakers, most electronics manufac- ship station.
turers did not wish to implement the more costly
AMAX tuner design in their radios, so most AM
39.2.3 Motorola C-QUAM
radios today remain in mono with limited delity.
2006 to present: AM stereo gains new life through
the support for C-QUAM decoding in most receivers designed for HD Radio. These new digital
radios receive AM stereo signals, although the AM
transmitters are now limited to 10 kHz audio bandwidth and the HD receivers ip Left and Right channels in decoding C-QUAM stereo.

39.2 Broadcasting systems

C-QUAM was developed and promoted primarily by Motorola, a longtime manufacturer of two-way radio equipment. It became the dominant system by the late 1980s,
and was declared the ocial standard by the FCC in
1993. While many stations in the USA have since discontinued broadcasting in stereo, many still have the necessary equipment to do so. C-QUAM is still popular
in other parts of the world, such as Canada, Japan, and
Australia which it was declared the ocial standard.
QUAM uses quadrature phase and amplitude modulation: the phase of the audio is rotated ahead or behind the
carrier and the amplitude of each phase is also changed;
thus giving 16 points for reference (used also in dialup
modems to get past the 9,600 bit/s limit on analog lines).
The QUAM signal (left minus right, or L-R, information) is then phase modulated on the transmitter (the
QUAM exciter replaced the crystal in the AM transmitter) and the left plus right (or L+R) still modulated the
transmitter as it had in the past. C-QUAM is a modied QUAM and thus called compatible (the C-" in
C-QUAM).

The Magnavox PMX, Harris Corporation V-CPM, and

Motorola C-QUAM (CompatibleQuadrature Amplitude Modulation) were all based around modulating the
phase and amplitude of the carrier, placing the stereo information in the phase modulated portion, while the standard mono (L+R) information is in the amplitude modulation. The systems all did this in similar (but not completely compatible) ways. The original Harris Corporation system was later changed to match the Motorola CQUAM pilot tone for indicating the station was in stereo,
thus making it compatible with all C-QUAM receivers.
C-QUAM had been long criticized by the Kahn-Hazeltine
systems creator, Leonard Kahn as being inferior to his
system. First generation C-QUAM receivers suered
39.2.1 Harris System
from platform motion eects when listening to stations
received via skywave. Later improvements by Motorola
This system, known as V-CPM for Variable Angle Com- minimized the platform motion eect and increased aupatible Phase Multiplex, was developed by Harris Corpo- dio quality and stereo separation, especially on AMAXration, a major manufacturer of radio/TV transmitters. It certied receivers in the 1990s.
incorporated a left minus right component which was frequency modulated by about 1 kHz. Harris is the successor to the pioneer Gates radio line, which has changed its 39.2.4 Kahn-Hazeltine
name in 2014 to Gates-Air. The Harris system eventually
changed their pilot tone to be compatible with C-QUAM, The Kahn-Hazeltine system also called ISB was develafter C-QUAM became the more popular and eventu- oped by American engineer Leonard R. Kahn and the
ally, the FCC approved standard. CKLW in Windsor, Hazeltine Corporation. This system used an entirely difOntario, Canada (also serving nearby Detroit, Michigan) ferent principleusing independently modulated upper
was among the rst stations to broadcast in Harris AM and lower sidebands. While a station using the system

39.3. ADOPTION IN THE UNITED STATES

would sound best with proper decoding, it was also possible to use two standard AM radios (one tuned above
and the other below the primary carrier) to achieve the
stereophonic eect, although with poor stereo separation
and delity compared to a proper Kahn system AM stereo
receiver. One of the best known stations to use the Kahn
system was 890/WLS, Chicago. WLS still transmits in
AM stereo today but uses the Motorola C-QUAM system instead.
However, the Kahn system suered from lower stereo
separation above 5 kHz (reaching none at 7 kHz whereas
FM stereo has 40 dB or more separation at 15 kHz) and
the radio antenna array on directional AM (common on
a lot of nighttime and some daytime stations) had to have
a at response across the entire 20 kHz AM channel. If
the array had a higher reactance value (leading to a higher
Standing wave ratio) on one side of the frequency vs the
other, it would aect the audio response of that channel
and thus the stereo signal would be aected. Also, Kahn
refused to license any radio receivers manufacturers with
his design, although multi-system receivers were manufactured by various companies such as Sony, Sansui, and
Sanyo, which could receive any of the four AM stereo
systems.
Nonetheless, this system remained competitive with CQUAM into the late 1980s and Kahn was very vocal about
its advantages over Motorolas system. Kahn led a lawsuit claiming that the Motorola system did not meet FCC
emission bandwidth specications, but by that time, CQUAM had already been declared as the single standard
for AM stereo in the USA.
Kahns AM stereo design was later revamped for monaural use and used in the Power-Side system, in which a
decreased signal in one sideband is used to improve coverage and loudness, especially with directional antenna
arrays. Power-Side became the basis for CAM-D, Compatible AM Digital, a new digital system being promoted
by Leonard Kahn and used on several AM stations.
Kahn receiver chips have also been used as an inexpensive method for providing high frequency (world band)
receivers with synchronous detection technology.

39.2.5

Belar System

229
company of the same name) was dropped due to issues
with its design though it was much easier to implement
than the other systems. It and the Kahn system did not
suer from platform motion (which was a killer for AM
stereo at night; platform motion is where the stereo balance would shift from one side to the other and then back
to center) but the use of low level frequency modulation
did not permit a high separation of L and R channels.

39.3 Adoption in the United States

In 1975, the Federal Communications Commission
(FCC) started a series of ve-year tests to determine
which of the ve competing standards would be selected. By the end of the testing period, the Belar system was dropped. In 1980, the FCC announced that the
Magnavox system would become the standard. This announcement was met with harsh criticism and a series
of lawsuits. On March 4, 1982, the FCC revoked their
endorsement to the Magnavox standard and let the marketplace decide, meaning that all four standards were allowed. After the 1982 decision, many stations implemented one of the four standards. Initially, all systems
remained competitive, but by the later 1980s, Motorola
C-QUAM had a clear majority of stations and receivers.
Around this same time, Harris Corporation dropped their
system and instead endorsed C-QUAM. During this time,
radio manufactures either made receivers which decoded
just one system, or decoded all four. The multiple systems used greatly confused consumers and severely impacted consumer adoption. As a result of this confusion,
and the continued growth of the FM band, interest in AM
stereo dwindled.
In 1993, the FCC declared Motorolas C-QUAM system the standard. To ensure that all AM stereo receivers
maintained the same sound quality, the National Association of Broadcasters and the Electronic Industries Association started the AMAX certication program.

39.4 Global adoption

In the early 1980s, other countries, most notably Canada,

Australia and Japan approved and implemented AM
The Belar system was used in limited number of stations, stereo systems. Most governments approved a single
such as WJR. The Belar system, originally designed by standard, usually Motorolas C-QUAM, which greatly reRCA in the 1950s, was a simple FM/AM modulation duced confusion and increased user adoption.
system,[2] with an attenuated L-R signal frequency modulating the carrier (with a 400 s pre-emphasis) in the Following the launch of the American-owned, ship-based
extent of +/- 320 Hz around the center frequency, and pirate radio station Laser 558 o the British coast, there
the L+R doing the normal high level AM modulation were announcements that another such station, provision(usually referred to as plate modulation in transmitters ally called Stereo Hits 576, would soon follow, using AM
using a tube in the nal stage, where the audio is applied stereo on an adjacent frequency to Laser. Nothing ever
to the plate voltage of the tube; in solid state transmitters, came of this project and 576 kHz was adopted by Radio
various dierent techniques are available that are more Caroline instead.
ecient at lower power levels). The Belar system (by the In many countries, especially those where the AM band

230
is still dominant, AM stereo radios are still manufactured
and stations still broadcast stereo signals.

39.5 Current status

Globally, interest in and use of AM stereo has been declining steadily since the 1990s, as many music stations
have continued to move to the FM band. As a result,
the vast majority of AM stations broadcast news/talk or
sports/sports talk formats. Many of the stations that initially implemented AM stereo are clear-channel 50,000watt stations, and are more concerned with listening range
than stereo sound (although there is no proof that use of
AM stereo aects listening range). As a result, these stations still have the necessary equipment to broadcast in
stereo, but it is left unused (or converted to HD Radio).
Also, many former AM stereo stations were bought up by
broadcasting conglomerates, which generally discourage
AM stereo broadcasting. In the United States, most stations currently using AM stereo are small, independently
owned and broadcast a variety or music format.
United States: AM Stereo radio stations in the
United States
Japan: Between 1992 and 1996, 16 commercial
broadcasting companies in Japan adopted C-QUAM
because of the narrow Japanese FM band; it covers only 14 MHz (76-90 MHz), as opposed to the
20.5 MHz used in the rest of the world (87.5-108
MHz). However, it is now quite rare to see AM radios with the stereo function at appliance stores in
Japan because of the decline in AM stereo stations
and the limited available area, mainly in densely
populated areas. 13 of the 16 stereo stations have
since reverted to mono, 11 since the start of 2010
(ja:AM
), leaving only 3 stations broadcasting in stereo.
Australia: AM stereo was popular in Australia because AM covers a wide geographic area compared
to FM, in addition to the governments adoption
of a single standard (Motorola C-QUAM) several
years sooner than the USA, and Australias relatively late adoption of FM (the frequencies in the
FM band were originally allocated for TV). As of
June 2008 no Melbourne AM stations broadcast CQUAM AM stereo. At its peak popularity in the late
1980s the majority of stations did.
Europe: After some experiments in the 1980s,
AM stereo was deemed to be unsuitable for the
crowded band conditions and narrow bandwidths associated with AM broadcasting in Europe. However, Motorola C-QUAM AM stereo remains in use
today on a handful of stations in Italy and Greece.
Canada: AM stereo was more widely adopted in
Canada than in the USA. This may have been due

CHAPTER 39. AM STEREO

to the Canadian governments decision to use a single standard, and the Canadian Radio-television and
Telecommunications Commission (CRTC) licensing stations by format and their hit/non-hit rules for
FM (hence, more music stations on AM). However,
unlike in the USA, some former AM stereo stations
have moved to the FM band and left the AM band
altogether instead of simply reverting to mono.

39.6 Surround sound

On February 26, 2010, KCJJ (AM 1630) in Coralville,
Iowa, aired a four-hour quadraphonic radio broadcast of
the Robb Spewak show. The show spotlighted music
from the quadraphonic era on the 40th anniversary of
the formats release in America and was engineered by
Tab Patterson. All the music was from discrete 4-channel
tapes, then encoded into Dolby Pro-Logic II and transmitted using their stereo C-QUAM transmitter.

39.7 Decline in use

Radio stations around the world are converting to various systems of digital radio, such as Digital Radio Mondiale, DAB or HD Radio (in the United States). Some
of these digital radio systems, most notably HD Radio
have hybrid modes which let a station broadcast a standard AM signal along with the digital information. While
these transmission modes allow standard AM, they are
not compatible with any AM stereo system (meaning both
cannot be broadcast at the same time).
Digital AM broadcasting systems, such as HD Radio have
been criticized by supporters of AM stereo as sounding
harsh and articial, but supporters of Digital systems
argue that the extended frequency response, increased dynamic range, lack of noise and lower distortion make up
for the compression artifacts. However, HD Radio also
increases adjacent channel noise due to the digital sidebands, which pose serious problems for nighttime broadcasts. Some have proposed to use HD Radio in the daytime and AM stereo at night. Many HD radios are based
on a common chipset that decodes C-QUAM.

39.8 References
[1] Mehrab, Gerald J. (2008-02-01).
AM Stereo.
WA2FNQ web site. Northport, New York. Retrieved
2010-09-26.
[2] AM Stereo articles from Radio-Electronics Dec77,
Popular-Electronics Dec78, and Popular-Electronics
Aug80

39.9. EXTERNAL LINKS

39.9 External links

France Bleu (French)
AM stereo tuner source
An A.M. Stereo enthusiasts website
Another AM stereo enthusiasts website
AM Stereo Audio Soundbites over the air
Technical data on AM HD/IBOC
Amateur experiments with AM stereo

231

Chapter 40

Shortwave radio
For other uses, see Shortwave (disambiguation).
medium wave band, which ends approximately at 1.6
Shortwave radio is radio transmission using shortwave MHz.
There are also other denitions of the shortwave frequency interval:
1.71 to 30 MHz in ITU Region 2 (North and South
America...)
1.8 (160 meter radio amateur band start) to 30 MHz
2.3 (120 meter band start) to 30 MHz
2.3 (120 meter band start) to 26.1 MHz (11 meter
band end)[1][2]
In Germany and perhaps Austria the ITU Region 1
shortwave frequency interval can be subdivided in:

A solid-state, digital shortwave receiver

frequencies, generally 1.630 MHz (187.410.0 m), just

above the medium wave AM broadcast band.
Radio waves in this band can be reected or refracted
from a layer of electrically charged atoms in the atmosphere called the ionosphere. Therefore short waves directed at an angle into the sky can be reected back
to Earth at great distances, beyond the horizon. This
is called skywave or skip propagation. Thus shortwave
radio can be used for very long distance communication, in contrast to radio waves of higher frequency which
travel in straight lines (line-of-sight propagation) and are
limited by the visual horizon, about 40 miles. Shortwave radio is used for broadcasting of voice and music
to shortwave listeners over very large areas; sometimes
entire continents or beyond. It is also used for military
over-the-horizon radar, diplomatic communication, and
two-way international communication by amateur radio
enthusiasts for hobby, educational and emergency purposes.

de:Grenzwelle (border waves): 1.605-3.8

MHz and de:Kurzwelle (shortwaves) 3.8-30
MHz[3]
Grenzwelle: 1.605-4 MHz and Kurzwelle
(shortwaves) 4-30 MHz
In Germany these shortwave frequency intervals
have also been seen used:
3-30 MHz[4][5] e.g. some accept that high
frequency is the same as short wave. In
reality, the denition of the shortwave frequency band is a mess, and therefore the
shortwave frequencies can not be exactly
equal high frequencies.
the above other denitions[6]

Shortwave radio received its name because the

wavelengths in this band are shorter than 200 m
(1500 kHz) which marked the original upper limit of the
40.1 Frequency classications
medium frequency band rst used for radio communications. The broadcast medium wave band now extends
The widest popular denition of the shortwave frequency above the 200 m/1500 kHz limit, and the amateur radio
interval is the ITU Region 1 (EU+Africa+Russia...) def- 1.8 MHz 2.0 MHz band (known as the "top band") is
inition, and is the span 1.630 MHz, just above the the lowest-frequency band considered to be 'shortwave'.
232

40.2. HISTORY

40.2 History
40.2.1

Development

233
wireless services to shortwave and the overall volume of
transoceanic shortwave communications had vastly increased. Shortwave also ended the need for multimilliondollar investments in new transoceanic telegraph cables
and massive longwave wireless stations, although some
existing transoceanic telegraph cables and commercial
longwave communications stations remained in use until the 1960s.

The cable companies began to lose large sums of money

in 1927, and a serious nancial crisis threatened the viability of cable companies that were vital to strategic
British interests. The British government convened the
Imperial Wireless and Cable Conference[12] in 1928 to
examine the situation that had arisen as a result of the
competition of Beam Wireless with the Cable Services.
It recommended and received Government approval for
all overseas cable and wireless resources of the Empire to
Radio Amateurs carried out the rst shortwave transmissions be merged into one system controlled by a newly formed
over a long distance before Guglielmo Marconi.
company in 1929, Imperial and International Communications Ltd. The name of the company was changed to
Early radio telegraphy had used long wave transmissions. Cable and Wireless Ltd. in 1934.
The drawbacks to this system included a very limited
spectrum available for long distance communication, and
the very expensive transmitters, receivers and gigantic an- 40.2.2 Amateur use of shortwave propagatennas that were required. It was also dicult to beam
tion
the radio wave directionally with long wave, resulting in
a major loss of power over long distances. Prior to the Amateur radio operators also discovered that long1920s, the shortwave frequencies above 1.5 MHz were distance communication was possible on shortwave
regarded as useless for long distance communication and bands. Early long-distance services used surface wave
were designated in many countries for amateur use.[7]
propagation at very low frequencies,[13] which are attenGuglielmo Marconi, pioneer of radio, commissioned his
assistant Charles Samuel Franklin to carry out a large
scale study into the transmission characteristics of short
wavelength waves and to determine their suitability for
long distance transmissions. Franklin rigged up a large
antenna at Poldhu Wireless Station, Cornwall, running on
25 kW of power. In June and July 1923, wireless transmissions were completed during nights on 97 meters from
Poldhu to Marconis yacht Elettra in the Cape Verde Islands.[8]

uated along the path. Longer distances and higher frequencies using this method meant more signal attenuation. This, and the diculties of generating and detecting
higher frequencies, made discovery of shortwave propagation dicult for commercial services.
Radio amateurs may have conducted the rst successful
transatlantic tests[14] in December 1921, operating in the
200 meter mediumwave band (1500 kHz)the shortest
wavelength then available to amateurs. In 1922 hundreds
of North American amateurs were heard in Europe at 200
meters and at least 20 North American amateurs heard
amateur signals from Europe. The rst two-way communications between North American and Hawaiian amateurs began in 1922 at 200 meters. Although operation on
wavelengths shorter than 200 meters was technically illegal (but tolerated as the authorities mistakenly believed at
rst that such frequencies were useless for commercial or
military use), amateurs began to experiment with those
wavelengths using newly available vacuum tubes shortly
after World War I.

In September 1924, Marconi transmitted daytime and

nighttime on 32 meters from Poldhu to his yacht in Beirut.
Franklin went on to rene the directional transmission,
by inventing the curtain array aerial system.[9][10] In July
1924, Marconi entered into contracts with the British
General Post Oce (GPO) to install high speed shortwave telegraphy circuits from London to Australia, India, South Africa and Canada as the main element of the
Imperial Wireless Chain. The UK-to-Canada shortwave
Beam Wireless Service went into commercial operation
on 25 October 1926. Beam Wireless Services from the Extreme interference at the upper edge of the 150UK to Australia, South Africa and India went into service 200 meter bandthe ocial wavelengths allocated to
in 1927.[8]
amateurs by the Second National Radio Conference[15]
Shortwave communications began to grow rapidly in the in 1923forced amateurs to shift to shorter and shorter
1920s,[11] similar to the internet in the late 20th century. wavelengths; however, amateurs were limited by reguBy 1928, more than half of long distance communica- lation to wavelengths longer than 150 meters (2 MHz).
tions had moved from transoceanic cables and longwave A few fortunate amateurs who obtained special permis-

234

CHAPTER 40. SHORTWAVE RADIO

sion for experimental communications below 150 meters

completed hundreds of long distance two way contacts on
100 meters (3 MHz) in 1923 including the rst transatlantic two way contacts.[16]

Season. During the winter months of the Northern

or Southern hemispheres, the AM/MW broadcast
band tends to be more favorable because of longer
hours of darkness.

By 1924 many additional specially licensed amateurs

were routinely making transoceanic contacts at distances
of 6,000 miles (~9,600 km) and more. On 21 September several amateurs in California completed two way
contacts with an amateur in New Zealand. On 19 October amateurs in New Zealand and England completed
a 90-minute two-way contact nearly halfway around the
world. On October 10, the Third National Radio Conference made three shortwave bands available to U.S.
amateurs[17] at 80 meters (3.75 MHz), 40 meters (7
MHz) and 20 meters (14 MHz). These were allocated worldwide, while the 10-meter band (28 MHz) was
created by the Washington International Radiotelegraph
Conference[18] on 25 November 1927. The 15-meter
band (21 MHz) was opened to amateurs in the United
States on 1 May 1952.

Solar ares produce a large increase in D region ionization so high, sometimes for periods of several
minutes, all skywave propagation is nonexistent.

40.3 Propagation characteristics

Shortwave radio frequency energy is capable of reaching
any location on the Earth as it is inuenced by ionospheric
reection back to the earth by the ionosphere, (a phenomenon known as "skywave propagation). A typical
phenomenon of shortwave propagation is the occurrence
of a skip zone (see rst gure on that page) where reception fails. With a xed working frequency, large changes
in ionospheric conditions may create skip zones at night.

40.4 Types of modulation

Further information: Modulation
Several dierent types of modulation are used to impress
information on a short-wave transmission.
Amplitude modulation is the simplest type and the most
commonly used for shortwave broadcasting. The instantaneous amplitude of the carrier is controlled by the amplitude of the signal (speech, or music, for example). At
the receiver, a simple detector recovers the desired modulation signal from the carrier.
Single sideband transmission is a form of amplitude modulation but in eect lters the result of modulation. An
amplitude-modulated signal has frequency components
both above and below the carrier frequency. If one set
of these components is eliminated as well as the residual carrier, only the remaining set is transmitted. This
saves power in the transmission, as roughly 2/3 of the energy sent by an AM signal is unnecessary to recover the
information contained on it. It also saves bandwidth, allowing about one-half the carrier frequency spacing to be
used. The drawback is that the receiver is more complicated, since it must re-recreate the carrier to recover the
signal. Small errors in the detector process can greatly affect the pitch of the received signal, so single side band is
not usual for music or general broadcast. Single side band
is used for long-range voice communications by ships
and aircraft, Citizens Band, and amateur radio operators.
LSB (lower sideband) is generally used below 9 MHz and
USB (upper sideband) above 9 MHz.

As a result of the multi-layer structure of the ionosphere, propagation often simultaneously occurs on different paths, scattered by the E or F region and with
dierent numbers of hops, a phenomenon that may be
disturbed for certain techniques. Particularly for lower
frequencies of the shortwave band, absorption of radio
frequency energy in the lowest ionospheric layer, the D
layer, may impose a serious limit. This is due to collisions of electrons with neutral molecules, absorbing some
of a radio frequency's energy and converting it to heat.[19] Vestigal sideband transmits the carrier and one complete
Predictions of skywave propagation depend on:
side-band, but lters out the redundant side-band. It is a
compromise between AM and SSB, allowing simple re The distance from the transmitter to the target re- ceivers to be used but requiring almost as much transmitter power as AM. One advantage is that only half the
ceiver.
bandwidth of an AM signal is used. It can be heard in the
Time of day. During the day, frequencies higher transmission of certain radio time signal stations.
than approximately 12 MHz can travel longer dis- Continuous wave (CW) is on-and-o keying of a carrier,
tances than lower ones. At night, this property is used only for Morse code communications.
reversed.
Narrow-band frequency modulation (NBFM) is mainly
With lower frequencies the dependence on the time used in the higher HF frequencies (typically above 20
of the day is mainly due to the lowest ionospheric MHz). Because of the larger bandwidth required, NBFM
layer, the D Layer, forming only during the day is much more commonly used for VHF communication.
when photons from the sun break up atoms into ions Regulations limit the bandwidth of a signal transmitted
in the HF bands, and the advantages of frequency modand free electrons.

40.6. SHORTWAVE BROADCASTING

ulation are greatest if the FM signal is allowed to have a
wider bandwidth. NBFM is limited to short-range SW
transmissions due to the multiphasic distortions created
by the ionosphere.[20]
Digital Radio Mondiale (DRM) is a digital modulation for
use on bands below 30 MHz.
Radioteletype, fax, digital, slow-scan television and other
systems use forms of frequency-shift keying or audio subcarriers on a shortwave carrier. These generally require
special equipment to decode, such as software on a computer equipped with a sound card.

40.5 Uses
Some major uses of the shortwave radio band are:
International broadcasting primarily by governmentsponsored propaganda, international news (for example, the BBC World Service) or cultural stations
to foreign audiences: the most common use of all.
Domestic broadcasting: to widely dispersed populations with few longwave, mediumwave and FM
stations serving them; or for specialty political, religious and alternative media networks; or of individual commercial and non-commercial paid broadcasts.
Oceanic air trac control uses the HF/shortwave
band for long distance communication to aircraft
over the oceans and poles, which are far beyond the
range of traditional VHF frequencies. Modern systems also include satellite communications, such as
ADS-C/CPDLC

235
Numbers Stations are operated by government agencies, and are used to communicate with clandestine
operatives working within foreign countries. However, no denitive proof of such use has emerged.
Because the vast majority of these broadcasts contain nothing but the recitation of blocks of numbers,
in various languages, with occasional bursts of music, they have become known colloquially as Number Stations. Perhaps the most noted Number Station is the Lincolnshire Poacher, named after the
18th century English folk song, which is transmitted
just before the sequences of numbers.
Amateur radio operators at the 80/75, 60, 40, 30,
20, 17, 15, 12, and 10-meter bands.
Time signal and radio clock stations: In North
America, WWV radio and WWVH radio transmit
at these frequencies: 2.5 MHz, 5 MHz, 10 MHz, and
15 MHz; and WWV also transmits on 20 & 25 MHz.
The CHU radio station in Canada transmits on the
following frequencies: 3.33 MHz, 7.85 MHz, and
14.67 MHz. Other similar radio clock stations transmit on various shortwave and longwave frequencies
around the world. The shortwave transmissions are
primarily intended for human reception, while the
longwave stations are generally used for automatic
synchronization of watches and clocks.
Over-the-horizon radar: From 1976 to 1989,
the Soviet Union's Russian Woodpecker over-thehorizon radar system blotted out numerous shortwave broadcasts daily.

The term DXing, in the context of listening to radio signals of any user of the shortwave band, is the activity of
monitoring distant stations. In the context of amateur radio operators, the term DXing refers to the two-way
communications with a distant station, using shortwave
Utility stations transmitting messages not intended
radio frequencies.
for the general public, such as aircraft ying between
continents, encrypted diplomatic messages, weather The Asia-Pacic Telecommunity estimates that there are
approximately 600,000,000 shortwave broadcast-radio
reporting, or ships at sea.
receivers in use in 2002.[21] WWCR claims that there are
Clandestine stations. These are stations that broad- 1.5 billion shortwave receivers worldwide.[22]
cast on behalf of various political movements, including rebel or insurrectionist forces, and are normally unauthorised by the government-in-charge of 40.6 Shortwave broadcasting
the country in question. Clandestine broadcasts
may emanate from transmitters located in rebelcontrolled territory or from outside the country en- See International broadcasting for details on the history
tirely, using another countrys transmission facili- and practice of broadcasting to foreign audiences.
ties. Clandestine stations were used during World See Shortwave relay station for the actual kinds of inteWar II to transmit news from the Allied point of grated technologies used to bring high power signals to lisview into Axis-controlled areas. Although the Nazis teners.
conscated many radios and executed their owners,
many people continued to listen.

40.6.1 Frequency allocations

Numbers Stations These stations regularly appear

and disappear all over the shortwave radio band but Main article: Shortwave bands
are unlicensed and untraceable. It is believed that

236

CHAPTER 40. SHORTWAVE RADIO

The World Radiocommunication Conference (WRC),

organized under the auspices of the International
Telecommunication Union, allocates bands for various
services in conferences every few years. The last WRC
took place in 2007.
At WRC-97 in 1997, the following bands were allocated
for international broadcasting. AM shortwave broadcasting channels are allocated with a 5 kHz separation for
traditional analog audio broadcasting.
Although countries generally follow the table above,
there may be small dierences between countries or regions. For example, in the ocial bandplan of the
Netherlands,[23] the 49 m band starts at 5.95 MHz, the
41 m band ends at 7.45 MHz, the 11 m band starts at
25.67 MHz, and the 120, 90 and 60 m bands are absent altogether. Additionally, international broadcasters sometimes operate outside the normal WRC-allocated bands
or use o-channel frequencies. This is done for practical
reasons, or to attract attention in crowded bands (60m,
49m, 40m, 41m, 31m, 25m).
The new digital audio broadcasting format for shortwave
DRM operates 10 kHz or 20 kHz channels. There are
some ongoing discussions with respect to specic band
allocation for DRM, as it mainly transmitted in 10 kHz
format.
The power used by shortwave transmitters ranges from
less than one watt for some experimental and amateur radio transmissions to 500 kilowatts and higher
for intercontinental broadcasters and over-the-horizon
radar. Shortwave transmitting centers often use specialized antenna designs (like the ALLISS antenna technology) to concentrate radio energy at the target area.

40.6.2

Advantages

Shortwave does possess a number of advantages over

newer technologies, including the following:

continues to be widespread[25] (in many of these

countries some domestic stations also used shortwave).
Many newer shortwave receivers are portable and
can be battery-operated, making them useful in difcult circumstances. Newer technology includes
hand-cranked radios which provide power without
batteries.
Shortwave radios can be used in situations where
Internet or satellite communications service is temporarily or long-term unavailable (or unaordable).
Shortwave radio travels much farther than broadcast
FM (88-108 MHz). Shortwave broadcasts can be
easily transmitted over a distance of several thousands of kilometers, including from one continent
to another.
Particularly in tropical regions, SW is somewhat
less prone to interference from thunderstorms than
medium wave radio, and is able to cover a large geographic area with relatively low power (and hence
cost). Therefore, in many of these countries it is
widely used for domestic broadcasting.
Very little infrastructure is required for longdistance two-way communications using shortwave
radio. All one needs is a pair of transceivers, each
with an antenna, and a source of energy (such as a
battery, a portable generator, or the electrical grid).
This makes shortwave radio one of the most robust
means of communications, which can be disrupted
only by interference or bad ionospheric conditions.
Modern digital transmission modes such as MFSK
and Olivia are even more robust, allowing successful
reception of signals well below the noise oor of a
conventional receiver.

Diculty of censoring programming by authorities

in restrictive countries: unlike their relative ease 40.6.3 Disadvantages
in monitoring the Internet, government authorities
face technical diculties monitoring which stations Shortwave radios benets are sometimes regarded as be(sites) are being listened to (accessed). For example, ing outweighed by its drawbacks, including:
during the Russian coup against President Mikhail
Gorbachev, when his access to communications was
In most Western countries, shortwave radio ownerlimited, Gorbachev was able to stay informed by
ship is usually limited to true enthusiasts, since most
[24]
means of the BBC World Service on shortwave.
new standard radios do not receive the shortwave
band. Therefore, Western audiences are limited.
Low-cost shortwave radios are widely available in
all but the most repressive countries in the world.
Simple shortwave regenerative receivers can be easily built with a few parts.
In many countries (particularly in most developing
nations and in the Eastern bloc during the Cold War
era) ownership of shortwave receivers has been and

In the developed world, shortwave reception is very

dicult in urban areas because of excessive noise
from switched-mode power adapters, uorescent or
LED light sources, internet modems and routers,
computers and many other sources of radio interference.

40.8. AMATEUR RADIO

237
wave radio. Many international broadcasters (such as Radio Canada International , the BBC and Radio Australia)
oer live streaming audio on their websites. Shortwave
listeners, or SWLs, can obtain QSL cards from broadcasters, utility stations or amateur radio operators as trophies of the hobby. Some stations even give out special
certicates, pennants, stickers and other tokens and promotional materials to shortwave listeners.

40.8 Amateur radio

Main article: Amateur radio
The practice of operating a shortwave radio transmitter
for non-commercial two-way communications is known
as amateur radio. Licenses are granted by authorized government agencies.

A pennant sent to overseas listeners by Radio Budapest in the late

1980s

Amateur radio operators have made many technical advancements in the eld of radio, and make themselves
available to transmit emergency communications when
normal communications channels fail. Some amateurs
practice operating o the power grid so as to be prepared
for power loss. Many amateur radio operators started out
as Shortwave Listeners (SWLs) and actively encourage
SWLs to become amateur radio operators.

40.7 Shortwave listening

Main article: Shortwave listening
Many hobbyists listen to shortwave broadcasters without
operating their own transmitters. In some cases, the goal
is to hear as many stations from as many countries as possible (DXing); others listen to specialized shortwave utility, or ute, transmissions such as maritime, naval, aviation, or military signals. Others focus on intelligence
signals from numbers stations, stations which transmit
strange broadcast usually for intelligence operations, or
the two way communications by amateur radio operators.
Some short wave listeners behave analogously to lurkers on the Internet, in that they listen only and never
make any attempt to send out their own signals. Other
listeners participate in clubs, or actively send and receive
QSL cards, or become involved with amateur radio and
start transmitting on their own.
Many listeners tune the shortwave bands for the programmes of stations broadcasting to a general audience (such as Radio Taiwan International, Voice of Russia, China Radio International, Radio Canada International, Voice of America, Radio France Internationale,
BBC World Service, Radio Australia, Radio Netherlands, Voice of Korea, Radio Free Sarawak etc.). Today,
through the evolution of the Internet, the hobbyist can listen to shortwave signals via remotely controlled shortwave
receivers around the world, even without owning a short-

40.9 Utility stations

Main article: Utility station
Utility stations are stations that do not intentionally broadcast to the general public (although their signals can be
received by anybody with appropriate equipment). There
are shortwave bands allocated to the use of merchant
shipping, marine weather, and ship-to-shore stations; for
aviation weather and air-to-ground communications; for
military communications; for long-distance governmental purposes, and for other non-broadcast communications. Many radio hobbyists specialize in listening to
ute broadcasts, which often originate from geographic
locations without known shortwave broadcasters.

40.10 Unusual signals

The short wave bands are also used by unlicensed individuals who may want mostly short-range party line like
communications. Two examples are the use of HF for
communication between shing boats in many areas of
the world, and the unlicensed use of the 11-meter band,
which is eectively permitted in some areas of the world.
Unlicensed operators, called pirates, can cause signal
interference to licensed stations. Many third-world coun-

238
tries have shops selling HF transmitter radios to any customer without regard to license or operator knowledge.
As of 2012, there were virtually no national or international eorts to control such pirate operations.

CHAPTER 40. SHORTWAVE RADIO

Hymnen (196667), Kurzwellen (1968)adapted for the
Beethoven Bicentennial in Opus 1970 with ltered and
distorted snippets of Beethoven piecesSpiral (1968),
Pole, Expo (both 196970), and Michaelion (1997).

The short wave bands are also used for various experiments, some continuing for years. In 2011, signals traceable to China regularly sent powerful HF transmissions
scanning wide ranges of HF frequencies, perhaps to determine the maximum usable frequency (MUF) or other
variables.

Holger Czukay, a student of Stockhausen, was one of the

rst to use shortwave in a rock music context. In 1975,
German electronic music band Kraftwerk recorded a full
length concept album around simulated radiowave and
shortwave sounds, entitled Radio-Activity. Among others, The The whose Radio Cineola monthly broadcasts
[26]
The B-52s,
Numbers stations are broadcasts on shortwave radio that draw heavily on shortwave radio sound,
Shearwater,
Tom
Robinson,
Peter
Gabriel,
Pukka Orare coded into groups of numbers. Their content is genAMM,
John
Duncan,
Orchestral
Manoeuvres
in
chestra,
erally encrypted and their purpose remains a mystery.
the Dark (on their Dazzle Ships album), Pat Metheny,
Aphex Twin, Boards of Canada, PressureWorks, Rush,
Able Tasmans, Team Sleep, Underworld, Meat Beat
40.11 Shortwave broadcasts and Manifesto, Tim Hecker, Jonny Greenwood of Radiohead,
Roger Waters (on Radio KAOS album), Wilco, code 000
music
and Samuel Trim have also used or been inspired by
shortwave broadcasts.
Some musicians have been attracted to the unique aural
characteristics of shortwave radio whichdue to the nature of amplitude modulation, varying propagation conditions, and the presence of interferencegenerally has
lower delity than local broadcasts (particularly via FM
stations). Shortwave transmissions often have bursts of
distortion, and hollow sounding loss of clarity at cer40.12 Shortwaves future
tain aural frequencies, altering the harmonics of natural
sound and creating at times a strange spacey quality
due to echoes and phase distortion. Evocations of shortwave reception distortions have been incorporated into Further information: The future of shortwave listening
rock and classical compositions, by means of delays or
feedback loops, equalizers, or even playing shortwave ra- The development of direct broadcasts from satellites has
dios as live instruments. Snippets of broadcasts have been reduced the demand for shortwave receiver hardware, but
mixed into electronic sound collages and live musical in- there are still a great number of shortwave broadcasters.
struments, by means of analogue tape loops or digital A new digital radio technology, Digital Radio Mondiale
samples. Sometimes the sounds of instruments and exist- (DRM), is expected to improve the quality of shortwave
ing musical recordings are altered by remixing or equal- audio from very poor to standards comparable to the FM
izing, with various distortions added, to replicate the gar- broadcast band. The future of shortwave radio is threatbled eects of shortwave radio reception.
ened by the rise of power line communication (PLC), also
The rst attempts by serious composers to incorporate known as Broadband over Power Lines (BPL), which uses
radio eects into music may be those of the Russian a data stream transmitted over unshielded power lines. As
physicist and musician Lon Theremin, who perfected a the BPL frequencies used overlap with shortwave bands,
form of radio oscillator as a musical instrument in 1928 severe distortions can make listening to analog short(regenerative circuits in radios of the time were prone to wave radio signals near power lines dicult or impossibreaking into oscillation, adding various tonal harmonics ble. However, because shortwave is a cheap and eective
to music and speech); and in the same year, the develop- way to receive communications in countries with poor inment of a French instrument called the Ondes Martenot frastructure, it will be around for years to come.
by its inventor Maurice Martenot, a French cellist and former wireless telegrapher. A notable chamber piece by
Mexican composer Silvestre RevueltasOcho x radio,
1933features a complex texture of pseudo-mariachi
musics, overlapping and cross-fading as if heard from distant stations: quite similar to shortwave radio signal propagation disturbance. John Cage used actual radios (of unspecied wavelength) live on several occasions, starting
in 1942 with Credo in Us, while Karlheinz Stockhausen
used shortwave radio and eects in works including

Shortwave use by hobbyists and licensed amateur ham radio operators continues, and after declining interest for a
few years due to competing interests in computers and
other communication devices, a new resurgence of interest has occurred as evidenced by the increase of new amateur operator licenses issued worldwide. Some hobbyists have combined amateur radio HF with computers for
experimental and established data modes that can communicate very close to under the noise oor of receivers
- e.g. WSJT, WSPR.

40.14. REFERENCES

40.13 See also

ALLISS a very large rotatable antenna system
used in international broadcasting
Amateur radio also uses the shortwave bands, but
with power levels under 2 kW
International broadcasting

239

[8] John Bray (2002). Innovation and the Communications

Revolution: From the Victorian Pioneers to Broadband Internet. IET. pp. 7375.
[9] Beauchamp, K. G. (2001). History of Telegraphy. IET. p.
234. ISBN 0-85296-792-6. Retrieved 2007-11-23.
[10] Burns, R. W. (1986). British Television: The Formative
Years. IET. p. 315. ISBN 0-86341-079-0. Retrieved
2007-11-23.

List of American shortwave broadcasters

List of shortwave radio broadcasters
Long wave

[11] Full text of Beyond the ionosphere : fty years of satellite communication"". Archive.org. Retrieved 2012-0831.

Medium wave

[12] Cable and Wireless Plc History

Shortwave bands shortwave spectrum allocation

[13] Stormfax. Marconi Wireless on Cape Cod

shortwave relay station the fundamental way in

which programmes are broadcast on shortwave

[14] 1921 - Club Station 1BCG and the Transatlantic Tests.

Radio Club of America. Retrieved 2009-09-05.

SSB a method of radio signal modulation

40.14 References
[1] Inconsistent article: itwissen.info: KW (Kurzwelle) SW
(short wave) Quote: "... Der KW-Frequenzbereich (SW)
liegt zwischen 3 MHz und 30 MHz [<1. denition]
... Kurzwelle ist auch eine sendetechnische Bezeichnung
fr Rundfunk im Frequenzbereich zwischen 2,3 MHz und
26,1 MHz [<2. denition] ...
[2] oldtimeradio.de: Kleines Radio-Lexikon Quote: "...
Kurzwellen, Kurzwellenbereich ... Wellenbereich, der
von den Rundfunksendern (je nach geographischer Lage)
von 11 bis 120 m = 26.100 bis 2.300 kHz ...
[3] darc.de: Amateurfunk Frequenzen Quote: "... Grenzwelle (Kurzwelle) ..., de:Grenzwelle Quote: "... Als
Grenzwelle wird der Frequenzbereich zwischen 1605 kHz
und 3800 kHz bezeichnet, weil er auf der Grenze zwischen Mittelwelle und Kurzwelle liegt ...
[4] Inconsistent article: Die Meterbnder der Kurzwelle
Quote: "...Bereich der Kurzwelle von 3.000 kHz bis
30.000 kHz ... [tabel] ... 120 m ... 2.300 kHz ... 2.495
kHz ... Tropenband ...
[5] Universal-Lexikon: Kurzwellen Quote: "... entsprechend
Frequenzen von 30-3 MHz ...
[6] Grundig Satellit 1000 TR6002, schematic See at the bottom of the schematic, just below the transformer. In the
schematic it is written that the rst shortwave band starts
at 1.6 MHz (just after the band end of MW/AM): KW1SW1-OC1 1,6 .... 5,0 MHz
[7] Frederik Nebeker (6 May 2009). Dawn of the Electronic
Age: Electrical Technologies in the Shaping of the Modern
World, 1914 to 1945. John Wiley & Sons. pp. 157.
ISBN 978-0-470-40974-9.

[15] Radio Service Bulletin No. 72, pp. 9-13. Bureau of

Navigation, Department of Commerce. 1923-04-02. Retrieved 2009-09-05.
[16] Archived November 30, 2009, at the Wayback Machine.
[17] Recommendations for Regulation of Radio: October 610, 1924. Earlyradiohistory.us. Retrieved 2012-08-31.
[18] http://www.twiar.org/aaarchives/WB008.txt
[19] Karl Rawer:"Wave Propagation in the Ionosphere.
Kluwer, Dordrecht 1993 ISBN 0-7923-0775-5
[20] Ian Robertson Sinclair, Audio and Hi-Fi Handbook,
Newnes, 2000 ISBN 0-7506-4975-5 pp. 195-196
[21] Archived February 10, 2005, at the Wayback Machine.
[22] Arlyn T. Anderson. Changes at the BBC World Service:
Documenting the World Services Move From Shortwave to
Web Radio in North America, Australia, and New Zealand,
Journal of Radio Studies 2005, Vol. 12, No. 2, Pages
286-304 doi:10.1207/s15506843jrs1202_8 mentioned in
WWCR FAQ
[23] Nationaal Frequentieplan
[24] http://www.w4uvh.net/dxld7078.txt
[25] Habrat, Marek. Odbiornik Roksana (Radio constructors recollections)". Retrieved 2008-08-05.
[26] Archived December 18, 2011, at the Wayback Machine.

Ulrich L. Rohde, Jerry Whitaker Communications

Receivers, Third Edition McGraw Hill, New York,
NY, 2001, ISBN 0-07-136121-9.

240

40.15 External links

SWLing.com - A beginners guide to shortwave radio listening.
Glenn Hauser's World of Radio website
Space Weather and Radio Propagation Center View
live and historical data and images of space weather
and radio propagation.
Short-wave radio, Snap and crackle goes pop, Life
in the old wireless yet The Economist article describing pros and cons of short wave radio since the
Cold War.
Short-Wave Radio Telephone is Success in Tests
Popular Mechanics, July 1931, mid page experiments carried out for the French and British governments
Que Escuchar en la Onda Corta en Espaol website

CHAPTER 40. SHORTWAVE RADIO

Chapter 41

Amplitude modulation signalling system

The amplitude modulation signalling system (AMSS
or the AM signalling system) is a digital system for
adding low bit rate information to an analogue amplitude
modulated broadcast signal in the same manner as the
Radio Data System (RDS) for frequency modulated (FM)
broadcast signals.
This system has been standardized in March 2006 by
ETSI (TS 102 386) as an extension to the Digital Radio
Mondiale (DRM) system.

41.1 Broadcasting
AMSS data are broadcast from the following transmitters:
LW
RTL France: 234 kHz
SW
BBC World Service: 15.575 MHz
Formerly it was also used by:
MW
Truckradio 531 kHz
BBC World Service: 648 kHz
Deutschlandradio Kultur: 990 kHz

41.2 External links

ETSI TS 102 386 v1.2.1 (2006-03) Technical
Specication - Digital Radio Mondial (DRM); AM
signalling system (AMSS)" (PDF, 100 197 bytes).
ETSI. March 2006. Retrieved 2009-12-07.
ETSI TS 102 386 V1.2.1 (2006-03) directly from
ETSI Publications Download Area (account or free
registration required)
241

Murphy, Andrew; Poole, Ranulph (January 2006).

The AM Signalling System: AMSS does your
radio know what its listening to?" (PDF, 172 312
bytes). EBU technical review. EBU.
Lindsay Cornell (January 29, 2007). The AM Signalling System (AMSS)" (PDF, 183KiB). Broadcast
Papers. External link in |publisher= (help)

Chapter 42

Sideband

The power of an AM signal plotted against frequency.

Key: fc is the carrier frequency, fm is the maximum modulation
frequency

Sidebands are evident in this spectrogram of an AM broadcast

(The carrier is highlighted in red, the two mirrored audio spectra
(green) are the lower and upper sideband).

In radio communications, a sideband is a band of

frequencies higher than or lower than the carrier frequency, containing power as a result of the modulation
process. The sidebands consist of all the Fourier components of the modulated signal except the carrier. All
forms of modulation produce sidebands.

broadcasting, which would otherwise take up an unacceptable amount of bandwidth. Transmission in which
only one sideband is transmitted is called single-sideband
transmission or SSB. SSB is the predominant voice mode
on shortwave radio other than shortwave broadcasting.
Amplitude modulation of a carrier signal normally results Since the sidebands are mirror images, which sideband
in two mirror-image sidebands. The signal components is used is a matter of convention.
above the carrier frequency constitute the upper side- In SSB, the carrier is suppressed, signicantly reducing
band (USB), and those below the carrier frequency conthe electrical power (by up to 12 dB) without aecting
stitute the lower sideband (LSB). In conventional AM the information in the sideband. This makes for more eftransmission, the carrier and both sidebands are present,
cient use of transmitter power and RF bandwidth, but
sometimes called double sideband amplitude modula- a beat frequency oscillator must be used at the receiver
tion (DSB-AM).
to reconstitute the carrier. Another way to look at an
In some forms of AM, the carrier may be removed, producing double sideband with suppressed carrier (DSBSC). An example is the stereophonic dierence (L-R)
information transmitted in stereo FM broadcasting on a
38 kHz subcarrier. The receiver locally regenerates the
subcarrier by doubling a special 19 kHz pilot tone, but in
other DSB-SC systems, the carrier may be regenerated
directly from the sidebands by a Costas loop or squaring
loop. This is common in digital transmission systems
such as BPSK where the signal is continually present.

SSB receiver is as an RF-to-audio frequency transposer:

in USB mode, the dial frequency is subtracted from each
radio frequency component to produce a corresponding
audio component, while in LSB mode each incoming radio frequency component is subtracted from the dial frequency.

Sidebands can also interfere with adjacent channels. The

part of the sideband that would overlap the neighboring channel must be suppressed by lters, before or after
modulation (often both). In Broadcast band frequency
If part of one sideband and all of the other remain, it modulation (FM), subcarriers above 75 kHz are limited
is called vestigial sideband, used mostly with television to a small percentage of modulation and are prohibited
242

42.2. REFERENCES
above 99 kHz altogether to protect the 75 kHz normal
deviation and 100 kHz channel boundaries. Amateur
radio and public service FM transmitters generally utilize
5 kHz deviation.

42.1 See also

Independent sideband
Single-sideband modulation for more technical information about sideband modulation
Sideband computing is a distributed computing
method using a separate channel than the main communication channel.
Out-of-band communications involve a separate
channel other than the main communication channel.
Side lobe
TV transmitter

42.2 References
General
This article incorporates public domain material
from the General Services Administration document
Federal Standard 1037C (in support of MIL-STD188).
partly from Department of The Army Technical
Manual TM 11-685 Fundamentals of Single Sideband Communications

243

Chapter 43

Types of radio emissions

The International Telecommunication Union uses an internationally agreed system for classifying radio frequency signals. Each type of radio emission is classied
according to its bandwidth, method of modulation, nature
of the modulating signal, and type of information transmitted on the carrier signal. It is based on characteristics
of the signal, not on the transmitter used.

43.1.2 Type of modulation

43.1.3 Type of modulating signal
Types 4 and 5 were removed from use with the 1982 Radio Regulations. In previous editions, they had indicated
facsimile and video, respectively.

An emission designation is of the form BBBB 123 45,

where BBBB is the bandwidth of the signal, 1 is a letter
43.1.4
indicating the type of modulation used of the main carrier
(not including any subcarriers which is why FM stereo is
F8E and not D8E), 2 is a digit representing the type of 43.1.5
modulating signal again of the main carrier, 3 is a letter
corresponding to the type of information transmitted, 4 is 43.1.6
a letter indicating the practical details of the transmitted
information, and 5 is a letter that represents the method 43.2
of multiplexing. The 4 and 5 elds are optional.

Type of transmitted information

Details of information
Multiplexing

Common examples

This designation system was agreed at the 1979 World 43.2.1 Broadcasting
Administrative Radio Conference (WARC 79), and gave
rise to the Radio Regulations that came into force on 1 A3E or A3E G Ordinary amplitude modulation used
January 1982. A similar designation system had been in
for low frequency and medium frequency AM
use under prior Radio Regulations.
broadcasting
F8E, F8E H FM broadcasting for radio transmissions
on VHF, and as the audio component of analogue
television transmissions.

43.1 Designation details

43.1.1

Bandwidth

C3F, C3F N Analogue PAL, SCAM, or NTSC television video signals (formerly type A5C, until 1982)
C7W ATSC digital television, commonly on VHF or
UHF
G7W DVB-T, ISDB-T, or DTMB digital television,
commonly on VHF or UHF

The bandwidth (BBBB above) is expressed as four characters: three digits and one letter. The letter occupies the
position normally used for a decimal point, and indicates 43.2.2 Two-way radio
what unit of frequency is used to express the bandwidth.
The letter H indicates Hertz, K indicates kiloHertz, M A3E AM speech communication used for aeronautical
communications
indicates megaHertz, and G indicates gigaHertz. For instance, 500H means 500 Hz, and 2M50 means 2.5
MHz. The rst character must be a digit between 1 and F3E FM speech communication often used for marine
radio and many other VHF communications
9; it may not be the digit 0 or a letter.
244

43.3. NOTES
20K0 F3E Wide FM, 20.0 kHz width, 5 kHz deviation, still widely used for Ham Radio, NOAA
weather radio, marine, and aviation users
11K2 F3E Narrow FM, 11.25 kHz bandwidth, 2.5
kHz deviation All Part 90 Land Mobile Radio Service (LMRS) users were required to upgrade to narrowband equipment by 2013-01-01.
6K00 F3E Even Narrower FM, future roadmap for
Land Mobile Radio Service (LMRS), already required on 700 MHz public safety band
J3E SSB speech communication, used on HF bands by
marine, aeronautical and amateur users
R3E SSB with reduced carrier (AME) speech communication, primarily used on HF bands by the military
(a.k.a. compatible sideband)

43.2.3

Low-speed data

N0N Continuous, unmodulated carrier, formerly common for radio direction nding (RDF) in marine and
aeronautical navigation.
A1A Signalling by keying the carrier directly, a.k.a.
Continuous Wave (CW) or On-O Keying (OOK),
currently used in amateur radio. This is often but
not necessarily Morse code.
A2A Signalling by transmitting a modulated tone with
a carrier, so that it can easily be heard using an ordinary AM receiver. It was formerly widely used
for station identication of non-directional beacons,
usually but not exclusively Morse code (an example of a modulated continuous wave, as opposed to
A1A, above).
F1B Frequency-shift keying (FSK) telegraphy, such as
RTTY.[lower-alpha 1]
F1C High frequency Radiofax
F2D Data transmission by frequency modulation of a
radio frequency carrier with an audio frequency FSK
subcarrier. Often called AFSK/FM.
J2B Phase-shift keying such as PSK31 (BPSK31)
There is some overlap in signal types, so a transmission
might legitimately be described by two or more designators. In such cases, there is usually a preferred conventional designator.

245

43.3 Notes
[1] The designators F1B and F1D should be used for FSK radiotelegraphy and data transmissions, no matter how the
radio frequency signal is generated (common examples are
Audio FSK used to modulate an SSB transmitter or direct
FSK modulation of an FM transmitter via varactor diode).
However, occasionally the alternatives J2B and J2D are
used to designate FSK signals generated by audio modulation of an SSB transmitter.

43.4 Further reading

Complete List of Radio Regulations. Retrieved
2011-12-17.
Radio Regulations, ITU, Geneva, 1982
Radio Regulations, Edition of 2004, Volume 2 - Appendices, Appendix 1, ITU, Geneva, 2004
Radiocommunications Vocabulary, Recommendation ITU-R V.573-4, ITU-R, Geneva, 2000
Determination of Necessary Bandwidths Including
Examples for their Calculation, Recommendation
ITU-R SM.1138, Geneva, 1995
Emission characteristics of radio transmissions, Australian Communications Authority, Canberra
Notes Regarding Designation of Emission, Industry
Canada, 1982
Eckersley, R.J. Amateur Radio Operating Manual,
3rd edition, Radio Society of Great Britain, 1985,
ISBN 0-900612-69-X
TRC-43 Designation of Emissions, Class of Station and Nature of Service - Industry Canada

Chapter 44

Modulation (disambiguation)
Modulationes for 6 voices, Zarlino

Modulation is the process of varying one or more properties of a high-frequency periodic waveform.

Modulations, Jrgen Plaetner

Modulation, Modulations, Modulate, and Modulator

may also refer to:

Module Modulations, Carl Ludwig Hbsch (b.1966)

Transcendental Modulations, George Perle

44.1 Economics
44.3.2 Albums
Modulation (European Union), an authorized reduction in direct aid to producers

44.2 Science

Modulate (album), a rock/electronica album by Bob

Mould

Immunomodulation therapy

Modulator (EP), an electronica EP by Information

Society

Neuromodulation (disambiguation)

44.3 Music
Modulation (music), a change of key
Modulating subject, a fugue subject which modulates
Modulate (band), UK electronic band
The Modulations, 1970s American band
Modulation (music radio program), a weekly music
radio program, broadcast via Jeerson Public Radio.
Modulations A History of Electronic Music by Peter Shapiro, 2000 accompanying book to 1998 documentary

44.3.1

Modulations (lm), 1998 lm and soundtrack album, with 2000 book about the history of electronic
music

Classical compositions

Modulating Prelude, KV. 624 Mozart

L'art de la modulation F-A. Philidor
Modulation, Johannes Fritsch
Clothes-pin modulation, Ernst Reijseger
246

Chapter 45

Electronics
This article is about the technical eld of electronics.
For personal/home-use electronic devices, see consumer
electronics. For the scientic magazine, see Electronics
(magazine).
Electronics is the science of controlling electrical en-

Electronics is distinct from electrical and electromechanical science and technology, which deal with the
generation, distribution, switching, storage, and conversion of electrical energy to and from other energy forms
using wires, motors, generators, batteries, switches,
relays, transformers, resistors, and other passive components. This distinction started around 1906 with the
invention by Lee De Forest of the triode, which made
electrical amplication of weak radio signals and audio
signals possible with a non-mechanical device. Until
1950 this eld was called radio technology because its
principal application was the design and theory of radio
transmitters, receivers, and vacuum tubes.
Today, most electronic devices use semiconductor components to perform electron control. The study of semiconductor devices and related technology is considered a
branch of solid-state physics, whereas the design and construction of electronic circuits to solve practical problems
come under electronics engineering. This article focuses
on engineering aspects of electronics.

Surface-mount electronic components

ergy electrically, in which the electrons have a fundamen45.1 Branches of electronics

tal role. Electronics deals with electrical circuits that involve active electrical components such as vacuum tubes,
transistors, diodes, integrated circuits, associated passive Electronics has branches as follows:
electrical components, and interconnection technologies.
Commonly, electronic devices contain circuitry consist1. Digital electronics
ing primarily or exclusively of active semiconductors supplemented with passive elements; such a circuit is described as an electronic circuit.
2. Analogue electronics
The science of Electronics is also considered to be a
branch of Physics and Electrical Engineering.[1]
The nonlinear behaviour of active components and their
ability to control electron ows makes amplication of
weak signals possible, and electronics is widely used in
information processing, telecommunication, and signal
processing. The ability of electronic devices to act as
switches makes digital information processing possible.
Interconnection technologies such as circuit boards, electronics packaging technology, and other varied forms of
communication infrastructure complete circuit functionality and transform the mixed components into a regular
working system.
247

3. Microelectronics
4. Circuit design
5. Integrated circuits
6. Optoelectronics
7. Semiconductor devices
8. Embedded systems

248

CHAPTER 45. ELECTRONICS

RF ampliers, cathode ray tubes, specialist audio equipment, guitar ampliers and some microwave devices.
In April 1955 the IBM 608 was the rst IBM product
to use transistor circuits without any vacuum tubes and is
believed to be the worlds rst all-transistorized calculator
to be manufactured for the commercial market.[3][4] The
608 contained more than 3,000 germanium transistors.
Thomas J. Watson Jr. ordered all future IBM products to
use transistors in their design. From that time on transistors were almost exclusively used for computer logic and
peripherals.

Electronics Technician performing a voltage check on a power

circuit card in the air navigation equipment room aboard the aircraft carrier USS Abraham Lincoln (CVN 72).

45.2 Electronic devices and components

Main article: Electronic component
An electronic component is any physical entity in an
electronic system used to aect the electrons or their associated elds in a manner consistent with the intended
function of the electronic system. Components are generally intended to be connected together, usually by being soldered to a printed circuit board (PCB), to create
an electronic circuit with a particular function (for example an amplier, radio receiver, or oscillator). Components may be packaged singly, or in more complex
groups as integrated circuits. Some common electronic
components are capacitors, inductors, resistors, diodes,
transistors, etc. Components are often categorized as active (e.g. transistors and thyristors) or passive (e.g. resistors, diodes, inductors and capacitors).

45.4 Types of circuits

Circuits and components can be divided into two groups:
analog and digital. A particular device may consist of circuitry that has one or the other or a mix of the two types.

45.4.1 Analog circuits

Main article: Analog electronics
Most analog electronic appliances, such as radio re-

45.3 History of electronic components

Further information: Timeline of electrical and electronic engineering
Vacuum tubes (Thermionic valves) were among the earliest electronic components. They were almost solely responsible for the electronics revolution of the rst half of
the Twentieth Century. They took electronics from parlor
tricks and gave us radio, television, phonographs, radar,
long distance telephony and much more. They played
a leading role in the eld of microwave and high power
transmission as well as television receivers until the middle of the 1980s.[2] Since that time, solid state devices
have all but completely taken over. Vacuum tubes are still
used in some specialist applications such as high power

Hitachi J100 adjustable frequency drive chassis

ceivers, are constructed from combinations of a few types

of basic circuits. Analog circuits use a continuous range
of voltage or current as opposed to discrete levels as in
digital circuits.
The number of dierent analog circuits so far devised
is huge, especially because a 'circuit' can be dened as
anything from a single component, to systems containing
thousands of components.

45.5. HEAT DISSIPATION AND THERMAL MANAGEMENT

Analog circuits are sometimes called linear circuits although many non-linear eects are used in analog circuits
such as mixers, modulators, etc. Good examples of analog circuits include vacuum tube and transistor ampliers,
operational ampliers and oscillators.

249
Registers
Multiplexers
Schmitt triggers

One rarely nds modern circuits that are entirely analog. Highly integrated devices:
These days analog circuitry may use digital or even mi Microprocessors
croprocessor techniques to improve performance. This
type of circuit is usually called mixed signal rather than
Microcontrollers
analog or digital.
Application-specic integrated circuit (ASIC)
Sometimes it may be dicult to dierentiate between
analog and digital circuits as they have elements of both
Digital signal processor (DSP)
linear and non-linear operation. An example is the com Field-programmable gate array (FPGA)
parator which takes in a continuous range of voltage but
only outputs one of two levels as in a digital circuit. Similarly, an overdriven transistor amplier can take on the
characteristics of a controlled switch having essentially 45.5 Heat dissipation and thermal
two levels of output. In fact, many digital circuits are acmanagement
tually implemented as variations of analog circuits similar
to this exampleafter all, all aspects of the real physical
Main article: Thermal management of electronic devices
world are essentially analog, so digital eects are only reand systems
alized by constraining analog behavior.
Heat generated by electronic circuitry must be dissipated
to prevent immediate failure and improve long term reliability. Heat dissipation is mostly achieved by passive
Main article: Digital electronics
conduction/convection. Means to achieve greater dissipation include heat sinks and fans for air cooling, and other
forms
of computer cooling such as water cooling. These
Digital circuits are electric circuits based on a number of
techniques
use convection, conduction, and radiation of
discrete voltage levels. Digital circuits are the most comheat
energy.
mon physical representation of Boolean algebra, and are
the basis of all digital computers. To most engineers, the
terms digital circuit, digital system and logic are interchangeable in the context of digital circuits. Most dig- 45.6 Noise
ital circuits use a binary system with two voltage levels
labeled 0 and 1. Often logic 0 will be a lower volt- Main article: Electronic noise
age and referred to as Low while logic 1 is referred to
as High. However, some systems use the reverse def[5]
inition (0 is High) or are current based. Quite often Electronic noise is dened as unwanted disturbances
the logic designer may reverse these denitions from one superposed on a useful signal that tend to obscure its incircuit to the next as he sees t to facilitate his design. formation content. Noise is not the same as signal distortion caused by a circuit. Noise is associated with all
The denition of the levels as 0 or 1 is arbitrary.
electronic circuits. Noise may be electromagnetically or
Ternary (with three states) logic has been studied, and thermally generated, which can be decreased by lowering
some prototype computers made.
the operating temperature of the circuit. Other types of
Computers, electronic clocks, and programmable logic noise, such as shot noise cannot be removed as they are
controllers (used to control industrial processes) are con- due to limitations in physical properties.
structed of digital circuits. Digital signal processors are
another example.

45.4.2

Digital circuits

Building blocks:
Logic gates
Adders
Flip-ops
Counters

45.7 Electronics theory

Main article: Mathematical methods in electronics

Mathematical methods are integral to the study of electronics. To become procient in electronics it is also necessary to become procient in the mathematics of circuit
analysis.

250

CHAPTER 45. ELECTRONICS

Circuit analysis is the study of methods of solving generally linear systems for unknown variables such as the
voltage at a certain node or the current through a certain
branch of a network. A common analytical tool for this
is the SPICE circuit simulator.

Paper (SRBP, also known as Paxoline/Paxolin (trade

marks) and FR2) - characterised by its brown colour.
Health and environmental concerns associated with electronics assembly have gained increased attention in recent years, especially for products destined to the EuroAlso important to electronics is the study and understand- pean Union, with its Restriction of Hazardous Substances
Directive (RoHS) and Waste Electrical and Electronic
ing of electromagnetic eld theory.
Equipment Directive (WEEE), which went into force in
July 2006.

45.8 Electronics lab

45.11 Degradation

Main article: Electronic circuit simulation

Rasberry crazy ants have been known to consume the inDue to the complex nature of electronics theory, labora- sides of electrical wiring, and nest inside of electronics;
tory experimentation is an important part of the develop- they prefer DC to AC currents. This behavior is not well
ment of electronic devices. These experiments are used understood by scientists.[6]
to test or verify the engineers design and detect errors.
Historically, electronics labs have consisted of electronics devices and equipment located in a physical space, al- 45.12 See also
though in more recent years the trend has been towards
electronics lab simulation software, such as CircuitLogix,
Outline of electronics
Multisim, and PSpice.
Atomtronics

45.9 Computer
(CAD)

aided

design

Main article: Electronic design automation

Todays electronics engineers have the ability to design
circuits using premanufactured building blocks such as
power supplies, semiconductors (i.e. semiconductor
devices, such as transistors), and integrated circuits.
Electronic design automation software programs include
schematic capture programs and printed circuit board design programs. Popular names in the EDA software world
are NI Multisim, Cadence (ORCAD), EAGLE PCB and
Schematic, Mentor (PADS PCB and LOGIC Schematic),
Altium (Protel), LabCentre Electronics (Proteus), gEDA,
KiCad and many others.

45.10 Construction methods

Main article: Electronic packaging
Many dierent methods of connecting components have
been used over the years. For instance, early electronics often used point to point wiring with components
attached to wooden breadboards to construct circuits.
Cordwood construction and wire wrap were other methods used. Most modern day electronics now use printed
circuit boards made of materials such as FR4, or the
cheaper (and less hard-wearing) Synthetic Resin Bonded

Audio engineering
Broadcast engineering
Computer engineering
Electronic engineering
Electronics engineering technology
Fuzzy electronics
Index of electronics articles
List of mechanical, electrical and electronic equipment manufacturing companies by revenue
Marine electronics
Power electronics
Robotics

45.13 References
[1] Electronics, Encyclopedia Britannica.
Britannica. September 2016.

Encyclopedia

[2] Sgo Okamura (1994). History of Electron Tubes. IOS

Press. p. 5. ISBN 978-90-5199-145-1. Retrieved 5 December 2012.
[3] Bashe, Charles J.; et al. (1986). IBMs Early Computers.
MIT. p. 386.

45.15. EXTERNAL LINKS

[4] Pugh, Emerson W.; Johnson, Lyle R.; Palmer, John H.

(1991). IBMs 360 and early 370 systems. MIT Press. p.
34. ISBN 0-262-16123-0.
[5] IEEE Dictionary of Electrical and Electronics Terms
ISBN 978-0-471-42806-0
[6] Andrew R Hickey (May 15, 2008). "'Crazy' Ant Invasion
Frying Computer Equipment.

45.14 Further reading

The Art of Electronics ISBN 978-0-521-37095-0

45.15 External links

Electronics at DMOZ
Navy 1998 Navy Electricity and Electronics Training Series (NEETS)
DOE 1998 Electrical Science, Fundamentals Handbook, 4 vols.
Vol. 1, Basic Electrical Theory, Basic DC
Theory
Vol. 2, DC Circuits, Batteries, Generators,
Motors
Vol. 3, Basic AC Theory, Basic AC Reactive Components, Basic AC Power, Basic AC
Generators
Vol. 4, AC Motors, Transformers, Test Instruments & Measuring Devices, Electrical Distribution Systems

251

Chapter 46

Telecommunication
Not to be confused with Teleconnection.
intelligence of any nature by wire, radio, optical
Telecommunication is the transmission of signs, or other electromagnetic systems.[1][2] Telecommunication occurs when the exchange of information between communication participants includes the use of
technology. It is transmitted either electrically over physical media, such as cables, or via electromagnetic radiation.[3][4][5][6][7][8] Such transmission paths are often divided into communication channels which aord the advantages of multiplexing. The term is often used in its
plural form, telecommunications, because it involves
many dierent technologies.

Earth station at the satellite communication facility in Raisting,

Bavaria, Germany

Early means of communicating over a distance included

visual signals, such as beacons, smoke signals, semaphore
telegraphs, signal ags, and optical heliographs.[9] Other
examples of pre-modern long-distance communication
included audio messages such as coded drumbeats, lungblown horns, and loud whistles. 20th and 21st century technologies for long-distance communication usually involve electrical and electromagnetic technologies, such as telegraph, telephone, and teleprinter,
networks, radio, microwave transmission, ber optics,
and communications satellites.
A revolution in wireless communication began in the rst
decade of the 20th century with the pioneering developments in radio communications by Guglielmo Marconi,
who won the Nobel Prize in Physics in 1909. Other
notable pioneering inventors and developers in the eld
of electrical and electronic telecommunications include
Charles Wheatstone and Samuel Morse (inventors of
the telegraph), Alexander Graham Bell (inventor of the
telephone), Edwin Armstrong and Lee de Forest (inventors of radio), as well as Vladimir K. Zworykin, John Logie Baird and Philo Farnsworth (some of the inventors of
television).

46.1 Etymology
The word telecommunication was adapted from the
French.[7] It is a compound of the Greek prex teleVisualization from the Opte Project of the various routes through (-), meaning distant, and the Latin communicare,
meaning to share, and its written use was recorded in
a portion of the Internet
1904 by the French engineer and novelist douard Essignals, messages, writings, images and sounds or tauni.[10][11] The prex tel means far, far o, op252

46.2. HISTORY
erating over distance... from Greek tele-, combining
form of tele far o, afar, at or to a distance, related
to teleos (genitive telos) end, goal, completion, result,
from PIE root *kwel-"; tel also means " far in space
and time.[12] Communication was rst used as an English word in the late 14th century. It comes from Old
French comunicacion (14c., Modern French communication), from Latin communicationem (nominative communicatio), noun of action from past participle stem of
communicare to share, divide out; communicate, impart, inform; join, unite, participate in, literally to make
common, from communis.[13]

253
In 1792, Claude Chappe, a French engineer, built the rst
xed visual telegraphy system (or semaphore line) between Lille and Paris.[15] However semaphore suered
from the need for skilled operators and expensive towers at intervals of ten to thirty kilometres (six to nineteen miles). As a result of competition from the electrical telegraph, the last commercial line was abandoned in
1880.[16]

Homing pigeons have occasionally been used throughout history by dierent cultures. Pigeon post is thought
to have Persians roots and was used by the Romans
to aid their military. Frontinus said that Julius Caesar
used pigeons as messengers in his conquest of Gaul.[17]
The Greeks also conveyed the names of the victors
46.2 History
at the Olympic Games to various cities using homing
pigeons.[18] In the early 19th century, the Dutch governFor more details on this topic, see History of telecom- ment used the system in Java and Sumatra. And in 1849,
Paul Julius Reuter started a pigeon service to y stock
munication.
prices between Aachen and Brussels, a service that operated for a year until the gap in the telegraph link was
closed.[19]

46.2.1

Beacons and pigeons

46.2.2 Telegraph and telephone
Sir Charles Wheatstone and Sir William Fothergill Cooke
invented the electric telegraph in 1837.[20] Also, the rst
commercial electrical telegraph is purported to have been
constructed by Wheatstone and Cooke and opened on 9
April 1839. Both inventors viewed their device as an
improvement to the [existing] electromagnetic telegraph
not as a new device.[21]
Samuel Morse independently developed a version of the
electrical telegraph that he unsuccessfully demonstrated
on 2 September 1837. His code was an important advance over Wheatstones signaling method. The rst
transatlantic telegraph cable was successfully completed
on 27 July 1866, allowing transatlantic telecommunication for the rst time.[22]

A replica of one of Chappes semaphore towers

In the Middle Ages, chains of beacons were commonly

used on hilltops as a means of relaying a signal. Beacon
chains suered the drawback that they could only pass a
single bit of information, so the meaning of the message
such as the enemy has been sighted had to be agreed
upon in advance. One notable instance of their use was
during the Spanish Armada, when a beacon chain relayed
a signal from Plymouth to London.[14]

The conventional telephone was invented independently

by Alexander Bell and Elisha Gray in 1876.[23] Antonio
Meucci invented the rst device that allowed the electrical transmission of voice over a line in 1849. However
Meuccis device was of little practical value because it relied upon the electrophonic eect and thus required users
to place the receiver in their mouth to hear what was being said.[24] The rst commercial telephone services were
set-up in 1878 and 1879 on both sides of the Atlantic in
the cities of New Haven and London.[25][26]

46.2.3 Radio and television

In 1832, James Lindsay gave a classroom demonstration
of wireless telegraphy to his students. By 1854, he was
able to demonstrate a transmission across the Firth of Tay
from Dundee, Scotland to Woodhaven, a distance of two

254

CHAPTER 46. TELECOMMUNICATION

miles (3 km), using water as the transmission medium.[27]

In December 1901, Guglielmo Marconi established wireless communication between St. Johns, Newfoundland
(Canada) and Poldhu, Cornwall (England), earning him
the 1909 Nobel Prize in physics (which he shared with
Karl Braun).[28] However small-scale radio communication had already been demonstrated in 1893 by Nikola
Tesla in a presentation to the National Electric Light
Association.[29]
On 25 March 1925, John Logie Baird was able to demonstrate the transmission of moving pictures at the London department store Selfridges. Bairds device relied
upon the Nipkow disk and thus became known as the
mechanical television. It formed the basis of experimental broadcasts done by the British Broadcasting Corporation beginning 30 September 1929.[30] However, for most
of the twentieth century televisions depended upon the
cathode ray tube invented by Karl Braun. The rst version of such a television to show promise was produced
by Philo Farnsworth and demonstrated to his family on 7
September 1927.[31]

46.2.4

Computers and the Internet

On 11 September 1940, George Stibitz was able to transmit problems using teletype to his Complex Number Calculator in New York and receive the computed results
back at Dartmouth College in New Hampshire.[32] This
conguration of a centralized computer or mainframe
with remote dumb terminals remained popular throughout the 1950s. However, it was not until the 1960s
that researchers started to investigate packet switching a technology that would allow chunks of data
to be sent to dierent computers without rst passing
through a centralized mainframe. A four-node network
emerged on 5 December 1969; this network would become ARPANET, which by 1981 would consist of 213
nodes.[33]
ARPANET development centered around the Request
for Comment process and on 7 April 1969, RFC 1 was
published. This process is important because ARPANET
eventually merged with other networks to form the
Internet and many of the protocols the Internet relies
upon today were specied through the Request for Comment process. In September 1981, RFC 791 introduced
the Internet Protocol v4 (IPv4) and RFC 793 introduced
the Transmission Control Protocol (TCP) thus creating the TCP/IP protocol that much of the Internet relies
upon today.
However, not all important developments were made
through the Request for Comment process. Two popular link protocols for local area networks (LANs) also
appeared in the 1970s. A patent for the token ring protocol was led by Olof Soderblom on 29 October 1974
and a paper on the Ethernet protocol was published by
Robert Metcalfe and David Boggs in the July 1976 issue

of Communications of the ACM.[34][35]

46.3 Key concepts

A number of key concepts reoccur throughout the literature on modern telecommunication theory and systems.
Some of these concepts are discussed below.

46.3.1 Basic elements

Telecommunications is primarily divided up between
wired and wireless subtypes. Overall though, a basic
telecommunication system consists of three main parts
that are always present in some form or another:
A transmitter that takes information and converts it
to a signal.
A transmission medium, also called the physical
channel that carries the signal. An example of this
is the free space channel.
A receiver that takes the signal from the channel and
converts it back into usable information for the recipient.
For example, in a radio broadcasting station the stations
large power amplier is the transmitter; and the broadcasting antenna is the interface between the power amplier and the free space channel. The free space channel
is the transmission medium; and the receivers antenna is
the interface between the free space channel and the receiver. Next, the radio receiver is the destination of the
radio signal, and this is where it is converted from electricity to sound for people to listen to.
Sometimes, telecommunication systems are duplex
(two-way systems) with a single box of electronics working as both the transmitter and a receiver, or a transceiver.
For example, a cellular telephone is a transceiver.[36]
The transmission electronics and the receiver electronics
within a transceiver are actually quite independent of each
other. This can be readily explained by the fact that radio
transmitters contain power ampliers that operate with
electrical powers measured in watts or kilowatts, but radio receivers deal with radio powers that are measured in
the microwatts or nanowatts. Hence, transceivers have to
be carefully designed and built to isolate their high-power
circuitry and their low-power circuitry from each other, as
to not cause interference.
Telecommunication over xed lines is called point-topoint communication because it is between one transmitter and one receiver. Telecommunication through radio
broadcasts is called broadcast communication because it
is between one powerful transmitter and numerous lowpower but sensitive radio receivers.[36]

46.3. KEY CONCEPTS

Telecommunications in which multiple transmitters and
multiple receivers have been designed to cooperate and to
share the same physical channel are called multiplex systems. The sharing of physical channels using multiplexing often gives very large reductions in costs. Multiplexed
systems are laid out in telecommunication networks, and
the multiplexed signals are switched at nodes through to
the correct destination terminal receiver.

46.3.2

Analog versus digital communications

Communications signals can be sent either by analog signals or digital signals. There are analog communication
systems and digital communication systems. For an analog signal, the signal is varied continuously with respect
to the information. In a digital signal, the information is
encoded as a set of discrete values (for example, a set
of ones and zeros). During the propagation and reception, the information contained in analog signals will inevitably be degraded by undesirable physical noise. (The
output of a transmitter is noise-free for all practical purposes.) Commonly, the noise in a communication system
can be expressed as adding or subtracting from the desirable signal in a completely random way. This form of
noise is called additive noise, with the understanding that
the noise can be negative or positive at dierent instants
of time. Noise that is not additive noise is a much more
dicult situation to describe or analyze, and these other
kinds of noise will be omitted here.
On the other hand, unless the additive noise disturbance
exceeds a certain threshold, the information contained in
digital signals will remain intact. Their resistance to noise
represents a key advantage of digital signals over analog
signals.[37]

46.3.3

Telecommunication networks

A telecommunications network is a collection of transmitters, receivers, and communications channels that

send messages to one another. Some digital communications networks contain one or more routers that work
together to transmit information to the correct user. An
analog communications network consists of one or more
switches that establish a connection between two or more
users. For both types of network, repeaters may be necessary to amplify or recreate the signal when it is being transmitted over long distances. This is to combat
attenuation that can render the signal indistinguishable
from the noise.[38] Another advantage of digital systems
over analog is that their output is easier to store in memory, i.e. two voltage states (high and low) are easier to
store than a continuous range of states.

255

46.3.4 Communication channels

The term channel has two dierent meanings. In one

meaning, a channel is the physical medium that carries
a signal between the transmitter and the receiver. Examples of this include the atmosphere for sound communications, glass optical bers for some kinds of optical
communications, coaxial cables for communications by
way of the voltages and electric currents in them, and free
space for communications using visible light, infrared
waves, ultraviolet light, and radio waves. This last channel
is called the free space channel. The sending of radio
waves from one place to another has nothing to do with
the presence or absence of an atmosphere between the
two. Radio waves travel through a perfect vacuum just as
easily as they travel through air, fog, clouds, or any other
kind of gas.
The other meaning of the term channel in telecommunications is seen in the phrase communications channel, which is a subdivision of a transmission medium so
that it can be used to send multiple streams of information simultaneously. For example, one radio station can
broadcast radio waves into free space at frequencies in the
neighborhood of 94.5 MHz (megahertz) while another radio station can simultaneously broadcast radio waves at
frequencies in the neighborhood of 96.1 MHz. Each radio station would transmit radio waves over a frequency
bandwidth of about 180 kHz (kilohertz), centered at frequencies such as the above, which are called the carrier
frequencies. Each station in this example is separated
from its adjacent stations by 200 kHz, and the dierence
between 200 kHz and 180 kHz (20 kHz) is an engineering allowance for the imperfections in the communication
system.
In the example above, the free space channel has
been divided into communications channels according
to frequencies, and each channel is assigned a separate
frequency bandwidth in which to broadcast radio waves.
This system of dividing the medium into channels according to frequency is called "frequency-division multiplexing". Another term for the same concept is "wavelengthdivision multiplexing", which is more commonly used in
optical communications when multiple transmitters share
the same physical medium.
Another way of dividing a communications medium into
channels is to allocate each sender a recurring segment of
time (a time slot, for example, 20 milliseconds out of
each second), and to allow each sender to send messages
only within its own time slot. This method of dividing
the medium into communication channels is called "timedivision multiplexing" (TDM), and is used in optical ber
communication. Some radio communication systems use
TDM within an allocated FDM channel. Hence, these
systems use a hybrid of TDM and FDM.

256

46.3.5

CHAPTER 46. TELECOMMUNICATION

Modulation

Bangladesh's Narshingdi district, isolated villagers use

cellular phones to speak directly to wholesalers and arThe shaping of a signal to convey information is known range a better price for their goods. In Cte d'Ivoire, cofas modulation. Modulation can be used to represent a fee growers share mobile phones to follow hourly variadigital message as an analog waveform. This is com- tions in coee prices and sell at the best price.[44]
monly called keying a term derived from the older
use of Morse Code in telecommunications and several
keying techniques exist (these include phase-shift keying, Macroeconomics
frequency-shift keying, and amplitude-shift keying). The
"Bluetooth" system, for example, uses phase-shift keying On the macroeconomic scale, Lars-Hendrik Rller and
to exchange information between various devices.[39][40] Leonard Waverman suggested a causal link between
In addition, there are combinations of phase-shift keying good telecommunication infrastructure and economic
[45][46]
Few dispute the existence of a correlation
and amplitude-shift keying which is called (in the jargon growth.
although
some
argue it is wrong to view the relationship
of the eld) "quadrature amplitude modulation" (QAM)
[47]
as
causal.
that are used in high-capacity digital radio communication systems.
Because of the economic benets of good telecommuModulation can also be used to transmit the informa- nication infrastructure, there is increasing worry about
tion of low-frequency analog signals at higher frequen- the inequitable access to telecommunication services
cies. This is helpful because low-frequency analog signals amongst various countries of the worldthis is known
cannot be eectively transmitted over free space. Hence as the digital divide. A 2003 survey by the International
the information from a low-frequency analog signal must Telecommunication Union (ITU) revealed that roughly a
be impressed into a higher-frequency signal (known as third of countries have fewer than one mobile subscripthe "carrier wave") before transmission. There are sev- tion for every 20 people and one-third of countries have
eral dierent modulation schemes available to achieve fewer than one land-line telephone subscription for every
this [two of the most basic being amplitude modulation 20 people. In terms of Internet access, roughly half of all
(AM) and frequency modulation (FM)]. An example of countries have fewer than one out of 20 people with Interthis process is a disc jockeys voice being impressed into net access. From this information, as well as educational
a 96 MHz carrier wave using frequency modulation (the data, the ITU was able to compile an index that measures
voice would then be received on a radio as the channel the overall ability of citizens to access and use informa[48]
96 FM).[41] In addition, modulation has the advantage tion and communication technologies. Using this measure, Sweden, Denmark and Iceland received the highthat it may use frequency division multiplexing (FDM).
est ranking while the African countries Nigeria, Burkina
Faso and Mali received the lowest.[49]

46.4 Society
Telecommunication has a signicant social, cultural and
economic impact on modern society. In 2008, estimates
placed the telecommunication industry's revenue at $4.7
trillion or just under 3 percent of the gross world product (ocial exchange rate).[42] Several following sections
discuss the impact of telecommunication on society.

46.4.2 Social impact

Telecommunication has played a signicant role in social

relationships. Nevertheless, devices like the telephone
system were originally advertised with an emphasis on the
practical dimensions of the device (such as the ability to
conduct business or order home services) as opposed to
the social dimensions. It was not until the late 1920s and
1930s that the social dimensions of the device became a
46.4.1 Economic impact
prominent theme in telephone advertisements. New promotions started appealing to consumers emotions, stressMicroeconomics
ing the importance of social conversations and staying
[50]
On the microeconomic scale, companies have used connected to family and friends.
telecommunications to help build global business em- Since then the role that telecommunications has played
pires. This is self-evident in the case of online retailer in social relations has become increasingly important. In
Amazon.com but, according to academic Edward Lenert, recent years, the popularity of social networking sites has
even the conventional retailer Walmart has beneted from increased dramatically. These sites allow users to combetter telecommunication infrastructure compared to its municate with each other as well as post photographs,
competitors.[43] In cities throughout the world, home events and proles for others to see. The proles can list
owners use their telephones to order and arrange a va- a persons age, interests, sexual preference and relationriety of home services ranging from pizza deliveries to ship status. In this way, these sites can play important
electricians. Even relatively poor communities have been role in everything from organising social engagements to
noted to use telecommunication to their advantage. In courtship.[51]

46.6. MODERN MEDIA

Prior to social networking sites, technologies like short
message service (SMS) and the telephone also had a signicant impact on social interactions. In 2000, market
research group Ipsos MORI reported that 81% of 15- to
24-year-old SMS users in the United Kingdom had used
the service to coordinate social arrangements and 42% to
irt.[52]

46.4.3

Other impacts

In cultural terms, telecommunication has increased the

publics ability to access music and lm. With television,
people can watch lms they have not seen before in their
own home without having to travel to the video store or
cinema. With radio and the Internet, people can listen to
music they have not heard before without having to travel
to the music store.
Telecommunication has also transformed the way people
receive their news. A survey led in 2006 by the non-prot
Pew Internet and American Life Project found that when
just over 3,000 people living in the United States were
asked where they got their news yesterday, more people
said television or radio than newspapers. The results are
summarised in the following table (the percentages add up
to more than 100% because people were able to specify
more than one source).[53]
Telecommunication has had an equally signicant impact on advertising. TNS Media Intelligence reported
that in 2007, 58% of advertising expenditure in the
United States was spent on mediums that depend upon
telecommunication.[54] The results are summarised in the
following table.

46.5 Government
Many countries have enacted legislation which conforms
to the International Telecommunication Regulations established by the International Telecommunication Union
(ITU), which is the leading UN agency for information
and communication technology issues.[55] In 1947, at
the Atlantic City Conference, the ITU decided to afford international protection to all frequencies registered
in a new international frequency list and used in conformity with the Radio Regulation. According to the ITUs
Radio Regulations adopted in Atlantic City, all frequencies referenced in the International Frequency Registration Board, examined by the board and registered on the
International Frequency List shall have the right to international protection from harmful interference.[56]
From a global perspective, there have been political
debates and legislation regarding the management of
telecommunication and broadcasting. The history of
broadcasting discusses some debates in relation to balancing conventional communication such as printing and
telecommunication such as radio broadcasting.[57] The

257
onset of World War II brought on the rst explosion of international broadcasting propaganda.[57] Countries, their
governments, insurgents, terrorists, and militiamen have
all used telecommunication and broadcasting techniques
to promote propaganda.[57][58] Patriotic propaganda for
political movements and colonization started the mid1930s. In 1936, the BBC broadcast propaganda to the
Arab World to partly counter similar broadcasts from
Italy, which also had colonial interests in North Africa.[57]
Modern insurgents, such as those in the latest Iraq war,
often use intimidating telephone calls, SMSs and the distribution of sophisticated videos of an attack on coalition troops within hours of the operation. The Sunni
insurgents even have their own television station, AlZawraa, which while banned by the Iraqi government,
still broadcasts from Erbil, Iraqi Kurdistan, even as coalition pressure has forced it to switch satellite hosts several
times.[58]
On 10 November 2014, President Obama recommended
the Federal Communications Commission reclassify
broadband Internet service as a telecommunications service in order to preserve net neutrality.[59][60]

46.6 Modern media

46.6.1 Worldwide equipment sales
According to data collected by Gartner[61][62] and Ars
Technica[63] sales of main consumers telecommunication
equipment worldwide in millions of units was:

46.6.2 Telephone
In a telephone network, the caller is connected to the person they want to talk to by switches at various telephone
exchanges. The switches form an electrical connection
between the two users and the setting of these switches
is determined electronically when the caller dials the
number. Once the connection is made, the callers
voice is transformed to an electrical signal using a small
microphone in the callers handset. This electrical signal
is then sent through the network to the user at the other
end where it is transformed back into sound by a small
speaker in that persons handset.
The landline telephones in most residential homes are
analogthat is, the speakers voice directly determines
the signals voltage. Although short-distance calls may be
handled from end-to-end as analog signals, increasingly
telephone service providers are transparently converting
the signals to digital signals for transmission. The advantage of this is that digitized voice data can travel sideby-side with data from the Internet and can be perfectly
reproduced in long distance communication (as opposed
to analog signals that are inevitably impacted by noise).

258

CHAPTER 46. TELECOMMUNICATION

dled together in a single cable.[68] Lastly, improvements
in multiplexing have led to an exponential growth in the
data capacity of a single bre.[69][70]
Assisting communication across many modern optic bre networks is a protocol known as Asynchronous Transfer Mode (ATM). The ATM protocol allows for the sideby-side data transmission mentioned in the second paragraph. It is suitable for public telephone networks because it establishes a pathway for data through the network and associates a trac contract with that pathway.
The trac contract is essentially an agreement between
the client and the network about how the network is to
handle the data; if the network cannot meet the conditions
of the trac contract it does not accept the connection.
This is important because telephone calls can negotiate a
contract so as to guarantee themselves a constant bit rate,
something that will ensure a callers voice is not delayed
in parts or cut o completely.[71] There are competitors
to ATM, such as Multiprotocol Label Switching (MPLS),
that perform a similar task and are expected to supplant
ATM in the future.[72][73]

46.6.3 Radio and television

Main articles: Radio, Television, and Broadcasting
In a broadcast system, the central high-powered
Optical ber provides cheaper bandwidth for long distance communication.

Mobile phones have had a signicant impact on telephone

networks. Mobile phone subscriptions now outnumber
xed-line subscriptions in many markets. Sales of mobile phones in 2005 totalled 816.6 million with that gure being almost equally shared amongst the markets of
Asia/Pacic (204 m), Western Europe (164 m), CEMEA
(Central Europe, the Middle East and Africa) (153.5 m),
North America (148 m) and Latin America (102 m).[64]
In terms of new subscriptions over the ve years from
1999, Africa has outpaced other markets with 58.2%
growth.[65] Increasingly these phones are being serviced
by systems where the voice content is transmitted digitally
such as GSM or W-CDMA with many markets choosing
to depreciate analog systems such as AMPS.[66]
There have also been dramatic changes in telephone communication behind the scenes. Starting with the operation
of TAT-8 in 1988, the 1990s saw the widespread adoption
of systems based on optical bers. The benet of communicating with optic bers is that they oer a drastic
increase in data capacity. TAT-8 itself was able to carry
10 times as many telephone calls as the last copper cable
laid at that time and todays optic bre cables are able to
carry 25 times as many telephone calls as TAT-8.[67] This
increase in data capacity is due to several factors: First,
optic bres are physically much smaller than competing
technologies. Second, they do not suer from crosstalk
which means several hundred of them can be easily bun-

DVB-T
ATSC
ISDB-T
DTMB

Digital television standards and their adoption worldwide

broadcast
tower
transmits
a
high-frequency
electromagnetic wave to numerous low-powered receivers. The high-frequency wave sent by the tower
is modulated with a signal containing visual or audio
information. The receiver is then tuned so as to pick up
the high-frequency wave and a demodulator is used to
retrieve the signal containing the visual or audio information. The broadcast signal can be either analog (signal
is varied continuously with respect to the information)
or digital (information is encoded as a set of discrete
values).[36][74]
The broadcast media industry is at a critical turning point
in its development, with many countries moving from
analog to digital broadcasts. This move is made possible by the production of cheaper, faster and more capable integrated circuits. The chief advantage of digital
broadcasts is that they prevent a number of complaints
common to traditional analog broadcasts. For television,

46.6. MODERN MEDIA

259

In digital television broadcasting, there are three competing standards that are likely to be adopted worldwide.
These are the ATSC, DVB and ISDB standards; the adoption of these standards thus far is presented in the captioned map. All three standards use MPEG-2 for video
compression. ATSC uses Dolby Digital AC-3 for audio compression, ISDB uses Advanced Audio Coding
(MPEG-2 Part 7) and DVB has no standard for audio
compression but typically uses MPEG-1 Part 3 Layer
2.[77][78] The choice of modulation also varies between
the schemes. In digital audio broadcasting, standards are
much more unied with practically all countries choosing
to adopt the Digital Audio Broadcasting standard (also
known as the Eureka 147 standard). The exception is the
United States which has chosen to adopt HD Radio. HD
Radio, unlike Eureka 147, is based upon a transmission
method known as in-band on-channel transmission that
allows digital information to piggyback on normal AM
or FM analog transmissions.[79]

Media Layers

Host Layers

this includes the elimination of problems such as snowy an amplitude modulated subcarrier is used for stereo FM.
pictures, ghosting and other distortion. These occur because of the nature of analog transmission, which means
that perturbations due to noise will be evident in the nal 46.6.4 Internet
output. Digital transmission overcomes this problem because digital signals are reduced to discrete values upon
data unit
layers
reception and hence small perturbations do not aect the
Application
nal output. In a simplied example, if a binary message
Data
Network Process to Application
1011 was transmitted with signal amplitudes [1.0 0.0 1.0
1.0] and received with signal amplitudes [0.9 0.2 1.1 0.9]
Presentation
Data
Data Representation
it would still decode to the binary message 1011 a perand Encryption
fect reproduction of what was sent. From this example,
Session
a problem with digital transmissions can also be seen in
Data
Interhost Communication
that if the noise is great enough it can signicantly alter
Transport
the decoded message. Using forward error correction a
Segments
End-to-End Connections
receiver can correct a handful of bit errors in the resulting
and Reliability
message but too much noise will lead to incomprehensible
output and hence a breakdown of the transmission.[75][76]
Network
Packets

Path Determination and

Logical Addressing (IP)

Frames

Physical Addressing
(MAC and LLC)

Bits

Media, Signal and

Binary Transmission

Data Link
Physical

The OSI reference model

The Internet is a worldwide network of computers and

computer networks that communicate with each other using the Internet Protocol.[83] Any computer on the Internet has a unique IP address that can be used by other computers to route information to it. Hence, any computer on
the Internet can send a message to any other computer using its IP address. These messages carry with them the
originating computers IP address allowing for two-way
communication. The Internet is thus an exchange of mes[84]
However, despite the pending switch to digital, analog sages between computers.
television remains being transmitted in most countries. It is estimated that the 51% of the information owAn exception is the United States that ended analog tele- ing through two-way telecommunications networks in the
vision transmission (by all but the very low-power TV year 2000 were owing through the Internet (most of
stations) on 12 June 2009[80] after twice delaying the the rest (42%) through the landline telephone). By the
switchover deadline,Kenya also ended analog television year 2007 the Internet clearly dominated and captured
transmission in December 2014 after multiple delays. 97% of all the information in telecommunication netFor analog television, there are three standards in use works (most of the rest (2%) through mobile phones).[85]
for broadcasting color TV (see a map on adoption here). As of 2008, an estimated 21.9% of the world populaThese are known as PAL (German designed), NTSC tion has access to the Internet with the highest access
(North American designed), and SECAM (French de- rates (measured as a percentage of the population) in
signed). (It is important to understand that these are the North America (73.6%), Oceania/Australia (59.5%) and
ways of sending color TV, and they do not have anything Europe (48.1%).[86] In terms of broadband access, Iceto do with the standards for black & white TV, which land (26.7%), South Korea (25.4%) and the Netherlands
also vary from country to country.) For analog radio, the (25.3%) led the world.[87]
switch to digital radio is made more dicult by the fact
that analog receivers are sold at a small fraction of the The Internet works in part because of protocols that govprice of digital receivers.[81][82] The choice of modulation ern how the computers and routers communicate with
for analog radio is typically between amplitude (AM) or each other. The nature of computer network communifrequency modulation (FM). To achieve stereo playback, cation lends itself to a layered approach where individual
protocols in the protocol stack run more-or-less indepen-

260
dently of other protocols. This allows lower-level protocols to be customized for the network situation while
not changing the way higher-level protocols operate. A
practical example of why this is important is because it
allows an Internet browser to run the same code regardless of whether the computer it is running on is connected
to the Internet through an Ethernet or Wi-Fi connection.
Protocols are often talked about in terms of their place
in the OSI reference model (pictured on the right), which
emerged in 1983 as the rst step in an unsuccessful attempt to build a universally adopted networking protocol
suite.[88]

CHAPTER 46. TELECOMMUNICATION

ternet chat), BitTorrent (le sharing) and XMPP (instant
messaging).
Voice over Internet Protocol (VoIP) allows data packets to be used for synchronous voice communications.
The data packets are marked as voice type packets and
can be prioritized by the network administrators so that
the real-time, synchronous conversation is less subject to
contention with other types of data trac which can be
delayed (i.e. le transfer or email) or buered in advance
(i.e. audio and video) without detriment. That prioritization is ne when the network has sucient capacity for all
the VoIP calls taking place at the same time and the network is enabled for prioritization i.e. a private corporate
style network, but the Internet is not generally managed
in this way and so there can be a big dierence in the
quality of VoIP calls over a private network and over the
public Internet.[92]

For the Internet, the physical medium and data link protocol can vary several times as packets traverse the globe.
This is because the Internet places no constraints on what
physical medium or data link protocol is used. This leads
to the adoption of media and protocols that best suit the
local network situation. In practice, most intercontinental communication will use the Asynchronous Transfer
Mode (ATM) protocol (or a modern equivalent) on top 46.6.5 Local area networks and wide area
of optic ber. This is because for most intercontinental
networks
communication the Internet shares the same infrastructure as the public switched telephone network.
Despite the growth of the Internet, the characteristics
At the network layer, things become standardized with of local area networks (LANs)--computer networks that
the Internet Protocol (IP) being adopted for logical ad- do not extend beyond a few kilometersremain distinct.
dressing. For the World Wide Web, these IP addresses This is because networks on this scale do not require all
are derived from the human readable form using the the features associated with larger networks and are ofDomain Name System (e.g. 72.14.207.99 is derived from ten more cost-eective and ecient without them. When
www.google.com). At the moment, the most widely used they are not connected with the Internet, they also have
version of the Internet Protocol is version four but a move the advantages of privacy and security. However, purto version six is imminent.[89]
posefully lacking a direct connection to the Internet does
At the transport layer, most communication adopts ei- not provide assured protection from hackers, military
ther the Transmission Control Protocol (TCP) or the User forces, or economic powers. These threats exist if there
Datagram Protocol (UDP). TCP is used when it is es- are any methods for connecting remotely to the LAN.
sential every message sent is received by the other computer whereas UDP is used when it is merely desirable.
With TCP, packets are retransmitted if they are lost and
placed in order before they are presented to higher layers.
With UDP, packets are not ordered or retransmitted if
lost. Both TCP and UDP packets carry port numbers with
them to specify what application or process the packet
should be handled by.[90] Because certain applicationlevel protocols use certain ports, network administrators
can manipulate trac to suit particular requirements. Examples are to restrict Internet access by blocking the trafc destined for a particular port or to aect the performance of certain applications by assigning priority.

Wide area networks (WANs) are private computer networks that may extend for thousands of kilometers. Once
again, some of their advantages include privacy and security. Prime users of private LANs and WANs include
armed forces and intelligence agencies that must keep
their information secure and secret.

In the mid-1980s, several sets of communication protocols emerged to ll the gaps between the data-link layer
and the application layer of the OSI reference model.
These included Appletalk, IPX, and NetBIOS with the
dominant protocol set during the early 1990s being IPX
due to its popularity with MS-DOS users. TCP/IP existed at this point, but it was typically only used by large
Above the transport layer, there are certain protocols government and research facilities.[93]
that are sometimes used and loosely t in the session
As the Internet grew in popularity and its trac was reand presentation layers, most notably the Secure Sockquired to be routed into private networks, the TCP/IP
ets Layer (SSL) and Transport Layer Security (TLS) proprotocols replaced existing local area network technolotocols. These protocols ensure that data transferred begies. Additional technologies, such as DHCP, allowed
[91]
tween two parties remains completely condential. FiTCP/IP-based computers to self-congure in the netnally, at the application layer, are many of the protocols
work. Such functions also existed in the AppleTalk/ IPX/
Internet users would be familiar with such as HTTP (web
NetBIOS protocol sets.[94]
browsing), POP3 (e-mail), FTP (le transfer), IRC (InWhereas Asynchronous Transfer Mode (ATM) or Multi-

46.9. REFERENCES
protocol Label Switching (MPLS) are typical data-link
protocols for larger networks such as WANs; Ethernet and Token Ring are typical data-link protocols for
LANs. These protocols dier from the former protocols
in that they are simpler, e.g., they omit features such as
quality of service guarantees, and oer collision prevention. Both of these dierences allow for more economical
systems.[95]

261
Outline of telecommunication
Push-button telephone
Telecommunications Industry Association
Telecoms resilience
Wavelength-division multiplexing

Wired communication
Despite the modest popularity of IBM Token Ring in
the 1980s and 1990s, virtually all LANs now use either
wired or wireless Ethernet facilities. At the physical layer,
most wired Ethernet implementations use copper twisted- 46.9 References
pair cables (including the common 10BASE-T networks).
However, some early implementations used heavier coax46.9.1 Citations
ial cables and some recent implementations (especially
high-speed ones) use optical bers.[96] When optic bers [1] Article 1.3 (PDF), ITU Radio Regulations, International
are used, the distinction must be made between multiTelecommunication Union, 2012
mode bers and single-mode bers. Multimode bers can
be thought of as thicker optical bers that are cheaper to [2] Constitution and Convention of the International
Telecommunication Union, Annex (Geneva, 1992)
manufacture devices for, but that suers from less usable
bandwidth and worse attenuation implying poorer long- [3] Denition of telecommunication. Yahoo. Retrieved 28
distance performance.[97]
February 2013.

46.7 Transmission capacity

The eective capacity to exchange information worldwide through two-way telecommunication networks grew
from 281 petabytes of (optimally compressed) information in 1986, to 471 petabytes in 1993, to 2.2 (optimally compressed) exabytes in 2000, and to 65 (optimally
compressed) exabytes in 2007.[85] This is the informational equivalent of two newspaper pages per person per
day in 1986, and six entire newspapers per person per
day by 2007.[98] Given this growth, telecommunications
play an increasingly important role in the world economy
and the global telecommunications industry was about a
$4.7 trillion sector in 2012.[42][99] The service revenue of
the global telecommunications industry was estimated to
be $1.5 trillion in 2010, corresponding to 2.4% of the
worlds gross domestic product (GDP).[42]

46.8 See also

Active networks
Busy override
Digital Revolution
Dual-tone multi-frequency signaling
Information Age
List of telecommunications encryption terms
Nanonetwork
New media

[4] Telecommunication. Collins English Dictionary. Retrieved 28 February 2013.

[5] Telecommunication. Vocabulary.com. Retrieved 28
February 2013.
[6] Telecommunication. Merriam-Webster Dictionary. Retrieved 28 February 2013.
[7] Telecommunication. Oxford Dictionaries. Oxford University Press. Retrieved 28 February 2013.
[8] Telecommunication.
February 2013.

Dictionary.com.

Retrieved 28

[9] Websters denition: 2) technology that deals with

telecommunication usually used in plural"; Concise Encyclopedia denition: Communication n parties at a distance from one another...."; and the Online Etymology
Dictionary: telecommunication (n.) 1932, from French
tlcommunication (see tele- + communication)."; and: "
1930s: from French tlcommunication, from tl- 'at a
distance' + communication 'communication' ", Oxford online.
[10] Jean-Marie Dilhac, From tele-communicare to Telecommunications, 2004.
[11] Telecommunication, tele- and communication, New Oxford American Dictionary (2nd edition), 2005.
[12] http://www.etymonline.com/index.php?term=tele-&
allowed_in_frame=0
[13] http://www.etymonline.com/index.php?term=
communication&allowed_in_frame=0
[14] David Ross, The Spanish Armada, Britain Express, accessed October 2007.
[15] Les Tlgraphes Chappe, Cdrick Chatenet, l'Ecole Centrale de Lyon, 2003.

262

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[16] CCIT/ITU-T 50 Years of Excellence, International

Telecommunication Union, 2006.
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[18] Blechman, Andrew (2007). Pigeons-The fascinating saga
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[19] Chronology: Reuters, from pigeons to multimedia
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[22] The Atlantic Cable, Bern Dibner, Burndy Library Inc.,
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[23] Elisha Gray, Oberlin College Archives, Electronic Oberlin
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[25] Connected Earth: The telephone, BT, 2006.
[26] History of AT&T, AT&T, 2006.
[27] James Bowman Lindsay, Macdonald Black, Dundee City
Council, 1999.
[28] Tesla Biography, Ljubo Vujovic, Tesla Memorial Society
of New York, 1998.
[29] Teslas Radio Controlled Boat, Twenty First Century
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[38] ATIS Telecom Glossary 2000, ATIS Committee T1A1

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[39] Haykin, pp 344403.
[40] Bluetooth Specication Version 2.0 + EDR (p 27), Bluetooth, 2004.
[41] Haykin, pp 88126.
[42] Worldwide Telecommunications Industry Revenues, Internet Engineering Task Force, June 2010.
[43] Lenert, Edward (December 1998). A Communication Theory Perspective on Telecommunications Policy. Journal of Communication. 48 (4): 323.
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[44] Mireille Samaan (April 2003). The Eect of Income Inequality on Mobile Phone Penetration. Boston University Honors thesis. Archived from the original (PDF) on
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[45] Rller, Lars-Hendrik; Leonard Waverman (2001).
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[46] Qiang, Rossotto, 2009, Economic Impact of Broadband,
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[47] Riaz, Ali (1997). The role of telecommunications in economic growth: proposal for an alternative framework of
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[30] The Pioneers, MZTV Museum of Television, 2006.

[31] Philo Farnsworth, Neil Postman, TIME Magazine, 29
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[32] George Stlibetz, Kerry Redshaw, 1996.
[33] Hafner, Katie (1998). Where Wizards Stay Up Late: The
Origins Of The Internet. Simon & Schuster. ISBN 0-68483267-4.
[34] Data transmission system,
4,293,948, October 1974.

Olof Solderblom,

PN

[35] Ethernet: Distributed Packet Switching for Local Computer Networks, Robert M. Metcalfe and David R. Boggs,
Communications of the ACM (pp 395-404, Vol. 19, No.
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[36] Haykin, Simon (2001). Communication Systems (4th ed.).
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[37] Ambardar, Ashok (1999). Analog and Digital Signal Processing (2nd ed.). Brooks/Cole Publishing Company. pp.
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[49] World Telecommunication Development Report 2003,

International Telecommunication Union, 2003.
[50] Fischer, Claude S. "'Touch Someone': The Telephone
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[51] How do you know your love is real? Check Facebook.
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[52] I Just Text To Say I Love You, Ipsos MORI, September
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[53] Online News: For many home broadband users, the internet is a primary news source (PDF). Pew Internet
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[54] 100 Leading National Advertisers (PDF). Advertising
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[55] International Telecommunication Union : About ITU.
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[57] Wood, James & Science Museum (Great Britain) "History
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Republished by Googlebooks. Accessed 21 July 2009.
[58] Gareld, Andrew. "The U.S. Counter-propaganda Failure
in Iraq", FALL 2007, The Middle East Quarterly, Volume
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[59] Wyatt, Edward (10 November 2014). Obama Asks
F.C.C. to Adopt Tough Net Neutrality Rules. New York
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[60] NYT Editorial Board (14 November 2014). Why the
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[61] Computer sales review, guardian.co.uk, 2009.
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[78] Audio, Digital Video Broadcasting Project, 2003.
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[80] Brian Stelter (13 June 2009). Changeover to Digital TV
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[81] GE 72664 Portable AM/FM Radio, Amazon.com, June
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[82] DAB Products, World DAB Forum, 2006.
[83] Robert E. Kahn and Vinton G. Cerf, What Is The Internet
(And What Makes It Work), December 1999. (specically see footnote xv)
[84] How Internet Infrastructure Works, HowStuWorks.com,
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[85] The Worlds Technological Capacity to Store, Communicate, and Compute Information, Martin Hilbert
and Priscila Lpez (2011), Science, 332(6025), 6065;
free access to the study through here: martinhilbert.net/
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[63] PC early history, arstechnica.com, 2005.

[64] Gartner Says Top Six Vendors Drive Worldwide Mobile
Phone Sales to 21% Growth in 2005, Gartner Group, 28
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[65] Africa Calling, Victor and Irene Mbarika, IEEE Spectrum, May 2006.
[66] Ten Years of GSM in Australia, Australia Telecommunications Association, 2003.
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[86] World Internet Users and Population Stats, internetworldstats.com, 19 March 2007.
[87] OECD Broadband Statistics, Organisation for Economic
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[88] History of the OSI Reference Model, The TCP/IP Guide
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[89] Introduction to IPv6, Microsoft Corporation, February
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[68] Optical bre waveguide, Saleem Bhatti, 1995.

[90] Stallings, pp 683702.

[69] Fundamentals of DWDM Technology, CISCO Systems,

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[91] T. Dierks and C. Allen, The TLS Protocol Version 1.0,

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[70] Report: DWDM No Match for Sonet, Mary Jander, Light

Reading, 2006.

[92] Multimedia, Crucible (2011-05-07). VoIP, Voice over

Internet Protocol and Internet telephone calls.

[71] Stallings, William (2004). Data and Computer Communications (7th edition (intl) ed.). Pearson Prentice Hall. pp.
337366. ISBN 0-13-183311-1.
[72] MPLS is the future, but ATM hangs on, John Dix, Network World, 2002

[93] Martin, Michael (2000). Understanding the Network (The

Networkers Guide to AppleTalk, IPX, and NetBIOS),
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[94] Ralph Droms, Resources for DHCP, November 2003.

[73] Lazar, Irwin (22 February 2011). The WAN Road

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[95] Stallings, pp. 500526.

[74] How Radio Works, HowStuWorks.com, 2006.

[97] Fiber Optic Cable Tutorial, Arc Electronics. Retrieved

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[75] Digital Television in Australia, Digital Television News

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[76] Stallings, William (2004). Data and Computer Communications (7th edition (intl) ed.). Pearson Prentice Hall.
ISBN 0-13-183311-1.

[96] Stallings, pp 514516.

[98] video animation The Economist.

[99] Introduction to the Telecommunications Industry, Internet
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264

46.9.2

CHAPTER 46. TELECOMMUNICATION

Bibliography

Goggin, Gerard, Global Mobile Media (New York:

Routledge, 2011), p. 176. ISBN 978-0415469180.
Haring, John (2008). Telecommunications. In
David R. Henderson (ed.). Concise Encyclopedia
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46.10 External links

International Telecommunication Union (ITU)
ATIS Telecom Glossary
Federal Communications Commission
IEEE Communications Society
International Telecommunication Union
Ericssons Understanding Telecommunications at
the Wayback Machine (archived 13 April 2004) (Ericsson removed the book from their site in September 2005)

Chapter 47

Waveform
For other uses, see Waveform (disambiguation).
A waveform is the shape and form of a signal such as a

is aected by both the input signal and conditions under

which it is recorded.[1]
A periodic waveforms include these while t is time, is
wavelength, a is amplitude and is phase:

Sine

Sine wave (t, , a, ) = a sin 2t

. The ampli
tude of the waveform follows a trigonometric sine
function with respect to time.

Square

Square
wave
(t, , a, )
=
{
a,
(t )mod < duty
. This waveform is
a, otherwise
commonly used to represent digital information.
A square wave of constant period contains odd
harmonics that decrease at 6 dB/octave.

Triangle

Sawtooth

2t
Triangle wave (t, , a, ) = 2a
arcsin sin

. It contains odd harmonics that decrease at 12

dB/octave.

Sine, square, triangle, and sawtooth waveforms

2t
Sawtooth wave (t, , a, ) = 2a
arctan tan 2
. This looks like the teeth of a saw. Found often in time bases for display scanning. It is used as
the starting point for subtractive synthesis, as a sawtooth wave of constant period contains odd and even
harmonics that decrease at 6 dB/octave.

wave moving in a physical medium or an abstract representation.

In many cases the medium in which the wave propagates

does not permit a direct observation of the true form. In
these cases, the term waveform refers to the shape of a
graph of the varying quantity against time. An instrument
called an oscilloscope can be used to pictorially represent Other waveforms are often called composite waveforms
a wave as a repeating image on a screen.
and can often be described as a combination of a numTo be more specic, a waveform is depicted by a graph ber of sinusoidal waves or other basis functions added tothat shows the changes in a recorded signals amplitude gether.
over the duration of recording.[1] The amplitude of the The Fourier series describes the decomposition of pesignal is measured on the y -axis (vertical), and time on riodic waveforms, such that any periodic waveform can
the x -axis (horizontal).[1]
be formed by the sum of a (possibly innite) set of fundamental and harmonic components. Finite-energy nonperiodic waveforms can be analyzed into sinusoids by the
Fourier transform.

47.1 Examples of waveforms

Most programs show waveforms to give the user a visual
aid of what has been recorded. If the waveform is of low
or high height (with respect to the x axis), the recording was most likely conducted under conditions with a
low or high input volume, respectively. From this example, it follows that the curve represented by the waveform

47.2 See also

265

AC waveform
Arbitrary waveform generator

266
Spectrum analyzer
Waveform monitor
Waveform viewer
Wave packet

47.3 References
Yuchuan Wei, Qishan Zhang. Common Waveform
Analysis: A New And Practical Generalization of
Fourier Analysis. Springer US, Aug 31, 2000
Waveform Denition
[1] Waveform Denition. techterms.com. Retrieved 201512-09.

47.4 Further reading

Hao He, Jian Li, and Petre Stoica. Waveform design for active sensing systems: a computational approach. Cambridge University Press, 2012.
Solomon W. Golomb, and Guang Gong. Signal design for good correlation: for wireless communication, cryptography, and radar. Cambridge University Press, 2005.
Jayant, Nuggehally S and Noll, Peter. Digital coding
of waveforms: principles and applications to speech
and video. Englewood Clis, NJ, 1984.
M. Soltanalian. Signal Design for Active Sensing
and Communications. Uppsala Dissertations from
the Faculty of Science and Technology (printed by
Elanders Sverige AB), 2014.
Nadav Levanon, and Eli Mozeson. Radar signals.
Wiley. com, 2004.
Jian Li, and Petre Stoica, eds. Robust adaptive
beamforming. New Jersey: John Wiley, 2006.
Fulvio Gini, Antonio De Maio, and Lee Patton, eds.
Waveform design and diversity for advanced radar
systems. Institution of engineering and technology,
2012.
John J. Benedetto, Ioannis Konstantinidis, and Muralidhar Rangaswamy. "Phase-coded waveforms
and their design. IEEE Signal Processing Magazine,
26.1 (2009): 22-31.

47.5 External links

Collection of single cycle waveforms sampled from
various sources

CHAPTER 47. WAVEFORM

Chapter 48

Analog signal
For a broader coverage related to this topic, see Signal additional noise or distortion. In analog systems, it is dif(electronics).
cult to detect when such degradation occurs. However,
in digital systems, degradation can not only be detected
An analog signal is any continuous signal for which the but corrected as well.
time varying feature (variable) of the signal is a representation of some other time varying quantity, i.e., analogous
to another time varying signal. For example, in an analog
audio signal, the instantaneous voltage of the signal varies
continuously with the pressure of the sound waves. It differs from a digital signal, in which the continuous quantity
is a representation of a sequence of discrete values which
can only take on one of a nite number of values.[1][2] The
term analog signal usually refers to electrical signals; however, mechanical, pneumatic, hydraulic, human speech,
and other systems may also convey or be considered analog signals.
An analog signal uses some property of the medium to
convey the signals information. For example, an aneroid
barometer uses rotary position as the signal to convey
pressure information. In an electrical signal, the voltage,
current, or frequency of the signal may be varied to represent the information.
Any information may be conveyed by an analog signal;
often such a signal is a measured response to changes in
physical phenomena, such as sound, light, temperature,
position, or pressure. The physical variable is converted
to an analog signal by a transducer. For example, in
sound recording, uctuations in air pressure (that is to say,
sound) strike the diaphragm of a microphone which induces corresponding uctuations in the current produced
by a coil in an electromagnetic microphone, or the voltage produced by a condenser microphone. The voltage or
the current is said to be an analog of the sound.

48.1 Advantages
tages

and

disadvan-

The primary disadvantage of analog signals is that any

system has noise i.e., unwanted variation. As the signal is copied and re-copied, or transmitted over long distances, or electronically processed, the unavoidable noise
introduced by each step in the signal path is additive,
progressively degrading the signal-to-noise ratio, until in
extreme cases the signal can be overwhelmed. This is
called generation loss. Noise can show up as hiss and
intermodulation distortion in audio signals, or snow in
video signals. This degradation is impossible to recover,
since there is no sure way to distinguish the noise from the
signal; amplifying the signal to recover attenuated parts of
the signal amplies the noise (distortion/interference) as
well. Digital signals can often be transmitted, stored and
processed without introducing noise. Electrically, analog
noise can be diminished by shielding, good connections
and several cable types such as coaxial or twisted pair.

48.2 See also

An analog signal has a theoretically innite resolution. In

practice an analog signal is subject to electronic noise and
distortion introduced by communication channels and
signal processing operations, which can progressively degrade the signal-to-noise ratio (SNR). In contrast, digital
signals have a nite resolution. Converting an analog signal to digital form introduces a constant low-level noise
called quantization noise into the signal which determines
the noise oor, but once in digital form the signal can in
general be processed or transmitted without introducing

267

Ampex
Analog audio
Analog device
Analog signal processing
Analog sound vs. digital sound
Analog video
Analog-to-digital converter
Digital audio
Digital video

268
Magnetic tape
Magnetic recording
Video tape

48.3 References
[1] Digital signals.
[2] Analog vs. Digital.

CHAPTER 48. ANALOG SIGNAL

Chapter 49

Baseband
49.1.2 Baseband channel

A baseband channel or lowpass channel (or system, or

network) is a communication channel that can transfer
frequencies that are very near zero.[4] Examples are serial cables and local area networks (LANs), as opposed to
passband channels such as radio frequency channels and
passband ltered wires of the analog telephone network.
Frequency division multiplexing (FDM) allows an analog
telephone wire to carry a baseband telephone call, concurrently as one or several carrier-modulated telephone
calls.

49.1.3 Digital baseband transmission

Spectrum of a baseband signal, energy E per unit frequency as
a function of frequency f. The total energy is the area under the
line.

Baseband is a signal that has a very narrow frequency

range, i.e. a spectral magnitude that is nonzero only for
frequencies in the vicinity of the origin (termed f = 0)
and negligible elsewhere.[1] In telecommunications and
signal processing, baseband signals are transmitted without modulation, that is, without any shift in the range
of frequencies of the signal,[2] and are low frequency contained within the band of frequencies from close to
0 hertz up to a higher cut-o frequency or maximum
bandwidth. Baseband can be synonymous with lowpass
or non-modulated, and is dierentiated from passband,
bandpass, carrier-modulated, intermediate frequency, or
radio frequency (RF).

49.1 Various uses

49.1.1

Main article: Line code

Digital baseband transmission, also known as line coding,[5] aims at transferring a digital bit stream over baseband channel, typically an unltered wire, contrary to
passband transmission, also known as carrier-modulated
transmission.[6] Passband transmission makes communication possible over a bandpass ltered channel, such as
the telephone network local-loop or a band-limited wireless channel.

Baseband transmission in Ethernet

The word BASE in Ethernet physical layer standards,
for example 10BASE5, 100BASE-TX and 1000BASESX, implies baseband digital transmission (i.e. that a line
code and an unltered wire are used).

49.1.4 Baseband processor

Baseband bandwidth

A baseband bandwidth is equal to the highest frequency

of a signal or system, or an upper bound on such
frequencies,[3] for example the upper cut-o frequency
of a Lowpass lter. By contrast, passband bandwidth is
the dierence between a highest frequency and a nonzero
lowest frequency.

A baseband processor also known as BP or BBP is used

to process the down-converted digital signal to retrieve
essential data for the wireless digital system. The baseband processing block in receivers is usually responsible
for providing observable data: code pseudo-ranges and
carrier phase measurements, as well as navigation data.

269

270

49.1.5

CHAPTER 49. BASEBAND

Baseband signal

Power

A baseband signal or lowpass signal is a signal that can include frequencies that are very near zero, by comparison
with its highest frequency (for example, a sound waveform can be considered as a baseband signal, whereas a
radio signal or any other modulated signal is not).[7]

49.1.6

Equivalent baseband signal

An equivalent baseband signal or equivalent lowpass signal isin analog and digital modulation methods for
(band-pass) signals with constant or varying carrier frequency (for example ASK, PSK QAM, and FSK)a
complex valued representation of the modulated physical
signal (the so-called passband signal or RF signal). The
equivalent baseband signal is Z(t) = I(t)+jQ(t) where
I(t) is the inphase signal, Q(t) the quadrature phase signal, and j the imaginary unit. In a digital modulation
method, the I(t) and Q(t) signals of each modulation
symbol are evident from the constellation diagram. The
frequency spectrum of this signal includes negative as
well as positive frequencies. The physical passband signal
corresponds to

I(t) cos(t) Q(t) sin(t) = Re{Z(t)ejt }

[8]

where is the carrier angular frequency in rad/s.

49.2 Modulation
A signal at baseband is often used to modulate a higher
frequency carrier signal in order that it may be transmitted via radio. Modulation results in shifting the signal up to much higher frequencies (radio frequencies, or
RF) than it originally spanned. A key consequence of
the usual double-sideband amplitude modulation (AM) is
that the range of frequencies the signal spans (its spectral
bandwidth) is doubled. Thus, the RF bandwidth of a signal (measured from the lowest frequency as opposed to 0
Hz) is twice its baseband bandwidth. Steps may be taken
to reduce this eect, such as single-sideband modulation.
Some transmission schemes such as frequency modulation use even more bandwidth.
The gure shows what happens with AM modulation:

49.3 See also

Complex envelope
Broadband
Narrowband
Wideband

Signal at baseband

frequency

Signal at RF (radio frequency)

Comparison of the equivalent baseband version of a signal and

its AM-modulated (double-sideband) RF version, showing the
typical doubling of the occupied bandwidth.

49.4 References
[1] Leon W. Couch II (1993). Digital and Analog Communication Systems. Prentice Hall.
[2] B.P. Lathi (1983). Modern Digital and Analog Communication Systems. Holt, Rinehart and Winston.
[3] Mischa Schwartz (1970). Information, Transmission,
Modulation and Noise: A Unied Approach to Communication Systems. McGraw-Hill.
[4] Chris C. Bissell and David A. Chapman (1992). Digital
Signal Transmission. Cambridge University Press. ISBN
0-521-42557-3.
[5] Mikael Gustavsson and J. Jacob Wikner (2000). CMOS
Data Converters for Communications. Springer. ISBN 07923-7780-X.
[6] Jan W. M. Bergmans (1996). Digital Baseband Transmission and Recording. Springer. ISBN 0-7923-9775-4.
[7] Steven Alan Tretter (1995). Communication System Design Using Dsp Algorithms: With Laboratory Experiments
for the TMS320C30. Springer. ISBN 0-306-45032-1.
[8] Proakis, John G. Digital Communications, 4th edition.
McGraw-Hill, 2001. p150

Chapter 50

Demodulation
Demodulation is extracting the original informationbearing signal from a modulated carrier wave. A demodulator is an electronic circuit (or computer program in a
software-dened radio) that is used to recover the information content from the modulated carrier wave.[1] There
are many types of modulation so there are many types
of demodulators. The signal output from a demodulator
may represent sound (an analog audio signal), images (an
analog video signal) or binary data (a digital signal).
These terms are traditionally used in connection with
radio receivers, but many other systems use many kinds
of demodulators. For example, in a modem, which is a
contraction of the terms modulator/demodulator, a demodulator is used to extract a serial digital data stream
from a carrier signal which is used to carry it through a
telephone line, coaxial cable, or optical ber.

brose Fleming invented the Fleming valve or thermionic

diode which could also rectify an AM signal.

50.2 Techniques
There are several ways of demodulation depending on
how parameters of the base-band signal such as amplitude, frequency or phase are transmitted in the carrier
signal. For example, for a signal modulated with a linear modulation like AM (amplitude modulation), we can
use a synchronous detector. On the other hand, for a
signal modulated with an angular modulation, we must
use an FM (frequency modulation) demodulator or a PM
(phase modulation) demodulator. Dierent kinds of circuits perform these functions.

Many techniques such as carrier recovery, clock recovery, bit slip, frame synchronization, rake receiver, pulse
compression, Received Signal Strength Indication, error
50.1 History
detection and correction, etc., are only performed by deDemodulation was rst used in radio receivers. In the modulators, although any specic demodulator may perwireless telegraphy radio systems used during the rst form only some or none of these techniques.
3 decades of radio (1884-1914) the transmitter did not Many things can act as a demodulator, if they pass the
communicate audio (sound) but transmitted information radio waves on nonlinearly. For example, near a powerful
in the form of pulses of radio waves that represented text radio station, it has been known for the metal sides of a
messages in Morse code. Therefore, the receiver merely van to demodulate the radio signal as sound.
had to detect the presence or absence of the radio signal, and produce a click sound. The device that did this
was called a detector. The rst detectors were coherers, 50.3 AM radio
simple devices that acted as a switch. The term detector
stuck, was used for other types of demodulators and conAn AM signal encodes the information onto the carrier
tinues to be used to the present day for a demodulator in
wave by varying its amplitude in direct sympathy with the
a radio receiver.
analogue signal to be sent. There are two methods used
The rst type of modulation used to transmit sound over to demodulate AM signals:
radio waves was amplitude modulation (AM), invented
The envelope detector is a very simple method of
by Reginald Fessendon around 1900. An AM radio signal can be demodulated by rectifying it, removing the rademodulation that does not require a coherent dedio frequency pulses on one side of the carrier, convertmodulator. It consists of an envelope detector that
can be a rectier (anything that will pass current in
ing it from alternating current (AC) to a pulsating direct
current (DC). The amplitude of the DC varies with the
one direction only) or other non-linear that enhances
modulating audio signal, so it can drive an earphone. Fesone half of the received signal over the other and a
sendon invented the rst AM demodulator in 1904 called
low-pass lter. The rectier may be in the form of
the electrolytic detector, consisting of a short needle dipa single diode or may be more complex. Many natping into a cup of dilute acid. The same year John Amural substances exhibit this rectication behaviour,
271

272

CHAPTER 50. DEMODULATION

which is why it was the earliest modulation and de- 50.5 PM
modulation technique used in radio. The lter is
usually an RC low-pass type but the lter function Main article: Phase modulation
can sometimes be achieved by relying on the limited frequency response of the circuitry following
the rectier. The crystal set exploits the simplicity
of AM modulation to produce a receiver with very
50.6 QAM
few parts, using the crystal as the rectier and the
limited frequency response of the headphones as the
Main article: QAM Receiver
lter.

The product detector multiplies the incoming sig- QAM demodulation requires a coherent receiver.
nal by the signal of a local oscillator with the same
frequency and phase as the carrier of the incoming
signal. After ltering, the original audio signal will
50.7 See also
result.
SSB is a form of AM in which the carrier is reduced or
suppressed entirely, which require coherent demodulation. For further reading, see sideband.

50.4 FM radio
Frequency modulation (FM) has numerous advantages
over AM such as better delity and noise immunity.
However, it is much more complex to both modulate and
demodulate a carrier wave with FM and AM predates it
by several decades.
There are several common types of FM demodulators:
The quadrature detector, which phase shifts the signal by 90 degrees and multiplies it with the unshifted
version. One of the terms that drops out from this
operation is the original information signal, which is
selected and amplied.
The signal is fed into a PLL and the error signal is
used as the demodulated signal.
The most common is a Foster-Seeley discriminator.
This is composed of an electronic lter which decreases the amplitude of some frequencies relative
to others, followed by an AM demodulator. If the
lter response changes linearly with frequency, the
nal analog output will be proportional to the input
frequency, as desired.
A variant of the Foster-Seeley discriminator called
the ratio detector[2]
Another method uses two AM demodulators, one
tuned to the high end of the band and the other to
the low end, and feed the outputs into a dierence
amplier.
Using a digital signal processor, as used in softwaredened radio.

Detection theory
Detector (radio)
Fax demodulator

50.8 References
[1] Demodulator - Denitions from Dictionary.com. dictionary.reference.com. Retrieved 2008-05-16.
[2] The ratio detector

Chapter 51

Low-pass lter
A low-pass lter is a lter that passes signals with
a frequency lower than a certain cuto frequency and
attenuates signals with frequencies higher than the cuto
frequency. The exact frequency response of the lter depends on the lter design. The lter is sometimes called a
high-cut lter, or treble cut lter in audio applications.
A low-pass lter is the complement of a high-pass lter.
Low-pass lters exist in many dierent forms, including
electronic circuits such as a hiss lter used in audio, antialiasing lters for conditioning signals prior to analogto-digital conversion, digital lters for smoothing sets of
data, acoustic barriers, blurring of images, and so on. The
moving average operation used in elds such as nance
is a particular kind of low-pass lter, and can be analyzed with the same signal processing techniques as are
used for other low-pass lters. Low-pass lters provide a
smoother form of a signal, removing the short-term uctuations, and leaving the longer-term trend.

pass lter (low frequency is long wavelength), to avoid

confusion.

51.1.3 Electronics
In an electronic low-pass RC lter for voltage signals,
high frequencies in the input signal are attenuated, but
the lter has little attenuation below the cuto frequency
determined by its RC time constant. For current signals,
a similar circuit, using a resistor and capacitor in parallel,
works in a similar manner. (See current divider discussed
in more detail below.)

Electronic low-pass lters are used on inputs to

subwoofers and other types of loudspeakers, to block high
pitches that they can't eciently reproduce. Radio transmitters use low-pass lters to block harmonic emissions
that might interfere with other communications. The tone
knob on many electric guitars is a low-pass lter used to
Filter designers will often use the low-pass form as a
reduce the amount of treble in the sound. An integrator
prototype lter. That is, a lter with unity bandwidth and
is another time constant low-pass lter.[1]
impedance. The desired lter is obtained from the prototype by scaling for the desired bandwidth and impedance Telephone lines tted with DSL splitters use low-pass and
and transforming into the desired bandform (that is low- high-pass lters to separate DSL and POTS signals sharing the same pair of wires.[2][3]
pass, high-pass, band-pass or band-stop).

51.1 Examples

Low-pass lters also play a signicant role in the sculpting of sound created by analogue and virtual analogue
synthesisers. See subtractive synthesis.

Examples of low-pass lters occur in acoustics, optics and

electronics.

51.2 Ideal and real lters

51.1.1

Acoustics

A sti physical barrier tends to reect higher sound frequencies, and so acts as a low-pass lter for transmitting
sound. When music is playing in another room, the low
notes are easily heard, while the high notes are attenuated.

51.1.2

Optics

An ideal low-pass lter completely eliminates all frequencies above the cuto frequency while passing those below unchanged; its frequency response is a rectangular
function and is a brick-wall lter. The transition region
present in practical lters does not exist in an ideal lter. An ideal low-pass lter can be realized mathematically (theoretically) by multiplying a signal by the rectangular function in the frequency domain or, equivalently,
convolution with its impulse response, a sinc function, in
the time domain.

An optical lter with the same function can correctly be However, the ideal lter is impossible to realize without
called a low-pass lter, but conventionally is called a long- also having signals of innite extent in time, and so gen273

274

CHAPTER 51. LOW-PASS FILTER

10

sin(x)
x

Cutoff frequency

1.0

0.8

10

3.01 dB

Gain (dB)

0.6
0.4

Slope: 20 dB/decade

20

30

0.2
40

-6

-4

-2

50
Passband

-0.2
60
0.001

0.01

Stopband

0.1

10

100

1000

Angular frequency (rad/s)

The sinc function, the impulse response of an ideal low-pass lter.

erally needs to be approximated for real ongoing signals,

because the sinc functions support region extends to all
past and future times. The lter would therefore need to
have innite delay, or knowledge of the innite future and
past, in order to perform the convolution. It is eectively
realizable for pre-recorded digital signals by assuming extensions of zero into the past and future, or more typically
by making the signal repetitive and using Fourier analysis.
Real lters for real-time applications approximate the
ideal lter by truncating and windowing the innite impulse response to make a nite impulse response; applying that lter requires delaying the signal for a moderate
period of time, allowing the computation to see a little
bit into the future. This delay is manifested as phase shift.
Greater accuracy in approximation requires a longer delay.
An ideal low-pass lter results in ringing artifacts via the
Gibbs phenomenon. These can be reduced or worsened
by choice of windowing function, and the design and
choice of real lters involves understanding and minimizing these artifacts. For example, simple truncation
[of sinc] causes severe ringing artifacts, in signal reconstruction, and to reduce these artifacts one uses window
functions which drop o more smoothly at the edges.[4]
The WhittakerShannon interpolation formula describes
how to use a perfect low-pass lter to reconstruct a
continuous signal from a sampled digital signal. Real
digital-to-analog converters use real lter approximations.

51.3 Continuous-time low-pass lters

There are many dierent types of lter circuits, with different responses to changing frequency. The frequency
response of a lter is generally represented using a Bode
plot, and the lter is characterized by its cuto frequency
and rate of frequency rollo. In all cases, at the cuto

The gain-magnitude frequency response of a rst-order (onepole) low-pass lter. Power gain is shown in decibels (i.e., a 3 dB
decline reects an additional half-power attenuation). Angular
frequency is shown on a logarithmic scale in units of radians per
second.

frequency, the lter attenuates the input power by half or

3 dB. So the order of the lter determines the amount
of additional attenuation for frequencies higher than the
cuto frequency.
A rst-order lter, for example, reduces the signal
amplitude by half (so power reduces by a factor of
4, or 6 dB), every time the frequency doubles (goes
up one octave); more precisely, the power rollo approaches 20 dB per decade in the limit of high frequency. The magnitude Bode plot for a rst-order
lter looks like a horizontal line below the cuto
frequency, and a diagonal line above the cuto frequency. There is also a knee curve at the boundary between the two, which smoothly transitions between the two straight line regions. If the transfer
function of a rst-order low-pass lter has a zero
as well as a pole, the Bode plot attens out again,
at some maximum attenuation of high frequencies;
such an eect is caused for example by a little bit of
the input leaking around the one-pole lter; this onepoleone-zero lter is still a rst-order low-pass. See
Polezero plot and RC circuit.
A second-order lter attenuates high frequencies
more steeply. The Bode plot for this type of lter
resembles that of a rst-order lter, except that it
falls o more quickly. For example, a second-order
Butterworth lter reduces the signal amplitude to
one fourth its original level every time the frequency
doubles (so power decreases by 12 dB per octave,
or 40 dB per decade). Other all-pole second-order
lters may roll o at dierent rates initially depending on their Q factor, but approach the same nal
rate of 12 dB per octave; as with the rst-order lters, zeroes in the transfer function can change the
high-frequency asymptote. See RLC circuit.
Third- and higher-order lters are dened similarly.

51.4. ELECTRONIC LOW-PASS FILTERS

In general, the nal rate of power rollo for an
order- n all-pole lter is 6n dB per octave (i.e., 20n
dB per decade).

275

Vin
R

On any Butterworth lter, if one extends the horizontal

line to the right and the diagonal line to the upper-left
(the asymptotes of the function), they intersect at exactly
the cuto frequency. The frequency response at the cuto
frequency in a rst-order lter is 3 dB below the horizontal line. The various types of lters (Butterworth lter,
Chebyshev lter, Bessel lter, etc.) all have dierentlooking knee curves. Many second-order lters have
peaking or resonance that puts their frequency response
at the cuto frequency above the horizontal line. Furthermore, the actual frequency where this peaking occurs can
be predicted without calculus, as shown by Cartwright[5]
et al. For third-order lters, the peaking and its frequency
of occurrence can too be predicted without calculus as re- Passive, rst order low-pass RC lter
cently shown by Cartwright[6] et al. See electronic lter for
other types.
RC lter

Vout

The meanings of 'low' and 'high'that is, the cuto frequencydepend on the characteristics of the lter. The
term low-pass lter merely refers to the shape of the lters response; a high-pass lter could be built that cuts o
at a lower frequency than any low-pass lterit is their
responses that set them apart. Electronic circuits can be
devised for any desired frequency range, right up through
microwave frequencies (above 1 GHz) and higher.

51.3.1

Laplace notation

One simple low-pass lter circuit consists of a resistor

in series with a load, and a capacitor in parallel with the
load. The capacitor exhibits reactance, and blocks lowfrequency signals, forcing them through the load instead.
At higher frequencies the reactance drops, and the capacitor eectively functions as a short circuit. The combination of resistance and capacitance gives the time constant
of the lter = RC (represented by the Greek letter tau).
The break frequency, also called the turnover frequency
or cuto frequency (in hertz), is determined by the time
constant:

Continuous-time lters can also be described in terms

of the Laplace transform of their impulse response, in a f = 1 = 1
c
2
2RC
way that lets all characteristics of the lter be easily analyzed by considering the pattern of poles and zeros of or equivalently (in radians per second):
the Laplace transform in the complex plane. (In discrete
time, one can similarly consider the Z-transform of the
1
1
impulse response.)
c = =

RC
For example, a rst-order low-pass lter can be described
This circuit may be understood by considering the time
in Laplace notation as:
the capacitor needs to charge or discharge through the
resistor:
1
Output
=K
Input
s + 1
where s is the Laplace transform variable, is the lter time constant, and K is the gain of the lter in the
passband .

51.4 Electronic low-pass lters

51.4.1

First order

At low frequencies, there is plenty of time for the

capacitor to charge up to practically the same voltage
as the input voltage.
At high frequencies, the capacitor only has time to
charge up a small amount before the input switches
direction. The output goes up and down only a small
fraction of the amount the input goes up and down.
At double the frequency, theres only time for it to
charge up half the amount.
Another way to understand this circuit is through the concept of reactance at a particular frequency:

276

CHAPTER 51. LOW-PASS FILTER

Since direct current (DC) cannot ow through the capacitance respectively. The circuit forms a harmonic
capacitor, DC input must ow out the path marked oscillator for current and will resonate in a similar way as
Vout (analogous to removing the capacitor).
an LC circuit will. The main dierence that the presence
of the resistor makes is that any oscillation induced in the
Since alternating current (AC) ows very well circuit will die away over time if it is not kept going by a
through the capacitor, almost as well as it ows source. This eect of the resistor is called damping. The
through solid wire, AC input ows out through presence of the resistance also reduces the peak resonant
the capacitor, eectively short circuiting to ground frequency somewhat. Some resistance is unavoidable in
(analogous to replacing the capacitor with just a real circuits, even if a resistor is not specically included
wire).
as a component. An ideal, pure LC circuit is an abstraction for the purpose of theory.
The capacitor is not an on/o object (like the block or
pass uidic explanation above). The capacitor variably There are many applications for this circuit. They are
acts between these two extremes. It is the Bode plot and used in many dierent types of oscillator circuits. Another important application is for tuning, such as in radio
frequency response that show this variability.
receivers or television sets, where they are used to select
a narrow range of frequencies from the ambient radio
waves. In this role the circuit is often referred to as a
RL lter
tuned circuit. An RLC circuit can be used as a bandMain article: RL lter
pass lter, band-stop lter, low-pass lter or high-pass
lter. The RLC lter is described as a second-order cirA resistorinductor circuit or RL lter is an electric cir- cuit, meaning that any voltage or current in the circuit
cuit composed of resistors and inductors driven by a can be described by a second-order dierential equation
voltage or current source. A rst order RL circuit is com- in circuit analysis.
posed of one resistor and one inductor and is the simplest
type of RL circuit.

51.4.3 Higher order passive lters

A rst order RL circuit is one of the simplest analogue

innite impulse response electronic lters. It consists of
Higher order passive lters, can also be constructed (see
a resistor and an inductor, either in series driven by a
diagram for a third order example).
voltage source or in parallel driven by a current source.
L3

L1

51.4.2

Second order

Vout

Vin

RLC lter

C2

R4

Main article: RLC circuit

An RLC circuit (the letters R, L and C can be in other
A third-order low-pass lter (Cauer topology). The lter becomes a Butterworth lter with cuto frequency c=1 when (for
example) C2 =4/3 farad, R4 =1 ohm, L1 =3/2 henry and L3 =1/2
henry.

in

out

51.4.4 Active electronic realization

Another type of electrical circuit is an active low-pass lter.
In the operational amplier circuit shown in the gure,
the cuto frequency (in hertz) is dened as:

RLC circuit as a low-pass lter

orders) is an electrical circuit consisting of a resistor, an

1
inductor, and a capacitor, connected in series or in paral- fc = 2R2 C
lel. The RLC part of the name is due to those letters being
the usual electrical symbols for resistance, inductance and or equivalently (in radians per second):

51.4. ELECTRONIC LOW-PASS FILTERS

277

R2
R1

vin

vout

where Qc (t) is the charge stored in the capacitor at time t .

Substituting equation Q into equation I gives i(t) = C d vd out
t
, which can be substituted into equation V so that:

vin (t) vout (t) = RC

This equation can be discretized. For simplicity, assume

that samples of the input and output are taken at evenly
spaced points in time separated by T time. Let the samples of vin be represented by the sequence (x1 , x2 , ..., xn ) ,
and let vout be represented by the sequence (y1 , y2 , ..., yn )
, which correspond to the same points in time. Making
these substitutions:

An active low-pass lter

c =

d vout
dt

1
R2 C

The gain in the passband is R2 /R1 , and the stopband

drops o at 6 dB per octave (that is 20 dB per decade)
yi yi1
as it is a rst-order lter.
xi yi = RC
T

51.4.5

And rearranging terms gives the recurrence relation

Discrete-time realization

For another method of conversion from continuous- to

discrete-time, see Bilinear transform.

contribution Input

z (
yi = xi

output previous from Inertia

}|
( }|
){ z
){
T
RC
+ yi1
.
RC + T
RC + T

Many digital lters are designed to give low-pass characteristics. Both innite impulse response and nite im- That is, this discrete-time implementation of a simple RC
pulse response low pass lters as well as lters using low-pass lter is the exponentially weighted moving averFourier transforms are widely used.
age
Simple innite impulse response lter
where

yi = xi +(1)yi1

T
RC + T

The eect of an innite impulse response low-pass lter

can be simulated on a computer by analyzing an RC lBy denition, the smoothing factor 0 1 . The exters behavior in the time domain, and then discretizing
pression for yields the equivalent time constant RC in
the model.
terms of the sampling period T and smoothing factor
:

(
RC = T

vin

vout

Recalling that
fc =

A simple low-pass RC lter

1
2RC

so RC =

1
2fc

then and fc are related by:

From the circuit diagram to the right, according to

2T fc
=
Kirchhos Laws and the denition of capacitance:
2T fc + 1
and

278

CHAPTER 51. LOW-PASS FILTER

51.5 See also

fc =

(1 )2T

If = 0.5 , then the RC time constant is equal to the sampling period. If 0.5 , then RC is signicantly larger
than the sampling interval, and T RC .
The lter recurrence relation provides a way to determine
the output samples in terms of the input samples and the
preceding output. The following pseudocode algorithm
simulates the eect of a low-pass lter on a series of digital samples:
// Return RC low-pass lter output samples, given input
samples, // time interval dt, and time constant RC function lowpass(real[0..n] x, real dt, real RC) var real[0..n]
y var real := dt / (RC + dt) y[0] := x[0] for i from 1 to
n y[i] := * x[i] + (1-) * y[i-1] return y
The loop that calculates each of the n outputs can be
refactored into the equivalent:
for i from 1 to n y[i] := y[i-1] + * (x[i] - y[i-1])
That is, the change from one lter output to the next
is proportional to the dierence between the previous
output and the next input. This exponential smoothing property matches the exponential decay seen in the
continuous-time system. As expected, as the time constant RC increases, the discrete-time smoothing parameter decreases, and the output samples (y1 , y2 , ..., yn )
respond more slowly to a change in the input samples
(x1 , x2 , ..., xn ) ; the system has more inertia. This lter
is an innite-impulse-response (IIR) single-pole low-pass
lter.
Finite impulse response
Finite-impulse-response lters can be built that approximate to the sinc function time-domain response of an
ideal sharp-cuto low-pass lter. In practice, the timedomain response must be time truncated and is often of a
simplied shape; in the simplest case, a running average
can be used, giving a square time response.[7]
Fourier transformation
For minimum distortion the nite impulse response lter
has an unbounded number of coecients.
For non-realtime ltering, to achieve a low pass lter, the
entire signal is usually taken as a looped signal, the Fourier
transform is taken, ltered in the frequency domain, followed by an inverse Fourier transform. Only O(n log(n))
operations are required compared to O(n2 ) for the time
domain ltering algorithm.
This can also sometimes be done in real-time, where
the signal is delayed long enough to perform the Fourier
transformation on shorter, overlapping blocks.

Baseband
DSL lter

51.6 References
[1] Sedra, Adel; Smith, Kenneth C. (1991). Microelectronic
Circuits, 3 ed. Saunders College Publishing. p. 60. ISBN
0-03-051648-X.
[2] ADSL lters explained. Epanorama.net. Retrieved
2013-09-24.
[3] Home Networking Local Area Network. Pcweenie.com. 2009-04-12. Retrieved 2013-09-24.
[4] Mastering Windows: Improving Reconstruction
[5] K. V. Cartwright, P. Russell and E. J. Kaminsky,Finding
the maximum magnitude response (gain) of second-order
lters without calculus, Lat. Am. J. Phys. Educ. Vol. 6,
No. 4, pp. 559-565, 2012.
[6] Cartwright, K. V.; P. Russell; E. J. Kaminsky (2013).
Finding the maximum and minimum magnitude responses (gains) of third-order lters without calculus
(PDF). Lat. Am. J. Phys. Educ. 7 (4): 582587.
[7] Signal recovery from noise in electronic instrumentation
T H Whilmshurst

51.7 External links

Low-pass lter
Low Pass Filter java simulator
ECE 209: Review of Circuits as LTI Systems, a
short primer on the mathematical analysis of (electrical) LTI systems.
ECE 209: Sources of Phase Shift, an intuitive explanation of the source of phase shift in a low-pass lter. Also veries simple passive LPF transfer function by means of trigonometric identity.

Chapter 52

Digital data
This article is about broad technical and mathematical For devices with only a few switches (such as the butinformation regarding digital data. For alternate or more tons on a joystick), the status of each can be encoded as
specic uses, see Digital (disambiguation).
bits (usually 0 for released and 1 for pressed) in a single
word. This is useful when combinations of key presses
are meaningful, and is sometimes used for passing the
Digital data, in information theory and information systems, are discrete, discontinuous representations of infor- status of modier keys on a keyboard (such as shift and
control). But it does not scale to support more keys than
mation or works, as contrasted with continuous, or analog
signals which behave in a continuous manner, or represent the number of bits in a single byte or word.
information using a continuous function.
Although digital representations are the subject matter of
discrete mathematics, the information represented can be
either discrete, such as numbers and letters, or it can be
continuous, such as sounds, images, and other measurements.

Devices with many switches (such as a computer keyboard) usually arrange these switches in a scan matrix,
with the individual switches on the intersections of x and
y lines. When a switch is pressed, it connects the corresponding x and y lines together. Polling (often called
scanning in this case) is done by activating each x line in
sequence and detecting which y lines then have a signal,
thus which keys are pressed. When the keyboard processor detects that a key has changed state, it sends a signal
to the CPU indicating the scan code of the key and its
new state. The symbol is then encoded, or converted into
a number, based on the status of modier keys and the
desired character encoding.

The word digital comes from the same source as the words
digit and digitus (the Latin word for nger), as ngers are
often used for discrete counting. Mathematician George
Stibitz of Bell Telephone Laboratories used the word digital in reference to the fast electric pulses emitted by
a device designed to aim and re anti-aircraft guns in
1942.[1] The term is most commonly used in computing
A custom encoding can be used for a specic application
and electronics, especially where real-world information
is converted to binary numeric form as in digital audio with no loss of data. However, using a standard encoding
such as ASCII is problematic if a symbol such as '' needs
and digital photography.
to be converted but is not in the standard.
It is estimated that in the year 1986 less than 1% of the
52.1 Symbol to digital conversion worlds technological capacity to store[2]information was
digital and in 2007 it was already 94%. The year 2002
is assumed to be the year when human kind was able to
Since symbols (for example, alphanumeric characters) store more information in digital than in analog format
are not continuous, representing symbols digitally is (the beginning of the digital age").[3][4]
rather simpler than conversion of continuous or analog information to digital. Instead of sampling and quantization
as in analog-to-digital conversion, such techniques as
52.2 Properties of digital informapolling and encoding are used.

tion
A symbol input device usually consists of a group of
switches that are polled at regular intervals to see which
switches are switched. Data will be lost if, within a sin- All digital information possesses common properties that
gle polling interval, two switches are pressed, or a switch distinguish it from analog data with respect to communiis pressed, released, and pressed again. This polling can cations:
be done by a specialized processor in the device to pre Synchronization: Since digital information is convent burdening the main CPU. When a new symbol has
been entered, the device typically sends an interrupt, in a
veyed by the sequence in which symbols are orspecialized format, so that the CPU can read it.
dered, all digital schemes have some method for
279

280

CHAPTER 52. DIGITAL DATA

determining the beginning of a sequence. In written or spoken human languages synchronization is
typically provided by pauses (spaces), capitalization,
and punctuation. Machine communications typically use special synchronization sequences.

Language: All digital communications require a

formal language, which in this context consists of
all the information that the sender and receiver of
the digital communication must both possess, in advance, in order for the communication to be successful. Languages are generally arbitrary and specify
the meaning to be assigned to particular symbol sequences, the allowed range of values, methods to be
used for synchronization, etc.

would actually produce a larger signal (therefore be

more dicult to transfer) than analog data. However, digital data can be compressed. Compression
reduces the amount of bandwidth space needed to
send information. Data can be compressed, sent
and then decompressed at the site of consumption.
This makes it possible to send much more information and result in, for example, digital television signals oering more room on the airwave spectrum
for more television channels.[4]

52.3 Historical digital systems

Even though digital signals are generally associated with

Errors: Disturbances (noise) in analog communi- the binary electronic digital systems used in modern eleccations invariably introduce some, generally small tronics and computing, digital systems are actually andeviation or error between the intended and actual cient, and need not be binary or electronic.
communication. Disturbances in a digital communication do not result in errors unless the disturbance
Written text (due to the limited character set and the
is so large as to result in a symbol being misinteruse of discrete symbols - the alphabet in most cases)
preted as another symbol or disturb the sequence of
symbols. It is therefore generally possible to have
The abacus was created sometime between 1000 BC
an entirely error-free digital communication. Furand 500 BC, it later became a form of calculation
ther, techniques such as check codes may be used
frequency. Nowadays it can be used as a very adto detect errors and guarantee error-free communivanced, yet basic digital calculator that uses beads on
cations through redundancy or retransmission. Errows to represent numbers. Beads only have meanrors in digital communications can take the form of
ing in discrete up and down states, not in analog insubstitution errors in which a symbol is replaced by
between states.
another symbol, or insertion/deletion errors in which
A beacon is perhaps the simplest non-electronic digan extra incorrect symbol is inserted into or deleted
ital signal, with just two states (on and o). In parfrom a digital message. Uncorrected errors in digticular, smoke signals are one of the oldest examples
ital communications have unpredictable and generof
a digital signal, where an analog carrier (smoke)
ally large impact on the information content of the
is
modulated
with a blanket to generate a digital sigcommunication.
nal (pus) that conveys information.
Copying: Because of the inevitable presence of
Morse code uses six digital statesdot, dash, intranoise, making many successive copies of an analog
character gap (between each dot or dash), short gap
communication is infeasible because each genera(between each letter), medium gap (between words),
tion increases the noise. Because digital communiand long gap (between sentences)to send mescations are generally error-free, copies of copies can
sages via a variety of potential carriers such as elecbe made indenitely.
tricity or light, for example using an electrical telegraph or a ashing light.
Granularity: The digital representation of a continuously variable analog value typically involves a
The Braille system was the rst binary format for
selection of the number of symbols to be assigned
character encoding, using a six-bit code rendered as
to that value. The number of symbols determines
dot patterns.
the precision or resolution of the resulting datum.
The dierence between the actual analog value and
Flag semaphore uses rods or ags held in particular
the digital representation is known as quantization
positions to send messages to the receiver watching
error. For example, if the actual temperature is
them some distance away.
23.234456544453 degrees, but if only two digits
(23) are assigned to this parameter in a particu International maritime signal ags have distinctive
lar digital representation, the quantizing error is:
markings that represent letters of the alphabet to al0.234456544453. This property of digital commulow ships to send messages to each other.
nication is known as granularity.
More recently invented, a modem modulates an ana Compressible: According to Miller, Uncomlog carrier signal (such as sound) to encode binary
pressed digital data is very large, and in its raw form
electrical digital information, as a series of binary

52.6. FURTHER READING

digital sound pulses. A slightly earlier, surprisingly
reliable version of the same concept was to bundle a
sequence of audio digital signal and no signal information (i.e. sound and silence) on magnetic
cassette tape for use with early home computers.

52.4 See also

Analog-to-digital converter
Binary number
Comparison of analog and digital recording
Data (computing)
Digital architecture
Digital art
Digital control
Digital divide
Digital electronics
Digital innity
Digital native
Digital physics
Digital recording
Digital Revolution
Digital video
Digital-to-analog converter

52.5 References
[1] Ceruzzi, Paul E (June 29, 2012). Computing - A Concise
History. MIT Press. ISBN 978-0-262-51767-6.
[2] The Worlds Technological Capacity to Store, Communicate, and Compute Information, especially Supporting
online material, Martin Hilbert and Priscila Lpez (2011),
Science (journal), 332(6025), 60-65; free access to the article through here: martinhilbert.net/WorldInfoCapacity.
html
[3] video animation on The Worlds Technological Capacity
to Store, Communicate, and Compute Information from
1986 to 2010
[4] Miller, Vincent (2011). Understanding digital culture.
London: Sage Publications. sec. Convergence and the
contemporary media experience. ISBN 978-1-84787497-9.

281

52.6 Further reading

Tocci, R. 2006. Digital Systems: Principles and Applications (10th Edition). Prentice Hall. ISBN 013-172579-3

Chapter 53

Public switched telephone network

The public switched telephone network (PSTN) is
the aggregate of the worlds circuit-switched telephone
networks that are operated by national, regional, or local telephony operators, providing infrastructure and services for public telecommunication. The PSTN consists
of telephone lines, ber optic cables, microwave transmission links, cellular networks, communications satellites, and undersea telephone cables, all interconnected by
switching centers, thus allowing most telephones to communicate with each other. Originally a network of xedline analog telephone systems, the PSTN is now almost
entirely digital in its core network and includes mobile
and other networks, as well as xed telephones.[1]
The technical operation of the PSTN adheres to the standards created by the ITU-T. These standards allow dierent networks in dierent countries to interconnect seamlessly. The E.163 and E.164 standards provide a single
global address space for telephone numbers. The combination of the interconnected networks and the single
numbering plan allow telephones around the world to dial
each other.

53.1 History (USA)

The rst telephones had no network but were in private
use, wired together in pairs. Users who wanted to talk to
dierent people had as many telephones as necessary for
the purpose. A user who wished to speak whistled loudly
into the transmitter until the other party heard.
However, a bell was added soon for signaling, so an attendant no longer need wait for the whistle, and then a
switch hook. Later telephones took advantage of the exchange principle already employed in telegraph networks.
Each telephone was wired to a local telephone exchange,
and the exchanges were wired together with trunks. Networks were connected in a hierarchical manner until they
spanned cities, countries, continents and oceans. This
was the beginning of the PSTN, though the term was not
used for many decades.

frequency, culminating in the SS7 network that connected

most exchanges by the end of the 20th century.
The growth of the PSTN meant that teletrac engineering techniques needed to be deployed to deliver quality
of service (QoS) guarantees for the users. The work of
A. K. Erlang established the mathematical foundations of
methods required to determine the capacity requirements
and conguration of equipment and the number of personnel required to deliver a specic level of service.
In the 1970s the telecommunications industry began implementing packet switched network data services using
the X.25 protocol transported over much of the end-toend equipment as was already in use in the PSTN.
In the 1980s the industry began planning for digital services assuming they would follow much the same pattern
as voice services, and conceived a vision of end-to-end
circuit switched services, known as the Broadband Integrated Services Digital Network (B-ISDN). The B-ISDN
vision has been overtaken by the disruptive technology of
the Internet.
At the turn of the 21st century, the oldest parts of the
telephone network still use analog technology for the last
mile loop to the end user. However, digital technologies
such as DSL, ISDN, FTTx, and cable modems have become more common in this portion of the network.
Several large private telephone networks are not linked
to the PSTN, usually for military purposes. There are
also private networks run by large companies which are
linked to the PSTN only through limited gateways, such
as a large private branch exchange (PBX).

53.2 Operators
The task of building the networks and selling services to
customers fell to the network operators. The rst company to be incorporated to provide PSTN services was
the Bell Telephone Company in the United States.

In some countries, however, the job of providing teleAutomation introduced pulse dialing between the phone phone networks fell to government as the investment reand the exchange, and then among exchanges, followed quired was very large and the provision of telephone serby more sophisticated address signaling including multi- vice was increasingly becoming an essential public utility.
282

53.5. SEE ALSO

For example, the General Post Oce in the United Kingdom brought together a number of private companies to
form a single nationalized company. In recent decades
however, these state monopolies were broken up or sold
o through privatization.

283
one end to another via telephone exchanges. The call is
switched using a call set up protocol (usually ISUP) between the telephone exchanges under an overall routing
strategy.

The call is carried over the PSTN using a 64 kbit/s channel, originally designed by Bell Labs. The name given
to this channel is Digital Signal 0 (DS0). The DS0 cir53.3 Regulation
cuit is the basic granularity of circuit switching in a telephone exchange. A DS0 is also known as a timeslot beIn most countries, the central has a regulator dedicated to cause DS0s are aggregated in time-division multiplexing
monitoring the provision of PSTN services in that coun- (TDM) equipment to form higher capacity communicatry. Their tasks may be for example to ensure that end tion links.
customers are not over-charged for services where mo- A Digital Signal 1 (DS1) circuit carries 24 DS0s on a
nopolies may exist. They may also regulate the prices North American or Japanese T-carrier (T1) line, or 32
charged between the operators to carry each others traf- DS0s (30 for calls plus two for framing and signaling) on
c.
an E-carrier (E1) line used in most other countries. In

53.4 Technology
53.4.1

modern networks, the multiplexing function is moved as

close to the end user as possible, usually into cabinets at
the roadside in residential areas, or into large business
premises.

Network topology

These aggregated circuits are conveyed from the initial

multiplexer to the exchange over a set of equipment colMain article: PSTN network topology
lectively known as the access network. The access network and inter-exchange transport use synchronous optiThe PSTN network architecture had to evolve over the cal transmission, for example, SONET and Synchronous
years to support increasing numbers of subscribers, calls, Digital Hierarchy (SDH) technologies, although some
connections to other countries, direct dialing and so on. parts still use the older PDH technology.
The model developed by the United States and Canada Within the access network, there are a number of referwas adopted by other nations, with adaptations for local ence points dened. Most of these are of interest mainly
markets.
to ISDN but one the V reference point is of more
The original concept was that the telephone exchanges general interest. This is the reference point between a
are arranged into hierarchies, so that if a call cannot be primary multiplexer and an exchange. The protocols at
handled in a local cluster, it is passed to one higher up this reference point were standardized in ETSI areas as
for onward routing. This reduced the number of connect- the V5 interface.
ing trunks required between operators over long distances
and also kept local trac separate.

53.4.3 Impact on IP standards

However, in modern networks the cost of transmission

and equipment is lower and, although hierarchies still exVoice quality over PSTN networks was used as the benchist, they are much atter, with perhaps only two layers.
mark for the development of the Telecommunications
Industry Association's TIA-TSB-116 standard on voicequality recommendations for IP telephony, to determine
53.4.2 Digital channels
acceptable levels of audio delay and echo.[2]
Main article: Telephone exchange
As described above, most automated telephone exchanges now use digital switching rather than mechanical or analog switching. The trunks connecting the exchanges are also digital, called circuits or channels. However analog two-wire circuits are still used to connect the
last mile from the exchange to the telephone in the home
(also called the local loop). To carry a typical phone call
from a calling party to a called party, the analog audio
signal is digitized at an 8 kHz sample rate with 8-bit resolution using a special type of nonlinear pulse code modulation known as G.711. The call is then transmitted from

53.5 See also

Internet area network (IAN)
Managed facilities-based voice network
Plain old telephone service (POTS)
PSTN network topology
Via Net Loss

284

CHAPTER 53. PUBLIC SWITCHED TELEPHONE NETWORK

53.6 References
[1] Kushnick, Bruce (7 January 2013). What Are the Public Switched Telephone Networks, 'PSTN' and Why You
Should Care?". Hungton Post Blog. Retrieved 11 April
2014.
[2] TIA TSB-116. Global.ihs.com. Retrieved 2011-11-20.

53.7 External links

Chapter 54

Channel (communications)
bles to transmit data and information. Twisted-pair wire
and coaxial cables are made of copper, and ber-optic
cable is made of glass.
In information theory, a channel refers to a theoretical
channel model with certain error characteristics. In this
more general view, a storage device is also a kind of channel, which can be sent to (written) and received from
(read).

54.1 Examples
Examples of communications channels include:
1. A connection between initiating and terminating
nodes of a circuit.
2. A single path provided by a transmission medium
via either
physical separation, such as by multipair cable
or
electrical separation, such as by frequencydivision or time-division multiplexing.
Old telephone wires are a challenging communications channel
for modern digital communications.

A communication channel or simply channel refers either to a physical transmission medium such as a wire, or
to a logical connection over a multiplexed medium such
as a radio channel in telecommunications and computer
networking. A channel is used to convey an information
signal, for example a digital bit stream, from one or several senders (or transmitters) to one or several receivers.
A channel has a certain capacity for transmitting information, often measured by its bandwidth in Hz or its data
rate in bits per second.
Communicating data from one location to another requires some form of pathway or medium. These pathways, called communication channels, use two types of
media: cable (twisted-pair wire, cable, and ber-optic
cable) and broadcast (microwave, satellite, radio, and infrared). Cable or wire line media use physical wires of ca285

3. A path for conveying electrical or electromagnetic

signals, usually distinguished from other parallel
paths.
A storage which can communicate a message
over time as well as space
The portion of a storage medium, such as a
track or band, that is accessible to a given reading or writing station or head.
A buer from which messages can be 'put' and
'got'. See Actor model and process calculi for
discussion on the use of channels.
4. In a communications system, the physical or logical
link that connects a data source to a data sink.
5. A specic radio frequency, pair or band of frequencies, usually named with a letter, number, or codeword, and often allocated by international agreement.
Examples:

286

CHAPTER 54. CHANNEL (COMMUNICATIONS)

Marine VHF radio uses some 88 channels in
the VHF band for two-way FM voice communication. Channel 16, for example, is 156.800
MHz. In the US, seven additional channels,
WX1 - WX7, are allocated for weather broadcasts.
Television channels such as North American
TV Channel 2 = 55.25 MHz, Channel 13 =
211.25 MHz. Each channel is 6 MHz wide.
Besides these physical channels, television
also has "virtual channels".
Wi-Fi consists of unlicensed channels 1-13
from 2412 MHz to 2484 MHz in 5 MHz steps.
The radio channel between an amateur radio
repeater and a ham uses two frequencies often
600 kHz (0.6 MHz) apart. For example, a repeater that transmits on 146.94 MHz typically
listens for a ham transmitting on 146.34 MHz.

world communication system in which the analog digital and digital analog blocks are out of the control of
the designer. The mathematical model consists of a transition probability that species an output distribution for
each possible sequence of channel inputs. In information
theory, it is common to start with memoryless channels
in which the output probability distribution only depends
on the current channel input.
A channel model may either be digital (quantied, e.g.
binary) or analog.

54.2.1 Digital channel models

In a digital channel model, the transmitted message is

modelled as a digital signal at a certain protocol layer. Underlying protocol layers, such as the physical layer transmission technique, is replaced by a simplied model. The
model may reect channel performance measures such as
All of these communications channels share the property bit rate, bit errors, latency/delay, delay jitter, etc. Examthat they transfer information. The information is carried ples of digital channel models are:
through the channel by a signal.
Binary symmetric channel (BSC), a discrete memoryless channel with a certain bit error probability

54.2 Channel models

A channel can be modelled physically by trying to calculate the physical processes which modify the transmitted signal. For example, in wireless communications the
channel can be modelled by calculating the reection o
every object in the environment. A sequence of random
numbers might also be added in to simulate external interference and/or electronic noise in the receiver.

Binary bursty bit error channel model, a channel

with memory
Binary erasure channel (BEC), a discrete channel
with a certain bit error detection (erasure) probability
Packet erasure channel, where packets are lost with
a certain packet loss probability or packet error rate

Statistically a communication channel is usually modelled

Arbitrarily varying channel (AVC), where the beas a triple consisting of an input alphabet, an output alphahavior and state of the channel can change randomly
bet, and for each pair (i, o) of input and output elements a
transition probability p(i, o). Semantically, the transition
probability is the probability that the symbol o is received 54.2.2 Analog channel models
given that i was transmitted over the channel.
Statistical and physical modelling can be combined. For In an analog channel model, the transmitted message is
example, in wireless communications the channel is often modelled as an analog signal. The model can be a linmodelled by a random attenuation (known as fading) of ear or non-linear, time-continuous or time-discrete (samthe transmitted signal, followed by additive noise. The at- pled), memoryless or dynamic (resulting in burst errors),
tenuation term is a simplication of the underlying physi- time-invariant or time-variant (also resulting in burst ercal processes and captures the change in signal power over rors), baseband, passband (RF signal model), real-valued
the course of the transmission. The noise in the model or complex-valued signal model. The model may reect
captures external interference and/or electronic noise in the following channel impairments:
the receiver. If the attenuation term is complex it also describes the relative time a signal takes to get through the
channel. The statistics of the random attenuation are decided by previous measurements or physical simulations.
Channel models may be continuous channel models in
that there is no limit to how precisely their values may
be dened.
Communication channels are also studied in a discretealphabet setting. This corresponds to abstracting a real

Noise model, for example

Additive white Gaussian noise (AWGN) channel, a linear continuous memoryless model
Phase noise model
Interference model, for example cross-talk (cochannel interference) and intersymbol interference
(ISI)

54.5. MULTI-TERMINAL CHANNELS, WITH APPLICATION TO CELLULAR SYSTEMS

Distortion model, for example a non-linear channel
model causing intermodulation distortion (IMD)
Frequency response model, including attenuation
and phase-shift

287

Digital bandwidth bit/s measures: gross bit rate (signalling rate), net bit rate (information rate), channel
capacity, and maximum throughput
Channel utilization

Group delay model

Link spectral eciency

Modelling of underlying physical layer transmission

techniques, for example a complex-valued
equivalent baseband model of modulation and
frequency response

Signal-to-noise ratio measures:

signal-tointerference ratio, Eb/No, carrier-to-interference
ratio in decibel

Radio frequency propagation model, for example

Log-distance path loss model
Fading model, for example Rayleigh fading,
Ricean fading, log-normal shadow fading and
frequency selective (dispersive) fading
Doppler shift model, which combined with
fading results in a time-variant system
Ray tracing models, which attempt to model
the signal propagation and distortions for specied transmitter-receiver geometries, terrain
types, and antennas

Bit-error rate (BER), packet-error rate (PER)

Latency in seconds: propagation time, transmission
time
Delay jitter

54.5 Multi-terminal channels, with

application to cellular systems
See also network topology

Mobility models, which also causes a time- In networks, as opposed to point-to-point communicavariant system
tion, the communication media is shared between multiple nodes (terminals). Depending on the type of communication, dierent terminals can cooperate or interfere on
each other. In general, any complex multi-terminal net54.3 Types
work can be considered as a combination of simplied
multi-terminal channels. The following channels are the
Digital (discrete) or analog (continuous) channel
principal multi-terminal channels which was rst intro Transmission medium, for example a bre channel duced in the eld of information theory:
Multiplexed channel
Computer network virtual channel
Simplex communication, duplex communication or
half duplex communication channel
Return channel
Uplink or downlink (upstream or downstream channel)
Broadcast channel, unicast channel or multicast
channel

54.4 Channel performance measures

These are examples of commonly used channel capacity
and performance measures:
Spectral bandwidth in Hertz
Symbol rate in baud, pulses/s or symbols/s

A point-to-multipoint channel, also known as broadcasting medium (not to be confused with broadcasting channel): In this channel, a single sender
transmits multiple messages to dierent destination
nodes. All wireless channels except radio links can
be considered as broadcasting media, but may not
always provide broadcasting service. The downlink
of a cellular system can be considered as a pointto-multipoint channel, if only one cell is considered
and inter-cell co-channel interference is neglected.
However, the communication service of a phone call
is unicasting.
Multiple access channel: In this channel, multiple
senders transmit multiple possible dierent messages over a shared physical medium to one or
several destination nodes. This requires a channel
access scheme, including a media access control
(MAC) protocol combined with a multiplexing
scheme. This channel model has applications in the
uplink of the cellular networks.
Relay channel: In this channel, one or several intermediate nodes (called relay, repeater or gap ller

288

CHAPTER 54. CHANNEL (COMMUNICATIONS)

nodes) cooperate with a sender to send the message to an ultimate destination node. Relay nodes
are considered as a possible add-on in the upcoming
cellular standards like 3GPP Long Term Evolution
(LTE).

Interference channel: In this channel, two dierent senders transmit their data to dierent destination nodes. Hence, the dierent senders can have
a possible cross-talk or co-channel interference on
the signal of each other. The inter-cell interference
in the cellular wireless communications is an example of the interference channel. In spread spectrum
systems like 3G, interference also occur inside the
cell if non-orthogonal codes are used.
A unicasting channel is a channel that provides a unicasting service, i.e. that sends data addressed to one
specic user. An established phone call is an example.
A broadcasting channel is a channel that provides a
broadcasting service, i.e. that sends data addressed
to all users in the network. Cellular network examples are the paging service as well as the Multimedia
Broadcast Multicast Service.
A multicasting channel is a channel where data is
addressed to a group of subscribing users. LTE examples are the Physical Multicast Channel (PMCH)
and MBSFN (Multicast Broadcast Single Frequency
Network).
From the above 4 basic multi-terminal channels, multiple access channel is the only one whose capacity region
is known. Even for the special case of the Gaussian scenario, the capacity region of the other 3 channels except
the broadcast channel is unknown in general.

54.6 See also

Channel capacity
Channel access method
Trac generation model

54.7 Reference
C. E. Shannon, A mathematical theory of communication, Bell System Technical Journal, vol. 27, pp.
379423 and 623656, (July and October, 1948)
Amin Shokrollahi, LDPC Codes: An Introduction

Chapter 55

Band-pass lter
passbands. A bandpass signal is a signal containing a
band of frequencies not adjacent to zero frequency, such
as a signal that comes out of a bandpass lter.[2]

0 dB

3 dB

An ideal bandpass lter would have a completely at

passband (e.g. with no gain/attenuation throughout) and
would completely attenuate all frequencies outside the
passband. Additionally, the transition out of the passband
would have brickwall characteristics.

B
f
fL

f0

fH

Bandwidth measured at half-power points (gain 3 dB, 2/2, or

about 0.707 relative to peak) on a diagram showing magnitude
transfer function versus frequency for a band-pass lter.

L
Vi

C
L

A medium-complexity example of a band-pass lter.

Vo

In practice, no bandpass lter is ideal. The lter does

not attenuate all frequencies outside the desired frequency
range completely; in particular, there is a region just outside the intended passband where frequencies are attenuated, but not rejected. This is known as the lter roll-o,
and it is usually expressed in dB of attenuation per octave
or decade of frequency. Generally, the design of a lter seeks to make the roll-o as narrow as possible, thus
allowing the lter to perform as close as possible to its
intended design. Often, this is achieved at the expense of
pass-band or stop-band ripple.
The bandwidth of the lter is simply the dierence between the upper and lower cuto frequencies. The shape
factor is the ratio of bandwidths measured using two
dierent attenuation values to determine the cuto frequency, e.g., a shape factor of 2:1 at 30/3 dB means the
bandwidth measured between frequencies at 30 dB attenuation is twice that measured between frequencies at 3 dB
attenuation.

Optical band-pass lters are common in photography and

A band-pass lter is a device that passes frequencies
theatre lighting work. These lters take the form of a
within a certain range and rejects (attenuates) frequentransparent coloured lm or sheet.
cies outside that range.

55.1 Description
An example of an analogue electronic band-pass lter
55.2 Q factor
is an RLC circuit (a resistorinductorcapacitor circuit).
These lters can also be created by combining a low-pass
lter with a high-pass lter.[1]
A band-pass lter can be characterised by its Q factor.
Bandpass is an adjective that describes a type of lter or The Q-factor is the inverse of the fractional bandwidth.
ltering process; it is to be distinguished from passband, A high-Q lter will have a narrow passband and a low-Q
which refers to the actual portion of aected spectrum. lter will have a wide passband. These are respectively
Hence, one might say A dual bandpass lter has two referred to as narrow-band and wide-band lters.
289

290

55.3 Applications
Bandpass lters are widely used in wireless transmitters
and receivers. The main function of such a lter in a
transmitter is to limit the bandwidth of the output signal to the band allocated for the transmission. This prevents the transmitter from interfering with other stations.
In a receiver, a bandpass lter allows signals within a selected range of frequencies to be heard or decoded, while
preventing signals at unwanted frequencies from getting
through. A bandpass lter also optimizes the signal-tonoise ratio and sensitivity of a receiver.
In both transmitting and receiving applications, welldesigned bandpass lters, having the optimum bandwidth
for the mode and speed of communication being used,
maximize the number of signal transmitters that can exist
in a system, while minimizing the interference or competition among signals.
Outside of electronics and signal processing, one example of the use of band-pass lters is in the atmospheric
sciences. It is common to band-pass lter recent meteorological data with a period range of, for example, 3 to 10
days, so that only cyclones remain as uctuations in the
data elds.
In neuroscience, visual cortical simple cells were rst
shown by David Hubel and Torsten Wiesel to have response properties that resemble Gabor lters, which are
band-pass.[3]

55.4 See also

Atomic line lter
Audio crossover
Band-stop lter

55.5 References
[1] E. R. Kanasewich (1981). Time Sequence Analysis in Geophysics. University of Alberta. p. 260. ISBN 0-88864074-9.
[2] Belle A. Shenoi (2006). Introduction to digital signal processing and lter design. John Wiley and Sons. p. 120.
ISBN 978-0-471-46482-2.
[3] Norman Stuart Sutherland (1979). Tutorial Essays in Psychology. Lawrence Erlbaum Associates. p. 68. ISBN
0-470-26652-X.

55.6 External links

Media related to Bandpass lters at Wikimedia Commons

CHAPTER 55. BAND-PASS FILTER

Chapter 56

Frequency-division multiplexing
In telecommunications, frequency-division multiplexing (FDM) is a technique by which the total bandwidth
available in a communication medium is divided into a
series of non-overlapping frequency sub-bands, each of
which is used to carry a separate signal. This allows a
single transmission medium such as the radio spectrum,
a cable or optical ber to be shared by multiple independent signals. Another use is to carry separate serial bits
or segments of a higher rate signal in parallel.
The most natural example of frequency-division multiplexing is radio and television broadcasting, in which
multiple radio signals at dierent frequencies pass
through the air at the same time. Another example is
cable television, in which many television channels are
carried simultaneously on a single cable. FDM is also
used by telephone systems to transmit multiple telephone
calls through high capacity trunklines, communications
satellites to transmit multiple channels of data on uplink and downlink radio beams, and broadband DSL
modems to transmit large amounts of computer data
through twisted pair telephone lines, among many other
uses.
An analogous technique called wavelength division multiplexing is used in ber-optic communication, in which
multiple channels of data are transmitted over a single
optical ber using dierent wavelengths (frequencies) of
light.

56.1 How it works

The passband of an FDM channel carrying digital data, modulated by QPSK quadrature phase-shift keying.

backing the data onto the carrier.

The result of modulating (mixing) the carrier with the
baseband signal is to generate sub-frequencies near the
carrier frequency, at the sum (fC + fB) and dierence
(fC fB) of the frequencies. The information from the
modulated signal is carried in sidebands on each side of
the carrier frequency. Therefore, all the information carried by the channel is in a narrow band of frequencies
clustered around the carrier frequency, this is called the
passband of the channel.
Similarly, additional baseband signals are used to modulate carriers at other frequencies, creating other channels
of information. The carriers are spaced far enough apart
in frequency that the band of frequencies occupied by
each channel, the passbands of the separate channels, do
not overlap. All the channels are sent through the transmission medium, such as a coaxial cable, optical ber,
or through the air using a radio transmitter. As long as
the channel frequencies are spaced far enough apart that
none of the passbands overlap, the separate channels will
not interfere with each another. Thus the available bandwidth is divided into slots or channels, each of which
can carry a separate modulated signal.

The multiple separate information (modulation) signals

that are sent over an FDM system, such as the video signals of the television channels that are sent over a cable
TV system, are called baseband signals. At the source
end, for each frequency channel, an electronic oscillator
generates a carrier signal, a steady oscillating waveform
at a single frequency that serves to carry information.
The carrier is much higher in frequency than the baseband
signal. The carrier signal and the baseband signal are
combined in a modulator circuit. The modulator alters For example, the coaxial cable used by cable television
some aspect of the carrier signal, such as its amplitude, systems has a bandwidth of about 1000 MHz, but the
frequency, or phase, with the baseband signal, piggy- passband of each television channel is only 6 MHz wide,
291

292

CHAPTER 56. FREQUENCY-DIVISION MULTIPLEXING

so there is room for many channels on the cable (in mod- DFSG can take similar steps where a direct formation of
ern digital cable systems each channel in turn is subdi- a number of super groups can be obtained in the 8 kHz
vided into subchannels and can carry up to 10 digital tele- the DFSG also eliminates group equipment and can oer:
vision channels).
Reduction in cost 7% to 13%
At the destination end of the cable or ber, or the radio receiver, for each channel a local oscillator produces
Less equipment to install and maintain
a signal at the carrier frequency of that channel, that is
Increased reliability due to less equipment
mixed with the incoming modulated signal. The frequencies subtract, producing the baseband signal for that chanBoth DTL and DFSG can t the requirement of low dennel again. This is called demodulation. The resulting
sity system (using DTL) and higher density system (using
baseband signal is ltered out of the other frequencies and
DFSG). The DFSG terminal is similar to DTL terminal
output to the user.
except instead of two super groups many super groups are
combined. A Mastergroup of 600 channels (10 supergroups) is an example based on DFSG.

56.2 Telephone

For long distance telephone connections, 20th century 56.3 Other examples
telephone companies used L-carrier and similar co-axial
cable systems carrying thousands of voice circuits multi- FDM can also be used to combine signals before nal
plexed in multiple stages by channel banks.
modulation onto a carrier wave. In this case the carrier
For shorter distances, cheaper balanced pair cables were signals are referred to as subcarriers: an example is stereo
used for various systems including Bell System K- and N- FM transmission, where a 38 kHz subcarrier is used to
Carrier. Those cables didn't allow such large bandwidths, separate the left-right dierence signal from the central
so only 12 voice channels (double sideband) and later 24 left-right sum channel, prior to the frequency modula(single sideband) were multiplexed into four wires, one tion of the composite signal. An analog NTSC televipair for each direction with repeaters every several miles, sion channel is divided into subcarrier frequencies for
approximately 10 km. See 12-channel carrier system. video, color, and audio. DSL uses dierent frequencies
By the end of the 20th Century, FDM voice circuits had for voice and for upstream and downstream data transmisbecome rare. Modern telephone systems employ digital sion on the same conductors, which is also an example of
transmission, in which time-division multiplexing (TDM) frequency duplex.
is used instead of FDM.
Where frequency-division multiplexing is used as to alSince the late 20th century digital subscriber lines (DSL) low multiple users to share a physical communications
have used a Discrete multitone (DMT) system to divide channel, it is called frequency-division multiple access
(FDMA).[1]
their spectrum into frequency channels.
The concept corresponding to frequency-division multi- FDMA is the traditional way of separating radio signals
plexing in the optical domain is known as wavelength- from dierent transmitters.
division multiplexing.
In the 1860s and 70s, several inventors attempted FDM
under the names of acoustic telegraphy and harmonic
telegraphy. Practical FDM was only achieved in the elec56.2.1 Group and supergroup
tronic age. Meanwhile, their eorts led to an elementary
understanding of electroacoustic technology, resulting in
A once commonplace FDM system, used for example in
the invention of the telephone.
L-carrier, uses crystal lters which operate at the 8 MHz
range to form a Channel Group of 12 channels, 48 kHz
bandwidth in the range 8140 to 8188 kHz by selecting
carriers in the range 8140 to 8184 kHz selecting upper 56.4 See also
sideband this group can then be translated to the standard
Orthogonal
frequency-division
multiplexing
range 60 to 108 kHz by a carrier of 8248 kHz. Such sys(OFDM)
tems are used in DTL (Direct To Line) and DFSG (Directly formed super group).
AN/UCC-4 an example of FDM implementation
132 voice channels (2SG + 1G) can be formed using
DTL plane the modulation and frequency plan are given
in FIG1 and FIG2 use of DTL technique allows the formation of a maximum of 132 voice channels that can be
placed direct to line. DTL eliminates group and super
group equipment.

56.5 References
[1] White, Curt (2007). Data Communications and Computer
Networks. Boston, MA: Thomson Course Technology.

56.5. REFERENCES

pp. 140143. ISBN 1-4188-3610-9.

General
Harold P.E. Stern, Samy A. Mahmoud (2006).
Communication Systems: Analysis and Design,
Prentice Hall. ISBN 0-13-040268-0.

293

Chapter 57

Line code

An example of Dierential Manchester encoding

An example of coding a binary signal using rectangular pulse
amplitude modulation with polar non-return-to-zero code

An example of Biphase mark code

An example of Bipolar encoding, or AMI.

An example of MLT-3 encoding.

57.1 Line coding

Line coding consists of representing the digital signal to
be transported, by a waveform that is optimally tuned for
the specic properties of the physical channel (and of
the receiving equipment). The pattern of voltage, curEncoding of 11011000100 in Manchester encoding
rent or photons used to represent the digital data on a
transmission link is called line encoding. The common
In telecommunication, a line code is a code chosen for types of line encoding are unipolar, polar, bipolar, and
use within a communications system for transmitting a Manchester encoding.
digital signal down a line. Line coding is often used for For reliable clock recovery at the receiver, one usually imdigital data transport. Some line codes are digital base- poses a maximum run length constraint on the generated
band modulation or digital baseband transmission channel sequence, i.e., the maximum number of consecmethods, and these are baseband line codes that are used utive ones or zeros is bounded to a reasonable number. A
when the line can carry DC components.
clock period is recovered by observing transitions in the

11011000100

294

57.2. DISPARITY

295

received sequence, so that a maximum run length guarantees such clock recovery, while sequences without such
a constraint could seriously hamper the detection quality.

Ease error detection and correction

After line coding, the signal is put through a physical

channel", either a "transmission medium" or "data storage medium".[1][2] Sometimes the characteristics of two
very dierent-seeming channels are similar enough that
the same line code is used for them. The most common
physical channels are:

Eliminate a dc component

the line-coded signal can directly be put on a

transmission line, in the form of variations of the
voltage or current (often using dierential signaling).
the line-coded signal (the "baseband signal) undergoes further pulse shaping (to reduce its frequency
bandwidth) and then modulated (to shift its frequency) to create an RF signal that can be sent
through free space.

Minimize spectral content

57.2 Disparity
The disparity of a bit pattern is the dierence in the
number of one bits vs the number of zero bits. The running disparity is the running total of the disparity of all
previously transmitted words.[3]
Unfortunately, most long-distance communication channels cannot transport a DC component. The DC component is also called the disparity, the bias, or the DC coecient. The simplest possible line code, unipolar, gives
too many errors on such systems, because it has an unbounded DC component.

Most line codes eliminate the DC component such

the line-coded signal can be used to turn on and o
codes are called DC-balanced, zero-DC, DC-free, zeroa light source in free-space optical communication,
bias, DC equalized, etc. There are three ways of elimimost commonly used in an infrared remote control.
nating the DC component:
the line-coded signal can be printed on paper to create a bar code.
Use a constant-weight code. In other words, each
transmitted code word is corrected such that ev the line-coded signal can be converted to magneery code word that contains some positive or negtized spots on a hard drive or tape drive.
ative levels also contains enough of the opposite
levels, such that the average level over each code
the line-coded signal can be converted to pits on an
word is zero. For example, Manchester code and
optical disc.
Interleaved 2 of 5.
Some of the more common or binary line codes include:

Use a paired disparity code. In other words, the

transmitter has to make sure that every code word
that averages to a negative level is paired with another code word that averages to a positive level.
Therefore, it must keep track of the running DC
buildup, and always pick the code word that pushes
the DC level back towards zero. The receiver is designed so that either code word of the pair decodes
to the same data bits. For example, AMI, 8B10B,
4B3T, etc.
Use a scrambler. For example, the scrambler specied in RFC 2615 for 64b/66b encoding.

An arbitrary bit pattern in various binary line code formats

57.3 Polarity

Each line code has advantages and disadvantages. The Bipolar line codes have two polarities, are generally imparticular line code used is chosen to meet one or more plemented as RZ, and have a radix of three since there
are three distinct output levels One of the principle adof the following criteria:
vantages of this type of code, is that it can completely
eliminate any DC component. This is important if the
Minimize transmission hardware
signal must pass through a transformer or a long trans Facilitate synchronization
mission line.

296
Unfortunately, several long-distance communication
channels have polarity ambiguity. To compensate, several people have designed polarity-insensitive transmission systems.[4][5][6][7] There are three ways of providing
unambiguous reception of 0 bits or 1 bits over such
channels:
Pair each code word with the polarity-inverse of
that code word. The receiver is designed so that either code word of the pair decodes to the same data
bits, such as alternate mark inversion, Dierential
Manchester encoding, coded mark inversion, Miller
encoding, etc.
dierential coding each symbol relative to the previous symbol, such as MLT-3 encoding, NRZI, etc.
invert the whole stream when inverted syncwords are
detected

57.4 Synchronization
Main article: clock recovery
Line coding should make it possible for the receiver to
synchronize itself to the phase of the received signal. If
the synchronization is not ideal, then the signal to be decoded will not have optimal dierences (in amplitude)
between the various digits or symbols used in the line
code. This will increase the error probability in the received data.
Biphase line codes require at least one transition per bit
time. This makes it easier to synchronize the transceivers
and detect errors, however, the baud rate is greater than
that of NRZ codes.

CHAPTER 57. LINE CODE

2B1Q
4B5B
4B3T
6b/8b encoding
Hamming Code
8b/10b encoding
64b/66b encoding
128b/130b encoding
Coded mark inversion (CMI)
Conditioned Diphase
Eight-to-Fourteen Modulation (EFM), used in
Compact Discs
EFMPlus, used in DVDs
RZ Return-to-zero
NRZ Non-return-to-zero
NRZI Non-return-to-zero, inverted
Manchester code, with its variants Dierential
Manchester and Biphase mark code
pulse-position modulation, a generalization of
Manchester code
Miller encoding, also known as Delay encoding
or Modied Frequency Modulation, with Modied
Miller encoding as a variant
MLT-3 Encoding
Hybrid Ternary Codes
Surround by complement (SBC)

57.5 Other considerations

It is also preferred for the line code to have a structure
that will enable error detection. Note that the line-coded
signal and a signal produced at a terminal may dier, thus
requiring translation.
A line code will typically reect technical requirements of
the transmission medium, such as optical ber or shielded
twisted pair. These requirements are unique for each
medium, because each one has dierent behavior related
to interference, distortion, capacitance and loss of amplitude.

57.6 Common line codes

TC-PAM
Optical line codes:
Carrier-Suppressed Return-to-Zero
Alternate-Phase Return-to-Zero
Three of Six, Fiber Optical (TS-FO)

57.7 See also

Channel coding
Source coding
Modulation

AMI

Physical layer

Modied AMI codes: B8ZS, B6ZS, B3ZS, HDB3

Self-synchronizing code and bit synchronization

57.9. EXTERNAL LINKS

57.8 References
[1] Karl Paulsen.
ums.2007.

Coding for Magnetic Storage Medi-

[2] Abdullatif Glass; Nidhal Abdulaziz; and Eesa Bastaki

(2007), Slope line coding for telecommunication networks, IEEE International Conference on Signal Processing and Communication, Dubai: IEEE: 1537, Line codes
... facilitates the transmission of data over telecommunication and computer networks and its storage in multimedia systems.
[3] Jens Krger. Data Transmission at High Rates via Kapton Flexprints for the Mu3e Experiment. 2014. p. 16
[4] Peter E. K. Chow. Code converter for polarityinsensitive transmission systems. 1983.
[5] David A. Glanzer, Fieldbus Foundation. Fieldbus Application Guide ... Wiring and Installation. Section 4.7
Polarity. p. 10
[6] George C. Clark Jr., and J. Bibb Cain. Error-Correction
Coding for Digital Communications. 2013. p. 255.
quote: When PSK data modulation is used, the potential exists for an ambiguity in the polarity of the received
channel symbols. This problem can be solved in one of
two ways. First ... a so-called transparent code. ...
[7] Prakash C. Gupta. Data Communications and Computer
Networks. 2013. p. 13. quote: Another benet of
dierential encoding is its insensitivity to polarity of the
signal. ... If the leads of a twisted pair are accidentally
reversed...

This article incorporates public domain material

from the General Services Administration document
Federal Standard 1037C (in support of MIL-STD188).

57.9 External links

Line Coding Lecture No. 9
Line Coding in Digital Communication

297

Chapter 58

Local area network

IBM Compatible

Server

iMac

Ethernet

in 1974.[4] Ethernet was developed at Xerox PARC in

19731975,[5] and led as U.S. Patent 4,063,220. In
1976, after the system was deployed at PARC, Robert
Metcalfe and David Boggs published a seminal paper, Ethernet: Distributed Packet-Switching for Local Computer Networks.[6] ARCNET was developed by
Datapoint Corporation in 1976 and announced in 1977.[7]
It had the rst commercial installation in December 1977
at Chase Manhattan Bank in New York.[8]

O X Y G E N

"

"

&

&

home

The development and proliferation of personal computers using the CP/M operating system in the late 1970s,
and later DOS-based systems starting in 1981, meant that
A conceptual diagram of a local area network using 10BASE5 many sites grew to dozens or even hundreds of computEthernet
ers. The initial driving force for networking was generally
to share storage and printers, which were both expensive
LAN redirects here. For other uses, see LAN (disam- at the time. There was much enthusiasm for the concept
and for several years, from about 1983 onward, computer
biguation).
industry pundits would regularly declare the coming year
to be, The year of the LAN.[9][10][11]
A local area network (LAN) is a computer network that
interconnects computers within a limited area such as a In practice, the concept was marred by proliferation of
residence, school, laboratory, university campus or oce incompatible physical layer and network protocol implebuilding[1] and has its network equipment and intercon- mentations, and a plethora of methods of sharing renects locally managed. By contrast, a wide area network sources. Typically, each vendor would have its own type
(WAN), not only covers a larger geographic distance, but of network card, cabling, protocol, and network operalso generally involves leased telecommunication circuits ating system. A solution appeared with the advent of
Novell NetWare which provided even-handed support for
or Internet links.
dozens of competing card/cable types, and a much more
Ethernet and Wi-Fi are the two most common transmissophisticated operating system than most of its competision technologies in use for local area networks. Histors. Netware dominated[12] the personal computer LAN
torical technologies include ARCNET, Token ring, and
business from early after its introduction in 1983 until
AppleTalk.
the mid-1990s when Microsoft introduced Windows NT
Advanced Server and Windows for Workgroups.
ctrl

ctrl

ctrl

<

>

pgup

pgdn

end

fn

Laptop computer

58.1 History

IBM Compatible

Of the competitors to NetWare, only Banyan Vines had

comparable technical strengths, but Banyan never gained
a secure base. Microsoft and 3Com worked together to
create a simple network operating system which formed
the base of 3Coms 3+Share, Microsofts LAN Manager
and IBMs LAN Server - but none of these was particularly successful.

The increasing demand and use of computers in universities and research labs in the late 1960s generated
the need to provide high-speed interconnections between
computer systems. A 1970 report from the Lawrence Radiation Laboratory detailing the growth of their OctoDuring the same period, Unix workstations were using
pus network gave a good indication of the situation.[2][3]
TCP/IP based networking. Although this market segA number of experimental and early commercial LAN ment is now much reduced, the technologies developed
technologies were developed in the 1970s. Cambridge in this area continue to be inuential on the Internet and
Ring was developed at Cambridge University starting
298

58.5. SEE ALSO

in both Linux and Apple Mac OS X networkingand
the TCP/IP protocol has now almost completely replaced
IPX, AppleTalk, NBF, and other protocols used by the
early PC LANs.

58.2 Cabling
Early LAN cabling had generally been based on various grades of coaxial cable. Shielded twisted pair was
used in IBMs Token Ring LAN implementation, but
in 1984, StarLAN showed the potential of simple unshielded twisted pair by using Cat3 cablethe same
simple cable used for telephone systems. This led to
the development of 10BASE-T (and its successors) and
structured cabling which is still the basis of most commercial LANs today.
While ber-optic cabling is common for links between
switches, use of ber to the desktop is rare.[13]

58.3 Wireless media

Many LANs are now based partly or wholly on wireless
technologies. Smartphones, tablet computers and laptops
typically have wireless networking support built-in. In
a wireless local area network, users may move unrestricted in the coverage area. Wireless networks have
become popular in residences and small businesses, because of their ease of installation. Guests are often offered Internet access via a hotspot service.

58.4 Technical aspects

Network topology describes the layout of interconnections between devices and network segments. At the Data
Link Layer and Physical Layer, a wide variety of LAN
topologies have been used, including ring, bus, mesh and
star, but the most common LAN topology in use today
is switched Ethernet. At the higher layers, NetBEUI,
IPX/SPX, AppleTalk and others were once common, but
the Internet Protocol Suite (TCP/IP) is now the standard.

299
virtual private network technologies. Depending on how
the connections are established and secured, and the distance involved, such linked LANs may also be classied
as a metropolitan area network (MAN) or a wide area
network (WAN).

58.5 See also

LAN messenger
LAN party
Network interface controller

58.6 References
[1] Gary A. Donahue (June 2007).
O'Reilly. p. 5.

Network Warrior.

[2] Samuel F. Mendicino (1970-12-01). Octopus: The

Lawrence Radiation Laboratory Network. Rogerdmoore.ca. Archived from the original on 2010-10-11.
[3] THE LAWRENCE RADIATION LABORATORY
OCTOPUS. Courant symposium series on networks.
Osti.gov. 29 Nov 1970. OSTI 4045588.
[4] A brief informal history of the Computer Laboratory.
University of Cambridge. 20 December 2001. Archived
from the original on 2010-10-11.
[5] Ethernet Prototype Circuit Board. Smithsonian National Museum of American History. Retrieved 2007-0902.
[6] Ethernet: Distributed Packet-Switching For Local Computer Networks. Acm.org. Retrieved 2010-10-11.
[7] ARCNET Timeline. ARCNETworks magazine. Fall
1998. Archived from the original (PDF) on 2010-10-11.
[8] Lamont Wood (2008-01-31). The LAN turns 30, but
will it reach 40?". Computerworld.com. Retrieved 201606-02.
[9] "'The Year of The LAN' is a long-standing joke, and I
freely admit to being the comedian that rst declared it in
1982..., Robert Metcalfe, InfoWorld Dec 27, 1993

Simple LANs generally consist of cabling and one or

more switches. A switch can be connected to a router,
cable modem, or ADSL modem for Internet access. A
[10] "...you will remember numerous computer magazines, over
LAN can include a wide variety of other network denumerous years, announcing 'the year of the LAN.'",
vices such as rewalls, load balancers, and sensors;[14] and
Quotes in 1999
more complex LANs are characterized by their use of redundant links with switches using the spanning tree pro- [11] "...a bit like the Year of the LAN which computer industry
pundits predicted for the good part of a decade..., Christotocol to prevent loops, their ability to manage diering
pher Herot
trac types via quality of service (QoS), and to segregate trac with VLANs.
LANs can maintain connections with other LANs via
leased lines, leased services, or across the Internet using

[12] Wayne Spivak (2001-07-13). Has Microsoft Ever Read

the History Books?". VARBusiness. Archived from the
original on 2010-10-11.

300

[13] Big pipe on campus: Ohio institutions implement a 10Gigabit Ethernet switched-ber backbone to enable highspeed desktop applications over UTP copper, Communications News, 2005-03-01, As alternatives were considered, ber to the desk was evaluated, yet only briey due to
the added costs for ber switches, cables and NICs. Copper is still going to be a driving force to the desktop for the
future, especially as long as the price for ber components
remains higher than for copper.
[14] A Review of the Basic Components of a Local Area Network (LAN)". NetworkBits.net. Retrieved 2008-04-08.

58.7 External links

CHAPTER 58. LOCAL AREA NETWORK

Chapter 59

Narrowband
In radio, narrowband describes a channel in which the
bandwidth of the message does not signicantly exceed
the channels coherence bandwidth.
In the study of wired channels, narrowband implies that
the channel under consideration is suciently narrow that
its frequency response can be considered at. The message bandwidth will therefore be less than the coherence
bandwidth of the channel. That is, no channel has perfectly at fading, but the analysis of many aspects of wireless systems is greatly simplied if at fading can be assumed.

59.3 References
[1] FCC Order issued in December of 2004

59.4 External links

Narrowband can also be used with the audio spectrum to

describe sounds which occupy a narrow range of frequencies.
In telephony, narrowband is usually considered to cover
frequencies 3003400 Hz.

59.1 Two-way radio narrowband

Two-Way Radio Narrowbanding refers to a U.S. Federal
Communications Commission (FCC) Order issued in
December 2004 requiring all CFR 47 Part 90 VHF (150174 MHz) and UHF (421-470 MHz) PLMR (Private
Land Mobile Radio) licensees operating legacy wideband
(25 kHz bandwidth) voice or data/SCADA systems to
migrate to narrowband (12.5 kHz bandwidth or equivalent) systems by January 1, 2013.[1]

59.2 See also

Electromagnetic Interference
Land Mobile Radio Service
Rural Internet
Broadband
Wideband
Ultra-wideband
301

FCC website
FCC Part 90 LMR VHF/UHF Narrowbanding Information and Licensee Resources
Narrowbanding Resource Guide for 2013

Chapter 60

Wideband
Ultra-wideband

For the automotive term, see Wideband (automotive).

In communications, a system is wideband when the message bandwidth signicantly exceeds the coherence bandwidth of the channel. Some communication links have
such a high data rate that they are forced to use a wide
bandwidth; other links may have relatively low data rates,
but deliberately use a wider bandwidth than necessary
for that data rate in order to gain other advantages; see
spread spectrum.

Wideband audio

60.2 References
[1] Unied Communications Architecture Basics. Cisco
Systems. Retrieved 2012-11-09.
[2] US Trademark Search. United States Patent and Trademark Oce. Retrieved 2008-10-08.

A wideband antenna is one with approximately or exactly the same operating characteristics over a very wide
passband. It is distinguished from broadband antennas,
where the passband is large, but the antenna gain and/or
radiation pattern need not stay the same over the passband.
The term Wideband Audio or (also termed HD Voice or
Wideband Voice) denotes a telephony using a wideband
codec, which uses a greater frequency range of the audio
spectrum than conventional voiceband telephone calls,
resulting in a clearer sound. Wideband in this context
is usually considered to cover frequencies in the range of
507,000 Hz, therefore allowing audio with richer tones
and better quality.[1]

[3] WideBand Corporation web site. WideBand Corporation. Retrieved 2009-03-04.

[4] http://www.widebandtechnology.com
[5] Forester research Shift from broadband to wideband

60.3 External links

According to the United States Patent and Trademark Ofce, WIDEBAND is a registered trademark of WideBand Corporation, a USA-based manufacturer of
Gigabit Ethernet equipment.[2][3]
Within Australia and New Zealand, the word WIDEBAND is a registered trademark of Wideband Technology Pty Ltd, an Australian-based company specialising
in data and communication equipment.[4]
In some contexts wideband is distinguished from
broadband in being broader.[5]

60.1 See also

Narrowband
Broadband
Broadband Internet access
302

WideBand Corporation

Chapter 61

Data transmission
Data transfer redirects here. For sharing data between
dierent programs or schemas, see Data exchange.

61.1 Distinction between related

subjects

Data transmission, digital transmission or digital

communications is the transfer of data (a digital bit
stream or a digitized analog signal[1] ) over a pointto-point or point-to-multipoint communication channel.
Examples of such channels are copper wires, optical
bers, wireless communication channels, storage media and computer buses. The data are represented as
an electromagnetic signal, such as an electrical voltage,
radiowave, microwave, or infrared signal.

Courses and textbooks in the eld of data transmission[1]

as well as digital transmission[2][3] and digital communications[4][5] have similar content.

Analog or analogue transmission is a transmission method

of conveying voice, data, image, signal or video information using a continuous signal which varies in amplitude,
phase, or some other property in proportion to that of
a variable. The messages are either represented by a sequence of pulses by means of a line code (baseband transmission), or by a limited set of continuously varying wave
forms (passband transmission), using a digital modulation
method. The passband modulation and corresponding
demodulation (also known as detection) is carried out
by modem equipment. According to the most common
denition of digital signal, both baseband and passband
signals representing bit-streams are considered as digital
transmission, while an alternative denition only considers the baseband signal as digital, and passband transmission of digital data as a form of digital-to-analog conversion.

Digital transmission or data transmission traditionally belongs to telecommunications and electrical engineering.
Basic principles of data transmission may also be covered within the computer science/computer engineering topic of data communications, which also includes
computer networking or computer communication applications and networking protocols, for example routing,
switching and inter-process communication. Although
the Transmission control protocol (TCP) involves the
term transmission, TCP and other transport layer protocols are typically not discussed in a textbook or course
about data transmission, but in computer networking.

The term tele transmission involves the analog as well

as digital communication. In most textbooks, the term
analog transmission only refers to the transmission of an
analog message signal (without digitization) by means of
an analog signal, either as a non-modulated baseband
signal, or as a passband signal using an analog modulation method such as AM or FM. It may also include
analog-over-analog pulse modulatated baseband signals
such as pulse-width modulation. In a few books within
the computer networking tradition, analog transmission
also refers to passband transmission of bit-streams using
Data transmitted may be digital messages originating digital modulation methods such as FSK, PSK and ASK.
from a data source, for example a computer or a key- Note that these methods are covered in textbooks named
board. It may also be an analog signal such as a phone digital transmission or data transmission, for example.[1]
call or a video signal, digitized into a bit-stream for example using pulse-code modulation (PCM) or more ad- The theoretical aspects of data transmission are covered
vanced source coding (analog-to-digital conversion and by information theory and coding theory.
data compression) schemes. This source coding and decoding is carried out by codec equipment.

61.2 Protocol layers and sub-topics

Courses and textbooks in the eld of data transmission

typically deal with the following OSI model protocol layers and topics:
Layer 1, the physical layer:
303

304

CHAPTER 61. DATA TRANSMISSION

Channel coding including
Digital modulation schemes
Line coding schemes
Forward error correction (FEC) codes
Bit synchronization
Multiplexing
Equalization
Channel models

Layer 2, the data link layer:

Telephone exchanges have become digital and software

controlled, facilitating many value added services. For
example, the rst AXE telephone exchange was presented in 1976. Since the late 1980s, digital communication to the end user has been possible using Integrated
Services Digital Network (ISDN) services. Since the
end of the 1990s, broadband access techniques such as
ADSL, Cable modems, ber-to-the-building (FTTB) and
ber-to-the-home (FTTH) have become widespread to
small oces and homes. The current tendency is to replace traditional telecommunication services by packet
mode communication such as IP telephony and IPTV.

Channel access schemes, media access control Transmitting analog signals digitally allows for greater
(MAC)
signal processing capability. The ability to process a com Packet mode communication and Frame syn- munications signal means that errors caused by random
processes can be detected and corrected. Digital signals
chronization
can also be sampled instead of continuously monitored.
Error detection and automatic repeat request
The multiplexing of multiple digital signals is much sim(ARQ)
pler to the multiplexing of analog signals.
Flow control
Because of all these advantages, and because recent ad Layer 6, the presentation layer:
vances in wideband communication channels and solidstate electronics have allowed scientists to fully real Source coding (digitization and data compres- ize these advantages, digital communications has grown
sion), and information theory.
quickly. Digital communications is quickly edging out
Cryptography (may occur at any layer)
analog communication because of the vast demand to
transmit computer data and the ability of digital communications to do so.

61.3 Applications and history

Data (mainly but not exclusively informational) has
been sent via non-electronic (e.g. optical, acoustic,
mechanical) means since the advent of communication.
Analog signal data has been sent electronically since the
advent of the telephone. However, the rst data electromagnetic transmission applications in modern time were
telegraphy (1809) and teletypewriters (1906), which are
both digital signals. The fundamental theoretical work
in data transmission and information theory by Harry
Nyquist, Ralph Hartley, Claude Shannon and others during the early 20th century, was done with these applications in mind.

The digital revolution has also resulted in many digital telecommunication applications where the principles
of data transmission are applied. Examples are secondgeneration (1991) and later cellular telephony, video
conferencing, digital TV (1998), digital radio (1999),
telemetry, etc.

Data transmission, digital transmission or digital communications is the physical transfer of data (a digital
bit stream or a digitized analog signal[1]) over a pointto-point or point-to-multipoint communication channel.
Examples of such channels are copper wires, optical
bers, wireless communication channels, storage media
and computer buses. The data are represented as an
electromagnetic signal, such as an electrical voltage, raData transmission is utilized in computers in computer diowave, microwave, or infrared signal.
buses and for communication with peripheral equipment While analog transmission is the transfer of a continuvia parallel ports and serial ports such as RS-232 (1969), ously varying analog signal over an analog channel, digital
Firewire (1995) and USB (1996). The principles of data communications is the transfer of discrete messages over
transmission are also utilized in storage media for Error a digital or an analog channel. The messages are either
detection and correction since 1951.
represented by a sequence of pulses by means of a line
Data transmission is utilized in computer networking
equipment such as modems (1940), local area networks
(LAN) adapters (1964), repeaters, hubs, microwave
links, wireless network access points (1997), etc.
In telephone networks, digital communication is utilized
for transferring many phone calls over the same copper
cable or ber cable by means of Pulse code modulation (PCM), i.e. sampling and digitization, in combination with Time division multiplexing (TDM) (1962).

code (baseband transmission), or by a limited set of continuously varying wave forms (passband transmission),
using a digital modulation method. The passband modulation and corresponding demodulation (also known as
detection) is carried out by modem equipment. According to the most common denition of digital signal, both
baseband and passband signals representing bit-streams
are considered as digital transmission, while an alternative denition only considers the baseband signal as dig-

61.6. ASYNCHRONOUS AND SYNCHRONOUS DATA TRANSMISSION

ital, and passband transmission of digital data as a form
of digital-to-analog conversion.
Data transmitted may be digital messages originating
from a data source, for example a computer or a keyboard. It may also be an analog signal such as a phone
call or a video signal, digitized into a bit-stream for example using pulse-code modulation (PCM) or more advanced source coding (analog-to-digital conversion and
data compression) schemes. This source coding and decoding is carried out by codec equipment.

305

Multi-drop:
Bus network
Mesh network
Ring network
Star network
Wireless network
Point-to-point
Simplex

61.4 Serial and parallel transmis61.6 Asynchronous

and
synsion
chronous data transmission
In telecommunications, serial transmission is the sequential transmission of signal elements of a group representing a character or other entity of data. Digital serial transmissions are bits sent over a single wire, frequency or
optical path sequentially. Because it requires less signal
processing and less chances for error than parallel transmission, the transfer rate of each individual path may be
faster. This can be used over longer distances as a check
digit or parity bit can be sent along it easily.
In telecommunications, parallel transmission is the simultaneous transmission of the signal elements of a character or other entity of data. In digital communications,
parallel transmission is the simultaneous transmission of
related signal elements over two or more separate paths.
Multiple electrical wires are used which can transmit
multiple bits simultaneously, which allows for higher data
transfer rates than can be achieved with serial transmission. This method is used internally within the computer,
for example the internal buses, and sometimes externally
for such things as printers, The major issue with this is
skewing because the wires in parallel data transmission have slightly dierent properties (not intentionally)
so some bits may arrive before others, which may corrupt
the message. A parity bit can help to reduce this. However, electrical wire parallel data transmission is therefore
less reliable for long distances because corrupt transmissions are far more likely.

61.5 Types of
channels

communication

Main article: communication channel

Some communications channel types include:

Main article: comparison of synchronous and asynchronous signalling

Asynchronous start-stop transmission uses start and
stop bits to signify the beginning bit ASCII character
would actually be transmitted using 10 bits. For example, 0100 0001 would become "1 0100 0001 0". The
extra one (or zero, depending on parity bit) at the start
and end of the transmission tells the receiver rst that a
character is coming and secondly that the character has
ended. This method of transmission is used when data
are sent intermittently as opposed to in a solid stream. In
the previous example the start and stop bits are in bold.
The start and stop bits must be of opposite polarity. This
allows the receiver to recognize when the second packet
of information is being sent.
Synchronous transmission uses no start and stop bits,
but instead synchronizes transmission speeds at both the
receiving and sending end of the transmission using clock
signal(s) built into each component. A continual stream
of data is then sent between the two nodes. Due to there
being no start and stop bits the data transfer rate is quicker
although more errors will occur, as the clocks will eventually get out of sync, and the receiving device would have
the wrong time that had been agreed in the protocol for
sending/receiving data, so some bytes could become corrupted (by losing bits). Ways to get around this problem
include re-synchronization of the clocks and use of check
digits to ensure the byte is correctly interpreted and received

61.7 See also

Computer networking

Data transmission circuit

Information theory

Full-duplex

Media (communication)

Half-duplex

Signal processing

306
Telecommunication
Transmission (disambiguation)

61.8 Notes
[1] A. P. Clark, Principles of Digital Data Transmission,
Published by Wiley, 1983
[2] David R. Smith, Digital Transmission Systems, Kluwer
International Publishers, 2003, ISBN 1-4020-7587-1.
See table-of-contents.
[3] Sergio Benedetto, Ezio Biglieri, Principles of Digital
Transmission: With Wireless Applications, Springer
2008, ISBN 0-306-45753-9, ISBN 978-0-306-45753-1.
See table-of-contents
[4] Simon Haykin, Digital Communications, John Wiley
& Sons, 1988. ISBN 978-0-471-62947-4. See table-ofcontents.
[5] John Proakis, Digital Communications, 4th edition,
McGraw-Hill, 2000. ISBN 0-07-232111-3. See tableof-contents.

CHAPTER 61. DATA TRANSMISSION

Chapter 62

Carrier frequency
Not to be confused with the rate of occurrence within a
living population of a broken chromosome that causes a
genetic disorder in molecular biology..
In telecommunication systems, Carrier frequency is a
technical term used to indicate:
Vaguely speaking, the center frequency or the
frequency of a carrier wave
The nominal frequency or the center frequency of
an analog frequency modulation, phase modulation,
or double-sideband suppressed-carrier transmission
(DSB-SC) (AM-suppressed carrier), radio wave
The frequency of the unmodulated electromagnetic
wave at the output of a conventional amplitudemodulated (AM-unsupressed carrier), or frequencymodulated (FM), or phase-modulated (PM) radio
transmitter
The nominal frequency or center frequency of various kinds of radio signals with digital modulation
-- provided that the message bit stream is a random
uncorrelated sequence of equally probable ones and
zeroes (marks and spaces)

307

Chapter 63

Frequency modulation synthesis

In audio and music, frequency modulation synthesis
(or FM synthesis) is a form of audio synthesis where
the timbre of a simple waveform (such as a square, triangle, or sawtooth) is changed by modulating its frequency
with a modulator frequency that is also in the audio range,
resulting in a more complex waveform and a dierentsounding tone that can also be described as gritty if it
is a thick and dark timbre. The frequency of an oscillator
is altered or distorted, in accordance with the amplitude
of a modulating signal. (Dodge & Jerse 1997, p. 115)

a special case of QAM, with phase modulation simply

making the implementation resilient against undesirable
drift in frequency of carrier waves due to self-modulation
or due to DC bias in the modulating wave.[1]

FM synthesis using analog oscillators may result in pitch

instability. However, FM synthesis can also be implemented digitally, the latter proving to be more 'reliable'
and is currently seen as standard practice. Digital FM
synthesis (using the more frequency-stable phase modulation variant) was the basis of several commercial musical
instruments beginning as early as 1977. The Synclavier
I, manufactured by New England Digital Corporation beginning in 1977, included a 32-voice digital FM synthesizer. Yamahas groundbreaking DX7 brought FM to the
forefront of synthesis in the mid-1980s.

plemented FM on his instruments in the mid-1960s, prior

to Yamahas patent. His 158, 258 and 259 dual oscillator modules had a specic FM control voltage input,[2]
and the model 208 (Music Easel) had a modulation oscillator hard-wired to allow FM as well as AM of the primary oscillator.[3] These early applications used analog
oscillators, and this capability was also followed by other
modular synthesizers and portable synthesizers including
Minimoog and ARP Odyssey.

As noted earlier, FM synthesis was the basis of some of

the early generations of digital synthesizers, most notable
being those from New England Digital Corporation and
Yamaha. Yamahas popular DX7 synthesizer was ubiquitous throughout the 1980s. Several other models by
Yamaha provided variations and evolutions of FM synFM synthesis can create both harmonic and inharmonic thesis during that decade.
sounds. For synthesizing harmonic sounds, the modulat- Yamaha had patented its hardware implementation of
ing signal must have a harmonic relationship to the origi- FM in the 1980s, allowing it and New England Digital
nal carrier signal. As the amount of frequency modulation Corporation (under license from Yamaha) to nearly moincreases, the sound grows progressively more complex. nopolize the market for that technology until the midThrough the use of modulators with frequencies that are 1990s. Casio developed a related form of synthesis called
non-integer multiples of the carrier signal (i.e. non har- phase distortion synthesis, used in its CZ range of synmonic), atonal and tonal bell-like and percussive sounds thesizers. It had a similar (but slightly dierently decan easily be created.
rived) sound quality to the DX series. Don Buchla im-

63.1 History
The technique of the digital implementation of frequency
modulation, which was developed by John Chowning
(Chowning 1973, cited in Dodge & Jerse 1997, p. 115)
at Stanford University in 1967-68, was patented in 1975
and later licensed to Yamaha.
The implementation commercialized by Yamaha (US
Patent 4018121 Apr 1977 or U.S. Patent 4,018,121) is
actually based on phase modulation, but the results end
up being equivalent mathematically as both are essentially

With the expiration of the Stanford University FM patent

in 1995, digital FM synthesis can now be implemented
freely by other manufacturers. The FM synthesis patent
brought Stanford $20 million before it expired, making
it (in 1994) the second most lucrative licensing agreement in Stanfords history.[4] FM today is mostly found
in software-based synths such as FM8 by Native Instruments or Sytrus by Image-Line, but it has also been incorporated into the synthesis repertoire of some modern digital synthesizers, usually coexisting as an option alongside
other methods of synthesis such as subtractive, samplebased synthesis, additive synthesis, and other techniques.
The degree of complexity of the FM in such hardware
synths may vary from simple 2-operator FM, to the highly
exible 6-operator engines of the Korg Kronos and Alesis
Fusion, to creation of FM in extensively modular engines

308

63.4. SEE ALSO

309

such as those in the latest synthesisers by Kurzweil Music

Systems.
New hardware synths specically marketed for their FM
capabilities disappeared from the market after the release of the Yamaha SY99 and FS1R, and even those
marketed their highly powerful FM abilities as counterparts to sample-based synthesis and formant synthesis respectively. However, well-developed FM synthesis options are a feature of Nord Lead synths manufactured
by Clavia, the Alesis Fusion range, the Korg Oasys and
Kronos and the Modor NF-1. Various other synthesizers oer limited FM abilities to supplement their main
engines.
Most recently, in 2016, Korg released the Korg Volca
FM, an FM iteration of the Korg Volca series of compact, aordable desktop modules.

and a lemma of Bessel function,

cos( sin ) = J0 () + 2

J2n () cos(2n)

n=1

sin( sin ) = 2

J2n+1 () sin((2n + 1))

n=0

(Source: Kreh, Martin (2012), Bessel

Function (PDF), Gottingen Summer School
on Number Theory, Gottingen, Germany,
July 29, 2012August 18, 2012, pp. 56)
as following:
sin (c + sin(m ))

= sin(c ) cos( sin(m )) + cos(c ) sin( sin(m ))

[
]
[

= sin(c ) J0 () + 2
J2n () cos(2nm ) + cos(c ) 2
J2n+1 () sin
n=1

n=0

= J0 () sin(c ) + J1 ()2 cos(c ) sin(m ) + J2 ()2 sin(c ) cos(2m ) + J3 (

63.2 Spectral analysis

= J0 () sin(c ) +

Jn () [ sin(c + nm ) + (1)n sin(c nm ) ]

n=1

The spectrum generated by FM synthesis with one modulator is expressed as follows:[5][6]

For modulation signal m(t) = B sin(m t) , the carrier
signal is
(

F M (t) = A sin

(c + B sin(m )) d
(

)
B
= A sin c t
(cos(m t) 1)
m
(
)
B
= A sin c t +
(sin(m t /2) + 1)
m
If we were to ignore the constant phase terms on the carrier c = B/m and the modulator m = /2 , nally we would get the following expression, as seen on
Chowning 1973 and Roads 1996, p. 232:

Jn () sin(c + nm )

( Jn (x) = (1)n Jn (x))

n=

63.4 See also

Additive synthesis
Chiptune
Digital synthesizer
Electronic music
Sound card
Sound chip
Video game music

F M (t) A sin (c t + sin(m t))

63.5 References
(
)

n
= A J0 () sin(c t) +
Jn () [ sin((c + n m ) t) + (1) sin((c n m ) t) ]
Chowning, J. (1973). The Synthesis of Complex
n=1
Audio Spectra by Means of Frequency Modulation

(PDF). Journal of the Audio Engineering Society.

Jn () sin((c + n m ) t)
= A
21 (7). (also available in PDF as digital version
n=
2/13/2007)
where c , m are angular frequencies ( = 2f ) of
carrier and modulator, = B/m is frequency modula Chowning, John; Bristow, David (1986). FM Thetion index, and amplitudes Jn () is n -th Bessel function
ory & Applications - By Musicians For Musicians.
of rst kind, respectively.[note 1]
Tokyo: Yamaha. ISBN 4-636-17482-8.

63.3 Footnote
[1] above expression is transformed using trigonometric addition formulas
sin(x y) = sin x cos y cos x sin y

Roads, Curtis (1996). The Computer Music Tutorial.

MIT Press. ISBN 978-0-262-68082-0.
Dodge, Charles; Jerse, Thomas A. (1997). Computer Music: Synthesis, Composition and Performance. New York: Schirmer Books. ISBN 0-02864682-7.

310

[1] Rob Hordijk. FM synthesis on Modular. Nord Modular

& Micro Modular V3.03 tips & tricks. Clavia DMI AB.
[2] Dr. Hubert Howe (1960s). Buchla Electronic Music System: Users Manual written for CBS Musical Instruments
(Buchla 100 Owners Manual). Educational Research Department, CBS Musical Instruments, Columbia Broadcasting System. p. 7. At this point we may consider various
additional signal modications that we may wish to make
to the series of tones produced by the above example. For
instance, if we would like to add frequency modulation to
the tones, it is necessary to patch another audio signal into
the jack connected by a line to the middle dial on the Model
158 Dual Sine-Sawtooth Oscillator. ...
[3] Atten Strange (1974). Programming and Metaprogramming in the Electro-Organism - An Operating Directive for
the Music Easel. Buchla and Associates.
[4] Stanford University News Service (06/07/94), Music synthesis approaches sound quality of real instruments
[5] Chowning 1973, pp. 12
[6] Doering, Ed. Frequency Modulation Mathematics. Retrieved 2013-04-11.

63.6 External links

An Introduction To FM, by Bill Schottstaedt
FM tutorial
Synth Secrets, Part 12: An Introduction To Frequency Modulation, by Gordon Reid
Synth Secrets, Part 13: More On Frequency Modulation, by Gordon Reid
Paul Wiens Synth School: Part 3
F.M. Synthesis including complex operator analysis
Part 1 of a 2-part YouTube tutorial on FM synthesis
with numerous audio examples

CHAPTER 63. FREQUENCY MODULATION SYNTHESIS

Chapter 64

Constant envelope
Constant envelope is achieved when a sinusoidal waveform reaches equilibrium in a specic system. This happens when negative feedback in a control system, such as
in radio automatic gain control or in an amplier reaches
steady state. Steady state, as dened in electrical engineering, occurs after a system becomes settled. To
be more specic, control systems are unstable until they
reach a steady state. Constant envelope needs to occur for the system to be stable, where there is the least
amount of noise and feedback gain has rendered the system steady. Feedback is used to create a feedback signal
to control gain, reduce distortion, control output voltage,
improve stability or create instability, as in an oscillator.
Some examples of constant envelope modulations are as
FSK, GFSK, MSK, GMSK and Fehers IJF - All constant envelope modulations allow power ampliers to operate at or near saturation levels.[1] Although, the power
spectrum eciency of a non-constant amplitude envelope [2] is always higher than that of a constant envelope
modulation.[3]

64.1 See also

Envelope (waves)

64.2 References
[1] Advantages of Constant Envelope Modulation.
mag.com. Retrieved 5 April 2016.

sss-

[2] Patent EP2284996A1 - Closed loop power control of

non-constant envelope waveforms using sample/hold.
google.ch. Retrieved 5 April 2016.
[3] 8.5: Nonconstant Envelope Modulation.
spec.com. Retrieved 5 April 2016.

global-

311

Chapter 65

Angle modulation
Angle modulation is a class of analog modulation.
These techniques are based on altering the angle (or
phase) of a carrier signal to transmit data. This as opposed to varying the amplitude of the carrier, such as in
amplitude modulation transmission.
Angle Modulation is modulation in which the angle of
a sine-wave carrier is varied by a modulating wave.
Frequency modulation (FM) and phase modulation (PM)
are the two main types of angle modulation. In frequency
modulation, the modulating signal causes the carrier frequency to vary. These variations are controlled by both
the frequency and the amplitude of the modulating wave.
In phase modulation, the phase of the carrier is controlled
by the modulating waveform.

65.1 See also

Polar modulation

312

Chapter 66

Phase modulation
This article is about the analog modulation. For the
digital version, see Phase-shift keying.
Phase modulation (PM) is a modulation pattern that encodes information as variations in the instantaneous phase
of a carrier wave.
Phase modulation is widely used for transmitting radio
waves and is an integral part of many digital transmission
coding schemes that underlie a wide range of technologies
like WiFi, GSM and satellite television.
Phase modulation is closely related to frequency modulation (FM); it is often used as an intermediate step
to achieve FM. Mathematically both phase and frequency modulation can be considered a special case of
quadrature amplitude modulation (QAM).
PM is used for signal and waveform generation in digital
synthesizers, such as the Yamaha DX7 to implement FM
synthesis. A related type of sound synthesis called phase The modulating wave (blue) is modulating the carrier wave
(red), resulting the PM signal (green). g(x) = /2 * sin(2*2t+
distortion is used in the Casio CZ synthesizers.
/2*sin(3*2t))

66.1 Theory

modulated signal at that point. It can also be viewed as a

change of the frequency of the carrier signal, and phase
modulation can thus be considered a special case of FM
PM changes the phase angle of the complex envelope in
in which the carrier frequency modulation is given by the
direct proportion to the message signal.
time derivative of the phase modulation.
Suppose that the signal to be sent (called the modulating
The modulation signal could here be
or message signal) is m(t) and the carrier onto which the
signal is to be modulated is
m(t) = cos (c t + hm (t))
c(t) = Ac sin (c t + c ) .

The mathematics of the spectral behavior reveals that

there are two regions of particular interest:

Annotated:

For small amplitude signals, PM is similar to

amplitude modulation (AM) and exhibits its unfortunate doubling of baseband bandwidth and poor efciency.

carrier(time) = (carrier amplitude)*sin(carrier

frequency*time + phase shift)
This makes the modulated signal

For a single large sinusoidal signal, PM is similar to

FM, and its bandwidth is approximately
y(t) = Ac sin (c t + m(t) + c ) .
This shows how m(t) modulates the phase - the greater
m(t) is at a point in time, the greater the phase shift of the
313

2 (h + 1) fM

314

CHAPTER 66. PHASE MODULATION

where fM = m /2 and h is the modulation
index dened below. This is also known as
Carsons Rule for PM.

66.2 Modulation index

As with other modulation indices, this quantity indicates
by how much the modulated variable varies around its unmodulated level. It relates to the variations in the phase
of the carrier signal:

h =
where is the peak phase deviation. Compare to the
modulation index for frequency modulation.

66.3 See also

Angle modulation
Automatic frequency control
Modulation for a list of other modulation techniques
Polar modulation
Electro-optic modulator for Pockels Eect phase
modulation for applying sidebands to a monochromatic wave

Chapter 67

Bit rate
For disk drives, see Data transfer rate (disk drive).
Rb =

1
,
Tb

In telecommunications and computing, bit rate (sometimes written bitrate or as a variable R[1] ) is the number The gross bit rate is related to the symbol rate or modof bits that are conveyed or processed per unit of time.
ulation rate, which is expressed in bauds or symbols per
The bit rate is quantied using the bits per second unit second. However, the gross bit rate and the baud value
(symbol: "bit/s"), often in conjunction with an SI prex are equal only when there are only two levels per symsuch as "kilo" (1 kbit/s = 1000 bit/s), "mega" (1 Mbit/s bol, representing 0 and 1, meaning that each symbol of a
= 1000 kbit/s), "giga" (1 Gbit/s = 1000 Mbit/s) or "tera" data transmission system carries exactly one bit of data;
(1 Tbit/s = 1000 Gbit/s).[2] The non-standard abbrevia- for example, this is not the case for modern modulation
tion "bps" is often used to replace the standard symbol systems used in modems and LAN equipment.[10]
bit/s, so that, for example, 1 Mbps is used to mean For most line codes and modulation methods:
one million bits per second.
One byte per second (1 B/s) corresponds to 8 bit/s.

Symbol rate Gross bit rate

More specically, a line code (or baseband transmission scheme) representing the data using pulse-amplitude
modulation with 2N dierent voltage levels, can transfer
67.1 Prexes
N bit/pulse. A digital modulation method (or passband
transmission scheme) using 2N dierent symbols, for exWhen quantifying large bit rates, SI prexes (also known
ample 2N amplitudes, phases or frequencies, can transfer
as metric prexes or decimal prexes) are used, thus:
N bit/symbol. This results in:
Binary prexes are sometimes used for bit rates .[3][4] The
International Standard (IEC 80000-13) species dierent
Gross bit rate = Symbol rate N
abbreviations for binary and decimal (SI) prexes (e.g.
1 KiB/s = 1024 B/s = 8192 bit/s, and 1 MiB/s = 1024 An exception from the above is some self-synchronizing
KiB/s).
line codes, for example Manchester coding and return-tozero (RTZ) coding, where each bit is represented by two
pulses (signal states), resulting in:

67.2 In data communications

67.2.1

Gross bit rate = Symbol rate/2

Gross bit rate

In digital communication systems, the physical layer gross

bitrate,[5] raw bitrate,[6] data signaling rate,[7] gross data
transfer rate[8] or uncoded transmission rate[6] (sometimes
written as a variable R [5][6] or f [9] ) is the total number
of physically transferred bits per second over a communication link, including useful data as well as protocol overhead.

A theoretical upper bound for the symbol rate in baud,

symbols/s or pulses/s for a certain spectral bandwidth in
hertz is given by the Nyquist law:
Symbol rate Nyquist rate = 2 bandwidth

In practice this upper bound can only be approached for

line coding schemes and for so-called vestigal sideband
digital modulation. Most other digital carrier-modulated
schemes, for example ASK, PSK, QAM and OFDM, can
In case of serial communications, the gross bit rate is re- be characterized as double sideband modulation, resulting
lated to the bit transmission time Tb as:
in the following relation:
315

316

CHAPTER 67. BIT RATE

Symbol rate Bandwidth

bit rate is between 12 and 72 Mbit/s inclusive of errorcorrecting codes.

In case of parallel communication, the gross bit rate is The net bit rate of ISDN2 Basic Rate Interface (2 Bgiven by
channels + 1 D-channel) of 64+64+16 = 144 kbit/s also
refers to the payload data rates, while the D channel signalling rate is 16 kbit/s.
n

log2 Mi
The net bit rate of the Ethernet 100Base-TX physical
Ti
i=1
layer standard is 100 Mbit/s, while the gross bitrate is
where n is the number of parallel channels, Mi is the num- 125 Mbit/second, due to the 4B5B (four bit over ve bit)
ber of symbols or levels of the modulation in the i-th encoding. In this case, the gross bit rate is equal to the
channel, and Ti is the symbol duration time, expressed symbol rate or pulse rate of 125 megabaud, due to the
NRZI line code.
in seconds, for the i-th channel.
In communications technologies without forward error
correction and other physical layer protocol overhead,
67.2.2 Information rate
there is no distinction between gross bit rate and physical layer net bit rate. For example, the net as well as
The physical layer net bitrate,[11] information rate,[5] gross bit rate of Ethernet 10Base-T is 10 Mbit/s. Due to
useful bit rate,[12] payload rate,[13] net data trans- the Manchester line code, each bit is represented by two
fer rate,[8] coded transmission rate,[6] eective data pulses, resulting in a pulse rate of 20 megabaud.
rate[6] or wire speed (informal language) of a digital
communication channel is the capacity excluding the The connection speed of a V.92 voiceband modem typphysical layer protocol overhead, for example time divi- ically refers to the gross bit rate, since there is no addision multiplex (TDM) framing bits, redundant forward tional error-correction code. It can be up to 56,000 bit/s
error correction (FEC) codes, equalizer training symbols downstreams and 48,000 bit/s upstreams. A lower bit rate
and other channel coding. Error-correcting codes are may be chosen during the connection establishment phase
common especially in wireless communication systems, due to adaptive modulation - slower but more robust modbroadband modem standards and modern copper-based ulation schemes are chosen in case of poor signal-to-noise
high-speed LANs. The physical layer net bitrate is the ratio. Due to data compression, the actual data transmisdatarate measured at a reference point in the interface sion rate or throughput (see below) may be higher.
between the datalink layer and physical layer, and may The channel capacity, also known as the Shannon capacconsequently include data link and higher layer overhead. ity, is a theoretical upper bound for the maximum net
In modems and wireless systems, link adaptation (auto- bitrate, exclusive of forward error correction coding, that
matic adaption of the data rate and the modulation and/or is possible without bit errors for a certain physical analog
error coding scheme to the signal quality) is often ap- node-to-node communication link.
plied. In that context, the term peak bitrate denotes
the net bitrate of the fastest and least robust transmission
mode, used for example when the distance is very short
between sender and transmitter.[14] Some operating systems and network equipment may detect the "connection
speed"[15] (informal language) of a network access technology or communication device, implying the current
net bit rate. Note that the term line rate in some textbooks is dened as gross bit rate,[13] in others as net bit
rate.

Net bit rate Channel capacity

The channel capacity is proportional to the analog bandwidth in hertz. This proportionality is called Hartleys
law. Consequently, the net bit rate is sometimes called
digital bandwidth capacity in bit/s.

67.2.3 Network throughput

The relationship between the gross bit rate and net bit rate Main article: Throughput
is aected by the FEC code rate according to the following.
The term throughput, essentially the same thing as digital
bandwidth consumption, denotes the achieved average
Net bit rate Gross bit rate code rate
useful bit rate in a computer network over a logical or
physical communication link or through a network node,
The connection speed of a technology that involves for- typically measured at a reference point above the datalink
ward error correction typically refers to the physical layer layer. This implies that the throughput often excludes
net bit rate in accordance with the above denition.
data link layer protocol overhead. The throughput is afFor example, the net bitrate (and thus the connection fected by the trac load from the data source in question,
speed) of an IEEE 802.11a wireless network is the net as well as from other sources sharing the same network
bit rate of between 6 and 54 Mbit/s, while the gross resources. See also Measuring network throughput.

67.4. ENCODING BIT RATE

67.2.4

Goodput (data transfer rate)

Main article: Goodput

317
If lossy data compression is used on audio or visual data,
dierences from the original signal will be introduced;
if the compression is substantial, or lossy data is decompressed and recompressed, this may become noticeable in
the form of compression artifacts. Whether these aect
the perceived quality, and if so how much, depends on the
compression scheme, encoder power, the characteristics
of the input data, the listeners perceptions, the listeners
familiarity with artifacts, and the listening or viewing environment.

Goodput or data transfer rate refers to the achieved average net bit rate that is delivered to the application layer,
exclusive of all protocol overhead, data packets retransmissions, etc. For example, in the case of le transfer, the
goodput corresponds to the achieved le transfer rate.
The le transfer rate in bit/s can be calculated as the le
size (in bytes) divided by the le transfer time (in sec- The bitrates in this section are approximately the minonds) and multiplied by eight.
imum that the average listener in a typical listening or
As an example, the goodput or data transfer rate of a viewing environment, when using the best available comV.92 voiceband modem is aected by the modem phys- pression, would perceive as not signicantly worse than
ical layer and data link layer protocols. It is sometimes the reference standard:
higher than the physical layer data rate due to V.44 data
compression, and sometimes lower due to bit-errors and
automatic repeat request retransmissions.

67.4 Encoding bit rate

If no data compression is provided by the network equipIn digital multimedia, bit rate often refers to the numment or protocols, we have the following relation:
ber of bits used per unit of playback time to represent a
continuous medium such as audio or video after source
Goodput Throughput Maximum throughcoding (data compression). The encoding bit rate of a
put Net bit rate
multimedia le is the size of a multimedia le in bytes divided by the playback time of the recording (in seconds),
for a certain communication path.
multiplied by eight.

67.2.5

Progress trends

These are examples of physical layer net bit rates in proposed communication standard interfaces and devices:

For realtime streaming multimedia, the encoding bit rate

is the goodput that is required to avoid interrupt:
Encoding bit rate = Required goodput

The term average bitrate is used in case of variable bitrate

For more examples, see List of device bit rates, Spectral multimedia source coding schemes. In this context, the
eciency comparison table and OFDM system compar- peak bit rate is the maximum number of bits required
ison table.
for any short-term block of compressed data.[16]

67.3 Multimedia
In digital multimedia, bitrate represents the amount of
information, or detail, that is stored per unit of time of a
recording. The bitrate depends on several factors:

A theoretical lower bound for the encoding bit rate for

lossless data compression is the source information rate,
also known as the entropy rate.
Entropy rate Multimedia bit rate

67.4.1 Audio

The original material may be sampled at dierent CD-DA

frequencies.
CD-DA, the standard audio CD, is said to have a data rate
The samples may use dierent numbers of bits.
of 44.1 kHz/16, meaning that the audio data was sampled
44,100 times per second and with a bit depth of 16. CD The data may be encoded by dierent schemes.
DA is also stereo, using a left and right channel, so the
The information may be digitally compressed by dif- amount of audio data per second is double that of mono,
where only a single channel is used.
ferent algorithms or to dierent degrees.
The bit rate of PCM audio data can be calculated with the
Generally, choices are made about the above factors in following formula:
order to achieve the desired trade-o between minimizing the bitrate and maximizing the quality of the material
when it is played.
bit rate = sample rate bit depth channels

318

CHAPTER 67. BIT RATE

For example, the bit rate of a CD-DA recording (44.1

kHz sampling rate, 16 bits per sample and 2 channels)
can be calculated as follows:

44, 100 16 2 = 1, 411, 200 bit/s = 1, 411.2 kbit/s

The cumulative size of a length of PCM audio data (excluding a le header or other metadata) can be calculated
using the following formula:

6 kbit/s minimum bitrate available through the

open-source Opus codec
8 kbit/s telephone quality using speech codecs
32-500 kbit/s lossy audio as used in Ogg Vorbis
256 kbit/s Digital Audio Broadcasting (DAB)
MP2 bit rate required to achieve a high quality
signal[17]

400 kbit/s1,411 kbit/s lossless audio as used

in formats such as Free Lossless Audio Codec,
WavPack, or Monkeys Audio to compress CD ausize in bits = sample ratebit depthchannelslength ofdio
time

The cumulative size in bytes can be found by dividing the

le size in bits by the number of bits in a byte, which is 8:

size in bytes =

size in bits
8

Therefore, 80 minutes (4,800 seconds) of CD-DA data

requires 846,720,000 bytes of storage:

1,411.2 kbit/s Linear PCM sound format of CDDA

5,644.8 kbit/s DSD, which is a trademarked implementation of PDM sound format used on Super
Audio CD[18]
6.144 Mbit/s E-AC-3 (Dolby Digital Plus), which
is an enhanced coding system based on the AC-3
codec

9.6 Mbit/s DVD-Audio, a digital format for deliv44, 100 16 2 4, 800

= 846, 720, 000 bytes 847 MB ering high-delity audio content on a DVD. DVD8
Audio is not intended to be a video delivery format and is not the same as video DVDs containing
concert lms or music videos. These discs cannot
MP3
be played on a standard DVD-player without DVDAudio logo.[19]
The MP3 audio format provides lossy data compression.
Audio quality improves with increasing bitrate:
18 Mbit/s advanced lossless audio codec based on
32 kbit/s generally acceptable only for speech

Meridian Lossless Packing

96 kbit/s generally used for speech or low-quality 67.4.2 Video

streaming
16 kbit/s videophone quality (minimum necessary
128 or 160 kbit/s mid-range bitrate quality
for a consumer-acceptable talking head picture using various video compression schemes)
192 kbit/s medium quality bitrate
128384
kbit/s

business-oriented
256 kbit/s a commonly used high-quality bitrate
videoconferencing quality using video compression
320 kbit/s highest level supported by the MP3 standard

400 kbit/s YouTube 240p videos (using H.264)[20]

750 kbit/s YouTube 360p videos (using H.264)[20]

Other audio
700 bit/s lowest bitrate open-source speech codec
Codec2, but barely recognizable yet, sounds much
better at 1.2 kbit/s

1 Mbit/s YouTube 480p videos (using H.264)[20]

1.15 Mbit/s max VCD quality (using MPEG1
compression)[21]
2.5 Mbit/s YouTube 720p videos (using H.264)[20]

800 bit/s minimum necessary for recognizable

speech, using the special-purpose FS-1015 speech
codecs

3.5 Mbit/s typ Standard-denition television quality (with bit-rate reduction from MPEG-2 compression)

2.15 kbit/s minimum bitrate available through the

open-source Speex codec

3.8 Mbit/s YouTube 720p (at 60fps mode) videos

(using H.264)[20]

67.6. REFERENCES

319

4.5 Mbit/s YouTube 1080p videos (using H.264)[20]

6.8 Mbit/s YouTube 1080p (at 60 fps mode) videos
(using H.264)[20]

67.6 References

MPEG2

[1] Gupta, Prakash C (2006). Data Communications and

Computer Networks. PHI Learning. Retrieved 10 July
2011.

8 to 15 Mbit/s typ HDTV quality (with bit-rate

reduction from MPEG-4 AVC compression)

[2] International Electrotechnical Commission (2007).

Prexes for binary multiples. Retrieved 4 February
2014.

9.8 Mbit/s max

compression)[22]

DVD

(using

19 Mbit/s approximate HDV 720p (using MPEG2

compression)[23]
24 Mbit/s max AVCHD (using MPEG4 AVC
compression)[24]
25 Mbit/s approximate HDV 1080i (using
MPEG2 compression)[23]
29.4 Mbit/s max HD DVD
40 Mbit/s max 1080p Blu-ray Disc (using
MPEG2, MPEG4 AVC or VC-1 compression)[25]

67.4.3

Notes

For technical reasons (hardware/software protocols,

overheads, encoding schemes, etc.) the actual bit rates
used by some of the compared-to devices may be signicantly higher than what is listed above. For example, telephone circuits using law or A-law companding (pulse
code modulation) yield 64 kbit/s.

67.5 See also

Dolby AC-3
Audio bit depth
Average bitrate
Bandwidth (computing)
Baud (symbol rate)
Bit-synchronous operation
Clock rate
Code rate
Constant bitrate
Data rate units
Data signaling rate
List of device bit rates
Measuring network throughput
Orders of magnitude (bit rate)
Spectral eciency
Variable bitrate

[3] Schlosser, S. W., Grin, J. L., Nagle, D. F., & Ganger,

G. R. (1999). Filling the memory access gap: A
case for on-chip magnetic storage (No. CMU-CS-99174). CARNEGIE-MELLON UNIV PITTSBURGH PA
SCHOOL OF COMPUTER SCIENCE.
[4] Monitoring le transfers that are in progress from WebSphere MQ Explorer. Retrieved 10 October 2014.
[5] Guimares, Dayan Adionel (2009). section 8.1.1.3 Gross
Bit Rate and Information Rate. Digital Transmission:
A Simulation-Aided Introduction with VisSim/Comm. Spinger. Retrieved 10 July 2011.
[6] Kaveh Pahlavan, Prashant Krishnamurthy (2009).
Networking Fundamentals.
John Wiley & Sons.
Retrieved 10 July 2011.
[7] Network Dictionary. Javvin Technologies. 2007. Retrieved 10 July 2011.
[8] Harte, Lawrence; Kikta, Roman; Levine, Richard (2002).
3G wireless demystied. McGraw-Hill Professional. Retrieved 10 July 2011.
[9] J.S. Chitode (2008). Principles of Digital Communication.
Technical Publication. Retrieved 10 July 2011.
[10] Lou Frenzel. Whats The Dierence Between Bit Rate
And Baud Rate?". Electronic Design. 2012.
[11] Theodory S. Rappaport, Wireless communications: principles and practice, Prentice Hall PTR, 2002
[12] Lajos Hanzo, Peter J. Cherriman, Jrgen Streit, Video
compression and communications: from basics to H.261,
H.263, H.264, MPEG4 for DVB and HSDPA-style adaptive turbo-transceivers, Wiley-IEEE, 2007.
[13] V.S.Bagad, I.A.Dhotre, Data Communication Systems,
Technical Publications, 2009.
[14] Sudhir Dixit, Ramjee Prasad Wireless IP and building the
mobile Internet, Artech House
[15] Guy Hart-Davis,Mastering Microsoft Windows Vista
home: premium and basic, John Wiley and Sons, 2007
[16] Khalid Sayood, Lossless compression handbook, Academic Press, 2003.
[17] Page 26 of BBC R&D White Paper WHP 061 June 2003,
DAB: An introduction to the DAB Eureka system and
how it works http://downloads.bbc.co.uk/rd/pubs/whp/
whp-pdf-files/WHP061.pdf

320

[18] Extremetech.com, Leslie Shapiro, 2 July 2001. Surround

Sound: The High-End: SACD and DVD-Audio. Retrieved
19 May 2010. 2 channels, 1-bit, 2822.4 kHz DSD audio
(2x1x2,822,400)= 5,644,800 bits/s
[19] Understanding DVD-Audio (PDF). Sonic Solutions.
Archived from the original (PDF) on 4 March 2012. Retrieved 23 April 2014.
[20] YouTube bit rates. Retrieved 10 October 2014.
[21] MPEG1 Specications. UK: ICDia. Retrieved 11 July
2011.
[22] DVD-MPEG dierences. Sourceforge. Retrieved 11
July 2011.
[23] HDV Specications (PDF), HDV Information.
[24] Avchd Information. AVCHD Info. Retrieved 11 July
2011.
[25] 3.3 Video Streams, Blu-ray Disc Format 2.B Audio Visual Application Format Specications for BD-ROM Version 2.4 (PDF) (white paper), May 2010, p. 17.

This article incorporates public domain material from

the General Services Administration document Federal
Standard 1037C (in support of MIL-STD-188).

67.7 External links

DVD-HQ bit rate calculator Calculate bit rate for
various types of digital video media.
Maximum PC - Do Higher MP3 Bit Rates Pay O?

CHAPTER 67. BIT RATE

Chapter 68

Symbol rate
In digital communications, symbol rate, also known
in case of a line code, this corresponds to 1,000
as baud rate and modulation rate, is the number of
pulses per second. The symbol duration time is
symbol changes, waveform changes, or signaling events,
1/1,000 second = 1 millisecond.
across the transmission medium per time unit using a digitally modulated signal or a line code. The symbol rate is
measured in baud (Bd) or symbols per second. In the case
of a line code, the symbol rate is the pulse rate in pulses
per second. Each symbol can represent or convey one 68.1.1 Relationship to gross bitrate
or several bits of data. The symbol rate is related to the
gross bitrate expressed in bits per second.
The term baud rate has sometimes incorrectly been used
to mean bit rate, since these rates are the same in old
modems as well as in the simplest digital communication
links using only one bit per symbol, such that binary 0
68.1 Symbols
is represented by one symbol, and binary 1 by another
symbol. In more advanced modems and data transmisA symbol may be described as either a pulse in digital sion techniques, a symbol may have more than two states,
baseband transmission or a tone in passband transmission so it may represent more than one binary digit (a binary
using modems, representing an integer number of bits. A digit always represents one of exactly two states). For this
theoretical denition of a symbol is a waveform, a state reason, the baud rate value will often be lower than the
or a signicant condition of the communication channel gross bit rate.
that persists for a xed period of time. A sending device
places symbols on the channel at a xed and known sym- Example of use and misuse of baud rate: It is correct
bol rate, and the receiving device has the job of detect- to write the baud rate of my COM port is 9,600 if we
ing the sequence of symbols in order to reconstruct the mean that the bit rate is 9,600 bit/s, since there is one
transmitted data. There may be a direct correspondence bit per symbol in this case. It is not correct to write the
between a symbol and a small unit of data. For exam- baud rate of Ethernet is 100 megabaud" or the baud rate
ple, each symbol may encode one or several binary digits of my modem is 56,000 if we mean bit rate. See below
or 'bits. The data may also be represented by the tran- for more details on these techniques.
sitions between symbols, or even by a sequence of many The dierence between baud (or signalling rate) and
symbols.
the data rate (or bit rate) is like a man using a single
The symbol duration time, also known as unit interval, semaphore ag who can move his arm to a new position
can be directly measured as the time between transitions once each second, so his signalling rate (baud) is one symby looking into an eye diagram of an oscilloscope. The bol per second. The ag can be held in one of eight distinct positions: Straight up, 45 left, 90 left, 135 left,
symbol duration time T can be calculated as:
straight down (which is the rest state, where he is sending no signal), 135 right, 90 right, and 45 right. Each
signal (symbol) carries three bits of information. It takes
1
Ts =
three binary digits to encode eight states. The data rate
fs
is three bits per second. In the Navy, more than one ag
pattern and arm can be used at once, so the combinations
where f is the symbol rate.
of these produce many symbols, each conveying several
bits, a higher data rate.
A simple example: A baud rate of 1 kBd =
1,000 Bd is synonymous to a symbol rate of
1,000 symbols per second. In case of a modem,
this corresponds to 1,000 tones per second, and

If N bits are conveyed per symbol, and the gross bit rate is
R, inclusive of channel coding overhead, the symbol rate
can be calculated as:
321

322

fs =

CHAPTER 68. SYMBOL RATE

bits, resulting in a gross bit rate of 3420 10 =
34,200 bit/s. However, the modem is said to operate
at a net bit rate of 33,800 bit/s, excluding physical
layer overhead.

R
N

In that case M = 2N dierent symbols are used. In a modem, these may be sinewave tones with unique combina68.1.3 Line codes for baseband transmistions of amplitude, phase and/or frequency. For example,
sion
in a 64QAM modem, M = 64. In a line code, these may
be M dierent voltage levels.
In case of a baseband channel such as a telegraph line, a
By taking information per pulse N in bit/pulse to be the serial cable or a Local Area Network twisted pair cable,
base-2-logarithm of the number of distinct messages M data is transferred using line codes; i.e., pulses rather than
that could be sent, Hartley[1] constructed a measure of sinewave tones. In this case the baud rate is synonymous
the gross bitrate R as:
to the pulse rate in pulses/second.

R = fs log2 (M )

The maximum baud rate or pulse rate for a base band

channel is called the Nyquist rate, and is double the bandwidth (double the cut-o frequency).

where fs is the baud rate in symbols/second or The simplest digital communication links (such as individual wires on a motherboard or the RS-232 serial
pulses/second. (See Hartleys law).
port/COM port) typically have a symbol rate equal to the
gross bit rate.

68.1.2

Modems for passband transmission

Common communication links such as 10 Mbit/s

Modulation is used in passband ltered channels such as Ethernet (10Base-T), USB, and FireWire typically have
telephone lines, radio channels and other frequency divi- a symbol rate slightly lower than the data bit rate, due
to the overhead of extra non-data symbols used for selfsion multiplex (FDM) channels.
synchronizing code and error detection.
In a digital modulation method provided by a modem,
each symbol is typically a sine wave tone with certain fre- J. M. Emile Baudot (18451903) worked out a vequency, amplitude and phase.Symbol rate, baud rate, is level code (ve bits per character) for telegraphs which
was standardized internationally and is commonly called
the number of transmitted tones per second.
Baudot code.
One symbol can carry one or several bits of information. In voiceband modems for the telephone network, More than two voltage levels are used in advanced techniques such as FDDI and 100/1,000 Mbit/s Ethernet
it is common for one symbol to carry up to 7 bits.
LANs, and others, to achieve high data rates.
Conveying more than one bit per symbol or bit per pulse
has advantages. It reduces the time required to send a 1,000 Mbit/s Ethernet LAN cables use four wire pairs in
given quantity of data over a limited bandwidth. A high full duplex (250 Mbit/s per pair in both directions simulspectral eciency in (bit/s)/Hz can be achieved; i.e., a taneously), and many bits per symbol to encode their data
high bit rate in bit/s although the bandwidth in hertz may payloads.
be low.
The maximum baud rate for a passband for common 68.1.4 Digital television and OFDM exammodulation methods such as QAM, PSK and OFDM is
ple
approximately equal to the passband bandwidth.
In digital television transmission the symbol rate calculaVoiceband modem examples:
tion is:
A V.22bis modem transmits 2400 bit/s using 1200
Bd (1200 symbol/s), where each quadrature amplitude modulation symbol carries two bits of
information. The modem can generate M=22 =4 different symbols. It requires a bandwidth of 1200 Hz
(equal to the baud rate). The carrier frequency is
1800 Hz, meaning that the lower cut o frequency
is 1,800 1,200/2 = 1,200 Hz, and the upper cuto
frequency is 1,800 + 1,200/2 = 2,400 Hz.

symbol rate in symbols per second = (Data rate

in bits per second 204) / (188 bits per symbol)
The 204 is the number of bytes in a packet including the
16 trailing Reed-Solomon error checking and correction
bytes. The 188 is the number of data bytes (187 bytes)
plus the leading packet sync byte (0x47).

The bits per symbol is the (modulations power of

A V.34 modem may transmit symbols at a baud rate 2)*(Forward Error Correction). So for example in 64of 3,420 Bd, and each symbol can carry up to ten QAM modulation 64 = 26 so the bits per symbol is 6. The

68.2. MODULATION

323

Forward Error Correction (FEC) is usually expressed as

a fraction; i.e., 1/2, 3/4, etc. In the case of 3/4 FEC, for
every 3 bits of data, you are sending out 4 bits, one of
which is for error correction.

from low signal-to-noise ratio. In that case, a modem or

network adapter may automatically choose a slower and
more robust modulation scheme or line code, using fewer
bits per symbol, in view to reduce the bit error rate.

Example:

An optimal symbol set design takes into account channel

bandwidth, desired information rate, noise characteristics
of the channel and the receiver, and receiver and decoder
complexity.

given bit rate = 18096263

Modulation type = 64-QAM
FEC = 3/4

68.2 Modulation
then
Many data transmission systems operate by the
modulation of a carrier signal.
For example, in
18096263 204 18096263 4 204
frequency-shift
keying
(FSK),
the
frequency
of a tone
=
= 4363638
rate symbol =
6
3 188
6 34 188
is varied among a small, xed set of possible values.
In a synchronous data transmission system, the tone
In digital terrestrial television (DVB-T, DVB-H and sim- can only be changed from one frequency to another
ilar techniques) OFDM modulation is used; i.e., multi- at regular and well-dened intervals. The presence of
carrier modulation. The above symbol rate should then one particular frequency during one of these intervals
be divided by the number of OFDM sub-carriers in view constitutes a symbol. (The concept of symbols does not
to achieve the OFDM symbol rate. See the OFDM sys- apply to asynchronous data transmission systems.) In a
tem comparison table for further numerical details.
modulated system, the term modulation rate may be
used synonymously with symbol rate.

68.1.5

Relationship to chip rate

Some communication links (such as GPS transmissions,

CDMA cell phones, and other spread spectrum links)
have a symbol rate much higher than the data rate (they
transmit many symbols called chips per data bit). Representing one bit by a chip sequence of many symbols overcomes co-channel interference from other transmitters
sharing the same frequency channel, including radio jamming, and is common in military radio and cell phones.
Despite the fact that using more bandwidth to carry the
same bit rate gives low channel spectral eciency in
(bit/s)/Hz, it allows many simultaneous users, which results in high system spectral eciency in (bit/s)/Hz per
unit of area.

68.2.1 Binary modulation

If the carrier signal has only two states, then only one bit
of data (i.e., a 0 or 1) can be transmitted in each symbol. The bit rate is in this case equal to the symbol rate.
For example, a binary FSK system would allow the carrier to have one of two frequencies, one representing a 0
and the other a 1. A more practical scheme is dierential
binary phase-shift keying, in which the carrier remains
at the same frequency, but can be in one of two phases.
During each symbol, the phase either remains the same,
encoding a 0, or jumps by 180, encoding a 1. Again,
only one bit of data (i.e., a 0 or 1) is transmitted by each
symbol. This is an example of data being encoded in the
transitions between symbols (the change in phase), rather
than the symbols themselves (the actual phase). (The reason for this in phase-shift keying is that it is impractical
to know the reference phase of the transmitter.)

In these systems, the symbol rate of the physically transmitted high-frequency signal rate is called chip rate,
which also is the pulse rate of the equivalent base band
signal. However, in spread spectrum systems, the term
symbol may also be used at a higher layer and refer to
one information bit, or a block of information bits that are
modulated using for example conventional QAM modu- 68.2.2 N-ary modulation, N greater than 2
lation, before the CDMA spreading code is applied. Using the latter denition, the symbol rate is equal to or By increasing the number of states that the carrier signal
can take, the number of bits encoded in each symbol can
lower than the bit rate.
be greater than one. The bit rate can then be greater than
the symbol rate. For example, a dierential phase-shift
keying system might allow four possible jumps in phase
68.1.6 Relationship to bit error rate
between symbols. Then two bits could be encoded at each
The disadvantage of conveying many bits per symbol is symbol interval, achieving a data rate of double the symthat the receiver has to distinguish many signal levels or bol rate. In a more complex scheme such as 16-QAM,
symbols from each other, which may be dicult and four bits of data are transmitted in each symbol, resulting
cause bit errors in case of a poor phone line that suers in a bit rate of four times the symbol rate.

324

68.2.3

CHAPTER 68. SYMBOL RATE

Data rate versus error rate

Modulating a carrier increases the frequency range, or

bandwidth, it occupies. Transmission channels are generally limited in the bandwidth they can carry. The bandwidth depends on the symbol (modulation) rate (not directly on the bit rate). As the bit rate is the product of the
symbol rate and the number of bits encoded in each symbol, it is clearly advantageous to increase the latter if the
former is xed. However, for each additional bit encoded
in a symbol, the constellation of symbols (the number of
states of the carrier) doubles in size. This makes the states
less distinct from one another which in turn makes it more
dicult for the receiver to detect the symbol correctly in
the presence of disturbances on the channel.
The history of modems is the attempt at increasing the bit
rate over a xed bandwidth (and therefore a xed maximum symbol rate), leading to increasing bits per symbol.
For example, the V.29 species 4 bits per symbol, at a
symbol rate of 2,400 baud, giving an eective bit rate of
9,600 bits per second.
The history of spread spectrum goes in the opposite direction, leading to fewer and fewer data bits per symbol
in order to spread the bandwidth. In the case of GPS, we
have a data rate of 50 bit/s and a symbol rate of 1.023
Mchips/s. If each chip is considered a symbol, each symbol contains far less than one bit (50 bit/s / 1,023 ksymbols/s = ~0.000,05 bits/symbol).
The complete collection of M possible symbols over a
particular channel is called a M-ary modulation scheme.
Most modulation schemes transmit some integer number
of bits per symbol b, requiring the complete collection to
contain M = 2^b dierent symbols. Most popular modulation schemes can be described by showing each point
on a constellation diagram, although a few modulation
schemes (such as MFSK, DTMF, pulse-position modulation, spread spectrum modulation) require a dierent
description.

68.3 Signicant condition

In telecommunication, concerning the modulation of a
carrier, a signicant condition is one of the signal's parameters chosen to represent information.[2]
A signicant condition could be an electric current (voltage, or power level), an optical power level, a phase value,
or a particular frequency or wavelength. The duration of a
signicant condition is the time interval between successive signicant instants.[2] A change from one signicant
condition to another is called a signal transition. Information can be transmitted either during the given time interval, or encoded as the presence or absence of a change in
the received signal.[3]
Signicant conditions are recognized by an appropriate
device called a receiver, demodulator, or decoder. The

decoder translates the actual signal received into its intended logical value such as a binary digit (0 or 1), an
alphabetic character, a mark, or a space. Each signicant
instant is determined when the appropriate device assumes a condition or state usable for performing a specic
function, such as recording, processing, or gating.[2]

68.4 See also

Chip rate
Gross bit rate, also known as data signaling rate or
line rate.
Bandwidth
Bitrate
Constellation diagram, which shows (on a graph or
2D oscilloscope image) how a given signal state (a
symbol) can represent three or four bits at once.
List of device bandwidths
Pulse-code modulation

68.5 References
[1] D. A. Bell (1962). Information Theory; and its Engineering Applications (3rd ed.). New York: Pitman.
[2] Federal Standard 1037C. National Communications
System. 1996-07-07.
[3] System Design and Engineering Standard for Tactical
Communications. Mil-Std-188-200. United States Department of Defense. 1983-05-28.

68.6 External links

What is the Symbol rate?
On the origins of serial communications and data
encoding. Retrieved January 4, 2007.
Whats The Dierence Between Bit Rate And Baud
Rate?, Electronic Design Magazine

Chapter 69

Digital signal
This article is about digital signals in electronics. For digital data and systems, see Digital data. For digital signals
that specically represent analog waveforms, see Digital
signal (signal processing). For other uses, see Digital signal (disambiguation).
For a broader coverage related to this topic, see Signal
(electrical engineering).
A digital signal is a signal that represents a sequence of

With digital signals, system noise, provided it is not too

great, will not aect system operation whereas noise always degrades the operation of analog signals to some degree.

69.1 Denitions
The term digital signal has related denitions in dierent
contexts:

A binary signal, also known as a logic signal, is a digital signal

with two distinguishable levels

discrete values.[1][2] A logic signal is a digital signal with

only two possible values,[3][4] and describes an arbitrary
bit stream. Other types of digital signals can represent
three-valued logic or higher valued logics.
A ve level PAM digital signal
A digital signal is a physical quantity that alternates between a discrete set of waveforms.[5] Alternatively, a digital signal may be considered to be the sequence of codes
represented by such a physical quantity.[6] The physical quantity may be a variable electric current or voltage, the intensity, phase or polarization of an optical
or other electromagnetic eld, acoustic pressure, the
magnetization of a magnetic storage media, etcetera.
Digital signals are present in all digital electronics, notably computing equipment and data transmission.

69.1.1 In digital electronics

In digital electronics a digital signal is a pulse train (a
pulse amplitude modulated signal), i.e. a sequence of
xed-width square-wave electrical pulses or light pulses,
each occupying one of a discrete number of levels of
amplitude.[7][8] A special case is a logic signal or a binary signal, which varies between a low and a high signal
level.

69.1.2 In signal processing

Main article: digital signal (signal processing)

A received digital signal may be impaired by noise and distortions

without necessarily aecting the digits

In digital signal processing, a digital signal is a representation of a physical signal that is a sampled and quantied.
A digital signal is an abstraction which is discrete in time
and amplitude. The signals value only exists at regular
time intervals, since only the values of the corresponding physical signal at those sampled moments are significant for further digital processing. The digital signal is

325

326

CHAPTER 69. DIGITAL SIGNAL

x[t]

modulated signal, allowing baseband transmission;

or

7
6
5
4
3
2
1
0

1 2 3 4 5 6 7 8 9 10 11 12 13

In signal processing, a digital signal is an abstraction that is discrete in time and amplitude, meaning it only exists at certain time
instants.

2. a digital modulation scheme, allowing passband

transmission over long wires or over a limited radio
frequency band. Such a carrier-modulated sine wave
is considered a digital signal in literature on digital
communications and data transmission,[9] but considered as a bit-stream converted to an analog signal
in electronics and computer networking.[10]

69.2 Logic signal

a sequence of codes drawn from a nite set of values.[6]

The digital signal may be stored, processed or transmitted
physically as a pulse code modulation (PCM) signal.

A logic signal waveform: (1) low level, (2) high level, (3) rising
edge, and (4) falling edge.

In computer architecture and other digital systems, a

waveform that switches between two voltage levels (or
less commonly, other waveforms) representing the two
states of a Boolean value (0 and 1, or Low and High, or
false and true) is referred to as a digital signal or logic signal or binary signal when it is interpreted in terms of only
two possible digits.
A frequency shift keying (FSK) signal is alternating between two
waveforms, and allows passband transmission. It is considered
digital in literature on data transmission.

69.1.3

In communications

The clock signal is a special digital signal that is used to

synchronize many (but not all) digital circuits. The image
shown can be considered the waveform of a clock signal.
Logic changes are triggered either by the rising edge or
the falling edge.
The given diagram is an example of the practical pulse
and therefore we have introduced two new terms that are:
Rising edge: the transition from a low voltage (level
1 in the diagram) to a high voltage (level 2).

An AMI coded digital signal used in baseband transmission (line

coding)

In digital communications, a digital signal is a continuoustime physical signal, alternating between a discrete number of waveforms,[5] representing a bit stream message.
The shape of the waveform depends the transmission
scheme, which may be either:

Falling edge: the transition from a high voltage to a

low one.

Although in a highly simplied and idealized model of a

digital circuit we may wish for these transitions to occur
instantaneously, no real world circuit is purely resistive
and therefore no circuit can instantly change voltage levels. This means that during a short, nite transition time
the output may not properly reect the input, and will not
1. a line coding scheme, which produces a pulse- correspond to either a logically high or low voltage.

69.6. SEE ALSO

327

69.3 Logic voltage levels

Main article: Logic level

sensitive ip-op. When this is done the input is measured at those points in time, and the signal from that time
is passed through to the output and the output is then held
steady till the next clock.

The two states of a wire are usually represented by some

measurement of an electrical property: Voltage is the
most common, but current is used in some logic families. A threshold is designed for each logic family. When
below that threshold, the signal is low, when above high.

This process is the basis of synchronous logic, and the

system is also used in digital signal processing.

69.4 Modulation

69.6 See also

Main article: Modulation Digital_modulation_methods

To create a digital signal, an analog signal must be modulated with a control signal to produce it. As we have
already seen, the simplest modulation, a type of unipolar
line coding is simply to switch on and o a DC signal, so
that high voltages are a '1' and low voltages are '0'.
In digital radio schemes one or more carrier waves are
amplitude or frequency or phase modulated with a signal
to produce a digital signal suitable for transmission.
In Asymmetric Digital Subscriber Line over telephone
wires, ADSL does not primarily use binary logic; the digital signals for individual carriers are modulated with different valued logics, depending on the Shannon capacity
of the individual channel.

69.5 Clocking

However, asynchronous logic also exists, which uses no

single clock, and generally operates more quickly, and
may use less power, but is signicantly harder to design.

Intersymbol interference in digital communication

69.7 References
[1] Digital Design with CPLD Applications and VHDL By
Robert K. Dueck: A digital representation can have only
specic discrete values
[2] Proakis, John G.; Manolakis, Dimitris G. (2007-01-01).
Digital Signal Processing. Pearson Prentice Hall. ISBN
9780131873742.
[3] Digital Signal. Retrieved 2016-08-13.
[4] Paul Horowitz; Wineld Hill (2015). The Art of Electronics. Cambridge University Press. ISBN 9780521809269.
[5] Analogue and Digital Communication Techniques: A
digital signal is a complex waveform and can be dened
as a discrete waveform having a nite set of levels
[6] Vinod Kumar Khanna, Digital Signal Processing, 2009:
A digital signal is a special form of discrete-time signal
which is discrete in both time and amplitude, obtained by
permitting each value (sample) of a discrete-time signal to
acquire a nite set of values (quantization), assigning it a
numerical symbol according to a code ... A digital signal
is a sequence or list of numbers drawn from a nite set.

Clock

[7] B. SOMANATHAN NAIR, Digital electronics and logic

design 2002: Digital signals are xed-width pulses, which
occupy only one of two levels of amplitude.

Data

[8] Joseph Migga Kizza, Computer Network Security 2005

tsu

th
tco

Q
Clocking digital signals through a clocked ip-op

Often digital signals are sampled by a clock signal at

regular intervals by passing the signal through an edge

[9] J.S.Chitode, Communication Systems, 2008: When a

digital signal is transmitted over a long distance, it needs
CW modulation.
[10] Fred Halsall, Computer Networking and the Internet: In
order to transmit a digital signal over an analog subscriber
line, modulated transmission must be used; thas is the
electrical signal that represents the binary bit stream of
the source (digital) output must rst be converted to an
analog signal that is compatible with a (telephony) speech
signal.

Chapter 70

Digital-to-analog converter
For digital television converter boxes, see digital televi- tems. Very high speed test equipment, especially samsion adapter.
pling oscilloscopes, may also use discrete DACs.
In electronics, a digital-to-analog converter (DAC,

70.1 Overview

f(t)

t
8-channel Cirrus Logic CS4382 digital-to-analog converter as
used in a sound card.

Ideally sampled signal.

A DAC converts an abstract nite-precision number (usually

a xed-point binary number) into a physical quantity
D/A, DA, D2A, or D-to-A) is a device that converts
(e.g.,
a voltage or a pressure). In particular, DACs are
a digital signal into an analog signal. An analog-to-digital
often
used
to convert nite-precision time series data to
converter (ADC) performs the reverse function.
a continually varying physical signal.
There are several DAC architectures; the suitability of a
An ideal DAC converts the abstract numbers into a conDAC for a particular application is determined by three
main parameters: resolution, maximum sampling fre- ceptual sequence of impulses that are then processed by a
reconstruction lter using some form of interpolation to
quency and accuracy. Due to the complexity and the
need for precisely matched components, all but the most ll in data between the impulses. A conventional practical DAC converts the numbers into a piecewise conspecialized DACs are implemented as integrated circuits
(ICs). Digital-to-analog conversion can degrade a signal, stant function made up of a sequence of rectangular funcso a DAC should be specied that has insignicant errors tions that is modeled with the zero-order hold. Other
DAC methods such as those based on delta-sigma moduin terms of the application.
lation) produce a pulse-density modulated output that can
DACs are commonly used in music players to convert be similarly ltered to produce a smoothly varying signal.
digital data streams into analog audio signals. They are
also used in televisions and mobile phones to convert dig- As per the NyquistShannon sampling theorem, a DAC
ital video data into analog video signals which connect to can reconstruct the original signal from the sampled
the screen drivers to display monochrome or color im- data provided that its bandwidth meets certain requireages. These two applications use DACs at opposite ends ments (e.g., a baseband signal with bandwidth less than
of the speed/resolution trade-o. The audio DAC is a the Nyquist frequency). Digital sampling introduces
low speed high resolution type while the video DAC is quantization error that manifests as low-level noise added
a high speed low to medium resolution type. Discrete to the reconstructed signal.
DACs would typically be extremely high speed low reso- Instead of impulses, a conventional practical DAC uplution power hungry types, as used in military radar sys- dates the analog voltage at uniform sampling intervals,
328

70.2. APPLICATIONS

329

f(t)

t
Piecewise constant output of a conventional DAC lacking a
reconstruction lter. In a practical DAC, a lter or the nite
bandwidth of the device smooths out the step response into a continuous curve.

by a microphone, then the analog signal is converted to

a digital stream by an ADC. The digital stream is then
divided into network packets where it may be sent along
with other digital data, not necessarily audio. The packets
are then received at the destination, but each packet may
take a completely dierent route and may not even arrive
at the destination in the correct time order. The digital
voice data is then extracted from the packets and assembled into a digital data stream. A DAC converts this back
into an analog electrical signal, which drives an audio amplier, which in turn drives a loudspeaker, which nally
produces sound.

70.2.1 Audio

Most modern audio signals are stored in digital form (for

which is then interpolated via a reconstruction lter to
example MP3s and CDs) and in order to be heard through
continuously varied levels.
speakers they must be converted into an analog signal.
These numbers are written to the DAC, typically with a DACs are therefore found in CD players, digital music
clock signal that causes each number to be latched in se- players, and PC sound cards.
quence, at which time the DAC output voltage changes
Specialist standalone DACs can also be found in high-end
rapidly from the previous value to the value represented
hi- systems. These normally take the digital output of a
by the currently latched number. The eect of this is that
compatible CD player or dedicated transport (which is
the output voltage is held in time at the current value until
basically a CD player with no internal DAC) and convert
the next input number is latched, resulting in a piecewise
the signal into an analog line-level output that can then be
constant or staircase-shaped output. This is equivalent to
fed into an amplier to drive speakers.
a zero-order hold operation and has an eect on the freSimilar digital-to-analog converters can be found in
quency response of the reconstructed signal.
digital speakers such as USB speakers, and in sound
The fact that DACs output a sequence of piecewise concards.
stant values (known as zero-order hold in sample data
textbooks) or rectangular pulses causes multiple harmon- In VoIP (Voice over IP) applications, the source must
ics above the Nyquist frequency. Usually, these are re- rst be digitized for transmission, so it undergoes convermoved with a low pass lter acting as a reconstruction sion via an analog-to-digital converter, and is then reconstructed into analog using a DAC on the receiving partys
lter in applications that require it.
end.
Other DAC methods (e.g., methods based on delta-sigma
modulation) produce a pulse-density modulated signal
that can then be ltered in a similar way to produce a
smoothly varying signal.

Digital input

70.2 Applications
D0
D1
D2
D3
D4
D5
D6
D7

8-Bit DAC

Analog Voltage

Top-loading CD player and external digital-to-analog converter.

A simplied functional diagram of an 8-bit DAC

DACs and ADCs are part of an enabling technology that 70.2.2 Video
has contributed greatly to the digital revolution. To illustrate, consider a typical long-distance telephone call. The Video sampling tends to work on a completely dierent
callers voice is converted into an analog electrical signal scale altogether thanks to the highly nonlinear response

330

CHAPTER 70. DIGITAL-TO-ANALOG CONVERTER

both of cathode ray tubes (for which the vast majority of digital video foundation work was targeted) and
the human eye, using a gamma curve to provide an
appearance of evenly distributed brightness steps across
the displays full dynamic range - hence the need to use
RAMDACs in computer video applications with deep
enough colour resolution to make engineering a hardcoded value into the DAC for each output level of each
channel impractical (e.g. an Atari ST or Sega Genesis
would require 24 such values; a 24-bit video card would
need 768...). Given this inherent distortion, it is not unusual for a television or video projector to truthfully claim
a linear contrast ratio (dierence between darkest and
brightest output levels) of 1000:1 or greater, equivalent
to 10 bits of audio precision even though it may only accept signals with 8-bit precision and use an LCD panel
that only represents 6 or 7 bits per channel.
Video signals from a digital source, such as a computer,
must be converted to analog form if they are to be displayed on an analog monitor. As of 2007, analog inputs
were more commonly used than digital, but this changed
as at panel displays with DVI and/or HDMI connections
became more widespread. A video DAC is, however, incorporated in any digital video player with analog outputs. The DAC is usually integrated with some memory
(RAM), which contains conversion tables for gamma correction, contrast and brightness, to make a device called
a RAMDAC.
A device that is distantly related to the DAC is the
digitally controlled potentiometer, used to control an analog signal digitally.

70.2.3

Mechanical

IBM Selectric typewriter uses a mechanical digital-to-analog converter to control its typeball.

A one-bit mechanical actuator assumes two positions:

one when on, another when o. The motion of several
one-bit actuators can be combined and weighted with a
whietree mechanism to produce ner steps. The IBM
Selectric typewriter uses such as system. When a typewriter key is pressed, it moves a metal bar (interposer)
down that has several lugs. The lugs are the information
bits. When a key is pressed, its interposer is moved by the

motor. If a lug is present at one position, it will move the

corresponding selector bail (bar); if the lug is not present,
the selector bail stays where it is. The discrete motions of
the bails are combined by a whie tree, and the output
controls the rotation and tilt of the Selectrics typeball.[1]

70.3 Types
The most common types of electronic DACs are:
The pulse-width modulator, the simplest DAC type.
A stable current or voltage is switched into a lowpass analog lter with a duration determined by the
digital input code. This technique is often used for
electric motor speed control, but has many other applications as well.
Oversampling DACs or interpolating DACs such as
the delta-sigma DAC, use a pulse density conversion technique. The oversampling technique allows
for the use of a lower resolution DAC internally.
A simple 1-bit DAC is often chosen because the
oversampled result is inherently linear. The DAC
is driven with a pulse-density modulated signal, created with the use of a low-pass lter, step nonlinearity (the actual 1-bit DAC), and negative feedback loop, in a technique called delta-sigma modulation. This results in an eective high-pass lter
acting on the quantization (signal processing) noise,
thus steering this noise out of the low frequencies
of interest into the megahertz frequencies of little
interest, which is called noise shaping. The quantization noise at these high frequencies is removed or
greatly attenuated by use of an analog low-pass lter
at the output (sometimes a simple RC low-pass circuit is sucient). Most very high resolution DACs
(greater than 16 bits) are of this type due to its high
linearity and low cost. Higher oversampling rates
can relax the specications of the output low-pass
lter and enable further suppression of quantization
noise. Speeds of greater than 100 thousand samples per second (for example, 192 kHz) and resolutions of 24 bits are attainable with delta-sigma
DACs. A short comparison with pulse-width modulation shows that a 1-bit DAC with a simple rstorder integrator would have to run at 3 THz (which
is physically unrealizable) to achieve 24 meaningful
bits of resolution, requiring a higher-order low-pass
lter in the noise-shaping loop. A single integrator is
a low-pass lter with a frequency response inversely
proportional to frequency and using one such integrator in the noise-shaping loop is a rst order deltasigma modulator. Multiple higher order topologies
(such as MASH) are used to achieve higher degrees
of noise-shaping with a stable topology.
The binary-weighted DAC, which contains individual electrical components for each bit of the DAC

70.4. PERFORMANCE
connected to a summing point. These precise voltages or currents sum to the correct output value.
This is one of the fastest conversion methods but suffers from poor accuracy because of the high precision required for each individual voltage or current.
Such high-precision components are expensive, so
this type of converter is usually limited to 8-bit resolution or less.

331
Most DACs, shown earlier in this list, rely on a constant reference voltage to create their output value.
Alternatively, a multiplying DAC [2] takes a variable
input voltage for their conversion. This puts additional design constraints on the bandwidth of the
conversion circuit.

Switched resistor DAC contains a parallel re- 70.4 Performance

sistor network. Individual resistors are enabled or bypassed in the network based on the DACs are very important to system performance. The
digital input.
most important characteristics of these devices are:
Switched current source DAC, from which
dierent current sources are selected based on Resolution The number of possible output levels the
the digital input.
DAC is designed to reproduce. This is usually stated
as the number of bits it uses, which is the base two
Switched capacitor DAC contains a parallogarithm of the number of levels. For instance a 1
lel capacitor network. Individual capacitors
bit DAC is designed to reproduce 2 (21 ) levels while
are connected or disconnected with switches
an 8 bit DAC is designed for 256 (28 ) levels. Resolubased on the input.
tion is related to the eective number of bits which
The R-2R ladder DAC which is a binary-weighted
is a measurement of the actual resolution attained
DAC that uses a repeating cascaded structure of reby the DAC. Resolution determines color depth in
sistor values R and 2R. This improves the precision
video applications and audio bit depth in audio apdue to the relative ease of producing equal valuedplications.
matched resistors (or current sources).
Maximum sampling rate A measurement of the max The Successive-Approximation or Cyclic DAC,
imum speed at which the DACs circuitry can operwhich successively constructs the output during each
ate and still produce the correct output. As stated
cycle. Individual bits of the digital input are proabove, the NyquistShannon sampling theorem decessed each cycle until the entire input is accounted
nes a relationship between this and the bandwidth
for.
of the sampled signal.
The thermometer-coded DAC, which contains an Monotonicity The ability of a DACs analog output to
equal resistor or current-source segment for each
move only in the direction that the digital input
possible value of DAC output. An 8-bit thermomemoves (i.e., if the input increases, the output doesn't
ter DAC would have 255 segments, and a 16-bit
dip before asserting the correct output.) This charthermometer DAC would have 65,535 segments.
acteristic is very important for DACs used as a
This is perhaps the fastest and highest precision
low frequency signal source or as a digitally proDAC architecture but at the expense of high cost.
grammable trim element.
Conversion speeds of >1 billion samples per second
have been reached with this type of DAC.
Total harmonic distortion and noise (THD+N) A
measurement of the distortion and noise introduced
Hybrid DACs, which use a combination of the
to the signal by the DAC. It is expressed as a perabove techniques in a single converter. Most DAC
centage of the total power of unwanted harmonic
integrated circuits are of this type due to the didistortion and noise that accompany the desired
culty of getting low cost, high speed and high precisignal. This is a very important DAC characteristic
sion in one device.
for dynamic and small signal DAC applications.
The segmented DAC, which combines the
thermometer-coded principle for the most sig- Dynamic range A measurement of the dierence between the largest and smallest signals the DAC can
nicant bits and the binary-weighted princireproduce expressed in decibels. This is usually reple for the least signicant bits. In this way, a
lated to resolution and noise oor.
compromise is obtained between precision (by
the use of the thermometer-coded principle)
and number of resistors or current sources (by Other measurements, such as phase distortion and jitter,
the use of the binary-weighted principle). The can also be very important for some applications, some of
full binary-weighted design means 0% seg- which (e.g. wireless data transmission, composite video)
mentation, the full thermometer-coded design may even rely on accurate production of phase-adjusted
signals.
means 100% segmentation.

332

CHAPTER 70. DIGITAL-TO-ANALOG CONVERTER

Glitch impulse area (glitch energy)

Linear PCM audio sampling usually works on the basis

of each bit of resolution being equivalent to 6 decibels of
amplitude (a 2x increase in volume or precision).
Non-linear PCM encodings (A-law / -law, ADPCM,
NICAM) attempt to improve their eective dynamic
ranges by a variety of methods - logarithmic step sizes
between the output signal strengths represented by each
data bit (trading greater quantisation distortion of loud
signals for better performance of quiet signals)

Response uncertainty
Time nonlinearity (TNL)

70.6 See also

Integral linearity
IS

70.5 Figures of merit

Static performance:
Dierential nonlinearity (DNL) shows how
much two adjacent code analog values deviate
from the ideal 1 LSB step.[3]
Integral nonlinearity (INL) shows how much
the DAC transfer characteristic deviates from
an ideal one. That is, the ideal characteristic
is usually a straight line; INL shows how much
the actual voltage at a given code value diers
from that line, in LSBs (1 LSB steps).
Gain
Oset
Noise is ultimately limited by the thermal
noise generated by passive components such as
resistors. For audio applications and in room
temperatures, such noise is usually a little less
than 1 V (microvolt) of white noise. This
limits performance to less than 20~21 bits even
in 24-bit DACs.
Frequency domain performance
Spurious-free dynamic range (SFDR) indicates in dB the ratio between the powers of
the converted main signal and the greatest undesired spur.
Signal-to-noise and distortion ratio (SNDR)
indicates in dB the ratio between the powers
of the converted main signal and the sum of
the noise and the generated harmonic spurs

Modem
RAMDAC

70.7 References
[1] Joachim Duebbers, IBM Selectric Typewriter Learning
Program 10-3A: Input
[2] Multiplying DACs, exible building blocks (PDF).
Analog Devices inc. 2010. Retrieved 29 March 2012.
[3] ADC and DAC Glossary - Maxim

70.8 Further reading

Kester, Walt, The Data Conversion Handbook,
ISBN 0-7506-7841-0
S. Norsworthy, Richard Schreier, Gabor C. Temes,
Delta-Sigma Data Converters. ISBN 0-7803-10454.
Mingliang Liu, Demystifying Switched-Capacitor
Circuits. ISBN 0-7506-7907-7.
Behzad Razavi, Principles of Data Conversion System Design. ISBN 0-7803-1093-4.
Phillip E. Allen, Douglas R. Holberg, CMOS Analog
Circuit Design. ISBN 0-19-511644-5.
Robert F. Coughlin, Frederick F. Driscoll, Operational Ampliers and Linear Integrated Circuits.
ISBN 0-13-014991-8.

i-th harmonic distortion (HDi) indicates the

power of the i-th harmonic of the converted
main signal

A Anand Kumar, Fundamentals of Digital Circuits.

ISBN 81-203-1745-9, ISBN 978-81-203-1745-1.

Total harmonic distortion (THD) is the sum of

the powers of all HDi

Ndjountche Tertulien, CMOS Analog Integrated

Circuits: High-Speed and Power-Ecient Design.
ISBN 978-1-4398-5491-4.

If the maximum DNL error is less than 1 LSB,

then the D/A converter is guaranteed to be
monotonic. However, many monotonic converters may have a maximum DNL greater
than 1 LSB.
Time domain performance:

70.9 External links

ADC and DAC Glossary

Chapter 71

Analog transmission
Analog or analogue transmission is a transmission
method of conveying voice, data, image, signal or video
information using a continuous signal which varies in
amplitude, phase, or some other property in proportion
to that of a variable. It could be the transfer of an analog
source signal, using an analog modulation method such
as frequency modulation (FM) or amplitude modulation
(AM), or no modulation at all.

71.3 Types of analog transmissions

Most analog transmissions fall into one of several categories. Until recently, most telephony and voice communication was primarily analog in nature, as was most
television and radio transmission. Early telecommunication devices utilized analog-to-digital conversion devices
called modulator/demodulators, or modems, to convert
Some textbooks also consider passband data transmission analog signals to digital signals and back.
using a digital modulation method such as ASK, PSK and
QAM, i.e. a sinewave modulated by a digital bit-stream,
as analog transmission and as an analog signal. Others
dene that as digital transmission and as a digital signal. 71.4 Benets and drawbacks
Baseband data transmission using line codes, resulting in
a pulse train, are always considered as digital transmission, although the source signal may be a digitized analog The analog transmission is still very popular, in particular
for shorter distances, due to signicantly lower costs and
signal.
complex multiplexing and timing equipment is unnecessary, and in small short-haul systems that simply do not
need multiplexed digital transmission.[2]

71.1 Descriptions

However, in situations where a signal often has high

signal-to-noise ratio and cannot achieve source linearity, or in long distance, high output systems, analog is
71.2 Modes of transmission
unattractive due to attenuation problems. Furthermore,
as digital techniques continue to be rened, analog sysAnalog transmission can be conveyed in many dierent tems are increasingly becoming legacy equipment.[2]
fashions:
Recently, some nations, such as the Netherlands,
have completely ceased analog transmissions (analogue
ber-optic cable
switch-o) on certain media, such as television,[3] for the
purposes of the government saving money.[4]
twisted-pair or coax cable
Via air

71.5 See also

Via water
There are two basic kinds of analog transmission, both
based on how they modulate data to combine an input
signal with a carrier signal. Usually, this carrier signal
is a specic frequency, and data is transmitted through
its variations. The two techniques are amplitude modulation (AM), which varies the amplitude of the carrier
signal, and frequency modulation (FM), which modulates
the frequency of the carrier.[1]

333

Analog television
Analog to digital converter
Modulation
Signal

334

71.6 References
[1] The Froehlich/Kent Encyclopedia of Telecommunications By Allen Kent, Froehlich E. Froehlich.1991 Marcel
Dekker. ISBN 0-8247-2900-5
[2] Telecommunication System Engineering By Roger L.
Freeman.2004 John Wiley and Sons. ISBN 0-471-451339
[3] Netherlands Ends Analog Transmission - Goodbye antenna, hello digital... - dslreports.com
[4] http://www.nytimes.com/aponline/technology/
AP-Netherlands-TV.html?_r=2&oref=slogin&oref=
slogin

CHAPTER 71. ANALOG TRANSMISSION

Chapter 72

Phase-shift keying
Phase-shift keying (PSK) is a digital modulation
scheme that conveys data by changing (modulating) the
phase of a reference signal (the carrier wave). The modulation is impressed by varying the sine and cosine inputs
at a precise time. It is widely used for wireless LANs,
RFID and Bluetooth communication.
Any digital modulation scheme uses a nite number of
distinct signals to represent digital data. PSK uses a nite number of phases, each assigned a unique pattern of
binary digits. Usually, each phase encodes an equal number of bits. Each pattern of bits forms the symbol that
is represented by the particular phase. The demodulator,
which is designed specically for the symbol-set used by
the modulator, determines the phase of the received signal and maps it back to the symbol it represents, thus recovering the original data. This requires the receiver to
be able to compare the phase of the received signal to a
reference signal such a system is termed coherent (and
referred to as CPSK).
Alternatively, instead of operating with respect to a constant reference wave, the broadcast can operate with respect to itself. Changes in phase of a single broadcast
waveform can be considered the signicant items. In this
system, the demodulator determines the changes in the
phase of the received signal rather than the phase (relative to a reference wave) itself. Since this scheme depends on the dierence between successive phases, it is
termed dierential phase-shift keying (DPSK). DPSK
can be signicantly simpler to implement than ordinary
PSK, since there is no need for the demodulator to have a
copy of the reference signal to determine the exact phase
of the received signal (it is a non-coherent scheme).[1] In
exchange, it produces more erroneous demodulation.

All convey data by changing some aspect of a base signal, the carrier wave (usually a sinusoid), in response to
a data signal. In the case of PSK, the phase is changed
to represent the data signal. There are two fundamental
ways of utilizing the phase of a signal in this way:

By viewing the phase itself as conveying the information, in which case the demodulator must have
a reference signal to compare the received signals
phase against; or

By viewing the change in the phase as conveying information dierential schemes, some of which do
not need a reference carrier (to a certain extent).

A convenient method to represent PSK schemes is on

a constellation diagram. This shows the points in the
complex plane where, in this context, the real and
imaginary axes are termed the in-phase and quadrature
axes respectively due to their 90 separation. Such a representation on perpendicular axes lends itself to straightforward implementation. The amplitude of each point
along the in-phase axis is used to modulate a cosine (or
sine) wave and the amplitude along the quadrature axis
to modulate a sine (or cosine) wave. By convention, inphase modulates cosine and quadrature modulates sine.

In PSK, the constellation points chosen are usually positioned with uniform angular spacing around a circle.
This gives maximum phase-separation between adjacent
points and thus the best immunity to corruption. They are
positioned on a circle so that they can all be transmitted
with the same energy. In this way, the moduli of the com72.1 Introduction
plex numbers they represent will be the same and thus so
will the amplitudes needed for the cosine and sine waves.
There are three major classes of digital modulation tech- Two common examples are binary phase-shift keying
niques used for transmission of digitally represented data: (BPSK) which uses two phases, and quadrature phaseshift keying (QPSK) which uses four phases, although
Amplitude-shift keying (ASK)
any number of phases may be used. Since the data to be
conveyed are usually binary, the PSK scheme is usually
Frequency-shift keying (FSK)
designed with the number of constellation points being a
Phase-shift keying (PSK)
power of 2.
335

336

72.1.1

CHAPTER 72. PHASE-SHIFT KEYING

Denitions

biometric passports, credit cards such as American Express's ExpressPay, and many other applications.[5]

For determining error-rates mathematically, some deBluetooth 2 will use /4 -DQPSK at its lower rate (2
nitions will be needed:
Mbit/s) and 8-DPSK at its higher rate (3 Mbit/s) when the
link between the two devices is suciently robust. Blue Eb = Energy-per-bit
tooth 1 modulates with Gaussian minimum-shift keying,
a binary scheme, so either modulation choice in version 2
Es = Energy-per-symbol = nEb with n bits per sym- will yield a higher data-rate. A similar technology, IEEE
bol
802.15.4 (the wireless standard used by ZigBee) also relies on PSK using two frequency bands: 868915 MHz
Tb = Bit duration
with BPSK and at 2.4 GHz with OQPSK.
Ts = Symbol duration
Both QPSK and 8PSK are widely used in satellite broadcasting. QPSK is still widely used in the streaming of
N0 /2 = Noise power spectral density (W/Hz)
SD satellite channels and some HD channels. High definition programming is delivered almost exclusively in
Pb = Probability of bit-error
8PSK due to the higher bitrates of HD video and the high
cost of satellite bandwidth.[6] The DVB-S2 standard re Ps = Probability of symbol-error
quires support for both QPSK and 8PSK. The chipsets
Q(x) will give the probability that a single sample taken used in new satellite set top boxes, such as Broadcom's
and are backward compatible
from a random process with zero-mean and unit-variance 7000 series support 8PSK
[7]
with
the
older
standard.
Gaussian probability density function will be greater or
equal to x . It is a scaled form of the complementary Historically, voice-band synchronous modems such as the
Gaussian error function:
Bell 201, 208, and 209 and the CCITT V.26, V.27, V.29,
V.32, and V.34 used PSK.[8]
1
Q(x) =
2

e
x

t2 /2

1
dt = erfc
2

)
, x0

The error-rates quoted here are those in additive white

Gaussian noise (AWGN). These error rates are lower than
those computed in fading channels, hence, are a good theoretical benchmark to compare with.

72.3 Binary phase-shift

(BPSK)

keying

72.2 Applications
Owing to PSKs simplicity, particularly when compared
with its competitor quadrature amplitude modulation, it
is widely used in existing technologies.
The wireless LAN standard, IEEE 802.11b-1999,[2][3]
uses a variety of dierent PSKs depending on the data
rate required. At the basic rate of 1 Mbit/s, it uses
DBPSK (dierential BPSK). To provide the extended
rate of 2 Mbit/s, DQPSK is used. In reaching 5.5
Mbit/s and the full rate of 11 Mbit/s, QPSK is employed,
but has to be coupled with complementary code keying.
The higher-speed wireless LAN standard, IEEE 802.11g2003,[2][4] has eight data rates: 6, 9, 12, 18, 24, 36, 48
and 54 Mbit/s. The 6 and 9 Mbit/s modes use OFDM
modulation where each sub-carrier is BPSK modulated.
The 12 and 18 Mbit/s modes use OFDM with QPSK. The
fastest four modes use OFDM with forms of quadrature
amplitude modulation.

1
I

Constellation diagram example for BPSK.

BPSK (also sometimes called PRK, phase reversal keying, or 2PSK) is the simplest form of phase shift keying
(PSK). It uses two phases which are separated by 180
Because of its simplicity, BPSK is appropriate for low- and so can also be termed 2-PSK. It does not particucost passive transmitters, and is used in RFID standards larly matter exactly where the constellation points are posuch as ISO/IEC 14443 which has been adopted for sitioned, and in this gure they are shown on the real axis,

72.4. QUADRATURE PHASE-SHIFT KEYING (QPSK)

at 0 and 180. This modulation is the most robust of all
the PSKs since it takes the highest level of noise or distortion to make the demodulator reach an incorrect decision.
It is, however, only able to modulate at 1 bit/symbol (as
seen in the gure) and so is unsuitable for high data-rate
applications.
In the presence of an arbitrary phase-shift introduced by
the communications channel, the demodulator is unable
to tell which constellation point is which. As a result, the
data is often dierentially encoded prior to modulation.

337

72.4 Quadrature phase-shift keying (QPSK)

Q

01

11

BPSK is functionally equivalent to 2-QAM modulation.

72.3.1

Implementation

The general form for BPSK follows the equation:

sn (t) =

2Eb
cos(2fc t + (1 n)), n = 0, 1.
Tb

00

10

This yields two phases, 0 and . In the specic form,

binary data is often conveyed with the following signals:

s0 (t) =

2Eb
cos(2fc t + ) =
Tb

Constellation diagram for QPSK with Gray coding. Each adjacent symbol only diers by one bit.

2Eb
cos(2fc t)
Tb

Sometimes this is known as quadriphase PSK, 4-PSK, or

4-QAM. (Although the root concepts of QPSK and 42Eb
QAM are dierent, the resulting modulated radio waves
s1 (t) =
cos(2fc t)
Tb
are exactly the same.) QPSK uses four points on the constellation diagram, equispaced around a circle. With four
where fc is the frequency of the carrier-wave.
phases, QPSK can encode two bits per symbol, shown in
Hence, the signal-space can be represented by the single the diagram with Gray coding to minimize the bit error
basis function
rate (BER) sometimes misperceived as twice the BER
of BPSK.

The mathematical analysis shows that QPSK can be used

2
cos(2fc t)
(t) =
either to double the data rate compared with a BPSK sysTb
tem while maintaining the same bandwidth of the signal,

where1 is represented by Eb (t) and 0 is represented or to maintain the data-rate of BPSK but halving the bandby Eb (t) . This assignment is, of course, arbitrary. width needed. In this latter case, the BER of QPSK is exactly the same as the BER of BPSK - and deciding dierThis use of this basis function is shown at the end of the
ently is a common confusion when considering or describnext section in a signal timing diagram. The topmost
ing QPSK. The transmitted carrier can undergo numbers
signal is a BPSK-modulated cosine wave that the BPSK
of phase changes.
modulator would produce. The bit-stream that causes this
output is shown above the signal (the other parts of this Given that radio communication channels are allocated
by agencies such as the Federal Communication Comgure are relevant only to QPSK).
mission giving a prescribed (maximum) bandwidth, the
advantage of QPSK over BPSK becomes evident: QPSK
72.3.2 Bit error rate
transmits twice the data rate in a given bandwidth
compared to BPSK - at the same BER. The engiThe bit error rate (BER) of BPSK in AWGN can be cal- neering penalty that is paid is that QPSK transmitters
culated as:[9]
and receivers are more complicated than the ones for
BPSK. However, with modern electronics technology,
)
(
( )
2Eb
Eb
1
the penalty in cost is very moderate.
or
P
=
Pb = Q
erfc
e
N
2
N

As with BPSK, there are phase ambiguity problems at the

Since there is only one bit per symbol, this is also the receiving end, and dierentially encoded QPSK is often
used in practice.
symbol error rate.

338

72.4.1

CHAPTER 72. PHASE-SHIFT KEYING

Implementation

The implementation of QPSK is more general than that

of BPSK and also indicates the implementation of higherorder PSK. Writing the symbols in the constellation diagram in terms of the sine and cosine waves used to transmit them:

Conceptual transmitter structure for QPSK. The binary data

stream is split into the in-phase and quadrature-phase components. These are then separately modulated onto two orthogonal

(
2Es
)
sn (t) =
, n = 1, 2, 3,basis
4. functions. In this implementation, two sinusoids are used.
cos 2fc t + (2n 1)
Afterwards, the two signals are superimposed, and the resulting
Ts
4
signal is the QPSK signal. Note the use of polar non-return-toThis yields the four phases /4, 3/4, 5/4 and 7/4 as zero encoding. These encoders can be placed before for binary
needed.
data source, but have been placed after to illustrate the concepThis results in a two-dimensional signal space with unit tual dierence between digital and analog signals involved with
digital modulation.
basis functions

1 (t) =

2
cos(2fc t)
Ts

2
Receiver structure for QPSK. The matched lters can be replaced
sin(2fc t)
with correlators. Each detection device uses a reference threshold
Ts
The rst basis function is used as the in-phase component value to determine whether a 1 or 0 is detected.
of the signal and the second as the quadrature component
of the signal.
(
)
Hence, the signal constellation consists of the signal-space
2Eb
Pb = Q
.
4 points
N0

2 (t) =

(
)

Es /2, Es /2 .

However, in order to achieve the same bit-error probability as BPSK, QPSK uses twice the power (since two bits
are transmitted simultaneously).

The factors of 1/2 indicate that the total power is split

The symbol error rate is given by:
equally between the two carriers.
If the signal-to-noise ratio is high (as is necessary for
Comparing these basis functions with that for BPSK
practical QPSK systems) the probability of symbol error
shows clearly how QPSK can be viewed as two indepenmay be approximated:
dent BPSK signals. Note that the signal-space points for
BPSK do not need to split the symbol (bit) energy over
( )
the two carriers in the scheme shown in the BPSK conEs
stellation diagram.
Ps 2Q
N0
QPSK systems can be implemented in a number of ways.
An illustration of the major components of the transmitter The modulated signal is shown below for a short segment
and receiver structure are shown below.
of a random binary data-stream. The two carrier waves
are a cosine wave and a sine wave, as indicated by the
signal-space analysis above. Here, the odd-numbered bits
72.4.2 Bit error rate
have been assigned to the in-phase component and the
even-numbered bits to the quadrature component (taking
Although QPSK can be viewed as a quaternary modula- the rst bit as number 1). The total signal the sum of
tion, it is easier to see it as two independently modulated the two components is shown at the bottom. Jumps in
quadrature carriers. With this interpretation, the even (or phase can be seen as the PSK changes the phase on each
odd) bits are used to modulate the in-phase component component at the start of each bit-period. The topmost
of the carrier, while the odd (or even) bits are used to waveform alone matches the description given for BPSK
modulate the quadrature-phase component of the carrier. above.
BPSK is used on both carriers and they can be indepen- The binary data that is conveyed by this waveform is: 1
dently demodulated.
1 0 0 0 1 1 0.
As a result, the probability of bit-error for QPSK is the
The odd bits, highlighted here, contribute to the insame as for BPSK:

72.4. QUADRATURE PHASE-SHIFT KEYING (QPSK)

339
QPSK
135

45
t

45

135

Timing diagram for QPSK. The binary data stream is shown beneath the time axis. The two signal components with their bit
assignments are shown at the top, and the total combined signal
at the bottom. Note the abrupt changes in phase at some of the
bit-period boundaries.

OQPSK
135

45

45

135

phase component: 1 1 0 0 0 1 1 0

The even bits, highlighted here, contribute to the Dierence of the phase between QPSK and OQPSK
quadrature-phase component: 1 1 0 0 0 1 1 0

72.4.3

period, or half a symbol-period, the in-phase and quadrature components will never change at the same time. In
the constellation diagram shown on the right, it can be
seen that this will limit the phase-shift to no more than
90 at a time. This yields much lower amplitude uctuations than non-oset QPSK and is sometimes preferred
in practice.

Variants

Oset QPSK (OQPSK)

Q

01

The picture on the right shows the dierence in the behavior of the phase between ordinary QPSK and OQPSK.
It can be seen that in the rst plot the phase can change
by 180 at once, while in OQPSK the changes are never
greater than 90.

11

00

The modulated signal is shown below for a short segment of a random binary data-stream. Note the half
symbol-period oset between the two component waves.
The sudden phase-shifts occur about twice as often as for
QPSK (since the signals no longer change together), but
they are less severe. In other words, the magnitude of
jumps is smaller in OQPSK when compared to QPSK.

10

Signal doesn't cross zero, because only one bit of the symbol is
changed at a time

Oset quadrature phase-shift keying (OQPSK) is a variant

of phase-shift keying modulation using 4 dierent values
of the phase to transmit. It is sometimes called Staggered
quadrature phase-shift keying (SQPSK).

Timing diagram for oset-QPSK. The binary data stream is

shown beneath the time axis. The two signal components with
their bit assignments are shown the top and the total, combined
signal at the bottom. Note the half-period oset between the two
signal components.

Taking four values of the phase (two bits) at a time to

construct a QPSK symbol can allow the phase of the signal to jump by as much as 180 at a time. When the
signal is low-pass ltered (as is typical in a transmitter), /4QPSK
these phase-shifts result in large amplitude uctuations,
an undesirable quality in communication systems. By This variant of QPSK uses two identical constellations
osetting the timing of the odd and even bits by one bit- which are rotated by 45 ( /4 radians, hence the name)

340

CHAPTER 72. PHASE-SHIFT KEYING

Q

01
01

00

11

45

00

11

10
10

Dual constellation diagram for /4-QPSK. This shows the two

separate constellations with identical Gray coding but rotated by
45 with respect to each other.

Timing diagram for /4-QPSK. The binary data stream is shown

beneath the time axis. The two signal components with their bit
assignments are shown the top and the total, combined signal at
the bottom. Note that successive symbols are taken alternately
from the two constellations, starting with the 'blue' one.

sense that an integrate-and-dump oset QPSK detector

produces the same output no matter which kind of transmitter is used.[10]
These modulations carefully shape the I and Q waveforms such that they change very smoothly, and the signal stays constant-amplitude even during signal transitions. (Rather than traveling instantly from one symbol
to another, or even linearly, it travels smoothly around the
constant-amplitude circle from one symbol to the next.)

with respect to one another. Usually, either the even or

odd symbols are used to select points from one of the The standard description of SOQPSK-TG involves
constellations and the other symbols select points from ternary symbols.
the other constellation. This also reduces the phase-shifts
from a maximum of 180, but only to a maximum of 135
and so the amplitude uctuations of /4 QPSK are be- DPQPSK
tween OQPSK and non-oset QPSK.
Dual-polarization quadrature phase shift keying
One property this modulation scheme possesses is that if
(DPQPSK) or dual-polarization QPSK - involves the
the modulated signal is represented in the complex dopolarization multiplexing of two dierent QPSK signals,
main, it does not have any paths through the origin. In
thus improving the spectral eciency by a factor of 2.
other words, the signal does not pass through the origin.
This is a cost-eective alternative, to utilizing 16-PSK inThis lowers the dynamical range of uctuations in the sigstead of QPSK to double the spectral eciency.
nal which is desirable when engineering communications
signals.
On the other hand, /4 QPSK lends itself to easy demodulation and has been adopted for use in, for example,
TDMA cellular telephone systems.
The modulated signal is shown below for a short segment
of a random binary data-stream. The construction is the
same as above for ordinary QPSK. Successive symbols
are taken from the two constellations shown in the diagram. Thus, the rst symbol (1 1) is taken from the 'blue'
constellation and the second symbol (0 0) is taken from
the 'green' constellation. Note that magnitudes of the two
component waves change as they switch between constellations, but the total signals magnitude remains constant
(constant envelope). The phase-shifts are between those
of the two previous timing-diagrams.

72.5 Higher-order PSK

Any number of phases may be used to construct a PSK
constellation but 8-PSK is usually the highest order PSK
constellation deployed. With more than 8 phases, the
error-rate becomes too high and there are better, though
more complex, modulations available such as quadrature
amplitude modulation (QAM). Although any number of
phases may be used, the fact that the constellation must
usually deal with binary data means that the number of
symbols is usually a power of 2 to allow an integer number of bits per symbol.

72.5.1 Bit error rate

SOQPSK
For the general M -PSK there is no simple expression for
The license-free shaped-oset QPSK (SOQPSK) is in- the symbol-error probability if M > 4 . Unfortunately,
teroperable with Feher-patented QPSK (FQPSK), in the it can only be obtained from:

72.6. DIFFERENTIAL PHASE-SHIFT KEYING (DPSK)

341

Ps 2Q

010
011

110

001

2s sin

)
M

The bit-error probability for M -PSK can only be determined exactly once the bit-mapping is known. However,
when Gray coding is used, the most probable error from
one symbol to the next produces only a single bit-error
and

111
I

Pb

000

(Using Gray coding allows us to approximate the Lee distance of the errors as the Hamming distance of the errors
in the decoded bitstream, which is easier to implement in
hardware.)

101
100

The graph on the left compares the bit-error rates of

BPSK, QPSK (which are the same, as noted above), 8PSK and 16-PSK. It is seen that higher-order modulations
exhibit higher error-rates; in exchange however they deliver a higher raw data-rate.

Constellation diagram for 8-PSK with Gray coding.

Ps = 1

Bounds on the error rates of various digital modulation

schemes can be computed with application of the union
bound to the signal constellation.

pr (r ) dr

where
pr (r )
1 2s sin2 r
2 e

V =

V e(V

2
4s cos r ) /2

72.6 Dierential phase-shift keying (DPSK)

dV

r12 + r22 ,

72.6.1 Dierential encoding

r = tan1 (r2 /r1 ) ,

Es
N0

and
(
)
r1 N
Es , N0 /2 and r2 N (0, N0 /2)
are jointly Gaussian random variables.
s =

BER

10

Main article: dierential coding

Dierential phase shift keying (DPSK) is a common form
of phase modulation that conveys data by changing the
phase of the carrier wave. As mentioned for BPSK and
QPSK there is an ambiguity of phase if the constellation
is rotated by some eect in the communications channel
through which the signal passes. This problem can be
overcome by using the data to change rather than set the
phase.

10

-2

10

-4

10

-6

For example, in dierentially encoded BPSK a binary '1'

may be transmitted by adding 180 to the current phase
and a binary '0' by adding 0 to the current phase. Another variant of DPSK is Symmetric Dierential Phase
Shift keying, SDPSK, where encoding would be +90 for
a '1' and 90 for a '0'.

BPSK / QPSK
8-PSK
16-PSK
10

1
Ps
k

-8

10

Eb/N0 (dB)

12

14

16

18

Bit-error rate curves for BPSK, QPSK, 8-PSK and 16-PSK,

AWGN channel.

This may be approximated for high M and high Eb /N0

by:

In dierentially encoded QPSK (DQPSK), the phaseshifts are 0, 90, 180, 90 corresponding to data '00',
'01', '11', '10'. This kind of encoding may be demodulated in the same way as for non-dierential PSK but the
phase ambiguities can be ignored. Thus, each received
symbol is demodulated to one of the M points in the constellation and a comparator then computes the dierence

342

CHAPTER 72. PHASE-SHIFT KEYING

in phase between this received signal and the preceding

one. The dierence encodes the data as described above.
Symmetric Dierential Quadrature Phase Shift Keying
(SDQPSK) is like DQPSK, but encoding is symmetric,
using phase shift values of 135, 45, +45 and +135.

of demodulating as usual and ignoring carrier-phase ambiguity, the phase between two successive received symbols is compared and used to determine what the data
must have been. When dierential encoding is used in
this manner, the scheme is known as dierential phaseThe modulated signal is shown below for both DBPSK shift keying (DPSK). Note that this is subtly dierent
and DQPSK as described above. In the gure, it is as- from just dierentially encoded PSK since, upon recepsumed that the signal starts with zero phase, and so there tion, the received symbols are not decoded one-by-one to
constellation points but are instead compared directly to
is a phase shift in both signals at t = 0 .
one another.
Call the received symbol in the k th timeslot rk and let it
have phase k . Assume without loss of generality that
the phase of the carrier wave is zero. Denote the AWGN
term as nk . Then

Timing diagram for DBPSK and DQPSK. The binary data stream
is above the DBPSK signal. The individual bits of the DBPSK
signal are grouped into pairs for the DQPSK signal, which only
changes every T = 2T .

Analysis shows that dierential encoding approximately

doubles the error rate compared to ordinary M -PSK but
this may be overcome by only a small increase in Eb /N0
. Furthermore, this analysis (and the graphical results below) are based on a system in which the only corruption is
additive white Gaussian noise(AWGN). However, there
will also be a physical channel between the transmitter
and receiver in the communication system. This channel
will, in general, introduce an unknown phase-shift to the
PSK signal; in these cases the dierential schemes can
yield a better error-rate than the ordinary schemes which
rely on precise phase information.

rk =

Es ejk + nk

The decision variable for the k 1 th symbol and the k

symbol is the phase dierence between rk and rk1 .
That is, if rk is projected onto rk1 , the decision is taken
on the phase of the resultant complex number:
th

rk rk1
= Es ej(k k1 ) +

Es ejk nk1 + Es ejk1 nk +nk nk1

where superscript * denotes complex conjugation. In the

absence of noise, the phase of this is k k1 , the
phase-shift between the two received signals which can
be used to determine the data transmitted.
The probability of error for DPSK is dicult to calculate
in general, but, in the case of DBPSK it is:
Pb = 12 eEb /N0 ,

72.6.2

BER

10

Demodulation

which, when numerically evaluated, is only slightly worse

than ordinary BPSK, particularly at higher Eb /N0 values.

10

-2

10

-4

10

-6

10

-8

Using DPSK avoids the need for possibly complex

carrier-recovery schemes to provide an accurate phase
estimate and can be an attractive alternative to ordinary
PSK.

BPSK / QPSK
DBPSK
DQPSK

Eb/N0 (dB)

10

12

14

16

BER comparison between DBPSK, DQPSK and their nondierential forms using gray-coding and operating in white noise.

In optical communications, the data can be modulated

onto the phase of a laser in a dierential way. The modulation is a laser which emits a continuous wave, and a
Mach-Zehnder modulator which receives electrical binary data. For the case of BPSK for example, the laser
transmits the eld unchanged for binary '1', and with
reverse polarity for '0'. The demodulator consists of a
delay line interferometer which delays one bit, so two bits
can be compared at one time. In further processing, a
photodiode is used to transform the optical eld into an
electric current, so the information is changed back into
its original state.

The bit-error rates of DBPSK and DQPSK are comFor a signal that has been dierentially encoded, there is pared to their non-dierential counterparts in the graph
an obvious alternative method of demodulation. Instead to the right. The loss for using DBPSK is small enough

72.7. CHANNEL CAPACITY

343

compared to the complexity reduction that it is often

used in communications systems that would otherwise
use BPSK. For DQPSK though, the loss in performance
compared to ordinary QPSK is larger and the system designer must balance this against the reduction in complexity.

72.6.3

Example:
BPSK

bk will still be decoded correctly. Thus, the 180 phase

ambiguity does not matter.
Dierential schemes for other PSK modulations may be
devised along similar lines. The waveforms for DPSK are
the same as for dierentially encoded PSK given above
since the only change between the two schemes is at the
receiver.

Dierentially encoded The BER curve for this example is compared to ordi-

nary BPSK on the right. As mentioned above, whilst the

error-rate is approximately doubled, the increase needed
in Eb /N0 to overcome this is small. The increase in
Eb /N0 required to overcome dierential modulation in
coded systems, however, is larger - typically about 3 dB.
The performance degradation is a result of noncoherent
Dierential encoding/decoding system diagram.
transmission - in this case it refers to the fact that tracking
th
At the k time-slot call the bit to be modulated bk , the of the phase is completely ignored.
dierentially encoded bit ek and the resulting modulated
signal mk (t) . Assume that the constellation diagram positions the symbols at 1 (which is BPSK). The dieren- 72.7 Channel capacity
tial encoder produces:
4.5

ek = ek1 bk

3.5

10

Channel capacity

where indicates binary or modulo-2 addition.

10

BPSK
QPSK
8 PSK
16 PSK
16 QAM

BPSK
Diff. enc BPSK

-2

3
2.5
2
1.5
1

BER

0.5
10

-4

0
-5

10

15

20

SNR [dB]
10

-6

Given a xed bandwidth, channel capacity vs. SNR for some

common modulation schemes
10

-8

Like all M-ary modulation schemes with M = 2b symbols, when given exclusive access to a xed bandwidth,
BER comparison between BPSK and dierentially encoded BPSK the channel capacity of any phase shift keying modulation scheme rises to a maximum of b bits per symbol as
with gray-coding operating in white noise.
the signal-to-noise ratio increases, due to the ShannonSo ek only changes state (from binary '0' to binary '1' or Hartley Theorem.
from binary '1' to binary '0') if bk is a binary '1'. Otherwise it remains in its previous state. This is the description of dierentially encoded BPSK given above.
72.8 See also
0

Eb/N0 (dB)

10

12

14

The received signal is demodulated to yield ek = 1 and

then the dierential decoder reverses the encoding procedure and produces:

bk = ek ek1
Therefore, bk = 1 if ek and ek1 dier and bk = 0 if they
are the same. Hence, if both ek and ek1 are inverted,

Dierential coding
Modulation for an overview of all modulation
schemes
Phase modulation (PM) the analogue equivalent
of PSK
Polar modulation

344

CHAPTER 72. PHASE-SHIFT KEYING

PSK31

Couch, Leon W. II (1997). Digital and Analog

Communications. Upper Saddle River, NJ: PrenticeHall. ISBN 0-13-081223-4.

PSK63
Binary oset carrier modulation

Haykin, Simon (1988). Digital Communications.

Toronto, Canada: John Wiley & Sons. ISBN 0-47162947-2.

72.9 Notes
[1] Best, R. E.; Kuznetsov, N. V.; Leonov, G. A.;
Yuldashev, M. V.; Yuldashev, R. V. Tutorial
on dynamic analysis of the Costas loop.
Annual Reviews in Control.
arXiv:1511.04435 .
doi:10.1016/j.arcontrol.2016.08.003.
[2] IEEE Std 802.11-1999: Wireless LAN Medium Access
Control (MAC) and Physical Layer (PHY) Specications
the overarching IEEE 802.11 specication. Archived
August 28, 2007, at the Wayback Machine.
[3] IEEE Std 802.11b-1999 (R2003) the IEEE 802.11b
specication.
[4] IEEE Std 802.11g-2003 the IEEE 802.11g specication.
[5] Understanding the Requirements of ISO/IEC 14443 for
Type B Proximity Contactless Identication Cards, Application Note, Rev. 2056BRFID11/05, 2005, ATMEL
[6] How Communications Satellites Work.
2014.

Planet Fox.

[7] http://www.broadcom.com/products/
set-top-box-and-media-processors/satellite/bcm7325
[8] Local and Remote Modems (PDF). Black Box. Black
Box Network Services. Retrieved December 20, 2015.
[9] Communications Systems, H. Stern & S. Mahmoud, Pearson Prentice Hall, 2004, p283
[10] Tom Nelson, Erik Perrins, and Michael Rice. Common
detectors for Tier 1 modulations. T. Nelson, E. Perrins,
M. Rice. Common detectors for shaped oset QPSK
(SOQPSK) and Feher-patented QPSK (FQPSK)" Nelson, T.; Perrins, E.; Rice, M. (2005). Common detectors for shaped oset QPSK (SOQPSK) and Feherpatented QPSK (FQPSK)". GLOBECOM '05. IEEE
Global Telecommunications Conference, 2005. pp. 5 pp.
doi:10.1109/GLOCOM.2005.1578470. ISBN 0-78039414-3. ISBN 0-7803-9414-3

72.10 References
The notation and theoretical results in this article are
based on material presented in the following sources:
Proakis, John G. (1995). Digital Communications.
Singapore: McGraw Hill. ISBN 0-07-113814-5.

Chapter 73

Frequency-shift keying
mark frequency and the 0 is called the space frequency.
The time domain of an FSK modulated carrier is illustrated in the gures to the right.

73.1 Implementations
Modems

Data

of

FSK

Reference implementations of FSK modems exist and are

documented in detail.[3] The demodulation of a binary
FSK signal can be done using the Goertzel algorithm very
eciently, even on low-power microcontrollers.[4]

Carrier

73.2 Other forms of FSK

73.2.1 Continuous-phase frequency-shift
keying

Modulated Signal

Main article: continuous-phase frequency-shift keying

An example of binary FSK

In principle FSK can be implemented by using completely independent free-running oscillators, and switching between them at the beginning of each symbol period.
In general, independent oscillators will not be at the same
phase and therefore the same amplitude at the switch-over
instant, causing sudden discontinuities in the transmitted
signal.

Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is transmitted
through discrete frequency changes of a carrier signal.[1]
The technology is used for communication systems such
as amateur radio, caller ID and emergency broadcasts.
The simplest FSK is binary FSK (BFSK). BFSK uses
a pair of discrete frequencies to transmit binary (0s and
1s) information.[2] With this scheme, the 1 is called the

In practice, many FSK transmitters use only a single oscillator, and the process of switching to a dierent frequency at the beginning of each symbol period preserves
the phase. The elimination of discontinuities in the phase
(and therefore elimination of sudden changes in amplitude) reduces sideband power, reducing interference with
neighboring channels.

73.2.2 Gaussian frequency-shift keying

Rather than directly modulating the frequency with the
digital data symbols, instantaneously changing the frequency at the beginning of each symbol period, Gaussian frequency-shift keying (GFSK) lters the data pulses

345

346

CHAPTER 73. FREQUENCY-SHIFT KEYING

with a Gaussian lter to make the transitions smoother.

This lter has the advantage of reducing sideband power,
reducing interference with neighboring channels, at the
cost of increasing intersymbol interference. It is used
by DECT, Bluetooth,[5] Cypress WirelessUSB, Nordic
Semiconductor,[6] Texas Instruments LPRF, Z-Wave and
Wavenis devices. For basic data rate Bluetooth the minimum deviation is 115 kHz.

one; the other, the space, represents a binary zero.

AFSK diers from regular frequency-shift keying in performing the modulation at baseband frequencies. In radio
applications, the AFSK-modulated signal normally is being used to modulate an RF carrier (using a conventional
technique, such as AM or FM) for transmission.
AFSK is not always used for high-speed data communications, since it is far less ecient in both power and bandwidth than most other modulation modes. In addition to
its simplicity, however, AFSK has the advantage that encoded signals will pass through AC-coupled links, including most equipment originally designed to carry music or
speech.

A GFSK modulator diers from a simple frequency-shift

keying modulator in that before the baseband waveform
(levels 1 and +1) goes into the FSK modulator, it is
passed through a Gaussian lter to make the transitions
smoother so to limit its spectral width. Gaussian ltering
is a standard way for reducing spectral width; it is called
AFSK is used in the U.S. based Emergency Alert System
"pulse shaping" in this application.
to notify stations of the type of emergency, locations afIn ordinary non-ltered FSK, at a jump from 1 to +1 fected, and the time of issue without actually hearing the
or +1 to 1, the modulated waveform changes rapidly, text of the alert.
which introduces large out-of-band spectrum. If we
change the pulse going from 1 to +1 as 1, .98, .93
..... +.93, +.98, +1, and we use this smoother pulse to de- 73.2.6 Continuous 4 level FM
termine the carrier frequency, the out-of-band spectrum
will be reduced.[7]
Phase 1 radios in the Project 25 system use continuous 4
level FM (C4FM) modulation.[8][9]

73.2.3

Minimum-shift keying

Main article: Minimum-shift keying

Minimum frequency-shift keying or minimum-shift keying (MSK) is a particular spectrally ecient form of coherent FSK. In MSK, the dierence between the higher
and lower frequency is identical to half the bit rate. Consequently, the waveforms that represent a 0 and a 1 bit
dier by exactly half a carrier period. The maximum
frequency deviation is = 0.25 fm, where fm is the maximum modulating frequency. As a result, the modulation
index m is 0.5. This is the smallest FSK modulation index
that can be chosen such that the waveforms for 0 and 1
are orthogonal.

73.3 Applications
In 1910, Reginald Fessenden invented a two-tone method
of transmitting Morse code. Dots and dashes were replaced with dierent tones of equal length.[10] The intent
was to minimize transmission time.
Some early CW transmitters employed an arc converter
that could not be conveniently keyed. Instead of turning
the arc on and o, the key slightly changed the transmitter frequency in a technique known as the compensationwave method.[11] The compensation-wave was not used
at the receiver. Spark transmitters used for this method
consumed a lot of bandwidth and caused interference, so
it was discouraged by 1921.[12]

Most early telephone-line modems used audio frequencyshift keying (AFSK) to send and receive data at rates up
to about 1200 bits per second. The Bell 103 and Bell
Main article: Gaussian minimum shift keying
202 modems used this technique.[13] Even today, North
American caller ID uses 1200 baud AFSK in the form
A variant of MSK called Gaussian minimum shift keying of the Bell 202 standard. Some early microcomputers
(GMSK) is used in the GSM mobile phone standard.
used a specic form of AFSK modulation, the Kansas
City standard, to store data on audio cassettes. AFSK is
still widely used in amateur radio, as it allows data trans73.2.5 Audio FSK
mission through unmodied voiceband equipment.

73.2.4

Gaussian minimum shift keying

Audio frequency-shift keying (AFSK) is a modulation

technique by which digital data is represented by changes
in the frequency (pitch) of an audio tone, yielding an
encoded signal suitable for transmission via radio or
telephone. Normally, the transmitted audio alternates between two tones: one, the mark, represents a binary

AFSK is also used in the United States Emergency Alert

System to transmit warning information. It is used at
higher bitrates for Weathercopy used on Weatheradio by
NOAA in the U.S.
The CHU shortwave radio station in Ottawa, Canada
broadcasts an exclusive digital time signal encoded using

73.6. EXTERNAL LINKS

347

AFSK modulation.

[9] Steve Ford. ARRLs VHF Digital Handbook. 2008. p.

6-2.

FSK is commonly used in Caller ID and remote metering

applications: see FSK standards for use in Caller ID and [10] Morse 1925, p. 44; Morse cites British patent 2,617/11.
remote metering for more details
[11] Bureau of Standards 1922, pp. 415416
[12] Little 1921, p. 125

73.4 See also

[13] Kennedy & Davis 1992, pp. 549550

Amplitude-shift keying (ASK)

Continuous-phase frequency-shift keying (CPFSK)
Dual-tone multi-frequency (DTMF), another encoding technique representing data by pairs of audio
frequencies
Frequency-change signaling
Multiple frequency-shift keying (MFSK)
Orthogonal
(OFDM)

frequency

division

Bureau of Standards (1922), The Principles Underlying Radio Communication (Second ed.), U.S.
Army Signal Corps, Radio Communications Pamphlet No. 40. Revised to April 24, 1921.
Little, D. G. (April 1921), Continuous Wave Radio
Communication, Electric Journal, 18: 124129
Morse, A. H. (1925), Radio: Beam and Broadcast,
London: Ernest Benn Limited

multiplexing

Phase-shift keying (PSK)

Federal Standard 1037C
MIL-STD-188
spread spectrum frequency shift keying (S-FSK)

73.5 References
[1] Kennedy, G.; Davis, B. (1992). Electronic Communication
Systems (4th ed.). McGraw-Hill International. ISBN 007-112672-4., p 509
[2] FSK: Signals and Demodulation (B. Watson)
http://www.xn--sten-cpa.se/share/text/tektext/
digital-modulation/FSK_signals_demod.pdf
[3] Teaching DSP through the Practical Case Study of an FSK
Modem (TI) http://www.ti.com/lit/an/spra347/spra347.
pdf
[4] FSK Modulation and Demodulation With the MSP430
Microcontroller (TI) http://www.ti.com/lit/an/slaa037/
slaa037.pdf
[5] Sweeney, D. An introduction to bluetooth a standard for
short range wireless networking Proceedings. 15th Annual IEEE International ASIC/SOC Conference, Rochester,
NY, USA, 25-28 Sept. 2002, pp. 474475. 2002. http://
ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1158106
[6] Nordic Semiconductor. nRF24LU1+ Preliminary Product Specication v1.2
[7] Bhagwat, Pravin (10 May 2005). Bluetooth: 1.Applications, Technology and Performance. p. 21. Retrieved 27
May 2015.
[8] Essam Atalla et al. A Practical Step Forward Toward
Software-Dened Radio Transmitters. p. 1.

73.6 External links

dFSK: Distributed Frequency Shift Keying Modulation in Dense Sensor Networks
M Nasseri, J Kim, M Alam - Proceedings of the
17th Communications & Networking, 2014, Unied metric calculation of sampling-based turbocoded noncoherent MFSK for mobile channel
J Kim, P Raorane, M Nasseri, M Alam - Proceedings of the 46th Annual Simulation Symposium, 2013, Performance analysis of samplingbased turbo coded NCQFSK for image data transmission

Chapter 74

Amplitude-shift keying
Amplitude-shift keying (ASK) is a form of amplitude much of the signal is transmitted at reduced power.
modulation that represents digital data as variations in the
amplitude of a carrier wave. In an ASK system, the binary
symbol 1 is represented by transmitting a xed-amplitude
carrier wave and xed frequency for a bit duration of T
seconds. If the signal value is 1 then the carrier signal
will be transmitted; otherwise, a signal value of 0 will be ASK diagram
transmitted.
Any digital modulation scheme uses a nite number of ASK system can be divided into three blocks. The rst
distinct signals to represent digital data. ASK uses a - one represents the transmitter, the second one is a linear
nite number of amplitudes, each assigned a unique pat- model of the eects of the channel, the third one shows
tern of binary digits. Usually, each amplitude encodes the structure of the receiver. The following notation is
an equal number of bits. Each pattern of bits forms the used:
symbol that is represented by the particular amplitude.
The demodulator, which is designed specically for the
symbol-set used by the modulator, determines the amplitude of the received signal and maps it back to the symbol
it represents, thus recovering the original data. Frequency
and phase of the carrier are kept constant.
Like AM, an ASK is also linear and sensitive to atmospheric noise, distortions, propagation conditions on different routes in PSTN, etc. Both ASK modulation and
demodulation processes are relatively inexpensive. The
ASK technique is also commonly used to transmit digital
data over optical ber. For LED transmitters, binary 1
is represented by a short pulse of light and binary 0 by
the absence of light. Laser transmitters normally have a
xed bias current that causes the device to emit a low
light level. This low level represents binary 0, while a
higher-amplitude lightwave represents binary 1.

ht(f) is the carrier signal for the transmission

hc(f) is the impulse response of the channel
n(t) is the noise introduced by the channel
hr(f) is the lter at the receiver
L is the number of levels that are used for transmission
T is the time between the generation of two symbols
Dierent symbols are represented with dierent voltages.
If the maximum allowed value for the voltage is A, then
all the possible values are in the range [A, A] and they
are given by:

The simplest and most common form of ASK operates as

2A
a switch, using the presence of a carrier wave to indicate vi = L 1 i A; i = 0, 1, . . . , L 1
a binary one and its absence to indicate a binary zero.
This type of modulation is called on-o keying (OOK), the dierence between one voltage and the other is:
and is used at radio frequencies to transmit Morse code
(referred to as continuous wave operation),
2A
=
More sophisticated encoding schemes have been develL1
oped which represent data in groups using additional amplitude levels. For instance, a four-level encoding scheme Considering the picture, the symbols v[n] are generated
can represent two bits with each shift in amplitude; an randomly by the source S, then the impulse generator creeight-level scheme can represent three bits; and so on. ates impulses with an area of v[n]. These impulses are
These forms of amplitude-shift keying require a high sent to the lter ht to be sent through the channel. In
signal-to-noise ratio for their recovery, as by their nature other words, for each symbol a dierent carrier wave is
sent with the relative amplitude.
348

74.1. PROBABILITY OF ERROR

349

Out of the transmitter, the signal s(t) can be expressed in The probability of making an error is given by:
the form:

s(t) =

v[n] ht (t nTs )

Pe = Pe|H0 PH0 +Pe|H1 PH1 + +Pe|HL1 PHL1 =

L1

Pe|Hk PHk

k=0

n=

where, for example, Pe|H0 is the conditional probability

In the receiver, after the ltering through hr (t) the signal of making an error given that a symbol v0 has been sent
and PH0 is the probability of sending a symbol v0.
is:
If the probability of sending any symbol is the same, then:
z(t) = nr (t) +

v[n] g(t nTs )

PHi =

n=

where we use the notation:

1
L

If we represent all the probability density functions on the

same plot against the possible value of the voltage to be
transmitted, we get a picture like this (the particular case
of L = 4 is shown):

nr (t) = n(t) hr (f )
g(t) = ht (t) hc (f ) hr (t)
where * indicates the convolution between two signals.
After the A/D conversion the signal z[k] can be expressed
in the form:

The probability of making an error after a single symbol

has been sent is the area of the Gaussian function falling
n=k
under the functions for the other symbols. It is shown in
cyan for just one of them. If we call P + the area under
In this relationship, the second term represents the symbol
one side of the Gaussian, the sum of all the areas will be:
to be extracted. The others are unwanted: the rst one is
2LP + 2P + . The total probability of making an error
the eect of noise, the third one is due to the intersymbol
can be expressed in the form:
interference.

z[k] = nr [k] + v[k]g[0] +

v[n]g[k n]

If the lters are chosen so that g(t) will satisfy the Nyquist
(
)
1
ISI criterion, then there will be no intersymbol interferPe = 2 1
P+
ence and the value of the sum will be zero, so:
L

z[k] = nr [k] + v[k]g[0]

the transmission will be aected only by noise.

We have now to calculate the value of P + . In order to do

that, we can move the origin of the reference wherever we
want: the area below the function will not change. We are
in a situation like the one shown in the following picture:

74.1 Probability of error

The probability density function of having an error of a
given size can be modelled by a Gaussian function; the
mean value will be the relative sent value, and its variance
will be given by:

2
N

N (f ) |Hr (f )|2 df

it does not matter which Gaussian function we are considering, the area we want to calculate will be the same. The
value we are looking for will be given by the following
integral:

where N (f ) is the spectral density of the noise within

(
)

2
x2
1
1
Ag(0)
the band and Hr (f) is the continuous Fourier transform P + =

e 2N dx = erfc
Ag(0)
2
of the impulse response of the lter hr (f).
2N
2(L 1)N
L1

350
where erfc(x) is the complementary error function.
Putting all these results together, the probability to make
an error is:
from this formula we can easily understand that the probability to make an error decreases if the maximum amplitude of the transmitted signal or the amplication of the
system becomes greater; on the other hand, it increases
if the number of levels or the power of noise becomes
greater.
This relationship is valid when there is no intersymbol interference, i.e. g(t) is a Nyquist function.

74.2 See also

Frequency-shift keying (FSK)

74.3 External links

Calculating the Sensitivity of an Amplitude Shift
Keying (ASK) Receiver

CHAPTER 74. AMPLITUDE-SHIFT KEYING

Chapter 75

Binary number
In mathematics and digital electronics, a binary number
is a number expressed in the binary numeral system or
base-2 numeral system which represents numeric values using two dierent symbols: typically 0 (zero) and 1
(one). The base-2 system is a positional notation with a
radix of 2. Because of its straightforward implementation
in digital electronic circuitry using logic gates, the binary
system is used internally by almost all modern computers
and computer-based devices. Each digit is referred to as
a bit.

75.1 History
The modern binary number system was devised by
Gottfried Leibniz in 1679 and appears in his article Explication de l'Arithmtique Binaire (published in 1703).
Systems related to binary numbers have appeared earlier
in multiple cultures including ancient Egypt, China, and
India. Leibniz was specically inspired by the Chinese I
Ching.

75.1.1

form the eye of Horus, although this has been disputed).

Horus-Eye fractions are a binary numbering system for
fractional quantities of grain, liquids, or other measures,
in which a fraction of a hekat is expressed as a sum of the
binary fractions 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64. Early
forms of this system can be found in documents from the
Fifth Dynasty of Egypt, approximately 2400 BC, and its
fully developed hieroglyphic form dates to the Nineteenth
Dynasty of Egypt, approximately 1200 BC.[1]
The method used for ancient Egyptian multiplication is
also closely related to binary numbers. In this method,
multiplying one number by a second is performed by a
sequence of steps in which a value (initially the rst of
the two numbers) is either doubled or has the rst number
added back into it; the order in which these steps are to
be performed is given by the binary representation of the
second number. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, which dates
to around 1650 BC.[2]

75.1.2 China

Egypt

See also: Ancient Egyptian mathematics

The scribes of ancient Egypt used two dierent sys-

Arithmetic values represented by parts of the Eye of Horus

tems for their fractions, Egyptian fractions (not related to

the binary number system) and Horus-Eye fractions (so Daoist Bagua
called because many historians of mathematics believe
that the symbols used for this system could be arranged to The I Ching dates from the 9th century BC in China.[3]
351

352

CHAPTER 75. BINARY NUMBER

The binary notation in the I Ching is used to interpret its 75.1.6

quaternary divination technique.[4]

Leibniz and the I Ching

It is based on taoistic duality of yin and yang.[5] eight trigrams (Bagua) and a set of 64 hexagrams (sixty-four
gua), analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of
ancient China.[3]
The contemporary scholar Shao Yong rearranged the
hexagrams in a format that resembles modern binary
numbers, although he did not intend his arrangement to
be used mathematically.[4] Viewing the least signicant
bit on top of single hexagrams in Shao Yongs square and
reading along rows either from bottom right to top left
with solid lines as 0 and broken lines as 1 or from top left
to bottom right with solid lines as 1 and broken lines as 0
hexagrams can be interpreted as sequence from 0 to 63.
[6]

75.1.3

India

The Indian scholar Pingala (c. 2nd century BC) developed a binary system for describing prosody.[7][8] He used
binary numbers in the form of short and long syllables
(the latter equal in length to two short syllables), making it
similar to Morse code.[9][10] Pingalas Hindu classic titled
Chandastra (8.23) describes the formation of a matrix
in order to give a unique value to each meter. The binary
representations in Pingalas system increases towards the
right, and not to the left like in the binary numbers of the
modern, Western positional notation.[11][12]

75.1.4

Other cultures

Gottfried Leibniz

The full title of Leibnizs article is translated into English

as the Explanation of Binary Arithmetic, which uses only
the characters 1 and 0, with some remarks on its usefulness, and on the light it throws on the ancient Chinese gures of Fu Xi".[15] (1703). Leibnizs system uses 0 and 1,
like the modern binary numeral system. An example of
Leibnizs binary numeral system is as follows:[15]

The residents of the island of Mangareva in French Poly0 0 0 1 numerical value 20

nesia were using a hybrid binary-decimal system before
1450.[13] Slit drums with binary tones are used to encode
0 0 1 0 numerical value 21
messages across Africa and Asia.[5] Sets of binary combi0 1 0 0 numerical value 22
nations similar to the I Ching have also been used in traditional African divination systems such as If as well as in
1 0 0 0 numerical value 23
medieval Western geomancy. The base-2 system utilized
in geomancy had long been widely applied in sub-Saharan
Leibniz interpreted the hexagrams of the I Ching as evAfrica.
idence of binary calculus.[16] As a Sinophile, Leibniz
was aware of the I Ching, noted with fascination how its
hexagrams correspond to the binary numbers from 0 to
75.1.5 Western predecessors to Leibniz
111111, and concluded that this mapping was evidence of
In 1605 Francis Bacon discussed a system whereby let- major Chinese accomplishments in the sort of philosophters of the alphabet could be reduced to sequences of ical mathematics he admired.[17] Leibniz was rst introbinary digits, which could then be encoded as scarcely duced to the I Ching through his contact with the French
visible variations in the font in any random text.[14] Im- Jesuit Joachim Bouvet, who visited China in 1685 as a
portantly for the general theory of binary encoding, he missionary. Leibniz saw the I Ching hexagrams as an afadded that this method could be used with any objects rmation of the universality of his own religious beliefs as
at all: provided those objects be capable of a twofold a Christian.[16] Binary numerals were central to Leibnizs
dierence only; as by Bells, by Trumpets, by Lights and theology. He believed that binary numbers were symTorches, by the report of Muskets, and any instruments bolic of the Christian idea of creatio ex nihilo or creation
out of nothing.[18]
of like nature.[14] (See Bacons cipher.)

75.2. REPRESENTATION
[A concept that] is not easy to impart to
the pagans, is the creation ex nihilo through
Gods almighty power. Now one can say that
nothing in the world can better present and
demonstrate this power than the origin of
numbers, as it is presented here through the
simple and unadorned presentation of One and
Zero or Nothing.
Leibnizs letter to the Duke of Brunswick
attached with the I Ching hexagrams[16]

75.1.7

Later developments

353
at the helm. Their Complex Number Computer, completed 8 January 1940, was able to calculate complex
numbers. In a demonstration to the American Mathematical Society conference at Dartmouth College on 11
September 1940, Stibitz was able to send the Complex
Number Calculator remote commands over telephone
lines by a teletype. It was the rst computing machine
ever used remotely over a phone line. Some participants
of the conference who witnessed the demonstration were
John von Neumann, John Mauchly and Norbert Wiener,
who wrote about it in his memoirs.[22][23][24]
The Z1 computer, which was designed and built by
Konrad Zuse between 1935 and 1938, used Boolean logic
and binary oating point numbers.[25]

75.2 Representation
Any number can be represented by any sequence of bits
(binary digits), which in turn may be represented by any
mechanism capable of being in two mutually exclusive
states. Any of the following rows of symbols can be interpreted as the binary numeric value of 667.

HH : MM : SS
8
4
2
1
1+0
=

0+0+0+0 1+2+0 1+2+4+0 0+0+4 1+0+0+8

=
=
=
=
=

1 0 3 7 4 9
George Boole

10 : 37 : 49

In 1854, British mathematician George Boole published

a landmark paper detailing an algebraic system of logic
that would become known as Boolean algebra. His logi- A binary clock might use LEDs to express binary values. In this
clock, each column of LEDs shows a binary-coded decimal nucal calculus was to become instrumental in the design of
meral of the traditional sexagesimal time.
digital electronic circuitry.[19]
In 1937, Claude Shannon produced his masters thesis at
MIT that implemented Boolean algebra and binary arithmetic using electronic relays and switches for the rst
time in history. Entitled A Symbolic Analysis of Relay and Switching Circuits, Shannons thesis essentially
founded practical digital circuit design.[20]

The numeric value represented in each case is dependent

upon the value assigned to each symbol. In a computer,
the numeric values may be represented by two dierent
voltages; on a magnetic disk, magnetic polarities may be
used. A positive, "yes", or on state is not necessarily
equivalent to the numerical value of one; it depends on
In November 1937, George Stibitz, then working at Bell the architecture in use.
Labs, completed a relay-based computer he dubbed the In keeping with customary representation of numerals usModel K (for "Kitchen, where he had assembled it), ing Arabic numerals, binary numbers are commonly writwhich calculated using binary addition.[21] Bell Labs au- ten using the symbols 0 and 1. When written, binary nuthorized a full research program in late 1938 with Stibitz merals are often subscripted, prexed or suxed in order

354
to indicate their base, or radix. The following notations
are equivalent:

CHAPTER 75. BINARY NUMBER

000, 001, 002, ... 007, 008, 009, (rightmost
digit is reset to zero, and the digit to its left is
incremented)

100101 binary (explicit statement of format)

010, 011, 012, ...

100101b (a sux indicating binary format; also

known as Intel convention[26][27] )

...

100101B (a sux indicating binary format)

bin 100101 (a prex indicating binary format)

090, 091, 092, ... 097, 098, 099, (rightmost

two digits are reset to zeroes, and next digit is
incremented)
100, 101, 102, ...

1001012 (a subscript indicating base-2 (binary) no75.3.2

tation)

Binary counting

%100101 (a prex indicating binary format; also

known as Motorola convention[26][27] )
0b100101 (a prex indicating binary format, common in programming languages)
6b100101 (a prex indicating number of bits in binary format, common in programming languages)
When spoken, binary numerals are usually read digit-bydigit, in order to distinguish them from decimal numerals.
For example, the binary numeral 100 is pronounced one
zero zero, rather than one hundred, to make its binary nature explicit, and for purposes of correctness. Since the
binary numeral 100 represents the value four, it would be
confusing to refer to the numeral as one hundred (a word
that represents a completely dierent value, or amount).
Alternatively, the binary numeral 100 can be read out as
four (the correct value), but this does not make its binary nature explicit.

75.3 Counting in binary

This counter shows how to count in binary from numbers zero

through thirty-one.

Binary counting follows the same procedure, except that

only the two symbols 0 and 1 are available. Thus, after a
digit reaches 1 in binary, an increment resets it to 0 but
also causes an increment of the next digit to the left:
0000,
0001, (rightmost digit starts over, and next digit
is incremented)
0010, 0011, (rightmost two digits start over,
and next digit is incremented)
0100, 0101, 0110, 0111, (rightmost three digits start over, and the next digit is incremented)

Counting in binary is similar to counting in any other

1000, 1001, 1010, 1011, 1100, 1101, 1110,
number system. Beginning with a single digit, count1111 ...
ing proceeds through each symbol, in increasing order.
Before examining binary counting, it is useful to briey
discuss the more familiar decimal counting system as a In the binary system, each digit represents an increasing
power of 2, with the rightmost digit representing 20 , the
frame of reference.
next representing 21 , then 22 , and so on. The equivalent
decimal representation of a binary number is sum of the
powers of 2 which each digit represents. For example,
75.3.1 Decimal counting
the binary number 100101 is converted to decimal form
Decimal counting uses the ten symbols 0 through 9. as follows:
Counting begins with the incremental substitution of the
1001012 = [ ( 1 ) 25 ] + [ ( 0 ) 24 ] + [ ( 0
least signicant digit (rightmost digit) which is often
) 2 3 ] + [ ( 1 ) 22 ] + [ ( 0 ) 21 ] + [ ( 1 )
called the rst digit. When the available symbols for this
20 ]
position are exhausted, the least signicant digit is reset
to 0, and the next digit of higher signicance (one po1001012 = [ 1 32 ] + [ 0 16 ] + [ 0 8 ] +
sition to the left) is incremented (overow), and incre[14]+[02]+[11]
mental substitution of the low-order digit resumes. This
method of reset and overow is repeated for each digit of
1001012 = 3710
signicance. Counting progresses as follows:

75.5. BINARY ARITHMETIC

355

75.4 Fractions

7 + 9 6, carry 1 (since 7 + 9 = 16 = 6 + (1
101 ) )

Fractions in binary only terminate if the denominator has

2 as the only prime factor. As a result, 1/10 does not have
a nite binary representation, and this causes 10 0.1 not
to be precisely equal to 1 in oating point arithmetic. As
an example, to interpret the binary expression for 1/3 =
.010101..., this means: 1/3 = 0 21 + 1 22 + 0
23 + 1 24 + ... = 0.3125 + ... An exact value cannot
be found with a sum of a nite number of inverse powers
of two, the zeros and ones in the binary representation of
1/3 alternate forever.

This is known as carrying. When the result of an addition

exceeds the value of a digit, the procedure is to carry
the excess amount divided by the radix (that is, 10/10)
to the left, adding it to the next positional value. This is
correct since the next position has a weight that is higher
by a factor equal to the radix. Carrying works the same
way in binary:
1 1 1 1 1 (carried digits) 0 1 1 0 1 + 1 0 1 1 1 ------------= 1 0 0 1 0 0 = 36

In this example, two numerals are being added together:

011012 (1310 ) and 101112 (2310 ). The top row shows
75.5 Binary arithmetic
the carry bits used. Starting in the rightmost column, 1 +
1 = 102 . The 1 is carried to the left, and the 0 is written at
Arithmetic in binary is much like arithmetic in other nu- the bottom of the rightmost column. The second column
meral systems. Addition, subtraction, multiplication, and from the right is added: 1 + 0 + 1 = 10 again; the 1 is
2
division can be performed on binary numerals.
carried, and 0 is written at the bottom. The third column:
1 + 1 + 1 = 112 . This time, a 1 is carried, and a 1 is
written in the bottom row. Proceeding like this gives the
75.5.1 Addition
nal answer 1001002 (36 decimal).
Main article: binary adder
When computers must add two numbers, the rule that: x
The simplest arithmetic operation in binary is addition. xor y = (x + y) mod 2 for any two bits x and y allows for
very fast calculation, as well.

A
B

Long carry method

A simplication for many binary addition problems is

the Long Carry Method or Brookhouse Method of Binary Addition. This method is generally useful in any binary addition where one of the numbers contains a long
string of ones. It is based on the simple premise that
under the binary system, when given a string of digits composed entirely of n ones (where: n is any integer
The circuit diagram for a binary half adder, which adds two bits length), adding 1 will result in the number 1 followed by
together, producing sum and carry bits.
a string of n zeros. That concept follows, logically, just
as in the decimal system, where adding 1 to a string of n
Adding two single-digit binary numbers is relatively sim- 9s will result in the number 1 followed by a string of n 0s:
ple, using a form of carrying:
Binary Decimal 1 1 1 1 1 likewise 9 9 9 9 9 + 1 + 1
1
0+00
00000100000
0+11
Such long strings are quite common in the binary sys1+01
tem. From that one nds that large binary numbers can
be added using two simple steps, without excessive carry
1 + 1 0, carry 1 (since 1 + 1 = 2 = 0 + (1
operations. In the following example, two numerals are
21 ) )
being added together: 1 1 1 0 1 1 1 1 1 02 (95810 ) and
Adding two 1 digits produces a digit 0, while 1 will 1 0 1 0 1 1 0 0 1 12 (69110 ), using the traditional carry
have to be added to the next column. This is similar to method on the left, and the long carry method on the right:
what happens in decimal when certain single-digit num- Traditional Carry Method Long Carry Method vs. 1 1 1 1
bers are added together; if the result equals or exceeds the 1 1 1 1 (carried digits) 1 1 carry the 1 until it is one
value of the radix (10), the digit to the left is incremented: digit past the string below 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1
1 1 1 0 cross out the string, + 1 0 1 0 1 1 0 0 1 1 + 1 0 1
5 + 5 0, carry 1 (since 5 + 5 = 10 = 0 + (1
0 1 1 0 0 1 1 and cross out the digit that was added to it
101 ) )

356

CHAPTER 75. BINARY NUMBER

=1100111000111001110001

A B = A + not B + 1

The top row shows the carry bits used. Instead of the
standard carry from one column to the next, the lowestordered 1 with a 1 in the corresponding place value
beneath it may be added and a 1 may be carried to one
digit past the end of the series. The used numbers must
be crossed o, since they are already added. Other long
strings may likewise be cancelled using the same technique. Then, simply add together any remaining digits
normally. Proceeding in this manner gives the nal answer of 1 1 0 0 1 1 1 0 0 0 12 (164910 ). In our simple example using small numbers, the traditional carry method
required eight carry operations, yet the long carry method
required only two, representing a substantial reduction of
eort.

75.5.3 Multiplication

Addition table

Multiplication in binary is similar to its decimal counterpart. Two numbers A and B can be multiplied by partial
products: for each digit in B, the product of that digit in
A is calculated and written on a new line, shifted leftward
so that its rightmost digit lines up with the digit in B that
was used. The sum of all these partial products gives the
nal result.
Since there are only two digits in binary, there are only
two possible outcomes of each partial multiplication:
If the digit in B is 0, the partial product is also 0
If the digit in B is 1, the partial product is equal to
A

The binary addition table is similar, but not the same, as

the truth table of the logical disjunction operation . The For example, the binary numbers 1011 and 1010 are multiplied as follows:
dierence is that 1 1 = 1 , while 1 + 1 = 10 .
1 0 1 1 (A) 1 0 1 0 (B) --------- 0 0 0 0 Corresponds
to the rightmost 'zero' in B + 1 0 1 1 Corresponds to
75.5.2 Subtraction
the next 'one' in B + 0 0 0 0 + 1 0 1 1 --------------- = 1 1
01110
Further information: signed number representations and
Binary numbers can also be multiplied with bits after a
twos complement
binary point:
Subtraction works in much the same way:
000
0 1 1, borrow 1
101
110
Subtracting a 1 digit from a 0 digit produces the digit
1, while 1 will have to be subtracted from the next column. This is known as borrowing. The principle is the
same as for carrying. When the result of a subtraction is
less than 0, the least possible value of a digit, the procedure is to borrow the decit divided by the radix (that
is, 10/10) from the left, subtracting it from the next positional value.
* * * * (starred columns are borrowed from) 1 1 0 1 1
1 0 1 0 1 1 1 ---------------- = 1 0 1 0 1 1 1 * (starred
columns are borrowed from) 1 0 1 1 1 1 1 - 1 0 1 0 1 1
---------------- = 0 1 1 0 1 0 0
Subtracting a positive number is equivalent to adding
a negative number of equal absolute value. Computers use signed number representations to handle negative
numbersmost commonly the twos complement notation. Such representations eliminate the need for a separate subtract operation. Using twos complement notation subtraction can be summarized by the following formula:

1 0 1 . 1 0 1 A (5.625 in decimal) 1 1 0 . 0 1 B (6.25

in decimal) ------------------- 1 . 0 1 1 0 1 Corresponds
to a 'one' in B + 0 0 . 0 0 0 0 Corresponds to a 'zero'
in B + 0 0 0 . 0 0 0 + 1 0 1 1 . 0 1 + 1 0 1 1 0 . 1 -------------------------- = 1 0 0 0 1 1 . 0 0 1 0 1 (35.15625 in
decimal)
See also Booths multiplication algorithm.
Multiplication table
The binary multiplication table is the same as the truth
table of the logical conjunction operation .

75.5.4 Division
See also: Division algorithm

Long division in binary is again similar to its decimal

counterpart.
In the example below, the divisor is 1012 , or 5 decimal,
while the dividend is 110112 , or 27 decimal. The procedure is the same as that of decimal long division; here,
the divisor 1012 goes into the rst three digits 1102 of the
dividend one time, so a 1 is written on the top line. This
result is multiplied by the divisor, and subtracted from the

75.7. CONVERSION TO AND FROM OTHER NUMERAL SYSTEMS

357

rst three digits of the dividend; the next digit (a 1) is of one) forms the binary value, as each remainder must
included to obtain a new three-digit sequence:
be either zero or one when dividing by two. For example,
(357)10 is expressed as (101100101).[28]
1 ___________ 1 0 1 ) 1 1 0 1 1 1 0 1 ----- 0 0 1
The procedure is then repeated with the new sequence, Conversion from base-2 to base-10 simply inverts the preceding algorithm. The bits of the binary number are used
continuing until the digits in the dividend have been exone by one, starting with the most signicant (leftmost)
hausted:
bit. Beginning with the value 0, the prior value is dou1 0 1 ___________ 1 0 1 ) 1 1 0 1 1 1 0 1 ----- 1 1 1 bled, and the next bit is then added to produce the next
1 0 1 ----- 1 0
value. This can be organized in a multi-column table. For
Thus, the quotient of 110112 divided by 1012 is 1012 , as example, to convert 100101011012 to decimal:
shown on the top line, while the remainder, shown on the
bottom line, is 102 . In decimal, 27 divided by 5 is 5, with
a remainder of 2.

75.5.5

Square root

The result is 119710 . Note that the rst Prior Value of

0 is simply an initial decimal value. This method is an
The process of taking a binary square root digit by digit application of the Horner scheme.
is the same as for a decimal square root, and is explained
The fractional parts of a number are converted with simhere. An example is:
ilar methods. They are again based on the equivalence of
1 0 0 1 --------- 1010001 1 --------- 101 01 0 -------- shifting with doubling or halving.
1001 100 0 -------- 10001 10001 10001 ------- 0
In a fractional binary number such as 0.110101101012 ,
the rst digit is 12 , the second ( 12 )2 = 41 , etc. So if there
is a 1 in the rst place after the decimal, then the number
75.6 Bitwise operations
is at least 12 , and vice versa. Double that number is at
least 1. This suggests the algorithm: Repeatedly double
the number to be converted, record if the result is at least
Main article: bitwise operation
1, and then throw away the integer part.
Though not directly related to the numerical interpretation of binary symbols, sequences of bits may be manipulated using Boolean logical operators. When a string of
binary symbols is manipulated in this way, it is called a
bitwise operation; the logical operators AND, OR, and
XOR may be performed on corresponding bits in two binary numerals provided as input. The logical NOT operation may be performed on individual bits in a single
binary numeral provided as input. Sometimes, such operations may be used as arithmetic short-cuts, and may
have other computational benets as well. For example,
an arithmetic shift left of a binary number is the equivalent of multiplication by a (positive, integral) power of
2.

For example, ( 13 ) 10 , in binary, is:

Thus the repeating decimal fraction 0.3... is equivalent to

the repeating binary fraction 0.01... .
Or for example, 0.110 , in binary, is:

This is also a repeating binary fraction 0.00011... . It may

as a surprise that terminating decimal fractions can
75.7 Conversion to and from other come
have repeating expansions in binary. It is for this reason
numeral systems
that many are surprised to discover that 0.1 + ... + 0.1, (10
additions) diers from 1 in oating point arithmetic. In
fact, the only binary fractions with terminating expansions
75.7.1 Decimal
are of the form of an integer divided by a power of 2,
To convert from a base-10 integer to its base-2 (binary) which 1/10 is not.
equivalent, the number is divided by two. The remainder The nal conversion is from binary to decimal fractions.
is the least-signicant bit. The quotient is again divided by The only diculty arises with repeating fractions, but
two; its remainder becomes the next least signicant bit. otherwise the method is to shift the fraction to an integer,
This process repeats until a quotient of one is reached. convert it as above, and then divide by the appropriate
The sequence of remainders (including the nal quotient power of two in the decimal base. For example:

358

CHAPTER 75. BINARY NUMBER

x=

1100.101110 . . .

x2 =

1100101110.01110 . . .

x2=

11001.01110 . . .

x (2 2) =
1100010101
x = 1100010101/111110
6

x=

To convert a hexadecimal number into its decimal equivalent, multiply the decimal equivalent of each hexadecimal digit by the corresponding power of 16 and add the
resulting values:
C0E716 = (12 163 ) + (0 162 ) + (14 161 )
+ (7 160 ) = (12 4096) + (0 256) + (14
16) + (7 1) = 49,38310

(789/62)10

Another way of converting from binary to decimal, of- 75.7.3 Octal

ten quicker for a person familiar with hexadecimal, is to
do so indirectlyrst converting ( x in binary) into ( x Main article: Octal
in hexadecimal) and then converting ( x in hexadecimal)
into ( x in decimal).
Binary is also easily converted to the octal numeral sysFor very large numbers, these simple methods are inef- tem, since octal uses a radix of 8, which is a power of two
cient because they perform a large number of multi- (namely, 23 , so it takes exactly three binary digits to repplications or divisions where one operand is very large. resent an octal digit). The correspondence between octal
A simple divide-and-conquer algorithm is more eective and binary numerals is the same as for the rst eight digits
asymptotically: given a binary number, it is divided by of hexadecimal in the table above. Binary 000 is equiva10k , where k is chosen so that the quotient roughly equals lent to the octal digit 0, binary 111 is equivalent to octal
the remainder; then each of these pieces is converted to 7, and so forth.
decimal and the two are concatenated. Given a decimal
number, it can be split into two pieces of about the same
size, each of which is converted to binary, whereupon the
rst converted piece is multiplied by 10k and added to the
second converted piece, where k is the number of decimal Converting from octal to binary proceeds in the same
digits in the second, least-signicant piece before conver- fashion as it does for hexadecimal:
sion.
658 = 110 1012

75.7.2

Hexadecimal

Main article: Hexadecimal

178 = 001 1112

And from binary to octal:

1011002 = 101 1002 grouped = 548

Binary may be converted to and from hexadecimal somewhat more easily. This is because the radix of the hex100112 = 010 0112 grouped with padding =
adecimal system (16) is a power of the radix of the binary
238
system (2). More specically, 16 = 24 , so it takes four
digits of binary to represent one digit of hexadecimal, as
And from octal to decimal:
shown in the adjacent table.
To convert a hexadecimal number into its binary equivalent, simply substitute the corresponding binary digits:
3A16 = 0011 10102
E716 = 1110 01112

658 = (6 81 ) + (5 80 ) = (6 8) + (5 1) =
5310
1278 = (1 82 ) + (2 81 ) + (7 80 ) = (1
64) + (2 8) + (7 1) = 8710

To convert a binary number into its hexadecimal equiva- 75.8 Representing real numbers
lent, divide it into groups of four bits. If the number of
bits isn't a multiple of four, simply insert extra 0 bits at
Non-integers can be represented by using negative powthe left (called padding). For example:
ers, which are set o from the other digits by means of a
radix point (called a decimal point in the decimal system).
10100102 = 0101 0010 grouped with padding
For example, the binary number 11.012 thus means:
= 5216
110111012 = 1101 1101 grouped = DD16

75.10. NOTES

359

75.10 Notes

For a total of 3.25 decimal.

p
2a

All dyadic rational numbers

have a terminating binary
numeralthe binary representation has a nite number
of terms after the radix point. Other rational numbers
have binary representation, but instead of terminating,
they recur, with a nite sequence of digits repeating indenitely. For instance
110
310

12
112

= 0.01010101012

1210
1710

11002
= 10001
= 0.10110100 10110100
2
10110100...2

The phenomenon that the binary representation of any

rational is either terminating or recurring also occurs in
other radix-based numeral systems. See, for instance, the
explanation in decimal. Another similarity is the existence of alternative representations for any terminating
representation, relying on the fact that 0.111111 is the
sum of the geometric series 21 + 22 + 23 + ... which is
1.
Binary numerals which neither terminate nor recur represent irrational numbers. For instance,
0.10100100010000100000100 does have a pattern, but it is not a xed-length recurring pattern, so
the number is irrational

[1] Chrisomalis, Stephen (2010), Numerical Notation: A

Comparative History, Cambridge University Press, pp.
4243, ISBN 9780521878180.
[2] Rudman, Peter Strom (2007), How Mathematics Happened: The First 50,000 Years, Prometheus Books, pp.
135136, ISBN 9781615921768.
[3] Edward Hacker; Steve Moore; Lorraine Patsco (2002). I
Ching: An Annotated Bibliography. Routledge. p. 13.
ISBN 978-0-415-93969-0.
[4] Redmond & Hon (2014), p. 227.
[5] Jonathan Shectman (2003). Groundbreaking Scientic Experiments, Inventions, and Discoveries of the 18th Century.
Greenwood Publishing. p. 29. ISBN 978-0-313-320156.
[6] Zhonglian, Shi; Wenzhao, Li; Poser, Hans (2000).
Leibniz Binary System and Shao Yongs Xiantian Tu
in :Das Neueste ber China: G.W. Leibnizens Novissima
Sinica von 1697 : Internationales Symposium, Berlin 4.
bis 7. Oktober 1997. Stuttgart: Franz Steiner Verlag. pp.
165170. ISBN 3515074481.
[7] Sanchez, Julio; Canton, Maria P. (2007). Microcontroller
programming: the microchip PIC. Boca Raton, Florida:
CRC Press. p. 37. ISBN 0-8493-7189-9.
[8] W. S. Anglin and J. Lambek, The Heritage of Thales,

Springer, 1995, ISBN 0-387-94544-X

1.0110101000001001111001100110011111110

is the binary representation of 2 , the square root

of 2, another irrational. It has no discernible [9] Binary Numbers in Ancient India
pattern. See irrational number.
[10] Math for Poets and Drummers (pdf, 145KB)
[11] Binary Numbers in Ancient India.

75.9 See also

Binary code
Binary-coded decimal
Finger binary
Gray code
Linear feedback shift register
Oset binary
Quibinary
Reduction of summands
Redundant binary representation
Repeating decimal
SZTAKI Desktop Grid searches for generalized binary number systems up to dimension 11.
Twos complement

[12] Stakhov, Alexey; Olsen, Scott Anthony (2009). The mathematics of harmony: from Euclid to contemporary mathematics and computer science. ISBN 978-981-277-582-5.
[13] Bender, Andrea; Beller, Sieghard (16 December 2013).
Mangarevan invention of binary steps for easier calculation. Proceedings of the National Academy of Sciences.
doi:10.1073/pnas.1309160110.
[14] Bacon, Francis (1605). The Advancement of Learning.
London. pp. Chapter 1.
[15] Leibniz G., Explication de l'Arithmtique Binaire, Die
Mathematische Schriften, ed. C. Gerhardt, Berlin 1879,
vol.7, p.223; Engl. transl.
[16] J.E.H. Smith (2008). Leibniz: What Kind of Rationalist?:
What Kind of Rationalist?. Springer. p. 415. ISBN 9781-4020-8668-7.
[17] Aiton, Eric J. (1985). Leibniz: A Biography. Taylor &
Francis. pp. 2458. ISBN 0-85274-470-6.
[18] Yuen-Ting Lai (1998). Leibniz, Mysticism and Religion.
Springer. pp. 149150. ISBN 978-0-7923-5223-5.

360

CHAPTER 75. BINARY NUMBER

[19] Boole, George (2009) [1854]. An Investigation of the

Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities (Macmillan, Dover
Publications, reprinted with corrections [1958] ed.). New
York: Cambridge University Press. ISBN 978-1-10800153-3.

How to Convert from Decimal to Binary at wikiHow

[20] Shannon, Claude Elwood (1940). A symbolic analysis of

relay and switching circuits. Cambridge: Massachusetts
Institute of Technology.

Quick reference on Howto read binary

[21] National Inventors Hall of Fame George R. Stibitz. 20

August 2008. Retrieved 5 July 2010.
[22] George Stibitz : Bio. Math & Computer Science Department, Denison University. 30 April 2004. Retrieved
5 July 2010.
[23] Pioneers The people and ideas that made a dierence
George Stibitz (19041995)". Kerry Redshaw. 20 February 2006. Retrieved 5 July 2010.
[24] George Robert Stibitz Obituary. Computer History
Association of California. 6 February 1995. Retrieved 5
July 2010.
[25] Konrad Zuses Legacy: The Architecture of the Z1 and
Z3 (PDF). IEEE Annals of the History of Computing. 19
(2): 515. 1997. doi:10.1109/85.586067.
[26] Kveler, Gerd; Schwoch, Dietrich (2013) [1996].
Arbeitsbuch Informatik - eine praxisorientierte Einfhrung in die Datenverarbeitung mit Projektaufgabe (in
German). Vieweg-Verlag, reprint: Springer-Verlag.
doi:10.1007/978-3-322-92907-5.
ISBN 978-3-52804952-2. 9783322929075. Retrieved 2015-08-05.
[27] Kveler, Gerd; Schwoch, Dietrich (2007-10-04).
Informatik fr Ingenieure und Naturwissenschaftler: PCund Mikrocomputertechnik, Rechnernetze (in German).
2 (5 ed.). Vieweg, reprint: Springer-Verlag. ISBN
3834891916. 9783834891914. Retrieved 2015-08-05.
[28] Base System. Retrieved 31 August 2016.

75.11 References
Sanchez, Julio; Canton, Maria P. (2007). Microcontroller programming: the microchip PIC. Boca Raton,
FL: CRC Press. p. 37. ISBN 0-8493-7189-9.
Redmond, Georey; Hon, Tze-Ki (2014). Teaching
the I Ching. Oxford University Press. ISBN 0-19976681-9.

75.12 External links

Binary System at cut-the-knot
Conversion of Fractions at cut-the-knot
Binary Digits at Math Is Fun

Learning exercise for children at CircuitDesign.info

Binary Counter with Kids
Magic Card Trick

Binary converter to HEX/DEC/OCT with direct access to bits

Sir Francis Bacons BiLiteral Cypher system, predates binary number system.
Leibniz' binary numeral system, 'De progressione
dyadica', 1679, online and analyzed on BibNum
[click ' tlcharger' for English analysis]

75.12. EXTERNAL LINKS

361

Chapter 76

Bit
This article is about the unit of information. For other the medium (card or tape) conceptually carried an array
uses, see Bit (disambiguation).
of hole positions; each position could be either punched
through or not, thus carrying one bit of information. The
The bit is a basic unit of information in computing and encoding of text by bits was also used in Morse code
digital communications.[1] A bit can have only one of (1844) and early time of digital communications matwo values, and may therefore be physically implemented chines such as teletypes and stock ticker machines (1870).
with a two-state device. These values are most commonly represented as either a 0or1. The term bit is a
portmanteau of binary digit.[2] In information theory,
the bit is equivalent to the unit shannon,[3] named after
Claude Shannon.
The two values can also be interpreted as logical values (true/false, yes/no), algebraic signs (+/), activation
states (on/o), or any other two-valued attribute. The
correspondence between these values and the physical
states of the underlying storage or device is a matter of
convention, and dierent assignments may be used even
within the same device or program. The length of a binary number may be referred to as its bit-length.

Ralph Hartley suggested the use of a logarithmic measure

of information in 1928.[6] Claude E. Shannon rst used
the word bit in his seminal 1948 paper A Mathematical
Theory of Communication.[7] He attributed its origin to
John W. Tukey, who had written a Bell Labs memo on
9 January 1947 in which he contracted binary information digit to simply bit. Interestingly, Vannevar Bush
had written in 1936 of bits of information that could be
stored on the punched cards used in the mechanical computers of that time.[8] The rst programmable computer
built by Konrad Zuse used binary notation for numbers.

In information theory, one bit is typically dened as the 76.2 Physical representation
uncertainty of a binary random variable that is 0 or 1
with equal probability,[4] or the information that is gained
A bit can be stored by a digital device or other physiwhen the value of such a variable becomes known.[5]
cal system that exists in either of two possible distinct
In quantum computing, a quantum bit or qubit is a states. These may be the two stable states of a ip-op,
quantum system that can exist in superposition of two two positions of an electrical switch, two distinct voltage
classical (i.e., non-quantum) bit values.
or current levels allowed by a circuit, two distinct levThe symbol for bit, as a unit of information, is either sim- els of light intensity, two directions of magnetization or
ply bit (recommended by the IEC 80000-13:2008 stan- polarization, the orientation of reversible double stranded
dard) or lowercase b (recommended by the IEEE 1541- DNA, etc.
2002 standard). A group of eight bits is commonly called Bits can be implemented in several forms. In most modone byte, but historically the size of the byte is not strictly ern computing devices, a bit is usually represented by an
dened.
electrical voltage or current pulse, or by the electrical state
of a ip-op circuit.

76.1 History
The encoding of data by discrete bits was used in the
punched cards invented by Basile Bouchon and JeanBaptiste Falcon (1732), developed by Joseph Marie
Jacquard (1804), and later adopted by Semen Korsakov,
Charles Babbage, Hermann Hollerith, and early computer manufacturers like IBM. Another variant of that
idea was the perforated paper tape. In all those systems,

For devices using positive logic, a digit value of 1 (or

a logical value of true) is represented by a more positive voltage relative to the representation of 0. The specic voltages are dierent for dierent logic families and
variations are permitted to allow for component aging
and noise immunity. For example, in transistortransistor
logic (TTL) and compatible circuits, digit values 0 and 1
at the output of a device are represented by no higher than
0.4 volts and no lower than 2.6 volts, respectively; while
TTL inputs are specied to recognize 0.8 volts or below

362

76.4. INFORMATION CAPACITY AND INFORMATION COMPRESSION

as 0 and 2.2 volts or above as 1.

76.2.1

Transmission and processing

363

ever, the lower-case letter b is widely used as well and

was recommended by the IEEE 1541 Standard (2002).
In contrast, the upper case letter B is the standard and
customary symbol for byte.

Bits are transmitted one at a time in serial transmission,

and by a multiple number of bits in parallel transmission. 76.3.1 Multiple bits
A bitwise operation optionally process bits one at a time.
Data transfer rates are usually measured in decimal SI Multiple bits may be expressed and represented in several
multiples of the unit bit per second (bit/s), such as kbit/s. ways. For convenience of representing commonly reoccurring groups of bits in information technology, several
units of information have traditionally been used. The
most common is the unit byte, coined by Werner Buch76.2.2 Storage
holz in July 1956, which historically was used to repreIn the earliest non-electronic information processing de- sent the group of bits used to encode a single character
vices, such as Jacquards loom or Babbages Analytical of text (until UTF-8 multibyte encoding took over) in a
[10][11]
and for this reason it was used as the baEngine, a bit was often stored as the position of a me- computer
sic
addressable
element
in many computer architectures.
chanical lever or gear, or the presence or absence of a
The
trend
in
hardware
design
converged on the most comhole at a specic point of a paper card or tape. The
mon
implementation
of
using
eight bits per byte, as it is
rst electrical devices for discrete logic (such as elevator
widely
used
today.
However,
because
of the ambiguity of
and trac light control circuits, telephone switches, and
relying
on
the
underlying
hardware
design,
the unit octet
Konrad Zuses computer) represented bits as the states of
was
dened
to
explicitly
denote
a
sequence
of eight bits.
electrical relays which could be either open or closed.
When relays were replaced by vacuum tubes, starting in Computers usually manipulate bits in groups of a xed
the 1940s, computer builders experimented with a vari- size, conventionally named "words". Like the byte, the
ety of storage methods, such as pressure pulses traveling number of bits in a word also varies with the hardware
down a mercury delay line, charges stored on the inside design, and is typically between 8 and 80 bits, or even
surface of a cathode-ray tube, or opaque spots printed on more in some specialized computers. In the 21st century,
glass discs by photolithographic techniques.
retail personal or server computers have a word size of 32
In the 1950s and 1960s, these methods were largely sup- or 64 bits.
planted by magnetic storage devices such as magnetic The International System of Units denes a series of decicore memory, magnetic tapes, drums, and disks, where a mal prexes for multiples of standardized units which are
bit was represented by the polarity of magnetization of a commonly also used with the bit and the byte. The precertain area of a ferromagnetic lm, or by a change in po- xes kilo (103 ) through yotta (1024 ) increment by multilarity from one direction to the other. The same principle ples of 1000, and the corresponding units are the kilobit
was later used in the magnetic bubble memory developed (kbit) through the yottabit (Ybit).
in the 1980s, and is still found in various magnetic strip
items such as metro tickets and some credit cards.
In modern semiconductor memory, such as dynamic
random-access memory, the two values of a bit may be
represented by two levels of electric charge stored in a
capacitor. In certain types of programmable logic arrays
and read-only memory, a bit may be represented by the
presence or absence of a conducting path at a certain point
of a circuit. In optical discs, a bit is encoded as the presence or absence of a microscopic pit on a reective surface. In one-dimensional bar codes, bits are encoded as
the thickness of alternating black and white lines.

76.3 Unit and symbol

The bit is not dened in the International System of Units
(SI). However, the International Electrotechnical Commission issued standard IEC 60027, which species that
the symbol for binary digit should be bit, and this should
be used in all multiples, such as kbit, for kilobit.[9] How-

76.4 Information capacity and information compression

When the information capacity of a storage system or a
communication channel is presented in bits or bits per
second, this often refers to binary digits, which is a
computer hardware capacity to store binary code (0 or
1, up or down, current or not, etc.). Information capacity
of a storage system is only an upper bound to the actual
quantity of information stored therein. If the two possible values of one bit of storage are not equally likely,
that bit of storage will contain less than one bit of information. Indeed, if the value is completely predictable,
then the reading of that value will provide no information at all (zero entropic bits, because no resolution of
uncertainty and therefore no information). If a computer
le that uses n bits of storage contains only m < n bits of
information, then that information can in principle be encoded in about m bits, at least on the average. This princi-

364

CHAPTER 76. BIT

ple is the basis of data compression technology. Using an Some authors also dene a binit as an arbitrary informaanalogy, the hardware binary digits refer to the amount of tion unit equivalent to some xed but unspecied number
storage space available (like the number of buckets avail- of bits.[13]
able to store things), and the information content the lling, which comes in dierent levels of granularity (ne
or coarse, that is, compressed or uncompressed informa- 76.7 See also
tion). When the granularity is ner (when information is
more compressed), the same bucket can hold more.
Integer (computer science)
For example, it is estimated that the combined technolog Primitive data type
ical capacity of the world to store information provides
1,300 exabytes of hardware digits in 2007. However,
Trit (Trinary digit)
when this storage space is lled and the corresponding
content is optimally compressed, this only represents 295
Bitstream
exabytes of information.[12] When optimally compressed,
the resulting carrying capacity approaches Shannon infor Entropy (information theory)
mation or information entropy.
Baud (bits per second)

76.5 Bit-based computing

Certain bitwise computer processor instructions (such as
bit set) operate at the level of manipulating bits rather than
manipulating data interpreted as an aggregate of bits.
In the 1980s, when bitmapped computer displays became
popular, some computers provided specialized bit block
transfer (bitblt or blit) instructions to set or copy the
bits that corresponded to a given rectangular area on the
screen.
In most computers and programming languages, when
a bit within a group of bits, such as a byte or word, is
referred to, it is usually specied by a number from 0
upwards corresponding to its position within the byte or
word. However, 0 can refer to either the most or least
signicant bit depending on the context.

Binary numeral system

Ternary numeral system
Shannon (unit)

76.8 Notes
76.9 References
[1] http://www.merriam-webster.com/dictionary/bit
[2] Mackenzie, Charles E. (1980). Coded Character Sets, History and Development. The Systems Programming Series
(1 ed.). Addison-Wesley Publishing Company, Inc. p.
xii. ISBN 0-201-14460-3. LCCN 77-90165. Retrieved
2016-05-22.
[3] https://www.unc.edu/~{}rowlett/units/dictB.html#bit

76.6 Other information units

[4] John B. Anderson, Rolf Johnnesson (2006) Understanding Information Transmission.

Main article: Units of information

[5] Simon Haykin (2006), Digital Communications

[6] Norman Abramson (1963), Information theory and cod-

Other units of information, sometimes used in informaing. McGraw-Hill.

tion theory, include the natural digit also called a nat or
nit and dened as log2 e ( 1.443) bits, where e is the [7] Shannon, Claude. A Mathematical Theory of Communication. Bell Labs Technical Journal. Archived from the
base of the natural logarithms; and the dit, ban, or hartley,
original (PDF) on 2010-08-15.
[6]
dened as log2 10 ( 3.322) bits. This value, slightly
3
less than 10/3, may be understood because 10 = 1000 [8] Bush, Vannevar (1936). Instrumental analysis. Bulletin
1024 = 210 : three decimal digits are slightly less informaof the American Mathematical Society. 42 (10): 649669.
tion than ten binary digits, so one decimal digit is slightly
doi:10.1090/S0002-9904-1936-06390-1.
less than 10/3 binary digits. Conversely, one bit of information corresponds to about ln 2 ( 0.693) nats, or [9] National Institute of Standards and Technology (2008),
Guide for the Use of the International System of Units.
log10 2 ( 0.301) hartleys. As with the inverse ratio, this
Online version.
value, approximately 3/10, but slightly more, corresponds
10
3
to the fact that 2 = 1024 ~ 1000 = 10 : ten binary digits [10] Bemer, RW; Buchholz, Werner (1962), 4, Natural Data
are slightly more information than three decimal digits, so
Units, in Buchholz, Werner, Planning a Computer System
Project Stretch (PDF), pp. 3940
one binary digit is slightly more than 3/10 decimal digits.

76.10. EXTERNAL LINKS

[11] Bemer, RW (1959), A proposal for a generalized card

code of 256 characters, Communications of the ACM, 2
(9): 1923, doi:10.1145/368424.368435
[12] The Worlds Technological Capacity to Store, Communicate, and Compute Information, especially Supporting
online material, Martin Hilbert and Priscila Lpez (2011),
Science (journal), 332(6025), 60-65; free access to the article through here: martinhilbert.net/WorldInfoCapacity.
html
[13] Amitabha Bhattacharya, Digital Communication

76.10 External links

Bit Calculator - Convert between bit, byte, kilobit,
kilobyte, megabit, megabyte, gigabit, gigabyte
BitXByteConverter - Best tool for le size, storage
capacity, digital information and data conversion

365

Chapter 77

Baud
For other uses, see Baud (disambiguation).

accordance with the rules for SI units. That is, the rst
letter of its symbol is uppercase (Bd), but when the unit
is spelled out, it should be written in lowercase (baud)
In telecommunication and electronics, baud (/bd/, unit
symbol Bd) is the unit for symbol rate or modulation except when it begins a sentence.
rate in symbols per second or pulses per second. It is The baud is scaled using standard metric prexes, so that
the number of distinct symbol changes (signaling events) for example
made to the transmission medium per second in a digitally modulated signal or a line code.
1 kBd (kilobaud) = 1000 Bd
Digital data modem manufacturers commonly dene the
1 MBd (megabaud) = 1000 kBd
baud as the modulation rate of data transmission and express it as bits per second.[1]
1 GBd (gigabaud) = 1000 MBd.
Baud is related to gross bit rate expressed as bits per second.

77.2 Relationship to gross bit rate

77.1 Denitions

The symbol rate is related to gross bit rate expressed in

bit/s. The term baud has sometimes incorrectly been used
[2]
The symbol duration time, also known as unit interval, to mean bit rate, since these rates are the same in old
can be directly measured as the time between transitions modems as well as in the simplest digital communication
by looking into an eye diagram of an oscilloscope. The links using only one bit per symbol, such that binary 0
is represented by one symbol, and binary 1 by another
symbol duration time T can be calculated as:
symbol. In more advanced modems and data transmission
techniques, a symbol may have more than two states, so
it may represent more than one bit. A bit (binary digit)
1
Ts = ,
always represents one of two states.
fs
where f is the symbol rate. There is also a chance of If N bits are conveyed per symbol, and the gross bit rate is
R, inclusive of channel coding overhead, the symbol rate
miscommunication which leads to ambiguity.
f can be calculated as
Example: a baud of 1 kBd = 1,000 Bd is synonymous to a symbol rate of 1,000 symbols per
second. In case of a modem, this corresponds
to 1,000 tones per second, and in case of a line
code, this corresponds to 1,000 pulses per second. The symbol duration time is 1/1,000 second = 1 millisecond.

fs =

R
.
N

By taking information per pulse N in bit/pulse to be the

base-2-logarithm of the number of distinct messages M
that could be sent, Hartley[3] constructed a measure of
the gross bitrate R as

In digital systems (i.e., using discrete/discontinuous values) with binary code, 1 Bd = 1 bit/s. By contrast, nonR = fs N where N = log2 (M ).
digital (or analog) systems use a continuous range of values to represent information and in these systems the ex- In that case M = 2N dierent symbols are used. In a moact informational size of 1 Bd varies.
dem, these may be sinewave tones with unique combinaThe baud unit is named after mile Baudot, the inventor tions of amplitude, phase and/or frequency. For example,
of the Baudot code for telegraphy, and is represented in in a 64QAM modem, M=64, and so the bit rate is N =
366

77.5. EXTERNAL LINKS

log2 (64) = 6 times the baud. In a line code, these may be
M dierent voltage levels.
The ratio is not necessarily even an integer; in 4B3T coding, the bit rate is 4/3 baud. (A typical basic rate interface
with a 160 kbit/s raw data rate operates at 120 kBd.)
Codes with many symbols, and thus a bit rate higher than
the symbol rate, are most useful on channels such as telephone lines with a limited bandwidth but a high signal-tonoise ratio within that bandwidth. In other applications,
the bit rate is less than the symbol rate. Manchester coding and modied frequency modulation have a bit rate
equal to 1/2 the baud. Eight-to-fourteen modulation as
used on audio CDs has bit rate which 8/17 of the baud.

77.3 See also

Bandwidth
Baudot code
Bitrate
Constellation diagram, which shows (on a graph or
2D oscilloscope image) how a given signal state (a
symbol) can represent three or more bits at once
List of device bandwidths
Modem
Modulation
Nyquist rate
PCM
Symbol rate
8-N-1

77.4 References
[1] AT&T, Bell System Data Communications Technical
Reference, Data Set 103F Interface Specication, May
1964
[2] Banks, Michael A. (1990). BITS, BAUD RATE, AND
BPS Taking the Mystery Out of Modem Speeds. Brady
Books/Simon & Schuster. Retrieved 17 September 2014.
[3] D. A. Bell (1962). Information Theory and its Engineering Applications (3rd ed.). New York: Pitman. OCLC
1626214.

367

77.5 External links

Martin, Nicolas (January 2000). On the origins of
serial communications and data encoding. dBulletin, the dBASE Developers Bulletin (7). Retrieved
January 4, 2007.
Frenzel, Lou (April 27, 2012). Whats The Difference Between Bit Rate And baud?". Electronic
Design Magazine.

Chapter 78

Constellation diagram
[1]

A constellation diagram is a representation of a signal modulated by a digital modulation scheme such as

quadrature amplitude modulation or phase-shift keying.
It displays the signal as a two-dimensional X-Y plane
scatter diagram in the complex plane at symbol sampling
instants. In a more abstract sense, it represents the possible symbols that may be selected by a given modulation
scheme as points in the complex plane. Measured constellation diagrams can be used to recognize the type of
interference and distortion in a signal.
Q

and imaginary axes are often called the in phase, or I-axis,

and the quadrature, or Q-axis, respectively. Plotting several symbols in a scatter diagram produces the constellation diagram. The points on a constellation diagram are
called constellation points. They are a set of modulation
symbols which compose the modulation alphabet.
Also a diagram of the ideal positions, signal space diagram, in a modulation scheme can be called a constellation diagram. In this sense the constellation is not a
scatter diagram but a representation of the scheme itself.
The example shown here is for 8-PSK, which has also
been given a Gray coded bit assignment.

010
011

110

78.1 Interpretation
Q

001

111
I

000

0000

0100

1100

1000

0001

0101

1101

1001

101
I

100
A constellation diagram for Gray encoded 8-PSK.

By representing a transmitted symbol as a complex number and modulating a cosine and sine carrier signal with
the real and imaginary parts (respectively), the symbol
can be sent with two carriers on the same frequency. They
are often referred to as quadrature carriers. A coherent
detector is able to independently demodulate these carriers. This principle of using two independently modulated
carriers is the foundation of quadrature modulation. In
pure phase modulation, the phase of the modulating symbol is the phase of the carrier itself and this is the best
representation of the modulated signal.

0011

0111

1111

1011

0010

0110

1110

1010

A constellation diagram for rectangular 16-QAM.

Upon reception of the signal, the demodulator examines

the received symbol, which may have been corrupted by
the channel or the receiver (e.g. additive white Gaussian noise, distortion, phase noise or interference). It
As the symbols are represented as complex numbers, they selects, as its estimate of what was actually transmitted,
can be visualized as points on the complex plane. The real that point on the constellation diagram which is closest (in
368

78.3. REFERENCES
a Euclidean distance sense) to that of the received symbol. Thus it will demodulate incorrectly if the corruption
has caused the received symbol to move closer to another
constellation point than the one transmitted.
This is maximum likelihood detection. The constellation
diagram allows a straightforward visualization of this process imagine the received symbol as an arbitrary point
in the I-Q plane and then decide that the transmitted symbol is whichever constellation point is closest to it.
For the purpose of analyzing received signal quality, some
types of corruption are very evident in the constellation
diagram. For example:
Gaussian noise shows as fuzzy constellation points
Non-coherent single frequency interference shows
as circular constellation points
Phase noise shows as rotationally spreading constellation points
Attenuation causes the corner points to move towards the center
A constellation diagram visualises phenomena similar to
those an eye pattern does for one-dimensional signals.
The eye pattern can be used to see timing jitter in one
dimension of modulation.

78.2 See also

Eye diagram
Modulation error ratio
Error vector magnitude
Quadrature amplitude modulation

78.3 References
[1] ANDREW S. TANENBAUM. COMPUTER NETWORKS. PRENTICE HALL. pp. 131132. ISBN
0-13-212695-8.

369

Chapter 79

Complex number
engineering, and statistics. The Italian mathematician
Gerolamo Cardano is the rst known to have introduced
complex numbers. He called them ctitious during his
attempts to nd solutions to cubic equations in the 16th
century.[2]

Im
b

a+bi

79.1 Overview
Complex numbers allow solutions to certain equations
that have no solutions in real numbers. For example, the
equation

Re

(x + 1)2 = 9

has no real solution, since the square of a real number

cannot be negative. Complex numbers provide a solution
to this problem. The idea is to extend the real numbers
2
A complex number can be visually represented as a pair of num- with the imaginary unit i where i = 1, so that solutions
bers (a, b) forming a vector on a diagram called an Argand dia- to equations like the preceding one can be found. In this
gram, representing the complex plane. Re is the real axis, Im case the solutions are 1 + 3i and 1 3i, as can be veris the imaginary axis, and i is the imaginary unit which satises ied using the fact that i2 = 1:
i2 = 1.

A complex number is a number that can be expressed in ((1 + 3i) + 1)2 = (3i)2 = (32 )(i2 ) = 9(1) = 9,
the form a + bi, where a and b are real numbers and i is
the imaginary unit, satisfying the equation i2 = 1.[1] In ((13i)+1)2 = (3i)2 = (3)2 (i2 ) = 9(1) = 9.
this expression, a is the real part and b is the imaginary
According to the fundamental theorem of algebra, all
part of the complex number.
polynomial equations with real or complex coecients
Complex numbers extend the concept of the one- in a single variable have a solution in complex numbers.
dimensional number line to the two-dimensional complex
plane by using the horizontal axis for the real part and the
vertical axis for the imaginary part. The complex number 79.1.1 Denition
a + bi can be identied with the point (a, b) in the complex plane. A complex number whose real part is zero is A complex number is a number of the form a + bi, where
said to be purely imaginary, whereas a complex number a and b are real numbers and i is the imaginary unit, satwhose imaginary part is zero is a real number. In this way, isfying i2 = 1. For example, 3.5 + 2i is a complex
the complex numbers are a eld extension of the ordinary number.
real numbers, in order to solve problems that cannot be The real number a is called the real part of the complex
solved with real numbers alone.
number a + bi; the real number b is called the imaginary
As well as their use within mathematics, complex num- part of a + bi. By this convention the imaginary part does
bers have practical applications in many elds, includ- not include the imaginary unit: hence b, not bi, is the
ing physics, chemistry, biology, economics, electrical imaginary part.[3][4] The real part of a complex number z
370

79.1. OVERVIEW

371

79.1.3 Complex plane

Im
z=x+iy

y
r

Im
b

z=a+bi

Re

r
y

Main article: Complex plane

A complex number can be viewed as a point or position

a Re

Figure 1: A complex number plotted as a point (red) and position vector (blue) on an Argand diagram; a+bi is the rectangular
expression of the point.

z=xiy

vector in a two-dimensional Cartesian coordinate system

called the complex plane or Argand diagram (see Pedoe
1988 and Solomentsev 2001), named after Jean-Robert
An illustration of the complex plane. The real part of a complex Argand. The numbers are conventionally plotted using
number z = x + iy is x, and its imaginary part is y.
the real part as the horizontal component, and imaginary
part as vertical (see Figure 1). These two values used to
identify a given complex number are therefore called its
is denoted by Re(z) or (z); the imaginary part of a com- Cartesian, rectangular, or algebraic form.
plex number z is denoted by Im(z) or (z). For example,
A position vector may also be dened in terms of its magnitude and direction relative to the origin. These are emphasized in a complex numbers polar form. Using the
Re(3.5 + 2i) = 3.5
polar form of the complex number in calculations may
Im(3.5 + 2i) = 2.
lead to a more intuitive interpretation of mathematical
results. Notably, the operations of addition and multipliHence, in terms of its real and imaginary parts, a complex
cation take on a very natural geometric character when
number z is equal to Re(z) + Im(z) i . This expression
complex numbers are viewed as position vectors: addiis sometimes known as the Cartesian form of z.
tion corresponds to vector addition while multiplication
A real number a can be regarded as a complex number corresponds to multiplying their magnitudes and adding
a + 0i whose imaginary part is 0. A purely imaginary their arguments (i.e. the angles they make with the x
number bi is a complex number 0 + bi whose real part is axis). Viewed in this way the multiplication of a complex
zero. It is common to write a for a + 0i and bi for 0 + number by i corresponds to rotating the position vector
bi. Moreover, when the imaginary part is negative, it is counterclockwise by a quarter turn (90) about the oricommon to write a bi with b > 0 instead of a + (b)i, gin: (a+bi)i = ai+bi2 = -b+ai.
for example 3 4i instead of 3 + (4)i.
The set of all complex numbers is denoted by , C or C .

79.1.2

Notation

Some authors[5] write a + ib instead of a + bi, particularly when b is a radical. In some disciplines, in particular
electromagnetism and electrical engineering, j is used instead of i,[6] since i is frequently used for electric current.
In these cases complex numbers are written as a + bj or
a + jb.

79.1.4 History in brief

Main section: History
The solution in radicals (without trigonometric functions)
of a general cubic equation contains the square roots of
negative numbers when all three roots are real numbers,
a situation that cannot be rectied by factoring aided by
the rational root test if the cubic is irreducible (the socalled casus irreducibilis). This conundrum led Italian

372

CHAPTER 79. COMPLEX NUMBER

mathematician Gerolamo Cardano to conceive of complex numbers in around 1545, though his understanding
was rudimentary.

Im

Work on the problem of general polynomials ultimately

led to the fundamental theorem of algebra, which shows
that with complex numbers, a solution exists to every
polynomial equation of degree one or higher. Complex
numbers thus form an algebraically closed eld, where
any polynomial equation has a root.

Many mathematicians contributed to the full development of complex numbers. The rules for addition, subtraction, multiplication, and division of complex numbers were developed by the Italian mathematician Rafael
Bombelli.[7] A more abstract formalism for the complex
numbers was further developed by the Irish mathematician William Rowan Hamilton, who extended this abstraction to the theory of quaternions.

Re

79.2 Relations
79.2.1

z=x+iy

Equality

z=xiy

Two complex numbers are equal if and only if both their

Geometric representation of z and its conjugate z in the complex
real and imaginary parts are equal. In symbols:
plane

z1 = z2 (Re(z1 ) = Re(z2 ) Im(z1 ) = Im(z2 )).

79.2.2

Ordering

axis. Conjugating twice gives the original complex number: z = z .

The real and imaginary parts of a complex number z can
be extracted using the conjugate:

Because complex numbers are naturally thought of as

existing on a two-dimensional plane, there is no natural
linear ordering on the set of complex numbers.[8]
Re (z) = 12 (z + z),
There is no linear ordering on the complex numbers that
1
is compatible with addition and multiplication. Formally, Im (z) = 2i (z z).
we say that the complex numbers cannot have the struc- Moreover, a complex number is real if and only if it
ture of an ordered eld. This is because any square in an equals its conjugate.
ordered eld is at least 0, but i2 = 1.
Conjugation distributes over the standard arithmetic operations:

79.3 Elementary operations

79.3.1

Conjugate

See also: Complex conjugate

The complex conjugate of the complex number z = x + yi
is dened to be x yi. It is denoted by either z or z*.
Formally, for any complex number z:

z + w = z + w,

z w = z w,

zw = zw,

(z/w) = z/w.

79.3.2 Addition and subtraction

z = Re(z) Im(z) i.

Complex numbers are added by separately adding the real

Geometrically, z is the reection of z about the real and imaginary parts of the summands. That is to say:

79.3. ELEMENTARY OPERATIONS

373

(a + bi)(c + di) = ac + bci + adi + bidi

(distributive property)

b
b
+
a

= ac + bidi + bci +
adi (commutative property of additionthe order of the summands can
be changed)
= ac + bdi2 + (bc +
ad)i (commutative and
distributive properties)
= (ac bd) + (bc + ad)i
(fundamental property of
the imaginary unit).

The division of two complex numbers is dened in terms

of complex multiplication, which is described above, and
real division. When at least one of c and d is non-zero,
we have

Addition of two complex numbers can be done geometrically by

constructing a parallelogram.

a + bi
=
c + di
(a + bi) + (c + di) = (a + c) + (b + d)i.

ac + bd
c2 + d2

(
+

bc ad
c 2 + d2

Using the visualization of complex numbers in the complex plane, the addition has the following geometric interpretation: the sum of two complex numbers A and B,
interpreted as points of the complex plane, is the point
X obtained by building a parallelogram, three of whose
vertices are O, A and B. Equivalently, X is the point such
that the triangles with vertices O, A, B, and X, B, A, are
congruent.

79.3.3

Multiplication and division

The multiplication of two complex numbers is dened by

the following formula:

(a + bi)(c + di) = (ac bd) + (bc + ad)i.

In particular, the square of the imaginary unit is 1:

i2 = i i = 1.

i.

Division can be dened in this way because of the following observation:

Similarly, subtraction is dened by

(a + bi) (c + di) = (a c) + (b d)i.

a + bi
(a + bi) (c di)
=
=
c + di
(c + di) (c di)

) (
)
ac + bd
bc ad
+ 2
i.
c2 + d2
c + d2

As shown earlier, c di is the complex conjugate of the

denominator c + di. At least one of the real part c and
the imaginary part d of the denominator must be nonzero
for division to be dened. This is called "rationalization"
of the denominator (although the denominator in the nal
expression might be an irrational real number).

79.3.4 Reciprocal
The reciprocal of a nonzero complex number z = x + yi
is given by
z
z
x
y
1
=
= 2
= 2
2
i.
2
2
z
z z
x +y
x +y
x + y2
This formula can be used to compute the multiplicative
inverse of a complex number if it is given in rectangular
coordinates. Inversive geometry, a branch of geometry
studying reections more general than ones about a line,
can also be expressed in terms of complex numbers. In
the network analysis of electrical circuits, the complex
conjugate is used in nding the equivalent impedance
when the maximum power transfer theorem is used.

The preceding denition of multiplication of general

complex numbers follows naturally from this fundamental property of the imaginary unit. Indeed, if i is treated 79.3.5 Square root
as a number so that di means d times i, the above multiplication rule is identical to the usual rule for multiplying See also: Square roots of negative and complex numbers
two sums of two terms.

374

CHAPTER 79. COMPLEX NUMBER

The square roots of a + bi (with b 0) are ( + i) , OP in a counterclockwise direction. This idea leads to the
where
polar form of complex numbers.

a+

The absolute value (or modulus or magnitude) of a complex number z = x + yi is

a2 + b2
2

r = |z| =

and

= sgn(b)

a +

x2 + y 2 .

If z is a real number (i.e., y = 0), then r = | x |. In general,

by Pythagoras theorem, r is the distance of the point P
representing the complex number z to the origin. The
square of the absolute value is

a2 + b2
,
2

where sgn is the signum function. This can be

seen by
squaring ( + i) to obtain a + bi.[9][10] Here a2 + b2
2
2
2
is called the modulus of a + bi, and the square root sign in- |z| = z z = x + y .
dicates the square root with non-negative
real part,
called

where z is the complex conjugate of z .

the principal square root; also a2 + b2 = z z ,
The argument of z (in many applications referred to as the
where z = a + bi .[11]
phase) is the angle of the radius OP with the positive
real axis, and is written as arg(z) . As with the modulus,
the argument can be found from the rectangular form x+
79.4 Polar form
yi :[12]
Main article: Polar coordinate system

arctan( xy )

arctan( x ) +

arctan( y )
x
= arg(z) =
2

indeterminate

Im
y
r

Re

if x > 0
if x < 0 and y
if x < 0 and y
if x = 0 and y
if x = 0 and y
if x = 0 and y

0
<0
>0
<0
= 0.

Normally, as given above, the principal value in the interval (,] is chosen. Values in the range [0,2) are
obtained by adding 2 if the value is negative. The value
of is expressed in radians in this article. It can increase
by any integer multiple of 2 and still give the same angle. Hence, the arg function is sometimes considered as
multivalued. The polar angle for the complex number 0
is indeterminate, but arbitrary choice of the angle 0 is
common.
The value of equals the result of atan2: =
atan2(imaginary, real) .

Together, r and give another way of representing complex numbers, the polar form, as the combination of modFigure 2: The argument and modulus r locate a point on an
ulus and argument fully specify the position of a point
i
Argand diagram; r(cos +i sin ) or re are polar expressions
on the plane. Recovering the original rectangular coof the point.
ordinates from the polar form is done by the formula
called trigonometric form

79.4.1

Absolute value and argument

z = r(cos + i sin ).
An alternative way of dening a point P in the complex
plane, other than using the x- and y-coordinates, is to use Using Eulers formula this can be written as
the distance of the point from O, the point whose coordinates are (0, 0) (the origin), together with the angle subtended between the positive real axis and the line segment z = rei .

79.5. EXPONENTIATION

Im

z=re

375

Im
_
r ei/2

r Re

x=z
Im
_ i(+2)/3
3
r e

_
3
r ei/3
_
/3 3r Re

_
r ei(+22)/3
3

x =z
Im

_
r ei(+2)/5
_
_
5
5
r ei(+22)/5
r ei/5
_
/5 5r Re
_
_
5
r ei(+32)/5 5r ei(+42)/5
5

x 5=z

_ i(+2)/2
r e

_
/2 r Re

_ i/4
r e
_
_ i(+22)/4 /4 4r Re
4
r e
_ i(+32)/4
4
r e
4

x 4=z

Im
_
6
r ei(+22)/6

4
3

x 2=z
Im
_ i(+2)/4
4
r e

5+5i

_
r ei(+2)/6
_
6
r ei/6
_
_ i(+32)/6 /6 6r Re
6
r e
_ i(+52)/6
_
6
6
r ei(+42)/6 r e
6

x 6=z

Visualisation of the square to sixth roots of a complex number z,

in polar form rei where = arg z and r = |z | if z is real,
= 0 or . Principal roots are in black.

2+i

1
0

3+i

Multiplication of 2 + i (blue triangle) and 3 + i (red triangle).

The red triangle is rotated to match the vertex of the blue one and
stretched by 5, the length of the hypotenuse of the blue triangle.

In other words, the absolute values are multiplied and

the arguments are added to yield the polar form of the
product. For example, multiplying by i corresponds to
a quarter-turn counter-clockwise, which gives back i2 =
1. The picture at the right illustrates the multiplication
of

Using the cis function, this is sometimes abbreviated to

(2 + i)(3 + i) = 5 + 5i.

z = r cis .

Since the real and imaginary part of 5 + 5i are equal, the

argument of that number is 45 degrees, or /4 (in radian).
On the other hand, it is also the sum of the angles at the
origin of the red and blue triangles are arctan(1/3) and
arctan(1/2), respectively. Thus, the formula

In angle notation, often used in electronics to represent a

phasor with amplitude r and phase , it is written as[13]

1
1
= arctan + arctan
4
2
3

z = r.

79.4.2

holds. As the arctan function can be approximated highly

eciently, formulas like thisknown as Machin-like
Multiplication and division in polar formulasare used for high-precision approximations of
form
.

Formulas for multiplication, division and exponentiation Similarly, division is given by

are simpler in polar form than the corresponding formulas
in Cartesian coordinates. Given two complex numbers z1 z1
r1
=
(cos(1 2 ) + i sin(1 2 )) .
= r1 (cos 1 + i sin 1 ) and z2 = r2 (cos 2 + i sin 2 ),
z2
r2
because of the well-known trigonometric identities

79.5 Exponentiation
cos(a) cos(b) sin(a) sin(b) = cos(a + b)
cos(a) sin(b) + sin(a) cos(b) = sin(a + b)

79.5.1 Eulers formula

we may derive

Eulers formula states that, for any real number x,

z1 z2 = r1 r2 (cos(1 + 2 ) + i sin(1 + 2 )).

eix = cos x + i sin x

376

CHAPTER 79. COMPLEX NUMBER

where e is the base of the natural logarithm. This can be

proved through induction by observing that

= n ln(r(cos + i sin ))
= {n(ln(r) + ( + k2)i)|k Z}
= {n ln(r) + ni + nk2i|k Z}.

i = 1,
4

i = 1,

i = 1,

i = i,

i = 1,

i7 = i,

i = i,
i = i,

When n is an integer, this simplies to de Moivres formula:

and so on, and by considering the Taylor series expansions

of eix , cos x and sin x:
z n = (r(cos + i sin ))n = rn (cos n + i sin n).
The nth roots of z are given by
(ix)2
(ix)3
(ix)4
(ix)5
(ix)6
(ix)7
(ix)8
e = 1 + ix +
+
+
+
+
+
+
+
2!
3!
4!
5!
6!
7! ( 8!(
)
(
))

+ 2k
+ 2k
n
n
+ i sin
ix3
x4
ix5
x6
ix7
x8 z = r cos
x2
n
n

+
+

+
+
= 1 + ix
2!
3!
4!
5!
6!
7!
8!
for any integer k satisfying
0 k n 1. Here n r is
)
(
)
(
5
7
x2
x4
x6
x8
x3 thexusual
x(positive)
nth root of the positive real number r.
= 1
+

+
+ i x
+

+
2!
4!
6!
8!
3! While
5! the7!nth root of a positive real number r is chosen to
be the positive real number c satisfying cn = r there is no
= cos x + i sin x .
natural way of distinguishing one particular complex nth
root of a complex number. Therefore, the nth root of z
The rearrangement of terms is justied because each se- is considered as a multivalued function (in z), as opposed
ries is absolutely convergent.
to a usual function f, for which f(z) is a uniquely dened
number. Formulas such as
ix

79.5.2

Natural logarithm

n
zn = z
Eulers formula allows us to observe that, for any complex
number
(which holds for positive real numbers), do in general not
hold for complex numbers.
z = r(cos + i sin ).
where r is a non-negative real number, one possible value
for z's natural logarithm is

79.6 Properties
79.6.1 Field structure

ln(z) = ln(r) + i

The set C of complex numbers is a eld. Briey, this

means that the following facts hold: rst, any two comBecause cos and sin are periodic functions, the natural plex numbers can be added and multiplied to yield anlogarithm may be considered a multi-valued function, other complex number. Second, for any complex number
with:
z, its additive inverse z is also a complex number; and
third, every nonzero complex number has a reciprocal
complex number. Moreover, these operations satisfy a
ln(z) = {ln(r) + ( + 2k)i | k Z}
number of laws, for example the law of commutativity of
addition and multiplication for any two complex numbers
z1 and z2 :

79.5.3

Integer and fractional exponents

We may use the identity

ln(ab ) = b ln(a)

z1 + z2 = z2 + z1 ,
z1 z2 = z2 z1 .

These two laws and the other requirements on a eld can

to dene complex exponentiation, which is likewise be proven by the formulas given above, using the fact that
the real numbers themselves form a eld.
multi-valued:
Unlike the reals, C is not an ordered eld, that is to say,
it is not possible to dene a relation z1 < z2 that is comln(z n ) = ln((r(cos + i sin ))n )
patible with the addition and multiplication. In fact, in

79.7. FORMAL CONSTRUCTION

377

any ordered eld, the square of any element is necessarily 79.6.4 Characterization as a topological
positive, so i2 = 1 precludes the existence of an ordering
eld
on C.
When the underlying eld for a mathematical topic or The preceding characterization of C describes only the
construct is the eld of complex numbers, the topics algebraic aspects of C. That is to say, the properties of
name is usually modied to reect that fact. For example: nearness and continuity, which matter in areas such as
complex analysis, complex matrix, complex polynomial, analysis and topology, are not dealt with. The following
description of C as a topological eld (that is, a eld that
and complex Lie algebra.
is equipped with a topology, which allows the notion of
convergence) does take into account the topological properties. C contains a subset P (namely the set of positive
79.6.2 Solutions of polynomial equations real numbers) of nonzero elements satisfying the following three conditions:
Given any complex numbers (called coecients) a0 , ,
P is closed under addition, multiplication and taking
an, the equation
inverses.
an z n + + a1 z + a0 = 0
has at least one complex solution z, provided that at least
one of the higher coecients a1 , , an is nonzero. This
is the statement of the fundamental theorem of algebra.
Because of this fact, C is called an algebraically closed
eld. This property does not hold for the eld of rational
numbers Q (the polynomial x2 2 does not have a rational root, since 2 is not a rational number) nor the real
numbers R (the polynomial x2 + a does not have a real
root for a > 0, since the square of x is positive for any real
number x).
There are various proofs of this theorem, either by analytic methods such as Liouvilles theorem, or topological
ones such as the winding number, or a proof combining
Galois theory and the fact that any real polynomial of odd
degree has at least one real root.
Because of this fact, theorems that hold for any algebraically closed eld, apply to C. For example, any nonempty complex square matrix has at least one (complex)
eigenvalue.

If x and y are distinct elements of P, then either x

y or y x is in P.
If S is any nonempty subset of P, then S + P = x + P
for some x in C.
Moreover, C has a nontrivial involutive automorphism x
x* (namely the complex conjugation), such that x x*
is in P for any nonzero x in C.
Any eld F with these properties can be endowed with a
topology by taking the sets B(x, p) = { y | p (y x)(y
x)* P } as a base, where x ranges over the eld and
p ranges over P. With this topology F is isomorphic as a
topological eld to C.
The only connected locally compact topological elds are
R and C. This gives another characterization of C as a
topological eld, since C can be distinguished from R because the nonzero complex numbers are connected, while
the nonzero real numbers are not.

79.7 Formal construction

79.7.1 Formal development

79.6.3

Algebraic characterization

The eld C has the following three properties: rst, it has

characteristic 0. This means that 1 + 1 + + 1 0 for any
number of summands (all of which equal one). Second,
its transcendence degree over Q, the prime eld of C, is
the cardinality of the continuum. Third, it is algebraically
closed (see above). It can be shown that any eld having
these properties is isomorphic (as a eld) to C. For example, the algebraic closure of Qp also satises these three
properties, so these two elds are isomorphic. Also, C is
isomorphic to the eld of complex Puiseux series. However, specifying an isomorphism requires the axiom of
choice. Another consequence of this algebraic characterization is that C contains many proper subelds that
are isomorphic to C.

Above, complex numbers have been dened by introducing i, the imaginary unit, as a symbol. More rigorously,
the set C of complex numbers can be dened as the set
R2 of ordered pairs (a, b) of real numbers. In this notation, the above formulas for addition and multiplication
read
(a, b) + (c, d) = (a + c, b + d)
(a, b) (c, d) = (ac bd, bc + ad).
It is then just a matter of notation to express (a, b) as a +
bi.
Though this low-level construction does accurately describe the structure of the complex numbers, the following equivalent denition reveals the algebraic nature of

378

CHAPTER 79. COMPLEX NUMBER

C more immediately. This characterization relies on the

notion of elds and polynomials. A eld is a set endowed
with addition, subtraction, multiplication and division operations that behave as is familiar from, say, rational numbers. For example, the distributive law

The conjugate z corresponds to the transpose of the matrix.

(x + y)z = xz + yz

Though this representation of complex numbers with matrices is the most common, many
( other
) representations
arise from matrices other than 01 1
that square to the
0
negative of the identity matrix. See the article on 2 2
real matrices for other representations of complex numbers.

must hold for any three elements x, y and z of a eld. The

set R of real numbers does form a eld. A polynomial
p(X) with real coecients is an expression of the form

79.8 Complex analysis

an X n + + a1 X + a0
where the a0 , ..., an are real numbers. The usual addition
and multiplication of polynomials endows the set R[X]
of all such polynomials with a ring structure. This ring is
called polynomial ring.
The quotient ring R[X]/(X 2 + 1) can be shown to be a
eld. This extension eld contains two square roots of
1, namely (the cosets of) X and X, respectively. (The
cosets of) 1 and X form a basis of R[X]/(X 2 + 1) as a
real vector space, which means that each element of the
extension eld can be uniquely written as a linear combination in these two elements. Equivalently, elements of
the extension eld can be written as ordered pairs (a, b)
of real numbers. Moreover, the above formulas for addition etc. correspond to the ones yielded by this abstract
algebraic approachthe two denitions of the eld C
are said to be isomorphic (as elds). Together with the
above-mentioned fact that C is algebraically closed, this
Color wheel graph of sin(1/ z). Black parts inside refer to numalso shows that C is an algebraic closure of R.
bers having large absolute values.

79.7.2

Matrix representation of complex Main article: Complex analysis

numbers

Complex numbers a + bi can also be represented by 2

2 matrices that have the following form:
(
a
b

)
b
.
a

The study of functions of a complex variable is known

as complex analysis and has enormous practical use in
applied mathematics as well as in other branches of mathematics. Often, the most natural proofs for statements in
real analysis or even number theory employ techniques
from complex analysis (see prime number theorem for
an example). Unlike real functions, which are commonly
represented as two-dimensional graphs, complex functions have four-dimensional graphs and may usefully be
illustrated by color-coding a three-dimensional graph to
suggest four dimensions, or by animating the complex
functions dynamic transformation of the complex plane.

Here the entries a and b are real numbers. The sum and
product of two such matrices is again of this form, and
the sum and product of complex numbers corresponds to
the sum and product of such matrices. The geometric
description of the multiplication of complex numbers can
also be expressed in terms of rotation matrices by using
this correspondence between complex numbers and such
79.8.1 Complex exponential and related
matrices. Moreover, the square of the absolute value of
functions
a complex number expressed as a matrix is equal to the
determinant of that matrix:
The notions of convergent series and continuous functions
in (real) analysis have natural analogs in complex analysis.




A sequence of complex numbers is said to converge if and
a
b
 = (a2 ) ((b)(b)) = a2 + b2 .
|z|2 = 
only if its real and imaginary parts do. This is equivalent
b a

79.9. APPLICATIONS

379

to the (, )-denition of limits, where the absolute value

of real numbers is replaced by the one of complex numbers. From a more abstract point of view, C, endowed
with the metric

Consequently, they are in general multi-valued. For =

1 / n, for some natural number n, this recovers the nonuniqueness of nth roots mentioned above.

Complex numbers, unlike real numbers, do not in general satisfy the unmodied power and logarithm identities, particularly when navely treated as single-valued
d(z1 , z2 ) = |z1 z2 |
functions; see failure of power and logarithm identities.
is a complete metric space, which notably includes the For example, they do not satisfy
triangle inequality
abc = (ab )c .
|z1 + z2 | |z1 | + |z2 |

Both sides of the equation are multivalued by the denition of complex exponentiation given here, and the values
Like in real analysis, this notion of convergence is used on the left are a subset of those on the right.
to construct a number of elementary functions: the
exponential function exp(z), also written ez , is dened as
79.8.2 Holomorphic functions
the innite series
for any two complex numbers z1 and z2 .

exp(z) := 1 + z +

z2
z3
zn
+
+ =
.
21 321
n!
n=0

A function f : C C is called holomorphic if it satises the CauchyRiemann equations. For example, any
R-linear map C C can be written in the form

and the series dening the real trigonometric functions

sine and cosine, as well as hyperbolic functions such f (z) = az + bz
as sinh also carry over to complex arguments without
with complex coecients a and b. This map is holomorchange. Eulers identity states:
phic if and only if b = 0. The second summand bz is realdierentiable, but does not satisfy the CauchyRiemann
equations.
exp(i) = cos() + i sin()
Complex analysis shows some features not apparent in
real analysis. For example, any two holomorphic functions f and g that agree on an arbitrarily small open subset
of C necessarily agree everywhere. Meromorphic funcexp(i) = 1
tions, functions that can locally be written as f(z)/(z
z )n with a holomorphic function f, still share some of
Unlike in the situation of real numbers, there is an 0
the features of holomorphic functions. Other functions
innitude of complex solutions z of the equation
have essential singularities, such as sin(1/z) at z = 0.
for any real number , in particular

exp(z) = w

79.9 Applications

for any complex number w 0. It can be shown that

any such solution zcalled complex logarithm of w Complex numbers have essential concrete applications in
satises
a variety of scientic and related areas such as signal processing, control theory, electromagnetism, uid dynamics, quantum mechanics, cartography, and vibration anallog(x + iy) = ln |w| + i arg(w),
ysis. Some applications of complex numbers are:
where arg is the argument dened above, and ln the
(real) natural logarithm. As arg is a multivalued function,
79.9.1 Control theory
unique only up to a multiple of 2, log is also multivalued.
The principal value of log is often taken by restricting the
In control theory, systems are often transformed from the
imaginary part to the interval (,].
time domain to the frequency domain using the Laplace
Complex exponentiation z is dened as
transform. The systems poles and zeros are then analyzed in the complex plane. The root locus, Nyquist plot,
and Nichols plot techniques all make use of the complex
z = exp( log z).
plane.

380

CHAPTER 79. COMPLEX NUMBER

In the root locus method, it is especially important Since the voltage in an AC circuit is oscillating, it can be
whether the poles and zeros are in the left or right half represented as
planes, i.e. have real part greater than or less than zero.
If a linear, time-invariant (LTI) system has poles that are
V (t) = V0 ejt = V0 (cos t + j sin t) ,
in the right half plane, it will be unstable,

To obtain the measurable quantity, the real part is taken:

all in the left half plane, it will be stable,

[ jt ]
= V0 cos t.
on the imaginary axis, it will have marginal stability. v(t) = Re(V ) = Re V0 e
The complex-valued signal V (t) is called the analytic repIf a system has zeros in the right half plane, it is a resentation of the real-valued, measurable signal v(t) .
[14]
nonminimum phase system.

79.9.2

Improper integrals

79.9.6 Signal analysis

Complex numbers are used in signal analysis and other

elds for a convenient description for periodically varying
signals. For given real functions representing actual physical quantities, often in terms of sines and cosines, corresponding complex functions are considered of which the
real parts are the original quantities. For a sine wave of
a given frequency, the absolute value | z | of the corre79.9.3 Fluid dynamics
sponding z is the amplitude and the argument arg(z) is
In uid dynamics, complex functions are used to describe the phase.
potential ow in two dimensions.
If Fourier analysis is employed to write a given realvalued signal as a sum of periodic functions, these periodic functions are often written as complex valued func79.9.4 Dynamic equations
tions of the form
In applied elds, complex numbers are often used to compute certain real-valued improper integrals, by means of
complex-valued functions. Several methods exist to do
this; see methods of contour integration.

In dierential equations, it is common to rst nd all complex roots r of the characteristic equation of a linear dif- x(t) = Re{X(t)}
ferential equation or equation system and then attempt to
solve the system in terms of base functions of the form and
f(t) = ert . Likewise, in dierence equations, the complex roots r of the characteristic equation of the dierence equation system are used, to attempt to solve the X(t) = Aeit = aei eit = aei(t+)
system in terms of base functions of the form f(t) = rt .
where represents the angular frequency and the complex number A encodes the phase and amplitude as ex79.9.5 Electromagnetism and electrical en- plained above.

gineering
Main article: Alternating current

This use is also extended into digital signal processing and

digital image processing, which utilize digital versions
of Fourier analysis (and wavelet analysis) to transmit,
compress, restore, and otherwise process digital audio
signals, still images, and video signals.

In electrical engineering, the Fourier transform is used

to analyze varying voltages and currents. The treatment Another example, relevant to the two side bands of
of resistors, capacitors, and inductors can then be uni- amplitude modulation of AM radio, is:
ed by introducing imaginary, frequency-dependent resistances for the latter two and combining all three in a
)
(
single complex number called the impedance. This ap- cos(( + )t) + cos (( )t) = Re ei(+)t + ei()t
(
)
proach is called phasor calculus.
= Re (eit + eit ) eit
(
)
In electrical engineering, the imaginary unit is denoted by
= Re 2 cos(t) eit
j, to avoid confusion with I, which is generally in use to
(
)
= 2 cos(t) Re eit
denote electric current, or, more particularly, i, which is
generally in use to denote instantaneous electric current.
= 2 cos(t) cos (t) .

79.10. HISTORY

79.9.7

381

Quantum mechanics

The complex number eld is intrinsic to the mathematical

formulations of quantum mechanics, where complex
Hilbert spaces provide the context for one such formulation that is convenient and perhaps most standard. The
original foundation formulas of quantum mechanicsthe
Schrdinger equation and Heisenbergs matrix mechanicsmake use of complex numbers.

79.9.8

Relativity

In special and general relativity, some formulas for the

metric on spacetime become simpler if one takes the time
component of the spacetime continuum to be imaginary.
(This approach is no longer standard in classical relativity,
but is used in an essential way in quantum eld theory.)
Complex numbers are essential to spinors, which are a
Construction of a regular pentagon using straightedge and comgeneralization of the tensors used in relativity.
pass.

79.9.9

Geometry

Fractals

unity, it can be shown that it is not possible to construct a

regular nonagon using only compass and straightedge a
purely geometric problem.

Another example are Gaussian integers, that is, numbers

Certain fractals are plotted in the complex plane, e.g. the
of the form x + iy, where x and y are integers, which can
Mandelbrot set and Julia sets.
be used to classify sums of squares.
Triangles

79.9.11 Analytic number theory

Every triangle has a unique Steiner inellipsean ellipse

inside the triangle and tangent to the midpoints of the
three sides of the triangle. The foci of a triangles Steiner
inellipse can be found as follows, according to Mardens
theorem:[15][16] Denote the triangles vertices in the complex plane as a = xA + yAi, b = xB + yBi, and c = xC +
yCi. Write the cubic equation (xa)(xb)(xc)=0 , take its
derivative, and equate the (quadratic) derivative to zero.
Mardens Theorem says that the solutions of this equation are the complex numbers denoting the locations of
the two foci of the Steiner inellipse.

79.9.10

Algebraic number theory

As mentioned above, any nonconstant polynomial equation (in complex coecients) has a solution in C. A fortiori, the same is true if the equation has rational coefcients. The roots of such equations are called algebraic
numbers they are a principal object of study in algebraic
number theory. Compared to Q, the algebraic closure
of Q, which also contains all algebraic numbers, C has
the advantage of being easily understandable in geometric terms. In this way, algebraic methods can be used
to study geometric questions and vice versa. With algebraic methods, more specically applying the machinery of eld theory to the number eld containing roots of

Main article: Analytic number theory

Analytic number theory studies numbers, often integers
or rationals, by taking advantage of the fact that they
can be regarded as complex numbers, in which analytic
methods can be used. This is done by encoding numbertheoretic information in complex-valued functions. For
example, the Riemann zeta function (s) is related to the
distribution of prime numbers.

79.10 History
The earliest eeting reference to square roots of negative
numbers can perhaps be said to occur in the work of the
Greek mathematician Hero of Alexandria in the 1st century AD, where in his Stereometrica he considers, apparently in error, the volume of an impossible frustum of a

pyramid to arrive at the term 81144=3i 7 in his calculations, although negative quantities were not conceived
of in Hellenistic mathematics and Heron merely replaced

it by its positive ( 14481=3 7 ).[17]

The impetus to study complex numbers proper rst arose
in the 16th century when algebraic solutions for the roots
of cubic and quartic polynomials were discovered by

382

CHAPTER 79. COMPLEX NUMBER

Italian mathematicians (see Niccol Fontana Tartaglia,

Gerolamo Cardano). It was soon realized that these formulas, even if one was only interested in real solutions,
sometimes required the manipulation of square roots of
negative numbers. As an example, Tartaglias formula for
a cubic equation of the form x3 =px+q [18] gives the solution to the equation x3 = x as

1
( 1)1/3 +
( 1)1/3

trigonometric functions. For instance, in 1730 Abraham

de Moivre noted that the complicated identities relating
trigonometric functions of an integer multiple of an angle
to powers of trigonometric functions of that angle could
be simply re-expressed by the following well-known formula which bears his name, de Moivres formula:

(cos + i sin )n = cos n + i sin n.

)
.

At rst glance this looks like nonsense. However formal

calculations with complex numbers show thatthe equa
tion z3 = i has solutions i, 23 + 12 i and 2 3 + 12 i .
1/3
Substituting these in turn for 1 in Tartaglias cubic
formula and simplifying, one gets 0, 1 and 1 as the solutions of x3 x = 0. Of course this particular equation can
be solved at sight but it does illustrate that when general
formulas are used to solve cubic equations with real roots
then, as later mathematicians showed rigorously, the use
of complex numbers is unavoidable. Rafael Bombelli was
the rst to explicitly address these seemingly paradoxical
solutions of cubic equations and developed the rules for
complex arithmetic trying to resolve these issues.

In 1748 Leonhard Euler went further and obtained Eulers

formula of complex analysis:

cos + i sin = ei
by formally manipulating complex power series and observed that this formula could be used to reduce any
trigonometric identity to much simpler exponential identities.
The idea of a complex number as a point in the complex plane (above) was rst described by Caspar Wessel
in 1799, although it had been anticipated as early as 1685
in Walliss De Algebra tractatus.

Wessels memoir appeared in the Proceedings of the

The term imaginary for these quantities was coined by Copenhagen Academy but went largely unnoticed. In
Ren Descartes in 1637, although he was at pains to stress 1806 Jean-Robert Argand independently issued a pamtheir imaginary nature[19]
phlet on complex numbers and provided a rigorous proof
of the fundamental theorem of algebra. Gauss had earlier
published an essentially topological proof of the theorem
[...] sometimes only imaginary, that is one
in 1797 but expressed his doubts at the time about the
can imagine as many as I said in each equatrue metaphysics of the square root of 1. It was not
tion, but sometimes there exists no quantity
until 1831 that he overcame these doubts and published
that matches that which we imagine.
his treatise on complex numbers as points in the plane,
([...] quelquefois seulement imaginaires
largely establishing modern notation and terminology. In
cest--dire que lon peut toujours en imaginer
the beginning of 19th century, other mathematicians disautant que j'ai dit en chaque quation, mais
covered independently the geometrical representation of
quil ny a quelquefois aucune quantit qui corthe complex numbers: Bue, Mourey, Warren, Franais
responde celle quon imagine.)
and his brother, Bellavitis.[20]
A further source of confusion was that the equation
2
1 = 1 1=1 seemed to be capriciously inconsis
tent with the algebraic identity a b= ab , which is valid
for non-negative real numbers a and b, and which was
also used in complex number calculations with one of
a, b positive and the other negative. The incorrect use

of this identity (and the related identity 1a = a1 ) in the

case when both a and b are negative even bedeviled Euler.
This diculty eventually led to the convention of using
the special symbol i in place of 1 to guard against this
mistake. Even so, Euler considered it natural to introduce students to complex numbers much earlier than we
do today. In his elementary algebra text book, Elements
of Algebra, he introduces these numbers almost at once
and then uses them in a natural way throughout.

The English mathematician G. H. Hardy remarked that

Gauss was the rst mathematician to use complex numbers in 'a really condent and scientic way' although
mathematicians such as Niels Henrik Abel and Carl Gustav Jacob Jacobi were necessarily using them routinely
before Gauss published his 1831 treatise.[21] Augustin
Louis Cauchy and Bernhard Riemann together brought
the fundamental ideas of complex analysis to a high state
of completion, commencing around 1825 in Cauchys
case.

The common terms used in the theory are chiey due

to the founders. Argand called cos +i sin the direction

factor, and r= a2 +b2 the modulus; Cauchy (1828) called

cos +i sin the reduced form (l'expression rduite) and
apparently introduced the term argument; Gauss used i

In the 18th century complex numbers gained wider use, for 1 , introduced the term complex number for a +
as it was noticed that formal manipulation of complex ex- bi, and called a2 + b2 the norm. The expression direcpressions could be used to simplify calculations involving tion coecient, often used for cos + i sin , is due to

79.12. SEE ALSO

383

Hankel (1867), and absolute value, for modulus, is due to

Weierstrass.
Later classical writers on the general theory include {z = aI + bJ : a, b R}
Richard Dedekind, Otto Hlder, Felix Klein, Henri
Poincar, Hermann Schwarz, Karl Weierstrass and many is also isomorphic to the2 eld C, and gives an alternative
complex structure on R . This is generalized by the noothers.
tion of a linear complex structure.

79.11 Generalizations and related

notions
The process of extending the eld R of reals to C is
known as CayleyDickson construction. It can be carried
further to higher dimensions, yielding the quaternions H
and octonions O which (as a real vector space) are of dimension 4 and 8, respectively. In this context the complex
numbers have been called the binarions.[22]

Hypercomplex numbers also generalize R, C, H, and O.

For example, this notion contains the split-complex numbers, which are elements of the ring R[x]/(x2 1) (as
opposed to R[x]/(x2 + 1)). In this ring, the equation a2 =
1 has four solutions.
The eld R is the completion of Q, the eld of rational
numbers, with respect to the usual absolute value metric.
Other choices of metrics on Q lead to the elds Qp of
p-adic numbers (for any prime number p), which are
thereby analogous to R. There are no other nontrivial
ways of completing Q than R and Qp, by Ostrowskis
theorem. The algebraic closures Qp of Qp still carry a
norm, but (unlike C) are not complete with respect to it.
The completion Cp of Qp turns out to be algebraically
closed. This eld is called p-adic complex numbers by
analogy.

However, just as applying the construction to reals loses

the property of ordering, more properties familiar from
real and complex numbers vanish with increasing dimension. The quaternions are only a skew eld, i.e. for some
x, y: xy yx for two quaternions, the multiplication of
octonions fails (in addition to not being commutative) to
The elds R and Qp and their nite eld extensions, inbe associative: for some x, y, z: (xy)z x(yz).
cluding C, are local elds.
Reals, complex numbers, quaternions and octonions
are all normed division algebras over R. However, by
Hurwitzs theorem they are the only ones. The next step
in the CayleyDickson construction, the sedenions, in fact 79.12 See also
fails to have this structure.
Algebraic surface
The CayleyDickson construction is closely related to the
regular representation of C, thought of as an R-algebra
(an R-vector space with a multiplication), with respect to
the basis (1, i). This means the following: the R-linear
map

Circular motion using complex numbers

Complex-base system
Complex geometry

C C, z 7 wz

Complex square root

for some xed complex number w can be represented by a

2 2 matrix (once a basis has been chosen). With respect
to the basis (1, i), this matrix is

Domain coloring
Eisenstein integer

(
)
Re(w) Im(w)
Im(w)
Re(w)
i.e., the one mentioned in the section on matrix representation of complex numbers above. While this is a linear
representation of C in the 2 2 real matrices, it is not the
only one. Any matrix
(
)
p q
J=
,
r p

p2 + qr + 1 = 0

has the property that its square is the negative of the identity matrix: J 2 = I. Then

Eulers identity
Gaussian integer
Mandelbrot set
Quaternion
Riemann sphere (extended complex plane)
Root of unity
Unit complex number

384

79.13 Notes
[1] Charles P. McKeague (2011), Elementary Algebra,
Brooks/Cole, p. 524, ISBN 978-0-8400-6421-9
[2] Burton (1995, p. 294)
[3] Complex Variables (2nd Edition), M.R. Spiegel, S. Lipschutz, J.J. Schiller, D. Spellman, Schaums Outline Series, Mc Graw Hill (USA), ISBN 978-0-07-161569-3
[4] Aufmann, Richard N.; Barker, Vernon C.; Nation,
Richard D. (2007), Chapter P, College Algebra and
Trigonometry (6 ed.), Cengage Learning, p. 66, ISBN 0618-82515-0
[5] For example Ahlfors (1979).
[6] Brown, James Ward; Churchill, Ruel V. (1996), Complex
variables and applications (6th ed.), New York: McGrawHill, p. 2, ISBN 0-07-912147-0, In electrical engineering,
the letter j is used instead of i.

CHAPTER 79. COMPLEX NUMBER

. When (q/2)2 (p/3)3 is negative

(casus irreducibilis), the second cube root should be regarded as the complex conjugate of the rst one.
3

q/2

(q/2)2 (p/3)3

[19] Descartes, Ren (1954) [1637], La Gomtrie | The Geometry of Ren Descartes with a facsimile of the rst edition, Dover Publications, ISBN 0-486-60068-8, retrieved
20 April 2011
[20] Caparrini, Sandro (2000), On the Common Origin of
Some of the Works on the Geometrical Interpretation of
Complex Numbers, in Kim Williams (ed.), Two Cultures, Birkhuser, p. 139, ISBN 3-7643-7186-2 Extract
of page 139
[21] Hardy, G. H.; Wright, E. M. (2000) [1938], An Introduction to the Theory of Numbers, OUP Oxford, p. 189
(fourth edition), ISBN 0-19-921986-9
[22] Kevin McCrimmon (2004) A Taste of Jordan Algebras,
pp 64, Universitext, Springer ISBN 0-387-95447-3 MR
2014924

[7] Katz (2004, 9.1.4)

[8] http://mathworld.wolfram.com/ComplexNumber.html
[9] Abramowitz, Milton; Stegun, Irene A. (1964), Handbook
of mathematical functions with formulas, graphs, and
mathematical tables, Courier Dover Publications, p. 17,
ISBN 0-486-61272-4, Section 3.7.26, p. 17
[10] Cooke, Roger (2008), Classical algebra: its nature, origins, and uses, John Wiley and Sons, p. 59, ISBN 0-47025952-3, Extract: page 59

79.14 References
79.14.1 Mathematical references
Ahlfors, Lars (1979), Complex analysis (3rd ed.),
McGraw-Hill, ISBN 978-0-07-000657-7

[11] Ahlfors (1979, p. 3)

Conway, John B. (1986), Functions of One Complex

Variable I, Springer, ISBN 0-387-90328-3

[12] Kasana, H.S. (2005), Chapter 1, Complex Variables:

Theory And Applications (2nd ed.), PHI Learning Pvt.
Ltd, p. 14, ISBN 81-203-2641-5

Joshi, Kapil D. (1989), Foundations of Discrete

Mathematics, New York: John Wiley & Sons, ISBN
978-0-470-21152-6

[13] Nilsson, James William; Riedel, Susan A. (2008), Chapter 9, Electric circuits (8th ed.), Prentice Hall, p. 338,
ISBN 0-13-198925-1

Pedoe, Dan (1988), Geometry: A comprehensive

course, Dover, ISBN 0-486-65812-0

[14] Electromagnetism (2nd edition), I.S. Grant, W.R.

Phillips, Manchester Physics Series, 2008 ISBN 0-47192712-0
[15] Kalman, Dan (2008a), An Elementary Proof of Mardens Theorem, The American Mathematical Monthly,
115: 33038, ISSN 0002-9890
[16] Kalman, Dan (2008b), The Most Marvelous Theorem in
Mathematics, Journal of Online Mathematics and its Applications External link in |journal= (help)
[17] Nahin, Paul J. (2007), An Imaginary Tale: The Story
of 1, Princeton University Press, ISBN 978-0-69112798-9, retrieved 20 April 2011
[18] In modern notation, Tartaglias solution is based on
expanding the cube of the sum of two cube roots:

( 3 u+ 3 v)3 =3 3 uv( 3 u+ 3 v)+u+v With x= 3 u+ 3 v , p=

3 3 uv , q=u+v , u and v can be expressed in terms of p and

q as u=q/2+ (q/2)2 (p/3)3 and v=q/2 (q/2)2 (p/3)3

3
, respectively. Therefore, x= q/2+ (q/2)2 (p/3)3 +

Press, WH; Teukolsky, SA; Vetterling, WT; Flannery, BP (2007), Section 5.5 Complex Arithmetic, Numerical Recipes: The Art of Scientic
Computing (3rd ed.), New York: Cambridge University Press, ISBN 978-0-521-88068-8
Solomentsev, E.D. (2001), Complex number, in
Hazewinkel, Michiel, Encyclopedia of Mathematics,
Springer, ISBN 978-1-55608-010-4

79.14.2 Historical references

Burton, David M. (1995), The History of Mathematics (3rd ed.), New York: McGraw-Hill, ISBN 9780-07-009465-9
Katz, Victor J. (2004), A History of Mathematics,
Brief Version, Addison-Wesley, ISBN 978-0-32116193-2

79.16. EXTERNAL LINKS

Nahin, Paul J. (1998), An Imaginary Tale: The Story

of 1 , Princeton University Press, ISBN 0-69102795-1

A gentle introduction to the history of
complex numbers and the beginnings of
complex analysis.
H.D. Ebbinghaus; H. Hermes; F. Hirzebruch; M.
Koecher; K. Mainzer; J. Neukirch; A. Prestel;
R. Remmert (1991), Numbers (hardcover ed.),
Springer, ISBN 0-387-97497-0
An advanced perspective on the historical development of the concept of number.

79.15 Further reading

The Road to Reality: A Complete Guide to the Laws
of the Universe, by Roger Penrose; Alfred A. Knopf,
2005; ISBN 0-679-45443-8. Chapters 47 in particular deal extensively (and enthusiastically) with
complex numbers.
Unknown Quantity: A Real and Imaginary History
of Algebra, by John Derbyshire; Joseph Henry Press;
ISBN 0-309-09657-X (hardcover 2006). A very
readable history with emphasis on solving polynomial equations and the structures of modern algebra.
Visual Complex Analysis, by Tristan Needham;
Clarendon Press; ISBN 0-19-853447-7 (hardcover,
1997). History of complex numbers and complex
analysis with compelling and useful visual interpretations.
Conway, John B., Functions of One Complex Variable I (Graduate Texts in Mathematics), Springer; 2
edition (12 September 2005). ISBN 0-387-903283.

79.16 External links

Hazewinkel, Michiel, ed. (2001), Complex number, Encyclopedia of Mathematics, Springer, ISBN
978-1-55608-010-4
Introduction to Complex Numbers from Khan
Academy

Imaginary Numbers on In Our Time at the BBC.

Eulers Investigations on the Roots of Equations at
Convergence. MAA Mathematical Sciences Digital
Library.

385
John and Bettys Journey Through Complex Numbers
The Origin of Complex Numbers by John H. Mathews and Russell W. Howell
Dimensions: a math lm. Chapter 5 presents an introduction to complex arithmetic and stereographic
projection. Chapter 6 discusses transformations of
the complex plane, Julia sets, and the Mandelbrot
set.

Chapter 80

Imaginary unit
systems engineering, the imaginary unit is normally denoted by j instead of i, because i is commonly used to
denote electric current.

+i

For the history of the imaginary unit, see Complex number History.

80.1 Denition
1

+1
The imaginary number i is dened solely by the property
that its square is 1:

i2 = 1 .
With i dened this way, it follows directly from algebra
that i and i are both square roots of 1.

i in the complex or cartesian plane. Real numbers lie on the horizontal axis, and imaginary numbers lie on the vertical axis

The imaginary unit or unit imaginary number (i) is

a solution to the quadratic equation x2 + 1 = 0. Since
there is no real number with this property, it extends the
real numbers, and under the assumption that the familiar
properties of addition and multiplication (namely closure,
associativity, commutativity and distributivity) continue
to hold for this extension, the complex numbers are generated by including it.
Imaginary numbers are an important mathematical concept, which extends the real number system to the complex number system , which in turn provides at least
one root for every nonconstant polynomial P(x). (See
Algebraic closure and Fundamental theorem of algebra.)
The term "imaginary" is used because there is no real
number having a negative square.

Although the construction is called imaginary, and although the concept of an imaginary number may be intuitively more dicult to grasp than that of a real number, the construction is perfectly valid from a mathematical standpoint. Real number operations can be extended
to imaginary and complex numbers by treating i as an
unknown quantity while manipulating an expression, and
then using the denition to replace any occurrence of i2
with 1. Higher integral powers of i can also be replaced
with i, 1, i, or 1:

i3 = i2 i = (1)i = i
i4 = i3 i = (i)i = (i2 ) = (1) = 1
i5 = i4 i = (1)i = i
Similarly, as with any non-zero real number:

There are two complex square roots of 1, namely i and

i, just as there are two complex square roots of every i0 = i11 = i1 i1 = i1 1 = i 1 = i = 1
i
i
i
real number other than zero, which has one double square
root.
As a complex number, i is represented in rectangular
In contexts where i is ambiguous or problematic, j or the form as 0 + i, having a unit imaginary component and no
Greek is sometimes used (see Alternative notations). real component (i.e., the real component is zero). In polar
In the disciplines of electrical engineering and control form, i is represented as 1 ei/2 , having an absolute value
386

80.3. PROPER USE

387

(or magnitude) of 1 and an argument (or angle) of /2 . In

the complex plane (also known as the Cartesian plane),
i is the point located one unit from the origin along the
imaginary axis (which is at a right angle to the real axis).

the automorphism group of the special orthogonal group

SO (2, R) has exactly 2 elements the identity and the
automorphism which exchanges CW (clockwise) and
CCW (counter-clockwise) rotations. See orthogonal
group.

All these ambiguities can be solved by adopting a more

rigorous denition of complex number, and explicitly
choosing one of the solutions to the equation to be the
Being a quadratic polynomial with no multiple root, the imaginary unit. For example, the ordered pair (0, 1), in
dening equation x2 = 1 has two distinct solutions, the usual construction of the complex numbers with twowhich are equally valid and which happen to be additive dimensional vectors.
and multiplicative inverses of each other. More precisely,
once a solution i of the equation has been xed, the value
i, which is distinct from i, is also a solution. Since the 80.3 Proper use
equation is the only denition of i, it appears that the definition is ambiguous (more precisely, not well-dened).
However, no ambiguity results as long as one or other of The imaginary unit is sometimes written 1 in advanced
the solutions is chosen and labelled as i, with the other mathematics contexts (as well as in less advanced popular
one then being labelled as i. This is because, although i texts). However, great care needs to be taken when maand i are not quantitatively equivalent (they are negatives nipulating formulas involving radicals. The radical sign
of each other), there is no algebraic dierence between notation is reserved either for the principal square root
i and i. Both imaginary numbers have equal claim to function, which is only dened for real x 0, or for the
being the number whose square is 1. If all mathemati- principal branch of the complex square root function. Atcal textbooks and published literature referring to imagi- tempting to apply the calculation rules of the principal
nary or complex numbers were rewritten with i replac- (real) square root function to manipulate the principal
ing every occurrence of +i (and therefore every occur- branch of the complex square root function can produce
rence of i replaced by (i) = +i), all facts and theorems false results:
would continue to be equivalently valid. The distinction

1
between the two roots x of x2 + 1 = 0 with one of them
= i i = 1 1 = (1) (1) =
labelled with a minus sign is purely a notational relic; nei1 = 1 (incorrect).
ther root can be said to be more primary or fundamental
than the other, and neither of them is positive or negSimilarly:
ative.

The issue can be a subtle one. The most precise expla

1
1
1
1 =
1 = i
=
i =
1
1 =
nation is to say that although the complex eld, dened
1
2
(incorrect).
as R[x]/(x + 1), (see complex number) is unique up to
isomorphism, it is not unique up to a unique isomorphism
there are exactly 2 eld automorphisms of R[x]/(x2 + The calculation rules
1) which keep each real number xed: the identity and
the automorphism sending x to x. See also Complex

conjugate and Galois group.
a b= ab
A similar issue arises if the complex numbers are interpreted as 2 2 real matrices (see matrix representation and
of complex numbers), because then both

80.2 i and i

(
X=

)
(
)
0 1
0 1
and X =
1
0
1 0

are solutions to the matrix equation

X 2 = I =

(
1
0

0
1

)
=

(
)
1
0
.
0 1

In this case, the ambiguity results from the geometric

choice of which direction around the unit circle is positive rotation. A more precise explanation is to say that

a
a
=
b
b
are only valid for real, non-negative values of a and b.[1]
These problems are avoided by writing and manipulating
expressions like i7, rather than 7. For a more thorough discussion, see Square root and Branch point.

80.4 Properties

388

CHAPTER 80. IMAGINARY UNIT

(
)2
( )2
2
2

(1 + i)
=
(1 + i)2
2
2

+i

1
(1 + 2i + i2 )
2
1
= (1 + 2i 1)
2
= i.
=

+1

Using the radical sign for the principal square root gives:

i=

2
(1 + i).
2

80.4.2 Cube roots

The two square roots of i in the complex plane

The three cube roots of i are:

i,

+i

3
i
+ ,
2
2

i
3

+ .
2
2
Similar to all of the roots of 1, all of the roots of i are
the vertices of regular polygons inscribed within the unit
circle in the complex plane.
+

+1

80.4.3 Multiplication and division

i

Multiplying a complex number by i gives:

i (a + bi) = ai + bi2 = b + ai.

The three cube roots of i in the complex plane

80.4.1

Square roots

i has two square roots, just like all complex numbers (except zero, which has a double root). These two roots can
be expressed as the complex numbers:[nb 1]

(This is equivalent to a 90 counter-clockwise rotation of

a vector about the origin in the complex plane.)
Dividing by i is equivalent to multiplying by the reciprocal
of i:

1
1 i
i
i
= = 2 =
= i.
i
i i
i
1
Using this identity to generalize division by i to all complex numbers gives:

(
)

2
2
2

+
i =
(1 + i).
2
2
2

Indeed, squaring both expressions:

a + bi
= i (a + bi) = ai bi2 = b ai.
i
(This is equivalent to a 90 clockwise rotation of a vector
about the origin in the complex plane.)

80.5. ALTERNATIVE NOTATIONS

80.4.4

Powers

389
surface the function is dened on in practice. Listed below are results for the most commonly chosen branch.

The powers of i repeat in a cycle expressible with the folA number raised to the ni power is:
lowing pattern, where n is any integer:
xni = cos(n ln x) + i sin(n ln x).

i4n = 1

The nith root of a number is:

i4n+1 = i
i4n+2 = 1
4n+3

x = cos

= i.

ni

This leads to the conclusion that

in = in mod 4

ln x
n

(
i sin

ln x
n

)
.

The imaginary-base logarithm of a number is:

logi (x) =

2 ln x
.
i

where mod represents the modulo operation. EquivaAs with any complex logarithm, the log base i is not
lently:
uniquely dened.
in = cos(n/2) + i sin(n/2)

The cosine of i is a real number:

e + 1/e
e2 + 1
=
1.54308064....
2
2e

i raised to the power of i

cos(i) = cosh(1) =

Making use of Eulers formula, ii is

And the sine of i is purely imaginary:

(
)i
2
ii = ei(/2+2k) = ei (/2+2k) = e(/2+2k)

sin(i) = i sinh(1) =

e 1/e
e2 1
i=
i 1.17520119 i....
2
2e

where k Z , the set of integers.

The principal value (for k = 0) is e/2 or approximately
0.207879576...[2]

80.4.5

Factorial

The factorial of the imaginary unit i is most often given

in terms of the gamma function evaluated at 1 + i:

i! = (1 + i) 0.4980 0.1549i.
Also,
|i!| =

80.4.6

[3]
sinh

Other operations

80.5 Alternative notations

In electrical engineering and related elds, the imaginary unit is normally denoted by j to avoid confusion with electric current as a function of time, traditionally denoted by i(t) or just i. The Python programming language also uses j to mark the imaginary part of a complex number. MATLAB associates both i and j with the imaginary unit, although 1i or 1j is preferable, for speed and improved
robustness.[4]
Some texts use the Greek letter iota () for the imaginary unit, to avoid confusion, especially with index
and subscripts.
Each of i, j, and k is an imaginary unit in the
quaternions. In bivectors and biquaternions an additional imaginary unit h is used.

Many mathematical operations that can be carried out

with real numbers can also be carried out with i, such
as exponentiation, roots, logarithms, and trigonometric 80.6 Matrices
functions. However, it should be noted that all of the following functions are complex multi-valued functions, and When 2 2 real matrices m are used for a source, and the
it should be clearly stated which branch of the Riemann number one (1) is identied with the identity matrix, and

390

CHAPTER 80. IMAGINARY UNIT

minus one (1) with the negative of the identity matrix,

then there are many solutions to m2 = 1. In fact, there
are many solutions to m2 = +1 and m2 = 0 also. Any such
m can be taken as a basis vector, along with 1, to form a
planar algebra.

80.7 See also

80.9 References
[1] Nahin, Paul J. (2010). An Imaginary Tale: The Story of
i [the square root of minus one]. Princeton University
Press. p. 12. ISBN 978-1-4008-3029-9. Extract of page
12
[2] The Penguin Dictionary of Curious and Interesting Numbers by David Wells, Page 26.
[3] "abs(i!)", WolframAlpha.

Complex plane

[4] MATLAB Product Documentation.

Imaginary number
Multiplicity (mathematics)
Root of unity
Unit complex number

80.8 Notes
[1] To nd such a number, one can solve the equation
(x + iy)2 = i
where x and y are real parameters to be determined, or
equivalently
x2 + 2ixy y2 = i.
Because the real and imaginary parts are always separate,
we regroup the terms:
x2 y2 + 2ixy = 0 + i
and by equating coecients, real part and real coecient
of imaginary part separately, we get a system of two equations:
x2 y2 = 0
2xy = 1.
Substituting y = 1/2x into the rst equation, we get
x2 1/4x2 = 0
x2 = 1/4x2
4x4 = 1
Because x is a real number, this equation has two real solutions for x: x = 1/2 and x = 1/2. Substituting either of
these results into the equation 2xy = 1 in turn, we will get
the corresponding result for y. Thus, the square roots of i
are the numbers 1/2 + i/2 and 1/2 i/2. (University
of Toronto Mathematics Network: What is the square root
of i? URL retrieved March 26, 2007.)

80.10 Further reading

Nahin, Paul J. (1998). An Imaginary Tale: The
Story of 1. Chichester: Princeton University
Press. ISBN 0-691-02795-1.

80.11 External links

Eulers work on Imaginary Roots of Polynomials at
Convergence

Chapter 81

Passband
A passband is the range of frequencies or wavelengths
that can pass through a lter. For example, a radio receiver contains a bandpass lter to select the frequency of
the desired radio signal out of all the radio waves picked
up by its antenna. The passband of a receiver is the range
of frequencies it can receive.
A bandpass-ltered signal (that is, a signal with energy
only in a passband), is known as a bandpass signal, in
contrast to a baseband signal.[1]

81.1 Filters
In telecommunications, optics, and acoustics, a passband
(a band-pass ltered signal) is the portion of the frequency
spectrum that is transmitted (with minimum relative loss
or maximum relative gain) by some ltering device. In
other words, it is a band of frequencies which passes
through some lter or set of lters. The accompanying
gure shows a schematic of a waveform being ltered by
a bandpass lter consisting of a highpass and a lowpass
lter.
Radio receivers generally include a tunable band-pass lter with a passband that is wide enough to accommodate
the bandwidth of the radio signal transmitted by a single
station.

81.2 Digital transmission

There are two main categories of digital communication
transmission methods: baseband and passband.

Unrestricted signal (upper diagram). Bandpass lter applied to

signal (middle diagram). Resulting passband signal (bottom diagram). A(f) is the frequency function of the signal or lter in
arbitrary units.

In baseband transmission, line coding is utilized,

resulting in a pulse train or pulse amplitude modulated (PAM) signal. This is typically used over nonltered wires such as ber optical cables and shortrange copper links, for example: V.29 (EIA/TIA232), V.35, IEEE 802.3, SONET/SDH.
In passband transmission, digital modulation
methods are employed so that only a limited frequency range is used in some bandpass ltered
391

channel. Passband transmission is typically utilized in wireless communication and in bandpass ltered channels such as POTS lines. It also allows
for frequency-division multiplexing. The digital bit
stream is converted rst into an equivalent baseband
signal, and then to a RF signal. On the receiver side a
demodulator is used to detect the signal and reverse
the modulation process. A combined equipment for
modulation and demodulation is called a modem.

392

81.3 Details
In general, there is an inverse relationship between the
width of a lters passband and the time required for the
lter to respond to new inputs. Broad passbands yield
faster response. This is a consequence of the mathematics
of Fourier analysis.
The limiting frequencies of a passband are dened as
those at which the relative intensity or power decreases to
a specied fraction of the maximum intensity or power.
This decrease in power is often specied to be the halfpower points, i.e., 3 dB below the maximum power.
The dierence between the limiting frequencies is called
the bandwidth, and is expressed in hertz (in the optical regime, in nanometers or micrometers of dierential
wavelength).
The related term "bandpass" is an adjective that describes
a type of lter or ltering process; it is frequently confused with passband, which refers to the actual portion
of aected spectrum. The two words are both compound
words that follow the English rules of formation: the primary meaning is the latter part of the compound, while
the modier is the rst part. Hence, one may correctly
say 'A dual bandpass lter has two passbands.

81.4 See also

Stopband
10PASS-TS

81.5 References
[1] Belle A. Shenoi (2006). Introduction to digital signal processing and lter design. John Wiley and Sons. p. 120.
ISBN 978-0-471-46482-2.

This article incorporates public domain material from

the General Services Administration document Federal
Standard 1037C (in support of MIL-STD-188).

CHAPTER 81. PASSBAND

Chapter 82

Radio frequency
RF currents applied to the body often do not cause
the painful sensation of electric shock as do lower
frequency currents.[3][4] This is because the current
changes direction too quickly to trigger depolarization of nerve membranes.

This article is about the generic oscillation. For the

radiation, see Radio wave. For the electronics, see Radio
frequency engineering.
RF redirects here. For other uses, see RF (disambiguation).

RF current can easily ionize air, creating a conductive path through it. This property is exploited by
high frequency units used in electric arc welding,
which use currents at higher frequencies than power
distribution uses.

Radio frequency (RF) is any of the electromagnetic wave frequencies that lie in the range extending
from around 3 kHz to 300 GHz, which include those
frequencies used for communications or radar signals.[1]
RF usually refers to electrical rather than mechanical oscillations. However, mechanical RF systems do exist (see
mechanical lter and RF MEMS).

Another property is the ability to appear to ow

through paths that contain insulating material, like
the dielectric insulator of a capacitor. This is because capacitive reactance in a circuit decreases with
frequency.

Although radio frequency is a rate of oscillation, the term

radio frequency or its abbreviation RF are used as a
synonym for radio i.e., to describe the use of wireless
communication, as opposed to communication via electric wires. Examples include:

In contrast, RF current can be blocked by a coil of

wire, or even a single turn or bend in a wire. This is
because the inductive reactance of a circuit increases
with frequency.

Radio-frequency identication
ISO/IEC 144432 Radio frequency power and signal interface[2]

When conducted by an ordinary electric cable, RF

current has a tendency to reect from discontinuities in the cable such as connectors and travel back
down the cable toward the source, causing a condition called standing waves. Therefore, RF current
must be carried by specialized types of cable called
transmission line.

82.1 Special properties of RF current

Electric currents that oscillate at radio frequencies
have special properties not shared by direct current or
alternating current of lower frequencies.

82.2 Radio communication

The energy in an RF current can radiate o a con- To receive radio signals an antenna must be used. Howductor into space as electromagnetic waves (radio ever, since the antenna will pick up thousands of radio
signals at a time, a radio tuner is necessary to tune into a
waves); this is the basis of radio technology.
particular frequency (or frequency range).[5] This is typ RF current does not penetrate deeply into electri- ically done via a resonator in its simplest form, a circal conductors but tends to ow along their surfaces; cuit with a capacitor and an inductor form a tuned cirthis is known as the skin eect. For this reason, cuit. The resonator amplies oscillations within a particwhen the human body comes in contact with high ular frequency band, while reducing oscillations at other
power RF currents it can cause supercial but seri- frequencies outside the band. Another method to isolate
ous burns called RF burns (Note that RF burns result a particular radio frequency is by oversampling (which
from electrical energy, while Radiation burns result gets a wide range of frequencies) and picking out the frefrom electromagnetic energy).
quencies of interest, as done in software dened radio.
393

394
The distance over which radio communications is useful depends signicantly on things other than wavelength,
such as transmitter power, receiver quality, type, size, and
height of antenna, mode of transmission, noise, and interfering signals. Ground waves, tropospheric scatter and
skywaves can all achieve greater ranges than line-of-sight
propagation. The study of radio propagation allows estimates of useful range to be made.

CHAPTER 82. RADIO FREQUENCY

82.5.1 Extremely low frequency RF

High-power extremely low frequency RF with electric
eld levels in the low kV/m range are known to induce
perceivable currents within the human body that create an annoying tingling sensation. These currents will
typically ow to ground through a body contact surface
such as the feet, or arc to ground where the body is well
insulated.[10][11]

82.3 Frequency bands

Main article: Radio spectrum

82.5.2 Microwaves
Main article: Microwave burn

82.4 In medicine

Microwave exposure at low-power levels below the

Specic absorption rate set by government regulatory
bodies are considered harmless non-ionizing radiation
and have no eect on the human body. However, levels
above the Specic absorption rate set by the U.S. Federal
Communications Commission are considered potentially
harmful (see Mobile phone radiation and health).

Radio frequency (RF) energy, in the form of radiating

waves or electrical currents, has been used in medical
treatments for over 75 years,[7] generally for minimally
invasive surgeries using radiofrequency ablation including the treatment of sleep apnea.[8] Magnetic resonance
imaging (MRI) uses radio frequency waves to generate Long-term human exposure to high-levels of microwaves
images of the human body.
is recognized to cause cataracts according to experiRadio frequencies at non-ablation energy levels are some- mental animal studies and epidemiological studies. The
times used as a form of cosmetic treatment that can mechanism is unclear but may include changes in heat
tighten skin, reduce fat (lipolysis), or promote healing.[9] sensitive enzymes that normally protect cell proteins in
the lens. Another mechanism that has been advanced is
RF diathermy is a medical treatment that uses RF indirect damage to the lens from pressure waves induced in
duced heat as a form of physical or occupational therthe aqueous humor.
apy and in surgical procedures. It is commonly used for
muscle relaxation. It is also a method of heating tissue High-power exposure to microwave RF is known to creelectromagnetically for therapeutic purposes in medicine. ate a range of eects from lower to higher power levels,
Diathermy is used in physical therapy and occupational ranging from unpleasant burning sensation on the skin
therapy to deliver moderate heat directly to pathologic le- and microwave auditory eect, to extreme pain at the
sions in the deeper tissues of the body. Surgically, the mid-range, to physical burning and blistering of skin and
extreme heat that can be produced by diathermy may internals at high power levels (see microwave burn).
be used to destroy neoplasms, warts, and infected tissues, and to cauterize blood vessels to prevent excessive bleeding. The technique is particularly valuable in
neurosurgery and surgery of the eye. Diathermy equip82.5.3 General RF exposure
ment typically operates in the short-wave radio frequency
(range 1100 MHz) or microwave energy (range 434
The 1999 revision of Canadian Safety Code 6 recom915 MHz).
mended electric eld limits of 100 kV/m for pulsed EMF
Pulsed electromagnetic eld therapy (PEMF) is a medi- to prevent air breakdown and spark discharges, mencal treatment that purportedly helps to heal bone tissue re- tioning rationale related to auditory eect and energyported in a recent NASA study. This method usually em- induced unconsciousness in rats.[12] The pulsed EMF
ploys electromagnetic radiation of dierent frequencies limit was removed in later revisions, however.[13]
- ranging from static magnetic elds, through extremely
low frequencies (ELF) to higher radio frequencies (RF) For health eects see electromagnetic radiation and
health.
administered in pulses.
For high-power RF (electromagnetic, not electrical) exposure see radiation burn.

82.5 Eects on the human body

For low-power RF exposure see radiation-induced cancer.

82.9. REFERENCES

82.6 As a weapon
See also: Directed energy weapons Microwave weapons

395
Frequency allocation
Frequency bandwidth
Frequency modulation

A heat ray is an RF harassment device that makes use of

microwave radio frequencies to create an unpleasant heating eect in the upper layer of the skin. A publicly known
heat ray weapon called the Active Denial System was developed by the US military as an experimental weapon to
deny the enemy access to an area. A death ray is a weapon
that delivers heat ray electromagnetic energy at levels that
injure human tissue. The inventor of the death ray, Harry
Grindell Matthews, claims to have lost sight in his left eye
while developing his death ray weapon based on a primitive microwave magnetron from the 1920s (note that a
typical microwave oven induces a tissue damaging cooking eect inside the oven at about 2 kV/m.)

82.7 Measurement
Since radio frequency radiation has both an electric and a
magnetic component, it is often convenient to express intensity of radiation eld in terms of units specic to each
component. The unit volts per meter (V/m) is used for the
electric component, and the unit amperes per meter (A/m)
is used for the magnetic component. One can speak of an
electromagnetic eld, and these units are used to provide
information about the levels of electric and magnetic eld
strength at a measurement location.

Plastic welding
Pulsed electromagnetic eld therapy
Spectrum management

82.9 References
[1] Denition of RADIO FREQUENCY.
MerriamWebster. Encyclopdia Britannica. n.d. Retrieved 6 August 2015.
[2] ISO/IEC 14443-2:2001 Identication cards Contactless integrated circuit(s) cards Proximity cards Part
2: Radio frequency power and signal interface. Iso.org.
2010-08-19. Retrieved 2011-11-08.
[3] Curtis, Thomas Stanley (1916). High Frequency Apparatus: Its Construction and Practical Application. USA:
Everyday Mechanics Company. p. 6.
[4] Mieny, C. J. (2003). Principles of Surgical Patient
Care (2nd ed.). New Africa Books. p. 136. ISBN
9781869280055.
[5] Brain, Marshall (2000-12-07). How Radio Works.
HowStuWorks.com. Retrieved 2009-09-11.

Another commonly used unit for characterizing an RF [6]

electromagnetic eld is power density. Power density is
most accurately used when the point of measurement is
far enough away from the RF emitter to be located in what [7]
is referred to as the far eld zone of the radiation pattern.
In closer proximity to the transmitter, i.e., in the near
eld zone, the physical relationships between the electric and magnetic components of the eld can be com- [8]
plex, and it is best to use the eld strength units discussed
above. Power density is measured in terms of power per
unit area, for example, milliwatts per square centimeter [9]
(mW/cm). When speaking of frequencies in the microwave range and higher, power density is usually used to
express intensity since exposures that might occur would
[10]
likely be in the far eld zone.

82.8 See also

Amplitude modulation
Electromagnetic Interference
Electromagnetic radiation
Electromagnetic spectrum
EMF measurement

Jerey S. Beasley; Gary M. Miller (2008). Modern Electronic Communication (9th ed.). pp. 45. ISBN 9780132251136.
Ruey J. Sung & Michael R. Lauer (2000). Fundamental
approaches to the management of cardiac arrhythmias.
Springer. p. 153. ISBN 978-0-7923-6559-4.
Melvin A. Shiman, Sid J. Mirrafati, Samuel M. Lam and
Chelso G. Cueteaux (2007). Simplied Facial Rejuvenation. Springer. p. 157. ISBN 978-3-540-71096-7.
Noninvasive Radio Frequency for Skin Tightening and
Body Contouring, Frontline Medical Communications,
2013
Limits of Human Exposure to Radiofrequency Electromagnetic Fields in the Frequency Range from 3 kHz to
300 GHz, Canada Safety Code 6, page 63

[11] Extremely Low Frequency Fields Environmental Health

Criteria Monograph No.238, chapter 5, page 121, WHO
[12] Limits of Human Exposure to Radiofrequency Electromagnetic Fields in the Frequency Range from 3 kHz to
300 GHz, Canada Safety Code 6,page 62
[13] http://www.hc-sc.gc.ca/ewh-semt/pubs/radiation/radio_
guide-lignes_direct/index-eng.php Safety Code 6:
Health Canadas Radiofrequency Exposure Guidelines Environmental and Workplace Health - Health Canada

396

82.10 External links

Denition of frequency bands (VLF, ELF etc.)
IK1QFK Home Page (vlf.it)
Radio, light, and sound waves, conversion between
wavelength and frequency
RF Terms Glossary

CHAPTER 82. RADIO FREQUENCY

Chapter 83

Pulse shaping
In electronics and telecommunications, pulse shaping way to do this is to start with a slower-rising pulse, and
is the process of changing the waveform of transmitted decrease the rise time, for example with a step recovery
pulses. Its purpose is to make the transmitted signal bet- diode circuit.
ter suited to its purpose or the communication channel,
typically by limiting the eective bandwidth of the transmission. By ltering the transmitted pulses this way, the 83.2 Pulse shaping lters
intersymbol interference caused by the channel can be
kept in control. In RF communication, pulse shaping is
essential for making the signal t in its frequency band.
Typically pulse shaping occurs after line coding and
modulation.

83.1 Need for pulse shaping

Transmitting a signal at high modulation rate through
a band-limited channel can create intersymbol interference. As the modulation rate increases, the signals bandwidth increases. When the signals bandwidth becomes
larger than the channel bandwidth, the channel starts to
introduce distortion to the signal. This distortion usually
manifests itself as intersymbol interference.

A typical NRZ coded signal is implicitly ltered with a sinc lter.

Not every lter can be used as a pulse shaping lter. The

lter itself must not introduce intersymbol interference
it needs to satisfy certain criteria. The Nyquist ISI
criterion is a commonly used criterion for evaluation, beThe signals spectrum is determined by the pulse shap- cause it relates the frequency spectrum of the transmitter
ing lter used by the transmitter. Usually the transmit- signal to intersymbol interference.
ted symbols are represented as a time sequence of dirac
delta pulses. This theoretical signal is then ltered with Examples of pulse shaping lters that are commonly
the pulse shaping lter, producing the transmitted signal. found in communication systems are:
The spectrum of the transmission is thus determined by
Sinc shaped lter
the lter.
In many base band communication systems the pulse
shaping lter is implicitly a boxcar lter. Its Fourier transform is of the form sin(x)/x, and has signicant signal
power at frequencies higher than symbol rate. This is
not a big problem when optical bre or even twisted pair
cable is used as the communication channel. However,
in RF communications this would waste bandwidth, and
only tightly specied frequency bands are used for single
transmissions. In other words, the channel for the signal
is band-limited. Therefore better lters have been developed, which attempt to minimise the bandwidth needed
for a certain symbol rate.

Raised-cosine lter
Gaussian lter
Sender side pulse shaping is often combined with a receiver side matched lter to achieve optimum tolerance
for noise in the system. In this case the pulse shaping is
equally distributed between the sender and receiver lters. The lters amplitude responses are thus pointwise
square roots of the system lters.

Other approaches that eliminate complex pulse shaping

lters have been invented. In OFDM, the carriers are
An example in other areas of electronics is the genera- modulated so slowly that each carrier is virtually unaftion of pulses where the rise time need to be short; one fected by the bandwidth limitation of the channel.
397

398

83.2.1

CHAPTER 83. PULSE SHAPING

Sinc lter

Main article: sinc lter

It is also called as Boxcar lter as its frequency domain

83.4 References
John G. Proakis, "Digital Communications, 3rd Edition" Chapter 9, McGraw-Hill Book Co., 1995.
ISBN 0-07-113814-5
National Instruments Signal Generator Tutorial,
Pulse Shaping to Improve Spectral Eciency
National Instruments Measurement Fundamentals
Tutorial, Pulse-Shape Filtering in Communications
Systems

Amplitude response of raised-cosine lter with various roll-o

factors

equivalent is a rectangular shape. Theoretically the best

pulse shaping lter would be the sinc lter, but it cannot
be implemented precisely. It is a non-causal lter with
relatively slowly decaying tails. It is also problematic from
a synchronisation point of view as any phase error results
in steeply increasing intersymbol interference.

83.2.2

Raised-cosine lter

Main article: raised-cosine lter

Raised-cosine lters are practical to implement and they
are in wide use. They have a congurable excess bandwidth, so communication systems can choose a trade o
between a simpler lter and spectral eciency.

83.2.3

Gaussian lter

Main article: Gaussian lter

This gives an output pulse shaped like a Gaussian function.

83.3 See also

Nyquist ISI criterion
Raised-cosine lter
Matched lter
Femtosecond pulse shaping
Pulse (signal processing)

Chapter 84

Digital signal processing

See also: Digital signal processor

numbers to integers is an example.

Digital signal processing (DSP) is the use of digital processing, such as by computers, to perform a wide variety
of signal processing operations. The signals processed
in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such
as time, space, or frequency.

The NyquistShannon sampling theorem states that a signal can be exactly reconstructed from its samples if the
sampling frequency is greater than twice the highest frequency of the signal, but this requires an innite number
of samples. In practice, the sampling frequency is often
signicantly higher than twice that required by the signals limited bandwidth.

Digital signal processing and analog signal processing

are subelds of signal processing. DSP applications include audio and speech signal processing, sonar, radar
and other sensor array processing, spectral estimation,
statistical signal processing, digital image processing, signal processing for telecommunications, control of systems, biomedical engineering, seismic data processing,
among others.

Theoretical DSP analyses and derivations are typically

performed on discrete-time signal models with no amplitude inaccuracies (quantization error), created by the
abstract process of sampling. Numerical methods require
a quantized signal, such as those produced by an analogto-digital converter (ADC). The processed result might
be a frequency spectrum or a set of statistics. But often it
is another quantized signal that is converted back to anaDigital signal processing can involve linear or nonlinear log form by a digital-to-analog converter (DAC).
operations. Nonlinear signal processing is closely related
to nonlinear system identication[1] and can be implemented in the time, frequency, and spatio-temporal do- 84.2 Domains
mains.
The application of digital computation to signal processing allows for many advantages over analog processing in
many applications, such as error detection and correction
in transmission as well as data compression.[2] DSP is applicable to both streaming data and static (stored) data.

84.1 Signal sampling

Main article: Sampling (signal processing)
The increasing use of computers has resulted in the increased use of, and need for, digital signal processing. To
digitally analyze and manipulate an analog signal, it must
be digitized with an analog-to-digital converter. Sampling is usually carried out in two stages, discretization
and quantization. Discretization means that the signal
is divided into equal intervals of time, and each interval is represented by a single measurement of amplitude.
Quantization means each amplitude measurement is approximated by a value from a nite set. Rounding real

In DSP, engineers usually study digital signals in

one of the following domains: time domain (onedimensional signals), spatial domain (multidimensional
signals), frequency domain, and wavelet domains. They
choose the domain in which to process a signal by making an informed assumption (or by trying dierent possibilities) as to which domain best represents the essential characteristics of the signal. A sequence of samples
from a measuring device produces a temporal or spatial
domain representation, whereas a discrete Fourier transform produces the frequency domain information, that is,
the frequency spectrum.

84.2.1 Time and space domains

Main article: Time domain
The most common processing approach in the time or
space domain is enhancement of the input signal through
a method called ltering. Digital ltering generally consists of some linear transformation of a number of sur-

399

400

CHAPTER 84. DIGITAL SIGNAL PROCESSING

rounding samples around the current sample of the input engineer can study the spectrum to determine which freor output signal. There are various ways to characterize quencies are present in the input signal and which are
lters; for example:
missing.
A linear lter is a linear transformation of input
samples; other lters are non-linear. Linear lters
satisfy the superposition condition, i.e. if an input
is a weighted linear combination of dierent signals,
the output is a similarly weighted linear combination
of the corresponding output signals.

In addition to frequency information, phase information

is often needed. This can be obtained from the Fourier
transform. With some applications, how the phase varies
with frequency can be a signicant consideration.

Filtering, particularly in non-realtime work can also be

achieved by converting to the frequency domain, applying the lter and then converting back to the time domain.
This is a fast, O(n log n) operation, and can give essen A causal lter uses only previous samples of the
tially any lter shape including excellent approximations
input or output signals; while a non-causal lter
to brickwall lters.
uses future input samples. A non-causal lter can
usually be changed into a causal lter by adding a There are some commonly used frequency domain transformations. For example, the cepstrum converts a signal
delay to it.
to the frequency domain through Fourier transform, takes
A time-invariant lter has constant properties over the logarithm, then applies another Fourier transform.
time; other lters such as adaptive lters change in This emphasizes the harmonic structure of the original
time.
spectrum.
A stable lter produces an output that converges Frequency domain analysis is also called spectrum- or
to a constant value with time, or remains bounded spectral analysis.
within a nite interval. An unstable lter can
produce an output that grows without bounds, with
84.2.3 Z-plane analysis
bounded or even zero input.
Digital lters come in both IIR and FIR types. FIR lters
have many advantages, but are computationally more demanding. Whereas FIR lters are always stable, IIR lters have feedback loops that may resonate when stimulated with certain input signals. The Z-transform provides
a tool for analyzing potential stability issues of digital IIR
lters. It is analogous to the Laplace transform, which is
A lter can be represented by a block diagram, which can
used to design analog IIR lters.
then be used to derive a sample processing algorithm to
implement the lter with hardware instructions. A lter
may also be described as a dierence equation, a collec84.2.4 Wavelet
tion of zeroes and poles or, if it is an FIR lter, an impulse
response or step response.
In numerical analysis and functional analysis, a discrete
The output of a linear digital lter to any given input wavelet transform (DWT) is any wavelet transform for
may be calculated by convolving the input signal with the which the wavelets are discretely sampled. As with other
impulse response.
wavelet transforms, a key advantage it has over Fourier
transforms is temporal resolution: it captures both frequency and location information.[lower-alpha 1]
A nite impulse response (FIR) lter uses only the
input signals, while an innite impulse response
lter (IIR) uses both the input signal and previous
samples of the output signal. FIR lters are always
stable, while IIR lters may be unstable.

84.2.2

Frequency domain

Main article: Frequency domain

Signals are converted from time or space domain to the
frequency domain usually through the Fourier transform.
The Fourier transform converts the signal information to
a magnitude and phase component of each frequency.
Often the Fourier transform is converted to the power
spectrum, which is the magnitude of each frequency component squared.

84.3 Applications

The main applications of DSP are audio signal processing, audio compression, digital image processing, video
compression, speech processing, speech recognition,
digital communications, digital synthesizers, radar, sonar,
nancial signal processing, seismology and biomedicine.
Specic examples are speech compression and transmission in digital mobile phones, room correction of
The most common purpose for analysis of signals in the sound in hi- and sound reinforcement applications,
frequency domain is analysis of signal properties. The weather forecasting, economic forecasting, seismic data

84.5. TECHNIQUES

401
tographs with software such as Photoshop.
However, when the application requirement is real-time,
DSP is often implemented using specialized microprocessors such as the DSP56000, the TMS320, or the
SHARC. These often process data using xed-point
arithmetic, though some more powerful versions use
oating point. For faster applications FPGAs[4] might be
used. Beginning in 2007, multicore implementations of
DSPs have started to emerge from companies including
Freescale and Stream Processors, Inc. For faster applications with vast usage, ASICs might be designed specifically. For slow applications, a traditional slower processor such as a microcontroller may be adequate. Also
a growing number of DSP applications are now being
implemented on embedded systems using powerful PCs
with multi-core processors.

An example of the 2D discrete wavelet transform that is used

in JPEG2000. The original image is high-pass ltered, yielding
the three large images, each describing local changes in brightness (details) in the original image. It is then low-pass ltered
and downscaled, yielding an approximation image; this image is
high-pass ltered to produce the three smaller detail images, and
low-pass ltered to produce the nal approximation image in the
upper-left.

processing, analysis and control of industrial processes,

medical imaging such as CAT scans and MRI, MP3 compression, computer graphics, image manipulation, hi-
loudspeaker crossovers and equalization, and audio effects for use with electric guitar ampliers.

84.5 Techniques
Bilinear transform
Discrete Fourier transform
Discrete-time Fourier transform
Filter design
LTI system theory
Minimum phase
Transfer function
Z-transform
Goertzel algorithm

84.4 Implementation
DSP algorithms have long been run on general-purpose
computers and digital signal processors. DSP algorithms
are also implemented on purpose-built hardware such
as application-specic integrated circuit (ASICs). Additional technologies for digital signal processing include
more powerful general purpose microprocessors, eldprogrammable gate arrays (FPGAs), digital signal controllers (mostly for industrial applications such as motor
control), and stream processors.[3]

s-plane

84.6 Related elds

Analog signal processing
Automatic control
Computer Engineering
Computer science

Depending on the requirements of the application, digital

signal processing tasks can be implemented on general
purpose computers.

Data compression

Often when the processing requirement is not real-time,

processing is economically done with an existing generalpurpose computer and the signal data (either input or output) exists in data les. This is essentially no dierent
from any other data processing, except DSP mathematical techniques (such as the FFT) are used, and the sampled data is usually assumed to be uniformly sampled
in time or space. For example: processing digital pho-

Electrical engineering

Dataow programming

Fourier analysis
Information theory
Machine learning
Real-time computing

402
Stream processing
Telecommunication
Time series
Wavelet

84.7 Notes
[1] Location in this case can represent location in space or
location in time.

84.8 References
[1] Billings, Stephen A. (Sep 2013). Nonlinear System Identication: NARMAX Methods in the Time, Frequency, and
Spatio-Temporal Domains. UK: Wiley. ISBN 978-1-11994359-4.
[2] Broesch, James D.; Stranneby, Dag; Walker, William
(2008-10-20). Digital Signal Processing: Instant access
(1 ed.). Butterworth-Heinemann - Newnes. p. 3. ISBN
9780750689762.
[3] Stranneby, Dag; Walker, William (2004). Digital Signal
Processing and Applications (2nd ed.). Elsevier. ISBN 07506-6344-8.
[4] JpFix (2006). FPGA-Based Image Processing Accelerator. Retrieved 2008-05-10.

84.9 Further reading

N. Ahmed and K.R. Rao (1975). Orthogonal
Transforms for Digital Signal Processing. SpringerVerlag (Berlin Heidelberg New York), ISBN 3540-06556-3.
Jonathan M. Blackledge, Martin Turner: Digital Signal Processing: Mathematical and Computational
Methods, Software Development and Applications,
Horwood Publishing, ISBN 1-898563-48-9
James D. Broesch: Digital Signal Processing Demystied, Newnes, ISBN 1-878707-16-7
Paul M. Embree, Damon Danieli: C++ Algorithms
for Digital Signal Processing, Prentice Hall, ISBN 013-179144-3

CHAPTER 84. DIGITAL SIGNAL PROCESSING

Ashfaq Khan: Digital Signal Processing Fundamentals, Charles River Media, ISBN 1-58450-281-9
Sen M. Kuo, Woon-Seng Gan: Digital Signal Processors: Architectures, Implementations, and Applications, Prentice Hall, ISBN 0-13-035214-4
Paul A. Lynn, Wolfgang Fuerst: Introductory Digital
Signal Processing with Computer Applications, John
Wiley & Sons, ISBN 0-471-97984-8
Richard G. Lyons: Understanding Digital Signal
Processing, Prentice Hall, ISBN 0-13-108989-7
Vijay Madisetti, Douglas B. Williams: The Digital
Signal Processing Handbook, CRC Press, ISBN 08493-8572-5
James H. McClellan, Ronald W. Schafer, Mark A.
Yoder: Signal Processing First, Prentice Hall, ISBN
0-13-090999-8
Bernard Mulgrew, Peter Grant, John Thompson:
Digital Signal Processing - Concepts and Applications, Palgrave Macmillan, ISBN 0-333-96356-3
Boaz Porat: A Course in Digital Signal Processing,
Wiley, ISBN 0-471-14961-6
John G. Proakis, Dimitris Manolakis: Digital Signal Processing: Principles, Algorithms and Applications, 4th ed, Pearson, April 2006, ISBN 9780131873742
John G. Proakis: A Self-Study Guide for Digital Signal Processing, Prentice Hall, ISBN 0-13-143239-7
Charles A. Schuler: Digital Signal Processing: A
Hands-On Approach, McGraw-Hill, ISBN 0-07829744-3
Doug Smith: Digital Signal Processing Technology:
Essentials of the Communications Revolution, American Radio Relay League, ISBN 0-87259-819-5
Smith, Steven W. (2002). Digital Signal Processing: A Practical Guide for Engineers and Scientists.
Newnes. ISBN 0-7506-7444-X.

Hari Krishna Garg: Digital Signal Processing Algorithms, CRC Press, ISBN 0-8493-7178-3

Stein, Jonathan Yaakov (2000-10-09). Digital Signal Processing, a Computer Science Perspective. Wiley. ISBN 0-471-29546-9.

P. Gaydecki: Foundations Of Digital Signal Processing: Theory, Algorithms And Hardware Design,
Institution of Electrical Engineers, ISBN 0-85296431-5

Stergiopoulos, Stergios (2000). Advanced Signal

Processing Handbook: Theory and Implementation
for Radar, Sonar, and Medical Imaging Real-Time
Systems. CRC Press. ISBN 0-8493-3691-0.

84.9. FURTHER READING

Van De Vegte, Joyce (2001). Fundamentals of Digital Signal Processing. Prentice Hall. ISBN 0-13016077-6.

403

Chapter 85

Direct digital synthesizer

The reference oscillator provides a stable time base for
the system and determines the frequency accuracy of the
DDS. It provides the clock to the NCO which produces
at its output a discrete-time, quantized version of the desired output waveform (often a sinusoid) whose period is
controlled by the digital word contained in the Frequency
Control Register. The sampled, digital waveform is converted to an analog waveform by the DAC. The output reconstruction lter rejects the spectral replicas produced
by the zero-order hold inherent in the analog conversion
process.

85.2 Performance

A DDS function generator.

Direct digital synthesizer (DDS) is a type of frequency

synthesizer used for creating arbitrary waveforms from
a single, xed-frequency reference clock. Applications
of DDS include: signal generation, local oscillators in
communication systems, function generators, mixers,
modulators,[1] sound synthesizers and as part of a digital phase-locked loop.[2]

85.1 Overview

A DDS has many advantages over its analog counterpart,

the phase-locked loop (PLL), including much better frequency agility, improved phase noise, and precise control of the output phase across frequency switching transitions. Disadvantages include spurs due mainly to truncation eects in the NCO, crossing spurs resulting from
high order (>1) Nyquist images, and a higher noise oor
at large frequency osets due mainly to the Digital-toanalog converter.[6]
Because a DDS is a sampled system, in addition to the
desired waveform at output frequency F , Nyquist images are also generated (the primary image is at F -F ,
where F is the reference clock frequency). In order to
reject these undesired images, a DDS is generally used in
conjunction with an analog reconstruction lowpass lter
as shown in Figure 1.[7]

85.2.1 Frequency agility

The output frequency of a DDS is determined by the
value stored in the frequency control register (FCR) (see
Fig.1), which in turn controls the NCO's phase accumuFigure 1 - Direct Digital Synthesizer block diagram
lator step size. Because the NCO operates in the discretetime domain, it changes frequency instantaneously at the
A basic Direct Digital Synthesizer consists of a fre- clock edge coincident with a change in the value stored
quency reference (often a crystal or SAW oscillator), a in the FCR. The DDS output frequency settling time is
numerically controlled oscillator (NCO) and a digital-to- determined mainly by the phase response of the reconanalog converter (DAC) [3] as shown in Figure 1.
struction lter. An ideal reconstruction lter with a linear
404

85.5. EXTERNAL LINKS AND FURTHER READING

405

phase response (meaning the output is simply a delayed

version of the input signal) would allow instantaneous frequency response at its output because a linear system can
not create frequencies not present at its input.[8]

[5] Jane Radatz, The IEEE Standard Dictionary of Electrical

and Electronics Terms, IEEE Standards Oce, New York,
NY, 1997

85.2.2

[7] Kroupa,Venceslav F.,Direct Digital Frequency Synthesizers, IEEE Press, 1999, ISBN 0-7803-3438-8

Phase noise and jitter

The superior close-in phase noise performance of a DDS

stems from the fact that it is a feed-forward system. In
a traditional phase locked loop (PLL), the frequency divider in the feedback path acts to multiply the phase noise
of the reference oscillator and, within the PLL loop bandwidth, impresses this excess noise onto the VCO output. A DDS on the other hand, reduces the reference
clock phase noise by the ratio fclk /fo because its output
is derived by fractional division of the clock. Reference
clock jitter translates directly to the output, but this jitter
is a smaller percentage of the output period (by the ratio above). Since the maximum output frequency is limited to fclk /2 , the output phase noise at close-in osets
is always at least 6dB below the reference clock phasenoise.[6]
At osets far removed from the carrier, the phase-noise
oor of a DDS is determined by the power sum of the
DAC quantization noise oor and the reference clock
phase noise oor.

85.3 See also

Numerically controlled oscillator
Digital-to-analog converter
Reconstruction lter
Crystal oscillator
Table-lookup synthesis
Multiple wavetable synthesis

85.4 References
[1] DDS Controls Waveforms in Test, Measurement, and
Communications. Analog Devices Corporation.
[2] Paul Kern (July 2007). Direct digital synthesis enables
digital PLLs (PDF). RFDesign.
[3] While some authors use the terms DDS and NCO
interchangeably,[4] by convention an NCO refers to the
digital (i.e. the discrete-time, discrete amplitude) portion
of a DDS[5]
[4] Numerically Controlled Oscillator. Lattice Semiconductor Corporation. 2009.

[6] Single-Chip Direct Digital Synthesis vs. the Analog

PLL. Analog Devices Corporation.

[8] Chen, C.T. (1970). Introduction to Linear System Theory. Holt, Rinehart and Winston, Inc. ISBN 978-0-03077155-2.

85.5 External links and further

reading
Tutorial on Digital Signal Synthesis (From Analog
Devices)
L. Cordesses, Direct Digital Synthesis: A Tool
for Periodic Wave Generation (Part 1)" IEEE Signal
Processing Magazine, DSP Tips & Tricks column, pp.
5054, Vol. 21, No. 4 July 2004.
L. Cordesses, Direct Digital Synthesis: A Tool for
Periodic Wave Generation (Part 2) IEEE Signal Processing Magazine, DSP Tips & Tricks column, pp.
110117, Vol. 21, No. 5, Sep. 2004.
Jouko Vankka & Kari A.I. Halonen (2010). Direct
Digital Synthesizers: Theory, Design and Applications. The Kluwer international series in Engineering and Computer Science. Boston, MA: Kluwer
Academic Publishers. ISBN 978-1-4419-4895-3.

Chapter 86

Fading
This article is about signal loss in telecommunications. frequently referred to as a deep fade and may result in
For other uses, see Fade (disambiguation).
temporary failure of communication due to a severe drop
In wireless communications, fading is variation of the in the channel signal-to-noise ratio.
A common example of deep fade is the experience of
stopping at a trac light and hearing an FM broadcast
degenerate into static, while the signal is re-acquired if
the vehicle moves only a fraction of a meter. The loss of
the broadcast is caused by the vehicle stopping at a point
where the signal experienced severe destructive interference. Cellular phones can also exhibit similar momentary
fades.

Frequency-selective time-varying fading causes a cloudy pattern

to appear on a spectrogram. Time is shown on the horizontal
axis, frequency on the vertical axis and signal strength as greyscale intensity.

attenuation of a signal with various variables. These variables include time, geographical position, and radio frequency. Fading is often modeled as a random process. A
fading channel is a communication channel that experiences fading. In wireless systems, fading may either be
due to multipath propagation, referred to as multipath
induced fading, or due to shadowing from obstacles affecting the wave propagation, sometimes referred to as
shadow fading.

Fading channel models are often used to model the effects of electromagnetic transmission of information over
the air in cellular networks and broadcast communication.
Fading channel models are also used in underwater acoustic communications to model the distortion caused by the
water.

86.2 Slow versus fast fading

The terms slow and fast fading refer to the rate at which
the magnitude and phase change imposed by the channel
on the signal changes. The coherence time is a measure
of the minimum time required for the magnitude change
or phase change of the channel to become uncorrelated
from its previous value.

86.1 Key concepts

The presence of reectors in the environment surrounding a transmitter and receiver create multiple paths that a
transmitted signal can traverse. As a result, the receiver
sees the superposition of multiple copies of the transmitted signal, each traversing a dierent path. Each signal copy will experience dierences in attenuation, delay
and phase shift while travelling from the source to the receiver. This can result in either constructive or destructive
interference, amplifying or attenuating the signal power
seen at the receiver. Strong destructive interference is
406

Slow fading arises when the coherence time of the

channel is large relative to the delay requirement
of the application.[1] In this regime, the amplitude
and phase change imposed by the channel can be
considered roughly constant over the period of use.
Slow fading can be caused by events such as shadowing, where a large obstruction such as a hill or
large building obscures the main signal path between
the transmitter and the receiver. The received power
change caused by shadowing is often modeled using
a log-normal distribution with a standard deviation
according to the log-distance path loss model.
Fast fading occurs when the coherence time of the
channel is small relative to the delay requirement
of the application. In this case, the amplitude and

86.4. SELECTIVE FADING

407

phase change imposed by the channel varies consid- two dierent paths, and at least one of the paths is changerably over the period of use.
ing (lengthening or shortening). This typically happens in
the early evening or early morning as the various layers
In a fast-fading channel, the transmitter may take advan- in the ionosphere move, separate, and combine. The two
tage of the variations in the channel conditions using time paths can both be skywave or one be groundwave.
diversity to help increase robustness of the communication to a temporary deep fade. Although a deep fade may
temporarily erase some of the information transmitted,
use of an error-correcting code coupled with successfully
transmitted bits during other time instances (interleaving)
can allow for the erased bits to be recovered. In a slowfading channel, it is not possible to use time diversity because the transmitter sees only a single realization of the
channel within its delay constraint. A deep fade therefore lasts the entire duration of transmission and cannot
be mitigated using coding.
The coherence time of the channel is related to a quantity known as the Doppler spread of the channel. When
a user (or reectors in its environment) is moving, the
users velocity causes a shift in the frequency of the signal transmitted along each signal path. This phenomenon
is known as the Doppler shift. Signals traveling along
dierent paths can have dierent Doppler shifts, corresponding to dierent rates of change in phase. The difference in Doppler shifts between dierent signal components contributing to a signal fading channel tap is known
as the Doppler spread. Channels with a large Doppler
spread have signal components that are each changing independently in phase over time. Since fading depends on
whether signal components add constructively or destructively, such channels have a very short coherence time.

Selective fading manifests as a slow, cyclic disturbance;

the cancellation eect, or null, is deepest at one particular frequency, which changes constantly, sweeping
through the received audio.
As the carrier frequency of a signal is varied, the magnitude of the change in amplitude will vary. The coherence
bandwidth measures the separation in frequency after
which two signals will experience uncorrelated fading.
In at fading, the coherence bandwidth of the channel is larger than the bandwidth of the signal. Therefore, all frequency components of the signal will experience the same magnitude of fading.
In frequency-selective fading, the coherence bandwidth of the channel is smaller than the bandwidth
of the signal. Dierent frequency components of
the signal therefore experience uncorrelated fading.

Since dierent frequency components of the signal are

aected independently, it is highly unlikely that all parts
of the signal will be simultaneously aected by a deep
fade. Certain modulation schemes such as orthogonal
frequency-division multiplexing (OFDM) and code division multiple access (CDMA) are well-suited to emIn general, coherence time is inversely related to Doppler ploying frequency diversity to provide robustness to fadspread, typically expressed as
ing. OFDM divides the wideband signal into many slowly
modulated narrowband subcarriers, each exposed to at
fading rather than frequency selective fading. This can be
1
combated by means of error coding, simple equalization
Tc
or adaptive bit loading. Inter-symbol interference is
Ds
avoided by introducing a guard interval between the symwhere Tc is the coherence time, Ds is the Doppler spread. bols. CDMA uses the rake receiver to deal with each echo
This equation is just an approximation,[2] to be exact, see separately.
Coherence time.
Frequency-selective fading channels are also dispersive,
in that the signal energy associated with each symbol
is spread out in time. This causes transmitted symbols
86.3 Block fading
that are adjacent in time to interfere with each other.
Equalizers are often deployed in such channels to comBlock fading is where the fading process is approxi- pensate for the eects of the intersymbol interference.
mately constant for a number of symbol intervals. [3] A The echoes may also be exposed to Doppler shift, resultchannel can be 'doubly block-fading' when it is block fad- ing in a time varying channel model.
ing in both the time and frequency domains.[4]
The eect can be counteracted by applying some
diversity scheme, for example OFDM (with subcarrier
interleaving and forward error correction), or by using
86.4 Selective fading
two receivers with separate antennas spaced a quarterwavelength apart, or a specially designed diversity reSelective fading or frequency selective fading is a radio ceiver with two antennas. Such a receiver continuously
propagation anomaly caused by partial cancellation of a compares the signals arriving at the two antennas and
radio signal by itself the signal arrives at the receiver by presents the better signal.

408

86.5 Fading models

Examples of fading models for the distribution of the attenuation are:
Dispersive fading models, with several echoes, each
exposed to dierent delay, gain and phase shift, often constant. This results in frequency selective fading and inter-symbol interference. The gains may
be Rayleigh or Rician distributed. The echoes may
also be exposed to Doppler shift, resulting in a time
varying channel model.
Nakagami fading
Log-normal shadow fading
Rayleigh fading
Rician fading
Two-Wave with Diuse Power (TWDP) fading
Weibull fading

86.6 Mitigation
Fading can cause poor performance in a communication
system because it can result in a loss of signal power without reducing the power of the noise. This signal loss can
be over some or all of the signal bandwidth. Fading can
also be a problem as it changes over time: communication
systems are often designed to adapt to such impairments,
but the fading can change faster than the adaptations can
be made. In such cases, the probability of experiencing a
fade (and associated bit errors as the signal-to-noise ratio
drops) on the channel becomes the limiting factor in the
links performance.
The eects of fading can be combated by using diversity
to transmit the signal over multiple channels that experience independent fading and coherently combining them
at the receiver. The probability of experiencing a fade in
this composite channel is then proportional to the probability that all the component channels simultaneously experience a fade, a much more unlikely event.
Diversity can be achieved in time, frequency, or space.
Common techniques used to overcome signal fading include:
Diversity reception and transmission
MIMO
OFDM
Rake receivers
Spacetime codes

CHAPTER 86. FADING

86.7 See also

Attenuation distortion
Backhoe fade
Diversity schemes
Fade margin
Fading distribution
Frequency of optimum transmission
Link budget
Lowest usable high frequency
Maximum usable frequency
Multipath propagation
OFDM
Rain fade
Rayleigh fading
Thermal Fade
Ultra-wideband

86.8 References
[1] Tse, David; Viswanath, Pramod (2006). Fundamentals
of Wireless Communication (4 ed.). Cambridge [Eng.]:
Cambridge University Press. p. 31. ISBN 0521845270.
[2] Lars Ahlin & Jens Zander, Principles of Wireless Communications, pp.126-130.
[3] Biglieri, Ezio; Caire, Giuseppe; Taricco, Giorgio (1999).
Coding for the Fading Channel: a Survey. In Byrnes,
J.S. Signal Processing for Multimedia. IOS Press. p. 253.
ISBN 978-90-5199-460-5.
[4] Muriel, Medard; Tse, David N. C. Spreading in blockfading channels (PDF). Conference Record of the
Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, 2000. 2. pp. 15981602.
doi:10.1109/ACSSC.2000.911259. Retrieved 2014-1020.

86.9 Literature
T.S. Rappaport, Wireless Communications: Principles and practice, Second Edition, Prentice Hall,
2002.
David Tse and Pramod Viswanath, Fundamentals
of Wireless Communication, Cambridge University
Press, 2005.

86.10. EXTERNAL LINKS

M. Awad, K. T. Wong & Z. Li, An Integrative
Overview of the Open Literatures Empirical Data on
the Indoor Radiowave Channels Temporal Properties, IEEE Transactions on Antennas & Propagation,
vol. 56, no. 5, pp. 14511468, May 2008.
P. Barsocchi, Channel models for terrestrial wireless
communications: a survey, CNR-ISTI technical report, April 2006.

86.10 External links

Fading due to multipath eect

409

Chapter 87

Attenuation
This article is about attenuation in physics. For other
uses, see Attenuation (disambiguation).

87.2 Ultrasound
Main article: Acoustic attenuation

In physics, attenuation (in some contexts also called extinction) is the gradual loss in intensity of any kind of
ux through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water attenuates
both light and sound.
In electrical engineering and telecommunications, attenuation aects the propagation of waves and signals in
electrical circuits, in optical bers, and in air (radio
waves). Electrical attenuators and optical attenuators are
commonly manufactured components in this eld.

One area of research in which attenuation gures strongly

is in ultrasound physics. Attenuation in ultrasound is
the reduction in amplitude of the ultrasound beam as a
function of distance through the imaging medium. Accounting for attenuation eects in ultrasound is important
because a reduced signal amplitude can aect the quality of the image produced. By knowing the attenuation
that an ultrasound beam experiences traveling through
a medium, one can adjust the input signal amplitude to
compensate for any loss of energy at the desired imaging
depth.[2]

87.1 Background

Ultrasound
attenuation
measurement
in
heterogeneous systems, like emulsions or colloids,
yields information on particle size distribution.
There is an ISO standard on this technique.[3]
Ultrasound attenuation can be used for extensional
rheology measurement.
There are acoustic
rheometers that employ Stokes law for measuring
extensional viscosity and volume viscosity.
Wave equations which take acoustic attenuation into account can be written on a fractional derivative form, see
the article on acoustic attenuation or e.g. the survey
paper.[4]

Frequency-dependent attenuation of electromagnetic radiation in

standard atmosphere.

87.2.1 Attenuation coecient

Attenuation coecients are used to quantify dierent
media according to how strongly the transmitted ultrasound amplitude decreases as a function of frequency.
The attenuation coecient ( ) can be used to determine
total attenuation in dB in the medium using the following
formula:

In many cases, attenuation is an exponential function

of the path length through the medium. In chemical
spectroscopy, this is known as the BeerLambert law.
In engineering, attenuation is usually measured in units
of decibels per unit length of medium (dB/cm, dB/km,
etc.) and is represented by the attenuation coecient
of the medium in question.[1] Attenuation also occurs in Attenuation = [dB/(MHz cm)] [cm] f[MHz]
earthquakes; when the seismic waves move farther away
from the epicenter, they grow smaller as they are attenu- As this equation shows, besides the medium length and
ated by the ground.
attenuation coecient, attenuation is also linearly depen410

87.5. ELECTROMAGNETIC

411

dent on the frequency of the incident ultrasound beam. earth (attenuation). This phenomenon is tied in to the
Attenuation coecients vary widely for dierent me- dispersion of the seismic energy with the distance. There
dia. In biomedical ultrasound imaging however, biologi- are two types of dissipated energy:
cal materials and water are the most commonly used media. The attenuation coecients of common biological
geometric dispersion caused by distribution of the
materials at a frequency of 1 MHz are listed below:[5]
seismic energy to greater volumes
dispersion as heat, also called intrinsic attenuation or
anelastic attenuation.
There are two general ways of acoustic energy losses:
absorption and scattering, for instance light scattering.[7]
Ultrasound propagation through homogeneous media is
associated only with absorption and can be characterized with absorption coecient only. Propagation
through heterogeneous media requires taking into account scattering.[8] Fractional derivative wave equations
can be applied for modeling of lossy acoustical wave
propagation, see also acoustic attenuation and Ref.[4]

87.3 Light attenuation in water

Shortwave radiation emitted from the sun have wavelengths in the visible spectrum of light that range from
360 nm (violet) to 750 nm (red). When the suns radiation reaches the sea-surface, the shortwave radiation is attenuated by the water, and the intensity of light decreases
exponentially with water depth. The intensity of light at
depth can be calculated using the Beer-Lambert Law.

87.5 Electromagnetic
Attenuation decreases the intensity of electromagnetic radiation due to absorption or scattering of photons. Attenuation does not include the decrease in intensity due to
inverse-square law geometric spreading. Therefore, calculation of the total change in intensity involves both the
inverse-square law and an estimation of attenuation over
the path.
The primary causes of attenuation in matter are the
photoelectric eect, compton scattering, and, for photon
energies of above 1.022 MeV, pair production.

87.5.1 Radiography

See Attenuation coecient.

In clear open waters, visible light is absorbed at the
longest wavelengths rst. Thus, red, orange, and yellow wavelengths are absorbed at higher water depths, and 87.5.2 Optics
blue and violet wavelengths reach the deepest in the water column. Because the blue and violet wavelengths are Main article: Transparent materials
absorbed last compared to the other wavelengths, open
ocean waters appear deep-blue to the eye.
Attenuation in ber optics, also known as transmission
In near-shore (coastal) waters, sea water contains more loss, is the reduction in intensity of the light beam (or
phytoplankton than the very clear central ocean wa- signal) with respect to distance travelled through a transters. Chlorophyll-a pigments in the phytoplankton ab- mission medium. Attenuation coecients in ber opsorb light, and the plants themselves scatter light, making tics usually use units of dB/km through the medium due
coastal waters less clear than open waters. Chlorophyll- to the relatively high quality of transparency of modern
a absorbs light most strongly in the shortest wavelengths optical transmission media. The medium is typically a
(blue and violet) of the visible spectrum. In near-shore ber of silica glass that connes the incident light beam
waters where there are high concentrations of phyto- to the inside. Attenuation is an important factor limiting
plankton, the green wavelength reaches the deepest in the the transmission of a digital signal across large distances.
water column and the color of water to an observer ap- Thus, much research has gone into both limiting the atpears green-blue or green.
tenuation and maximizing the amplication of the optical
signal. Empirical research has shown that attenuation in
optical ber is caused primarily by both scattering and
absorption.[9]
87.4 Earthquake
Attenuation in ber optics can be quantied using the folThe energy with which an earthquake aects a location lowing equation:[10]
depends on the running distance. The attenuation in the
signal of ground motion intensity plays an important role
(
)
in the assessment of possible strong groundshaking. A
(W) intensity Input
seismic wave loses energy as it propagates through the (dB) Attenuation = 10 log10 (W) intensity Output

412

CHAPTER 87. ATTENUATION

mirror
P

normal

Specular reection

being scattered. Thus, limits to spatial scales of visibility arise, depending on the frequency of the incident
lightwave and the physical dimension (or spatial scale) of
the scattering center, which is typically in the form of
some specic microstructural feature. For example, since
visible light has a wavelength scale on the order of one
micrometer (one millionth of a meter), scattering centers
will have dimensions on a similar spatial scale.
Thus, attenuation results from the incoherent scattering of light at internal surfaces and interfaces. In
(poly)crystalline materials such as metals and ceramics,
in addition to pores, most of the internal surfaces or interfaces are in the form of grain boundaries that separate tiny regions of crystalline order. It has recently been
shown that, when the size of the scattering center (or grain
boundary) is reduced below the size of the wavelength of
the light being scattered, the scattering no longer occurs
to any signicant extent. This phenomenon has given rise
to the production of transparent ceramic materials.
Likewise, the scattering of light in optical quality glass
ber is caused by molecular-level irregularities (compositional uctuations) in the glass structure. Indeed,
one emerging school of thought is that a glass is simply the limiting case of a polycrystalline solid. Within
this framework, domains exhibiting various degrees of
short-range order become the building-blocks of both
metals and alloys, as well as glasses and ceramics. Distributed both between and within these domains are microstructural defects that will provide the most ideal locations for the occurrence of light scattering. This same
phenomenon is seen as one of the limiting factors in the
transparency of IR missile domes.[13]

UV-Vis-IR absorption

Diuse reection

In addition to light scattering, attenuation or signal loss

can also occur due to selective absorption of specic
wavelengths, in a manner similar to that responsible for
the appearance of color. Primary material considerations
include both electrons and molecules as follows:

Light scattering
The propagation of light through the core of an optical
ber is based on total internal reection of the lightwave.
Rough and irregular surfaces, even at the molecular level
of the glass, can cause light rays to be reected in many
random directions. This type of reection is referred to
as "diuse reection", and it is typically characterized by
wide variety of reection angles. Most objects that can
be seen with the naked eye are visible due to diuse reection. Another term commonly used for this type of
reection is "light scattering". Light scattering from the
surfaces of objects is our primary mechanism of physical
observation. [11] [12] Light scattering from many common
surfaces can be modelled by lambertian reectance.
Light scattering depends on the wavelength of the light

At the electronic level, it depends on whether the

electron orbitals are spaced (or quantized) such
that they can absorb a quantum of light (or photon)
of a specic wavelength or frequency in the ultraviolet (UV) or visible ranges. This is what gives rise
to color.
At the atomic or molecular level, it depends on
the frequencies of atomic or molecular vibrations
or chemical bonds, how close-packed its atoms or
molecules are, and whether or not the atoms or
molecules exhibit long-range order. These factors
will determine the capacity of the material transmitting longer wavelengths in the infrared (IR), far IR,
radio and microwave ranges.

87.7. REFERENCES

413

The selective absorption of infrared (IR) light by a particular material occurs because the selected frequency of the
light wave matches the frequency (or an integral multiple
of the frequency) at which the particles of that material
vibrate. Since dierent atoms and molecules have dierent natural frequencies of vibration, they will selectively
absorb dierent frequencies (or portions of the spectrum)
of infrared (IR) light.

ITU-R P.525

87.5.3

Rain fade

Applications

In optical bers, attenuation is the rate at which the signal light decreases in intensity. For this reason, glass ber
(which has a low attenuation) is used for long-distance
ber optic cables; plastic ber has a higher attenuation
and, hence, shorter range. There also exist optical attenuators that decrease the signal in a ber optic cable intentionally.
Attenuation of light is also important in physical oceanography. This same eect is an important consideration in
weather radar, as raindrops absorb a part of the emitted
beam that is more or less signicant, depending on the
wavelength used.
Due to the damaging eects of high-energy photons, it is
necessary to know how much energy is deposited in tissue
during diagnostic treatments involving such radiation. In
addition, gamma radiation is used in cancer treatments
where it is important to know how much energy will be
deposited in healthy and in tumorous tissue.

87.5.4

Radio

Main article: Path loss

Attenuation is an important consideration in the modern
world of wireless telecommunication. Attenuation limits
the range of radio signals and is aected by the materials a
signal must travel through (e.g., air, wood, concrete, rain).
See the article on path loss for more information on signal
loss in wireless communication.

Mean free path

Path loss
Radiation length
Radiography

Wave propagation

87.7 References
[1] Essentials of Ultrasound Physics, James A. Zagzebski,
Mosby Inc., 1996.
[2] Diagnostic Ultrasound, Stewart C. Bushong and Benjamin
R. Archer, Mosby Inc., 1991.
[3] ISO 20998-1:2006 Measurement and characterization of
particles by acoustic methods
[4] S. P. Nsholm and S. Holm, On a Fractional Zener Elastic Wave Equation, Fract. Calc. Appl. Anal. Vol. 16, No
1 (2013), pp. 26-50, DOI: 10.2478/s13540-013-00031 Link to e-print
[5] Culjat, Martin O.; Goldenberg, David; Tewari, Priyamvada; Singh, Rahul S. (2010).
A Review of
Tissue Substitutes for Ultrasound Imaging.
Ultrasound in Medicine & Biology.
36 (6): 861
873. doi:10.1016/j.ultrasmedbio.2010.02.012. PMID
20510184.
[6] http://www.ndt.net/article/ultragarsas/63-2008-no.1_
03-jakevicius.pdf
[7] Bohren,C. F. and Human, D.R. Absorption and Scattering of Light by Small Particles, Wiley, (1983), ISBN
0-471-29340-7
[8] Dukhin, A.S. and Goetz, P.J. Ultrasound for characterizing colloids, Elsevier, 2002

87.6 See also

Acoustic attenuation
Attenuation length
Attenuator (genetics)
Cross section (physics)
Decibel
Electrical impedance
Environmental remediation for natural attenuation

[9] Telecommunications: A Boost for Fibre Optics, Z. Valy

Vardeny, Nature 416, 489491, 2002.
[10] Fibre Optics. Bell College. Archived from the original
on 2006-02-24.
[11] Kerker, M. (1909). The Scattering of Light (Academic,
New York)".
[12] Mandelstam, L.I. (1926). Light Scattering by Inhomogeneous Media. Zh. Russ. Fiz-Khim. Ova. 58: 381.
[13] Archibald, P.S. and Bennett, H.E., Scattering from infrared missile domes, Opt. Engr., Vol. 17, p.647 (1978)

414

87.8 External links

NISTs XAAMDI: X-Ray Attenuation and Absorption for Materials of Dosimetric Interest Database
NISTs XCOM: Photon Cross Sections Database
NISTs FAST: Attenuation and Scattering Tables
Underwater Radio Communication

CHAPTER 87. ATTENUATION

Chapter 88

Superheterodyne receiver

A 5-tube superheterodyne receiver made in Japan around 1955

One of the prototype superheterodyne receivers built at Armstrongs Signal Corps laboratory in Paris during World War I. It
is constructed in two sections, the mixer and local oscillator (left)
and three IF amplication stages and a detector stage (right). The
intermediate frequency was 75 kHz.

88.1 History
88.1.1 Background

Superheterodyne transistor radio circuit around 1975

A superheterodyne receiver (often shortened to superhet) is a type of radio receiver that uses frequency mixing
to convert a received signal to a xed intermediate frequency (IF) which can be more conveniently processed
than the original carrier frequency. It was invented by US
engineer Edwin Armstrong in 1918 during World War
I.[1] Virtually all modern radio receivers use the superheterodyne principle.

Superheterodyne is a contraction of supersonic heterodyne, where supersonic indicates frequencies above

the range of human hearing. The word heterodyne is
derived from the Greek roots hetero- dierent, and dyne power. In radio applications the term derives from
the heterodyne detector pioneered by Canadian inventor Reginald Fessenden in 1905, describing his proposed
method of producing an audible signal from the Morse
code transmissions of the new continuous wave transmitters. With the older spark gap transmitters then in use,
the Morse code signal consisted of short bursts of a heavily modulated carrier wave, which could be clearly heard
as a series of short chirps or buzzes in the receivers headphones. However, the signal from a continuous wave
transmitter did not have any such inherent modulation
and Morse Code from one of those would only be heard
as a series of clicks or thumps. Fessendens idea was to
run two Alexanderson alternators, one producing a carrier
frequency 3 kHz higher than the other. In the receivers
detector the two carriers would beat together to produce
a 3 kHz tone thus in the headphones the Morse signals
would then be heard as a series of 3 kHz beeps. For this
he coined the term heterodyne meaning generated by
a dierence (in frequency).

415

416

88.1.2

CHAPTER 88. SUPERHETERODYNE RECEIVER

Invention

start picking up stations on frequencies dierent from the

stations transmission frequency. Armstrong (and others)
eventually deduced that this was caused by a supersonic
heterodyne between the stations carrier frequency and
the regenerative receivers oscillation frequency. Thus if
a station was transmitting on 300 kHz and the oscillating
receiver was set to 400 kHz, the station would be heard
not only at the original 300 kHz, but also at 100 kHz and
700 kHz.

The superheterodyne principle was devised in 1918 by

U.S. Army Major Edwin Armstrong in France during
World War I.[2][3] He invented this receiver as a means of
overcoming the deciencies of early vacuum tube triodes
used as high-frequency ampliers in radio direction nding equipment. Unlike simple radio communication,
which only needs to make transmitted signals audible,
direction-nders measure the received signal strength, Armstrong realized that this was a potential solution to
which necessitates linear amplication of the actual car- the short wave amplication problem, since the beat
rier wave.
frequency still retained its original modulation, but on a
lower carrier frequency. To monitor a frequency of 1500
kHz for example, he could set up an oscillator at, for example, 1560 kHz, which would produce a heterodyne difference frequency of 60 kHz, a frequency that could then
be more conveniently amplied by the triodes of the day.
He termed this the "intermediate frequency" often abbreviated to IF.
In December 1919, Major E. H. Armstrong gave publicity to an indirect method
of obtaining short-wave amplication, called
the super-heterodyne. The idea is to reduce
the incoming frequency, which may be, say
1,500,000 cycles (200 meters), to some suitable super-audible frequency that can be amplied eciently, then passing this current
through a radio frequency amplier and nally
rectifying and carrying on to one or two stages
of audio frequency amplication.[4]

One of the rst amateur superheterodyne receivers, built in 1920

even before Armstrong published his paper. Due to the low gain
of early triodes it required 9 tubes, with 5 IF amplication stages,
and used an IF of around 50 kHz.

88.1.3 Development

In a triode radio-frequency (RF) amplier, if both the

plate (anode) and grid are connected to resonant circuits
tuned to the same frequency, stray capacitive coupling between the grid and the plate will cause the amplier to go
into oscillation if the stage gain is much more than unity.
In early designs, dozens (in some cases over 100) lowgain triode stages had to be connected in cascade to make
workable equipment, which drew enormous amounts of
power in operation and required a team of maintenance
engineers. The strategic value was so high, however, that
the British Admiralty felt the high cost was justied.
Armstrong realized that if radio direction-nding (RDF)
receivers could be operated at a higher frequency, this
would allow better detection of enemy shipping. However, at that time, no practical short wave (dened then
as any frequency above 500 kHz) amplier existed, due
to the limitations of existing triodes.

The rst commercial superheterodyne receiver,[5] the RCA Radiola AR-812, brought out March 4, 1924 priced at $286. It used 6
triodes: a mixer, local oscillator, two IF and two audio amplier
stages, with an IF of 45 kHz. It was a commercial success, with
better performance than competing receivers.

Armstrong was able to put his ideas into practice, and the
It had been noticed that when a regenerative receiver went technique was soon adopted by the military. However,
into oscillation, other nearby receivers would suddenly it was less popular when commercial radio broadcasting

88.2. DESIGN AND PRINCIPLE OF OPERATION

began in the 1920s, mostly due to the need for an extra tube (for the oscillator), the generally higher cost of
the receiver, and the level of technical skill required to
operate it. For early domestic radios, tuned radio frequency receivers (TRF) were more popular because they
were cheaper, easier for a non-technical owner to use, and
less costly to operate. Armstrong eventually sold his superheterodyne patent to Westinghouse, who then sold it
to RCA, the latter monopolizing the market for superheterodyne receivers until 1930.[6]
Early superheterodyne receivers used IFs as low as 20
kHz, often based on the self-resonance of iron-cored
transformers. This made them extremely susceptible to
image frequency interference, but at the time, the main
objective was sensitivity rather than selectivity. Using
this technique, a small number of triodes could be made
to do the work that formerly required dozens of triodes.
In the 1920s, commercial IF lters looked very similar to 1920s audio interstage coupling transformers, had
very similar construction and were wired up in an almost
identical manner, and so they were referred to as IF
transformers. By the mid-1930s however, superheterodynes were using much higher intermediate frequencies,
(typically around 440470 kHz), with tuned coils similar
in construction to the aerial and oscillator coils. However, the name IF transformer was retained and is still
used today. Modern receivers typically use a mixture of
ceramic resonator or SAW (surface-acoustic wave) resonators as well as traditional tuned-inductor IF transformers.

American Five" vacuum-tube superheterodyne AM

broadcast receiver from 1940s was cheap to manufacture
because it only required ve tubes.
By the 1930s, improvements in vacuum tube technology rapidly eroded the TRF receivers cost advantages,
and the explosion in the number of broadcasting stations
created a demand for cheaper, higher-performance receivers.
The development of the tetrode vacuum tube containing a
screen grid led to a multi-element tube in which the mixer
and oscillator functions could be combined, rst used in
the so-called autodyne mixer. This was rapidly followed
by the introduction of tubes specically designed for superheterodyne operation, most notably the pentagrid converter. By reducing the tube count, this further reduced
the advantage of preceding receiver designs.

417
ceivers was largely replaced by superheterodyne receivers. By the 1940s the vacuum-tube superheterodyne AM broadcast receiver was rened into a cheap-tomanufacture design called the "All American Five", because it only used ve vacuum tubes: usually a converter
(mixer/local oscillator), an IF amplier, a detector/audio
amp, audio power amp, and a rectier. From this time,
the superheterodyne design was used for virtually all commercial radio and TV receivers.

88.2 Design and principle of operation

RF
Filter

RF
Amplier Mixer

IF Amplier
Audio
& Filter
Demodulator Amplier

Local
Oscillator

Block diagram of a typical superheterodyne receiver. Red parts

are those that handle the incoming radio frequency (RF) signal;
green are parts that operate at the intermediate frequency (IF),
while blue parts operate at the modulation (audio) frequency.
The dotted line indicates that the local oscillator and RF lter
must be tuned in tandem.

The diagram at right shows the block diagram of a typical single-conversion superheterodyne receiver. The diagram has blocks that are common to superheterodyne
receivers.[7] The antenna collects the radio signal. The
tuned RF stage with optional RF amplier provides some
initial selectivity; it is necessary to suppress the image frequency (see below), and may also serve to prevent strong
out-of-passband signals from saturating the initial amplier. A local oscillator provides the mixing frequency; it
"All
is usually a variable frequency oscillator which is used
to tune the receiver to dierent stations. The frequency
mixer does the actual heterodyning that gives the superheterodyne its name; it changes the incoming radio frequency signal to a higher or lower, xed, intermediate
frequency (IF). The IF band-pass lter and amplier supply most of the gain and the narrowband ltering for
the radio. The demodulator extracts the audio or other
modulation from the IF radio frequency; the extracted
signal is then amplied by the audio amplier.

88.2.1 Circuit description

To receive a radio signal, a suitable antenna is required.

The output of the antenna may be very small, often only
a few microvolts. The signal from the antenna is tuned
and may be amplied in a so-called radio frequency (RF)
amplier, although this stage is often omitted. One or
By the mid-1930s, commercial production of TRF re- more tuned circuits at this stage block frequencies that
are far removed from the intended reception frequency.

418

CHAPTER 88. SUPERHETERODYNE RECEIVER

In order to tune the receiver to a particular station, the

frequency of the local oscillator is controlled by the tuning
knob (for instance). Tuning of the local oscillator and the
RF stage may use a variable capacitor, or varicap diode.[8]
The tuning of one (or more) tuned circuits in the RF stage
must track the tuning of the local oscillator.

88.2.2

Local oscillator and mixer

is changed. In most cases, a receivers input band is wider

than its IF center frequency. For example, a typical AM
broadcast band receiver covers 510 kHz to 1655 kHz (a
roughly 1160 kHz input band) with a 455 kHz IF frequency; an FM broadcast band receiver covers 88 MHz
to 108 MHz band with a 10.7 MHz IF frequency. In that
situation, the RF amplier must be tuned so the IF amplier does not see two stations at the same time. If the
AM broadcast band receiver LO were set at 1200 kHz, it
would see stations at both 745 kHz (1200455 kHz) and
1655 kHz. Consequently, the RF stage must be designed
so that any stations that are twice the IF frequency away
are signicantly attenuated. The tracking can be done
with a multi-section variable capacitor or some varactors
driven by a common control voltage. An RF amplier
may have tuned circuits at both its input and its output,
so three or more tuned circuits may be tracked. In practice, the RF and LO frequencies need to track closely but
not perfectly.[11][12]

The signal is then fed into a circuit where it is mixed with

a sine wave from a variable frequency oscillator known
as the local oscillator (LO). The mixer uses a non-linear
component to produce both sum and dierence beat frequencies signals,[9] each one containing the modulation
contained in the desired signal. The output of the mixer
may include the original RF signal at fRF, the local oscillator signal at fLO, and the two new heterodyne frequencies fRF + fLO and fRF fLO. The mixer may inadvertently produce additional frequencies such as thirdand higher-order intermodulation products. Ideally, the
IF bandpass lter removes all but the desired IF signal at 88.2.3 Intermediate frequency amplier
fIF. The IF signal contains the original modulation (transmitted information) that the received radio signal had at The stages of an intermediate frequency amplier (IF
amplier or IF strip) are tuned to a xed frequency
fRF.
that does not change as the receiving frequency changes.
Historically, vacuum tubes were expensive, so broadcast The xed frequency simplies optimization of the IF
AM receivers would save costs by employing a single amplier.[7] The IF amplier is selective around its centube as both a mixer and also as the local oscillator. The ter frequency fIF. The xed center frequency allows the
pentagrid converter tube would oscillate and also provide stages of the IF amplier to be carefully tuned for best
signal amplication as well as frequency shifting.[10]
performance (this tuning is called aligning the IF amThe frequency of the local oscillator fLO is set so the de- plier). If the center frequency changed with the receivsired reception radio frequency fRF mixes to fIF. There ing frequency, then the IF stages would have had to track
are two choices for the local oscillator frequency because their tuning. That is not the case with the superheterothe dominant mixer products are at fRF fLO. If the dyne.
local oscillator frequency is less than the desired recep- Typically, the IF center frequency fIF is chosen to be less
tion frequency, it is called low-side injection (fIF = fRF than the desired reception frequency fRF. The choice has
fLO); if the local oscillator is higher, then it is called
some performance advantages. First, it is easier and less
high-side injection (fIF = fLO fRF).
expensive to get high selectivity at a lower frequency. For
The mixer will process not only the desired input signal
at fRF, but also all signals present at its inputs. There
will be many mixer products (heterodynes). Most other
signals produced by the mixer (such as due to stations at
nearby frequencies) can be ltered out in the IF amplier; that gives the superheterodyne receiver its superior
performance. However, if fLO is set to fRF + fIF, then
an incoming radio signal at fLO + fIF will also produce
a heterodyne at fIF; the frequency fLO + fIF is called
the image frequency and must be rejected by the tuned
circuits in the RF stage. The image frequency is 2 fIF
higher (or lower) than the desired frequency fRF, so employing a higher IF frequency fIF increases the receivers
image rejection without requiring additional selectivity in
the RF stage.
To suppress the unwanted image, the tuning of the RF
stage and the LO may need to track each other. In some
cases, a narrow-band receiver can have a xed tuned RF
amplier. In that case, only the local oscillator frequency

the same bandwidth, a tuned circuit at a lower frequency

needs a lower Q. Stated another way, for the same lter technology, a higher center frequency will take more
IF lter stages to achieve the same selectivity bandwidth.
Second, it is easier and less expensive to get high gain
at a lower frequency. When used at high frequencies,
many ampliers show a constant gainbandwidth product (dominant pole) characteristic. If an amplier has a
gainbandwidth product of 100 MHz, then it would have
a voltage gain of 100 at 1 MHz but only 10 at 10 MHz. If
the IF amplier needed a voltage gain of 10,000, then it
would need only two stages with an IF at 1 MHz but four
stages at 10 MHz.
Usually the intermediate frequency is lower than the reception frequency fRF, but in some modern receivers
(e.g. scanners and spectrum analyzers) a higher IF frequency is used to minimize problems with image rejection or gain the benets of xed-tuned stages. The Rohde
& Schwarz EK-070 VLF/HF receiver covers 10 kHz to

88.3. ADVANCED DESIGNS

419

30 MHz.[13] It has a band switched RF lter and mixes the

input to a rst IF of 81.4 MHz. The rst LO frequency is
81.4 to 111.4 MHz, so the primary images are far away.
The rst IF stage uses a crystal lter with a 12 kHz bandwidth. There is a second frequency conversion (making a
triple-conversion receiver) that mixes the 81.4 MHz rst
IF with 80 MHz to create a 1.4 MHz second IF. Image
rejection for the second IF is not a major problem because the rst IF provides adequate image rejection and
the second mixer is xed tuned.

where the local oscillator is at a higher frequency than the

received signal (as is common), then the frequency spectrum of the original signal will be reversed. This must
be taken into account by the demodulator (and in the IF
ltering) in the case of certain types of modulation such
as single sideband.

In order to avoid interference to receivers, licensing authorities will avoid assigning common IF frequencies to
transmitting stations. Standard intermediate frequencies
used are 455 kHz for medium-wave AM radio, 10.7 MHz
for broadcast FM receivers, 38.9 MHz (Europe) or 45
MHz (US) for television, and 70 MHz for satellite and
terrestrial microwave equipment. To avoid tooling costs
associated with these components, most manufacturers
then tended to design their receivers around a xed range
of frequencies oered, which resulted in a worldwide de
facto standardization of intermediate frequencies.

To overcome obstacles such as image response, in some

cases multiple stages with two or more IFs of dierent
values are used. For example, for a receiver that can tune
from 500 kHz to 30 MHz, three frequency converters
might be used, and the radio would be referred to as a
triple conversion superheterodyne;[7]

In early superhets, the IF stage was often a regenerative

stage providing the sensitivity and selectivity with fewer
components. Such superhets were called super-gainers or
regenerodynes.

88.2.4

Bandpass lter

The IF stage includes a lter and/or multiple tuned circuits in order to achieve the desired selectivity. This ltering must therefore have a band pass equal to or less
than the frequency spacing between adjacent broadcast
channels. Ideally a lter would have a high attenuation to
adjacent channels, but maintain a at response across the
desired signal spectrum in order to retain the quality of
the received signal. This may be obtained using one or
more dual tuned IF transformers, a quartz crystal lter,
or a multipole ceramic crystal lter.[14]

88.2.5

Demodulation

The received signal is now processed by the demodulator

stage where the audio signal (or other baseband signal)
is recovered and then further amplied. AM demodulation requires the simple rectication of the RF signal (socalled envelope detection), and a simple RC low pass lter to remove remnants of the intermediate frequency.[15]
FM signals may be detected using a discriminator, ratio
detector, or phase-locked loop. Continuous wave (Morse
code) and single sideband signals require a product detector using a so-called beat frequency oscillator, and
there are other techniques used for dierent types of
modulation.[16] The resulting audio signal (for instance)
is then amplied and drives a loudspeaker.
When so-called high-side injection has been used,

88.3 Advanced designs

The reason that this is done is the diculty in obtaining

sucient selectivity in the front-end tuning with higher
shortwave frequencies.
With a 455 kHz IF it is easy to get adequate front end selectivity with broadcast band (under 1600 kHz) signals.
For example, if the station being received is on 600 kHz,
the local oscillator will be set to 600 + 455 = 1055 kHz.
But a station on 1510 kHz could also potentially produce
an IF of 455 kHz and so cause image interference. However, because 600 kHz and 1510 kHz are so far apart, it
is easy to design the front end tuning to reject the 1510
kHz frequency.
However at 30 MHz, things are dierent. The oscillator
would be set to 30.455 MHz to produce a 455 kHz IF,
but a station on 30.910 would also produce a 455 kHz
beat, so both stations would be heard at the same time.
But it is virtually impossible to design an RF tuned circuit that can adequately discriminate between 30 MHz
and 30.91 MHz, so one approach is to bulk downconvert whole sections of the shortwave bands to a lower
frequency, where adequate front-end tuning is easier to
arrange.
For example, the ranges 29 MHz to 30 MHz; 28 MHz
to 29 MHz etc. might be converted down to 2 MHz
to 3 MHz, there they can be tuned more conveniently.
This is often done by rst converting each block up to
a higher frequency (typically 40 MHz) and then using a
second mixer to convert it down to the 2 MHz to 3 MHz
range. The 2 MHz to 3 MHz IF is basically another
self-contained superheterodyne receiver, most likely with
a standard IF of 455 kHz.

88.3.1 Other uses

In the case of modern television receivers, no other technique was able to produce the precise bandpass characteristic needed for vestigial sideband reception, similar to
that used in the NTSC system rst approved by the U.S.
in 1941. By the 1980s these had been replaced with pre-

420

CHAPTER 88. SUPERHETERODYNE RECEIVER

cision electromechanical surface acoustic wave (SAW)

lters. Fabricated by precision laser milling techniques,
{
SAW lters are cheaper to produce, can be made to exf + 2fIF ,
tremely close tolerances, and are very stable in operation. fimg =
f 2fIF ,

88.3.2

Modern designs

Microprocessor technology allows replacing the superheterodyne receiver design by a software dened radio
architecture, where the IF processing after the initial IF
lter is implemented in software. This technique is already in use in certain designs, such as very low-cost FM
radios incorporated into mobile phones, since the system
already has the necessary microprocessor.
Radio transmitters may also use a mixer stage to produce
an output frequency, working more or less as the reverse
of a superheterodyne receiver.

iffLO > f injection) side (high

iffLO < f injection) side (low

For example, an AM broadcast station at 580 kHz is

tuned on a receiver with a 455 kHz IF. The local oscillator is tuned to 580 + 455 = 1035 kHz. But a signal
at 580 + 455 + 455 = 1490 kHz is also 455 kHz away
from the local oscillator; so both the desired signal and
the image, when mixed with the local oscillator, will also
appear at the intermediate frequency. This image frequency is within the AM broadcast band. Practical receivers have a tuning stage before the converter, to greatly
reduce the amplitude of image frequency signals; additionally, broadcasting stations in the same area have their
frequencies assigned to avoid such images.

The unwanted frequency is called the image of the wanted

frequency, because it is the mirror image of the desired
frequency reected fo . A receiver with inadequate lter88.4 Advantages and disadvan- ing at its input will pick up signals at two dierent frequencies simultaneously: the desired frequency and the
tages
image frequency. Any noise or random radio station at
the image frequency can interfere with reception of the
Superheterodyne receivers have essentially replaced all desired signal.
previous receiver designs. The development of modern
semiconductor electronics negated the advantages of de- Early Autodyne receivers typically used IFs of only 150
signs (such as the regenerative receiver) that used fewer kHz or so, as it was dicult to maintain reliable oscillavacuum tubes. The superheterodyne receiver oers supe- tion if higher frequencies were used. As a consequence,
rior sensitivity, frequency stability and selectivity. Com- most Autodyne receivers needed quite elaborate antenna
pared with the tuned radio frequency receiver (TRF) de- tuning networks, often involving double-tuned coils, to
sign, superhets oer better stability because a tuneable avoid image interference. Later superhets used tubes esoscillator is more easily realized than a tuneable am- pecially designed for oscillator/mixer use, which were
plier. Operating at a lower frequency, IF lters can able to work reliably with much higher IFs, reducing the
give narrower passbands at the same Q factor than an problem of image interference and so allowing simpler
equivalent RF lter. A xed IF also allows the use of and cheaper aerial tuning circuitry.
a crystal lter[7] or similar technologies that cannot be Sensitivity to the image frequency can be minimised only
tuned. Regenerative and super-regenerative receivers of- by (1) a lter that precedes the mixer or (2) a more comfered a high sensitivity, but often suer from stability plex mixer circuit [17] that suppresses the image. In most
problems making them dicult to operate.
receivers this is accomplished by a bandpass lter in the
Although the advantages of the superhet design are over- RF front end. In many tunable receivers, the bandpass
whelming, we note a few drawbacks that need to be tack- lter is tuned in tandem with the local oscillator.
led in practice.

88.4.1

Image frequency (f )

One major disadvantage to the superheterodyne receiver

is the problem of image frequency. In heterodyne receivers, an image frequency is an undesired input frequency equal to the station frequency plus twice the intermediate frequency. The image frequency results in two
stations being received at the same time, thus producing
interference. Image frequencies can be eliminated by sufcient attenuation on the incoming signal by the RF amplier lter of the superheterodyne receiver.

Image rejection is an important factor in choosing the

intermediate frequency of a receiver. The farther apart
the bandpass frequency and the image frequency are, the
more the bandpass lter will attenuate any interfering image signal. Since the frequency separation between the
bandpass and the image frequency is 2fIF , a higher intermediate frequency improves image rejection. It may be
possible to use a high enough rst IF that a xed-tuned
RF stage can reject any image signals.
The ability of a receiver to reject interfering signals at the
image frequency is measured by the image rejection ratio.
This is the ratio (in decibels) of the output of the receiver
from a signal at the received frequency, to its output for
an equal-strength signal at the image frequency.

88.6. REFERENCES

88.4.2

Local oscillator radiation

Further information: Electromagnetic compatibility

It is dicult to keep stray radiation from the local oscillator below the level that a nearby receiver can detect. The
receivers local oscillator can act like a low-power CW
transmitter. Consequently, there can be mutual interference in the operation of two or more superheterodyne receivers in close proximity.
In intelligence operations, local oscillator radiation gives
a means to detect a covert receiver and its operating frequency. The method was used by MI-5 during Operation
RAFTER.[18] This same technique is also used in radar
detector detectors used by trac police in jurisdictions
where radar detectors are illegal.

421

88.6 References
[1] Armstrong, Edwin H. (February 1921). A new system of
short wave amplication. Proc. of the IRE. New York:
Institute of Radio Engineers. 9 (1): 311. Retrieved 22
October 2013.
[2] The History of Amateur Radio. Luxorion date unknown. Retrieved 19 January 2011.
[3] Sarkar, Tapan K.; Mailloux, Robert J.; Oliner, Arthur A.;
Salazar-Palma, Magdalena; Sengupta, Dipak L. (2006),
History of Wireless, John Wiley and Sons, ISBN 0-47171814-9, p 110?
[4] Leutz, C. R. (December 1922), Notes on a SuperHeterodyne, QST, Hartford, CT: American Radio Relay
League, VI (5): 1114, p. 11

A method of signicantly reducing the local oscillator radiation from the receivers antenna is to use an RF amplier between the receivers antenna and its mixer stage.

[5] Malanowski, Gregory (2011). The Race for Wireless:

How Radio Was Invented (or Discovered?). Authorhouse.
p. 69. ISBN 1463437501.

88.4.3

[6] Katz, Eugenii. Edwin Howard Armstrong. History of

electrochemistry, electricity, and electronics. Eugenii Katz
homepage, Hebrew Univ. of Jerusalem. Archived from
the original on 2009-10-22. Retrieved 2008-05-10.

Local oscillator sideband noise

Local oscillators typically generate a single frequency signal that has negligible amplitude modulation but some
random phase modulation. Either of these impurities
spreads some of the signals energy into sideband frequencies. That causes a corresponding widening of the receivers frequency response, which would defeat the aim
to make a very narrow bandwidth receiver such as to receive low-rate digital signals. Care needs to be taken to
minimize oscillator phase noise, usually by ensuring that
the oscillator never enters a non-linear mode.

88.5 See also

H2X radar
Automatic gain control

[7] Carr, Joseph J. (2002), RF Components and Circuits,

Newnes, Chapter 3, ISBN 978-0-7506-4844-8
[8] Radio-frequency electronics: circuits and applications By
Jon B. Hagen -p.58 l. 12. Cambridge University Press,
1996 - Technology & Engineering. Retrieved 17 January
2011.
[9] The art of electronics. Cambridge University Press. 2006.
p. 886. Retrieved 17 January 2011.
[10] GB 426802, Improvements in or relating to superheterodyne radio receivers, published 12 October 1933
[11] Terman, Frederick Emmons (1943), Radio Engineers
Handbook, New York: McGraw-Hill. Pages 649652 describes design procedure for tracking with a pad capacitor
in the Chebyshev sense.

Single sideband modulation (demodulation)

[12] Rohde, Ulrich L.; Bucher, T. T. N. (1988), Communications Receivers: Principles & Design, New York: McGrawHill, ISBN 0-07-053570-1. Pages 155160 discuss frequency tracking. Pages 160164 discuss image rejection
and include an RF lter design that puts transmission zeros at both the local oscillator frequency and the unwanted
image frequency.

Tuned radio frequency receiver

[13] Rohde & Bucher 1988, pp. 4455

Reectional receiver

[14] Crystal lter types. QSL RF Circuit Design Ideas Date

unknown. Retrieved 17 January 2011.

Demodulator
Direct conversion receiver
VFO

Beat frequency
Heterodyne
Optical heterodyne detection
Superheterodyne transmitter

[15] Reception of Amplitude Modulated Signals - AM Demodulation (PDF). BC Internet education 6/14/2007.
Retrieved 17 January 2011.
[16] Basic Radio Theory. TSCM Handbook Ch.5 date unknown. Retrieved 17 January 2011.

422

CHAPTER 88. SUPERHETERODYNE RECEIVER

[17] United States Patent 7227912: Receiver with mirror frequency suppression by Wolfdietrich Georg Kasperkovitz,
2002/2007
[18] Wright, Peter (1987), Spycatcher: The Candid Autobiography of a Senior Intelligence Ocer, Penguin Viking,
ISBN 0-670-82055-5

88.7 Further reading

Whitaker, Jerry (1996). The Electronics Handbook.
CRC Press. p. 1172. ISBN 0-8493-8345-5.
US 706740, Fessenden, Reginald A., Wireless Signaling, published September 28, 1901, issued August 12, 1902
US 1050441, Fessenden, Reginald A., Electric Signaling Apparatus, published July 27, 1905, issued
January 14, 1913
US 1050728, Fessenden, Reginald A., Method of
Signaling, published August 21, 1906, issued January 14, 1913

88.8 External links

Who Invented the Superheterodyne? An article giving the history of the various inventors working on
the superheterodyne method.
An in-depth introduction to superheterodyne receivers
Superheterodyne
crowaves101.com

receivers

from

mi-

Multipage tutorial describing the superheterodyne

receiver and its technology

Chapter 89

Undersampling
(twice the upper cuto frequency), but is still able to reconstruct the signal.
When one undersamples a bandpass signal, the samples
are indistinguishable from the samples of a low-frequency
alias of the high-frequency signal. Such sampling is also
known as bandpass sampling, harmonic sampling, IF
sampling, and direct IF-to-digital conversion.[1]

89.1 Description
Fig 1: The top 2 graphs depict Fourier transforms of 2 dierent functions that produce the same results when sampled at a
particular rate. The baseband function is sampled faster than its
Nyquist rate, and the bandpass function is undersampled, eectively converting it to baseband. The lower graphs indicate how
identical spectral results are created by the aliases of the sampling
process.

4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0

Plot of sample rates (y axis) versus the upper edge frequency (x

axis) for a band of width 1; grays areas are combinations that
are allowed in the sense that no two frequencies in the band
alias to same frequency. The darker gray areas correspond to
undersampling with the maximum value of n in the equations of
this section.

The Fourier transforms of real-valued functions are symmetrical around the 0 Hz axis. After sampling, only
a periodic summation of the Fourier transform (called
discrete-time Fourier transform) is still available. The
individual, frequency-shifted copies of the original transform are called aliases. The frequency oset between adjacent aliases is the sampling-rate, denoted by fs. When
the aliases are mutually exclusive (spectrally), the original transform and the original continuous function, or a
frequency-shifted version of it (if desired), can be recovered from the samples. The rst and third graphs of Figure 1 depict a baseband spectrum before and after being
sampled at a rate that completely separates the aliases.
The second graph of Figure 1 depicts the frequency prole of a bandpass function occupying the band (A, A+B)
(shaded blue) and its mirror image (shaded beige). The
condition for a non-destructive sample rate is that the
aliases of both bands do not overlap when shifted by all
integer multiples of fs. The fourth graph depicts the spectral result of sampling at the same rate as the baseband
function. The rate was chosen by nding the lowest rate
that is an integer sub-multiple of A and also satises the
baseband Nyquist criterion: fs > 2B. Consequently, the
bandpass function has eectively been converted to baseband. All the other rates that avoid overlap are given
by these more general criteria, where A and A+B are replaced by fL and fH, respectively:[2][3]
2fL
fs n1
, for any integer n satisfying:

fH
1 n fH fL
2fH
n

In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpassltered signal at a sample rate below its Nyquist rate The highest n for which the condition is satised leads to
423

424

CHAPTER 89. UNDERSAMPLING

the lowest possible sampling rates.

Important signals of this sort include a radios
intermediate-frequency (IF), radio-frequency (RF)
signal, and the individual channels of a lter bank.
If n > 1, then the conditions result in what is sometimes
referred to as undersampling, bandpass sampling, or using a sampling rate less than the Nyquist rate (2fH). For
the case of a given sampling frequency, simpler formulae
for the constraints on the signals spectral band are given
below.

Spectrum of the FM radio band (88108 MHz) and its baseband

alias under 44 MHz (n = 5) sampling. An anti-alias lter quite
tight to the FM radio band is required, and theres not room for
stations at nearby expansion channels such as 87.9 without aliasing.

Spectrum of the FM radio band (88108 MHz) and its baseband

alias under 56 MHz (n = 4) sampling, showing plenty of room
for bandpass anti-aliasing lter transition bands. The baseband
image is frequency-reversed in this case (even n).

Example: Consider FM radio to illustrate the

idea of undersampling.
In the US, FM radio operates on the frequency
band from fL = 88 MHz to fH = 108 MHz.
The bandwidth is given by

W = fH fL = 108 MHz 88 MHz = 20 MHz

The sampling conditions are satised for

108 MHz
1 n 5.4 =
20 MHz

Therefore, n can be 1, 2, 3, 4, or 5.
The value n = 5 gives the lowest sampling frequencies interval 43.2 MHz < fs < 44 MHz
and this is a scenario of undersampling. In this
case, the signal spectrum ts between 2 and 2.5
times the sampling rate (higher than 86.488
MHz but lower than 108110 MHz).
A lower value of n will also lead to a useful
sampling rate. For example, using n = 4, the
FM band spectrum ts easily between 1.5 and
2.0 times the sampling rate, for a sampling rate
near 56 MHz (multiples of the Nyquist frequency being 28, 56, 84, 112, etc.). See the
illustrations at the right.
When undersampling a real-world signal, the
sampling circuit must be fast enough to capture
the highest signal frequency of interest. Theoretically, each sample should be taken during an innitesimally short interval, but this
is not practically feasible. Instead, the sampling of the signal should be made in a short
enough interval that it can represent the instantaneous value of the signal with the highest frequency. This means that in the FM radio example above, the sampling circuit must be able
to capture a signal with a frequency of 108
MHz, not 43.2 MHz. Thus, the sampling frequency may be only a little bit greater than 43.2
MHz, but the input bandwidth of the system
must be at least 108 MHz. Similarly, the accuracy of the sampling timing, or aperture uncertainty of the sampler, frequently the analog-todigital converter, must be appropriate for the
frequencies being sampled 108MHz, not the
lower sample rate.
If the sampling theorem is interpreted as requiring twice the highest frequency, then the
required sampling rate would be assumed to be
greater than the Nyquist rate 216 MHz. While
this does satisfy the last condition on the sampling rate, it is grossly oversampled.
Note that if a band is sampled with n > 1, then a
band-pass lter is required for the anti-aliasing
lter, instead of a lowpass lter.
As we have seen, the normal baseband condition for reversible sampling is that X(f) = 0 outside the interval:
( 12 fs , 12 fs ),
and the reconstructive interpolation function, or lowpass
lter impulse response, is sinc(t/T ).
To accommodate undersampling, the bandpass condition
is that X(f) = 0 outside the union of open positive and
negative frequency bands

89.3. REFERENCES

425

) ( n1 n )
n2 fs , n1
2 fs
2 fs , 2 fs
for some positive integer n .
which includes the normal baseband condition as case n = 1 (except that where the intervals come
together at 0 frequency, they can be
closed).
The corresponding interpolation function is the bandpass lter given by this dierence of lowpass impulse responses:

(
n sinc

nt
T

(
(n 1) sinc

(n 1)t
T

On the other hand, reconstruction is not usually the goal

with sampled IF or RF signals. Rather, the sample sequence can be treated as ordinary samples of the signal
frequency-shifted to near baseband, and digital demodulation can proceed on that basis, recognizing the spectrum
mirroring when n is even.
Further generalizations of undersampling for the case
of signals with multiple bands are possible, and signals
over multidimensional domains (space or space-time) and
have been worked out in detail by Igor Kluvnek.

89.2 See also

Drizzle (image processing)

89.3 References
[1] Walt Kester (2003). Mixed-signal and DSP design techniques. Newnes. p. 20. ISBN 978-0-7506-7611-3.
[2] Hiroshi Harada, Ramjee Prasad (2002). Simulation and
Software Radio for Mobile Communications. Artech
House. ISBN 1-58053-044-3.
[3] Angelo Ricotta. Undersampling SODAR Signals.

Chapter 90

Matched lter
In signal processing, a matched lter is obtained by
correlating a known signal, or template, with an unknown
signal to detect the presence of the template in the unknown signal.[1][2] This is equivalent to convolving the
unknown signal with a conjugated time-reversed version
of the template. The matched lter is the optimal linear
lter for maximizing the signal to noise ratio (SNR) in
the presence of additive stochastic noise. Matched lters
are commonly used in radar, in which a known signal is
sent out, and the reected signal is examined for common elements of the out-going signal. Pulse compression
is an example of matched ltering. It is so called because
impulse response is matched to input pulse signals. Twodimensional matched lters are commonly used in image
processing, e.g., to improve SNR for X-ray. Matched ltering is a demodulation technique with LTI (linear time
invariant) lters to maximize SNR.[3] It was originally
also known as a North lter.[4]

90.1 Derivation of the matched lter

90.1.1

vector) that is parallel with the signal, maximizing the inner product. This enhances the signal. When we consider
the additive stochastic noise, we have the additional challenge of minimizing the output due to noise by choosing
a lter that is orthogonal to the noise.
Let us formally dene the problem. We seek a lter, h
, such that we maximize the output signal-to-noise ratio,
where the output is the inner product of the lter and the
observed signal x .
Our observed signal consists of the desirable signal s and
additive noise v :

x = s + v.
Let us dene the covariance matrix of the noise, reminding ourselves that this matrix has Hermitian symmetry, a
property that will become useful in the derivation:

Rv = E{vv H }
where v H denotes the conjugate transpose of v , and E
denotes expectation. Let us call our output, y , the inner
product of our lter and the observed signal such that

Derivation via matrix algebra

The following section derives the matched lter for a

discrete-time system. The derivation for a continuoustime system is similar, with summations replaced with
integrals.

y=

h [k]x[k] = hH x = hH s + hH v = ys + yv .

k=

The matched lter is the linear lter, h , that maximizes

the output signal-to-noise ratio.
We now dene the signal-to-noise ratio, which is our objective function, to be the ratio of the power of the output
due to the desired signal to the power of the output due

to the noise:
h[n k]x[k].
y[n] =
k=

Though we most often express lters as the impulse re|ys |2

sponse of convolution systems, as above (see LTI system SNR =
.
E{|yv |2 }
theory), it is easiest to think of the matched lter in the
context of the inner product, which we will see shortly.
We rewrite the above:
We can derive the linear lter that maximizes output
signal-to-noise ratio by invoking a geometric argument.
The intuition behind the matched lter relies on corre|hH s|2
SNR
=
.
lating the received signal (a vector) with a lter (another
E{|hH v|2 }
426

90.1. DERIVATION OF THE MATCHED FILTER

We wish to maximize this quantity by choosing h . Expanding the denominator of our objective function, we
have

427

1/2

SNR =

1/2

|(Rv h) (Rv
1/2

s)|2

1/2

1/2

(Rv h) (Rv h)

2 |(Rv

1/2

2 (Rv

1/2

s) (Rv
H

1/2

s) (Rv

H
E{|hH v|2 } = E{(hH v)(hH v) } = hH E{vv H }h = hH RvThus,
h. our optimal matched lter is

Now, our SNR becomes

h = Rv1 s.
SNR =

|hH s|2
.
hH Rv h

We often choose to normalize the expected value of the

power of the lter output due to the noise to unity. That
is, we constrain

We will rewrite this expression with some matrix manipulation. The reason for this seemingly counterproductive
measure will become evident shortly. Exploiting the Her2
mitian symmetry of the covariance matrix Rv , we can E{|yv | } = 1.
write
This constraint implies a value of , for which we can
solve:
1/2

SNR =

1/2

|(Rv h) (Rv
1/2

s)|2

1/2

E{|yv |2 } = 2 sH Rv1 s = 1,

(Rv h) (Rv h)

We would like to nd an upper bound on this expres- yielding

sion. To do so, we rst recognize a form of the CauchySchwarz inequality:
1
=
,
H
s Rv1 s
|aH b|2 (aH a)(bH b),
giving us our normalized lter,
which is to say that the square of the inner product of two
vectors can only be as large as the product of the individ1
ual inner products of the vectors. This concept returns to h =
Rv1 s.
1
H
s
R
s
v
the intuition behind the matched lter: this upper bound
is achieved when the two vectors a and b are parallel. We
If we care to write the impulse response of the lter for
resume our derivation by expressing the upper bound on
the convolution system, it is simply the complex conjugate
our SNR in light of the geometric inequality above:
time reversal of h .
Though we have derived the matched lter in discrete
]
][
time,
extend the concept to continuous-time
1/2weH can
1/2
1/2
1/2
s)
s) if(Rwe
(Rv h) (Rv h) (R
v replace
v
1/2 H
1/2
systems
Rv with the continuous-time
|(Rv h) (Rv s)|2
SNR =

. of the noise, assuming a continautocorrelation

function
H
H
1/2
1/2
1/2
1/2
(Rv h) (Rv h)
(Rv h) (R
h) s(t) , continuous noise v(t) , and a continuous
v signal
uous
[

Our valiant matrix manipulation has now paid o. We lter h(t) .

see that the expression for our upper bound can be greatly
simplied:

90.1.2 Derivation via Lagrangian

1/2

SNR =

1/2

|(Rv h) (Rv
1/2

1/2

s)|2

Rv1 s.

(Rv h) (Rv h)
We can achieve this upper bound if we choose,

Alternatively, we may solve for the matched lter by

solving our maximization problem with a Lagrangian.
Again, the matched lter endeavors to maximize the output signal-to-noise ratio ( SNR ) of a ltered deterministic signal in stochastic additive noise. The observed sequence, again, is

Rv1/2 h = Rv1/2 s
x = s + v,
where is an arbitrary real number. To verify this, we
plug into our expression for the output SNR :
with the noise covariance matrix,

s)|2
s)

|sH Rv1 s|
sH Rv1 s

428

CHAPTER 90. MATCHED FILTER

Rv = E{vv H }.

90.2 The matched lter as a least

squares estimator

The signal-to-noise ratio is

90.2.1 Derivation

|ys |2
SNR =
.
E{|yv |2 }

Matched ltering can also be interpreted as a least squares

estimator for the optimal location and scaling of a given
model or template. Once again, let the observed sequence
be dened as

Evaluating the expression in the numerator, we have

xk = sk + vk ,
|ys |2 = ys H ys = hH ssH h.
and in the denominator,

E{|yv |2 } = E{yv H yv } = E{hH vv H h} = hH Rv h.

The signal-to-noise ratio becomes

SNR =

hH ssH h
.
hH Rv h

where vk is uncorrelated zero mean noise. The signal sk

is assumed to be a scaled and shifted version of a known
model sequence fk :

sk = 0 fkj0
We want to nd optimal estimates j and for the unknown shift j0 and scaling 0 by minimizing the least
squares residual between the observed sequence xk and a
probing sequence hjk :

If we now constrain the denominator to be 1, the prob2

(xk hjk )
j , = arg min
lem of maximizing SNR is reduced to maximizing the
j,
k
numerator. We can then formulate the problem using a
Lagrange multiplier:
The appropriate hjk will later turn out to be the matched
lter, but is as yet unspecied. Expanding xk and the
square within the sum yields
hH Rv h = 1
L = hH ssH h + (1 hH Rv h)

j , = arg min

j,

which we recognize as a generalized eigenvalue problem

hH (ssH )h = hH Rv h.
Since ssH is of unit rank, it has only one nonzero eigenvalue. It can be shown that this eigenvalue equals

j,

max = s

Rv1 s,

yielding the following optimal matched lter

1
h=
Rv1 s.
1
H
s Rv s
This is the same result found in the previous subsection.

h2jk 2

The rst term in brackets is a constant (since the observed

signal is given) and has no inuence on the optimal solution. The last term has constant expected value because
the noise is uncorrelated and has zero mean. We can
therefore drop both terms from the optimization. After
reversing the sign, we obtain the equivalent optimization
problem

j , = arg max 2
H

h L = ssH h Rv h = 0
(ssH )h = Rv h

(sk + vk )2 + 2

sk hjk

]
h2jk

Setting the derivative w.r.t. to zero gives an analytic

solution for :

sk hjk
= k 2
k hjk

Inserting this into our objective function yields a reduced

maximization problem for just j :

sk hjk 2

90.3. FREQUENCY-DOMAIN INTERPRETATION

429

a given false-alarm probability[8] ) is not necessarily optimal. What is commonly referred to as the Signal-to
2
( k sk hjk )

noise ratio (SNR), which is supposed to be maximized

by

j = arg max 2
j
a matched lter, in this context corresponds to 2 log(L)
k hjk
, where L is the (conditionally) maximized likelihood
The numerator can be upper-bounded by means of the ratio.[7] [nb 1]
Cauchy-Schwarz inequality:
The construction of the matched lter is based on a known
noise spectrum. In reality, however, the noise spectrum is

usually estimated from data and hence only known up to a

2
2
2

( k sk hjk )
k sk
k hjk
2
2

sk = const limited precision. For the case of an uncertain spectrum,

=
2
k hjk
k hjk
the matched lter may be generalized to a more robust
k
iterative procedure with favourable properties also in nonThe optimization problem assumes its maximum when Gaussian noise.[7]
equality holds in this expression. According to the properties of the Cauchy-Schwarz inequality, this is only possible when

hjk = sk = fkj0
for arbitrary non-zero constants or , and the optimal
solution is obtained at j = j0 as desired. Thus, our
probing sequence hjk must be proportional to the signal model fkj0 , and the convenient choice = 1 yields
the matched lter

hk = fk
Note that the lter is the mirrored
signal model. This

ensures that the operation k xk hjk to be applied in

order to nd the optimum is indeed the convolution between the observed sequence xk and the matched lter
hk . The ltered sequence assumes its maximum at the
position where the observed sequence xk best matches
(in a least-squares sense) the signal model fk .

90.2.2

Implications

The matched lter may be derived in a variety of ways,[2]

but as a special case of a least squares procedure it may
also be interpreted as a maximum likelihood method in
the context of a (coloured) Gaussian noise model and
the associated Whittle likelihood.[5] If the transmitted
signal possessed no unknown parameters (like time-ofarrival, amplitude,...), then the matched lter would, according to the Neyman-Pearson lemma, minimize the
error probability. However, since the exact signal generally is determined by unknown parameters that eectively are estimated (or tted) in the ltering process, the
matched lter constitutes a generalized maximum likelihood (test-) statistic.[6] The ltered time series may then
be interpreted as (proportional to) the prole likelihood,
the maximized conditional likelihood as a function of the
time parameter.[7] This implies in particular that the error
probability (in the sense of Neyman and Pearson, i.e.,
concerning maximization of the detection probability for

90.3 Frequency-domain interpretation

When viewed in the frequency domain, it is evident

that the matched lter applies the greatest weighting
to spectral components exhibiting the greatest signal-tonoise ratio (i.e., large weight where noise is relatively
low, and vice versa). In general this requires a nonat frequency response, but the associated distortion
is no cause for concern in situations such as radar and
digital communications, where the original waveform is
known and the objective is the detection of this signal
against the background noise. On the technical side, the
matched lter is a weighted least squares method based on
the (heteroscedastic) frequency-domain data (where the
weights are determined via the noise spectrum, see also
previous section), or equivalently, a least squares method
applied to the whitened data.

90.4 Examples
90.4.1 Matched lter in radar and sonar
Matched lters are often used in signal detection.[1] As
an example, suppose that we wish to judge the distance
of an object by reecting a signal o it. We may choose to
transmit a pure-tone sinusoid at 1 Hz. We assume that our
received signal is an attenuated and phase-shifted form of
the transmitted signal with added noise.
To judge the distance of the object, we correlate the received signal with a matched lter, which, in the case of
white (uncorrelated) noise, is another pure-tone 1-Hz sinusoid. When the output of the matched lter system exceeds a certain threshold, we conclude with high probability that the received signal has been reected o the object. Using the speed of propagation and the time that we
rst observe the reected signal, we can estimate the distance of the object. If we change the shape of the pulse in
a specially-designed way, the signal-to-noise ratio and the

430

CHAPTER 90. MATCHED FILTER

distance resolution can be even improved after matched where T is the time length of one bit.
ltering: this is a technique known as pulse compression. Thus, the signal to be sent by the transmitter is
Additionally, matched lters can be used in parameter
estimation problems (see estimation theory). To return
to our previous example, we may desire to estimate the
speed of the object, in addition to its position. To exploit the Doppler eect, we would like to estimate the
frequency of the received signal. To do so, we may correlate the received signal with several matched lters of
sinusoids at varying frequencies. The matched lter with
the highest output will reveal, with high probability, the
frequency of the reected signal and help us determine
the speed of the object. This method is, in fact, a sim- If we model our noisy channel as an AWGN channel,
ple version of the discrete Fourier transform (DFT). The white Gaussian noise is added to the signal. At the reDFT takes an N -valued complex input and correlates it ceiver end, for a Signal-to-noise ratio of 3 dB, this may
with N matched lters, corresponding to complex expo- look like:
nentials at N dierent frequencies, to yield N complexvalued numbers corresponding to the relative amplitudes
and phases of the sinusoidal components (see Moving target indication).

0 1 0 1 1 0 0 1 0 0

90.4.2

Matched lter in digital communications

The matched lter is also used in communications. In

the context of a communication system that sends binary
messages from the transmitter to the receiver across a A rst glance will not reveal the original transmitted senoisy channel, a matched lter can be used to detect the quence. There is a high power of noise relative to the
power of the desired signal (i.e., there is a low signal-totransmitted pulses in the noisy received signal.
noise ratio). If the receiver were to sample this signal at
the correct moments, the resulting binary message would
possibly belie the original transmitted one.
To increase our signal-to-noise ratio, we pass the received
signal through a matched lter. In this case, the lter should be matched to an NRZ pulse (equivalent to
a 1 coded in NRZ code). Precisely, the impulse response of the ideal matched lter, assuming white (uncorrelated) noise should be a time-reversed complexImagine we want to send the sequence 0101100100 conjugated scaled version of the signal that we are seekcoded in non polar Non-return-to-zero (NRZ) through a ing. We choose
certain channel.
Mathematically, a sequence in NRZ code can be de( )
t
scribed as a sequence of unit pulses or shifted rect funch(t) =
.
tions, each pulse being weighted by +1 if the bit is 1
T
and by 1 if the bit is 0. Formally, the scaling factor
In this case, due to symmetry, the time-reversed complex
for the k th bit is,
conjugate of h(t) is in fact h(t) , allowing us to call h(t)
the impulse response of our matched lter convolution
{
+1, if bit k is 1,
system.
ak =
1, if bit k is 0.
After convolving with the correct matched lter, the reWe can represent our message, M (t) , as the sum of sulting signal, Mfiltered (t) is,
shifted unit pulses:

M (t) =

k=

(
ak

t kT
T

Mfiltered (t) = M (t) h(t)

)
.

where denotes convolution.

90.6. NOTES

431

90.6 Notes

Which can now be safely sampled by the receiver at the

correct sampling instants, and compared to an appropriate threshold, resulting in a correct interpretation of the
binary message.

[1] The common reference to SNR has in fact been criticized

as somewhat misleading: "The interesting feature of this
approach is that theoretical perfection is attained without
aiming consciously at a maximum signal/noise ratio. As a
matter of quite incidental interest, it happens that the operation [...] does maximize the peak signal/noise ratio, but
this fact plays no part whatsoever in the present theory.
Signal/noise ratio is not a measure of information [...]."
(Woodward, 1953;[1] Sec.5.1).

90.7 References

P. M. (1953). Probability and information

0 1 0 1 1 0 0 1 0[1] Woodward,
0
theory with applications to radar. London: Pergamon
Press.
[2] Turin, G. L. (1960). An introduction to matched lters.
IRE Transactions on Information Theory. 6 (3): 311329.
doi:10.1109/TIT.1960.1057571.
[3] http://cnx.org/content/m10141/latest/

90.4.3

Matched lter in gravitational-wave

astronomy

Matched lters play a central role in gravitational-wave

astronomy.[9] The rst observation of gravitational waves
was based on large-scale ltering of each detectors output for signals resembling the expected shape, followed
by subsequent screening for coincident and coherent triggers between both instruments. False-alarm rates, and
with that, the statistical signicance of the detection were
then assessed using resampling methods.[10] Inference on
the astrophysical source parameters was eventually done
using Bayes methods based on parameterized theoretical
models for the signal waveform and (again) on the Whittle
likelihood.[11]

90.5 See also

Digital lter
Statistical signal processing
Whittle likelihood
Detection theory
Multiple comparisons problem
Channel capacity
Noisy channel coding theorem
Spectral density estimation

[4] After D.O. North who was among the rst to introduce
the concept: North, D. O. (1943). An analysis of the
factors which determine signal/noise discrimination in
pulsed carrier systems. Report PPR-6C, RCA Laboratories, Princeton, NJ.
Re-print: North, D. O. (1963). An analysis of the factors
which determine signal/noise discrimination in pulsedcarrier systems. Proceedings of the IEEE. 51 (7): 1016
1027. doi:10.1109/PROC.1963.2383.
See also: Jaynes, E. T. (2003). 14.6.1 The classical
matched lter". Probability theory: The logic of science.
Cambridge: Cambridge University Press.
[5] Choudhuri, N.; Ghosal, S.; Roy, A. (2004).
Contiguity of the Whittle measure for a Gaussian time series. Biometrika. 91 (4): 211218.
doi:10.1093/biomet/91.1.211.
[6] Mood, A. M.; Graybill, F. A.; Boes, D. C. IX. Tests of
hypotheses". Introduction to the theory of statistics (3rd
ed.). New York: McGraw-Hill.
[7] Rver, C. (2011). Student-t based lter for robust signal detection. Physical Review D. 84 (12): 122004.
arXiv:1109.0442 . doi:10.1103/PhysRevD.84.122004.
[8] Neyman, J.; Pearson, E. S. (1933). On the problem of the
most ecient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London, Series A.
231 (694706): 289337. doi:10.1098/rsta.1933.0009.
[9] Schutz, B. F. (1999). Gravitational wave astronomy.
Classical and Quantum Gravity. 16 (12A): A131
arXiv:gr-qc/9911034 .
doi:10.1088/0264A156.
9381/16/12A/307.
[10] Abbott, B. P.; et al. (The LIGO Scientic Collaboration,
the Virgo Collaboration) (2016).
GW150914:
First results from the search for binary black

432

CHAPTER 90. MATCHED FILTER

hole coalescence with Advanced LIGO.

Physical Review D (93): 122003. arXiv:1602.03839 .
doi:10.1103/PhysRevD.93.122003.
[11] Abbott, B. P.; et al. (The LIGO Scientic Collaboration, the Virgo Collaboration) (2016). Properties
of the binary black hole merger GW150914. Physical Review Letters (116): 241102. arXiv:1602.03840 .
doi:10.1103/PhysRevLett.116.241102.

90.8 Further reading

Turin, G. L. (1960). An introduction to matched
lters. IRE Transactions on Information Theory. 6
(3): 311329. doi:10.1109/TIT.1960.1057571.
Wainstein, L. A.; Zubakov, V. D. (1962). Extraction of signals from noise. Englewood Clis, NJ:
Prentice-Hall.
Melvin, W. L. (2004). A STAP overview. IEEE
Aerospace and Electronic Systems Magazine. 19 (1):
1935. doi:10.1109/MAES.2004.1263229.
Fish, A.; Gurevich, S.; Hadani, R.; Sayeed, A.;
Schwartz, O. (December 2011). Computing the
matched lter in linear time. arXiv:1112.4883
[cs.IT].

Chapter 91

Intersymbol interference
In telecommunication, Intersymbol Interference (ISI)
is a form of distortion of a signal in which one symbol
interferes with subsequent symbols. This is an unwanted
phenomenon as the previous symbols have similar eect
as noise, thus making the communication less reliable.
The spreading of the pulse beyond its allotted time interval causes it to interfere with neighboring pulses.[1] ISI is
usually caused by multipath propagation or the inherent
non-linear frequency response of a channel causing successive symbols to blur together.
The presence of ISI in the system introduces errors in the
decision device at the receiver output. Therefore, in the
design of the transmitting and receiving lters, the objective is to minimize the eects of ISI, and thereby deliver
the digital data to its destination with the smallest error
rate possible.

91.1.2 Bandlimited channels

Another cause of intersymbol interference is the transmission of a signal through a bandlimited channel, i.e.,
one where the frequency response is zero above a certain
frequency (the cuto frequency). Passing a signal through
such a channel results in the removal of frequency components above this cuto frequency. In addition, components of the frequency below the cuto frequency may
also be attenuated by the channel.

This ltering of the transmitted signal aects the shape of

the pulse that arrives at the receiver. The eects of ltering a rectangular pulse not only change the shape of the
pulse within the rst symbol period, but it is also spread
out over the subsequent symbol periods. When a message
is transmitted through such a channel, the spread pulse of
Ways to ght intersymbol interference include adaptive each individual symbol will interfere with following symequalization and error correcting codes.[2]
bols.
Bandlimited channels are present in both wired and wireless communications. The limitation is often imposed by
the desire to operate multiple independent signals through
the same area/cable; due to this, each system is typi91.1 Causes
cally allocated a piece of the total bandwidth available.
For wireless systems, they may be allocated a slice of
the electromagnetic spectrum to transmit in (for exam91.1.1 Multipath propagation
ple, FM radio is often broadcast in the 87.5 MHz - 108
MHz range). This allocation is usually administered by a
Main article: Multipath propagation
government agency; in the case of the United States this
is the Federal Communications Commission (FCC). In a
One of the causes of intersymbol interference is wired system, such as an optical ber cable, the allocation
multipath propagation in which a wireless signal from a will be decided by the owner of the cable.
transmitter reaches the receiver via multiple paths. The
causes of this include reection (for instance, the signal The bandlimiting can also be due to the physical propermay bounce o buildings), refraction (such as through ties of the medium - for instance, the cable being used in
the foliage of a tree) and atmospheric eects such as a wired system may have a cuto frequency above which
atmospheric ducting and ionospheric reection. Since practically none of the transmitted signal will propagate.
the various paths can be of dierent lengths, this results Communication systems that transmit data over bandlimin the dierent versions of the signal arriving at the re- ited channels usually implement pulse shaping to avoid
ceiver at dierent times. These delays mean that part or interference caused by the bandwidth limitation. If the
all of a given symbol will be spread into the subsequent channel frequency response is at and the shaping lter
symbols, thereby interfering with the correct detection has a nite bandwidth, it is possible to communicate with
of those symbols. Additionally, the various paths often no ISI at all. Often the channel response is not known bedistort the amplitude and/or phase of the signal, thereby forehand, and an adaptive equalizer is used to compensate
causing further interference with the received signal.
the frequency response.
433

434

CHAPTER 91. INTERSYMBOL INTERFERENCE

91.2 Eects on eye patterns

The eye diagram of a binary PSK system

For more details on eye patterns, see Eye pattern.

The eye diagram of the same system with multipath

eects added

One way to study ISI in a PCM or data transmission system experimentally is to apply the received wave to the 91.3 Countering ISI
vertical deection plates of an oscilloscope and to apply a
sawtooth wave at the transmitted symbol rate R (R = 1/T)
There are several techniques in telecommunication and
to the horizontal deection plates. The resulting display
data storage that try to work around the problem of interis called an eye pattern because of its resemblance to the
symbol interference.
human eye for binary waves. The interior region of the
eye pattern is called the eye opening. An eye pattern pro Design systems such that the impulse response is
vides a great deal of information about the performance
short enough that very little energy from one symof the pertinent system.
bol smears into the next symbol.
1. The width of the eye opening denes the time interval over which the received wave can be sampled
without error from ISI. It is apparent that the preferred time for sampling is the instant of time at
which the eye is open widest.
2. The sensitivity of the system to timing error is determined by the rate of closure of the eye as the sampling time is varied.
3. The height of the eye opening, at a specied sampling time, denes the margin over noise.
Consecutive raised-cosine impulses, demonstrating zero-ISI prop-

An eye pattern, which overlays many samples of a signal, erty

can give a graphical representation of the signal characteristics. The rst image below is the eye pattern for a
binary phase-shift keying (PSK) system in which a one is
Separate symbols in time with guard periods.
represented by an amplitude of 1 and a zero by an am Apply an equalizer at the receiver, that, broadly
plitude of +1. The current sampling time is at the center
speaking, attempts to undo the eect of the chanof the image and the previous and next sampling times are
nel by applying an inverse lter.
at the edges of the image. The various transitions from
one sampling time to another (such as one-to-zero, one Apply a sequence detector at the receiver, that atto-one and so forth) can clearly be seen on the diagram.
tempts to estimate the sequence of transmitted symbols using the Viterbi algorithm.
The noise margin - the amount of noise required to cause
the receiver to get an error - is given by the distance between the signal and the zero amplitude point at the sampling time; in other words, the further from zero at the 91.4 Intentional Intersymbol intersampling time the signal is the better. For the signal to
ference
be correctly interpreted, it must be sampled somewhere
between the two points where the zero-to-one and oneto-zero transitions cross. Again, the further apart these There exist also coded modulation systems that intentionpoints are the better, as this means the signal will be less ally builds a controlled amount of ISI into the system at
sensitive to errors in the timing of the samples at the re- the transmitter side, this is known under the name Fasterthan-Nyquist Signaling. Such a design trades a computaceiver.
tional complexity penalty at the receiver against a ShanThe eects of ISI are shown in the second image which
non capacity gain of the overall transceiver system. See
is an eye pattern of the same system when operating over [3]
for a recent survey of this technique.
a multipath channel. The eects of receiving delayed and
distorted versions of the signal can be seen in the loss of
denition of the signal transitions. It also reduces both the
noise margin and the window in which the signal can be 91.5 See also
sampled, which shows that the performance of the system
Nyquist ISI criterion
will be worse (i.e. it will have a greater bit error ratio).

91.8. EXTERNAL LINKS

91.6 References
[1] Lathi, B.P.; Ding, Zhi (2009). Modern Digital and Analog
Communication Systems (Fourth ed.). Oxford University
Press, Inc. p. 394. ISBN 9780195331455.
[2] Digital Communications by Simon Haykin, McMaster
University
[3] Faster than Nyquist Signaling, by J.B. Anderson, F.
Rusek, and V. Owall, Proceedings of the IEEE, Aug.
2013

91.7 Further reading

William J. Dally and John W. Poulton (1998). Digital Systems Engineering. Cambridge University
Press. pp. 280285. ISBN 9780521592925.
Herv Benoit (2002). Digital Television. Focal
Press. pp. 9091. ISBN 9780240516950.

91.8 External links

Denition of ISI from Federal Standard 1037C
Intersymbol Interference concept

435

Chapter 92

Phase synchronization
Phase synchronization is the process by which two or 92.3 External links
more cyclic signals tend to oscillate with a repeating sequence of relative phase angles.
A tutorial on calculating Phase locking and Phase synPhase synchronisation is usually applied to two wave- chronization in Matlab.
forms of the same frequency with identical phase angles
with each cycle. However it can be applied if there is
an integer relationship of frequency, such that the cyclic
signals share a repeating sequence of phase angles over
consecutive cycles. These integer relationships are called
Arnold tongues which follow from bifurcation of the circle map.
One example of phase synchronization of multiple oscillators can be seen in the behavior of Southeast Asian
reies. At dusk, the ies begin to ash periodically with
random phases and a gaussian distribution of native frequencies. As night falls, the ies, sensitive to one anothers behavior, begin to synchronize their ashing. After some time all the reies within a given tree (or even
larger area) will begin to ash simultaneously in a burst.
Thinking of the reies as biological oscillators, we can
dene the phase to be 0 during the ash and +180 exactly halfway until the next ash. Thus, when they begin
to ash in unison, they synchronize in phase.
One way to keep a local oscillator phase synchronized
with a remote transmitter uses a phase-locked loop.

92.1 See also

Algebraic connectivity
Alternator synchronization
Kuramoto model

92.2 References
Sync by S. H. Strogatz (2002).
Synchronization - A universal concept in nonlinear
sciences by A. Pikovsky, M. Rosenblum, J. Kurths
(2001)
436

Chapter 93

Asynchronous communication
For other uses, see Asynchrony.

bit transition times. Note that at the physical layer, this is

considered as synchronous serial communication. ExamIn telecommunications, asynchronous communication ples of packet mode data link protocols that can be/are
transferred using synchronous serial communication are
is transmission of data, generally without the use of an
external clock signal, where data can be transmitted in- the HDLC, Ethernet, PPP and USB protocols.
termittently rather than in a steady stream.[1] Any timing
required to recover data from the communication symbols is encoded within the symbols. The most signi- 93.3 Application layer
cant aspect of asynchronous communications is that data
is not transmitted at regular intervals, thus making possi- An asynchronous communication service or application
ble variable bit rate, and that the transmitter and receiver does not require a constant bit rate. Examples are le
clock generators do not have to be exactly synchronized transfer, email and the World Wide Web. An example
all the time.
of the opposite, a synchronous communication service, is
realtime streaming media, for example IP telephony, IPTV and video conferencing.

93.1 Physical layer

93.4 Electronically mediated communication

Main article: Asynchronous serial communication

In asynchronous serial communication the physical protocol layer, the data blocks are code words of a certain
word length, for example octets (bytes) or ASCII characters, delimited by start bits and stop bits. A variable
length space can be inserted between the code words.
No bit synchronization signal is required. This is sometimes called character oriented communication. Examples are the RS-232C serial standard, and MNP2 and V.2
modems and older.

93.2 Data link layer and higher

Asynchronous communication at the data link layer or
higher protocol layers is known as statistical multiplexing, for example asynchronous transfer mode (ATM). In
this case the asynchronously transferred blocks are called
data packets, for example ATM cells. The opposite is
circuit switched communication, which provides constant
bit rate, for example ISDN and SONET/SDH.

Electronically mediated communication often happens

asynchronously in that the participants do not communicate concurrently. Examples include email[2] and
bulletin-board systems, where participants send or post
messages at dierent times. The term asynchronous
communication acquired currency in the eld of online
learning, where teachers and students often exchange information asynchronously instead of synchronously (that
is, simultaneously), as they would in face-to-face or in
telephone conversations.

93.5 See also

The packets may be encapsulated in a data frame, with

a frame synchronization bit sequence indicating the start
of the frame, and sometimes also a bit synchronization
bit sequence, typically 01010101, for identication of the
437

Synchronization in telecommunications
Asynchronous serial communication
Asynchronous system
Asynchronous transfer mode (ATM)
Asynchronous circuit
Asynchrony

438
Anisochronous
Baud rate
Plesiochronous
Plesiochronous Digital Hierarchy (PDH)

93.6 References
[1] asynchronous. http://www.webopedia.com/: Webopedia. Archived from the original on 30 April 2011. Retrieved 2011-04-27. The term asynchronous is usually
used to describe communications in which data can be
transmitted intermittently rather than in a steady stream.
[2] Calladine, Richard (2006). A taxonomy of learning technologies: simplifying online learning for learners, professors, and designers. In Khosrowpour, Mehdi. Emerging
Trends and Challenges in Information Technology Management: 2006 Information Resources Management Association International Conference, Washington, DC, USA,
May 21-24, 2006. 1. Idea Group Inc (IGI). p. 249. ISBN
9781599040196. Retrieved 2014-09-03. Email and Internet Chat provide a good example of the dierence between synchronous and asynchronous technologies. Email
is generally responded to at the discretion of the user and
hence is described as asynchronous. However, when in
a Chat session each participant knows that the others are
waiting for their responses. The resulting conversations
are synchronous [...]

CHAPTER 93. ASYNCHRONOUS COMMUNICATION

Chapter 94

Multiple frequency-shift keying

Multiple frequency-shift keying (MFSK) is a variation
of frequency-shift keying (FSK) that uses more than two
frequencies. MFSK is a form of M-ary orthogonal modulation, where each symbol consists of one element from
an alphabet of orthogonal waveforms. M, the size of the
alphabet, is usually a power of two so that each symbol
represents log2 M bits.
M is usually between 2 and 64

94.1.1 2-tone MFSK

It is possible to combine two MFSK systems to increase the throughput of the link. Perhaps the most
widely used 2-tone MFSK system is dual-tone multifrequency (DTMF), better known by its AT&T trademark of Touch Tone. Another is the Multi-frequency
(MF) scheme used during the 20th century for in-band
signalling on trunks between telephone exchanges. Both
are examples of in-band signaling schemes, i.e., they
share the users communication channel.

Error Correction is generally also used

Symbols in the DTMF and MF alphabets are sent as tone

pairs; DTMF selects one tone from a high group and
one from a low group, while MF selects its two tones
from a common set. DTMF and MF use dierent tone
94.1 MFSK Fundamentals
frequencies largely to keep end users from interfering
with inter-oce signaling. In the 1970s, MF began to
In a M-ary signaling system like MFSK, an alphabet of be replaced by digital out-of-band signaling, a conversion
M tones is established and the transmitter selects one tone motivated in part by the widespread fraudulent use of MF
at a time from the alphabet for transmission. M is usually signals by end users known as phone phreaks.
a power of 2, so each tone transmission from the alphabet These signals are distinctive when received aurally as
represents log2 M data bits.
a rapid succession of tone pairs with almost musical
[1]
MFSK is classed as an M-ary orthogonal signaling quality.
scheme because each of the M tone detection lters at The simultaneous transmission of two tones directly at
the receiver responds only to its tone and not at all to the RF loses the constant-envelope property of the single tone
others; this independence provides the orthogonality.
system. Two simultaneous RF tones is in fact the classic
Like other M-ary orthogonal schemes, the required E /N0 stress test of an RF power amplier for measuring linratio for a given probability of error decreases as M in- earity and intermodulation distortion. However, two aucreases without the need for multisymbol coherent de- dio tones can be sent simultaneously on a conventional,
tection. In fact, as M approaches innity the required constant-envelope FM RF carrier, but the noncoherent
E /N0 ratio decreases asymptotically to the Shannon limit detection of the FM signal at the receiver would destroy
of 1.6 dB. However this decrease is slow with increas- any signal-to-noise ratio advantage the multitone scheme
ing M, and large values are impractical because of the ex- might have.
ponential increase in required bandwidth. Typical values
in practice range from 4 to 64, and MFSK is combined
with another forward error correction scheme to provide
additional (systematic) coding gain.
94.1.2
Like any other form of angle modulation that transmits
a single RF tone that varies only in phase or frequency,
MFSK produces a constant envelope. This signicantly
relaxes the design of the RF power amplier, allowing it
to achieve greater conversion eciencies than linear ampliers.

MFSK in HF communications

Skywave propagation on the high frequency bands introduces random distortions that generally vary with both
time and frequency. Understanding these impairments
helps one understand why MFSK is such an eective and
popular technique on HF.

439

440
Delay spread and coherence bandwidth
When several separate paths from transmitter to receiver
exist, a condition known as multipath, they almost never
have exactly the same length so they almost never exhibit
the same propagation delay. Small delay dierences,
or delay spread, smear adjacent modulation symbols together and cause unwanted intersymbol interference.
Delay spread is inversely proportional to its frequencydomain counterpart, coherence bandwidth. This is the
frequency range over which the channel gain is relatively
constant. This is because summing two or more paths
with dierent delays creates a comb lter even when the
individual paths have a at frequency response.
Coherence time and Doppler spread
Fading is a (usually random and undesired) change in path
gain with time. The maximum fade rate is limited by
the physics of the channel, such as the rate at which free
electrons form and are recombined in the ionosphere and
charged particle cloud velocities within the ionosphere.
The maximum interval over which the channel gain does
not appreciably change is the coherence time.
A fading channel eectively imposes an unwanted random amplitude modulation on the signal. Just as the
bandwidth of intentional AM increases with the modulation rate, fading spreads a signal over a frequency
range that increases with the fading rate. This is Doppler
spreading, the frequency domain counterpart of coherence time. The shorter the coherence time, the greater
the Doppler spread and vice versa.
Designing MFSK for HF
With appropriate parameter selection, MFSK can tolerate signicant Doppler or delay spreads, especially when
augmented with forward error correction. (Mitigating
large amounts of Doppler and delay spread is signicantly more challenging, but it is still possible). A long
delay spread with little Doppler spreading can be mitigated with a relatively long MFSK symbol period to allow
the channel to settle down quickly at the start of each
new symbol. Because a long symbol contains more energy than a short one for a given transmitter power, the
detector can more easily attain a suciently high signalto-noise ratio (SNR). The resultant throughput reduction
can be partly compensated with a large tone set so that
each symbol represents several data bits; a long symbol
interval allows these tones to be packed more closely in
frequency while maintaining orthogonality. This is limited by the exponential growth of tone set size with the
number of data bits/symbol.

CHAPTER 94. MULTIPLE FREQUENCY-SHIFT KEYING

more widely to maintain orthogonality.
The most challenging case is when the delay and Doppler
spreads are both large, i.e., the coherence bandwidth and
coherence time are both small. This is more common
on auroral and EME channels than on HF, but it can occur. A short coherence time limits the symbol time, or
more precisely, the maximum coherent detection interval at the receiver. If the symbol energy is too small
for an adequate per-symbol detection SNR, then one alternative is transmit a symbol longer than the coherence
time but to detect it with a lter much wider than one
matched to the transmitted symbol. (The lter should instead be matched to the tone spectrum expected at the
receiver). This will capture much of the symbol energy
despite Doppler spreading, but it will necessarily do so
ineciently. A wider tone spacing, i.e., a wider channel,
is also required. Forward error correction is especially
helpful in this case.
MFSK schemes for HF
Because of the wide variety of conditions found on HF,
a wide variety of MFSK schemes, some of them experimental, have been developed for HF. Some of them are:
MFSK8
MFSK16
Olivia MFSK
Coquelet
Piccolo
ALE (MIL-STD 188-141)
DominoF
DominoEX
THROB
CIS-36 MFSK or CROWD-36
XPA, XPA2
Piccolo was the original MFSK mode, developed for
British government communications by Harold Robin,
Donald Bailey and Denis Ralphs of the Diplomatic Wireless Service (DWS), a branch of the Foreign and Commonwealth Oce. It was rst used in 1962 [2] and
presented to the IEE in 1963. The current specication Piccolo Mark IV is still in limited use by the
UK government, mainly for point-to-point military radio
communications.[3][4]

Coquelet is a similar modulation system developed by the

[2]
Conversely, if the Doppler spread is large while the delay French government for similar applications.
spread is small, then a shorter symbol period may per- MFSK8 and MFSK16 were developed by Murray Greenmit coherent tone detection and the tones must be spaced man, ZL1BPU for amateur radio communications on HF.

94.3. REFERENCES
Olivia MFSK is also an amateur radio mode. Greenman
has also developed DominoF and DominoEX for NVIS
radio communications on the upper MF and lower HF
frequencies (1.8-7.3 MHz).
ALE (Automatic link establishment) is a protocol developed by the USA military and used mainly as an automatic signalling system between radios. It is used extensively for military and government communications
worldwide and by radio amateurs.[5] It is standardized as
MIL-STD-188-141B,[6] which succeeded the older version MIL-STD-188-141A.
CIS-36 MFSK or CROWD-36 is the western designation of a system similar to Piccolo developed in the former Soviet Union for military communications.[7][8]
XPA and XPA2 are ENIGMA-2000 [9] designations
for polytonic tranismissions, reportedly originating from
Russian Intelligence and Foreign Ministry stations.[10][11]
Recently the system was also described as MFSK-20.

94.1.3

VHF & UHF communications

MFSK modes used for VHF, UHF communications:

DTMF

441
frequency-hopping spread spectrum also uses many
dierent frequencies, where each symbol uses only
one frequency.
DTMF
Olivia MFSK
ALE (MIL-STD 188-141)
WSJT

94.3 References
[1] Scalsky, S.; Chace, M. (1999). Digital Signals Frequently Asked Questions (Version 5), Section 1-D.
World Utility Network (WUN). Retrieved 2012-11-27.
[2] Greenman, M.; ZL1BPU (2005). The World of Fuzzy
and Digital Modes. Archived from the original on April
24, 2009. Retrieved 2008-01-06.
[3] Klingenfuss, J. (2003). Radio Data Code Manual (17th
Ed.). Klingenfuss Publications. p. 163. ISBN 3-92450956-5.
[4] Cannon, Michael (1994). Eavesdropping on the British
Military. Dublin, Eire: Cara Press. pp. 103104.

FSK441

[5] Klingenfuss, J. (2003). Radio Data Code Manual (17th

Ed.). Klingenfuss Publications. pp. 7278. ISBN 3924509-56-5.

JT6M

[6] MIL-STD 188-141B (PDF). US Government.

JT65
PI4

[7] Klingenfuss, J. (2003). Radio Data Code Manual (17th

Ed.). Klingenfuss Publications. p. 91. ISBN 3-92450956-5.
[8] Scalsky, S.; Chace, M. (1999). Digital Signals Fre-

quently Asked Questions (Version 5), Table 5-E. World

FSK441, JT6M and JT65 are parts of the WSJT famUtility Network (WUN). Retrieved 2012-11-27.
ily or radio modulation systems, developed by Joe Taylor, K1JT, for long distance amateur radio VHF commu- [9] For information about ENIGMA and ENIGMA-2000 see
nications under marginal propagation conditions. These
Notes and References section in Letter beacon.
specialized MFSK modulation systems are used over troposcattering, EME (earth-moon-earth) and meteoscatter- [10] Beaumont, P. (May 2008). Undiminished (Atencion Uno
Dos Tres)". Monitoring Monthly. 3 (5): 69. ISSN 1749ing radio paths.
7809.

PI4[12] is a digital mode specically designed for VUSHF

beacon and propagation studies. The mode was devel- [11] Beaumont, P. (July 2008). Russian Intel (Atencion Uno
Dos Tres)". Monitoring Monthly. 3 (7): 69. ISSN 1749oped as part of the Next Generation Beacons project
7809.
among others used by the oldest amateur beacon in the
world OZ7IGY. A decoder for PI4 is available in the PI- [12] PI4
RX program developed by Poul-Erik Hansen, OZ1CKG.
DTMF was initially developed for telephone line signaling. It is frequently used for telecommand (remote control) applications over VHF and UHF voice channels.

94.4 Further reading

94.2 See also

Dehio, Leif. MFSK-systems (Multi Frequency

Shift Keying)". Retrieved 2008-02-21.: Samples of
a variety of MFSK signals.

Radioteletype

Ford, S.; WB8IMY (2001). ARRLs HF Digital

Handbook. ARRL. ISBN 0-87259-823-3.

442
Greenman, M.; ZL1BPU (2002). Digital Modes for
all Occasions. RSGB. ISBN 1-872309-82-8.
Greenman, M.; ZL1BPU (January 2001). MFSK
for the New Millennium. QST. ARRL: 1214.
Greenman, M.; ZL1BPU (2005). The World of
Fuzzy and Digital Modes. Archived from the original on August 31, 2006. Retrieved 2008-01-06.
Klingenfuss, J. (2003). Radio Data Code Manual (17th Ed.). Klingenfuss Publications. ISBN 3924509-56-5.
Ralphs, J.D. (1985). Principles and practice of
multi-frequency telegraphy (IEE Telecommunications Series). Peter Peregrinus Ltd. ISBN 0-86341022-7.
Scalsky, S.; Chace, M. (1999). Digital Signals Frequently Asked Questions (Version 5)". World Utility Network (WUN). Retrieved 2008-01-06.
M Nasseri, J Kim, M Alam - Proceedings of the
17th Communications & Networking, 2014, Unied metric calculation of sampling-based turbocoded noncoherent MFSK for mobile channel

CHAPTER 94. MULTIPLE FREQUENCY-SHIFT KEYING

Chapter 95

Dual-tone multi-frequency signaling

Tone dialing redirects here. For Ornette Coleman album, see Tone Dialing (album).
For the video game, see TouchTone.
Dual-tone multi-frequency signaling (DTMF) is

The keypads on telephones for the Autovon systems used all 16

DTMF signals. The red keys in the fourth column produce the A,
B, C, and D DTMF events.

DP) in the U.S. It functions by interrupting the current

in the local loop between the telephone exchange and the
calling party's telephone at a precise rate with a switch
in the telephone that is operated by the rotary dial as it
spins back to its rest position after having been rotated to
each desired number. The exchange equipment responds
to the dial pulses either directly by operating relays, or by
storing the number in a digit register recording the dialed
number. The physical distance for which this type of dialing was possible was restricted by electrical distortions
and was only possible on direct metallic links between
end points of a line. Placing calls over longer distances
required either operator assistance or provision of special subscriber trunk dialing equipment. Operators used
an earlier type of multi-frequency signaling.
Multi-frequency signaling is a group of signaling methods that use a mixture of two pure tone (pure sine wave)
sounds. Various MF signaling protocols were devised by
the Bell System and CCITT. The earliest of these were for
in-band signaling between switching centers, where longdistance telephone operators used a 16-digit keypad to
input the next portion of the destination telephone number in order to contact the next downstream long-distance
telephone operator. This semi-automated signaling and
switching proved successful in both speed and cost eectiveness. Based on this prior success with using MF by
specialists to establish long-distance telephone calls, dualtone multi-frequency signaling was developed for enduser signaling without the assistance of operators.

an in-band telecommunication signaling system using

the voice-frequency band over telephone lines between
telephone equipment and other communications devices
and switching centers. DTMF was rst developed in the
Bell System in the United States, and became known under the trademark Touch-Tone for use in push-button
telephones supplied to telephone customers, starting in
1963.[1] DTMF is standardized by ITU-T Recommenda- The DTMF system uses a set of eight audio frequencies
transmitted in pairs to represent 16 signals, represented by
tion Q.23. It is also known in the UK as MF4.
the ten digits, the letters A to D, and the symbols # and
The Touch-Tone system using a telephone keypad grad- *. As the signals are audible tones in the voice frequency
ually replaced the use of rotary dial and has become the range, they can be transmitted through electrical repeaters
industry standard for landline and mobile service. Other and ampliers, and over radio and microwave links, thus
multi-frequency systems are used for internal signaling eliminating the need for intermediate operators on longwithin the telephone network.
distance circuits.
AT&T described the product as a method for pushbutton signaling from customer stations using the voice trans95.1 Multifrequency signaling
mission path.[2] In order to prevent consumer telephones
from interfering with the MF-based routing and switching
Prior to the development of DTMF, telephone numbers between telephone switching centers, DTMF frequencies
were dialed by users with a loop-disconnect (LD) signal- dier from all of the pre-existing MF signaling protocols
ing, more commonly known as pulse dialing (dial pulse, between switching centers: MF/R1, R2, CCS4, CCS5,
443

444

CHAPTER 95. DUAL-TONE MULTI-FREQUENCY SIGNALING

and others that were later replaced by SS7 digital signaling. DTMF was known throughout the Bell System
by the trademark Touch-Tone. The term was rst used
by AT&T in commerce on July 5, 1960 and was introduced to the public on November 18, 1963, when the rst
push-button telephone was made available to the public.
It was a registered trademark by AT&T from September
4, 1962 to March 13, 1984. It is standardized by ITU-T
Recommendation Q.23. In the UK, it is also known as
MF4.

keys were dropped from most phones, and it was many

years before the two symbol keys became widely used for
vertical service codes such as *67 in the United States of
America and Canada to suppress caller ID.

95.2 #, *, A, B, C, and D

1 2 3 A

DTMF signaling tones can also be heard at the start or

end of some VHS (Video Home System) cassette tapes.
Information on the master version of the video tape is
encoded in the DTMF tone. The encoded tone provides
information to automatic duplication machines, such as
format, duration and volume levels, in order to replicate
the original video as closely as possible.

4 5 6 B

DTMF tones are used in some caller ID systems to transfer the caller ID information, but in the United States only
Bell 202 modulated FSK signaling is used to transfer the
data.

Public payphones that accept credit cards use these additional codes to send the information from the magnetic
strip.

The AUTOVON telephone system of the United States

Armed Forces used these signals to assert certain privilege and priority levels when placing telephone calls.[3]
Other vendors of compatible telephone equipment called Precedence is still a feature of military telephone netthe Touch-Tone feature tone dialing or DTMF, or used works, but using number combinations. For example, entheir other trade names such as Digitone by Northern tering 93 before a number is a priority call.
Electric Company in Canada.
Present-day uses of the A, B, C and D signals on teleAs a method of in-band signaling, DTMF signals were phone networks are few, and are exclusive to network
also used by cable television broadcasters to indicate the control. For example, the A key is used on some netstart and stop times of local commercial insertion points works to cycle through dierent carriers at will. The A,
during station breaks for the benet of cable companies. B, C and D tones are used in radio phone patch and reUntil out-of-band signaling equipment was developed in peater operations to allow, among other uses, control of
the 1990s, fast, unacknowledged DTMF tone sequences the repeater while connected to an active phone line.
could be heard during the commercial breaks of cable
channels in the United States and elsewhere. Previously, The *, #, A, B, C and D keys are still widely used worldterrestrial television stations used DTMF tones to control wide by amateur radio operators and commercial twoway radio systems for equipment control, repeater conremote transmitters.
trol, remote-base operations and some telephone communications systems.

7 8 9 C
0 # D
DTMF keypad layout.

The engineers had envisioned telephones being used to

access computers, and automated response systems. They
consulted with companies to determine the requirements.
This led to the addition of the number sign (#, ''pound'' or
diamond in this context, hash, square or gate in
the UK, and "octothorpe'' by the original engineers) and
asterisk or star (*) keys as well as a group of keys for
menu selection: A, B, C and D. In the end, the lettered

95.3 Keypad
The DTMF telephone keypad is laid out in a 44 matrix
of push buttons in which each row represents the low frequency component and each column represents the high
frequency component of the DTMF signal. Pressing a
key sends a combination of the row and column frequencies. For example, the key 1 produces a superimposition
of tones of 697 and 1209 hertz (Hz). Initial pushbutton
designs employed levers, so that each button activated two
contacts. The tones are decoded by the switching center
to determine the keys pressed by the user.

95.7. REFERENCES

445

95.7 References
[1] Dodd, Annabel Z. The essential guide to telecommunications. Prentice Hall PTR, 2002, p. 183.
[2] AT&T, Compatibility Bulletin No. 105
[3] What are the ABCD tones?" Tech FAQ
[4] AT&T (1968), Notes on Distance Dialing

95.8 Further reading

1209 Hz on 697 Hz to make the 1 tone

ITUs recommendations for implementing DTMF

services
Schenker, L (1960), Pushbutton Calling with a
Two-Group Voice-Frequency Code (PDF), The
Bell System Technical Journal, 39 (1): 235255,
ISSN 0005-8580.
Deininger, R.L. (July 4, 1960). Human Factors Engineering Studies of the Design and Use of Pushbutton Telephone Sets. Bell System Technical Journal.
39 (4): 9951012.

2 DTMF Receiver CMD CM8870CSI

Frank Durda, Dual Tone Multi-Frequency (TouchTone) Reference, 2006.

95.4 Decoding

ITU-T Recommendation Q.24 - Multifrequency

push-button signal reception

DTMF was originally decoded by tuned lter banks. By

the end of the 20th century, digital signal processing became the predominant technology for decoding. DTMF
decoding algorithms often use the Goertzel algorithm to
detect tones.

95.5 Other multiple frequency signals

National telephone systems dene other tones that indicate the status of lines, equipment, or the result of calls.
Such call-progress tones are often also composed of multiple frequencies and are standardized in each country.
The Bell System denes them in the Precise Tone Plan.[4]
However, such signaling systems are not considered to belong to the DTMF system.

95.6 See also

Selective calling
Special information tones

95.9 External links

ITU-T Recommendation Q.23 - Technical features
of push-button telephone sets

Chapter 96

On-o keying
On-o keying (OOK) denotes the simplest form of
amplitude-shift keying (ASK) modulation that represents
digital data at the presence or absence of a carrier wave.[1]
In its simplest form, the presence of a carrier for a specic
duration represents a binary one, while its absence for the
same duration represents a binary zero. Some more sophisticated schemes vary these durations to convey additional information. It is analogous to unipolar encoding
line code.
On-o keying is most commonly used to transmit
Morse code over radio frequencies (referred to as CW
(continuous wave) operation), although in principle any
digital encoding scheme may be used. OOK has
been used in the ISM bands to transfer data between
computers, for example.
OOK is more spectrally ecient than frequencyshift keying, but more sensitive to noise when using a regenerative receiver or a poorly implemented
superheterodyne receiver.[2] For a given data rate, the
bandwidth of a BPSK (Binary Phase Shift keying) signal
and the bandwidth of OOK signal are equal.
In addition to RF carrier waves, OOK is also used in
optical communication systems (e.g. IrDA).
In aviation, some possibly unmanned airports have equipment that let pilots key their VHF radio a number of times
in order to request an Automatic Terminal Information
Service broadcast, or turn on runway lights.

96.1 See also

Unipolar encoding

96.2 External links

Application Note - I'm OOK. You're OOK?

96.3 References
[1] Simple Binary Modulation One Bit at a Time

446

[2] L. ASH, DARRELL (1992). A comparison between ook

ask and fsk modulation techniques for radio links (PDF).
RF Monolithics. p. 6. Retrieved 24 February 2015.

Chapter 97

8VSB
This article is about the television modulation method.
For the SBE Certication, see Certied 8-VSB Specialist.

97.2 Throughput

In the 6 MHz (megahertz) channel used for broadcast

8VSB is the modulation method used for broadcast in the
ATSC, 8VSB carries a symbol rate of 10.76 megabaud, a
ATSC digital television standard. ATSC and 8VSB modgross bit rate of 32 Mbit/s, and a net bit rate of 19.39
ulation is used primarily in North America; in contrast,
Mbit/s of usable data. The net bit rate is lower due
the DVB-T standard uses COFDM.
to the addition of forward error correction codes. The
A modulation method species how the radio signal uc- eight signal levels are selected with the use of a trellis entuates to convey information. ATSC and DVB-T spec- coder. There are also similar modulations 2VSB, 4VSB,
ify the modulation used for over-the-air digital television; and 16VSB. 16VSB was notably intended to be used for
by comparison, QAM is the modulation method used ATSC digital cable, but quadrature amplitude modulafor cable. The specications for a cable-ready television, tion (QAM) has become the de facto industry standard
then, might state that it supports 8VSB (for broadcast TV) instead as it is cheap and readily available.
and QAM (for cable TV).
8VSB is an 8-level vestigial sideband modulation. In
essence, it converts a binary stream into an octal representation by amplitude modulating a sinusoidal carrier to
one of eight levels. 8VSB is capable of transmitting three
bits (23 =8) per symbol; in ATSC, each symbol includes 97.3 Power saving advantages
two bits from the MPEG transport stream which are trellis
modulated to produce a three-bit gure. The resulting
signal is then band-pass ltered with a Nyquist lter to A signicant advantage of 8VSB for broadcasters is that
remove redundancies in the side lobes, and then shifted it requires much less power to cover an area comparable
to that of the earlier NTSC system, and it is reportedly
up to the broadcast frequency.[1]
better at this than the most common alternative system,
COFDM. Part of the advantage is the lower peak to average power ratio needed compared to COFDM. An 8VSB
transmitter needs to have a peak power capability of 6 db
(four times) its average power. 8VSB is also more resistant to impulse noise. Some stations can cover the same
area while transmitting at an eective radiated power of
97.1 Modulation Technique
approximately 25% of analog broadcast power. While
NTSC and most other analog television systems also use
Vestigial sideband modulation (VSB) is a modulation a vestigial sideband technique, the unwanted sideband is
method which attempts to eliminate the spectral redun- ltered much more eectively in ATSC 8VSB transmisdancy of pulse-amplitude modulation (PAM) signals. sions. 8VSB uses a Nyquist lter to achieve this. Reed
Modulating a carrier by a real-valued data sequence re- Solomon error correction is the primary system used to
sults in a sum and a dierence frequency, resulting in two retain data integrity.
symmetrical carrier side-bands. The symmetry means
that one of the sidebands is redundant, so removing one
sideband still allows for demodulation. As lters with
zero transition bandwidth cannot be realized, the ltering
implemented leaves a vestige of the redundant sideband,
hence the name VSB.

In summer of 2005, the ATSC published standards for

Enhanced VSB, or E-VSB . Using forward error correction, the E-VSB standard will allow DTV reception on
low power handheld receivers with smaller antennas in
much the same way DVB-H does in Europe, but still using 8VSB transmission.

447

448

97.4 Disputes over ATSCs use

For some period of time, there had been a continuing
lobby for changing the modulation for ATSC to COFDM,
the way DVB-T is transmitted in Europe, and ISDB-T
in Japan. However, the FCC has always held that 8VSB
is the better modulation for use in U.S. digital television broadcasting. In a 1999 report, the Commission
found that 8VSB has better threshold or carrier-to-noise
(C/N) performance, has a higher data rate capability, requires less transmitter power for equivalent coverage, and
is more robust to impulse and phase noise.[2] As a result,
it denied in 2000 a petition for rulemaking from Sinclair
Broadcast Group requesting that broadcasters be allowed
to choose between 8VSB or COFDM as is most appropriate for their area of coverage.[3] The FCC report also acknowledged that COFDM would generally be expected
to perform better in situations where there is dynamic
multipath, such as mobile operation or in the presence
of trees that are moving in high winds. However, with
the introduction of 5th Generation demodulators in 2005
and subsequent improvements in generations 6 and 7, the
equalization span is now about 60 to +75 microseconds
(a 135 microsecond spread) and has virtually eliminated
multipath, both static and dynamic, in 8-VSB reception.
In comparison, the equalization span in COFDM is 100
to +100 microseconds (200 microsecond spread), but the
application of this much guard band space for COFDM
substantially reduces its useful payload. In fact, much of
Europe has adopted 1280720p as its HD standard for
DVB because of its reduced payload capacity. The introduction of DVT-T2 is meant to increase the ability
of terrestrial transmissions to carry 19201080p content.
19201080i has always been part of the 8-VSB scheme
from its inception, and its improved demodulators have
had no eect on its innate payload capacity.
Because of continued adoption of the 8VSB-based ATSC
standard in the U.S., and a large growing ATSC receiver
population, a switch to COFDM is now essentially impossible. Most analog terrestrial transmissions in the US
were turned o in June 2009, and 8VSB tuners are common to all new TVs, further complicating a future transition to COFDM.

CHAPTER 97. 8VSB

ably in most indoor test installations.

[4]

However, there were questions whether the COFDM receiver selected for these tests a transmitter monitor
lacking normal front end ltering colored these results.
Retests that were performed using the same COFDM receivers with the addition of a front end band pass lter
gave much improved results for the DVB-T receiver, but
further testing was not pursued.
The debate over 8VSB versus COFDM modulation is still
ongoing. Proponents of COFDM argue that it resists
multipath far better than 8VSB. This is important property of the modulation for receiving HDTV in e.g. moving vehicles that is not possible with 8VSB. Early 8VSB
DTV (digital television) receivers often had diculty receiving a signal in urban environments. Newer 8VSB receivers, however, are better at dealing with multipath, but
a moving receiver can still not receive the signal. Moreover, 8VSB modulation requires less power to transmit a
signal the same distance. In less populated areas, 8VSB
may outperform COFDM because of this. However, in
some urban areas, as well as for mobile use, COFDM may
oer better reception than 8VSB. Several enhanced
VSB systems were in development, most notably E-VSB,
A-VSB, and MPH. The deciencies in 8VSB in regards
to multipath reception can be dealt with by using additional forward error-correcting codes which decreases the
useful bit rate, such as that used by ATSC-M/H for Mobile/Handheld reception.
The vast majority of USA TV stations use COFDM for
their studio to transmitter links and news gathering operations. These are point-to-point communication links
and not broadcast transmissions.

97.6 See also

ATSC tuner
ATSC-M/H for Mobile/Handheld receivers

97.7 References
97.5 8VSB vs COFDM
The previously cited FCC Report also found that
COFDM has better performance in dynamic and high
level static multipath situations, and oers advantages
for single frequency networks and mobile reception.
Nonetheless, in 2001, a technical report compiled by the
COFDM Technical Group concluded that COFDM did
not oer any signicant advantages over 8VSB. The report recommended in conclusion that receivers be linked
to outdoor antennas raised to roughly 30 feet (9 m) in
height. Neither 8VSB nor COFDM performed accept-

[1] Sparano, David (1997). WHAT EXACTLY IS 8-VSB

ANYWAY?" (PDF). Retrieved 8 Nov 2012.
[2] DTV REPORT ON COFDM AND 8-VSB PERFORMANCE
(PDF), FCC Oce of Engineering and Technology,
archived (PDF) from the original on 14 April 2007, retrieved 2007-03-04, September 30, 1999.
[3] Sinclair Claims Wide Support For Dtv Petition, Television
Digest with Consumer Electronics, 1999, retrieved 200806-06, Oct 11, 1999.
[4] 8VSB/COFDM Comparison Report

97.8. EXTERNAL LINKS

97.8 External links

What exactly is 8-VSB anyway?

449

Chapter 98

Polar modulation
Polar modulation is analogous to quadrature modulation in the same way that polar coordinates are analogous
to Cartesian coordinates. Quadrature modulation makes
use of Cartesian coordinates, x and y. When considering quadrature modulation, the x axis is called the I (inphase) axis, and the y axis is called the Q (quadrature)
axis. Polar modulation makes use of polar coordinates, r
(amplitude) and (phase).
The quadrature modulator approach to digital radio transmission requires a linear RF power amplier which creates a design conict between improving power eciency
or maintaining amplier linearity. Compromising linearity causes degraded signal quality, usually by adjacent
channel degradation, which can be a fundamental factor in limiting network performance and capacity. Additional problems with linear RF power ampliers, including device parametric restrictions, temperature instability, power control accuracy, wideband noise and production yields are also common. On the other hand, compromising power eciency increases power consumption
(which reduces battery life in handheld devices) and generates more heat.
The issue of linearity in a power amplier can theoretically be mitigated by requiring that the input signal of
the power amplier be "constant envelope", i.e. contain
no amplitude variations. In a polar modulation system,
the power amplier input signal may vary only in phase.
Amplitude modulation is then accomplished by directly
controlling the gain of the power amplier through changing or modulating its supply voltage. Thus a polar modulation system allows the use of highly non-linear power
amplier architectures such as Class E and Class F.

Now that the amplitude change of the signal is known,

the phase error introduced by the amplier at each amplitude change can be used to pre-distort the signal. One
simply subtracts the phase error at each amplitude from
the modulating I and Q signals.

98.1 History
Polar modulation was originally developed by Thomas
Edison in his 1874 quadruplex telegraph this allowed
4 signals to be sent along a pair of lines, 2 in each direction. Sending a signal in each direction had already been
accomplished earlier, and Edison found that by combining amplitude and phase modulation (i.e., by polar modulation), he could double this to 4 signals hence, quadruplex.

98.2 See also

Angle modulation
Phase modulation
Phase shift keying (PSK)

98.3 External links

In order to create the Polar signal, the phase transfer of

the amplier must be known over at least a 17 dB amplitude range. As the phase transitions from one to another,
there will be an amplitude perturbation that can be calculated during the transition as,

Fundamentals of Digital Quadrature Modulation

Matsushita (formerly Tropian)
Sequoia Communications
RF Micro Devices
Skyworks
Anadigics, Inc

P (n) = I 2 (n) + Q2 (n)

where n is the number of samples of I and Q and should
be suciently large to allow an accurate tracing of the
signal. One hundred samples per symbol would be about
the lowest number that is workable.
450

Polar Modulation Ups Eciency in Mobile PA Designs - CommsDesign

Chapter 99

Continuous phase modulation

Continuous phase modulation (CPM) is a method for
modulation of data commonly used in wireless modems.
In contrast to other coherent digital phase modulation
techniques where the carrier phase abruptly resets to zero
at the start of every symbol (e.g. M-PSK), with CPM the
carrier phase is modulated in a continuous manner. For
instance, with QPSK the carrier instantaneously jumps
from a sine to a cosine (i.e. a 90 degree phase shift) whenever one of the two message bits of the current symbol
diers from the two message bits of the previous symbol. This discontinuity requires a relatively large percentage of the power to occur outside of the intended
band (e.g., high fractional out-of-band power), leading to
poor spectral eciency. Furthermore, CPM is typically
implemented as a constant-envelope waveform, i.e., the
transmitted carrier power is constant. Therefore, CPM is
attractive because the phase continuity yields high spectral eciency, and the constant envelope yields excellent power eciency. The primary drawback is the high
implementation complexity required for an optimal receiver.

99.1 Phase memory

Each symbol is modulated by gradually changing the
phase of the carrier from the starting value to the nal
value, over the symbol duration. The modulation and
demodulation of CPM is complicated by the fact that the
initial phase of each symbol is determined by the cumulative total phase of all previous transmitted symbols, which
is known as the phase memory. Therefore, the optimal
receiver cannot make decisions on any isolated symbol
without taking the entire sequence of transmitted symbols into account. This requires a Maximum Likelihood
Sequence Estimator (MLSE), which is eciently implemented using the Viterbi algorithm.

it is not smooth since the derivative of the phase is not

continuous. The spectral eciency of CPM can be further improved by using a smooth phase trajectory. This
is typically accomplished by ltering the phase trajectory
prior to modulation, commonly using a Raised Cosine or
a Gaussian lter. The raised cosine lter has zero crossings oset by exactly one symbol time, and so it can yield
a full-response CPM waveform that prevents Intersymbol
Interference (ISI).

99.3 Partial response CPM

Partial-response signaling, such as duo-binary signaling,
is a form of intentional ISI where a certain number of
adjacent symbols interfere with each symbol in a controlled manner. A MLSE must be used to optimally demodulate any signal in the presence of ISI. Whenever the
amount of ISI is known, such as with any partial-response
signaling scheme, MLSE can be used to determine the
exact symbol sequence (in the absence of noise). Since
the optimal demodulation of full-response CPM already
requires MLSE detection, using partial-response signaling requires little additional complexity, but can aord a
comparatively smoother phase trajectory, and thus, even
greater spectral eciency. One extremely popular form
of partial-response CPM is GMSK, which is used by
GSM in most of the worlds 2nd generation cell phones. It
is also used in 802.11 FHSS, Bluetooth, and many other
proprietary wireless modems.

99.4 Continuous-phase frequencyshift keying

Continuous-phase frequency-shift keying (CPFSK) is

a commonly used variation of frequency-shift keying
(FSK), which is itself a special case of analog frequency
99.2 Phase trajectory
modulation. FSK is a method of modulating digital
data onto a sinusoidal carrier wave, encoding the inforMinimum-shift keying (MSK) is another name for CPM mation present in the data to variations in the carriers
with an excess bandwidth of 1/2 and a linear phase trajec- instantaneous frequency between one of two frequentory. Although this linear phase trajectory is continuous, cies (referred to as the space frequency and mark fre451

452

CHAPTER 99. CONTINUOUS PHASE MODULATION

quency). In general, a standard FSK signal does not have

continuous phase, as the modulated waveform switches
instantaneously between two sinusoids with dierent frequencies.

CPM minimum distance calculator (MLSE/MLSD

bound)

As the name suggests, the phase of a CPFSK is in fact

continuous; this attribute is desirable for signals that are
to be transmitted over a bandlimited channel, as discontinuities in a signal introduce wideband frequency components. In addition, some classes of ampliers exhibit
nonlinear behavior when driven with nearly discontinuous signals; this could have undesired eects on the shape
of the transmitted signal.

99.4.1

Theory

If a nitely valued digital signal to be transmitted (the

message) is m(t), then the corresponding CPFSK signal
is
(

s(t) = Ac cos 2fc t + Df

m()d

where Ac represents the amplitude of the CPFSK signal,

fc is the base carrier frequency, and Df is a parameter
that controls the frequency deviation of the modulated
signal. The integral located inside of the cosine's argument is what gives the CPFSK signal its continuous phase;
an integral over any nitely valued function (which m(t)
is assumed to be) will not contain any discontinuities. If
the message signal is assumed to be causal, then the limits on the integral change to a lower bound of zero and a
higher bound of t.
Note that this does not mean that m(t) must be continuous; in fact, most ideal digital data waveforms contain
discontinuities. However, even a discontinuous message
signal will generate a proper CPFSK signal.

99.5 See also

MSK

99.6 References
Notation for the CPFSK waveform was taken from:
Leon W. Couch II, Digital and Analog Communication Systems, 6th Edition, Prentice-Hall, Inc.,
2001. ISBN 0-13-081223-4
S. Cheng, R. Iyer Sehshadri, M.C. Valenti, and D.
Torrieri, The capacity of noncoherent continuousphase frequency shift keying, in Proc. Conf. on Info.
Sci. and Sys (CISS), (Baltimore, MD), Mar. 2007.

Chapter 100

Minimum-shift keying
Q

01

orthogonal. A variant of MSK called GMSK is used in

the GSM mobile phone standard.

11

100.1 Mathematical
tion

The resulting
is represented by the
formula
s(t) =
( t signal
)
( t
)
aI (t) cos 2T
cos (2fc t)aQ (t) sin 2T
sin (2fc t)

00

representa-

where aI (t) and aQ (t) encode the even and odd information respectively with a sequence of square pulses of duration 2T. aI (t) has its pulse edges on t = [T, T, 3T, ...]
and aQ (t) on t = [0, 2T, 4T, ...] . The carrier frequency
is fc .

10

Using the trigonometric identity, this can be rewritten in a

form where the phase and frequency modulation are more
obvious,
[
]
Mapping changes in continuous phase. Each bit time, the carrier
t
s(t) = cos 2fc t + bk (t) 2T
+ k
phase changes by 90

where bk(t) is +1 when aI (t) = aQ (t) and 1 if they are

In digital modulation, minimum-shift keying (MSK) is of opposite signs, and k is 0 if aI (t) is 1, and othera type of continuous-phase frequency-shift keying that wise. Therefore, the signal is modulated in frequency and
was developed in the late 1950s and 1960s.[1] Similar to phase, and the phase changes continuously and linearly.
OQPSK, MSK is encoded with bits alternating between
quadrature components, with the Q component delayed
by half the symbol period.
100.2 Gaussian
minimum-shift
However, instead of square pulses as OQPSK uses,
MSK encodes each bit as a half sinusoid. This results
in a constant-modulus signal (constant envelope signal),
which reduces problems caused by non-linear distortion.
In addition to being viewed as related to OQPSK, MSK
can also be viewed as a continuous phase frequency shift
keyed (CPFSK) signal with a frequency separation of
one-half the bit rate.

keying
In digital communication, Gaussian minimum shift
keying or GMSK is a continuous-phase frequency-shift
keying modulation scheme.
GMSK is similar to standard minimum-shift keying
(MSK); however the digital data stream is rst shaped
with a Gaussian lter before being applied to a frequency
modulator, and typically has much narrower phase shift
angles than most MSK modulation systems. This has the
advantage of reducing sideband power, which in turn reduces out-of-band interference between signal carriers in
adjacent frequency channels.[2]

In MSK the dierence between the higher and lower frequency is identical to half the bit rate. Consequently, the
waveforms used to represent a 0 and a 1 bit dier by exactly half a carrier period. Thus, the maximum frequency
deviation is = 0.25 fm where fm is the maximum modulating frequency. As a result, the modulation index m
is 0.5. This is the smallest FSK modulation index that However, the Gaussian lter increases the modulation
can be chosen such that the waveforms for 0 and 1 are memory in the system and causes intersymbol inter453

454
ference, making it more dicult to dierentiate between dierent transmitted data values and requiring
more complex channel equalization algorithms such as
an adaptive equalizer at the receiver. GMSK has high
spectral eciency, but it needs a higher power level than
QPSK, for instance, in order to reliably transmit the same
amount of data.
GMSK is most notably used in the Global System for Mobile Communications (GSM) and the Automatic Identication System (AIS) for maritime navigation.

100.3 See also

Constellation diagram used to examine the modulation in signal space (not time).
Gaussian frequency-shift keying

100.4 Notes
[1] M.L Doelz and E.T. Heald, Minimum Shift Data Communication System, US Patent 2977417, 1958, http://www.
freepatentsonline.com/2977417.html
[2] Poole, Ian. What is GMSK Modulation - Gaussian Minimum Shift Keying. RadioElectronics.com. Retrieved
March 23, 2014.

100.5 References
Subbarayan Pasupathy, Minimum Shift Keying: A
Spectrally Ecient Modulation, IEEE Communications Magazine, 1979
R. de Buda, Fast FSK Signals and their Demodulation, Can. Elec. Eng. J. Vol. 1, Number 1, 1976.
F. Amoroso, Pulse and Spectrum Manipulation in the
Minimum (Frequency) Shift Keying (MSK) Format,
IEEE Trans.
Document from the University of Hull giving a thorough description of GMSK.

CHAPTER 100. MINIMUM-SHIFT KEYING

Chapter 101

Orthogonal frequency-division
multiplexing
Orthogonal
frequency-division
multiplexing 101.1 Example of applications
(OFDM) is a method of encoding digital data on
multiple carrier frequencies. OFDM has developed into The following list is a summary of existing OFDM based
a popular scheme for wideband digital communication, standards and products. For further details, see the Usage
used in applications such as digital television and audio section at the end of the article.
broadcasting, DSL Internet access, wireless networks,
powerline networks, and 4G mobile communications.
OFDM is a frequency-division multiplexing (FDM) 101.1.1 Wired
scheme used as a digital multi-carrier modulation
ADSL and VDSL broadband access via POTS
method. A large number of closely spaced orthogonal
copper wiring
[1]
sub-carrier signals are used to carry data on several
parallel data streams or channels. Each sub-carrier is
DVB-C2, an enhanced version of the DVB-C digital
modulated with a conventional modulation scheme (such
cable TV standard
as quadrature amplitude modulation or phase-shift key Power line communication (PLC)
ing) at a low symbol rate, maintaining total data rates similar to conventional single-carrier modulation schemes in
ITU-T G.hn, a standard which provides high-speed
the same bandwidth.
local area networking of existing home wiring
(power lines, phone lines and coaxial cables)[2]
The primary advantage of OFDM over single-carrier
schemes is its ability to cope with severe channel con TrailBlazer telephone line modems
ditions (for example, attenuation of high frequencies
in a long copper wire, narrowband interference and
Multimedia over Coax Alliance (MoCA) home netfrequency-selective fading due to multipath) without
working
complex equalization lters. Channel equalization is sim DOCSIS 3.1 Broadband delivery
plied because OFDM may be viewed as using many
slowly modulated narrowband signals rather than one
rapidly modulated wideband signal. The low symbol rate
101.1.2 Wireless
makes the use of a guard interval between symbols affordable, making it possible to eliminate intersymbol in The wireless LAN (WLAN) radio interfaces IEEE
terference (ISI) and utilize echoes and time-spreading (on
802.11a, g, n, ac and HIPERLAN/2
analogue TV these are visible as ghosting and blurring,
respectively) to achieve a diversity gain, i.e. a signal-to The digital radio systems DAB/EUREKA 147,
noise ratio improvement. This mechanism also facilitates
DAB+, Digital Radio Mondiale, HD Radio, Tthe design of single frequency networks (SFNs), where
DMB and ISDB-TSB
several adjacent transmitters send the same signal simul The terrestrial digital TV systems DVB-T and
taneously at the same frequency, as the signals from multiISDB-T
ple distant transmitters may be combined constructively,
rather than interfering as would typically occur in a tra The terrestrial mobile TV systems DVB-H, T-DMB,
ditional single-carrier system.
ISDB-T and MediaFLO forward link
The wireless personal area network (PAN) ultrawideband (UWB) IEEE 802.15.3a implementation
suggested by WiMedia Alliance
455

456

CHAPTER 101. ORTHOGONAL FREQUENCY-DIVISION MULTIPLEXING

The OFDM based multiple access technology OFDMA

is also used in several 4G and pre-4G cellular networks
and mobile broadband standards:

101.3 Characteristics and principles of operation

The mobility mode of the wireless MAN/broadband 101.3.1 Orthogonality

wireless access (BWA) standard IEEE 802.16e (or
Conceptually, OFDM is a specialized FDM, the addiMobile-WiMAX)
tional constraint being that all carrier signals are orthog The mobile broadband wireless access (MBWA) onal to one another.
standard IEEE 802.20
In OFDM, the sub-carrier frequencies are chosen so that
The downlink of the 3GPP Long Term Evolution the sub-carriers are orthogonal to each other, meaning
(LTE) fourth generation mobile broadband stan- that cross-talk between the sub-channels is eliminated
dard. The radio interface was formerly named and inter-carrier guard bands are not required. This
High Speed OFDM Packet Access (HSOPA), now greatly simplies the design of both the transmitter and
named Evolved UMTS Terrestrial Radio Access (E- the receiver; unlike conventional FDM, a separate lter
for each sub-channel is not required.
UTRA)
The orthogonality requires that the sub-carrier spacing is
f = Tk Hertz, where TU seconds is the useful symbol
U
101.2 Key features
duration (the receiver-side window size), and k is a positive integer, typically equal to 1. Therefore, with N subThe advantages and disadvantages listed below are fur- carriers, the total passband bandwidth will be B Nf
ther discussed in the Characteristics and principles of op- (Hz).
eration section below.
The orthogonality also allows high spectral eciency,
with a total symbol rate near the Nyquist rate for the
equivalent baseband signal (i.e. near half the Nyquist rate
101.2.1 Summary of advantages
for the double-side band physical passband signal). Al High spectral eciency as compared to other double most the whole available frequency band can be utilized.
sideband modulation schemes, spread spectrum, etc. OFDM generally has a nearly 'white' spectrum, giving it
benign electromagnetic interference properties with re Can easily adapt to severe channel conditions with- spect to other co-channel users.
out complex time-domain equalization.
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and
fading caused by multipath propagation
Ecient implementation using fast Fourier transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver lters are not required
(unlike conventional FDM)
Facilitates single frequency networks (SFNs) (i.e.
transmitter macrodiversity)

101.2.2

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR), requiring linear transmitter circuitry, which suers from
poor power eciency
Loss of eciency caused by cyclic prex/guard interval

A simple example: A useful symbol duration

TU = 1 ms would require a sub-carrier spacing of f = 11ms = 1 kHz (or an integer multiple
of that) for orthogonality. N = 1,000 subcarriers would result in a total passband bandwidth of Nf = 1 MHz. For this symbol
time, the required bandwidth in theory according to Nyquist is N=1/2TU = 0.5 MHz (i.e.,
half of the achieved bandwidth required by our
scheme). If a guard interval is applied (see
below), Nyquist bandwidth requirement would
be even lower. The FFT would result in N
= 1,000 samples per symbol. If no guard interval was applied, this would result in a base
band complex valued signal with a sample rate
of 1 MHz, which would require a baseband
bandwidth of 0.5 MHz according to Nyquist.
However, the passband RF signal is produced
by multiplying the baseband signal with a carrier waveform (i.e., double-sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz. A single-side band
(SSB) or vestigial sideband (VSB) modulation
scheme would achieve almost half that bandwidth for the same symbol rate (i.e., twice as
high spectral eciency for the same symbol al-

101.3. CHARACTERISTICS AND PRINCIPLES OF OPERATION

457

amount of time and vice versa.[7] As a comparison an

Intel Pentium III CPU at 1.266 GHz is able to calculate a
8 192 point FFT in 576 s using FFTW.[8] Intel Pentium
OFDM requires very accurate frequency synchronization M at 1.6 GHz does it in 387 s.[9] Intel Core Duo at 3.0
between the receiver and the transmitter; with frequency GHz does it in 96.8 s.[10]
deviation the sub-carriers will no longer be orthogonal,
causing inter-carrier interference (ICI) (i.e., cross-talk
between the sub-carriers). Frequency osets are typi- 101.3.3 Guard interval for elimination of
intersymbol interference
cally caused by mismatched transmitter and receiver oscillators, or by Doppler shift due to movement. While
Doppler shift alone may be compensated for by the re- One key principle of OFDM is that since low symbol
ceiver, the situation is worsened when combined with rate modulation schemes (i.e., where the symbols are relmultipath, as reections will appear at various frequency atively long compared to the channel time characterisosets, which is much harder to correct. This eect typ- tics) suer less from intersymbol interference caused by
ically worsens as speed increases,[3] and is an important multipath propagation, it is advantageous to transmit a
factor limiting the use of OFDM in high-speed vehicles. number of low-rate streams in parallel instead of a single
In order to mitigate ICI in such scenarios, one can shape high-rate stream. Since the duration of each symbol is
each sub-carrier in order to minimize the interference re- long, it is feasible to insert a guard interval between the
sulting in a non-orthogonal subcarriers overlapping.[4] For OFDM symbols, thus eliminating the intersymbol interexample, a low-complexity scheme referred to as WCP- ference.
OFDM (Weighted Cyclic Prex Orthogonal Frequency- The guard interval also eliminates the need for a pulseDivision Multiplexing) consists of using short lters at shaping lter, and it reduces the sensitivity to time synthe transmitter output in order to perform a potentially chronization problems.
non-rectangular pulse shaping and a near perfect reconstruction using a single-tap per subcarrier equalization.[5]
A simple example: If one sends a million
Other ICI suppression techniques usually increase drastisymbols per second using conventional singlecally the receiver complexity.[6]
carrier modulation over a wireless channel,
phabet length). It is however more sensitive to
multipath interference.

101.3.2

Implementation using the FFT algorithm

The orthogonality allows for ecient modulator and demodulator implementation using the FFT algorithm on
the receiver side, and inverse FFT on the sender side. Although the principles and some of the benets have been
known since the 1960s, OFDM is popular for wideband
communications today by way of low-cost digital signal
processing components that can eciently calculate the
FFT.
The time to compute the inverse-FFT or FFT transform
has to take less than the time for each symbol.,[7] which
for example for DVB-T (FFT 8k) means the computation
has to be done in 896 s or less.
For an 8192-point FFT this may be approximated to:[7]

then the duration of each symbol would be one

microsecond or less. This imposes severe constraints on synchronization and necessitates the
removal of multipath interference. If the same
million symbols per second are spread among
one thousand sub-channels, the duration of
each symbol can be longer by a factor of a thousand (i.e., one millisecond) for orthogonality
with approximately the same bandwidth. Assume that a guard interval of 1/8 of the symbol
length is inserted between each symbol. Intersymbol interference can be avoided if the multipath time-spreading (the time between the reception of the rst and the last echo) is shorter
than the guard interval (i.e., 125 microseconds). This corresponds to a maximum dierence of 37.5 kilometers between the lengths of
the paths.

The cyclic prex, which is transmitted during the guard

interval, consists of the end of the OFDM symbol copied
into the guard interval, and the guard interval is transmitted followed by the OFDM symbol. The reason that the
guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an inte[7]
ger number of sinusoid cycles for each of the multipaths
when it performs OFDM demodulation with the FFT. In
MIPS = Million instructions per second
some standards such as Ultrawideband, in the interest of
transmitted power, cyclic prex is skipped and nothing
The computational demand approximately scales linearly is sent during the guard interval. The receiver will then
with FFT size so a double size FFT needs double the have to mimic the cyclic prex functionality by copying
computational complexity
1.3 106
Tsymbol
147 456 2
=
1.3 106
896 106
= 428

MIPS =

458

CHAPTER 101. ORTHOGONAL FREQUENCY-DIVISION MULTIPLEXING

the end part of the OFDM symbol and adding it to the individual sub-channel noise and interference characterbeginning portion.
istics.

101.3.4

Simplied equalization

The eects of frequency-selective channel conditions, for

example fading caused by multipath propagation, can
be considered as constant (at) over an OFDM subchannel if the sub-channel is suciently narrow-banded
(i.e., if the number of sub-channels is suciently large).
This makes frequency domain equalization possible at
the receiver, which is far simpler than the time-domain
equalization used in conventional single-carrier modulation. In OFDM, the equalizer only has to multiply each
detected sub-carrier (each Fourier coecient) in each
OFDM symbol by a constant complex number, or a rarely
changed value.
Our example: The OFDM equalization in the
above numerical example would require one
complex valued multiplication per subcarrier
and symbol (i.e., N = 1000 complex multiplications per OFDM symbol; i.e., one million multiplications per second, at the receiver). The
FFT algorithm requires N log2 N = 10,000 [this is
imprecise: over half of these complex multiplications are trivial, i.e. = to 1 and are not implemented in software or HW]. complex-valued
multiplications per OFDM symbol (i.e., 10
million multiplications per second), at both the
receiver and transmitter side. This should be
compared with the corresponding one million
symbols/second single-carrier modulation case
mentioned in the example, where the equalization of 125 microseconds time-spreading using a FIR lter would require, in a naive implementation, 125 multiplications per symbol
(i.e., 125 million multiplications per second).
FFT techniques can be used to reduce the number of multiplications for an FIR lter based
time-domain equalizer to a number comparable with OFDM, at the cost of delay between
reception and decoding which also becomes
comparable with OFDM.

Some of the sub-carriers in some of the OFDM symbols

may carry pilot signals for measurement of the channel
conditions[11][12] (i.e., the equalizer gain and phase shift
for each sub-carrier). Pilot signals and training symbols
(preambles) may also be used for time synchronization
(to avoid intersymbol interference, ISI) and frequency
synchronization (to avoid inter-carrier interference, ICI,
caused by Doppler shift).
OFDM was initially used for wired and stationary wireless communications. However, with an increasing number of applications operating in highly mobile environments, the eect of dispersive fading caused by a combination of multi-path propagation and doppler shift is
more signicant. Over the last decade, research has been
done on how to equalize OFDM transmission over doubly
selective channels.[13][14][15]

101.3.5 Channel coding and interleaving

OFDM is invariably used in conjunction with channel
coding (forward error correction), and almost always uses
frequency and/or time interleaving.
Frequency (subcarrier) interleaving increases resistance
to frequency-selective channel conditions such as fading.
For example, when a part of the channel bandwidth fades,
frequency interleaving ensures that the bit errors that
would result from those subcarriers in the faded part of
the bandwidth are spread out in the bit-stream rather than
being concentrated. Similarly, time interleaving ensures
that bits that are originally close together in the bit-stream
are transmitted far apart in time, thus mitigating against
severe fading as would happen when travelling at high
speed.
However, time interleaving is of little benet in slowly
fading channels, such as for stationary reception, and
frequency interleaving oers little to no benet for narrowband channels that suer from at-fading (where the
whole channel bandwidth fades at the same time).

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-stream that is
presented to the error correction decoder, because when
such decoders are presented with a high concentration of
If dierential modulation such as DPSK or DQPSK is ap- errors the decoder is unable to correct all the bit errors,
plied to each sub-carrier, equalization can be completely and a burst of uncorrected errors occurs. A similar deomitted, since these non-coherent schemes are insensitive sign of audio data encoding makes compact disc (CD)
to slowly changing amplitude and phase distortion.
playback robust.
In a sense, improvements in FIR equalization using FFTs
or partial FFTs leads mathematically closer to OFDM,
but the OFDM technique is easier to understand and
implement, and the sub-channels can be independently
adapted in other ways than varying equalization coecients, such as switching between dierent QAM constellation patterns and error-correction schemes to match

A classical type of error correction coding used with

OFDM-based systems is convolutional coding, often
concatenated with Reed-Solomon coding. Usually, additional interleaving (on top of the time and frequency
interleaving mentioned above) in between the two layers
of coding is implemented. The choice for Reed-Solomon
coding as the outer error correction code is based on

101.3. CHARACTERISTICS AND PRINCIPLES OF OPERATION

the observation that the Viterbi decoder used for inner
convolutional decoding produces short error bursts when
there is a high concentration of errors, and Reed-Solomon
codes are inherently well-suited to correcting bursts of errors.
Newer systems, however, usually now adopt near-optimal
types of error correction codes that use the turbo decoding principle, where the decoder iterates towards the desired solution. Examples of such error correction coding types include turbo codes and LDPC codes, which
perform close to the Shannon limit for the Additive
White Gaussian Noise (AWGN) channel. Some systems that have implemented these codes have concatenated them with either Reed-Solomon (for example on
the MediaFLO system) or BCH codes (on the DVB-S2
system) to improve upon an error oor inherent to these
codes at high signal-to-noise ratios.[16]

101.3.6

Adaptive transmission

The resilience to severe channel conditions can be further

enhanced if information about the channel is sent over
a return-channel. Based on this feedback information,
adaptive modulation, channel coding and power allocation may be applied across all sub-carriers, or individually to each sub-carrier. In the latter case, if a particular
range of frequencies suers from interference or attenuation, the carriers within that range can be disabled or
made to run slower by applying more robust modulation
or error coding to those sub-carriers.

459

dierent users. OFDMA supports dierentiated quality

of service by assigning dierent number of sub-carriers
to dierent users in a similar fashion as in CDMA,
and thus complex packet scheduling or Media Access
Control schemes can be avoided. OFDMA is used in:
the mobility mode of the IEEE 802.16 Wireless
MAN standard, commonly referred to as WiMAX,
the IEEE 802.20 mobile Wireless MAN standard,
commonly referred to as MBWA,
the 3GPP Long Term Evolution (LTE) fourth
generation mobile broadband standard downlink.
The radio interface was formerly named High
Speed OFDM Packet Access (HSOPA), now
named Evolved UMTS Terrestrial Radio Access (EUTRA).
the now defunct Qualcomm/3GPP2 Ultra Mobile
Broadband (UMB) project, intended as a successor
of CDMA2000, but replaced by LTE.
OFDMA is also a candidate access method for the IEEE
802.22 Wireless Regional Area Networks (WRAN). The
project aims at designing the rst cognitive radio based
standard operating in the VHF-low UHF spectrum (TV
spectrum).

In Multi-carrier code division multiple access (MCCDMA), also known as OFDM-CDMA, OFDM is combined with CDMA spread spectrum communication for
The term discrete multitone modulation (DMT) denotes coding separation of the users. Co-channel interferOFDM based communication systems that adapt the ence can be mitigated, meaning that manual xed chantransmission to the channel conditions individually for nel allocation (FCA) frequency planning is simplied, or
each sub-carrier, by means of so-called bit-loading. Ex- complex dynamic channel allocation (DCA) schemes are
avoided.
amples are ADSL and VDSL.
The upstream and downstream speeds can be varied by
allocating either more or fewer carriers for each purpose.
101.3.8 Space diversity
Some forms of rate-adaptive DSL use this feature in real
time, so that the bitrate is adapted to the co-channel inIn OFDM based wide area broadcasting, receivers can
terference and bandwidth is allocated to whichever subbenet from receiving signals from several spatially disscriber needs it most.
persed transmitters simultaneously, since transmitters
will only destructively interfere with each other on a lim101.3.7 OFDM extended with multiple ac- ited number of sub-carriers, whereas in general they will
actually reinforce coverage over a wide area. This is very
cess
benecial in many countries, as it permits the operation of
national single-frequency networks (SFN), where many
OFDM in its primary form is considered as a digital mod- transmitters send the same signal simultaneously over the
ulation technique, and not a multi-user channel access same channel frequency. SFNs utilise the available specmethod, since it is utilized for transferring one bit stream trum more eectively than conventional multi-frequency
over one communication channel using one sequence of broadcast networks (MFN), where program content is
OFDM symbols. However, OFDM can be combined replicated on dierent carrier frequencies. SFNs also rewith multiple access using time, frequency or coding sep- sult in a diversity gain in receivers situated midway bearation of the users.
tween the transmitters. The coverage area is increased
In orthogonal frequency-division multiple access and the outage probability decreased in comparison to an
(OFDMA), frequency-division multiple access is MFN, due to increased received signal strength averaged
achieved by assigning dierent OFDM sub-channels to over all sub-carriers.

460

CHAPTER 101. ORTHOGONAL FREQUENCY-DIVISION MULTIPLEXING

Although the guard interval only contains redundant data,

which means that it reduces the capacity, some OFDMbased systems, such as some of the broadcasting systems,
deliberately use a long guard interval in order to allow
the transmitters to be spaced farther apart in an SFN, and
longer guard intervals allow larger SFN cell-sizes. A rule
of thumb for the maximum distance between transmitters
in an SFN is equal to the distance a signal travels during
the guard interval for instance, a guard interval of 200
microseconds would allow transmitters to be spaced 60
km apart.

PAPR requirements have so far limited OFDM applications to terrestrial systems.

The crest factor CF (in dB) for an OFDM system with n
uncorrelated sub-carriers is[17]
CF = 10 log ( n ) + Cfc
where CFc is the crest factor (in dB) for each sub-carrier.
(CFc is 3.01 dB for the sine waves used for BPSK and
QPSK modulation).

For example, the DVB-T signal in 2K mode is composed

of 1705 sub-carriers that are each QPSK-modulated, givA single frequency network is a form of transmitter ing a crest factor of 35.32 dB.[17]
macrodiversity. The concept can be further utilized in
dynamic single-frequency networks (DSFN), where the Many crest factor reduction techniques have been developed.
SFN grouping is changed from timeslot to timeslot.
is 120
OFDM may be combined with other forms of space di- The dynamic range required for an FM receiver
[18]
dB
while
DAB
only
require
about
90
dB.
As
a
comversity, for example antenna arrays and MIMO channels.
parison,
each
extra
bit
per
sample
increases
the
dynamic
This is done in the IEEE 802.11 Wireless LAN standards.
range with 6 dB.

101.3.9

Linear transmitter power amplier

An OFDM signal exhibits a high peak-to-average power

ratio (PAPR) because the independent phases of the subcarriers mean that they will often combine constructively.
Handling this high PAPR requires:

101.4 Eciency comparison between single carrier and

multicarrier

A high-resolution digital-to-analogue converter The performance of any communication system can be

measured in terms of its power eciency and bandwidth
(DAC) in the transmitter
eciency. The power eciency describes the ability of
A high-resolution analogue-to-digital converter communication system to preserve bit error rate (BER)
of the transmitted signal at low power levels. Bandwidth
(ADC) in the receiver
eciency reects how eciently the allocated bandwidth
A linear signal chain
is utilized and is dened as the throughput data rate per
Hertz in a given bandwidth. If the large number of subAny non-linearity in the signal chain will cause carriers are used, the bandwidth eciency of multicarrier
system such as OFDM with using optical ber channel is
intermodulation distortion that
dened as[19]
Raises the noise oor
May cause inter-carrier interference

Rs
= 2. BOF
DM

Generates out-of-band spurious radiation

The linearity requirement is demanding, especially for
transmitter RF output circuitry where ampliers are often
designed to be non-linear in order to minimise power consumption. In practical OFDM systems a small amount of
peak clipping is allowed to limit the PAPR in a judicious
trade-o against the above consequences. However, the
transmitter output lter which is required to reduce outof-band spurs to legal levels has the eect of restoring
peak levels that were clipped, so clipping is not an eective way to reduce PAPR.

Factor 2 is because of two polarization states in the ber.

where Rs is the symbol rate in giga symbol per second
(Gsps), and BOF DM is the bandwidth of OFDM signal.
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency division multiplexing .
So the bandwidth for multicarrier system is less in comparison with single carrier system and hence bandwidth
eciency of multicarrier system is larger than single carrier system.

There is only 1 dBm increase in receiver power, but we get

Although the spectral eciency of OFDM is attractive 76.7% improvement in bandwidth eciency with using
for both terrestrial and space communications, the high multicarrier transmission technique.

101.6. MATHEMATICAL DESCRIPTION

461

101.5 Idealized system model

This returns N parallel streams, each of which is converted to a binary stream using an appropriate symbol
This section describes a simple idealized OFDM system detector. These streams are then re-combined into a serial stream, s[n] , which is an estimate of the original bimodel suitable for a time-invariant AWGN channel.
nary stream at the transmitter.

101.5.1

Transmitter

101.6 Mathematical description

If N sub-carriers are used, and each sub-carrier is modulated using M alternative symbols, the OFDM symbol
alphabet consists of M N combined symbols.
The low-pass equivalent OFDM signal is expressed as:

N
1

An OFDM carrier signal is the sum of a number of or(t)

=
Xk ej2kt/T , 0 t < T,
thogonal sub-carriers, with baseband data on each subk=0
carrier being independently modulated commonly using
some type of quadrature amplitude modulation (QAM) where {Xk } are the data symbols, N is the number of
or phase-shift keying (PSK). This composite baseband sub-carriers, and T is the OFDM symbol time. The subsignal is typically used to modulate a main RF carrier.
carrier spacing of T1 makes them orthogonal over each
s[n] is a serial stream of binary digits. By inverse mul- symbol period; this property is expressed as:
tiplexing, these are rst demultiplexed into N parallel streams, and each one mapped to a (possibly com
1 T ( j2k1 t/T ) ( j2k2 t/T )
plex) symbol stream using some modulation constellae
e
dt
tion (QAM, PSK, etc.). Note that the constellations may
T 0

be dierent, so some streams may carry a higher bit-rate

1 T j2(k2 k1 )t/T
=
e
dt = k1 k2
than others.
T 0
An inverse FFT is computed on each set of symbols,

giving a set of complex time-domain samples. These where () denotes the complex conjugate operator and
samples are then quadrature-mixed to passband in the is the Kronecker delta.
standard way. The real and imaginary components are To avoid intersymbol interference in multipath fading
rst converted to the analogue domain using digital-to- channels, a guard interval of length Tg is inserted prior
analogue converters (DACs); the analogue signals are to the OFDM block. During this interval, a cyclic prethen used to modulate cosine and sine waves at the x is transmitted such that the signal in the interval Tg
carrier frequency, fc , respectively. These signals are then t < 0 equals the signal in the interval (T Tg ) t < T . The
summed to give the transmission signal, s(t) .
OFDM signal with cyclic prex is thus:

101.5.2

Receiver
(t) =

N
1

Xk ej2kt/T ,

Tg t < T

k=0

The low-pass signal above can be either real or complexvalued. Real-valued low-pass equivalent signals are typically transmitted at basebandwireline applications such
as DSL use this approach. For wireless applications,
the low-pass signal is typically complex-valued; in which
case, the transmitted signal is up-converted to a carrier
The receiver picks up the signal r(t) , which is then frequency fc . In general, the transmitted signal can be
quadrature-mixed down to baseband using cosine and represented as:
sine waves at the carrier frequency. This also creates signals centered on 2fc , so low-pass lters are used to re{
}
ject these. The baseband signals are then sampled and s(t) = (t)ej2fc t
digitised using analog-to-digital converters (ADCs), and
N
1

a forward FFT is used to convert back to the frequency

=
|Xk | cos (2[fc + k/T ]t + arg[Xk ])
domain.
k=0

462

CHAPTER 101. ORTHOGONAL FREQUENCY-DIVISION MULTIPLEXING

101.7 Usage
OFDM is used in:
Digital Audio Broadcasting (DAB)
Digital television DVB-T/T2 (terrestrial), DVB-H
(handheld), DMB-T/H, DVB-C2 (cable)
Wireless LAN IEEE 802.11a, IEEE 802.11g, IEEE
802.11n, IEEE 802.11ac, and IEEE 802.11ad
WiMAX
Li-Fi
ADSL (G.dmt/ITU G.992.1)

channels (several hundred) in order to overcome the intersymbol interference in the power line environment.[23]
The IEEE 1901 standards include two incompatible physical layers that both use OFDM.[24] The ITU-T G.hn
standard, which provides high-speed local area networking over existing home wiring (power lines, phone lines
and coaxial cables) is based on a PHY layer that species OFDM with adaptive modulation and a Low-Density
Parity-Check (LDPC) FEC code.[20]

101.7.4 Wireless local area networks

(LAN) and metropolitan area
networks (MAN)
OFDM is extensively used in wireless LAN and MAN
applications, including IEEE 802.11a/g/n and WiMAX.

The LTE and LTE Advanced 4G mobile phone stanIEEE 802.11a/g/n, operating in the 2.4 and 5 GHz bands,
dards
species per-stream airside data rates ranging from 6 to
Modern narrow and broadband power line 54 Mbit/s. If both devices can utilize HT mode (added
communications[20]
with 802.11n), the top 20 MHz per-stream rate is increased to 72.2 Mbit/s, with the option of data rates between 13.5 and 150 Mbit/s using a 40 MHz channel. Four
101.7.1 OFDM system comparison table
dierent modulation schemes are used: BPSK, QPSK,
16-QAM, and 64-QAM, along with a set of error corKey features of some common OFDM based systems are recting rates (1/25/6). The multitude of choices allows
presented in the following table.
the system to adapt the optimum data rate for the current
signal conditions.

101.7.2

ADSL
101.7.5 Wireless personal area networks
(PAN)

OFDM is used in ADSL connections that follow the

ANSI T1.413 and G.dmt (ITU G.992.1) standards, where
it is called discrete multitone modulation (DMT). DSL
achieves high-speed data connections on existing copper
wires. OFDM is also used in the successor standards
ADSL2, ADSL2+, VDSL, VDSL2, and G.fast. ADSL2
uses variable sub-carrier modulation, ranging from BPSK
to 32768QAM (in ADSL terminology this is referred to
as bit-loading, or bit per tone, 1 to 15 bits per sub-carrier).

OFDM is also now being used in the WiMedia/Ecma368 standard for high-speed wireless personal area networks in the 3.110.6 GHz ultrawideband spectrum (see
MultiBand-OFDM).

quencies. The fact that OFDM can cope with this frequency selective attenuation and with narrow-band interference are the main reasons it is frequently used in applications such as ADSL modems. However, DSL cannot
be used on every copper pair; interference may become
signicant if more than 25% of phone lines coming into
a central oce are used for DSL.

Much of Europe and Asia has adopted OFDM for terrestrial broadcasting of digital television (DVB-T, DVBH and T-DMB) and radio (EUREKA 147 DAB, Digital
Radio Mondiale, HD Radio and T-DMB).

101.7.6 Terrestrial digital radio and televiLong copper wires suer from attenuation at high fresion broadcasting

DVB-T

101.7.3

Powerline Technology

OFDM is used by many powerline devices to extend digital connections through power wiring. Adaptive modulation is particularly important with such a noisy channel as electrical wiring. Some medium speed smart metering modems, Prime and G3 use OFDM at modest frequencies (30100 kHz) with modest numbers of

By Directive of the European Commission, all television

services transmitted to viewers in the European Community must use a transmission system that has been
standardized by a recognized European standardization
body,[25] and such a standard has been developed and
codied by the DVB Project, Digital Video Broadcasting
(DVB); Framing structure, channel coding and modulation
for digital terrestrial television.[26] Customarily referred

101.7. USAGE

463

to as DVB-T, the standard calls for the exclusive use of BST-OFDM used in ISDB
COFDM for modulation. DVB-T is now widely used in
Europe and elsewhere for terrestrial digital TV.
The band-segmented transmission orthogonal frequency
division multiplexing (BST-OFDM) system proposed for
Japan (in the ISDB-T, ISDB-TSB, and ISDB-C broadcasting systems) improves upon COFDM by exploiting
SDARS
the fact that some OFDM carriers may be modulated difThe ground segments of the Digital Audio Radio Ser- ferently from others within the same multiplex. Some
vice (SDARS) systems used by XM Satellite Radio forms of COFDM already oer this kind of hierarchical
and Sirius Satellite Radio are transmitted using Coded modulation, though BST-OFDM is intended to make it
OFDM (COFDM).[27] The word coded comes from the more exible. The 6 MHz television channel may therefore be segmented, with dierent segments being moduse of forward error correction (FEC).[1]
ulated dierently and used for dierent services.
COFDM vs VSB
The question of the relative technical merits of COFDM
versus 8VSB for terrestrial digital television has been a
subject of some controversy, especially between European and North American technologists and regulators.
The United States has rejected several proposals to adopt
the COFDM based DVB-T system for its digital television services, and has instead opted for 8VSB (vestigial
sideband modulation) operation.
One of the major benets provided by COFDM is in rendering radio broadcasts relatively immune to multipath
distortion and signal fading due to atmospheric conditions
or passing aircraft. Proponents of COFDM argue it resists multipath far better than 8VSB. Early 8VSB DTV
(digital television) receivers often had diculty receiving a signal. Also, COFDM allows single-frequency networks, which is not possible with 8VSB.

It is possible, for example, to send an audio service on

a segment that includes a segment composed of a number of carriers, a data service on another segment and a
television service on yet another segmentall within the
same 6 MHz television channel. Furthermore, these may
be modulated with dierent parameters so that, for example, the audio and data services could be optimized
for mobile reception, while the television service is optimized for stationary reception in a high-multipath environment.

101.7.7 Ultra-wideband

Ultra-wideband (UWB) wireless personal area network

technology may also utilise OFDM, such as in Multiband
OFDM (MB-OFDM). This UWB specication is advocated by the WiMedia Alliance (formerly by both the
Multiband OFDM Alliance [MBOA] and the WiMedia
Alliance, but the two have now merged), and is one of
However, newer 8VSB receivers are far better at dealing the competing UWB radio interfaces.
with multipath, hence the dierence in performance may
diminish with advances in equalizer design.

101.7.8 FLASH-OFDM
Digital radio
COFDM is also used for other radio standards, for Digital
Audio Broadcasting (DAB), the standard for digital audio broadcasting at VHF frequencies, for Digital Radio
Mondiale (DRM), the standard for digital broadcasting
at shortwave and medium wave frequencies (below 30
MHz) and for DRM+ a more recently introduced standard for digital audio broadcasting at VHF frequencies.
(30 to 174 MHz)
The USA again uses an alternate standard, a proprietary
system developed by iBiquity dubbed HD Radio. However, it uses COFDM as the underlying broadcast technology to add digital audio to AM (medium wave) and
FM broadcasts.

Fast low-latency access with seamless hando orthogonal frequency division multiplexing (Flash-OFDM), also
referred to as F-OFDM, was based on OFDM and also
specied higher protocol layers. It was developed by Flarion, and purchased by Qualcomm in January 2006.[28][29]
Flash-OFDM was marketed as a packet-switched cellular bearer, to compete with GSM and 3G networks. As
an example, 450 MHz frequency bands previously used
by NMT-450 and C-Net C450 (both 1G analogue networks, now mostly decommissioned) in Europe are being
licensed to Flash-OFDM operators.

In Finland, the license holder Digita began deployment

of a nationwide "@450 wireless network in parts of
the country since April 2007. It was purchased by
Datame in 2011.[30] In February 2012 Datame announced
MHz network to competing
Both Digital Radio Mondiale and HD Radio are classied they would upgrade the 450
[31]
CDMA2000
technology.
as in-band on-channel systems, unlike Eureka 147 (DAB:
Digital Audio Broadcasting) which uses separate VHF or Slovak Telekom in Slovakia oers Flash-OFDM
UHF frequency bands instead.
connections[32] with a maximum downstream speed

464

CHAPTER 101. ORTHOGONAL FREQUENCY-DIVISION MULTIPLEXING

of 5.3 Mbit/s, and a maximum upstream speed of 1.8

Mbit/s, with a coverage of over 70 percent of Slovak
population. The Flash-OFDM network was switched o
in the majority of Slovakia on 30 September 2015.[33]
T-Mobile Germany uses Flash-OFDM to backhaul Wi-Fi
HotSpots on the Deutsche Bahns ICE high speed trains.
American wireless carrier Nextel Communications eld
tested wireless broadband network technologies including Flash-OFDM in 2005.[34] Sprint purchased the carrier in 2006 and decided to deploy the mobile version of WiMAX, which is based on Scalable Orthogonal Frequency Division Multiple Access (SOFDMA)
technology.[35]
Citizens Telephone Cooperative launched a mobile
broadband service based on Flash-OFDM technology to
subscribers in parts of Virginia in March 2006. The maximum speed available was 1.5 Mbit/s.[36] The service was
discontinued on April 30, 2009.[37]
Digiweb Ltd. launched a mobile broadband network using Flash-OFDM technology at 872 MHz in July 2007
in Ireland and Digiweb also owns a national 872 MHz license in Norway. Voice handsets are not yet available as
of November 2007. The deployment is live in a small
area north of Dublin only.
Butler Networks operates a Flash-OFDM network in
Denmark at 872 MHz.
In Netherlands, KPN-telecom will start a pilot around
July 2007.

101.8 History

October 1990: TH-CSF LER, rst OFDM equipment eld test, 34 Mbit/s in an 8 MHz channel, experiments in Paris area
December 1990: TH-CSF LER, rst OFDM test
bed comparison with VSB in Princeton USA
September 1992: TH-CSF LER, second generation
equipment eld test, 70 Mbit/s in an 8 MHz channel,
twin polarisations. Wuppertal, Germany
October 1992: TH-CSF LER, second generation
eld test and test bed with BBC, near London, UK
1993: TH-CSF show in Montreux SW, 4 TV channel and one HDTV channel in a single 8 MHz channel
1993: Morris: Experimental 150 Mbit/s OFDM
wireless LAN
1995: ETSI Digital Audio Broadcasting standard
EUreka: rst OFDM based standard
1997: ETSI DVB-T standard
1998: Magic WAND project demonstrates OFDM
modems for wireless LAN
1999: IEEE 802.11a wireless LAN standard (WiFi)
2000: Proprietary xed wireless access (V-OFDM,
FLASH-OFDM, etc.)
2002: IEEE 802.11g standard for wireless LAN
2004: IEEE 802.16 standard for wireless MAN
(WiMAX)
2004: ETSI DVB-H standard

1957: Kineplex, multi-carrier HF modem (R.R.

Mosier & R.G. Clabaugh)

2004: Candidate for IEEE 802.15.3a standard for

wireless PAN (MB-OFDM)

1966: Chang, Bell Labs: OFDM paper[38] and

patent[39]

2004: Candidate for IEEE 802.11n standard for

next generation wireless LAN

1971: Weinstein & Ebert proposed use of FFT and

guard interval[40]

2005: OFDMA is candidate for the 3GPP Long

Term Evolution (LTE) air interface E-UTRA downlink.

1985: Cimini described use of OFDM for mobile

communications
1985: Telebit Trailblazer Modem introduced a 512
carrier Packet Ensemble Protocol (18 432 bit/s)

2007: The rst complete LTE air interface

implementation was demonstrated, including
OFDM-MIMO, SC-FDMA and multi-user MIMO
uplink[42]

1987: Alard & Lasalle: COFDM for digital broadcasting

101.9 See also

1988: In September TH-CSF LER, rst experimental Digital TV link in OFDM, Paris area

ATSC standards

1989:
OFDM international patent application PCT/FR 89/00546, led in the name of
THOMSON-CSF, Fouche, de Couasnon, Travert,
Monnier and all[41]

Carrier interferometry
Single-carrier frequency-domain-equalization (SCFDE)
Single-carrier FDMA (SC-FDMA)

101.10. REFERENCES

101.10 References
[1] webe.org - 2GHz BAS Relocation Tech-Fair, COFDM
Technology Basics. 2007-03-02
[2] Ben-Tovim, Erez (February 2014). ITU G.hn - Broadband Home Networking. In Berger, Lars T.; Schwager, Andreas; Pagani, Pascal; Schneider, Daniel M. MIMO
Power Line Communications. Devices, Circuits, and Systems. CRC Press. ISBN 9781466557529.
[3] Robertson, P.; Kaiser, S. The eects of Doppler spreads
in OFDM(A) mobile radio systems, Vehicular Technology Conference, 1999. VTC 1999 - Fall. IEEE VTS.
Link
[4] Haas, R.; Belore, J.C. (1997). A Time-Frequency
Well-localized Pulse for Multiple Carrier Transmission. Wireless Personal Communications. 5 (1): 118.
doi:10.1023/A:1008859809455..
[5] Roque, D.; Siclet, C. (2013). Performances of Weighted
Cyclic Prex OFDM with Low-Complexity Equalization. IEEE Communications Letters. 17 (3): 439442.
doi:10.1109/LCOMM.2013.011513.121997..
[6] Jeon, W.G.; Chang, K.H.; Cho, Y.S. (1999). An equalization technique for orthogonal frequency-division multiplexing systems in time-variant multipath channels.
IEEE Transactions on Communications. 47 (1): 2732.
doi:10.1109/26.747810..

465

[15] Hrycak, T.; Das, S.; Matz, G.; Feichtinger, H. G.;

Low Complexity Equalization for Doubly Selective Channels Modeled by a Basis Expansion, Signal Processing, IEEE Transactions on, vol.PP, no.99, pp.1-1, 0
doi:10.1109/TSP.2010.2063426" Link
[16] Berger, Lars T.; Schwager, Andreas; Pagani, Pascal;
Schneider, Daniel M, eds. (February 2014). MIMO Power
Line Communications: Narrow and Broadband Standards,
EMC, and Advanced Processing. Devices, Circuits, and
Systems. CRC Press. p. 25. doi:10.1201/b16540-1.
ISBN 978-1-4665-5753-6.
[17] Bernhard Kaehs. The Crest Factor in DVB-T (OFDM)
Transmitter Systems and its Inuence on the Dimensioning of Power Components
[18] Digital Audio Broadcasting: Principles and Applications of
DAB, DAB + and DMB. 2009. p. 333. Retrieved 201307-04. (3rd edition 2009)
[19] William Shieh, Ivan Djordjevic. (2010). OFDM for Optical Communications. 525 B Street, Suite 1900, San
Diego, California 92101-4495, USA: Academic Press.
[20] Berger, Lars T.; Schwager, Andreas; Pagani, Pascal;
Schneider, Daniel M., eds. (February 2014). MIMO
Power Line Communications: Narrow and Broadband
Standards, EMC, and Advanced Processing. Devices, Circuits, and Systems. CRC Press. ISBN 9781466557529.
[21] 4QAM is equivalent to QPSK
[22] NR refers to Nordstrom-Robinson code

[7] sharif.ir - The suitability of OFDM as a modulation technique for wireless telecommunications, with a CDMA
comparison., October 1997
[8] tw.org - 1.266 GHz Pentium 3, 2006-06-20
[9] tw.org - 1.6 GHz Pentium M (Banias), GNU compilers,
2006-06-20
[10] tw.org - 3.0 GHz Intel Core Duo, Intel compilers, 32-bit
mode, 2006-10-09
[11] Coleri, S. Ergen, M. Puri, A. Bahai, A., Channel estimation techniques based on pilot arrangement in OFDM
systems. IEEE Transactions on Broadcasting, Sep 2002.
"Link
[12] Hoeher, P. Kaiser, S. Robertson, P. Two-dimensional
pilot-symbol-aided channel estimation by Wienerltering. IEEE International Conference on Acoustics,
Speech, and Signal Processing, ICASSP-97, 1997. Link
[13] Zemen, T.; Mecklenbrauker, C.F., Time-Variant
Channel Estimation Using Discrete Prolate Spheroidal
Sequences.
Signal Processing, IEEE Transactions
on, vol.53, no.9, pp.
3597- 3607, Sept.
2005
doi:10.1109/TSP.2005.853104" Link
[14] Zijian Tang; Cannizzaro, R.C.; Leus, G.; Banelli,
P., Pilot-Assisted Time-Varying Channel Estimation
for OFDM Systems, Signal Processing, IEEE Transactions on, vol.55, no.5, pp.2226-2238, May 2007
doi:10.1109/TSP.2007.893198" Link

[23] Hoch, Martin; Comparison of PLC G3 and Prime, 2011

IEEE Symposium on Powerline Communication and its
Applications
[24] Stefano Galli et al. (July 2008). Recent Developments
in the Standardization of Power Line Communications
within the IEEE. IEEE Communications Magazine. 46
(7): 6471. doi:10.1109/MCOM.2008.4557044. An
overview of P1901 PHY/MAC proposal.
[25] DIRECTIVE 95/47/EC OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL on the use of standards for the transmission of television signals
[26] ETSI Standard: EN 300 744 V1.5.1 (2004-11).
[27] http://www.commsdesign.com/article/printableArticle.
jhtml?articleID=12805708 Agere gets Sirius about
satellite radio design
[28] Qualcomm and Exoteq Sign OFDM/OFDMA License
Agreement. News release. Qualcomm. August 1, 2007.
Retrieved July 23, 2011.
[29] Qualcomm Completes Acquisition Of WiMAX Competitor. Network Computing. January 19, 2006. Retrieved July 23, 2011.
[30] Briey in English. @450-Network web site. Datame.
Retrieved July 23, 2011.
[31] Aleksi Kolehmainen (February 8, 2012). "@450 siirtyy cdma2000-tekniikkaan - jopa puhelut mahdollisia.
Tietoviikko (in Finnish).

466

CHAPTER 101. ORTHOGONAL FREQUENCY-DIVISION MULTIPLEXING

[32] Mapy pokrytia. Slovak Telekom web site (in Slovak).

Retrieved May 30, 2012.
[33] Slovak Telekom closed Flash-OFDM network. ceeitandtelecom. November 5, 2015.
[34] Nextel Flash-OFDM: The Best Network You May Never
Use. PC Magazine. March 2, 2005. Retrieved July 23,
2011.

Page on Orthogonal Frequency Division Multiplexing at http://www.iss.rwth-aachen.de/Projekte/

Theo/OFDM/node6.html accessed on 24 September 2007.
A tutorial on the signicance of Cyclic Prex (CP)
in OFDM Systems.
Siemens demos 360 Mbit/s wireless

[35] Sascha Segan (August 8, 2006). Sprint Nextel Goes To

The WiMax. PC Magazine. Retrieved July 23, 2011.

An Introduction to Orthogonal Frequency Division

Multiplex Technology

[36] Citizens Oers First Truly Mobile Wireless Internet in

Christiansburg and other parts of the New River Valley
(PDF). News release. Citizens Wireless. March 28, 2006.
Retrieved July 23, 2011.

Ali Imran Khan(2009), Student at National University of Computer and Emerging Sciences did ecient research with help of Dr. Khawar Khokhar
(Technical Member PTA)

[37] Thank you for supporting Citizens Mobile Broadband.

Citizens Wireless. 2009. Retrieved July 23, 2011.
[38] Chang, R. W. (1966). Synthesis of band-limited orthogonal signals for multi-channel data transmission.
Bell System Technical Journal. 45 (10): 17751796.
doi:10.1002/j.1538-7305.1966.tb02435.x.
[39] US 3488445
[40] S.Weinstein and P. Ebert, Data transmission by
frequency-division multiplexing using the discrete
Fourier transform, IEEE Transactions on Communication
Technology, vol. 19, no. 5, pp. 628634, October 1971.
[41] http://www.wipo.int/pctdb/en/wo.jsp?WO=1990/04893
[42] Nortel 3G World Congress Press Release

101.11 Further reading

M. Bank. System free of channel problems inherent
in changing mobile communication systems. Electronics Letters, 43(7), 2007 (401-402)
M. Bank, B. Hill, Miriam Bank. A wireless mobile
communication system without pilot signals Patent
PCT/Il N 2006000926, Patent PCT International
Application N0 PCT/IL 2006000926. Patent No.
7,986,740, Issue date: 26 July 2011

101.12 External links

Numerous useful links and resources for OFDM WCSP Group - University of South Florida (USF)
WiMAX Forum, WiMAX, the framework standard
for 4G mobile personal broadband
Stott, 1997 Technical presentation by J H Stott of
the BBCs R&D division, delivered at the 20 International Television Symposium in 1997; this URL
accessed 24 January 2006.

Short Introduction to OFDM - Tutorial written by

Prof. Debbah, head of the Alcatel-Lucent Chair on
exible radio.
Short free tutorial on COFDM by Mark Massel formerly at STMicroelectronics and in the digital TV
industry for many years.
A popular book on both COFDM and US ATSC by
Mark Massel
OFDM transmission step-by-step online experiment
Simulation of optical OFDM systems

Chapter 102

Wavelet modulation
Wavelet modulation, also known as fractal modulation, is a modulation technique that makes use of wavelet
transformations to represent the data being transmitted.
One of the objectives of this type of modulation is to send
data at multiple rates over a channel that is unknown.[1]
If the channel is not clear for one specic bit rate, meaning that the signal will not be received, the signal can be
sent at a dierent bit rate where the signal to noise ratio
is higher.

102.1 See also

Wavelet

102.2 References
[1] Wavelet Modulation in Gaussian and Rayleigh Fading
Channels, Manish J. Manglani, (Masters thesis)

467

Chapter 103

Trellis modulation
In telecommunication, trellis modulation (also known
as trellis coded modulation, or simply TCM) is a modulation scheme that transmits information with high eciency over band-limited channels such as telephone lines.
Gottfried Ungerboeck invented trellis modulation while
working for IBM in the 1970s, and rst described it in
a conference paper in 1976. It went largely unnoticed,
however, until he published a new, detailed exposition in
1982 that achieved sudden and widespread recognition.
In the late 1980s, modems operating over plain old telephone service (POTS) typically achieved 9.6 kbit/s by employing four bits per symbol QAM modulation at 2,400
baud (symbols/second). This bit rate ceiling existed despite the best eorts of many researchers, and some engineers predicted that without a major upgrade of the public phone infrastructure, the maximum achievable rate for
a POTS modem might be 14 kbit/s for two-way communication (3,429 baud 4 bits/symbol, using QAM).

called the key idea mapping by set partitions. This idea

groups symbols in a tree-like structure, then separates
them into two limbs of equal size. At each limb of the
tree, the symbols are further apart.
Though hard to visualize in multiple dimensions, a simple
one-dimension example illustrates the basic procedure.
Suppose the symbols are located at [1, 2, 3, 4, ...]. Place
all odd symbols in one group, and all even symbols in the
second group. (This is not quite accurate, because Ungerboeck was looking at the two dimensional problem, but
the principle is the same.) Take every other symbol in
each group and repeat the procedure for each tree limb.
He next described a method of assigning the encoded bit
stream onto the symbols in a very systematic procedure.
Once this procedure was fully described, his next step was
to program the algorithms into a computer and let the
computer search for the best codes. The results were astonishing. Even the most simple code (4 state) produced
error rates nearly one one-thousandth of an equivalent uncoded system. For two years Ungerboeck kept these results private and only conveyed them to close colleagues.
Finally, in 1982, Ungerboeck published a paper describing the principles of trellis modulation.

14 kbit/s is only 40% of the theoretical maximum bit

rate predicted by Shannons theorem for POTS lines (approximately 35 kbit/s).[1] Ungerboecks theories demonstrated that there was considerable untapped potential in
the system, and by applying the concept to new modem
standards, speed rapidly increased to 14.4, 28.8 and ulti- A urry of research activity ensued, and by 1990 the
mately 33.6 kbit/s.
International Telecommunication Union had published
modem standards for the rst trellis-modulated modem
at 14.4 kilobits/s (2,400 baud and 6 bits per symbol).
Over the next several years further advances in encod103.1 A new modulation method
ing, plus a corresponding symbol rate increase from
2,400 to 3,429 baud, allowed modems to achieve rates
up to 34.3 kilobits/s (limited by maximum power regulations to 33.8 kilobits/s). Today, the most common trellis-modulated V.34 modems use a 4-dimensional
set partitionachieved by treating two two-dimensional
symbols as a single lattice. This set uses 8, 16, or 32
state convolutional codes to squeeze the equivalent of 6
to 10 bits into each symbol the modem sends (for examTrellis diagram
ple, 2,400 baud 8 bits/symbol = 19,200 bit/s).
The name trellis derives from the fact that a state diagram
of the technique closely resembles a trellis lattice. The
scheme is basically a convolutional code of rates (r,r+1).
Ungerboecks unique contribution is to apply the parity
check for each symbol, instead of the older technique of
applying it to the bit stream then modulating the bits. He

Once manufacturers introduced modems with trellis

modulation, transmission rates increased to the point
where interactive transfer of multimedia over the telephone became feasible (a 200 kilobyte image and a 5
megabyte song could be downloaded in less than 1 minute
and 30 minutes, respectively). Sharing a oppy disk via

468

103.6. EXTERNAL LINKS

a BBS could be done in just a few minutes, instead of an
hour. Thus Ungerboecks invention played a key role in
the Information Age.

103.2 See also

Modems, for the history of various encoding modulations from 0.3 to 56 kbit/s
Trellis diagram, in the article about convolutional
codes

103.3 In popular culture

In the December 8, 1991 edition of the Dilbert comic
strip, Scott Adams refers to the mere mentioning of trellis code modulation as a means for stopping a casual conversation cold.[2]

103.4 Relevant papers

G. Ungerboeck, Channel coding with multilevel/phase signals, IEEE Trans. Inform. Theory,
vol. IT-28, pp. 5567, 1982.
G. Ungerboeck, Trellis-coded modulation with redundant signal sets part I: introduction, IEEE Communications Magazine, vol. 25-2, pp. 511, 1987.

103.5 References
[1] Forney, G. David; et al. (September 1984). Ecient
modulation for band-limited channels. IEEE Journal on
Selected Areas in Communications. 9: 632647.
[2] Dilbert Comic Strip.

103.6 External links

TCM tutorial
Oral-History:Gottfried Ungerboeck, Engineering
and Technology History Wiki (IEEE Global History
Network)

469

Chapter 104

Spread spectrum
In telecommunication and radio communication, spreadspectrum techniques are methods by which a signal (e.g.
an electrical, electromagnetic, or acoustic signal) generated with a particular bandwidth is deliberately spread in
the frequency domain, resulting in a signal with a wider
bandwidth. These techniques are used for a variety of
reasons, including the establishment of secure communications, increasing resistance to natural interference,
noise and jamming, to prevent detection, and to limit
power ux density (e.g. in satellite downlinks).

104.1 Spread-spectrum
munications

width. Ultra-wideband (UWB) is another modulation

technique that accomplishes the same purpose, based
on transmitting short duration pulses. Wireless standard
IEEE 802.11 uses either FHSS or DSSS in its radio interface.

telecom-

This is a technique in which a telecommunication signal

is transmitted on a bandwidth considerably larger than the
frequency content of the original information. Frequency
hopping is a basic modulation technique used in spread
spectrum signal transmission.
Spread-spectrum telecommunications is a signal structuring technique that employs direct sequence, frequency
hopping, or a hybrid of these, which can be used for multiple access and/or multiple functions. This technique decreases the potential interference to other receivers while
achieving privacy. Spread spectrum generally makes use
of a sequential noise-like signal structure to spread the
normally narrowband information signal over a relatively
wideband (radio) band of frequencies. The receiver correlates the received signals to retrieve the original information signal. Originally there were two motivations: either to resist enemy eorts to jam the communications
(anti-jam, or AJ), or to hide the fact that communication
was even taking place, sometimes called low probability
of intercept (LPI).
Frequency-hopping spread spectrum (FHSS), directsequence spread spectrum (DSSS), time-hopping spread
spectrum (THSS), chirp spread spectrum (CSS), and
combinations of these techniques are forms of spread
spectrum. Each of these techniques employs pseudorandom number sequences created using pseudorandom
number generators to determine and control the
spreading pattern of the signal across the allocated band470

Techniques known since the 1940s and used in

military communication systems since the 1950s
spread a radio signal over a wide frequency range
several magnitudes higher than minimum requirement. The core principle of spread spectrum is the
use of noise-like carrier waves, and, as the name implies, bandwidths much wider than that required for
simple point-to-point communication at the same
data rate.
Resistance to jamming (interference). DS (direct
sequence) is good at resisting continuous-time narrowband jamming, while FH (frequency hopping)
is better at resisting pulse jamming. In DS systems,
narrowband jamming aects detection performance
about as much as if the amount of jamming power is
spread over the whole signal bandwidth, when it will
often not be much stronger than background noise.
By contrast, in narrowband systems where the signal
bandwidth is low, the received signal quality will be
severely lowered if the jamming power happens to
be concentrated on the signal bandwidth.
Resistance to eavesdropping. The spreading code
(in DS systems) or the frequency-hopping pattern
(in FH systems) is often unknown by anyone for
whom the signal is unintended, in which case it
obscures the signal and reduces the chance of an
adversarys making sense of it. Moreover, for a
given noise power spectral density (PSD), spreadspectrum systems require the same amount of energy per bit before spreading as narrowband systems and therefore the same amount of power if
the bitrate before spreading is the same, but since
the signal power is spread over a large bandwidth,
the signal PSD is much lower often signicantly
lower than the noise PSD so that the adversary may be unable to determine whether the signal exists at all. However, for mission-critical applications, particularly those employing commer-

104.3. SPREAD-SPECTRUM CLOCK SIGNAL GENERATION

471

cially available radios, spread-spectrum radios do

not intrinsically provide adequate security; "...just
using spread-spectrum radio itself is not sucient
for communications security.[1]
Resistance to fading. The high bandwidth occupied
by spread-spectrum signals oer some frequency diversity, i.e. it is unlikely that the signal will encounter severe multipath fading over its whole bandwidth, and in other cases the signal can be detected
using e.g. a Rake receiver.
Multiple access capability, known as code-division
multiple access (CDMA) or code-division multiplexing (CDM). Multiple users can transmit simultaneously in the same frequency band as long as they
use dierent spreading codes

104.2 Invention of frequency hopping

Spread spectrum of a modern switching power supply (heating

up period) incl. waterfall diagram over a few minutes. Recorded
with a NF-5030 EMC-Analyzer

Further information: Frequency-hopping spread spectrum

concentrated at a single frequency (the desired clock frequency) and its harmonics. Practical synchronous digital systems radiate electromagnetic energy on a number
of narrow bands spread on the clock frequency and its
harmonics, resulting in a frequency spectrum that, at certain frequencies, can exceed the regulatory limits for electromagnetic interference (e.g. those of the FCC in the
United States, JEITA in Japan and the IEC in Europe).

Frequency-hopping may date back to radio pioneer

Jonathan Zenneck's 1908 German book Wireless Telegraphy although he states that Telefunken was using it
previously. It saw limited use by the German military
in World War I,[2] was put forward by Polish engineer
Leonard Danilewicz in 1929,[3] showed up in a patent in
the 1930s by Willem Broertjes (U.S. Patent 1,869,659,
issued Aug. 2, 1932),[4][5] and in the top-secret US Spread-spectrum clocking avoids this problem by using
Army Signal Corps World War II communications sys- one of the methods previously described to reduce the
tem named SIGSALY.
peak radiated energy and, therefore, its electromagnetic
During World War II, Golden Age of Hollywood actress emissions and so comply with electromagnetic compatiHedy Lamarr and Avant garde composer George Antheil bility (EMC) regulations.
developed and patented, intended jamming-resistant, ra- It has become a popular technique to gain regulatory apdio guidance system for use in Allied torpedoes under proval because it requires only simple equipment modUS Patent 2,292,387, receiving it on August 11, 1942. ication. It is even more popular in portable electronTheir approach was unique in that frequency coordination ics devices because of faster clock speeds and increaswas done with paper player piano rolls - a novel approach ing integration of high-resolution LCD displays into ever
which was never put in practice.[6]
smaller devices. Since these devices are designed to

104.3 Spread-spectrum clock signal generation

Spread-spectrum clock generation (SSCG) is used in
some synchronous digital systems, especially those containing microprocessors, to reduce the spectral density
of the electromagnetic interference (EMI) that these systems generate. A synchronous digital system is one that
is driven by a clock signal and, because of its periodic
nature, has an unavoidably narrow frequency spectrum.
In fact, a perfect clock signal would have all its energy

be lightweight and inexpensive, traditional passive, electronic measures to reduce EMI, such as capacitors or
metal shielding, are not viable. Active EMI reduction
techniques such as spread-spectrum clocking are needed
in these cases.
However, spread-spectrum clocking, like other kinds of
dynamic frequency change, can also create challenges for
designers. Principal among these is clock/data misalignment, or clock skew.
Note that this method does not reduce total radiated energy, and therefore systems are not necessarily less likely
to cause interference. Spreading energy over a larger
bandwidth eectively reduces electrical and magnetic

472
readings within narrow bandwidths. Typical measuring
receivers used by EMC testing laboratories divide the
electromagnetic spectrum into frequency bands approximately 120 kHz wide.[7] If the system under test were
to radiate all its energy in a narrow bandwidth, it would
register a large peak. Distributing this same energy into
a larger bandwidth prevents systems from putting enough
energy into any one narrowband to exceed the statutory
limits. The usefulness of this method as a means to
reduce real-life interference problems is often debated,
since it is perceived that spread-spectrum clocking hides
rather than resolves higher radiated energy issues by simple exploitation of loopholes in EMC legislation or certication procedures. This situation results in electronic
equipment sensitive to narrow bandwidth(s) experiencing much less interference, while those with broadband
sensitivity, or even operated at other higher frequencies
(such as a radio receiver tuned to a dierent station), will
experience more interference.
FCC certication testing is often completed with the
spread-spectrum function enabled in order to reduce the
measured emissions to within acceptable legal limits.
However, the spread-spectrum functionality may be disabled by the user in some cases. As an example, in the
area of personal computers, some BIOS writers include
the ability to disable spread-spectrum clock generation as
a user setting, thereby defeating the object of the EMI
regulations. This might be considered a loophole, but is
generally overlooked as long as spread-spectrum is enabled by default.
An ability to disable spread-spectrum clocking in computer systems is considered useful for overclocking, as
spread spectrum can lower maximum clock speed achievable due to clock skew.

104.4 See also

Direct-sequence spread spectrum
Open spectrum
Electromagnetic compatibility (EMC)
Electromagnetic interference (EMI)
Frequency allocation
Frequency-hopping spread spectrum
Orthogonal variable spreading factor (OVSF)
Process gain
Spread-spectrum time-domain reectometry
Time-hopping spread spectrum
HAVE QUICK military frequency-hopping UHF
radio voice communication system

CHAPTER 104. SPREAD SPECTRUM

Ultra-wideband
George Antheil
Hedy Lamarr
Defeat device

104.5 Notes
[1] Shaw, William T. (2006). Cyber Security for SCADA Systems. PennWell Books. p. 76. ISBN 9781593700683.
[2] Denis Winter, Haigs Command - A Reassessment
[3] Danilewicz later recalled: In 1929 we proposed to the
General Sta a device of my design for secret radio telegraphy which fortunately did not win acceptance, as it was a
truly barbaric idea consisting in constant changes of transmitter frequency. The commission did, however, see t to
grant me 5,000 zotych for executing a model and as encouragement to further work. Cited in Wadysaw Kozaczuk, Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War II,
1984, p. 27.
[4] http://www.idc.lnt.de/fileadmin/user_upload/rmt.pdf
[5] http://pigjump.com/
frequency-hopping-spread-spectrum-multiple-inventors/
[6] Ari Ben-Menahem, Historical Encyclopedia of Natural
and Mathematical Sciences, Volume 1, Springer Science
& Business Media - 2009, pages 4527-4530
[7] American National Standard for Electromagnetic Noise
and Field Strength Instrumentation, 10 Hz to 40 GHz
Specications, ANSI C63.2-1996, Section 8.2 Overall
Bandwidth

104.6 Sources
This article incorporates public domain material
from the General Services Administration document
Federal Standard 1037C (in support of MIL-STD188).
NTIA Manual of Regulations and Procedures for
Federal Radio Frequency Management
National Information Systems Security Glossary
History on spread spectrum, as given in Smart
Mobs, The Next Social Revolution, Howard Rheingold, ISBN 0-7382-0608-3
Wadysaw Kozaczuk, Enigma: How the German
Machine Cipher Was Broken, and How It Was Read
by the Allies in World War Two, edited and translated by Christopher Kasparek, Frederick, MD,
University Publications of America, 1984, ISBN 089093-547-5.

104.7. EXTERNAL LINKS

Andrew S. Tanenbaum and David J. Wetherall,
Computer Networks, Fifth Edition.

104.7 External links

HF Frequency Hopping
A short history of spread spectrum
HF VHF UHF Spread Spectrum Radio
CDMA and spread spectrum
Information about the use of spread spectrum for reduced AGP EMI
Spread Spectrum Scene newsletter
Presentations at 4/08 George Mason University conference on unlicensed spread spectrum history
Interview for the Indian press with Hedy Lamarrs
(the inventor of spread spectrum) son, Anthony
loder, on the impact of her invention

473

Chapter 105

Direct-sequence spread spectrum

In telecommunications, direct-sequence spread spectrum (DSSS) is a spread spectrum modulation technique
used to reduce overall signal interference. The spreading
of this signal makes the resulting wideband channel more
noisy, allowing for greater resistance to unintentional and
intentional interference.[1]
A method of achieving the spreading of a given signal
is provided by the modulation scheme. With DSSS, the
message signal is used to modulate a bit sequence known
as a Pseudo Noise (PN) code; this PN code consists of a
radio pulse that is much shorter in duration (larger bandwidth) than the original message signal. This modulation
of the message signal scrambles and spreads the pieces
of data, and thereby resulting in a bandwidth size nearly
identical to that of the PN sequence.[1] In this context, the
duration of the radio pulse for the PN code is referred to
as the chip duration. The smaller this duration, the larger
the bandwidth of the resulting DSSS signal; more bandwidth multiplexed to the message signal results in better
resistance against interference.[1][2]

construct the information signal.

105.3 Transmission method

Direct-sequence spread-spectrum transmissions multiply
the data being transmitted by a noise signal. This noise
signal is a pseudorandom sequence of 1 and 1 values; at
a frequency much higher than that of the original signal.
The resulting signal resembles white noise, like an audio recording of static. However, this noise-like signal is used to exactly reconstruct the original data at the
receiving end, by multiplying it by the same pseudorandom sequence (because 1 1 = 1, and 1 1 = 1).
This process, known as de-spreading, mathematically
constitutes a correlation of the transmitted PN sequence
with the PN sequence that the receiver already knows the
transmitter is using.

The resulting eect of enhancing signal to noise ratio on

Some practical and eective uses of DSSS include the the channel is called process gain. This eect can be made
Code Division Multiple Access (CDMA) channel access larger by employing a longer PN sequence and more chips
method and the IEEE 802.11b specication used in Wi- per bit, but physical devices used to generate the PN sequence impose practical limits on attainable processing
Fi networks.[3][4]
gain.

105.1 History
105.2 Features

While for useful process gain the transmitted DSSS signal must occupy much wider bandwidth than simple a.m.
of the original signal alone would require, its frequency
spectrum can be somewhat restricted for spectrum economy by a conventional analog bandpass lter to give a
roughly bell-shaped envelope centered on the carrier frequency. In contrast, frequency-hopping spread spectrum
which pseudo-randomly re-tunes the carrier, instead of
adding pseudo-random noise to the data, requires a uniform frequency response since any bandwidth shaping
would cause amplitude modulation of the signal by the
hopping code.

1. DSSS phase-shifts a sine wave pseudorandomly with

a continuous string of pseudonoise (PN) code symbols called "chips", each of which has a much
shorter duration than an information bit. That is,
each information bit is modulated by a sequence of
much faster chips. Therefore, the chip rate is much
If an undesired transmitter transmits on the same channel
higher than the information signal bit rate.
but with a dierent PN sequence (or no sequence at all),
2. DSSS uses a signal structure in which the sequence the de-spreading process has reduced processing gain for
of chips produced by the transmitter is already that signal. This eect is the basis for the code division
known by the receiver. The receiver can then use multiple access (CDMA) property of DSSS, which allows
the same PN sequence to counteract the eect of the multiple transmitters to share the same channel within the
PN sequence on the received signal in order to re- limits of the cross-correlation properties of their PN se474

105.7. REFERENCES
quences.

105.4 Benets
Resistance to unintended or intended jamming
Sharing of a single channel among multiple users
Reduced signal/background-noise level hampers
interception
Determination of relative timing between transmitter and receiver

475

105.7 References
[1] Haykin, Simon (2008). Communication systems (4 ed.).
John Wiley & Sons. pp. 48899. Retrieved 11 April
2015.
[2] DSSS - Direct Sequence Spread Spectrum - Telecom
ABC. www.telecomabc.com. Retrieved 2016-11-11.
[3] Rappaport, Theodore (January 2010). Wireless Communications Principles and Practice (2 ed.). Prentice-Hall,
Inc. p. 458. Retrieved 11 April 2015.
[4] Capacity, Coverage and Deployment Considerations for
IEEE 802.11G (PDF), Cisco Systems, Inc, 2005, p. 1

The Origins of Spread-Spectrum Communications

105.5 Uses
The United States GPS, European Galileo and Russian GLONASS satellite navigation systems; earlier
GLONASS used DSSS with a single PN code in
conjunction with FDMA, while latter GLONASS
used DSSS to achieve CDMA with multiple PN
codes
DS-CDMA (Direct-Sequence Code Division Multiple Access) is a multiple access scheme based on
DSSS, by spreading the signals from/to dierent
users with dierent codes. It is the most widely used
type of CDMA.
Cordless phones operating in the 900 MHz, 2.4 GHz
and 5.8 GHz bands
IEEE 802.11b 2.4 GHz Wi-Fi, and its predecessor
802.11-1999. (Their successor 802.11g uses both
OFDM and DSSS)
Automatic meter reading
IEEE 802.15.4 (used, e.g., as PHY and MAC
layer for ZigBee, or, as the physical layer for
WirelessHART)
Radio-controlled model Automotive vehicles

105.6 See also

Frequency-hopping spread spectrum
Linear feedback shift register
Barker code
Orthogonal frequency-division multiplexing
Complementary code keying

This article incorporates public domain material

from the General Services Administration document
Federal Standard 1037C.
NTIA Manual of Regulations and Procedures for
Federal Radio Frequency Management

105.8 External links

Civil Spread Spectrum History

Chapter 106

Chirp spread spectrum

106.2 Uses
Chirp spread spectrum was originally designed to compete with ultra-wideband for precision ranging and lowrate wireless networks in the 2.45 GHz band. However,
since the release of IEEE 802.15.4a (also known as IEEE
802.15.4a-2007), it is no longer actively being considered by the IEEE for standardization in the area of precision ranging. Currently, Nanotron Technologies, which
produces real-time location devices and was the primary
force behind getting CSS added to IEEE 802.15.4a, is the
only seller of wireless devices using CSS. In particular,
A linear frequency modulated upchirp in the time domain
their primary product, the nanoLOC TRX transceiver,
uses CSS and is marketed as a network device with realtime location and RFID abilities.[3] Some areas where this
In digital communications, chirp spread spectrum type of technology can be useful are medical applications,
(CSS) is a spread spectrum technique that uses wide- logistics (i.e. containers need to be tracked), and governband linear frequency modulated chirp pulses to encode ment/security applications.
information.[1] A chirp is a sinusoidal signal whose freChirp spread spectrum is ideal for applications requiring
quency increases or decreases over time (often with a
low power usage and needing relatively low data rates (1
polynomial expression for the relationship between time
Mbit/s or less). In particular, IEEE 802.15.4a species
and frequency). In the picture is an example of an
CSS as a technique for use in Low-Rate Wireless Personal
upchirpas you can see, the frequency increases linearly
Area Networks (LR-WPAN). However, whereas IEEE
over time.
802.15.4-2006 standard species that WPANs encompass an area of 10 m or less, IEEE 802.15.4a-2007, species CSS as a physical layer to be used when longer ranges
and devices moving at high speeds are part of your network. Nanotrons CSS implementation was actually seen
to work at a range of 570 meters between devices.[4] Fur106.1 Overview
ther, Nanotrons implementation can work at data rates of
up to 2 Mbit/s - higher than specied in 802.15.4a.[5] FiAs with other spread spectrum methods, chirp spread nally, the IEEE 802.15.4a PHY standard actually mixes
spectrum uses its entire allocated bandwidth to broad- CSS encoding techniques with dierential phase shift
cast a signal, making it robust to channel noise. Fur- keying modulation (DPSK) to achieve better data rates.
ther, because the chirps utilize a broad band of the spectrum, chirp spread spectrum is also resistant to multi-path Chirp spread spectrum may also be used in the future for
to detect and
fading even when operating at very low power. How- military applications as it is very dicult
[6]
intercept
when
operating
at
low
power.
ever, it is unlike direct-sequence spread spectrum (DSSS)
or frequency-hopping spread spectrum (FHSS) in that it Very similar frequency swept waveforms are used in
does not add any pseudo-random elements to the signal to frequency modulated continuous wave radars to meahelp distinguish it from noise on the channel, instead rely- sure range (distance); an unmodulated continuous wave
ing on the linear nature of the chirp pulse. Additionally, Doppler radar can only measure range-rate (relative vechirp spread spectrum is resistant to the Doppler eect, locity along the line of sight). FM-CW radars are very
which is typical in mobile radio applications.[2]
widely used as radio altimeters in aircraft.
476

106.5. EXTERNAL LINKS

106.3 See also

Bluetooth
IEEE 802.11
IEEE 802.15.4
IEEE 802.15.4a
IEEE 802.16
IEEE 802.20
IEEE 802.22
Spectral eciency comparison table
Zigbee

106.4 References
[1] IEEE Computer Society, (August 31, 2007). IEEE Standard 802.15.4a-2007. New York, NY: IEEE.
[2] Berni, A. J., & Gregg, W. D. (June 1973). On the utility
of chirp modulation for digital signaling, IEEE Transactions on Communications. Volume COM-21, 748-751.
[3] Nanotrons nanoLOC TRX Transceiver, Nanotron marketing
[4] , Nanotron Mine Test: slide 22
[5] Nanotron Technologies, (2007). nanoNET chirp based
wireless networks. Retrieved from http://www.nanotron.
com/EN/docs/WP/WP_CSS.pdf
[6] The Revenge of Chirp Spread Spectrum, Military applications

106.5 External links

Download the 802.15 standards from IEEE
IEEE 802.15 WPAN Low Rate Alternative PHY
Task Group 4a (TG4a)
Nanotron Technologies Frequently asked Questions
page
Nanotron Chirp Spread Spectrum page
Nanotron nanoNET Chirp Based Wireless Networks
About coexistence of IEEE 802.15.4aCSS with
IEEE 802.11b/g (2.45GHz WLAN)

477

Chapter 107

Frequency-hopping spread spectrum

FHSS redirects here.
(disambiguation).

For other uses, see FHSS

spectrum signals add minimal noise to the narrowfrequency communications, and vice versa. As a result, bandwidth can be used more eciently.

Frequency Hopping Spread Spectrum (FHSS) is a

method of transmitting radio signals by rapidly switching a carrier among many frequency channels, using a
pseudorandom sequence known to both transmitter and
107.2 Military use
receiver. It is used as a multiple access method in
the frequency-hopping code division multiple access
(FH-CDMA) scheme.
Spread-spectrum signals are highly resistant to delibFHSS is a wireless technology that spreads its signal over erate jamming, unless the adversary has knowledge
rapidly changing frequencies. Each available frequency of the spreading characteristics. Military radios use
band is divided into sub-frequencies. Signals rapidly cryptographic techniques to generate the channel sechange (hop) among these in a pre-determined order. quence under the control of a secret Transmission SecuInterference at a specic frequency will only aect the rity Key (TRANSEC) that the sender and receiver share
signal during that short interval. FHSS can, however, in advance.
cause interference with adjacent direct-sequence spread
spectrum (DSSS) systems. A sub-type of FHSS used
in Bluetooth wireless data transfer is adaptive frequency
hopping spread spectrum (AFH).

By itself, frequency hopping provides only limited protection against eavesdropping and jamming. Most modern military frequency hopping radios also employ separate encryption devices such as the KY-57. U.S.
military radios that use frequency hopping include the
JTIDS/MIDS family, HAVE QUICK and SINCGARS.

107.1 Spread-spectrum
Main article: Spread-spectrum

107.3 Civilian use

A spread-spectrum transmission oers three main advantages over a xed-frequency transmission:

In the US, since the Federal Communications Commission (FCC) amended rules to allow frequency hopping
1. Spread-spectrum signals are highly resistant to
spread spectrum systems in the unregulated 2.4 GHz
narrowband interference.
The process of reband, many consumer devices in that band have employed
collecting a spread signal spreads out the interfering
various spread-spectrum modes.
signal, causing it to recede into the background.
Some walkie-talkies that employ frequency-hopping
2. Spread-spectrum signals are dicult to intercept. A spread spectrum technology have been developed for unspread-spectrum signal may simply appear as an in- licensed use on the 900 MHz band. Several such racrease in the background noise to a narrowband re- dios are marketed under the name eXtreme Radio Serceiver. An eavesdropper may have diculty inter- vice (eXRS). Despite the names similarity to the FRS
cepting a transmission in real time if the pseudoran- allocation, the system is a proprietary design, rather than
dom sequence is not known.
an ocial FCC allocated service.
3. Spread-spectrum transmissions can share a fre- Motorola has deployed a business-banded, license-free
quency band with many types of conventional trans- digital radio that uses FHSS technology: the DTR series,
missions with minimal interference. The spread- models 410, 550 and 650.
478

107.6. VARIATIONS OF FHSS

479

107.4 Technical considerations

forces, who did not have the technology to follow the

sequence.[1]

The overall bandwidth required for frequency hopping

is much wider than that required to transmit the same
information using only one carrier frequency. However,
because transmission occurs only on a small portion of
this bandwidth at any given time, the eective interference bandwidth is really the same. Whilst providing
no extra protection against wideband thermal noise, the
frequency-hopping approach does reduce the degradation
caused by narrowband interference sources.

A Polish engineer and inventor, Leonard Danilewicz,

came up with the idea in 1929.[2] Several other patents
were taken out in the 1930s, including one by Willem
Broertjes (U.S. Patent 1,869,659, issued Aug. 2, 1932).

During World War II, the US Army Signal Corps was inventing a communication system called SIGSALY, which
incorporated spread spectrum in a single frequency context. However, SIGSALY was a top-secret communications system, so its existence did not become known until
One of the challenges of frequency-hopping systems is to the 1980s.
synchronize the transmitter and receiver. One approach
The most celebrated invention of frequency hopping was
is to have a guarantee that the transmitter will use all the
a patent awarded to actress Hedy Lamarr and comchannels in a xed period of time. The receiver can then
poser George Antheil, who in 1942 received U.S. Patent
nd the transmitter by picking a random channel and lis2,292,387 for their Secret Communications System.
tening for valid data on that channel. The transmitters
This intended early version of frequency hopping was
data is identied by a special sequence of data that is unsupposed to use a piano-roll to change among 88 frequenlikely to occur over the segment of data for this channel
cies, and was intended to make radio-guided torpedoes
and the segment can have a checksum for integrity and
harder for enemies to detect or to jam, but there is
further identication. The transmitter and receiver can
no record of a working device ever being produced.
use xed tables of channel sequences so that once synThe patent was rediscovered in the 1950s during patent
chronized they can maintain communication by following
searches when private companies independently develthe table. On each channel segment, the transmitter can
oped Code Division Multiple Access, a non-frequencysend its current location in the table.
hopping form of spread-spectrum, and has been cited nuIn the US, FCC part 15 on unlicensed system in the 902 merous times since.
928 MHz and 2.4 GHz bands permits more power than
A practical application of frequency hopping was develnon-spread-spectrum systems. Both frequency hopping
oped by Ray Zinn, co-founder of Micrel Corporation.
and direct sequence systems can transmit at 1 Watt. The
Zinn developed a method allowing radio devices to oplimit is increased from 1 milliwatt to 1 watt or a thousand
erate without the need to synchronize a receiver with a
times increase. The Federal Communications Commistransmitter. Using frequency hopping and sweep modes,
sion (FCC) prescribes a minimum number of channels
Zinns method is primarily applied in low data rate wireand a maximum dwell time for each channel.
less applications such as utility metering, machine and
In a real multipoint radio system, space allows multiple equipment monitoring and metering, and remote contransmissions on the same frequency to be possible us- trol. In 2006 Zinn received U.S. Patent 6,996,399 for
ing multiple radios in a geographic area. This creates the his Wireless device and method using frequency hoppossibility of system data rates that are higher than the ping and sweep modes.
Shannon limit for a single channel. Spread spectrum systems do not violate the Shannon limit. Spread spectrum
systems rely on excess signal to noise ratios for sharing
of spectrum. This property is also seen in MIMO and 107.6 Variations of FHSS
DSSS systems. Beam steering and directional antennas
also facilitate increased system performance by provid- Adaptive Frequency-hopping spread spectrum (AFH) (as
ing isolation between remote radios.
used in Bluetooth) improves resistance to radio frequency
interference by avoiding crowded frequencies in the hopping sequence. This sort of adaptive transmission is easier to implement with FHSS than with DSSS.
107.5 Multiple inventors
The key idea behind AFH is to use only the good frequencies, by avoiding the bad frequency channels
perhaps those bad frequency channels are experiencing
frequency selective fading, or perhaps some third party is
trying to communicate on those bands, or perhaps those
bands are being actively jammed. Therefore, AFH should
The German military made limited use of frequency hop- be complemented by a mechanism for detecting good/bad
ping for communication between xed command points channels.
in World War I to prevent eavesdropping by British However, if the radio frequency interference is itself dyPerhaps the earliest mention of frequency hopping in the
open literature is in radio pioneer Jonathan Zenneck's
book Wireless Telegraphy (German, 1908, English translation McGraw Hill, 1915), although Zenneck himself
states that Telefunken had already tried it.

480

CHAPTER 107. FREQUENCY-HOPPING SPREAD SPECTRUM

namic, then the strategy of bad channel removal, applied in AFH might not work well. For example, if
there are several colocated frequency-hopping networks
(as Bluetooth Piconet), then they are mutually interfering
and the strategy of AFH fails to avoid this interference.
The problem of dynamic interference, gradual reduction
of available hopping channels and backward compatibility with legacy bluetooth devices was resolved in version
1.2 of the Bluetooth Standard (2003). Other Strategies
for dynamic adaptation of the frequency hopping pattern
have been reported in the literature.[3] Such a situation
can often happen in the scenarios that use unlicensed
spectrum.
In addition, dynamic radio frequency interference is expected to occur in the scenarios related to cognitive radio, where the networks and the devices should exhibit
frequency-agile operation.
Chirp modulation can be seen as a form of frequencyhopping that simply scans through the available frequencies in consecutive order to communicate.

107.7 See also

Dynamic frequency hopping
List of multiple discoveries
Maximum length sequence
Orthogonal frequency-division multiplexing
Radio frequency sweep

107.8 Notes
[1] Denis Winter, Haigs Command - A Reassessment
[2] Danilewicz later recalled: In 1929 we proposed to the
General Sta a device of my design for secret radio telegraphy which fortunately did not win acceptance, as it was a
truly barbaric idea consisting in constant changes of transmitter frequency. The commission did, however, see t to
grant me 5,000 zotych for executing a model and as encouragement to further work. Cited in Wadysaw Kozaczuk, Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War II,
1984, p. 27.
[3] Petar Popovski; Hiroyuki Yomo; Ramjee Prasad (December 2006). Strategies For Adaptive Frequency Hopping
In The Unlicensed Bands (PDF). IEEE Wireless Communications. Retrieved 2008-03-02.

107.9 References
Wadysaw Kozaczuk, Enigma: How the German
Machine Cipher Was Broken, and How It Was Read

by the Allies in World War Two, edited and translated by Christopher Kasparek, Frederick, MD,
University Publications of America, 1984, ISBN 089093-547-5.

107.10 External links

FCC Part 15 Rules that cover frequency hopping
Frequency hopping in unlicensed spectrum describes strategies for adaptive hopping in crowded
spectrum, while considering the issues of radio etiquette and compliance with FCC Part 15 Rules

Chapter 108

Channel access method

In telecommunications and computer networks, a channel access method or multiple access method allows several terminals connected to the same multi-point
transmission medium to transmit over it and to share
its capacity.[1] Examples of shared physical media are
wireless networks, bus networks, ring networks and pointto-point links operating in half-duplex mode.

A related technique is wavelength division multiple access (WDMA), based on wavelength-division multiplexing (WDM), where dierent datastreams get dierent
colors in ber-optical communications. In the WDMA
case, dierent network nodes in a bus or hub network get
a dierent color.

An advanced form of FDMA is the orthogonal frequencydivision multiple access (OFDMA) scheme, for example
used in 4G cellular communication systems. In OFDMA,
each node may use several sub-carriers, making it possible to provide dierent quality of service (dierent data
rates) to dierent users. The assignment of sub-carriers
A channel-access scheme is also based on a multiple to users may be changed dynamically, based on the curaccess protocol and control mechanism, also known as rent radio channel conditions and trac load.
media access control (MAC). Media access control deals
with issues such as addressing, assigning multiplex channels to dierent users, and avoiding collisions. Media ac- 108.1.2 Time division multiple access
(TDMA)
cess control is a sub-layer in Layer 2 (data link layer) of
the OSI model and a component of the link layer of the
The time division multiple access (TDMA) channel acTCP/IP model.
cess scheme is based on the time-division multiplexing
(TDM) scheme, which provides dierent time-slots to
dierent data-streams (in the TDMA case to dierent
108.1 Fundamental types of chan- transmitters) in a cyclically repetitive frame structure.
For example, node 1 may use time slot 1, node 2 time
nel access schemes
slot 2, etc. until the last transmitter. Then it starts all
over again, in a repetitive pattern, until a connection is
These numerous channel access schemes which generally
ended and that slot becomes free or assigned to another
[2][3][1]
fall into the following categories:
node. An advanced form is Dynamic TDMA (DTDMA),
where a scheduling may give dierent time sometimes
but some times node 1 may use time slot 1 in rst frame
108.1.1 Frequency-division multiple ac- and use another time slot in next frame.
A channel-access scheme is based on a multiplexing
method, that allows several data streams or signals
to share the same communication channel or physical
medium. In this context. multiplexing is provided by the
physical layer.[lower-alpha 1]

cess (FDMA)

As an example, 2G cellular systems are based on a comThe frequency-division multiple access (FDMA) bination of TDMA and FDMA. Each frequency channel
channel-access scheme is based on the frequency- is divided into eight timeslots, of which seven are used
division multiplexing (FDM) scheme, which provides for seven phone calls, and one for signalling data.
dierent frequency bands to dierent data-streams. Statistical time division multiplexing multiple-access is
In the FDMA case, the data streams are allocated to typically also based on time-domain multiplexing, but not
dierent nodes or devices. An example of FDMA sys- in a cyclically repetitive frame structure. Due to its rantems were the rst-generation (1G) cell-phone systems, dom character it can be categorised as statistical multiwhere each phone call was assigned to a specic uplink plexing methods, making it possible to provide dynamic
frequency channel, and another downlink frequency bandwidth allocation. This requires a media access conchannel. Each message signal (each phone call) is trol (MAC) protocol, i.e. a principle for the nodes to take
modulated on a specic carrier frequency.
turns on the channel and to avoid collisions. Common
481

482

CHAPTER 108. CHANNEL ACCESS METHOD

examples are CSMA/CD, used in Ethernet bus networks ples include simple cellular radio systems and more adand hub networks, and CSMA/CA, used in wireless net- vanced cellular systems which use directional antennas
works such as IEEE 802.11.
and power modulation to rene spatial transmission patterns.

108.1.3

Code division multiple access

(CDMA)/Spread spectrum multi- 108.1.5 Power division multiple access
(PDMA)
ple access (SSMA)

The code division multiple access (CDMA) scheme is

based on spread spectrum, meaning that a wider radio
spectrum in Hertz is used than the data rate of each of
the transferred bit streams, and several message signals
are transferred simultaneously over the same carrier frequency, utilizing dierent spreading codes. The wide
bandwidth makes it possible to send with a very poor
signal-to-noise ratio of much less than 1 (less than 0 dB)
according to the Shannon-Heartly formula, meaning that
the transmission power can be reduced to a level below
the level of the noise and co-channel interference (cross
talk) from other message signals sharing the same frequency.

Power-division multiple access (PDMA) scheme is based

on using variable transmission power between users in order to share the available power on the channel. Examples
include multiple SCPC modems on a satellite transponder, where users get on demand a larger share of the
power budget to transmit at higher data rates.[4]

108.2 List of channel access methods

108.2.1 Circuit mode and channelization

methods
One form is direct sequence spread spectrum (DSCDMA), used for example in 3G cell phone systems.
Each information bit (or each symbol) is represented by The following are common circuit mode and
a long code sequence of several pulses, called chips. The channelization channel access methods:
sequence is the spreading code, and each message signal
Frequency-division multiple access (FDMA), based
(for example each phone call) uses a dierent spreading
on frequency-division multiplexing (FDM)
code.
Another form is frequency-hopping (FH-CDMA), where
the channel frequency is changing very rapidly according to a sequence that constitutes the spreading code.
As an example, the Bluetooth communication system is
based on a combination of frequency-hopping and either
CSMA/CA statistical time division multiplexing communication (for data communication applications) or TDMA
(for audio transmission). All nodes belonging to the same
user (to the same virtual private area network or piconet)
use the same frequency hopping sequency synchronously,
meaning that they send on the same frequency channel,
but CDMA/CA or TDMA is used to avoid collisions
within the VPAN. Frequency-hopping is used to reduce
the cross-talk and collision probability between nodes in
dierent VPANs.
Subdivisions of FH-CDMA are fast hopping where the
frequency of hopping is much higher than the message
frequency content and slow hopping where the hopping
frequency is comparable to message frequency content.
The subdivision is necessary as they are considerably different.

108.1.4

Space division multiple access

(SDMA)

Space-division multiple access (SDMA) transmits different information in dierent physical areas. Exam-

Wavelength
(WDMA)

division

multiple

access

Orthogonal frequency-division multiple access

(OFDMA), based on Orthogonal frequencydivision multiplexing (OFDM)
Single-carrier FDMA (SC-FDMA), a.k.a.
linearly-precoded OFDMA (LP-OFDMA),
based on single-carrier frequency-domainequalization (SC-FDE).
Time-division multiple access (TDMA), based on
time-division multiplexing (TDM)
Multi-Frequency Time Division Multiple Access (MF-TDMA)
Code division multiple access (CDMA), a.k.a.
Spread spectrum multiple access (SSMA)
Direct-sequence CDMA (DS-CDMA), based
on Direct-sequence spread spectrum (DSSS)
Frequency-hopping CDMA (FH-CDMA),
based on Frequency-hopping spread spectrum
(FHSS)
Orthogonal frequency-hopping multiple access (OFHMA)
Multi-carrier code division multiple access
(MC-CDMA)

108.3. HYBRID CHANNEL ACCESS SCHEME APPLICATION EXAMPLES

108.3 Hybrid
channel
access
scheme application examples

Space-division multiple access (SDMA)

Power-division multiple access (PDMA)

108.2.2

483

Packet mode methods

Note that hybrids of these techniques can be - and freThe following are examples of packet mode channel ac- quently are - used. Some examples:
cess methods:[1]
The GSM cellular system combines the use of frequency division duplex (FDD) to prevent inter Contention based random multiple access methods
ference between outward and return signals, with
Aloha
FDMA and TDMA to allow multiple handsets to
Slotted Aloha
work in a single cell.
Multiple Access with Collision Avoidance
GSM with the GPRS packet switched service com(MACA)
bines FDD and FDMA with slotted Aloha for reser Multiple Access with Collision Avoidance for
Wireless (MACAW)
Carrier sense multiple access (CSMA)
Carrier sense multiple access with collision detection (CSMA/CD) - suitable for wired networks
Carrier sense multiple access with collision
avoidance (CSMA/CA) - suitable for wireless
networks
Distributed
(DCF)

Coordination

Function

Carrier sense multiple access with collision

avoidance and Resolution using Priorities
(CSMA/CARP)
Carrier Sense Multiple Access/Bitwise Arbitration (CSMA/BA) Based on constructive interference (CAN-bus)
Token passing:
Token ring
Token bus
Polling
Resource reservation (scheduled) packet-mode
protocols

vation inquiries, and a Dynamic TDMA scheme for

transferring the actual data.
Bluetooth packet mode communication combines
frequency hopping (for shared channel access
among several private area networks in the same
room) with CSMA/CA (for shared channel access
inside a medium).
IEEE 802.11b wireless local area networks
(WLANs) are based on FDMA and DS-CDMA for
avoiding interference among adjacent WLAN cells
or access points. This is combined with CSMA/CA
for multiple access within the cell.
HIPERLAN/2 wireless networks combine FDMA
with dynamic TDMA, meaning that resource reservation is achieved by packet scheduling.
G.hn, an ITU-T standard for high-speed networking over home wiring (power lines, phone lines and
coaxial cables) employs a combination of TDMA,
Token passing and CSMA/CARP to allow multiple
devices to share the medium.

108.4 Denition within certain application areas

Dynamic Time Division Multiple Access (Dy108.4.1

namic TDMA)
Packet reservation multiple access (PRMA)
Reservation ALOHA (R-ALOHA)

Local and metropolitan area networks

In local area networks (LANs) and metropolitan area

networks (MANs), multiple access methods enable bus
networks, ring networks, hubbed networks, wireless net108.2.3 Duplexing methods
works and half duplex point-to-point communication, but
Where these methods are used for dividing forward are not required in full duplex point-to-point serial lines
and reverse communication channels, they are known as between network switches and routers, or in switched
networks (logical star topology). The most common
duplexing methods, such as:
multiple access method is CSMA/CD, which is used in
Ethernet. Although todays Ethernet installations typ Time division duplex (TDD)
ically are switched, CSMA/CD is utilized anyway to
Frequency division duplex (FDD)
achieve compatibility with hubs.

484

CHAPTER 108. CHANNEL ACCESS METHOD

108.4.2

Satellite communications

In satellite communications, multiple access is the capability of a communications satellite to function as a

portion of a communications link between more than
one pair of satellite terminals concurrently. Three types
of multiple access presently used with communications
satellites are code-division, frequency-division, and timedivision multiple access.

108.4.3

Switching centers

In telecommunication switching centers, multiple access

is the connection of a user to two or more switching
centers by separate access lines using a single message
routing indicator or telephone number.

108.5 Classications in the literature

Several ways of categorizing multiple-access schemes and
protocols have been used in the literature. For example, Daniel Minoli (2009)[5] identies ve principal types
of multiple-access schemes: FDMA, TDMA, CDMA,
SDMA, and Random access. R. Rom and M. Sidi
(1990)[6] categorize the protocols into Conict-free access protocols, Aloha protocols, and Carrier Sensing protocols.
The Telecommunications Handbook (Terplan and Morreale, 2000)[7] identies the following MAC categories:
Fixed assigned: TDMA, FDMA+WDMA, CDMA,
SDMA
Demand assigned (DA)
Reservation:
DA/TDMA,
DA/FDMA+DA/WDMA,
DA/CDMA,
DA/SDMA
Polling: Generalized polling, Distributed
polling, Token Passing, Implicit polling, Slotted access
Random access (RA): Pure RA (ALOHA,
GRA), Adaptive RA (TRA), CSMA, CSMA/CD,
CSMA/CA

108.6 See also

Radio resource management for inter-base station
interference control
Statistical multiplexing
Dynamic bandwidth allocation
Diversity scheme

108.7 Notes
[1] Multiplexing also may be used in full-duplex point-topoint communication between nodes in a switched network, which should not be considered as multiple access.

108.8 References
[1] Guowang Miao; Jens Zander; Ki Won Sung; Ben Slimane
(2016). Fundamentals of Mobile Data Networks. Cambridge University Press. ISBN 1107143217.
[2] Fundamentals of Communications Access Technologies:
FDMA, TDMA, CDMA, OFDMA, AND SDMA. Electronic Design. 2013-01-22. Retrieved 2014-08-28.
[3] Halit Eren (Nov 16, 2005). Wireless Sensors and Instruments: Networks, Design, and Applications. CRC Press.
p. 112. ISBN 9781420037401.
[4] Elinav, Doron; Rubin, Mati E.; Brener, Snir (Mar 6,
2014), Power Division Multiple Access, retrieved 2016-0629
[5] Daniel Minoli (3 February 2009). Satellite Systems Engineering in an IPv6 Environment. CRC Press. pp. 136.
ISBN 978-1-4200-7868-8. Retrieved 1 June 2012.
[6] Rom, Raphael; Sidi, Moshe (1990). Multiple Access Protocols: Performance and Analysis. SpringerVerlag/University of Michigan.
[7] Kornel Terplan (2000). The Telecommunications Handbook. CRC Press. pp. 266. ISBN 978-0-8493-3137-4.
Retrieved 1 June 2012.

This article incorporates public domain material from

the General Services Administration document Federal
Standard 1037C (in support of MIL-STD-188).

Chapter 109

Multi-carrier code division multiple access

Multi-Carrier Code Division Multiple Access (MC- 109.3 Variants
CDMA) is a multiple access scheme used in OFDMbased telecommunication systems, allowing the system to
support multiple users at the same time.
A number of alternative possibilities exist as to how this
MC-CDMA spreads each user symbol in the frequency frequency domain spreading can take place, such as by
domain. That is, each user symbol is carried over multi- using a long PN code and multiplying each data symbol,
ple parallel subcarriers, but it is phase shifted (typically 0 d, on a subcarrier by a chip from the PN code, c, or by
or 180 degrees) according to a code value. The code val- using short PN codes and spreading each data symbol by
ues dier per subcarrier and per user. The receiver com- an individual PN code i.e. d is multiplied by each
bines all subcarrier signals, by weighing these to compen- c and the resulting vector is placed on N subcarriers,
sate varying signal strengths and undo the code shift. The where N is the PN code length.
receiver can separate signals of dierent users, because Once frequency domain spreading has taken place and the
these have dierent (e.g. orthogonal) code values.
OFDM subcarriers have all been allocated values, OFDM
Since each data symbol occupies a much wider bandwidth modulation then takes place using the IFFT to produce an
(in hertz) than the data rate (in bit/s), a signal-to-noise- OFDM symbol; the OFDM guard interval is then added;
plus-interference ratio (if dened as signal power divided and if transmission is in the downlink direction each of
by total noise plus interference power in the entire trans- these resulting symbols are added together prior to transmission.
mission band) of less than 0 dB is feasible.
One way of interpreting MC-CDMA is to regard it as An alternative form of multi-carrier CDMA, called MCa direct-sequence CDMA signal (DS-CDMA) which is DS-CDMA or MC/DS-CDMA, performs spreading in
transmitted after it has been fed through an inverse FFT the time domain, rather than in the frequency domain in
the case of MC-CDMA for the special case where
(Fast Fourier Transform).
there is only one carrier, this reverts to standard DSCDMA.

109.1 Rationale

For the case of MC-DS-CDMA where OFDM is used as

the modulation scheme, the data symbols on the individWireless radio links suer from frequency-selective ual subcarriers are spread in time by multiplying the chips
channel interference. If the signal on one subcarrier ex- on a PN code by the data symbol on the subcarrier. For
periences an outage, it can still be reconstructed from the example, assume the PN code chips consist of {1, 1}
and the data symbol on the subcarrier is -j. The symbol
energy received over other subcarriers.
being modulated onto that carrier, for symbols 0 and 1,
will be -j for symbol 0 and +j for symbol 1.

109.2 Downlink: MC-CDM

In the downlink (one base station transmitting to one or
more terminals), MC-CDMA typically reduces to MultiCarrier Code Division Multiplexing. All user signals can
easily be synchronized, and all signals on one subcarrier
experience the same radio channel properties. In such
case a preferred system implementation is to take N user
bits (possibly but not necessarily for dierent destinations), to transform these using a Walsh Hadamard Transform, followed by an IFFT.

2-dimensional spreading in both the frequency and time

domains is also possible, and a scheme that uses 2-D
spreading is VSF-OFCDM (which stands for variable
spreading factor orthogonal frequency code-division multiplexing), which NTT DoCoMo is using for its 4G prototype system.
As an example of how the 2D spreading on VSF-OFCDM
works, if you take the rst data symbol, d0 , and a spreading factor in the time domain, SF , of length 4, and a
spreading factor in the frequency domain, SF of 2,
then the data symbol, d0 , will be multiplied by the length-

485

486

CHAPTER 109. MULTI-CARRIER CODE DIVISION MULTIPLE ACCESS

2 frequency-domain PN codes and placed on subcarriers

0 and 1, and these values on subcarriers 0 and 1 will then
be multiplied by the length-4 time-domain PN code and
transmitted on OFDM symbols 0, 1, 2 and 3.[1]

J.P.M.G. Linnartz, Performance Analysis of Synchronous MC-CDMA in mobile Rayleigh channels

with both Delay and Doppler spreads, IEEE VT,
Vol. 50, No. 6, Nov. 2001, pp 13751387. PDF

NTT DoCoMo has already achieved 5 Gbit/s transmissions to receivers travelling at 10 km/h using its 4G prototype system in a 100 MHz-wide channel. This 4G prototype system also uses a 12x12 antenna MIMO conguration, and turbo coding for error correction coding.[2]

K. Fazel and S. Kaiser, Multi-Carrier and Spread

Spectrum Systems: From OFDM and MC-CDMA to
LTE and WiMAX, 2nd Edition, John Wiley & Sons,
2008, ISBN 978-0-470-99821-2.

Summary
1. OFDMA with frequency spreading (MC-CDMA)
2. OFDMA with time spreading (MC-DS-CDMA and
MT-CDMA)
3. OFDMA with both time and frequency spreading (Orthogonal Frequency Code Division Multiple
Access(OFCDMA))

Hughes Software Systems, Multi Carrier Code Division Multiple Access, March 2002.
German Aerospace Center, Institute of Communications and Navigation, History of Multi-Carrier
Code Division Multiple Access (MC-CDMA) and
Multi-Carrier Spread Spectrum Workshop, November 2006.
Wireless Communication Reference Web Site, section about MC-CDMA, 2001.

109.4 References
109.6 See also
[1] http://citeseer.ist.psu.edu/atarashi02broadband.html
Broadband Packet Wireless Access Based On VSFOFCDM And MC/DS-CDMA (2002) Atarashi et
al.
[2] DoCoMo Achieves 5 Gbit/s Data Speed. NTT DoCoMo Press. 2007-02-09.

109.5 Literature
N. Yee, J.P.M.G. Linnartz and G. Fettweis, MultiCarrier CDMA in indoor wireless Radio Networks,
IEEE Personal Indoor and Mobile Radio Communications (PIMRC) Int. Conference, Sept. 1993,
Yokohama, Japan, pp. 109113 (1993: rst paper
proposing the system and the name MC-CDMA)
K. Fazel and L. Papke, On the performance of
convolutionally-coded CDMA/OFDM for mobile
communication system, IEEE Personal Indoor and
Mobile Radio Communications (PIMRC) Int. Conference, Sept. 1993, Yokohama, Japan, pp. 468
472
A. Chouly, A. Brajal, and S. Jourdan, Orthogonal multicarrier techniques applied to direct sequence spread spectrum CDMA systems, in Proceedings of Global Telecommunications Conference (GLOBECOM'93), pp. 17231728, Houston,
Tex, USA, November 1993.
N.Yee, J.P.M.G. Linnartz and G. Fettweis, MultiCarrier-CDMA in indoor wireless networks, IEICE Transaction on Communications, Japan, Vol.
E77-B, No. 7, July 1994, pp. 900904.

OFDMA, an alternative multiple access scheme for

OFDM systems, where the signals of dierent users
are separated in the frequency domain by allocating
dierent sub-carriers to dierent users.
Hybrid OFDM, This page covers Hybrid OFDM
referred as OFCDM which is a combination
of OFDM and CDMA.It provides comparison between MC/DS-CDMA,MC-CDMA and
OFCDM, Visit http://www.rfwireless-world.com/
Terminology/Hybrid-OFDM-OFCDM.html.

Chapter 110

Orthogonal frequency-division multiple

access
Averaging interferences from neighboring cells, by
using dierent basic carrier permutations between
users in dierent cells.

Orthogonal Frequency-Division Multiple Access

(OFDMA) is a multi-user version of the popular
orthogonal frequency-division multiplexing (OFDM)
digital modulation scheme. Multiple access is achieved
in OFDMA by assigning subsets of subcarriers to
individual users as shown in the illustration below. This
allows simultaneous low data rate transmission from
several users.

Interferences within the cell are averaged by using

allocation with cyclic permutations.
Enables Single Frequency Network coverage, where
coverage problem exists and gives excellent coverage.

110.1 Key features

Oers Frequency diversity by spreading the carriers

all over the used spectrum.

The advantages and disadvantages summarized below are

further discussed in the Characteristics and principles of
operation section. See also the list of OFDM Key features.

110.1.1

Claimed advantages over OFDM

with time-domain statistical multiplexing

Allows per channel or per subchannel power

110.1.3 Recognised
OFDMA

Allows simultaneous low-data-rate transmission

from several users.
Pulsed carrier can be avoided.
Lower maximum transmission power for low data
rate users.
Shorter delay, and constant delay.
Contention-based multiple access (collision avoidance) is simplied.
Further improves OFDM robustness to fading and
interference.
Combat narrow-band interference.

110.1.2

Claimed OFDMA Advantages

Flexibility of deployment across various frequency

bands with little needed modication to the air
interface.[1]
487

disadvantages

of

Higher sensitivity to frequency osets and phase

noise.[1]
Asynchronous data communication services such as
web access are characterised by short communication bursts at high data rate. Few users in a base station cell are transferring data simultaneously at low
constant data rate.
The complex OFDM electronics, including the FFT
algorithm and forward error correction, are constantly active independent of the data rate, which is
inecient from power consumption point of view,
while OFDM combined with data packet scheduling
may allow FFT algorithm to hibernate during certain
time intervals.
The OFDM diversity gain, and resistance to
frequency-selective fading, may partly be lost if very
few sub-carriers are assigned to each user, and if the
same carrier is used in every OFDM symbol. Adaptive sub-carrier assignment based on fast feedback
information about the channel, or sub-carrier frequency hopping, is therefore desirable.

 Dealing with co-channel interference from nearby

cells is more complex in OFDM than in CDMA. It
would require dynamic channel allocation with advanced coordination among adjacent base stations.

The fast channel feedback information and adaptive sub-carrier assignment is more complex than
CDMA fast power control.

Detect

110.2 Characteristics and principles of operation

S-to-P

CHAPTER 110. ORTHOGONAL FREQUENCY-DIVISION MULTIPLE ACCESS

Npoint
DFT

Subcarrier
Mapping

Mpoint
IDFT

P-to-S

488

Npoint
IDFT

Subcarrier
Demapping/
Equalization

Mpoint
DFT

*N<M
* S-to-P: Serial-to-Parallel

SC-FDMA

* P-to-S: Parallel-to-Serial

OFDMA

Based on feedback information about the channel conditions, adaptive user-to-subcarrier assignment can be
achieved.[2] If the assignment is done suciently fast, this
further improves the OFDM robustness to fast fading and 110.3 Usage
narrow-band cochannel interference, and makes it possible to achieve even better system spectral eciency.
OFDMA is used in:
Dierent numbers of sub-carriers can be assigned to different users, in view to support dierentiated Quality of
the mobility mode of the IEEE 802.16 Wireless
Service (QoS), i.e. to control the data rate and error probMAN standard, commonly referred to as WiMAX,
ability individually for each user.
OFDMA can be seen as an alternative to combining
OFDM with time division multiple access (TDMA)
or time-domain statistical multiplexing communication.
Low-data-rate users can send continuously with low
transmission power instead of using a pulsed highpower carrier. Constant delay, and shorter delay, can be
achieved.
OFDMA can also be described as a combination of frequency domain and time domain multiple access, where
the resources are partitioned in the time-frequency space,
and slots are assigned along the OFDM symbol index as
well as OFDM sub-carrier index.
OFDMA is considered as highly suitable for broadband
wireless networks, due to advantages including scalability and use of multiple antennas (MIMO)-friendliness,
and ability to take advantage of channel frequency
selectivity.[1]
In spectrum sensing cognitive radio, OFDMA is a possible approach to lling free radio frequency bands adaptively. Timo A. Weiss and Friedrich K. Jondral of the
University of Karlsruhe proposed a spectrum pooling system in which free bands sensed by nodes were immediately lled by OFDMA subbands.

the IEEE 802.20 mobile Wireless MAN standard,

commonly referred to as MBWA,
MoCA 2.0,
the downlink of the 3GPP Long Term Evolution
(LTE) fourth generation mobile broadband standard. The radio interface was formerly named
High Speed OFDM Packet Access (HSOPA), now
named Evolved UMTS Terrestrial Radio Access (EUTRA).
the Qualcomm Flarion Technologies Mobile FlashOFDM
the now defunct Qualcomm/3GPP2 Ultra Mobile
Broadband (UMB) project, intended as a successor
of CDMA2000, but replaced by LTE.
OFDMA is also a candidate access method for the IEEE
802.22 Wireless Regional Area Networks (WRAN). The
project aims at designing the rst cognitive radio based
standard operating in the VHF-low UHF spectrum (TV
spectrum).

110.8. EXTERNAL LINKS

489

110.8 External links

Orthogonal Frequency Division Multiple Access:
is it the multiple access system of the future?, S.
Srikanth, V. Kumaran, C. Manikandan et al., AUKBC Research Center, Anna University, India.
OFDMA subcarriers

110.4 Trademark and patents

The term OFDMA is claimed to be a registered trademark by Runcom Technologies Ltd., with various other
claimants to the underlying technologies through patents.

110.5 See also

Code division multiple access
Frequency division multiple access
Time division multiple access
Single-carrier FDMA (SC-FDMA), a.k.a. Linearly
precoded OFDMA (LP-OFDMA)
3GPP Long Term Evolution
WiMAX
WiBro

110.6 Notes
[1] Hujun Yin and Siavash Alamouti (August 2007).
OFDMA: A Broadband Wireless Access Technology. IEEE Sarno Symposium, 2006. IEEE: 14.
doi:10.1109/SARNOF.2006.4534773.
[2] Guowang Miao; Guocong Song (2014). Energy and spectrum ecient wireless network design. Cambridge University Press. ISBN 1107039886.

110.7 References
K. Fazel and S. Kaiser, Multi-Carrier and Spread
Spectrum Systems: From OFDM and MC-CDMA to
LTE and WiMAX, 2nd Edition, John Wiley & Sons,
2008, ISBN 978-0-470-99821-2.
Miriam Bank, M. Bank, M. Haridim, B. Hill
OFDMA in high-speed mobile systems, pilots and
simulation problems Int'l. J. of Communications,
1(4), 2007 (173-179)

Short Introduction to OFDM - Tutorial written by

Prof. Debbah, head of the Alcatel-Lucent Chair on
exible radio.
OFDMA Pioneer Runcom- Inventors and creators
of OFDMA
http://www.naun.org/journals/communications/
c-28.pdf - Miriam Bank, M. Bank, M. Haridim, B.
Hill OFDMA in high-speed mobile systems, pilots
and simulation problems
http://ieeexplore.ieee.org/xpl/login.jsp?tp=
&arnumber=1304951&url=http%3A%2F%
2Fieeexplore.ieee.org%2Fiel5%2F11%2F28985%
2F01304951.pdf%3Farnumber%3D1304951 - M.
Bank, On Increasing OFDM Method Frequency
Eciency Opportunity " IEEE Transaction on
Broadcasting, vol. 50 NO 2, June 2004.

Chapter 111

Class-D amplier
form with the same frequency spectrum, but with every
frequency uniformly magnied in amplitude.

Input

C
Low-pass lter
Switching controller
and output stage
Triangular wave generator

Block diagram of a basic switching or PWM (class-D) amplier

Note: For Clarity, Signal Periods are not shown to scale

A class-D amplier or switching amplier is an

electronic amplier in which the amplifying devices
(transistors, usually MOSFETs) operate as electronic
switches, and not as linear gain devices as in other ampliers. The signal to be amplied is a train of constant amplitude pulses, so the active devices switch rapidly back
and forth between a fully conductive and nonconductive
state. The analog signal to be amplied is converted to a
series of pulses by pulse width modulation, pulse density
modulation or other method before being applied to the
amplier. After amplication, the output pulse train can
be converted back to an analog signal by passing through
a passive low pass lter consisting of inductors and capacitors. The major advantage of a class-D amplier is
that it can be more ecient than analog ampliers, with
less power dissipated as heat in the active devices.
Output stages such as those used in pulse generators
are examples of class-D ampliers. However, the term
mostly applies to power ampliers intended to reproduce
signals with a bandwidth well below the switching frequency.

111.1 Basic operation

Class-D ampliers work by generating a train of square
pulses of xed amplitude but varying width and separation, the low-frequency portion of whose frequency spectrum is essentially the signal to be amplied. The highfrequency portion serves no purpose other than to create
a two level waveform. Because it has only two levels, it
can be amplied by simple switching. The output of such
a switch is an identical train of square pulses, except with
greater amplitude. Such amplication results in a wave-

A passive low-pass lter removes the unwanted highfrequency components, i.e., smooths the pulses out and
recovers the desired low-frequency signal. To maintain
high eciency, the lter is made with purely reactive
components (inductors and capacitors), which store the
excess energy until it is needed instead of converting
some of it into heat. The switching frequency is typically
chosen to be ten or more times the highest frequency of
interest in the input signal. This eases the requirements
placed on the output lter. In cost sensitive applications
the output lter is sometimes omitted. The circuit then
relies on the inductance of the loudspeaker to keep the
HF component from heating up the voice coil. It will also
need to implement a form of three-level (class-BD) modulation which reduces HF output, particularly when no
signal is present.
The structure of a class-D power stage is essentially
identical to that of a synchronously rectied buck converter (a type of non-isolated switched-mode power supply (SMPS)). Whereas buck converters usually function
as voltage regulators, delivering a constant DC voltage
into a variable load and can only source current (onequadrant operation), a class-D amplier delivers a constantly changing voltage into a xed load, where current
and voltage can independently change sign (four-quadrant
operation). A switching amplier must not be confused
with linear ampliers that use an SMPS as their source
of DC power. A switching amplier may use any type of
power supply (e.g., a car battery or an internal SMPS), but
the dening characteristic is that the amplication process itself operates by switching.
Theoretical power eciency of class-D ampliers is
100%. That is to say, all of the power supplied to it is
delivered to the load, none is turned to heat. This is because an ideal switch in its on state would conduct all the
current but have no voltage loss across it, hence no heat
would be dissipated. And when it is o, it would have the
full supply voltage across it but no leak current owing
through it, and again no heat would be dissipated. Realworld power MOSFETs are not ideal switches, but practical eciencies well over 90% are common. By contrast, linear AB-class ampliers are always operated with

490

111.4. DESIGN CHALLENGES

491

both current owing through and voltage standing across side the digital domain, forming a noise shaper which has
the power devices. An ideal class-B amplier has a the- lower noise in the audible frequency range.
oretical maximum eciency of 78%. Class A ampliers
(purely linear, with the devices always on) have a theoretical maximum eciency of 50% and some versions 111.4 Design challenges
have eciencies below 20%.

111.4.1 Switching speed

111.2 Terminology
The term class D is sometimes misunderstood as meaning a "digital" amplier. While some class-D amps may
indeed be controlled by digital circuits or include digital signal processing devices, the power stage deals with
voltage and current as a function of non-quantized time.
The smallest amount of noise, timing uncertainty, voltage
ripple or any other non-ideality immediately results in an
irreversible change of the output signal. The same errors in a digital system will only lead to incorrect results
when they become so large that a signal representing a
digit is distorted beyond recognition. Up to that point,
non-idealities have no impact on the transmitted signal.
Generally, digital signals are quantized in both amplitude
and wavelength, while analog signals are quantized in one
(e.g. PWM) or (usually) neither quantity.

111.3 Signal modulation

Two signicant design challenges for MOSFET driver

circuits in class-D ampliers are keeping dead times and
linear mode operation as short as possible. Dead time
is the period during a switching transition when both output MOSFETs are driven into Cut-O Mode and both
are o. Dead times need to be as short as possible to maintain an accurate low-distortion output signal, but dead times that are too short cause the MOSFET that is switching on to start conducting before the
MOSFET that is switching o has stopped conducting.
The MOSFETs eectively short the output power supply through themselves in a condition known as shootthrough. Meanwhile, the MOSFET drivers also need to
drive the MOSFETs between switching states as fast as
possible to minimize the amount of time a MOSFET is
in Linear Modethe state between Cut-O Mode and
Saturation Mode where the MOSFET is neither fully on
nor fully o and conducts current with a signicant resistance, creating signicant heat. Driver failures that allow
shoot-through and/or too much linear mode operation result in excessive losses and sometimes catastrophic failure
of the MOSFETs.[4]

The 2-level waveform is derived using pulse-width modulation (PWM), pulse density modulation (sometimes referred to as pulse frequency modulation), sliding mode 111.4.2 Electromagnetic interference
control (more commonly called self-oscillating modulation in the trade.[1] ) or discrete-time forms of modula- The switching power stage generates both high dV/dt and
dI/dt, which give rise to radiated emission whenever any
tion such as delta-sigma modulation.[2]
part of the circuit is large enough to act as an antenna.
The most basic way of creating the PWM signal is to use a In practice, this means the connecting wires and cables
high speed comparator ("C" in the block-diagram above) will be the most ecient radiators so most eort should
that compares a high frequency triangular wave with the go into preventing high-frequency signals reaching those:
audio input. This generates a series of pulses of which the
duty cycle is directly proportional with the instantaneous
Avoid capacitive coupling from switching signals
value of the audio signal. The comparator then drives a
into the wiring.
MOS gate driver which in turn drives a pair of high-power
Avoid inductive coupling from various current loops
switches (usually MOSFETs). This produces an ampliin the power stage into the wiring.
ed replica of the comparators PWM signal. The output
lter removes the high-frequency switching components
Use one unbroken ground plane and group all conof the PWM signal and recovers the audio information
nectors together, in order to have a common RF refthat the speaker can use.
erence for decoupling capacitors
DSP-based ampliers which generate a PWM signal directly from a digital audio signal (e. g. SPDIF) either
use a counter to time the pulse length[3] or implement a
digital equivalent of a triangle-based modulator. In either case, the time resolution aorded by practical clock
frequencies is only a few hundredths of a switching period, which is not enough to ensure low noise. In eect,
the pulse length gets quantized, resulting in quantization
distortion. In both cases, negative feedback is applied in-

Include the equivalent series inductance of lter capacitors and the parasitic capacitance of lter inductors in the circuit model before selecting components.
Wherever ringing is encountered, locate the inductive and capacitive parts of the resonant circuit that
causes it, and use parallel RC or series RL snubbers
to reduce the Q of the resonance.

492

CHAPTER 111. CLASS-D AMPLIFIER

Do not make the MOSFETs switch any faster than

needed to full eciency or distortion requirements. Distortion is more easily reduced using
negative feedback than by speeding up switching.

111.4.3

Power supply design

Very high power conversion eciency, usually better than 90% above one quarter of the ampliers
maximum power, and around 50% at low power levels.
Can operate from a digital signal source without requiring a digital-to-analog converter (DAC) to convert the signal to analog form rst.

Class-D ampliers place an additional requirement on

their power supply, namely that it be able to sink energy
returning from the load. Reactive (capacitive or inductive) loads store energy during part of a cycle and release
some of this energy back later. Linear ampliers will
dissipate this energy away, class-D ampliers return it to
the power supply which should somehow be able to store
it. In addition, half-bridge class D amps transfer energy
from one supply rail (e.g. the positive rail) to the other
(e.g. the negative) depending on the sign of the output
current. This happens regardless of whether the load is
resistive or not. The supply should either have enough
capacitive storage on both rails, or be able to transfer this
energy back.[5]

111.5 Error control

The actual output of the amplier is not just dependent on the content of the modulated PWM signal.
The power supply voltage directly amplitude-modulates
the output voltage, dead time errors make the output
impedance non-linear and the output lter has a strongly
load-dependent frequency response. An eective way to
combat errors, regardless of their source, is negative feedback. A feedback loop including the output stage can be
made using a simple integrator. To include the output lter, a PID controller is used, sometimes with additional
integrating terms. The need to feed the actual output signal back into the modulator makes the direct generation
of PWM from a SPDIF source unattractive.[6] Mitigating the same issues in an amplier without feedback requires addressing each separately at the source. Power
supply modulation can be partially canceled by measuring
the supply voltage to adjust signal gain before calculating
the PWM[7] and distortion can be reduced by switching
faster. The output impedance cannot be controlled other
than through feedback.

111.6 Advantages
Despite the complexity involved, a properly designed
class-D amplier oers the following benets:
Reduced power waste as heat dissipation and hence:
Reduction in cost, size and weight of the amplier
due to smaller (or no) heat sinks, and compact circuitry,

Boss Audio mono amp. The output stage is top left, the output
chokes are the two yellow toroids underneath.

111.7 Uses
Home theatre in a box systems. These economical home cinema systems are almost universally
equipped with class-D ampliers. On account of
modest performance requirements and straightforward design, direct conversion from digital audio to
PWM without feedback is most common.
Mobile phones. The internal loudspeaker is driven
by up to 1 W. Class D is used to preserve battery
lifetime.
Hearing aids. The miniature loudspeaker (known as
the receiver) is directly driven by a class-D amplier
to maximise battery life and can provide saturation
levels of 130 dB SPL or more.
Powered speakers
High-end audio is generally conservative with regards to adopting new technologies but class-D ampliers have made an appearance[8]
Active subwoofers
Sound Reinforcement and Live Sound. For very
high power amplication the powerloss of AB ampliers are unacceptable. Amps with several kilowatts of output power are available as class-D. The
Crest Audio CD3000, for example, is a class-D
power amplier that is rated at 1500 W per channel, yet it weighs only 21 kg (46 lb).[9] Similarly, the

111.10. EXTERNAL LINKS

Powersoft K10 is a class-D power amplier that is
rated at 6000 W per 2-Ohm channel, yet it weighs
only 12 kg (26.5 lb).[10]
Bass ampliers. Again, an area where portability is
important. Example: Yamaha BBT500H bass amplier which is rated at 500 W, and yet it weighs
less than 5 kg (11 lb).[11] The Promethean P500H
by Ibanez is also capable of delivering 500 W into a
4 Ohm load, and weighs only 2.9 kg (6.4 lb). Gallien Krueger MB500 and Eden WTX500, also rated
at 500 W weighs no more than 2 kg (4.4 lb).

111.8 See also

Class-A amplier (a linear, non-PWM, amplier
class)
Class-B amplier (a linear, non-PWM, amplier
class)
Class-C amplier (a non-PWM amplier class)
Class-T amplier (a proprietary implementation of
class D)
Delta-sigma modulation
Sliding mode control
Sinclair Radionics, which sold one of the rst commercial Class-D ampliers in 1964

111.9 References
[1] The generic analysis of sliding mode control is quite math
heavy. The specic case of 2-state self-oscillating classD ampliers is much more intuitive and can be found in
Globally Modulated Self-Oscillating Amplier with Improved Linearity, 37th AES Conference
[2] The Analog Devices AD1990 class-D audio power amplier is an example.
[3] Sandler et al., Ultra-Low Distortion Digital Power Amplication, Presented at the 91st AES convention
[4] Analytical and numerical analysis of dead-time distortion
in power inverters
[5] irf.com - IRAUDAMP7S, 25W-500W Scalable Output
Power Class D Audio Power Amplier Reference Design,
Using the IRS2092S Protected Digital Audio Driver, page
26, 2008-08-29
[6] Putzeys et al. All Ampliers etc., Presented at the AES
120th convention
[7] Boudreaux, Randy, Real-Time Power Supply Feedback
Reduces Power Conversion Requirements For Digital
Class D Ampliers

493

[8] Group review of high end class D oerings and roundtable discussion with amplier designers.
[9] Home > Products > CD 3000(r)". Crest Audio. Retrieved 2013-07-16.
[10] Burning man Festival K10
[11] Yamaha BBT 500H Specications

111.10 External links

Video tutorial explaining class-D ampliers with example 2x15W circuit
List of PWM Ampliers
Snchez Moreno, Sergio Class-D Audio Ampliers
- Theory and Design - Contains material on the theory and design of Class-D ampliers.
Haber, Eric Designing With class-D amplier ICs Some IC-oriented Class D design considerations
Harden, Paul Introduction to Class C,D,E and F,
The Handimans Guide to MOSFET Switched
Mode Ampliers, Part 1 - An article on basic digital RF amplier design intended for ham radio operators but applicable to audio class-D ampliers.

Chapter 112

RF power amplier
Not to be confused with Audio power amplier.
A radio frequency power amplier (RF power am-

Many modern RF ampliers operate in dierent modes,

called classes, to help achieve their design goals. Some
classes are class A, class B, class C and class E.[1] Class
D ampliers are rarely used for RF purposes because they
need even higher frequency devices.
Modern RF power ampliers use solid-state devices such
as bipolar junction transistors and MOSFETs.[2] Although transistors and other modern solid-state devices
have replaced vacuum tubes in most electronic devices,
tubes are still used in some high-power transmitters (see
Valve RF amplier).

112.1 Applications
An RF power amplier

The basic applications of the RF power amplier include

driving to another high power source, driving a transmitting antenna and exciting microwave cavity resonators.
Among these applications, driving transmitter antennas
is most well known. The transmitterreceivers are used
not only for voice and data communication but also for
weather sensing (in the form of a radar).

112.2 Wideband amplier design

Impedance transformations over large bandwidth are difcult to realize, thus most wideband ampliers use 50
output loading. Transistor output power is then limited to

Pout

Class C VHF power amplier based on the transistor MRF317.

plier) is a type of electronic amplier that converts a

low-power radio-frequency signal into a higher power signal. Typically, RF power ampliers drive the antenna
of a transmitter. Design goals often include gain, power
output, bandwidth, power eciency, linearity (low signal
compression at rated output), input and output impedance
matching, and heat dissipation.

(Vbr Vk )2
8Zo

Vbr is dened as the breakdown voltage

Vk is dened as the knee voltage
and typically Zo = 50
The loadline method is often used in RF power amplier
design.[3]

494

112.4. EXTERNAL LINKS

112.3 References
[1] Cloutier, Stephen R. Class E AM Transmitter Descriptions, Circuits, Etc.. www.classeradio.com. WA1QIX.
Retrieved 6 June 2015.
[2] MFJ Enterprises. Ameritron ALS-1300 1200-watt NO
TUNE TMOS-FET AMPLIFIER (PDF). MFJ Enterprises. Retrieved 6 June 2015.
[3] Matthew Ozalas (January 14, 2015). How to Design an
RF Power Amplier: The Basics. youtube.com. Retrieved 2015-02-10.

112.4 External links

Carlos Fuentes (October 2008). Microwave Power
Amplier Fundamentals (PDF). Retrieved 201303-05.
Khanifar, Ahmad. RF Power Amplier Design for
Digital Predistortion. www.linamptech.com. Retrieved 1 December 2014.

495

Chapter 113

Code division multiple access

This article is about a channel access method. For the In 1958, the USSR also started the development of the
mobile phone technology referred to as CDMA, see "Altai" national civil mobile phone service for cars, based
IS-95 and CDMA2000.
on the Soviet MRT-1327 standard. The phone system
weighed 11 kg (24 lb). It was placed in the trunk of
Code division multiple access (CDMA) is a channel the vehicles of high-ranking ocials and used a standard
handset in the passenger compartment. The main develaccess method used by various radio communication
opers of the Altai system were VNIIS (Voronezh Sci[1]
technologies.
ence Research Institute of Communications) and GSPI
CDMA is an example of multiple access, where several (State Specialized Project Institute). In 1963 this service
transmitters can send information simultaneously over a started in Moscow and in 1970 Altai service was used in
single communication channel. This allows several users 30 USSR cities.[7]
to share a band of frequencies (see bandwidth). To permit this without undue interference between the users,
CDMA employs spread-spectrum technology and a spe- 113.2 Uses
cial coding scheme (where each transmitter is assigned a
code).[1]
CDMA is used as the access method in many mobile
phone standards. IS-95, also called cdmaOne, and its
3G evolution CDMA2000, are often simply referred to
as CDMA"', but UMTS, the 3G standard used by GSM
carriers, also uses wideband CDMA, or W-CDMA, as
well as TD-CDMA and TD-SCDMA, as its radio technologies.

113.1 History
The technology of code division multiple access channels has long been known. In the Soviet Union (USSR),
the rst work devoted to this subject was published in
1935 by professor Dmitriy V. Ageev.[2] It was shown that
through the use of linear methods, there are three types
of signal separation: frequency, time and compensatory.
The technology of CDMA was used in 1957, when the
young military radio engineer Leonid Kupriyanovich in
Moscow, made an experimental model of a wearable automatic mobile phone, called LK-1 by him, with a base
station. LK-1 has a weight of 3 kg, 2030 km operating
distance, and 2030 hours of battery life.[3][4] The base
station, as described by the author, could serve several A CDMA2000 mobile phone
customers. In 1958, Kupriyanovich made the new experimental pocket model of mobile phone. This phone
One of the early applications for code division mulweighed 0.5 kg. To serve more customers, Kupriyanovich
tiplexing is in the Global Positioning System (GPS).
proposed the device, named by him as correllator.[5][6]
496

113.4. CODE DIVISION MULTIPLEXING (SYNCHRONOUS CDMA)

497

This predates and is distinct from its use in mobile locally generated code of the desired user. If the signal
phones.
matches the desired users code then the correlation function will be high and the system can extract that signal.
The Qualcomm standard IS-95, marketed as cd- If the desired users code has nothing in common with
maOne.
the signal the correlation should be as close to zero as
possible (thus eliminating the signal); this is referred to
The Qualcomm standard IS-2000, known as
as cross-correlation. If the code is correlated with the
CDMA2000, is used by several mobile phone comsignal at any time oset other than zero, the correlation
panies, including the Globalstar satellite phone netshould be as close to zero as possible. This is referred
work.
to as auto-correlation and is used to reject multi-path
[10]
The UMTS 3G mobile phone standard, which uses interference.
W-CDMA.
An analogy to the problem of multiple access is a room
(channel) in which people wish to talk to each other si CDMA has been used in the OmniTRACS satellite multaneously. To avoid confusion, people could take
system for transportation logistics.
turns speaking (time division), speak at dierent pitches
(frequency division), or speak in dierent languages
(code division). CDMA is analogous to the last example
113.3 Steps in CDMA modulation where people speaking the same language can understand
each other, but other languages are perceived as noise and
[8]
CDMA is a spread-spectrum multiple access tech- rejected. Similarly, in radio CDMA, each group of users
nique. A spread spectrum technique spreads the band- is given a shared code. Many codes occupy the same
width of the data uniformly for the same transmitted channel, but only users associated with a particular code
power. A spreading code is a pseudo-random code that can communicate.
has a narrow ambiguity function, unlike other narrow In general, CDMA belongs to two basic categories: synpulse codes. In CDMA a locally generated code runs chronous (orthogonal codes) and asynchronous (pseudoat a much higher rate than the data to be transmitted. random codes).
Data for transmission is combined via bitwise XOR (exclusive OR) with the faster code. The gure shows how
a spread spectrum signal is generated. The data signal
with pulse duration of Tb (symbol period) is XOR'ed with
the code signal with pulse duration of Tc (chip period). 113.4 Code division multiplexing
(Note: bandwidth is proportional to 1/T , where T = bit
(synchronous CDMA)
time.) Therefore, the bandwidth of the data signal is 1/Tb
and the bandwidth of the spread spectrum signal is 1/Tc
. Since Tc is much smaller than Tb , the bandwidth of
The digital modulation method is analogous to those used
the spread spectrum signal is much larger than the bandin simple radio transceivers. In the analog case, a low
width of the original signal. The ratio Tb /Tc is called the
frequency data signal is time multiplied with a high frespreading factor or processing gain and determines to a
quency pure sine wave carrier, and transmitted. This
certain extent the upper limit of the total number of users
is eectively a frequency convolution (WienerKhinchin
supported simultaneously by a base station.[9]
theorem) of the two signals, resulting in a carrier with
narrow sidebands. In the digital case, the sinusoidal carT
rier is replaced by Walsh functions. These are binary
Data Signal
square waves that form a complete orthonormal set. The
data signal is also binary and the time multiplication is
Pseudorandom Code
achieved with a simple XOR function. This is usually a
Transmitted signal:
Gilbert cell mixer in the circuitry.
b

Data Signal XOR with

the Pseudorandom

Tc

Generation of a CDMA signal

Each user in a CDMA system uses a dierent code to

modulate their signal. Choosing the codes used to modulate the signal is very important in the performance of
CDMA systems.[1] The best performance will occur when
there is good separation between the signal of a desired
user and the signals of other users. The separation of the
signals is made by correlating the received signal with the

Synchronous CDMA exploits mathematical properties

of orthogonality between vectors representing the data
strings. For example, binary string 1011 is represented
by the vector (1, 0, 1, 1). Vectors can be multiplied by
taking their dot product, by summing the products of their
respective components (for example, if u = (a, b) and v
= (c, d), then their dot product uv = ac + bd). If the dot
product is zero, the two vectors are said to be orthogonal
to each other. Some properties of the dot product aid understanding of how W-CDMA works. If vectors a and b
are orthogonal, then ab = 0 and:

498

CHAPTER 113. CODE DIVISION MULTIPLE ACCESS

a (a + b) = a2

since

a(a+b) = a2
b (a + b) = b2

since
since

b (a b) = b2

since

a a + a b = a2 + 0
aa+ab = a2 +0
b a + b b = 0 + b2
b a b b = 0 b2

Each user in synchronous CDMA uses a code orthogonal

to the others codes to modulate their signal. An example
of four mutually orthogonal digital signals is shown in the
gure. Orthogonal codes have a cross-correlation equal
to zero; in other words, they do not interfere with each
other. In the case of IS-95 64 bit Walsh codes are used to
encode the signal to separate dierent users. Since each
of the 64 Walsh codes are orthogonal to one another, the
signals are channelized into 64 orthogonal signals. The
following example demonstrates how each users signal
can be encoded and decoded.

113.4.1

Example

these vectors are usually constructed for ease of decoding,

for example columns or rows from Walsh matrices.) An
example of orthogonal functions is shown in the picture
on the right. These vectors will be assigned to individual users and are called the code, chip code, or chipping
code. In the interest of brevity, the rest of this example
uses codes, v, with only two bits.
Each user is associated with a dierent code, say v. A 1
bit is represented by transmitting a positive code, v, and a
0 bit is represented by a negative code, v. For example,
if v = (v0 , v1 ) = (1, 1) and the data that the user wishes
to transmit is (1, 0, 1, 1), then the transmitted symbols
would be
(v, v, v, v) = (v0 , v1 , v0 , v1 , v0 , v1 , v0 , v1 ) = (1, 1,
1, 1, 1, 1, 1, 1). For the purposes of this article, we
call this constructed vector the transmitted vector.
Each sender has a dierent, unique vector v chosen from
that set, but the construction method of the transmitted
vector is identical.
Now, due to physical properties of interference, if two
signals at a point are in phase, they add to give twice the
amplitude of each signal, but if they are out of phase,
they subtract and give a signal that is the dierence of the
amplitudes. Digitally, this behaviour can be modelled by
the addition of the transmission vectors, component by
component.
If sender0 has code (1, 1) and data (1, 0, 1, 1), and
sender1 has code (1, 1) and data (0, 0, 1, 1), and both
senders transmit simultaneously, then this table describes
the coding steps:
Because signal0 and signal1 are transmitted at the same
time into the air, they add to produce the raw signal:
(1, 1, 1, 1, 1, 1, 1, 1) + (1, 1, 1, 1,
1, 1, 1, 1) = (0, 2, 2, 0, 2, 0, 2, 0)
This raw signal is called an interference pattern. The receiver then extracts an intelligible signal for any known
sender by combining the senders code with the interference pattern. The following table explains how this
works, and shows that the signals do not interfere with
one another:
Further, after decoding, all values greater than 0 are interpreted as 1 while all values less than zero are interpreted
as 0. For example, after decoding, data0 is (2, 2, 2, 2),
but the receiver interprets this as (1, 0, 1, 1). Values of
exactly 0 means that the sender did not transmit any data,
as in the following example:
Assume signal0 = (1, 1, 1, 1, 1, 1, 1, 1) is transmitted alone. The following table shows the decode at the
receiver:

When the receiver attempts to decode the signal using

sender1s code, the data is all zeros, therefore the cross
Start with a set of vectors that are mutually orthogonal. correlation is equal to zero and it is clear that sender1 did
(Although mutual orthogonality is the only condition, not transmit any data.
An example of four mutually orthogonal digital signals.

113.5. ASYNCHRONOUS CDMA

113.5 Asynchronous CDMA

499
Ecient practical utilization of the xed frequency
spectrum

See also: Direct-sequence spread spectrum and near-far

In theory CDMA, TDMA and FDMA have exactly the
problem
same spectral eciency but practically, each has its own
challenges power control in the case of CDMA, timing
When mobile-to-base links cannot be precisely coordi- in the case of TDMA, and frequency generation/ltering
nated, particularly due to the mobility of the handsets, in the case of FDMA.
a dierent approach is required. Since it is not mathematically possible to create signature sequences that are TDMA systems must carefully synchronize the transmisboth orthogonal for arbitrarily random starting points and sion times of all the users to ensure that they are received
which make full use of the code space, unique pseudo- in the correct time slot and do not cause interference.
random or pseudo-noise (PN) sequences are used in Since this cannot be perfectly controlled in a mobile enasynchronous CDMA systems. A PN code is a binary vironment, each time slot must have a guard-time, which
sequence that appears random but can be reproduced in reduces the probability that users will interfere, but dea deterministic manner by intended receivers. These PN creases the spectral eciency. Similarly, FDMA systems
codes are used to encode and decode a users signal in must use a guard-band between adjacent channels, due to
Asynchronous CDMA in the same manner as the orthog- the unpredictable doppler shift of the signal spectrum beonal codes in synchronous CDMA (shown in the exam- cause of user mobility. The guard-bands will reduce the
ple above). These PN sequences are statistically uncor- probability that adjacent channels will interfere, but derelated, and the sum of a large number of PN sequences crease the utilization of the spectrum.
results in multiple access interference (MAI) that is approximated by a Gaussian noise process (following the Flexible allocation of resources
central limit theorem in statistics). Gold codes are an example of a PN suitable for this purpose, as there is low Asynchronous CDMA oers a key advantage in the exicorrelation between the codes. If all of the users are re- ble allocation of resources i.e. allocation of a PN codes to
ceived with the same power level, then the variance (e.g., active users. In the case of CDM (synchronous CDMA),
the noise power) of the MAI increases in direct propor- TDMA, and FDMA the number of simultaneous orthogtion to the number of users. In other words, unlike syn- onal codes, time slots and frequency slots respectively are
chronous CDMA, the signals of other users will appear xed hence the capacity in terms of number of simultaneas noise to the signal of interest and interfere slightly with ous users is limited. There are a xed number of orthogthe desired signal in proportion to number of users.
onal codes, time slots or frequency bands that can be alloAll forms of CDMA use spread spectrum process gain to
allow receivers to partially discriminate against unwanted
signals. Signals encoded with the specied PN sequence
(code) are received, while signals with dierent codes (or
the same code but a dierent timing oset) appear as
wideband noise reduced by the process gain.

cated for CDM, TDMA, and FDMA systems, which remain underutilized due to the bursty nature of telephony
and packetized data transmissions. There is no strict limit
to the number of users that can be supported in an asynchronous CDMA system, only a practical limit governed
by the desired bit error probability, since the SIR (Signal
to Interference Ratio) varies inversely with the number
of users. In a bursty trac environment like mobile telephony, the advantage aorded by asynchronous CDMA
is that the performance (bit error rate) is allowed to uctuate randomly, with an average value determined by the
number of users times the percentage of utilization. Suppose there are 2N users that only talk half of the time,
then 2N users can be accommodated with the same average bit error probability as N users that talk all of the time.
The key dierence here is that the bit error probability
for N users talking all of the time is constant, whereas it
is a random quantity (with the same mean) for 2N users
talking half of the time.

Since each user generates MAI, controlling the signal

strength is an important issue with CDMA transmitters.
A CDM (synchronous CDMA), TDMA, or FDMA receiver can in theory completely reject arbitrarily strong
signals using dierent codes, time slots or frequency
channels due to the orthogonality of these systems. This
is not true for Asynchronous CDMA; rejection of unwanted signals is only partial. If any or all of the unwanted signals are much stronger than the desired signal, they will overwhelm it. This leads to a general requirement in any asynchronous CDMA system to approximately match the various signal power levels as seen at
the receiver. In CDMA cellular, the base station uses a
fast closed-loop power control scheme to tightly control In other words, asynchronous CDMA is ideally suited to
a mobile network where large numbers of transmitters
each mobiles transmit power.
each generate a relatively small amount of trac at irregular intervals. CDM (synchronous CDMA), TDMA,
113.5.1 Advantages of asynchronous and FDMA systems cannot recover the underutilized resources inherent to bursty trac due to the xed numCDMA over other techniques
ber of orthogonal codes, time slots or frequency channels

500

CHAPTER 113. CODE DIVISION MULTIPLE ACCESS

that can be assigned to individual transmitters. For instance, if there are N time slots in a TDMA system and
2N users that talk half of the time, then half of the time
there will be more than N users needing to use more than
N time slots. Furthermore, it would require signicant
overhead to continually allocate and deallocate the orthogonal code, time slot or frequency channel resources.
By comparison, asynchronous CDMA transmitters simply send when they have something to say, and go o the
air when they don't, keeping the same PN signature sequence as long as they are connected to the system.

113.5.2

Spread-spectrum
of CDMA

characteristics

Most modulation schemes try to minimize the bandwidth of this signal since bandwidth is a limited resource.
However, spread spectrum techniques use a transmission
bandwidth that is several orders of magnitude greater
than the minimum required signal bandwidth. One of
the initial reasons for doing this was military applications
including guidance and communication systems. These
systems were designed using spread spectrum because of
its security and resistance to jamming. Asynchronous
CDMA has some level of privacy built in because the
signal is spread using a pseudo-random code; this code
makes the spread spectrum signals appear random or have
noise-like properties. A receiver cannot demodulate this
transmission without knowledge of the pseudo-random
sequence used to encode the data. CDMA is also resistant
to jamming. A jamming signal only has a nite amount
of power available to jam the signal. The jammer can
either spread its energy over the entire bandwidth of the
signal or jam only part of the entire signal.[11]
CDMA can also eectively reject narrow band interference. Since narrow band interference aects only a small
portion of the spread spectrum signal, it can easily be removed through notch ltering without much loss of information. Convolution encoding and interleaving can be
used to assist in recovering this lost data. CDMA signals
are also resistant to multipath fading. Since the spread
spectrum signal occupies a large bandwidth only a small
portion of this will undergo fading due to multipath at any
given time. Like the narrow band interference this will
result in only a small loss of data and can be overcome.
Another reason CDMA is resistant to multipath interference is because the delayed versions of the transmitted pseudo-random codes will have poor correlation with
the original pseudo-random code, and will thus appear as
another user, which is ignored at the receiver. In other
words, as long as the multipath channel induces at least
one chip of delay, the multipath signals will arrive at the
receiver such that they are shifted in time by at least one
chip from the intended signal. The correlation properties
of the pseudo-random codes are such that this slight delay causes the multipath to appear uncorrelated with the

intended signal, and it is thus ignored.

Some CDMA devices use a rake receiver, which exploits
multipath delay components to improve the performance
of the system. A rake receiver combines the information from several correlators, each one tuned to a dierent path delay, producing a stronger version of the signal
than a simple receiver with a single correlation tuned to
the path delay of the strongest signal.[12]
Frequency reuse is the ability to reuse the same radio
channel frequency at other cell sites within a cellular system. In the FDMA and TDMA systems frequency planning is an important consideration. The frequencies used
in dierent cells must be planned carefully to ensure
signals from dierent cells do not interfere with each
other. In a CDMA system, the same frequency can be
used in every cell, because channelization is done using
the pseudo-random codes. Reusing the same frequency
in every cell eliminates the need for frequency planning
in a CDMA system; however, planning of the dierent
pseudo-random sequences must be done to ensure that
the received signal from one cell does not correlate with
the signal from a nearby cell.[13]
Since adjacent cells use the same frequencies, CDMA
systems have the ability to perform soft hand os. Soft
hand os allow the mobile telephone to communicate simultaneously with two or more cells. The best signal quality is selected until the hand o is complete. This is different from hard hand os utilized in other cellular systems. In a hard hand o situation, as the mobile telephone
approaches a hand o, signal strength may vary abruptly.
In contrast, CDMA systems use the soft hand o, which
is undetectable and provides a more reliable and higher
quality signal.[13]

113.6 Collaborative CDMA

In a recent study, a novel collaborative multi-user
transmission and detection scheme called Collaborative
CDMA[14] has been investigated for the uplink that exploits the dierences between users fading channel signatures to increase the user capacity well beyond the
spreading length in multiple access interference (MAI)
limited environment. The authors show that it is possible to achieve this increase at a low complexity and high
bit error rate performance in at fading channels, which
is a major research challenge for overloaded CDMA systems. In this approach, instead of using one sequence per
user as in conventional CDMA, the authors group a small
number of users to share the same spreading sequence
and enable group spreading and despreading operations.
The new collaborative multi-user receiver consists of two
stages: group multi-user detection (MUD) stage to suppress the MAI between the groups and a low complexity maximum-likelihood detection stage to recover jointly
the co-spread users data using minimum Euclidean dis-

113.10. EXTERNAL LINKS

tance measure and users channel gain coefcients. In
CDMA, signal security is high.

113.7 See also

cdmaOne
CDMA2000
W-CDMA
Orthogonal variable spreading factor (OVSF), an
implementation of CDMA
Pseudo-random noise
Spread spectrum
CDMA Spectral Eciency
Comparison of mobile phone standards

113.8 Further reading

Viterbi, Andrew J. (1995). CDMA: Principles of
Spread Spectrum Communication (1st ed.). Prentice
Hall PTR. ISBN 0-201-63374-4.
CDMA Spectrum. Retrieved 2008-04-29.

113.9 References
[1] Guowang Miao; Jens Zander; Ki Won Sung; Ben Slimane (2016). Fundamentals of Mobile Data Networks.
Cambridge University Press. ISBN 1107143217.
[2] Ageev, D. V. (1935). Bases of the Theory of Linear
Selection. Code Demultiplexing. Proceedings of the
Leningrad Experimental Institute of Communication: 3
35.
[3] Nauka i Zhizn 8, 1957, p. 49
[4] Yuniy technik 7, 1957, p. 4344
[5] Nauka i Zhizn 10, 1958, p. 66
[6] Tekhnika Molodezhi 2, 1959, p. 1819
[7] First Russian Mobile Phone. September 18, 2006.
[8] Ipatov, Valeri (2000). Spread Spectrum and CDMA. John
Wiley & Sons, Ltd.
[9] Dubendorf, Vern A. (2003). Wireless Data Technologies.
John Wiley & Sons, Ltd.
[10] CDMA Spectrum. Retrieved 2008-04-29.
[11] Skylar, Bernard (2001). Digital Communications: Fundamentals and Applications (Second ed.). Prentice-Hall
PTR.

501

[12] Rapporteur, Theodore S. (2002). Wireless Communications, Principles and Practice. Prentice-Hall, Inc.
[13] Harte, Levine, Kikta, Lawrence, Richard, Romans
(2002). 3G Wireless Demystied. McGowan-Hill.
[14] Shakya, Indu L. (2011). High User Capacity Collaborative CDMA. IET Communications.

113.10 External links

CDMA Development Group
Talk at Princeton Institute for Advanced Study
on Solomon Golombs work on pseudorandom sequences

Chapter 114

Software-dened radio
Software-dened radio (SDR) is a radio
communication system where components that have
been typically implemented in hardware (e.g. mixers,
lters, ampliers, modulators/demodulators, detectors,
etc.) are instead implemented by means of software
on a personal computer or embedded system.[1] While
the concept of SDR is not new, the rapidly evolving
capabilities of digital electronics render practical many
processes which used to be only theoretically possible.

interference from other directions, allowing it to detect fainter transmissions.

Cognitive radio techniques: each radio measures the
spectrum in use and communicates that information
to other cooperating radios, so that transmitters can
avoid mutual interference by selecting unused frequencies.
Dynamic transmitter power adjustment, based on
information communicated from the receivers, lowering transmit power to the minimum necessary, reducing the near-far problem and reducing interference to others, and extending battery life in portable
equipment.

114.1 Overview
A basic SDR system may consist of a personal computer
equipped with a sound card, or other analog-to-digital
converter, preceded by some form of RF front end. Signicant amounts of signal processing are handed over to
the general-purpose processor, rather than being done in
special-purpose hardware (electronic circuits). Such a
design produces a radio which can receive and transmit
widely dierent radio protocols (sometimes referred to
as waveforms) based solely on the software used.

Wireless mesh network where every added radio

increases total capacity and reduces the power required at any one node.[3] Each node only transmits
loudly enough for the message to hop to the nearest node in that direction, reducing near-far problem
and reducing interference to others.

Software radios have signicant utility for the military

and cell phone services, both of which must serve a wide
variety of changing radio protocols in real time.
In the long term, software-dened radios are expected by
proponents like the SDRForum (now The Wireless Innovation Forum) to become the dominant technology in
radio communications. SDRs, along with software dened antennas are the enablers of the cognitive radio.

114.2 Operating principles

Software Dened Radio

Smart
Antenna

Output

A software-dened radio can be exible enough to avoid

the limited spectrum assumptions of designers of previous kinds of radios, in one or more ways including:[2]

Flexible
RF
Hardware

IF
DAC

ANTENNA

A/D
D/A

Digital
Front End

Input

Base Band
Processing

Waveform
RF
AMPLIFIER
FILTER

A/D
D/A

Modem
Error
Correction

HARDWARE

Software dened antennas adaptively lock onto a Software dened radio concept
directional signal, so that receivers can better reject
502

Software
Algorithms
Middleware
CORBA
Virtual Radio Machine

Hardware
FPGAs
DSPs
ASICs

Control

RF/IF

Spread spectrum and ultrawideband techniques allow several transmitters to transmit in the same
place on the same frequency with very little interference, typically combined with one or more error
detection and correction techniques to x all the errors caused by that interference.

Processing

Channelization
and
Sample Rate
Conversion

ADC

Encryption

SOFTWARE

Network
Routing
GUI

User

114.3. HISTORY

114.2.1

Ideal concept

The ideal receiver scheme would be to attach an analogto-digital converter to an antenna. A digital signal processor would read the converter, and then its software would
transform the stream of data from the converter to any
other form the application requires.
An ideal transmitter would be similar. A digital signal
processor would generate a stream of numbers. These
would be sent to a digital-to-analog converter connected
to a radio antenna.
The ideal scheme is not completely realizable due to the
actual limits of the technology. The main problem in both
directions is the diculty of conversion between the digital and the analog domains at a high enough rate and a
high enough accuracy at the same time, and without relying upon physical processes like interference and electromagnetic resonance for assistance.

114.2.2

Receiver architecture

Most receivers use a variable-frequency oscillator, mixer,

and lter to tune the desired signal to a common
intermediate frequency or baseband, where it is then sampled by the analog-to-digital converter. However, in some
applications it is not necessary to tune the signal to an
intermediate frequency and the radio frequency signal is
directly sampled by the analog-to-digital converter (after
amplication).
Real analog-to-digital converters lack the dynamic range
to pick up sub-microvolt, nanowatt-power radio signals.
Therefore, a low-noise amplier must precede the conversion step and this device introduces its own problems.
For example, if spurious signals are present (which is typical), these compete with the desired signals within the
ampliers dynamic range. They may introduce distortion in the desired signals, or may block them completely.
The standard solution is to put band-pass lters between
the antenna and the amplier, but these reduce the radios
exibility. Real software radios often have two or three
analog channel lters with dierent bandwidths that are
switched in and out.

114.3 History
The term digital receiver was coined in 1970 by a researcher at a United States Department of Defense laboratory. A laboratory called the Gold Room at TRW
in California created a software baseband analysis tool
called Midas, which had its operation dened in software.

503
Radio Proof-of-Concept' laboratory was developed there
that popularized Software Radio within various government agencies. This 1984 Software Radio was a digital
baseband receiver that provided programmable interference cancellation and demodulation for broadband signals, typically with thousands of adaptive lter taps, using
multiple array processors accessing shared memory.[4]
In 1991, Joe Mitola independently reinvented the term
software radio for a plan to build a GSM base station that
would combine Ferdensis digital receiver with E-Systems
Melpars digitally controlled communications jammers
for a true software-based transceiver. E-Systems Melpar
sold the software radio idea to the US Air Force. Melpar
built a prototype commanders tactical terminal in 199091 that employed Texas Instruments TMS320C30 processors and Harris digital receiver chip sets with digitally
synthesized transmission. That prototype didn't last long
because when E-Systems ECI Division manufactured the
rst limited production units, they decided to throw out
those useless C30 boards, replacing them with conventional RF ltering on transmit and receive, reverting to
a digital baseband radio instead of the SPEAKeasy like
IF ADC/DACs of Mitolas prototype. The Air Force
would not let Mitola publish the technical details of that
prototype, nor would they let Diane Wasserman publish
related software life cycle lessons learned because they
regarded it as a USAF competitive advantage. So instead, with USAF permission, in 1991 Mitola described
the architecture principles without implementation details in a paper, Software Radio: Survey, Critical Analysis and Future Directions which became the rst IEEE
publication to employ the term in 1992.[5] When Mitola presented the paper at the conference, Bob Prill of
GEC Marconi began his presentation following Mitola
with Joe is absolutely right about the theory of a software radio and we are building one. Prill gave a GEC
Marconi paper on PAVE PILLAR, a SPEAKeasy precursor. SPEAKeasy, the military software radio was formulated by Wayne Bonser, then of Rome Air Development Center (RADC), now Rome Labs; by Alan Margulies of MITRE Rome, NY; and then Lt Beth Kaspar,
the original DARPA SPEAKeasy project manager and by
others at Rome including Don Upmal. Although Mitolas
IEEE publications resulted in the largest global footprint
for software radio, Mitola privately credits that DoD lab
of the 1970s with its leaders Carl, Dave, and John with inventing the digital receiver technology on which he based
software radio once it was possible to transmit via software.

A few months after the National Telesystems Conference 1992, in an E-Systems corporate program review,
a vice-president of E-Systems Garland Division objected
to Melpars (Mitolas) use of the term software radio
without credit to Garland. Alan Jackson, Melpar VP of
The term software radio was coined in 1984 by a team marketing at that time asked the Garland VP if their laboat the Garland, Texas Division of E-Systems Inc. (now ratory or devices included transmitters. The Garland VP
Raytheon) to refer to a digital baseband receiver and pub- said No, of course not ours is a software radio relished in their E-Team company newsletter. A 'Software

504
ceiver. Al replied Then its a digital receiver but without
a transmitter, its not a software radio. Corporate leadership agreed with Al, so the publication stood. Many
amateur radio operators and HF radio engineers had realized the value of digitizing HF at RF and of processing
it with Texas Instruments TI C30 digital signal processors (DSPs) and their precursors during the 1980s and
early 1990s. Radio engineers at Roke Manor in the UK
and at an organization in Germany had recognized the
benets of ADC at the RF in parallel, so success has
many fathers. Mitolas publication of software radio in
the IEEE opened the concept to the broad community of
radio engineers. His landmark May 1995 special issue
of the IEEE Communications Magazine with the cover
Software Radio was widely regarded as watershed event
with thousands of academic citations. Mitola was introduced by Joao da Silva in 1997 at the First International
Conference on Software Radio as godfather of software
radio in no small part for his willingness to share such a
valuable technology in the public interest.
Perhaps the rst software-based radio transceiver was
designed and implemented by Peter Hoeher and Helmuth Lang at the German Aerospace Research Establishment (DLR, formerly DFVLR) in Oberpfaenhofen,
Germany, in 1988.[6] Both transmitter and receiver of an
adaptive digital satellite modem were implemented according to the principles of a software radio, and a exible hardware periphery was proposed.
The term software dened radio was coined in 1995
by Stephen Blust, who published a request for information from Bell South Wireless at the rst meeting of the Modular Multifunction Information Transfer Systems (MMITS) forum in 1996, organized by the
USAF and DARPA around the commercialization of
their SPEAKeasy II program. Mitola objected to Blusts
term, but nally accepted it as a pragmatic pathway towards the ideal software radio. Though the concept was
rst implemented with an IF ADC in the early 1990s,
software-dened radios have their origins in the defense
sector since the late 1970s in both the U.S. and Europe
(for example, Walter Tuttlebee described a VLF radio
that used an ADC and an 8085 microprocessor).[7] about
a year after the First International Conference in Brussels. One of the rst public software radio initiatives
was the U.S. DARPA-Air Force military project named
SpeakEasy. The primary goal of the SpeakEasy project
was to use programmable processing to emulate more
than 10 existing military radios, operating in frequency
bands between 2 and 2000 MHz.[8] Another SPEAKeasy
design goal was to be able to easily incorporate new
coding and modulation standards in the future, so that
military communications can keep pace with advances in
coding and modulation techniques.

CHAPTER 114. SOFTWARE-DEFINED RADIO

114.3.1 SPEAKeasy phase I

From 1990 to 1995, the goal of the SPEAKeasy program
was to demonstrate a radio for the U.S. Air Force tactical
ground air control party that could operate from 2 MHz
to 2 GHz, and thus could interoperate with ground force
radios (frequency-agile VHF, FM, and SINCGARS), Air
Force radios (VHF AM), Naval Radios (VHF AM and
HF SSB teleprinters) and satellites (microwave QAM).
Some particular goals were to provide a new signal format
in two weeks from a standing start, and demonstrate a
radio into which multiple contractors could plug parts and
software.
The project was demonstrated at TF-XXI Advanced
Warghting Exercise, and demonstrated all of these goals
in a non-production radio. There was some discontent with failure of these early software radios to adequately lter out of band emissions, to employ more than
the simplest of interoperable modes of the existing radios, and to lose connectivity or crash unexpectedly. Its
cryptographic processor could not change context fast
enough to keep several radio conversations on the air at
once. Its software architecture, though practical enough,
bore no resemblance to any other. The SPEAKeasy architecture was rened at the MMITS Forum between
1996 and 1999 and inspired the DoD integrated process
team (IPT) for programmable modular communications
systems (PMCS) to proceed with what became the Joint
Tactical Radio System (JTRS).
The basic arrangement of the radio receiver used an
antenna feeding an amplier and down-converter (see
Frequency mixer) feeding an automatic gain control,
which fed an analog to digital converter that was on a
computer VMEbus with a lot of digital signal processors
(Texas Instruments C40s). The transmitter had digital to
analog converters on the PCI bus feeding an up converter
(mixer) that led to a power amplier and antenna. The
very wide frequency range was divided into a few subbands with dierent analog radio technologies feeding
the same analog to digital converters. This has since become a standard design scheme for wide band software
radios.

114.3.2 SPEAKeasy phase II

The goal was to get a more quickly recongurable architecture, i.e., several conversations at once, in an open software architecture, with cross-channel connectivity (the
radio can bridge dierent radio protocols). The secondary goals were to make it smaller, cheaper, and weigh
less.
The project produced a demonstration radio only fteen
months into a three-year research project. The demonstration was so successful that further development was
halted, and the radio went into production with only a 4
MHz to 400 MHz range.

114.4. CURRENT USAGE

The software architecture identied standard interfaces
for dierent modules of the radio: radio frequency
control to manage the analog parts of the radio, modem control managed resources for modulation and
demodulation schemes (FM, AM, SSB, QAM, etc.),
waveform processing modules actually performed the
modem functions, key processing and cryptographic
processing managed the cryptographic functions, a
multimedia module did voice processing, a human interface provided local or remote controls, there was a
routing module for network services, and a control
module to keep it all straight.

505
that civilian users can more easily settle with a xed architecture, optimized for a specic function, and as such
more economical in mass market applications. Still, software dened radios inherent exibility can yield substantial benets in the longer run, once the xed costs of implementing it have gone down enough to overtake the cost
of iterated redesign of purpose built systems. This then
explains the increasing commercial interest in the technology.

SCA-based infrastructure software and rapid development tools for SDR education and research are provided
by the Open Source SCA Implementation EmbedThe modules are said to communicate without a central ded (OSSIE[9] ) project. The Wireless Innovation Forum
operating system. Instead, they send messages over the funded the SCA Reference Implementation project, an
PCI computer bus to each other with a layered protocol. open source implementation of the SCA specication.
As a military project, the radio strongly distin- (SCARI) can be downloaded for free.
guished red (unsecured secret data) and black
(cryptographically-secured data).
The project was the rst known to use FPGAs (eld programmable gate arrays) for digital processing of radio
data. The time to reprogram these was an issue limiting application of the radio. Today, the time to write a
program for an FPGA is still signicant, but the time to
download a stored FPGA program is around 20 milliseconds. This means an SDR could change transmission protocols and frequencies in one ftieth of a second, probably not an intolerable interruption for that task.

114.4.2 Amateur and home use

114.4 Current usage

114.4.1

Military

USA
The Joint Tactical Radio System (JTRS) was a program
of the US military to produce radios that provide exible and interoperable communications. Examples of radio terminals that require support include hand-held, vehicular, airborne and dismounted radios, as well as basestations (xed and maritime).
This goal is achieved through the use of SDR systems based on an internationally endorsed open Software Microtelecom Perseus - a HF SDR for the amateur radio market
Communications Architecture (SCA). This standard uses
CORBA on POSIX operating systems to coordinate var- A typical amateur software radio uses a direct converious software modules.
sion receiver. Unlike direct conversion receivers of the
The program is providing a exible new approach to meet more distant past, the mixer technologies used are based
diverse soldier communications needs through software on the quadrature sampling detector and the quadrature
programmable radio technology. All functionality and sampling exciter.[10][11][12][13]
expandability is built upon the SCA.
The receiver performance of this line of SDRs is directly
The SCA, despite its military origin, is under evaluation
by commercial radio vendors for applicability in their
domains. The adoption of general-purpose SDR frameworks outside of military, intelligence, experimental and
amateur uses, however, is inherently hampered by the fact

related to the dynamic range of the analog-to-digital converters (ADCs) utilized.[14] Radio frequency signals are
down converted to the audio frequency band, which is
sampled by a high performance audio frequency ADC.
First generation SDRs used a PC sound card to pro-

506

CHAPTER 114. SOFTWARE-DEFINED RADIO

vide ADC functionality. The newer software dened radios use embedded high performance ADCs that provide
higher dynamic range and are more resistant to noise and
RF interference.
A fast PC performs the digital signal processing (DSP)
operations using software specic for the radio hardware.
Several software radio eorts use the open source SDR
library DttSP.[15]
The SDR software performs all of the demodulation, ltering (both radio frequency and audio frequency), and
signal enhancement (equalization and binaural presentation). Uses include every common amateur modulation: morse code, single sideband modulation, frequency
modulation, amplitude modulation, and a variety of digital modes such as radioteletype, slow-scan television,
and packet radio.[16] Amateurs also experiment with new
modulation methods: for instance, the DREAM opensource project decodes the COFDM technique used by
Digital Radio Mondiale.
There is a broad range of hardware solutions for radio amateurs and home use. There are professionalgrade transceiver solutions, e.g. the Zeus ZS-1[17][18]
or the Flex Radio,[19] home-brew solutions,e.g. PicAStar transceiver, the SoftRock SDR kit,[20] and starter or
professional receiver solutions, e.g. the FiFi SDR[21] for
shortwave, or the Quadrus coherent multi-channel SDR
receiver[22] for short wave or VHF/UHF in direct digital
mode of operation.

GNU Radio logo

to-digital and digital-to-analog converters, combined with

recongurable free software. Its sampling and synthesis
bandwidth is a thousand times that of PC sound cards,
which enables wideband operation.
The HPSDR (High Performance Software Dened Radio) project uses a 16-bit 135 MSPS analog-to-digital
converter that provides performance over the range 0 to
55 MHz comparable to that of a conventional analogue
HF radio. The receiver will also operate in the VHF and
UHF range using either mixer image or alias responses.
Interface to a PC is provided by a USB 2.0 interface, although Ethernet could be used as well. The project is
modular and comprises a backplane onto which other
boards plug in. This allows experimentation with new
techniques and devices without the need to replace the
entire set of boards. An exciter provides 1/2 W of RF
over the same range or into the VHF and UHF range using image or alias outputs.[27]
WebSDR[28] is a project initiated by Pieter-Tjerk de Boer
providing access via browser to multiple SDR receivers
worldwide covering the complete shortwave spectrum.
Recently he has analyzed Chirp Transmitter signals using the coupled system of receivers.[29]

114.5 See also

List of software-dened radios
Digital radio
Digital signal processing
Internals of a low-cost DVB-T USB dongle that uses Realtek
RTL2832U (square IC on the right) as the controller and Rafael
Micro R820T (square IC on the left) as the tuner.

Radio Interface Layer

It has been discovered that some common low-cost DVBT USB dongles with the Realtek RTL2832U[23][24] controller and tuner, e.g. the Elonics E4000 or the Rafael
Micro R820T,[25] can be used as a wide-band SDR receiver. Recent experiments have proven the capability
of this setup to analyze perseids shower using the graves
radar signals.[26]

Software dened mobile network

More recently, the GNU Radio using primarily the

Universal Software Radio Peripheral (USRP) uses a USB
2.0 interface, an FPGA, and a high-speed set of analog-

Softmodem

Software GNSS Receiver

114.6 References
[1] Software Dened Radio: Architectures, Systems and
Functions (Markus Dillinger, Kambiz Madani, Nancy
Alonistioti) Page xxxiii (Wiley & Sons, 2003, ISBN 0470-85164-3)

114.7. FURTHER READING

507

[2] Staple, Gregory; Werbach, Kevin (March 2004). The

End of Spectrum Scarcity. IEEE Spectrum.

[23] Using DVB USB Stick as SDR Receiver http://sdr.

osmocom.org/trac/wiki/rtl-sdr

[3] Open Spectrum: A Global Pervasive Network.

[24] RTL-SDR Blog http://www.rtl-sdr.com

[4] P. Johnson, New Research Lab Leads to Unique Radio

Receiver, E-Systems Team, May 1985, Vol. 5, No. 4,
pp 6-7 http://chordite.com/team.pdf

[25] Support for the Rafael Micro R820T tuner in Cocoa Radio
http://www.alternet.us.com/?p=1814

[5] Mitola III, J. (1992). Software radios-survey, critical evaluation and future directions.
National
Telesystems Conference.
pp.
13/15 to 13/23.
doi:10.1109/NTC.1992.267870. ISBN 0-7803-0554-X.
[6] P. Hoeher and H. Lang, Coded-8PSK modem for xed
and mobile satellite services based on DSP, in Proc. First
Int. Workshop on Digital Signal Processing Techniques
Applied to Space Communications, ESA/ ESTEC, Noordwijk, Netherlands, Nov. 1988; ESA WPP-006, Jan.
1990, pp. 117-123.
[7] First International Workshop on Software Radio, Greece
1998
[8] RJ Lackey and DW Upmal contributed the article
Speakeasy: The Military Software Radio to the IEEE
Communications Magazine special issue that Mitola
edited and for which Mitola wrote the lead article Software Radio Architecture, in May 1995.
[9] OSSIE. vt.edu.
[10] Youngblood, Gerald (July 2002), A Software Dened
Radio for the Masses, Part 1 (PDF), QEX, American Radio Relay League: 19
[11] Youngblood, Gerald (SepOct 2002), A Software Dened Radio for the Masses, Part 2 (PDF), QEX,
American Radio Relay League: 1018
[12] Youngblood, Gerald (NovDec 2002), A Software
Dened Radio for the Masses, Part 3 (PDF), QEX,
American Radio Relay League: 110
[13] Youngblood, Gerald (MarApr 2003), A Software Dened Radio for the Masses, Part 4 (PDF), QEX,
American Radio Relay League: 2031
[14] Rick Lindquist; Joel R. Hailas (October 2005).
FlexRadio Systems; SDR-1000 HF+VHF Software
Dened Radio Redux. QST. Retrieved 2008-12-07.
[15] DttSP http://dttsp.sourceforge.net/
[16] http://sourceforge.net/projects/sdr Open source SDR
transceiver project using USRP and GNU Radio
[17] ZS-1 Project http://zs-1.ru
[18] ZS-1 Zeus Transceiver http://www.radioaficion.com/
HamNews/articles/9483-zeus-zs-1-sdr-transceiver.html
[19] Flex Radio SDR Transceiver http://www.flex-radio.com/
[20] SoftRock SDR Kits http://wb5rvz.com/sdr/
[21] FiFi SDR Receiver http://o28.sischa.net/fifisdr/trac
[22] Quadrus coherenet multi-channel SDR receiver http://
spectrafold.com/quadrus

[26] Perseids shower using graves radar. EB3FRN.

[27] HPSDR Web Site.
[28] WebSDR http://websdr.org
[29] Chirp Signals analyzed using SDR http://websdr.ewi.
utwente.nl:8901/chirps/

114.7 Further reading

Rohde, Ulrich L (February 2628, 1985). Digital
HF Radio: A Sampling of Techniques. Third International Conference on HF Communication Systems
and Techniques. London, England.
Software dened radio : architectures, systems, and
functions. Dillinger, Madani, Alonistioti. Wiley,
2003. 454 pages. ISBN 0-470-85164-3 ISBN
9780470851647
Cognitive Radio Technology. Bruce Fette. Elsevier Science & Technology Books, 2006. 656 pags.
ISBN 0-7506-7952-2 ISBN 9780750679527
Software Dened Radio for 3G, Burns.
House, 2002. ISBN 1-58053-347-7

Artech

Software Radio: A Modern Approach to Radio Engineering, Jerey H. Reed. Prentice Hall PTR, 2002.
ISBN 0-13-081158-0
Signal Processing Techniques for Software Radio,
Behrouz Farhang-Beroujeny. LuLu Press.
RF and Baseband Techniques for Software Dened
Radio, Peter B. Kenington. Artech House, 2005,
ISBN 1-58053-793-6
The ABCs of Software Dened Radio, Martin Ewing, AA6E. The American Radio Relay League,
Inc., 2012, ISBN 978-0-87259-632-0
Software Dened Radio using MATLAB & Simulink
and the RTL-SDR, R Stewart, K Barlee, D Atkinson,
L Crockett, Strathclyde Academic Media, September 2015. ISBN 978-0-9929787-2-3

114.8 External links

The worlds rst web-based software-dened receiver at the university of Twente, the Netherlands
Software-dened receivers connected to the Internet

508
Using software-dened television tuners as multimode HF / VHF / UHF receivers
Free SDR textbook: Software Dened Radio using
MATLAB & Simulink and the RTL-SDR

CHAPTER 114. SOFTWARE-DEFINED RADIO

Chapter 115

Cognitive radio
A cognitive radio (CR) is a radio that can be programmed and congured dynamically to use the best
wireless channels in its vicinity. Such a radio automatically detects available channels in wireless spectrum, then
accordingly changes its transmission or reception parameters to allow more concurrent wireless communications
in a given spectrum band at one location. This process is
a form of dynamic spectrum management.

of Technology in Stockholm) in 1998 and published in an

article by Mitola and Gerald Q. Maguire, Jr. in 1999. It
was a novel approach in wireless communications, which
Mitola later described as:
The point in which wireless personal digital assistants (PDAs) and the related networks are suciently computationally intelligent about radio resources and related
computer-to-computer communications to detect user communications needs as a function
of use context, and to provide radio resources
and wireless services most appropriate to those
needs.[1]

115.1 Description
In response to the operators commands, the cognitive engine is capable of conguring radio-system parameters.
These parameters include "waveform, protocol, operating frequency, and networking. This functions as an autonomous unit in the communications environment, exchanging information about the environment with the networks it accesses and other cognitive radios (CRs). A CR
monitors its own performance continuously, in addition
to reading the radios outputs"; it then uses this information to determine the RF environment, channel conditions, link performance, etc., and adjusts the radios
settings to deliver the required quality of service subject
to an appropriate combination of user requirements, operational limitations, and regulatory constraints.
Some smart radio proposals combine wireless mesh
networkdynamically changing the path messages take
between two given nodes using cooperative diversity;
cognitive radiodynamically changing the frequency
band used by messages between two consecutive nodes
on the path; and software-dened radiodynamically
changing the protocol used by message between two consecutive nodes.
J. H. Snider, Lawrence Lessig, David Weinberger, and
others say that low power smart radio is inherently superior to standard broadcast radio.

115.2 History

Cognitive radio is considered as a goal towards which

a software-dened radio platform should evolve: a fully
recongurable wireless transceiver which automatically
adapts its communication parameters to network and user
demands.
Traditional regulatory structures have been built for an
analog model and are not optimized for cognitive radio.
Regulatory bodies in the world (including the Federal
Communications Commission in the United States and
Ofcom in the United Kingdom) as well as dierent independent measurement campaigns found that most radio
frequency spectrum was ineciently utilized.[2] Cellular
network bands are overloaded in most parts of the world,
but other frequency bands (such as military, amateur radio and paging frequencies) are insuciently utilized.
Independent studies performed in some countries conrmed that observation, and concluded that spectrum utilization depends on time and place. Moreover, xed spectrum allocation prevents rarely used frequencies (those
assigned to specic services) from being used, even when
any unlicensed users would not cause noticeable interference to the assigned service. Regulatory bodies in the
world have been considering whether to allow unlicensed
users in licensed bands if they would not cause any interference to licensed users. These initiatives have focused
cognitive-radio research on dynamic spectrum access.

The rst cognitive radio wireless regional area network

The concept of cognitive radio was rst proposed by standard, IEEE 802.22, was developed by IEEE 802
Joseph Mitola III in a seminar at KTH (the Royal Institute LAN/MAN Standard Committee (LMSC)[3] and pub509

510
lished in 2011. This standard uses geolocation and spectrum sensing for spectral awareness. Geolocation combines with a database of licensed transmitters in the area
to identify available channels for use by the cognitive radio network. Spectrum sensing observes the spectrum
and identies occupied channels. IEEE 802.22 was designed to utilize the unused frequencies or fragments of
time in a location. This white space is unused television
channels in the geolocated areas. However, cognitive radio cannot occupy the same unused space all the time.
As spectrum availability changes, the network adapts to
prevent interference with licensed transmissions.[4]

115.3 Terminology
Depending on transmission and reception parameters,
there are two main types of cognitive radio:
Full Cognitive Radio (Mitola radio), in which every
possible parameter observable by a wireless node (or
network) is considered.[5]
Spectrum-Sensing Cognitive Radio, in which only the
radio-frequency spectrum is considered.
Other types are dependent on parts of the spectrum available for cognitive radio:

CHAPTER 115. COGNITIVE RADIO

Sensing-based Spectrum sharing:[10] In sensingbased spectrum sharing cognitive radio networks,
cognitive radio users rst listen to the spectrum allocated to the licensed users to detect the state of the
licensed users. Based on the detection results, cognitive radio users decide their transmission strategies. If the licensed users are not using the bands,
cognitive radio users will transmit over those bands.
If the licensed users are using the bands, cognitive
radio users share the spectrum bands with the licensed users by restricting their transmit power.

115.4 Technology
Although cognitive radio was initially thought of as a
software-dened radio extension (full cognitive radio),
most research work focuses on spectrum-sensing cognitive radio (particularly in the TV bands). The chief
problem in spectrum-sensing cognitive radio is designing
high-quality spectrum-sensing devices and algorithms for
exchanging spectrum-sensing data between nodes. It has
been shown that a simple energy detector cannot guarantee the accurate detection of signal presence,[11] calling
for more sophisticated spectrum sensing techniques and
requiring information about spectrum sensing to be regularly exchanged between nodes. Increasing the number
of cooperating sensing nodes decreases the probability of
false detection.[12]

Filling free RF bands adaptively, using OFDMA, is a possible approach. Timo A. Weiss and Friedrich K. Jondral
of the University of Karlsruhe proposed a spectrum pooling system, in which free bands (sensed by nodes) were
immediately lled by OFDMA subbands. Applications
of spectrum-sensing cognitive radio include emergencynetwork and WLAN higher throughput and transmissiondistance extensions. The evolution of cognitive radio to Unlicensed-Band Cognitive Radio, which can only ward cognitive networks is underway; the concept of cogutilize unlicensed parts of the radio frequency (RF) nitive networks is to intelligently organize a network of
spectrum. One such system is described in the IEEE cognitive radios.
802.15 Task Group 2 specications,[8] which focus
on the coexistence of IEEE 802.11 and Bluetooth.
Licensed-Band Cognitive Radio, capable of using
bands assigned to licensed users (except for unlicensed bands, such as the U-NII band or the ISM
band. The IEEE 802.22 working group is developing a standard for wireless regional area network
(WRAN), which will operate on unused television
channels.[6][7]

115.4.1 Functions

Spectrum mobility: Process by which a cognitiveradio user changes its frequency of operation. The main functions of cognitive radios are:[13][14]
Cognitive-radio networks aim to use the spectrum
in a dynamic manner by allowing radio terminals to
Power Control: Power control[15] is usually used for
operate in the best available frequency band, mainspectrum sharing CR systems to maximize the cataining seamless communication requirements durpacity of secondary users with interference power
ing transitions to better spectrum.
constraints to protect the primary users.
Spectrum sharing[9] : Spectrum sharing cognitive radio networks allow cognitive radio users to share the
spectrum bands of the licensed-band users. However, the cognitive radio users have to restrict their
transmit power so that the interference caused to the
licensed-band users is kept below a certain threshold.

Spectrum sensing: Detecting unused spectrum and

sharing it, without harmful interference to other
users; an important requirement of the cognitiveradio network is to sense empty spectrum. Detecting primary users is the most ecient way to detect
empty spectrum. Spectrum-sensing techniques may
be grouped into three categories:

115.5. APPLICATIONS
Transmitter detection: Cognitive radios must
have the capability to determine if a signal
from a primary transmitter is locally present
in a certain spectrum. There are several proposed approaches to transmitter detection:
Matched lter detection
Energy detection: Energy detection is a
spectrum sensing method that detects the
presence/absence of a signal just by measuring the received signal power.[16] This
signal detection approach is quite easy
and convenient for practical implementation. To implement energy detector,
however, noise variance information is required. It has been shown that an imperfect knowledge of the noise power (noise
uncertainty) may lead to the phenomenon
of the SNR wall, which is a SNR level below which the energy detector can not reliably detect any transmitted signal even
increasing the observation time.[17] It[18]
has also been shown that the SNR wall
is not caused by the presence of a noise
uncertainty itself, but by an insucient
renement of the noise power estimation
while the observation time increases.
Cyclostationary-feature detection: These
type of spectrum sensing algorithms
are motivated because most man-made
communication signals, such as BPSK,
QPSK, AM, OFDM, etc. exhibit cyclostationary behavior.[19] However, noise
signals (typically white noise) do not exhibit cyclostationary behavior. These detectors are robust against noise variance
uncertainty. The aim of such detectors
is to exploit the cyclostationary nature of
man-made communication signals buried
in noise. Cyclostationary detectors can be
either single cycle or multicycle cyclostatonary.

511
and then transmits within the null-space, such that
its subsequent transmission causes less interference
to the primary-user
Spectrum management: Capturing the best available spectrum to meet user communication requirements, while not creating undue interference to
other (primary) users. Cognitive radios should decide on the best spectrum band (of all bands available) to meet quality of service requirements; therefore, spectrum-management functions are required
for cognitive radios. Spectrum-management functions are classied as:
Spectrum analysis
Spectrum decision[22]
The practical implementation of spectrum-management
functions is a complex and multifaceted issue, since it
must address a variety of technical and legal requirements. An example of the former is choosing an appropriate sensing threshold to detect other users, while the
latter is exemplied by the need to meet the rules and
regulations set out for radio spectrum access in international (ITU radio regulations) and national (telecommunications law) legislation.

115.4.2 Versus intelligent antenna (IA)

An intelligent antenna (or smart antenna) is an antenna
technology that uses spatial beam-formation and spatial coding to cancel interference; however, applications are emerging for extension to intelligent multiple
or cooperative-antenna arrays for application to complex
communication environments. Cognitive radio, by comparison, allows user terminals to sense whether a portion
of the spectrum is being used in order to share spectrum
with neighbor users. The following table compares the
two:
Note that both techniques can be combined as illustrated
in many contemporary transmission scenarios.[23]

Wideband spectrum sensing: refers to spectrum Cooperative MIMO (CO-MIMO) combines both techsensing over large spectral bandwidth, typically hun- niques.
dreds of MHz or even several GHz. Since current ADC technology cannot aord the high sampling rate with high resolution, it requires revolutional techniques, e.g., compressive sensing and sub- 115.5 Applications
Nyquist sampling.[20]
CR can sense its environment and, without the interven Cooperative detection: Refers to spectrum- tion of the user, can adapt to the users communications
sensing methods where information from mul- needs while conforming to FCC rules in the United States.
tiple cognitive-radio users is incorporated for In theory, the amount of spectrum is innite; practically,
primary-user detection[21]
for propagation and other reasons it is nite because of the
desirability of certain spectrum portions. Assigned spec Interference-based detection
trum is far from being fully utilized, and ecient spec Null-space based CR: With the aid of multiple anten- trum use is a growing concern; CR oers a solution to
nas, CR detects the null-space of the primary-user this problem. A CR can intelligently detect whether any

512
portion of the spectrum is in use, and can temporarily
use it without interfering with the transmissions of other
users.[24] According to Bruce Fette, Some of the radios
other cognitive abilities include determining its location,
sensing spectrum use by neighboring devices, changing
frequency, adjusting output power or even altering transmission parameters and characteristics. All of these capabilities, and others yet to be realized, will provide wireless spectrum users with the ability to adapt to real-time
spectrum conditions, oering regulators, licenses and the
general public exible, ecient and comprehensive use
of the spectrum.
Examples of applications include:

CHAPTER 115. COGNITIVE RADIO

TV-broadcast bands. The IEEE 802.22 working group,
formed in November 2004, is tasked with dening the
air-interface standard for wireless regional area networks
(based on CR sensing) for the operation of unlicensed devices in the spectrum allocated to TV service.[30]

115.8 See also

Channel allocation schemes
Channel-dependent scheduling
Cognitive network

The application of CR networks to emergency and

public safety communications by utilizing white
space [25][26]

LTE Advanced

The potential of CR networks for executing dynamic

spectrum access (DSA) [27][28]

OFDMA

Application of CR networks to military action such

as chemical biological radiological and nuclear attack detection and investigation, command control,
obtaining information of battle damage evaluations,
battleeld surveillance, intelligence assistance, and
targeting. [29]

115.6 Simulation of CR networks

At present, modeling & simulation is the only paradigm
which allows the simulation of complex behavior in a
given environments cognitive radio networks. Network
simulators like OPNET, NetSim, MATLAB and NS2 can
be used to simulate a cognitive radio network. Areas of
research using network simulators include:
1. Spectrum sensing & incumbent detection
2. Spectrum allocation
3. Measurement and modeling of spectrum usage
4. Eciency of spectrum utilization

115.7 Future plans

Network Simulator

Radio resource management (RRM)

115.9 References
[1] (PDF) https://web.archive.org/web/20120917062752/
http://web.it.kth.se/~{}maguire/jmitola/Mitola_
Dissertation8_Integrated.pdf.
Archived from the
original (PDF) on 17 September 2012. Retrieved 7
January 2013. Missing or empty |title= (help)
[2] V. Valenta et al., Survey on spectrum utilization in Europe: Measurements, analyses and observations, Proceedings of the Fifth International Conference on Cognitive Radio Oriented Wireless Networks & Communications (CROWNCOM), 2010
[3] P802.22 (PDF). March 2014.
[4] Stevenson, C.; Chouinard, G.; Zhongding Lei; Wendong Hu; Shellhammer, S.; Caldwell, W. (2009). IEEE
802.22: The First Cognitive Radio Wireless Regional
Area Network Standard. IEEE Communications Magazine. 47: 130. doi:10.1109/MCOM.2009.4752688. Retrieved 2016-11-21.
[5] J. Mitola III and G. Q. Maguire, Jr., Cognitive radio:
making software radios more personal, IEEE Personal
Communications Magazine, vol. 6, nr. 4, pp. 1318,
Aug. 1999
[6] IEEE 802.22

The success of the unlicensed band in accommodating a

range of wireless devices and services has led the FCC
to consider opening further bands for unlicensed use. In
contrast, the licensed bands are underutilized due to static
frequency allocation. Realizing that CR technology has
the potential to exploit the ineciently utilized licensed
bands without causing interference to incumbent users,
the FCC released a Notice of Proposed Rule Making
which would allow unlicensed radios to operate in the

[7] Carl, Stevenson; G. Chouinard; Zhongding Lei; Wendong Hu; S. Shellhammer; W. Caldwell (January
2009). IEEE 802.22: The First Cognitive Radio
Wireless Regional Area Networks (WRANs) Standard
= IEEE Communications Magazine". IEEE Communications Magazine. US: IEEE. 47 (1): 130138.
doi:10.1109/MCOM.2009.4752688.
[8] IEEE 802.15.2

115.10. EXTERNAL LINKS

513

[9] S. Haykin, Cognitive Radio: Brain-empowered Wireless Communications, IEEE Journal on Selected Areas
of Communications, vol. 23, nr. 2, pp. 201220, Feb.
2005

[24] K. Kotobi, P. B. Mainwaring, C. S. Tucker, and S.

G. Biln., Data-Throughput Enhancement Using Data
Mining-Informed Cognitive Radio. Electronics 4, no. 2
(2015): 221-238.

[10] X. Kang et. al ``Sensing-Based Spectrum Sharing in Cognitive Radio Networks, IEEE Transactions on Vehicular
Technology, vol. 58, no. 8, pp. 4649-4654, Oct 2009.

[25] Villardi, G. P.; Abreu, G. Thadeu Freitas de; Harada,

H. (2012-06-01). TV White Space Technology: Interference in Portable Cognitive Emergency Network.
IEEE Vehicular Technology Magazine. 7 (2): 4753.
doi:10.1109/MVT.2012.2190221. ISSN 1556-6072.

[11] Niels Hoven, Rahul Tandra, and Prof. Anant Sahai

(February 11, 2005). Some Fundamental Limits on Cognitive Radio (PDF).
[12] J. Hillenbrand; Daimler-Chrysler AG, Sindelngen, Germany; T. A. Weiss; F. K. Jondral (2005). Calculation of
detection and false alarm probabilities in spectrum pooling systems (PDF). IEEE Communications Letters. 9 (4):
349351. doi:10.1109/LCOMM.2005.1413630. ISSN
1089-7798.
[13] Ian F. Akyildiz, W.-Y. Lee, M. C. Vuran, and S.
Mohanty, NeXt Generation/Dynamic Spectrum Access/Cognitive Radio Wireless Networks: A Survey,
Computer Networks (Elsevier) Journal, September 2006.
[14] Cognitive Functionality in Next Generation Wireless Networks
[15] X. Kang et. al Optimal power allocation for fading channels in cognitive radio networks: Ergodic capacity and
outage capacity, IEEE Trans. on Wireless Commun., vol.
8, no. 2, pp. 940950, Feb 2009.
[16] H. Urkowitz Energy detection of unknown deterministic signals, IEEE Proceedings, Apr.
1967.
doi:10.1109/PROC.1967.5573
[17] R. Tandra and A. Sahai, SNR walls for signal detection,
IEEE J. Sel. Topics Signal Process., vol. 2, no. 1, pp.
417, Feb. 2008. doi:10.1109/JSTSP.2007.914879
[18] A. Mariani, A. Giorgetti, and M. Chiani, Eects of Noise
Power Estimation on Energy Detection for Cognitive Radio Applications, IEEE Trans. Commun., vol. 50, no.
12, Dec., 2011.
[19] W. A. Gardner, Exploitation of spectral redundancy in
cyclostationary signals, IEEE Sig. Proc. Mag., vol. 8,
no. 2, pp. 1436, 1991. doi:10.1109/79.81007
[20] H. Sun, A. Nallanathan, C.-X. Wang, and Y.-F. Chen,
Wideband spectrum sensing for cognitive radio networks: a survey, IEEE Wireless Communications, vol.
20, no. 2, pp. 7481, April 2013.
[21] Z. Li, F.R. Yu, and M. Huang, A Distributed ConsensusBased Cooperative Spectrum Sensing in Cognitive Radios, IEEE Trans. Vehicular Technology, vol. 59, no.
1, pp. 383-393, Jan. 2010.
[22] The word cyclistationary is a error from the source passage, and the correct one is cyclostationary.
[23] B. Kouassi, I. Ghauri, L. Deneire, Reciprocity-based
cognitive transmissions using a MU massive MIMO approach. IEEE International Conference on Communications (ICC), 2013

[26] Ferrus, R.; Sallent, O.; Baldini, G.; Goratti, L. (201206-01). Public Safety Communications: Enhancement
Through Cognitive Radio and Spectrum Sharing Principles. IEEE Vehicular Technology Magazine. 7 (2): 54
61. doi:10.1109/MVT.2012.2190180. ISSN 1556-6072.
[27] Khattab, Ahmed; Perkins, Dmitri; Bayoumi, Magdy
(2013-01-01). Cognitive Radio Networks. Analog
Circuits and Signal Processing. Springer New York.
pp. 3339. doi:10.1007/978-1-4614-4033-8_4. ISBN
9781461440321.
[28] Tallon, J.; Forde, T. K.; Doyle, L. (2012-06-01).
Dynamic Spectrum Access Networks: Independent
Coalition Formation. IEEE Vehicular Technology Magazine. 7 (2): 6976. doi:10.1109/MVT.2012.2190218.
ISSN 1556-6072.
[29] Joshi, Gyanendra Prasad; Nam, Seung Yeob; Kim, Sung
Won (2013-08-22). Cognitive Radio Wireless Sensor Networks: Applications, Challenges and Research
Trends. Sensors (Basel, Switzerland). 13 (9): 11196
11228. doi:10.3390/s130911196. ISSN 1424-8220.
PMC 3821336 . PMID 23974152.
[30] Carlos Cordeiro, Kiran Challapali, and Dagnachew Birru.
Sai Shankar N. IEEE 802.22: An Introduction to the First
Wireless Standard based on Cognitive Radios JOURNAL
OF COMMUNICATIONS, VOL. 1, NO. 1, APRIL 2006

115.10 External links

Berkeley Wireless Research Center Cognitive Radio
Workshop rst workshop on cognitive radio; its
focus was mainly on research issues in topic
Center for Wireless Telecommunications (CWT),
Virginia Tech
Cognitive Radio Technologies Proceeding of Federal Communications Commission Federal Communications Commission rules on cognitive radio
IEEE DySPAN Conference

Chapter 116

Manchester code
In telecommunication and data storage, Manchester
coding (also known as phase encoding, or PE) is a line
code in which the encoding of each data bit is either low
then high, or high then low, of equal time. It therefore
has no DC bias, and is self-clocking, which means that
it may be inductively or capacitively coupled, and that a
clock signal can be recovered from the encoded data. As
a result, electrical connections using a Manchester code
are easily galvanically isolated using a network isolator
a simple one-to-one isolation transformer.
An example of Manchester encoding showing both conventions

116.3 Description
116.1 Background

Extracting the original data from the received encoded bit

(from Manchester as per 802.3):

The name comes from its development at the University Summary:

of Manchester, where the coding was used to store data on
the magnetic drum of the Manchester Mark 1 computer.
Each bit is transmitted in a xed time (the period).
Manchester coding is widely used (e.g., in 10BASE-T
A 0 is expressed by a low-to-high transition, a 1 by
Ethernet (IEEE 802.3); consumer IR protocols; see also
high-to-low transition (according to G.E. Thomas
RFID or near eld communication). There are more
conventionin the IEEE 802.3 convention, the recomplex codes, such as 8B/10B encoding, that use less
verse is true).[2]
bandwidth to achieve the same data rate but may be less
tolerant of frequency errors and jitter in the transmitter
The transitions which signify 0 or 1 occur at the midand receiver reference clocks.
point of a period.
According to Cisco, Manchester encoding introduces
Transitions at the start of a period are overhead and
some dicult frequency-related problems that make it
[1]
don't signify data.
unsuitable for use at higher data rates.

116.2 Features
Manchester code ensures frequent line voltage transitions,
directly proportional to the clock rate; this helps clock
recovery.
The DC component of the encoded signal is not dependent on the data and therefore carries no information, allowing the signal to be conveyed conveniently by media
(e.g., Ethernet) which usually do not convey a DC component.

Manchester code always has a transition at the middle of

each bit period and may (depending on the information
to be transmitted) have a transition at the start of the period also. The direction of the mid-bit transition indicates the data. Transitions at the period boundaries do
not carry information. They exist only to place the signal
in the correct state to allow the mid-bit transition. The
existence of guaranteed transitions allows the signal to be
self-clocking, and also allows the receiver to align correctly; the receiver can identify if it is misaligned by half
a bit period, as there will no longer always be a transition during each bit period. The price of these benets
is a doubling of the bandwidth requirement compared to
simpler NRZ coding schemes (or see also NRZI).

514

116.5. REFERENCES

116.3.1

515

Manchester encoding as phase- 116.5

shift keying

References

[1] http://docwiki.cisco.com/wiki/Ethernet_Technologies

Manchester encoding is a special case of binary phaseshift keying (BPSK), where the data controls the phase
of a square wave carrier whose frequency is the data rate.
Such a signal is easy to generate.

116.3.2

Conventions for representation of

data

[2] Forster, R. (2000). Manchester encoding: Opposing definitions resolved. Engineering Science & Education Journal. 9 (6): 278. doi:10.1049/esej:20000609.
[3] Tanenbaum, Andrew, S. (2002). Computer Networks (4th
Edition). Prentice Hall. pp. 274275. ISBN 0-13066102-3.
[4] Stallings, William (2004). Data and Computer Communications (7th ed.). Prentice Hall. pp. 137138. ISBN
0-13-100681-9.

This article incorporates public domain material from

the General Services Administration document Federal
Standard 1037C (in support of MIL-STD-188).

Encoding of 11011000100 in Manchester code (as per G. E.

Thomas)

There are two opposing conventions for the representations of data.

The rst of these was rst published by G. E. Thomas
in 1949 and is followed by numerous authors (e.g., Andy
Tanenbaum).[3] It species that for a 0 bit the signal levels
will be low-high (assuming an amplitude physical encoding of the data) - with a low level in the rst half of the
bit period, and a high level in the second half. For a 1 bit
the signal levels will be high-low.
The second convention is also followed by numerous authors (e.g., William Stallings [4] ) as well as by IEEE 802.4
(token bus) and lower speed versions of IEEE 802.3 (Ethernet) standards. It states that a logic 0 is represented by
a high-low signal sequence and a logic 1 is represented by
a low-high signal sequence.
If a Manchester encoded signal is inverted in communication, it is transformed from one convention to the other.
This ambiguity can be overcome by using dierential
Manchester encoding.

116.4 See also

Coded mark inversion
Dierential Manchester encoding
Self-clocking signal
Binary oset carrier modulation

Chapter 117

Non-return-to-zero
encoding acts on a clock edge or during a clock cycle
since all transitions happen in the given amount of time
representing the actual or implied integral clock cycle.
The real question is that of samplingthe high or low
state will be received correctly provided the transmission
line has stabilized for that bit when the physical line level
is sampled at the receiving end.

The binary signal is encoded using rectangular pulse amplitude

modulation with polar NRZ(L), or polar non-return-to-zero-level
code

NRZ can refer to any of the following serializer line

codes:

However, it is helpful to see NRZ transitions as happening on the trailing (falling) clock edge in order to compare
NRZ-Level to other encoding methods, such as the mentioned Manchester code, which requires clock edge information (is the XOR of the clock and NRZ, actually) see
the dierence between NRZ-Mark and NRZ-Inverted.

117.1 Unipolar non-return-to-zero

The NRZ code also can be classied as a polar or nonlevel

polar, where polar refers to a mapping to voltages of +V
and -V, and non-polar refers to a voltage mapping of +V
and 0, for the corresponding binary values of '0' and '1'. Main article: Unipolar encoding
One is represented by a DC bias on the transmission
In telecommunication, a non-return-to-zero (NRZ) line
code is a binary code in which ones are represented by
one signicant condition, usually a positive voltage, while
zeros are represented by some other signicant condition,
usually a negative voltage, with no other neutral or rest
condition. The pulses in NRZ have more energy than a
return-to-zero (RZ) code, which also has an additional
rest state beside the conditions for ones and zeros. NRZ Unipolar NRZ(L), or Unipolar non-return-to-zero level
is not inherently a self-clocking signal, so some additional
synchronization technique must be used for avoiding bit line (conventionally positive), while zero is represented
slips; examples of such techniques are a run length limited by the absence of bias - the line at 0 volts or grounded. For
this reason it is also known as on-o keying. In clock
constraint and a parallel synchronization signal.
language, a one transitions to or remains at a biased
For a given data signaling rate, i.e., bit rate, the NRZ code level on the trailing clock edge of the previous bit, while
requires only half the baseband bandwidth required by the zero transitions to or remains at no bias on the trailing
Manchester code (the passband bandwidth is the same). clock edge of the previous bit. Among the disadvantages
When used to represent data in an asynchronous commu- of unipolar NRZ is that it allows for long series without
nication scheme, the absence of a neutral state requires change, which makes synchronization dicult - although
other mechanisms for bit synchronization when a sepa- this is not unique to the unipolar case. One solution is to
rate clock signal is not available.
not send bytes without transitions. More critically, and
NRZ-Level itself is not a synchronous system but rather unique to unipolar NRZ, are issues related to the presan encoding that can be used in either a synchronous or ence of a transmitted DC level - the power spectrum of
asynchronous transmission environment, that is, with or the transmitted signal does not approach zero at zero frewithout an explicit clock signal involved. Because of this, quency. This leads to two signicant problems - rst, the
it is not strictly necessary to discuss how the NRZ-Level transmitted DC power leads to higher power losses than
516

117.4. NON-RETURN-TO-ZERO INVERTED

517

other encodings and second, the presence of a DC signal component requires that the transmission line be DC
coupled.

117.4 Non-return-to-zero inverted

117.2 Bipolar non-return-to-zero

level
One is represented by one physical level (usually a positive voltage), while zero is represented by another level
(usually a negative voltage). In clock language, in bipolar An example of the NRZI encoding
NRZ-Level the voltage swings from positive to negative
on the trailing edge of the previous bit clock cycle.
An example of this is RS-232, where one is 12 V to
5 V and zero is +5 V to +12 V.

117.3 Non-return-to-zero space

NRZ transition occurs for a zero

in

D Q

out

clk

Non-return-to-zero space

=1

Encoder for NRZI, toggle on one

=1

D Q

out

clk

in

Encoder for NRZS, toggle on zero

One is represented by no change in physical level, while

zero is represented by a change in physical level. In
clock language, the level transitions on the trailing clock
edge of the previous bit to represent a zero.
This change-on-zero is used by High-Level Data Link
Control and USB. They both avoid long periods of no
transitions (even when the data contains long sequences
of 1 bits) by using zero-bit insertion. HDLC transmitters insert a 0 bit after ve contiguous 1 bits (except when
transmitting the frame delimiter '01111110'). USB transmitters insert a 0 bit after six consecutive 1 bits. The receiver at the far end uses every transition both from
0 bits in the data and these extra non-data 0 bits to
maintain clock synchronization. The receiver otherwise
ignores these non-data 0 bits.

Non return to zero, inverted (NRZI) is a method

of mapping a binary signal to a physical signal for
transmission over some transmission media. The two
level NRZI signal has a transition at a clock boundary if
the bit being transmitted is a logical 1, and does not have
a transition if the bit being transmitted is a logical 0.
One is represented by a transition of the physical level,
while zero has no transition. Also, NRZI might take
the opposite convention, as in Universal Serial Bus (USB)
signalling, when in Mode 1, in which a transition occurs
when signaling zero, and a steady level when signaling
a one. The transition occurs on the leading edge of the
clock for the given bit. This distinguishes NRZI from
NRZ-Mark.
However, even NRZI can have long series of zeros (or
ones if transitioning on zero), and thus clock recovery
can be dicult unless some form of run length limited
(RLL) coding is used in addition to NRZI. Magnetic disk
and tape storage devices generally use xed-rate RLL
codes, while USB uses bit stung, which inserts an additional 0 bit after 6 consecutive 1 bits, thus forcing a
transition. While bit stung is ecient, it results in a
variable data rate because it takes slightly longer to send

518
a long string of 1 bits than it does to send a long string of
0 bits.

117.5 See also

Bipolar encoding
Enhanced Non-Return-to-Zero-Level E-NRZ-L
Return-to-zero
Line code
Universal asynchronous receiver/transmitter
Manchester code

117.6 References
Brey, Barry. The Intel Microprocessors, Columbus:
Pearson Prentice Hall. ISBN 0-13-119506-9
This article incorporates public domain material from
the General Services Administration document Federal
Standard 1037C (in support of MIL-STD-188).

CHAPTER 117. NON-RETURN-TO-ZERO

Chapter 118

Unipolar encoding
Unipolar encoding is a line code. A positive voltage represents a binary 1, and zero volts indicates a binary 0. It
is the simplest line code, directly encoding the bitstream,
and is analogous to on-o keying in modulation.
Its drawbacks are that it is not self-clocking and it has a
signicant DC component, which can be halved by using return-to-zero, where the signal returns to zero in the
middle of the bit period. With a 50% duty cycle each
rectangular pulse is only at a positive voltage for half of
the bit period. This is ideal if one symbol is sent much
more often than the other and power considerations are
necessary, and also makes the signal self-clocking.
NRZ(Non-Return-to-Zero) - Traditionally, a unipolar scheme was designed as a non-return-to-zero (NRZ)
scheme, in which the positive voltage denes bit 1 and
the zero voltage denes bit 0. It is called NRZ because
the signal does not return to zero at the middle of the
bit, as instead happens in other line coding schemes, such
as Manchester code. Compared with its polar counterpart, polar NRZ, this scheme applies a DC bias to the line
and unnecessarily wastes power The normalized power
(power required to send 1 bit per unit line resistance) is
double that for polar NRZ. For this reason, unipolar encoding is not normally used in data communications today.

118.1 See also

Bipolar encoding
Bipolar violation
On-o keying

519

Chapter 119

Bipolar encoding
advantage because the cable may then be used for longer
distances and to carry power for intermediate equipment
such as line repeaters.[2] The DC-component can be easily
and cheaply removed before the signal reaches the decoding circuitry.

An example of bipolar encoding, known as AMI (Alternate mark

inversion).

In telecommunication, bipolar encoding is a type of

return-to-zero (RZ) line code, where two nonzero values
are used, so that the three values are +, , and zero. Such
a signal is called a duobinary signal. Standard bipolar encodings are designed to be DC-balanced, spending
equal amounts of time in the + and states.
The reason why Bipolar encoding is classied as a return
to zero (RZ) is because when a bipolar encoded channel
is idle the line is held at a constant zero level; and when
it is transmitting bits the line is in either in a +V or -V
state corresponding to the binary bit being transmitted.
Thus, the line always returns to the zero level to denote
optionally a separation of bits or to denote idleness of the
line.

119.1 Alternate mark inversion

One kind of bipolar encoding is a paired disparity code,
of which the simplest example is alternate mark inversion. In this code, a binary 0 is encoded as zero volts, as
in unipolar encoding, whereas a binary 1 is encoded alternately as a positive voltage or a negative voltage. The
name arose because, in the context of a T-carrier, a binary '1' is referred to as a mark, while a binary '0' is
called a space.[1]

119.2 Voltage Build-up

119.3 Synchronization and Zeroes

Bipolar encoding is preferable to non-return-to-zero
whenever signal transitions are required to maintain synchronization between the transmitter and receiver. Other
systems must synchronize using some form of out-ofband communication, or add frame synchronization sequences that don't carry data to the signal. These alternative approaches require either an additional transmission
medium for the clock signal or a loss of performance due
to overhead, respectively. A bipolar encoding is an often
good compromise: runs of ones will not cause a lack of
transitions.
However, long sequences of zeroes remain an issue. Long
sequences of zero bits result in no transitions and a loss
of synchronization. Where frequent transitions are a requirement, a self-clocking encoding such as return-tozero or some other more complicated line code may be
more appropriate, though they introduce signicant overhead.
The coding was used extensively in rst-generation
PCM networks, and is still commonly seen on older
multiplexing equipment today, but successful transmission relies on no long runs of zeroes being present.[3] No
more than 15 consecutive zeros should ever be sent to ensure synchronization.
There are two popular ways to ensure that no more than
15 consecutive zeros are ever sent: robbed-bit signaling
and bit stung.
T-carrier uses robbed-bit signaling: the least-signicant
bit of the byte is simply forced to a 1 when necessary.

The modication of bit 7 causes a change to voice that is

The use of a bipolar code prevents a signicant build- undetectable by the human ear, but it is an unacceptable
up of DC, as the positive and negative pulses average to corruption of a data stream. Data channels are required
zero volts. Little or no DC-component is considered an to use some other form of pulse-stung,[2] such as al520

119.7. REFERENCES
ways setting bit 8 to '1', in order to maintain a sucient
density of ones. Of course, this lowers the eective data
throughput to 56 kbit/s per channel.[4]
If the characteristics of the input data do not follow the
pattern that every eighth bit is '1', the coder using alternate
mark inversion adds a '1' after seven consecutive zeros to
maintain synchronisation. On the decoder side, this extra
'1' added by the coder is removed, recreating the correct
data. Using this method the data sent between the coder
and the decoder is longer than the original data by less
than 1% on average.

119.4 Error detection

Another benet of bipolar encoding compared to unipolar is error detection. In the T-carrier example, the bipolar signals are regenerated at regular intervals so that signals diminished by distance are not just amplied, but detected and recreated anew. Weakened signals corrupted
by noise could cause errors, a mark interpreted as zero, or
zero as positive or negative mark. Every single-bit error
results in a violation of the bipolar rule. Each such bipolar
violation (BPV) is an indication of a transmission error.
(The location of BPV is not necessarily the location of
the original error).

119.5 Other T1 encoding schemes

Main article: Modied AMI code
For data channels, in order to avoid the need of always
setting bit 8 to 1, as described above, other T1 encoding
schemes (Modied AMI codes) ensure regular transitions
regardless of the data being carried. In this way, data
throughput of 64 kbit/s per channel is achieved. B8ZS is
a newer format for North America, where HDB3 is the
original line coding type used in Europe and Japan.
A very similar encoding scheme, with the logical positions reversed, is also used and is often referred to as
pseudoternary encoding. This encoding is otherwise
identical.

119.6 See also

MLT-3 encoding
polar encoding

119.7 References
[1] alternate mark inversion (AMI) signal, ATIS Telecom
Glossary 2000, last updated 28 February 2001, retrieved

521

25 January 2007 Archived June 9, 2007, at the Wayback

Machine.
[2] T1 Fundamentals, Revision 1.0, dated 23 January 1997,
by Digital Link, retrieved on 25 January 2007 Archived
January 29, 2007, at the Wayback Machine.
[3] All You Wanted to Know About T1 But Were Afraid to
Ask, Bob Wachtel, retrieved on 25 January 2007
[4] Telecom Dictionary, retrieved 25 January 2007

Chapter 120

Pulse wave

Amplitude

This article is about a pulse wave form. For a heart beat,

see Pulse.
This article is about a rectangular pulse train. For a Dirac
pulse train, see Sampling function.
For the aperiodic version, see Pulse function.
For other uses, see Pulse (disambiguation).
A pulse wave or pulse train is a kind of non-sinusoidal

threshold on the other. The result will be a precisely controlled pulse width, but it will not be bandlimited.
Acoustically, the rectangular wave has been described as
having a more narrow and nasal sound than a perfect
square wave, and its characteristic sound features prominently in many Steve Winwood songs.[2]

120.1 See also

Sampling function

0
0

T+

2T 2T+

3T 3T+

Pulse-width modulation

4T

Time

Sine wave

The shape of the pulse wave is dened by its duty cycle D, which
is the ratio between the pulse duration ( ) and the period (T)

waveform that is similar to a square wave, but does not

have the symmetrical shape associated with a perfect
square wave. It is a term common to synthesizer programming, and is a typical waveform available on many
synthesizers. The exact shape of the wave is determined
by the duty cycle of the oscillator. In many synthesizers, the duty cycle can be modulated (sometimes called
pulse-width modulation) for a more dynamic timbre.[1]
The pulse wave is also known as the rectangular wave,
the periodic version of the rectangular function.

Triangle wave
Square wave

120.2 References

The Fourier series expansion for a rectangular pulse wave

with period T and pulse time is
( n )
2

+
sin
cos
T n=1 n
T

f (t) =

)
2n
t
T

Note that, for symmetry, the starting time (t = 0) in this

expansion is halfway through the rst pulse. The phase
can be oset to match the accompanying graph by replacing t with t - /2.
A pulse wave can be created by subtracting a sawtooth
wave from a phase-shifted version of itself. If the sawtooth waves are bandlimited, the resulting pulse wave is
bandlimited, too. Another way to create one is with a
single ramp wave (sawtooth or triangle) and a comparator, with the ramp wave on one input, and a variable DC
522

[1] http://www.soundonsound.com/sos/feb00/articles/
synthsecrets.htm
[2] Synth Soloing in the Style of Steve Winwood.

Chapter 121

Discrete-time signal
121.2 See also

f(t)

Aliasing
Bernoulli process
Digital data
Discrete system

Discrete time and continuous time

Normalized frequency

Discrete sampled signal

Discrete signal redirects here. It is not to be confused

with Digital signal (electronics).

121.3 References
[1] Digital Signal Processing Prentice Hall - Pages 11-12

A discrete signal or discrete-time signal is a time series

consisting of a sequence of quantities. In other words, it is
a time series that is a function over a domain of integers.
Unlike a continuous-time signal, a discrete-time signal is
not a function of a continuous argument; however, it may
have been obtained by sampling from a continuous-time
signal, and then each value in the sequence is called a sample. When a discrete-time signal obtained by sampling a
sequence corresponds to uniformly spaced times, it has
an associated sampling rate; the sampling rate is not apparent in the data sequence, and so needs to be associated
as a characteristic unit of the system.

121.1 Acquisition
Discrete-time signals may have several origins, but can
usually be classied into one of two groups:[1]
By acquiring values of an analog signal at constant
or variable rate. This process is called sampling.[2]
By observing an inherently discrete-time process,
such as the weekly peak value of a particular economic indicator.
523

[2] Digital Signal Processing: Instant access. ButterworthHeinemann - Page 8

Gershenfeld, Neil A. (1999). The Nature of mathematical Modeling. Cambridge University Press.
ISBN 0-521-57095-6.
Wagner, Thomas Charles Gordon (1959). Analytical transients. Wiley.

Chapter 122

Forward error correction

Interleaver redirects here. For the ber-optic device,
see optical interleaver.
In telecommunication, information theory, and coding
theory, forward error correction (FEC) or channel
coding[1] is a technique used for controlling errors in
data transmission over unreliable or noisy communication channels. The central idea is the sender encodes
the message in a redundant way by using an errorcorrecting code (ECC). The American mathematician
Richard Hamming pioneered this eld in the 1940s and
invented the rst error-correcting code in 1950: the
Hamming (7,4) code.[2]
The redundancy allows the receiver to detect a limited
number of errors that may occur anywhere in the message, and often to correct these errors without retransmission. FEC gives the receiver the ability to correct errors without needing a reverse channel to request retransmission of data, but at the cost of a xed, higher forward
channel bandwidth. FEC is therefore applied in situations
where retransmissions are costly or impossible, such as
one-way communication links and when transmitting to
multiple receivers in multicast. FEC information is usually added to mass storage devices to enable recovery of
corrupted data, and is widely used in modems.

122.1 How it works

FEC is accomplished by adding redundancy to the transmitted information using an algorithm. A redundant bit
may be a complex function of many original information
bits. The original information may or may not appear
literally in the encoded output; codes that include the unmodied input in the output are systematic, while those
that do not are non-systematic.
A simplistic example of FEC is to transmit each data bit 3
times, which is known as a (3,1) repetition code. Through
a noisy channel, a receiver might see 8 versions of the
output, see table below.
This allows an error in any one of the three samples to be
corrected by majority vote or democratic voting. The
correcting ability of this FEC is:
Up to 1 bit of triplet in error, or
up to 2 bits of triplet omitted (cases not shown in
table).

Though simple to implement and widely used, this triple

modular redundancy is a relatively inecient FEC. Better
FEC codes typically examine the last several dozen, or
FEC processing in a receiver may be applied to a digital even the last several hundred, previously received bits to
bit stream or in the demodulation of a digitally modu- determine how to decode the current small handful of bits
lated carrier. For the latter, FEC is an integral part of the (typically in groups of 2 to 8 bits).
initial analog-to-digital conversion in the receiver. The
Viterbi decoder implements a soft-decision algorithm to
demodulate digital data from an analog signal corrupted 122.2 Averaging noise to reduce erby noise. Many FEC coders can also generate a bit-error
rors
rate (BER) signal which can be used as feedback to netune the analog receiving electronics.
The noisy-channel coding theorem establishes bounds on FEC could be said to work by averaging noise"; since
the theoretical maximum information transfer rate of a each data bit aects many transmitted symbols, the corchannel with some given noise level. Some advanced FEC ruption of some symbols by noise usually allows the original user data to be extracted from the other, uncorrupted
systems come very close to the theoretical maximum.
received symbols that also depend on the same user data.
The maximum fractions of errors or of missing bits that
can be corrected is determined by the design of the FEC
Because of this risk-pooling eect, digital comcode, so dierent forward error correcting codes are suitmunication systems that use FEC tend to work well
able for dierent conditions.
above a certain minimum signal-to-noise ratio and
not at all below it.
524

122.4. CONCATENATED FEC CODES FOR IMPROVED PERFORMANCE

525

This all-or-nothing tendency the cli eect

becomes more pronounced as stronger codes are
used that more closely approach the theoretical
Shannon limit.

Hamming ECC is commonly used to correct NAND

ash memory errors.[3] This provides single-bit error correction and 2-bit error detection. Hamming codes are
only suitable for more reliable single level cell (SLC)
NAND. Denser multi level cell (MLC) NAND requires
Interleaving FEC coded data can reduce the all or stronger multi-bit correcting ECC such as BCH or Reed
nothing properties of transmitted FEC codes when Solomon.[4][5] NOR Flash typically does not use any error
the channel errors tend to occur in bursts. However, correction.[4]
this method has limits; it is best used on narrowband
Classical block codes are usually decoded using harddata.
decision algorithms,[6] which means that for every inMost telecommunication systems use a xed channel put and output signal a hard decision is made whether it
code designed to tolerate the expected worst-case bit er- corresponds to a one or a zero bit. In contrast, convoror rate, and then fail to work at all if the bit error rate lutional codes are typically decoded using soft-decision
is ever worse. However, some systems adapt to the given algorithms like the Viterbi, MAP or BCJR algorithms,
channel error conditions: some instances of hybrid auto- which process (discretized) analog signals, and which almatic repeat-request use a xed FEC method as long as low for much higher error-correction performance than
the FEC can handle the error rate, then switch to ARQ hard-decision decoding.
when the error rate gets too high; adaptive modulation
and coding uses a variety of FEC rates, adding more
error-correction bits per packet when there are higher error rates in the channel, or taking them out when they are
not needed.

122.3 Types of FEC

Nearly all classical block codes apply the algebraic properties of nite elds. Hence classical block codes are often referred to as algebraic codes.
In contrast to classical block codes that often specify an
error-detecting or error-correcting ability, many modern
block codes such as LDPC codes lack such guarantees.
Instead, modern codes are evaluated in terms of their bit
error rates.

Most forward error correction correct only bit-ips, but

not bit-insertions or bit-deletions. In this setting, the
Hamming distance is the appropriate way to measure
The two main categories of FEC codes are block codes the bit error rate. A few forward error correction codes
and convolutional codes.
are designed to correct bit-insertions and bit-deletions,
such as Marker Codes and Watermark Codes. The
Block codes work on xed-size blocks (packets) Levenshtein distance is a more appropriate way to mea[7]
of bits or symbols of predetermined size. Practi- sure the bit error rate when using such codes.
cal block codes can generally be hard-decoded in
polynomial time to their block length.
Main articles: Block code and Convolutional code

Convolutional codes work on bit or symbol streams

of arbitrary length. They are most often soft decoded with the Viterbi algorithm, though other algorithms are sometimes used. Viterbi decoding allows
asymptotically optimal decoding eciency with increasing constraint length of the convolutional code,
but at the expense of exponentially increasing complexity. A convolutional code that is terminated
is also a 'block code' in that it encodes a block of
input data, but the block size of a convolutional
code is generally arbitrary, while block codes have
a xed size dictated by their algebraic characteristics. Types of termination for convolutional codes
include tail-biting and bit-ushing.

122.4 Concatenated FEC codes for

improved performance
Main article: Concatenated error correction codes

Classical (algebraic) block codes and convolutional

codes are frequently combined in concatenated coding schemes in which a short constraint-length Viterbidecoded convolutional code does most of the work and
a block code (usually Reed-Solomon) with larger symbol size and block length mops up any errors made by
the convolutional decoder. Single pass decoding with this
family of error correction codes can yield very low error rates, but for long range transmission conditions (like
There are many types of block codes, but among the clas- deep space) iterative decoding is recommended.
sical ones the most notable is Reed-Solomon coding be- Concatenated codes have been standard practice in satelcause of its widespread use on the Compact disc, the lite and deep space communications since Voyager 2 rst
DVD, and in hard disk drives. Other examples of clas- used the technique in its 1986 encounter with Uranus.
sical block codes include Golay, BCH, Multidimensional The Galileo craft used iterative concatenated codes to
parity, and Hamming codes.
compensate for the very high error rate conditions caused

526

CHAPTER 122. FORWARD ERROR CORRECTION

122.7 Local decoding and testing

of codes

by having a failed antenna.

122.5 Low-density
(LDPC)

parity-check

Main article: Low-density parity-check code

Main articles:
testable code

Locally decodable code and Locally

Sometimes it is only necessary to decode single bits of

the message, or to check whether a given signal is a codeword, and do so without looking at the entire signal. This
can make sense in a streaming setting, where codewords
are too large to be classically decoded fast enough and
where only a few bits of the message are of interest for
now. Also such codes have become an important tool in
computational complexity theory, e.g., for the design of
probabilistically checkable proofs.

Low-density parity-check (LDPC) codes are a class of

recently re-discovered highly ecient linear block codes
made from many single parity check (SPC) codes. They
can provide performance very close to the channel capacity (the theoretical maximum) using an iterated softdecision decoding approach, at linear time complexity in
terms of their block length. Practical implementations
rely heavily on decoding the constituent SPC codes in par- Locally decodable codes are error-correcting codes for
which single bits of the message can be probabilistically
allel.
recovered by only looking at a small (say constant) numLDPC codes were rst introduced by Robert G. Gallager ber of positions of a codeword, even after the codeword
in his PhD thesis in 1960, but due to the computational has been corrupted at some constant fraction of posieort in implementing encoder and decoder and the in- tions. Locally testable codes are error-correcting codes
troduction of ReedSolomon codes, they were mostly ig- for which it can be checked probabilistically whether a
nored until recently.
signal is close to a codeword by only looking at a small
LDPC codes are now used in many recent high-speed number of positions of the signal.
communication standards, such as DVB-S2 (Digital
video broadcasting), WiMAX (IEEE 802.16e standard
for microwave communications), High-Speed Wireless
LAN (IEEE 802.11n), 10GBase-T Ethernet (802.3an) 122.8 Interleaving
and G.hn/G.9960 (ITU-T Standard for networking over
power lines, phone lines and coaxial cable). Other LDPC Interleaving is frequently used in digital communication
codes are standardized for wireless communication stan- and storage systems to improve the performance of fordards within 3GPP MBMS (see fountain codes).
ward error correcting codes. Many communication channels are not memoryless: errors typically occur in bursts
rather than independently. If the number of errors within
a code word exceeds the error-correcting codes capa122.6 Turbo codes
bility, it fails to recover the original code word. Interleaving ameliorates this problem by shuing source symMain article: Turbo code
bols across several code words, thereby creating a more
uniform distribution of errors.[8] Therefore, interleaving
Turbo coding is an iterated soft-decoding scheme that is widely used for burst error-correction.
combines two or more relatively simple convolutional
codes and an interleaver to produce a block code that can
perform to within a fraction of a decibel of the Shannon
limit. Predating LDPC codes in terms of practical application, they now provide similar performance.

The analysis of modern iterated codes, like turbo codes

and LDPC codes, typically assumes an independent distribution of errors.[9] Systems using LDPC codes therefore typically employ additional interleaving across the
symbols within a code word.[10]

One of the earliest commercial applications of turbo coding was the CDMA2000 1x (TIA IS-2000) digital cellular
technology developed by Qualcomm and sold by Verizon
Wireless, Sprint, and other carriers. It is also used for the
evolution of CDMA2000 1x specically for Internet access, 1xEV-DO (TIA IS-856). Like 1x, EV-DO was developed by Qualcomm, and is sold by Verizon Wireless,
Sprint, and other carriers (Verizons marketing name for
1xEV-DO is Broadband Access, Sprints consumer and
business marketing names for 1xEV-DO are Power Vision and Mobile Broadband, respectively).

For turbo codes, an interleaver is an integral component and its proper design is crucial for good
performance.[8][11] The iterative decoding algorithm
works best when there are not short cycles in the factor
graph that represents the decoder; the interleaver is chosen to avoid short cycles.
Interleaver designs include:
rectangular (or uniform) interleavers (similar to the
method using skip factors described above)

122.9. LIST OF ERROR-CORRECTING CODES

convolutional interleavers
random interleavers (where the interleaver is a
known random permutation)

527
No word is completely lost and the missing letters can be
recovered with minimal guesswork.

122.8.2 Disadvantages of interleaving

S-random interleaver (where the interleaver is a

known random permutation with the constraint that Use of interleaving techniques increases total delay. This
no input symbols within distance S appear within a is because the entire interleaved block must be received
before the packets can be decoded.[16] Also interleavers
distance of S in the output).[12]
hide the structure of errors; without an interleaver, more
Another possible construction is a contention-free advanced decoding algorithms can take advantage of the
quadratic permutation polynomial (QPP).[13] It is error structure and achieve more reliable communication
used for example in the 3GPP Long Term Evolu- than a simpler decoder combined with an interleaver.
tion mobile telecommunication standard.[14]
In multi-carrier communication systems, interleaving
across carriers may be employed to provide frequency
diversity, e.g., to mitigate frequency-selective fading or
narrowband interference.[15]

122.8.1

Example

Transmission without interleaving:

122.9 List of
codes

error-correcting

AN codes
BCH code, which can be designed to correct any arbitrary number of errors per code block.
Berger code

Error-free message:
aaaabbbbccccddddeeeeffgggg Transmission with a burst error: aaaabbbbccc____deeeegggg

Constant-weight code

Here, each group of the same letter represents a 4-bit onebit error-correcting codeword. The codeword cccc is altered in one bit and can be corrected, but the codeword
dddd is altered in three bits, so either it cannot be decoded
at all or it might be decoded incorrectly.

Expander codes

With interleaving:

Goppa code, used in the McEliece cryptosystem

Error-free code words:

aaaabbbbccccddddeeeegggg
Interleaved:
abcdefgabcdefgabcdefgabcdefg Transmission with a burst error: abcdefgabcd____bcdefgabcdefg Received code words after
deinterleaving: aa_abbbbccccdddde_eef_g_gg

Convolutional code

Group codes
Golay codes, of which the Binary Golay code is of
practical interest

Hadamard code
Hagelbarger code
Hamming code

In each of the codewords aaaa, eeee, , gggg, only one

bit is altered, so one-bit error-correcting code will decode
everything correctly.

Latin square based code for non-white noise (prevalent for example in broadband over powerlines)

Transmission without interleaving:

Lexicographic code

Original transmitted sentence: ThisIsAnExampleOfInterleaving Received sentence with a burst error: ThisIs______pleOfInterleaving
The term AnExample ends up mostly unintelligible and
dicult to correct.
With interleaving:
Transmitted sentence:
ThisIsAnExampleOfInterleaving...
Error-free transmission:
TIEpfeaghsxlIrv.iAaenli.snmOten.
Received sentence with
a burst error:
TIEpfe______Irv.iAaenli.snmOten.
Received
sentence
after
deinterleaving:
T_isI_AnE_amp_eOfInterle_vin_...

Long code
Low-density parity-check code, also known as
Gallager code, as the archetype for sparse graph
codes
LT code, which is a near-optimal rateless erasure
correcting code (Fountain code)
m of n codes
Online code, a near-optimal rateless erasure correcting code
Polar code (coding theory)

528
Raptor code, a near-optimal rateless erasure correcting code
ReedSolomon error correction
ReedMuller code
Repeat-accumulate code
Repetition codes, such as Triple modular redundancy

CHAPTER 122. FORWARD ERROR CORRECTION

[5] Jim Cooke. The Inconvenient Truths of NAND Flash

Memory. 2007. p. 28. says For SLC, a code with a
correction threshold of 1 is sucient. t=4 required ... for
MLC.
[6] Baldi M.; Chiaraluce F. (2008). A Simple Scheme
for Belief Propagation Decoding of BCH and RS Codes
in Multimedia Transmissions. International Journal
of Digital Multimedia Broadcasting. 2008: 957846.
doi:10.1155/2008/957846.

Spinal code, a rateless, nonlinear code based on

pseudo-random hash functions [17]

[7] Shah, Gaurav; Molina, Andres; Blaze, Matt (2006).

Keyboards and covert channels (PDF). Proceedings of
the 15th conference on USENIX Security Symposium.

Tornado code, a near-optimal erasure correcting

code, and the precursor to Fountain codes

[8] B. Vucetic; J. Yuan (2000). Turbo codes: principles and

applications. Springer Verlag. ISBN 978-0-7923-7868-6.

Turbo code
WalshHadamard code

122.10 See also

Code rate
Erasure codes
Soft-decision decoder
Error detection and correction
Error-correcting codes with feedback
Burst error-correcting code

122.11 References
[1] Charles Wang; Dean Sklar; Diana Johnson (Winter 2001
2002). Forward Error-Correction Coding. Crosslink
The Aerospace Corporation magazine of advances in
aerospace technology. The Aerospace Corporation. 3 (1).
How Forward Error-Correcting Codes Work
[2] Hamming, R. W. (April 1950). Error Detecting and
Error Correcting Codes (PDF). Bell System Tech. J.
USA: AT&T. 29 (2): 147160. doi:10.1002/j.15387305.1950.tb00463.x. Retrieved 4 December 2012.
[3] Hamming codes for NAND ash memory devices.
EE Times-Asia. Apparently based on Micron Technical Note TN-29-08: Hamming Codes for NAND Flash
Memory Devices. 2005. Both say: The Hamming algorithm is an industry-accepted method for error detection
and correction in many SLC NAND ash-based applications.
[4] What Types of ECC Should Be Used on Flash Memory?". (Spansion application note). 2011. says: Both
Reed-Solomon algorithm and BCH algorithm are common ECC choices for MLC NAND ash. ... Hamming
based block codes are the most commonly used ECC for
SLC.... both Reed-Solomon and BCH are able to handle
multiple errors and are widely used on MLC ash.

[9] M. Luby, M. Mitzenmacher, A. Shokrollahi, D. Spielman,

V. Stemann (1997). Practical Loss-Resilient Codes.
Proc. 29th annual Association for Computing Machinery
(ACM) symposium on Theory of computation.
[10] Digital Video Broadcast (DVB); Second generation
framing structure, channel coding and modulation systems
for Broadcasting, Interactive Services, News Gathering
and other satellite broadband applications (DVB-S2)". En
302 307. ETSI (V1.2.1). April 2009.
[11] K. Andrews; et al. (November 2007). The Development
of Turbo and LDPC Codes for Deep-Space Applications.
Proc. of the IEEE. 95 (11).
[12] S. Dolinar and D. Divsalar. Weight Distributions for
Turbo Codes Using Random and Nonrandom Permutations. 1995.
[13] Takeshita, Oscar (2006).
Permutation Polynomial
Interleavers: An Algebraic-Geometric Perspective.
arXiv:cs/0601048 .
[14] 3GPP TS 36.212, version 8.8.0, page 14
[15] Digital Video Broadcast (DVB); Frame structure, channel coding and modulation for a second generation digital
terrestrial television broadcasting system (DVB-T2)". En
302 755. ETSI (V1.1.1). September 2009.
[16] Explaining Interleaving - W3techie. w3techie.com. Retrieved 2010-06-03.
[17] Perry, Jonathan; Balakrishnan, Hari; Shah, Devavrat
(2011). Rateless Spinal Codes. Proceedings of
the 10th ACM Workshop on Hot Topics in Networks.
doi:10.1145/2070562.2070568.

122.12 Further reading

Clark, George C., Jr.; Cain, J. Bibb (1981). ErrorCorrection Coding for Digital Communications. New
York: Plenum Press. ISBN 0-306-40615-2.
Wicker, Stephen B. (1995). Error Control Systems
for Digital Communication and Storage. Englewood
Clis NJ: Prentice-Hall. ISBN 0-13-200809-2.

122.13. EXTERNAL LINKS

Wilson, Stephen G. (1996). Digital Modulation and
Coding. Englewood Clis NJ: Prentice-Hall. ISBN
0-13-210071-1.
Error Correction Code in Single Level Cell NAND
Flash memories 16 February 2007
Error Correction Code in NAND Flash memories
29 November 2004
Observations on Errors, Corrections, & Trust of Dependent Systems, by James Hamilton, February 26,
2012

122.13 External links

Morelos-Zaragoza, Robert (2004). The Error Correcting Codes (ECC) Page. Retrieved 2006-03-05.

529

Chapter 123

Pulse-amplitude modulation
(a)

The number of possible pulse amplitudes in analog PAM

is theoretically innite. Digital PAM reduces the number
of pulse amplitudes to some power of two. For example,
in 4-level PAM there are 22 possible discrete pulse amplitudes; in 8-level PAM there are 23 possible discrete pulse
amplitudes; and in 16-level PAM there are 24 possible
discrete pulse amplitudes.

(1)
(2)

(b)

123.2 Uses
Principle of PAM: (1) original signal, (2) PAM signal, (a) amplitude of signal, (b) time

Pulse-amplitude modulation (PAM), is a form of signal modulation where the message information is encoded
in the amplitude of a series of signal pulses. It is an analog pulse modulation scheme in which the amplitudes of
a train of carrier pulses are varied according to the sample
value of the message signal. Demodulation is performed
by detecting the amplitude level of the carrier at every
single period.

123.2.1 Ethernet
Some versions of the Ethernet communication standard
are an example of PAM usage. In particular, 100BASETX and BroadR-Reach Ethernet standard, use three-level
PAM modulation (PAM-3), 1000BASE-T Gigabit Ethernet uses ve-level PAM-5 modulation[1] and 10GBASET 10 Gigabit Ethernet uses a Tomlinson-Harashima Precoded (THP) version of pulse-amplitude modulation
with 16 discrete levels (PAM-16), encoded in a twodimensional checkerboard pattern known as DSQ128.

123.2.2 Photo biology

123.1 Types

The concept is also used for the study of photosynthesis

using a specialized instrument that involves a
There are two types of pulse amplitude modulation:
spectrouorometric measurement of the kinetics of
uorescence rise and decay in the light-harvesting
1. Single polarity PAM: In this a suitable xed DC bias antenna of thylakoid membranes, thus querying various
is added to the signal to ensure that all the pulses are aspects of the state of the photosystems under dierent
positive.
environmental conditions.[2]
2. Double polarity PAM: In this the pulses are both
positive and negative.
Pulse-amplitude modulation is widely used in modulating
signal transmission of digital data, with non-baseband
applications having been largely replaced by pulse-code
modulation, and, more recently, by pulse-position modulation.

123.2.3 Electronic drivers for LED lighting

Pulse-amplitude modulation has also been developed for

the control of light-emitting diodes (LEDs), especially for
lighting applications.[3] LED drivers based on the PAM
technique oer improved energy eciency over systems
In particular, all telephone modems faster than 300 bit/s based upon other common driver modulation techniques
use quadrature amplitude modulation (QAM). (QAM such as pulse-width modulation (PWM) as the forward
uses a two-dimensional constellation).
current passing through an LED is relative to the intensity
530

123.4. REFERENCES
of the light output and the LED eciency increases as the
forward current is reduced.
Pulse-amplitude modulation LED drivers are able to synchronize pulses across multiple LED channels to enable
perfect colour matching. Due to the inherent nature of
PAM in conjunction with the rapid switching speed of
LEDs it is possible to use LED lighting as a means of
wireless data transmission at high speed.

123.2.4

Digital television

The (mostly) North American Advanced Television Systems Committee standards for digital television uses a
form of PAM to broadcast the data that makes up the
television signal. This system, known as 8VSB, is based
on a three-level PAM like 100BASE-TX, but uses additional processing to suppress one sideband and thus make
more ecient use of limited bandwidth. Using a single 6 MHz channel allocation, as dened in the previous
NTSC analog standard, 8VSB is capable of transmitting
32 Mbit/s. After accounting for error correcting codes
and other overhead, the data rate in the signal is 19.39
Mbit/s.

123.3 See also

Amplitude-shift keying
Carrier Sense Multiple Access
Pulse-code modulation
Pulse-position modulation
Pulse-width modulation
Pulse-density modulation
Pulse forming network
pulse width
Quadrature amplitude modulation
8VSB

123.4 References
[1] George Schroeder (2003-04-01). What PAM5 means to
you. EDN. Retrieved 2015-03-02.
[2] Schreiber, Ulrich (2004). Pulse-Amplitude-Modulation
(PAM) Fluorometry and Saturation Pulse Method: An
Overview. Dordrecht: Springer Netherlands. pp. 279
319. ISBN 978-1-4020-3217-2. Retrieved 2015-02-02.
[3] im Whitaker (January 2006). Closed-loop electronic
controllers drive LED systems. LED Lights Magazine.
Retrieved 2015-03-02.

531

Chapter 124

Pulse-position modulation
Pulse-position modulation (PPM) is a form of signal modulation in which M message bits are encoded by
transmitting a single pulse in one of 2M possible required
time-shifts.[1][2] This is repeated every T seconds, such
that the transmitted bit rate is M /T bits per second. It
is primarily useful for optical communications systems,
where there tends to be little or no multipath interference.

124.1 History
An ancient use of pulse-position modulation was the
Greek hydraulic semaphore system invented by Aeneas
Stymphalus around 350 B.C. that used the water clock
principle to time signals.[3] In this system, the draining of
water acts as the timing device, and torches are used to
signal the pulses. The system used identical water-lled
containers whose drain could be turned on and o, and a
oat with a rod marked with various predetermined codes
that represented military messages. The operators would
place the containers on hills so they could be seen from
each other at a distance. To send a message, the operators would use torches to signal the beginning and ending
of the draining of the water, and the marking on the rod
attached to the oat would indicate the message.

encoded relative to the previous, such that the receiver

must only measure the dierence in the arrival time of
successive pulses. It is possible to limit the propagation
of errors to adjacent symbols, so that an error in measuring the dierential delay of one pulse will aect only
two symbols, instead of aecting all successive measurements.

124.3 Sensitivity to multipath interference

Aside from the issues regarding receiver synchronization,

the key disadvantage of PPM is that it is inherently sensitive to multipath interference that arises in channels with
frequency-selective fading, whereby the receivers signal
contains one or more echoes of each transmitted pulse.
Since the information is encoded in the time of arrival
(either dierentially, or relative to a common clock), the
presence of one or more echoes can make it extremely
dicult, if not impossible, to accurately determine the
correct pulse position corresponding to the transmitted
pulse. Multipath in Pulse Position Modulation systems
can be easily mitigated by using the same techniques that
In modern times, pulse position modulation has origins in are used in Radar systems that rely totally on synchrotelegraph time-division multiplexing which dates back to nization and time of arrival of the received pulse to obtain
1853, and evolved alongside pulse code modulation and their range position in the presence of echoes.
pulse width modulation.[4] In the early 1960s, Don Mathers and Doug Spreng of NASA invented pulse position
modulation used in radio control (R/C) systems. PPM is
currently being used in ber optic communications, deep 124.4 Non-coherent detection
space communications, and continues to be used in R/C
systems.
One of the principal advantages of PPM is that it is an
M-ary modulation technique that can be implemented
non-coherently, such that the receiver does not need to
124.2 Synchronization
use a phase-locked loop (PLL) to track the phase of the
carrier. This makes it a suitable candidate for optical
One of the key diculties of implementing this technique communications systems, where coherent phase moduis that the receiver must be properly synchronized to align lation and detection are dicult and extremely expenthe local clock with the beginning of each symbol. There- sive. The only other common M-ary non-coherent modfore, it is often implemented dierentially as dierential ulation technique is M-ary Frequency Shift Keying (Mpulse-position modulation, whereby each pulse position is FSK), which is the frequency-domain dual to PPM.
532

124.7. SEE ALSO

124.5 PPM vs. M-FSK

PPM and M-FSK systems with the same bandwidth, average power, and transmission rate of M/T bits per second
have identical performance in an AWGN (Additive White
Gaussian Noise) channel. However, their performance
diers greatly when comparing frequency-selective and
frequency-at fading channels. Whereas frequencyselective fading produces echoes that are highly disruptive for any of the M time-shifts used to encode PPM
data, it selectively disrupts only some of the M possible
frequency-shifts used to encode data for M-FSK. On the
other hand, frequency-at fading is more disruptive for
M-FSK than PPM, as all M of the possible frequencyshifts are impaired by fading, while the short duration of
the PPM pulse means that only a few of the M time-shifts
are heavily impaired by fading.
Optical communications systems tend to have weak
multipath distortions, and PPM is a viable modulation
scheme in many such applications.

533
It begins with a start frame (state high for more than 2
ms). Each channel (up to 8) is encoded by the time of
the high state (PPM high state + 0.3 x (PPM low state) =
servo PWM pulse width). More sophisticated radio control systems are now often based on pulse-code modulation, which is more complex but oers greater exibility
and reliability. The advent of 2.4 GHz band FHSS radio control systems in the early 21st century changed this
still further. Pulse position modulation is also used for
communication to the ISO/IEC 15693 contactless smart
card as well as the HF implementation of the Electronic
Product Code (EPC) Class 1 protocol for RFID tags.

124.7 See also

Pulse-amplitude modulation
Pulse-code modulation
Pulse-density modulation
Pulse-width modulation

124.6 Applications for RF communications

Narrowband RF (radio frequency) channels with low
power and long wavelengths (i.e., low frequency) are affected primarily by at fading, and PPM is better suited
than M-FSK to be used in these scenarios. One common
application with these channel characteristics, rst used
in the early 1960s with top-end HF (as low as 27 MHz)
frequencies into the low-end VHF band frequencies (30
MHz to 75 MHz for RC use depending on location), is
the radio control of model aircraft, boats and cars, originally known as digital proportional radio control. PPM
is employed in these systems, with the position of each
pulse representing the angular position of an analogue
control on the transmitter, or possible states of a binary
switch. The number of pulses per frame gives the number of controllable channels available. The advantage of
using PPM for this type of application is that the electronics required to decode the signal are extremely simple, which leads to small, light-weight receiver/decoder
units. (Model aircraft require parts that are as lightweight
as possible).Servos made for model radio control include
some of the electronics required to convert the pulse to
the motor position the receiver is required to rst extract
the information from the received radio signal through its
intermediate frequency section, then demultiplex the separate channels from the serial stream, and feed the control
pulses to each servo.

124.6.1

PPM encoding for radio control

A complete PPM frame is about 22.5 ms (can vary between manufacturer)Signal low state is always 0.3 ms.

Ultra wideband

124.8 References
[1] K. T. Wong (March 2007). Narrowband PPM SemiBlind Spatial-Rake Receiver & Co-Channel Interference
Suppression (PDF). European Transactions on Telecommunications. The Hong Kong Polytechnic University. 18
(2): 193197. doi:10.1002/ett.1147.
[2] Yuichiro Fujiwara (2013). Self-synchronizing pulse position modulation with error tolerance. IEEE Transactions on Information Theory.
59: 53525362.
arXiv:1301.3369 . doi:10.1109/TIT.2013.2262094.
[3] Michael Lahanas. Ancient Greek Communication Methods.
[4] Ross Yeager & Kyle Pace. Copy of Communications
Topic Presentation: Pulse Code Modulation. Prezi.

Chapter 125

Pulse-code modulation
PCM redirects here. For other uses, see PCM (disam- characters punched in paper tape to send samples of imbiguation).
ages quantized to 5 levels; whether this is considered
PCM or not depends on how one interprets pulse code,
Pulse-code modulation (PCM) is a method used to but it involved transmission of quantized samples.
digitally represent sampled analog signals. It is the standard form of digital audio in computers, compact discs,
digital telephony and other digital audio applications. In
a PCM stream, the amplitude of the analog signal is sampled regularly at uniform intervals, and each sample is
quantized to the nearest value within a range of digital
steps.

In 1926, Paul M. Rainey of Western Electric patented a

facsimile machine which transmitted its signal using 5-bit
PCM, encoded by an opto-mechanical analog-to-digital
converter.[7] The machine did not go into production.[8]
British engineer Alec Reeves, unaware of previous work,
conceived the use of PCM for voice communication in
1937 while working for International Telephone and Telegraph in France. He described the theory and advantages,
but no practical application resulted. Reeves led for a
French patent in 1938, and his US patent was granted in
1943.[9] By this time Reeves had started working at the
Telecommunications Research Establishment (TRE).[8]

Linear pulse-code modulation (LPCM) is a specic

type of PCM where the quantization levels are linearly uniform.[5] This is in contrast to PCM encodings
where quantization levels vary as a function of amplitude (as with the A-law algorithm or the -law algorithm).
Though PCM is a more general term, it is often used to The rst transmission of speech by digital techniques, the
describe data encoded as LPCM.
SIGSALY encryption equipment, conveyed high-level
A PCM stream has two basic properties that determine Allied communications during World War II. In 1943 the
the streams delity to the original analog signal: the Bell Labs researchers who designed the SIGSALY system
sampling rate, which is the number of times per second became aware of the use of PCM binary coding as althat samples are taken; and the bit depth, which deter- ready proposed by Alec Reeves. In 1949 for the Canadian
mines the number of possible digital values that can be Navys DATAR system, Ferranti Canada built a workused to represent each sample.
ing PCM radio system that was able to transmit digitized
radar data over long distances.[10]

125.1 History

PCM in the late 1940s and early 1950s used a cathoderay coding tube with a plate electrode having encoding
perforations.[11][12] As in an oscilloscope, the beam was
swept horizontally at the sample rate while the vertical deection was controlled by the input analog signal, causing
the beam to pass through higher or lower portions of the
perforated plate. The plate collected or passed the beam,
producing current variations in binary code, one bit at a
time. Rather than natural binary, the grid of Goodalls
later tube was perforated to produce a glitch-free Gray
code, and produced all bits simultaneously by using a fan
beam instead of a scanning beam.

Early electrical communications started to sample signals

in order to interlace samples from multiple telegraphy
sources and to convey them over a single telegraph cable. The American inventor Moses G. Farmer conveyed
telegraph time-division multiplexing (TDM) as early as
1853. Electrical engineer W. M. Miner, in 1903, used
an electro-mechanical commutator for time-division multiplexing multiple telegraph signals; he also applied this
technology to telephony. He obtained intelligible speech
from channels sampled at a rate above 35004300 Hz; In the United States, the National Inventors Hall of Fame
[13]
and Claude Shanlower rates proved unsatisfactory. This was TDM, but has honored Bernard M. Oliver
[14]
[15]
as
the
inventors
of
PCM,
as described in
non
pulse-amplitude modulation (PAM) rather than PCM.
Communication System Employing Pulse Code ModIn 1920 the Bartlane cable picture transmission system,
ulation, U.S. Patent 2,801,281 led in 1946 and 1952,
named after its inventors Harry G. Bartholomew and
granted
in 1956. Another patent by the same title was
Maynard D. McFarlane,[6] used telegraph signaling of
534

125.4. DEMODULATION
led by John R. Pierce in 1945, and issued in 1948: U.S.
Patent 2,437,707. The three of them published The Philosophy of PCM in 1948.[16]

125.2 Implementations
PCM is the method of encoding generally used for uncompressed audio, although there are other methods such
as pulse-density modulation (used also on Super Audio
CD).

535

15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0

The 4ESS switch introduced time-division switching into the US telephone system in 1976, based on Sampling and quantization of a signal (red) for 4-bit LPCM
medium scale integrated circuit technology.[17]
LPCM is used for the lossless encoding of audio data 11, 13, 14, 15, 15, 15, 14, etc. Encoding these values
in the Compact disc Red Book standard (informally as binary numbers would result in the following set of
also known as Audio CD), introduced in 1982.
nibbles: 1000 (23 1+22 0+21 0+20 0=8+0+0+0=8),
AES3 (specied in 1985, upon which S/PDIF is 1000, 1001, 1011, 1101, 1110, 1111, 1111, 1111, 1110,
etc. These digital values could then be further processed
based) is a particular format using LPCM.
or analyzed by a digital signal processor. Several PCM
On PCs, PCM and LPCM often refer to the format streams could also be multiplexed into a larger aggreused in WAV (dened in 1991) and AIFF audio con- gate data stream, generally for transmission of multiple
tainer formats (dened in 1988). LPCM data may streams over a single physical link. One technique is
also be stored in other formats such as AU, raw au- called time-division multiplexing (TDM) and is widely
dio format (header-less le) and various multimedia used, notably in the modern public telephone system.
container formats.
The PCM process is commonly implemented on a single
LPCM has been dened as a part of the DVD (since integrated circuit generally referred to as an analog-to1995) and Blu-ray (since 2006) standards.[18][19][20] digital converter (ADC).
It is also dened as a part of various digital video
and audio storage formats (e.g. DV since 1995,[21]
AVCHD since 2006[22] ).
125.4 Demodulation
LPCM is used by HDMI (dened in 2002), a singlecable digital audio/video connector interface for To recover the original signal from the sampled data, a
demodulator can apply the procedure of modulation
transmitting uncompressed digital data.
in reverse. After each sampling period, the demodula RF64 container format (dened in 2007) uses tor reads the next value and shifts the output signal to
LPCM and also allows non-PCM bitstream stor- the new value. As a result of these transitions, the sigage: various compression formats contained in the nal has a signicant amount of high-frequency energy
RF64 le as data bursts (Dolby E, Dolby AC3, DTS, caused by aliasing. To remove these undesirable freMPEG-1/MPEG-2 Audio) can be disguised as quencies and leave the original signal, the demodulator
PCM linear.[23]
passes the signal through analog lters that suppress energy outside the expected frequency range (greater than
the Nyquist frequency fs /2 ).[note 1] The sampling theorem shows PCM devices can operate without introduc125.3 Modulation
ing distortions within their designed frequency bands if
In the diagram, a sine wave (red curve) is sampled and they provide a sampling frequency twice that of the input
quantized for PCM. The sine wave is sampled at regu- signal. For example, in telephony, the usable voice frelar intervals, shown as vertical lines. For each sample, quency band ranges from approximately 300 Hz to 3400
one of the available values (on the y-axis) is chosen by Hz. Therefore, per the NyquistShannon sampling thesome algorithm. This produces a fully discrete represen- orem, the sampling frequency (8 kHz) must be at least
tation of the input signal (blue points) that can be eas- twice the voice frequency (4 kHz) for eective reconily encoded as digital data for storage or manipulation. struction of the voice signal.
For the sine wave example at right, we can verify that The electronics involved in producing an accurate analog
the quantized values at the sampling moments are 8, 9, signal from the discrete data are similar to those used for

536

CHAPTER 125. PULSE-CODE MODULATION

generating the digital signal. These devices are Digital- 125.7 Digitization as part of the
to-analog converters (DACs). They produce a voltage or
PCM process
current (depending on type) that represents the value presented on their digital inputs. This output would then genIn conventional PCM, the analog signal may be processed
erally be ltered and amplied for use.
(e.g., by amplitude compression) before being digitized.
Once the signal is digitized, the PCM signal is usually subjected to further processing (e.g., digital data compres125.5 Standard sampling precision sion).

and rates

PCM with linear quantization is known as Linear PCM

(LPCM).[28]

Common sample depths for LPCM are 8, 16, 20 or 24 Some forms of PCM combine signal processing with coding. Older versions of these systems applied the processbits per sample.[1][2][3][24]
ing in the analog domain as part of the analog-to-digital
LPCM encodes a single sound channel. Support for mul- process; newer implementations do so in the digital dotichannel audio depends on le format and relies on in- main. These simple techniques have been largely renterweaving or synchronization of LPCM streams.[5][25] dered obsolete by modern transform-based audio comWhile two channels (stereo) is the most common for- pression techniques.
mat, some can support up to 8 audio channels (7.1
surround).[2][3]
DPCM encodes the PCM values as dierences beCommon sampling frequencies are 48 kHz as used with
DVD format videos, or 44.1 kHz as used in Compact
discs. Sampling frequencies of 96 kHz or 192 kHz can
be used on some newer equipment, with the higher value
equating to 6.144 megabit per second for two channels
at 16-bit per sample value, but the benets have been
debated.[26] The bitrate limit for LPCM audio on DVDVideo is also 6.144 Mbit/s, allowing 8 channels (7.1 surround) 48 kHz 16-bit per sample = 6,144 kbit/s.
There is a L32 bit PCM,[27] and there are many sound
cards that support it.

125.6 Limitations

tween the current and the predicted value. An algorithm predicts the next sample based on the previous
samples, and the encoder stores only the dierence
between this prediction and the actual value. If the
prediction is reasonable, fewer bits can be used to
represent the same information. For audio, this type
of encoding reduces the number of bits required per
sample by about 25% compared to PCM.
Adaptive DPCM (ADPCM) is a variant of DPCM
that varies the size of the quantization step, to allow further reduction of the required bandwidth for
a given signal-to-noise ratio.
Delta modulation is a form of DPCM which uses
one bit per sample.

In telephony, a standard audio signal for a single phone

There are potential sources of impairment implicit in any call is encoded as 8,000 analog samples per second, of 8
PCM system:
bits each, giving a 64 kbit/s digital signal known as DS0.
The default signal compression encoding on a DS0 is ei Choosing a discrete value that is near but not exactly ther -law (mu-law) PCM (North America and Japan) or
at the analog signal level for each sample leads to A-law PCM (Europe and most of the rest of the world).
These are logarithmic compression systems where a 12 or
quantization error.[note 2]
13-bit linear PCM sample number is mapped into an 8bit value. This system is described by international stan Between samples no measurement of the signal
dard G.711. An alternative proposal for a oating point
is made; the sampling theorem guarantees nonrepresentation, with 5-bit mantissa and 3-bit radix, was
ambiguous representation and recovery of the sigabandoned.
nal only if it has no energy at frequency fs/2 or
higher (one half the sampling frequency, known as Where circuit costs are high and loss of voice quality is acthe Nyquist frequency); higher frequencies will gen- ceptable, it sometimes makes sense to compress the voice
signal even further. An ADPCM algorithm is used to map
erally not be correctly represented or recovered.
a series of 8-bit -law or A-law PCM samples into a se As samples are dependent on time, an accurate clock ries of 4-bit ADPCM samples. In this way, the capacity
is required for accurate reproduction. If either the of the line is doubled. The technique is detailed in the
encoding or decoding clock is not stable, its fre- G.726 standard.
quency drift will directly aect the output quality Later it was found that even further compression was possible and additional standards were published. Some of
of the device.[note 3]

125.10. SEE ALSO

537

these international standards describe systems and ideas

which are covered by privately owned patents and thus
use of these standards requires payments to the patent
holders.

ing evolved alongside two analog methods, pulse width

modulation and pulse position modulation, in which the
information to be encoded is represented by discrete signal pulses of varying width or position, respectively. In
Some ADPCM techniques are used in Voice over IP com- this respect, PCM bears little resemblance to these other
forms of signal encoding, except that all can be used in
munications.
time division multiplexing, and the numbers of the PCM
codes are represented as electrical pulses. The device
that performs the coding and decoding function in a tele125.8 Encoding for serial trans- phone, or other, circuit is called a codec.

mission
Main article: Line code
See also: T-carrier and E-carrier

125.10 See also

AES3

PCM can be either return-to-zero (RZ) or non-return-tozero (NRZ). For a NRZ system to be synchronized using
in-band information, there must not be long sequences
of identical symbols, such as ones or zeroes. For binary
PCM systems, the density of 1-symbols is called onesdensity.[29]
Ones-density is often controlled using precoding techniques such as Run Length Limited encoding, where the
PCM code is expanded into a slightly longer code with
a guaranteed bound on ones-density before modulation
into the channel. In other cases, extra framing bits are
added into the stream which guarantee at least occasional
symbol transitions.
Another technique used to control ones-density is the use
of a scrambler polynomial on the raw data which will
tend to turn the raw data stream into a stream that looks
pseudo-random, but where the raw stream can be recovered exactly by reversing the eect of the polynomial. In
this case, long runs of zeroes or ones are still possible
on the output, but are considered unlikely enough to be
within normal engineering tolerance.
In other cases, the long term DC value of the modulated
signal is important, as building up a DC oset will tend to
bias detector circuits out of their operating range. In this
case special measures are taken to keep a count of the cumulative DC oset, and to modify the codes if necessary
to make the DC oset always tend back to zero.
Many of these codes are bipolar codes, where the pulses
can be positive, negative or absent. In the typical alternate
mark inversion code, non-zero pulses alternate between
being positive and negative. These rules may be violated
to generate special symbols used for framing or other special purposes.

125.9 Nomenclature
The word pulse in the term pulse-code modulation refers
to the pulses to be found in the transmission line. This
perhaps is a natural consequence of this technique hav-

Beta encoder
Equivalent pulse code modulation noise
G.711 ITU-T standard for audio companding. It
is primarily used in telephony.
NyquistShannon sampling theorem
Pulse-density modulation
Quantization (signal processing)
Sampling (signal processing)
Signal-to-quantization-noise ratio (SQNR) One
method of measuring quantization error.

125.11 Notes
[1] Some systems use digital ltering to remove some of the
aliasing, converting the signal from digital to analog at a
higher sample rate such that the analog anti-aliasing lter
is much simpler. In some systems, no explicit ltering is
done at all; as its impossible for any system to reproduce
a signal with innite bandwidth, inherent losses in the system compensate for the artifacts or the system simply
does not require much precision.
[2] Quantization error swings between -q/2 and q/2. In the
ideal case (with a fully linear ADC) it is uniformly distributed over this interval, with zero mean and variance of
q2 /12.
[3] A slight dierence between the encoding and decoding
clock frequencies is not generally a major concern; a small
constant error is not noticeable. Clock error does become
a major issue if the clock is not stable, however. A drifting clock, even with a relatively small error, will cause very
obvious distortions in audio and video signals, for example.

538

125.12 References
[1] Alvestrand, Harald Tveit; Salsman, James (May 1999).
RFC 2586 The Audio/L16 MIME content type. The
Internet Society. Retrieved 2010-03-16.
[2] Casner, S. (March 2007). RFC 4856 Media Type Registration of Payload Formats in the RTP Prole for Audio
and Video Conferences Registration of Media Type audio/L8. The IETF Trust. Retrieved 2010-03-16.
[3] Bormann, C.; Casner, S.; Kobayashi, K.; Ogawa, A. (January 2002). RFC 3190 RTP Payload Format for 12-bit
DAT Audio and 20- and 24-bit Linear Sampled Audio.
The Internet Society. Retrieved 2010-03-16.
[4] Audio Media Types. Internet Assigned Numbers Authority. Retrieved 2010-03-16.
[5] Linear Pulse Code Modulated Audio (LPCM)". Library
of Congress. Retrieved 2010-03-21.

CHAPTER 125. PULSE-CODE MODULATION

[20] Jim Taylor. DVD Frequently Asked Questions (and Answers) Audio details of DVD-Video. Retrieved 201003-20.
[21] How DV works. Archived from the original on 200712-06. Retrieved 2010-03-21.
[22] AVCHD Information Website AVCHD format specication overview. Retrieved 2010-03-21.
[23] EBU (July 2009), EBU Tech 3306 MBWF / RF64: An
Extended File Format for Audio (PDF), retrieved 201001-19
[24] RFC 3108 Conventions for the use of the Session Description Protocol (SDP) for ATM Bearer Connections.
May 2001. Retrieved 2010-03-16.
[25] PCM, Pulse Code Modulated Audio.
Congress. Retrieved 2009-07-18.

Library of

[6] The Bartlane Transmission System.

DigicamHistory.com. Archived from the original on February 10,
2010. Retrieved 7 January 2010.

[26] 24/192 Music Downloads, and why they do not make

sense. Chris Monty Montgomery. Retrieved 2013-0316.

[7] U.S. patent number 1,608,527; also see p. 8, Data conversion handbook, Walter Allan Kester, ed., Newnes, 2005,
ISBN 0-7506-7841-0.

[27] http://www.ypass.net/blog/2010/01/
pcm-audio-part-1-what-is-pcm/.
Missing or empty
|title= (help)

[8] John Vardalas (June 2013), Pulse Code Modulation: It all

Started 75 Years Ago with Alec Reeves, IEEE

[28] Linear Pulse Code Modulated Audio (LPCM)". The Library of Congress. Retrieved March 21, 2010.

[9] US 2272070

[29] Stallings, William, Digital Signaling Techniques, December 1984, Vol. 22, No. 12, IEEE Communications Magazine

[10] Porter, Arthur. So Many Hills to Climb (2004) Beckham

Publications Group
[11] R. W. Sears, Electron Beam Deection Tube for Pulse
Code Modulation, Bell Sys. Tech. J., Vol. 27 pp. 4457
[12] W. M. Goodall, Television by Pulse Code Modulation,
Bell Sys. Tech. J., Vol. 30 pp. 3349, 1951.
[13] Bernard Oliver. National Inventors Hall of Fame. Retrieved February 6, 2011.
[14] Claude Shannon. National Inventors Hall of Fame. Retrieved February 6, 2011.

125.13 Further reading

Franklin S. Cooper; Ignatius Mattingly (1969).
Computer-controlled PCM system for investigation of dichotic speech perception. Journal of
the Acoustical Society of America. 46: 115.
doi:10.1121/1.1972688.

[15] National Inventors Hall of Fame announces 2004 class of

inventors. Science Blog. February 11, 2004. Retrieved
February 6, 2011.

Ken C. Pohlmann (1985). Principles of Digital Audio (2nd ed.). Carmel, Indiana: Sams/Prentice-Hall
Computer Publishing. ISBN 0-672-22634-0.

[16] B. M. Oliver; J. R. Pierce & C. E. Shannon (Nov 1948).

The Philosophy of PCM. Proceeding of the IRE. 36
(11): 13241331. doi:10.1109/JRPROC.1948.231941.
ISSN 0096-8390.

D. H. Whalen, E. R. Wiley, Philip E. Rubin, and

Franklin S. Cooper (1990). The Haskins Laboratories pulse code modulation (PCM) system. Behavior Research Methods, Instruments, and Computers.
22 (6): 550559. doi:10.3758/BF03204440.

[17] Cambron, G. Keith, Global Networks: Engineering, Operations and Design, Page 345, John Wiley & Sons, Oct
17, 2012.
[18] Blu-ray Disc Association (March 2005), White paper Bluray Disc Format 2.B Audio Visual Application Format
Specications for BD-ROM (PDF), retrieved 2009-07-26
[19] DVD Technical Notes (DVD Video Book B) Audio
data specications. 1996-07-21. Retrieved 2010-03-16.

Bill Waggener (1995). Pulse Code Modulation Techniques (1st ed.). New York, NY: Van Nostrand
Reinhold. ISBN 0-442-01436-8.
Bill Waggener (1999). Pulse Code Modulation Systems Design (1st ed.). Boston, MA: Artech House.
ISBN 0-89006-776-7.

125.14. EXTERNAL LINKS

125.14 External links

PCM description on MultimediaWiki
Ralph Miller and Bob Badgley invented multi-level
PCM independently in their work at Bell Labs on
SIGSALY: U.S. Patent 3,912,868 led in 1943: Nary Pulse Code Modulation.
Information about PCM: A description of PCM
with links to information about subtypes of this format (for example Linear Pulse Code Modulation),
and references to their specications.
Summary of LPCM Contains links to information
about implementations and their specications.
How to control internal/external hardware using Microsofts Media Control Interface Contains information about, and specications for the implementation of LPCM used in WAV les.
RFC 4856 Media Type Registration of Payload
Formats in the RTP Prole for Audio and Video
Conferences audio/L8 and audio/L16 (March
2007)
RFC 3190 RTP Payload Format for 12-bit DAT
Audio and 20- and 24-bit Linear Sampled Audio
(January 2002)
RFC 3551 RTP Prole for Audio and Video Conferences with Minimal Control L8 and L16 (July
2003)

539

Chapter 126

Dierential pulse-code modulation

Dierential pulse-code modulation (DPCM) is a sig- 126.2 Option 2: analysis by synthenal encoder that uses the baseline of pulse-code modusis
lation (PCM) but adds some functionalities based on the
prediction of the samples of the signal. The input can be
The incorporation of the decoder inside the encoder alan analog signal or a digital signal.
lows quantization of the dierences, including nonlinear
If the input is a continuous-time analog signal, it needs to quantization, in the encoder, as long as an approximate
be sampled rst so that a discrete-time signal is the input inverse quantizer is used appropriately in the receiver.
to the DPCM encoder.
When the quantizer is uniform, the decoder regenerates
the dierences implicitly, as in this simple diagram that
Option 1: take the values of two consecutive sam- Cutler showed:
ples; if they are analog samples, quantize them; calculate the dierence between the rst one and the
next; the output is the dierence, and it can be further entropy coded.
Option 2: instead of taking a dierence relative to a
previous input sample, take the dierence relative to
the output of a local model of the decoder process;
in this option, the dierence can be quantized, which
allows a good way to incorporate a controlled loss in
the encoding.
Applying one of these two processes, short-term redundancy (positive correlation of nearby values) of the signal is eliminated; compression ratios on the order of 2
to 4 can be achieved if dierences are subsequently entropy coded, because the entropy of the dierence signal
is much smaller than that of the original discrete signal
treated as independent samples.

126.3 See also

DPCM was invented by C. Chapin Cutler at Bell Labs in

1950; his patent includes both methods.[1]

Adaptive DPCM
Delta modulation, a special case of DPCM where
the dierences eQ[n] are represented with 1 bit as

Pulse modulation methods

Delta-sigma modulation

126.1 Option 1: dierence be- 126.4 References

tween two consecutive quan[1] U.S. patent 2605361, C. Chapin Cutler, Dierential
tized samples
Quantization of Communication Signals, led June 29,
1950, issued July 29, 1952

The encoder performs the function of dierentiation; a

quantizer precedes the dierencing of adjacent quantized
samples; the decoder is an accumulator, which if correctly initialized exactly recovers the quantized signal.
540

Chapter 127

Adaptive dierential pulse-code

modulation
Adaptive dierential pulse-code modulation 127.2 Split-band or subband AD(ADPCM) is a variant of dierential pulse-code
PCM
modulation (DPCM) that varies the size of the quantization step, to allow further reduction of the required data
G.722[4] is an ITU-T standard wideband speech codec
bandwidth for a given signal-to-noise ratio.
operating at 48, 56 and 64 kbit/s, based on subband codTypically, the adaptation to signal statistics in ADPCM
ing with two channels and ADPCM coding of each.[5]
consists simply of an adaptive scale factor before quanBefore the digitization process, it catches the analog sigtizing the dierence in the DPCM encoder.[1]
nal and divides it in frequency bands with QMF lters
ADPCM was developed in the early 1970s at Bell Labs (quadrature mirror lters) to get two subbands of the sigfor voice coding, by P. Cummiskey, N. S. Jayant and nal. When the ADPCM bitstream of each subband is
James L. Flanagan.[2]
obtained, the results are multiplexed and the next step is
storage or transmission of the data. The decoder has to
perform the reverse process, that is, demultiplex and decode each subband of the bitstream and recombine them.

audio signal
input

127.1 In telephony

High band
QMF lter
Low band

In telephony, a standard audio signal for a single phone

call is encoded as 8000 analog samples per second, of 8
bits each, giving a 64 kbit/s digital signal known as DS0.
The default signal compression encoding on a DS0 is either -law (mu-law) PCM (North America and Japan) or
A-law PCM (Europe and most of the rest of the world).
These are logarithmic compression systems where a 13 or
14 bit linear PCM sample number is mapped into an 8 bit
value. This system is described by international standard
G.711. Where circuit costs are high and loss of voice
quality is acceptable, it sometimes makes sense to compress the voice signal even further. An ADPCM algorithm is used to map a series of 8 bit -law (or a-law)
PCM samples into a series of 4 bit ADPCM samples. In
this way, the capacity of the line is doubled. The technique is detailed in the G.726 standard.
Some ADPCM techniques are used in Voice over IP
communications. ADPCM was also used by Interactive
Multimedia Association for development of legacy audio
codec known as ADPCM DVI, IMA ADPCM or DVI4,
in the early 1990s.[3]

Referring to the coding process, in some applications as

voice coding, the subband that includes the voice is coded
with more bits than the others. It is a way to reduce the
le size.

127.3 Software
The Windows Sound System supported ADPCM in .wav
les.[6] The corresponding FFmpeg audio codecs are
adpcm-ms and adpcm-ima-wav.[7]

127.4 References

541

[1] Ken C. Pohlmann (2005). Principles of Digital Audio.

McGraw-Hill Professional. ISBN 978-0-07-144156-8.

542

CHAPTER 127. ADAPTIVE DIFFERENTIAL PULSE-CODE MODULATION

[2] P. Cummiskey, N. S. Jayant, and J. L. Flanagan, Adaptive quantization in dierential PCM coding of speech,
Bell Syst. Tech. J., vol. 52, pp. 11051118, Sept. 1973.
[3] Recommended Practices for Enhancing Digital Audio
Compatibility in Multimedia Systems - legacy IMA ADPCM specication, Retrieved on 2009-07-06
[4] ITU-T G.722 page ITU-T Recommendation G.722
(11/88), 7 kHz audio-coding within 64 kbit/s
[5] Jerry D. Gibson; Toby Berger; Tom Lookabaugh (1998).
Digital Compression for Multimedia. Morgan Kaufmann.
ISBN 978-1-55860-369-1.
[6] Dierences Between PCM/ADPCM Wave Files Explained. KB 89879 Revision 3.0. Microsoft Knowledge
Base. 2011-09-24. Retrieved 2013-12-30.
[7] FFmpeg General Documentation - Audio Codecs.
FFmpeg.org. Retrieved 2013-12-30.

Chapter 128

Delta modulation
Analog signals

dierential modulation. Dierential pulse-code modulation is the superset of DM.

Reference
Limits
Output

128.1 Principle

Delta-PWM signal

-1
1

Rather than quantizing the absolute value of the input

analog waveform, delta modulation quantizes the dierence between the current and the previous step, as shown
in the block diagram in Fig. 1.

0
Time

Principle of the delta PWM. The output signal (blue) is compared

with the limits (green). The limits (green) correspond to the reference signal (red), oset by a given value. Every time the output
signal reaches one of the limits, the PWM signal changes state.

MODULATOR

CHANNEL

Quantizer
+
-

A delta modulation (DM or -modulation) is an analogto-digital and digital-to-analog signal conversion technique used for transmission of voice information where
quality is not of primary importance. DM is the simplest form of dierential pulse-code modulation (DPCM)
where the dierence between successive samples are encoded into n-bit data streams. In delta modulation, the
transmitted data are reduced to a 1-bit data stream. Its
main features are:

DEMODULATOR
Integrator
Low pass

Filter

Integrator

Fig. 1 Block diagram of a -modulator/demodulator

The modulator is made by a quantizer which converts the

dierence between the input signal and the average of
the previous steps. In its simplest form, the quantizer can
be realized with a comparator referenced to 0 (two levels
quantizer), whose output is 1 or 0 if the input signal is
The analog signal is approximated with a series of positive or negative. It is also a bit-quantizer as it quansegments.
tizes only a bit at a time. The demodulator is simply an
integrator (like the one in the feedback loop) whose out Each segment of the approximated signal is com- put rises or falls with each 1 or 0 received. The integrator
pared of successive bits is determined by this com- itself constitutes a low-pass lter.
parison.

Only the change of information is sent, that is, only

an increase or decrease of the signal amplitude from 128.2 Transfer characteristics
the previous sample is sent whereas a no-change
condition causes the modulated signal to remain at The transfer characteristics of a delta modulated system
the same 0 or 1 state of the previous sample.
follows a signum function, as it quantizes only two levels
and also one-bit at a time.
To achieve high signal-to-noise ratio, delta modulation The two sources of noise in delta modulation are slope
must use oversampling techniques, that is, the analog sig- overload, when step size is too small to track the original
nal is sampled at a rate several times higher than the waveform, and granularity, when step size is too large.
Nyquist rate.
But a 1971 study shows that slope overload is less objecDerived forms of delta modulation are continuously vari- tionable compared to granularity than one might expect
able slope delta modulation, delta-sigma modulation, and based solely on SNR measures.[1]
543

544

CHAPTER 128. DELTA MODULATION

128.3 Output signal power

128.6 Applications

Contemporary applications of Delta Modulation includes, but is not limited to, recreating legacy synthesizer
waveforms. With the increasing availability of FPGAs
and game-related ASICs, sample rates are easily controlled so as to avoid slope overload and granularity issues. For example, the C64DTV used a 32 MHz sample
m(t) = A cos(t) ,
rate, providing ample dynamic range to recreate the SID
the modulated signal (derivative of the input signal) which output to acceptable levels.[3]
is transmitted by the modulator is
In delta modulation there is a restriction on the amplitude
of the input signal, because if the transmitted signal has a
large derivative (abrupt changes) then the modulated signal can not follow the input signal and slope overload occurs. E.g. if the input signal is

|m(t)|

max = A ,
whereas the condition to avoid slope overload is
|m(t)|

max = A < fs .
So the maximum amplitude of the input signal can be
Amax =

fs

where f is the sampling frequency and is the frequency

of the input signal and is step size in quantization. So
A is the maximum amplitude that DM can transmit
without causing the slope overload and the power of transmitted signal depends on the maximum amplitude.

128.4 Bit-rate
If the communication channel is of limited bandwidth,
there is the possibility of interference in either DM or
PCM. Hence, 'DM' and 'PCM' operate at same bit-rate
which is equal to N times the sampling frequency.

128.7 SBS Application 24 kbps

delta modulation
Delta Modulation was used by Satellite Business Systems
or SBS for its voice ports to provide long distance phone
service to large domestic corporations with a signicant
inter-corporation communications need (such as IBM).
This system was in service throughout the 1980s. The
voice ports used digitally implemented 24 kbit/s delta
modulation with Voice Activity Compression (VAC)
and echo suppressors to control the half second echo path
through the satellite. They performed formal listening
tests to verify the 24 kbit/s delta modulator achieved
full voice quality with no discernible degradation as
compared to a high quality phone line or the standard 64
kbit/s -law companded PCM. This provided an eight to
three improvement in satellite channel capacity. IBM developed the Satellite Communications Controller and the
voice port functions.

The original proposal in 1974, used a state-of-the-art

24 kbit/s delta modulator with a single integrator and a
Shindler Compander modied for gain error recovery.
128.5 Adaptive delta modulation
This proved to have less than full phone line speech quality. In 1977, one engineer with two assistants in the IBM
Adaptive delta modulation (ADM) was rst published Research Triangle Park, NC laboratory was assigned to
by Dr. John E. Abate (AT&T Bell Laboratories Fel- improve the quality.
low) in his doctorial thesis at NJ Institute Of Technol- The nal implementation replaced the integrator with a
ogy in 1968. ADM was later selected as the standard for
Predictor implemented with a two pole complex pair
all NASA communications between mission control and low-pass lter designed to approximate the long term avspace-craft.
erage speech spectrum. The theory was that ideally the
Adaptive delta modulation or [continuously variable slope integrator should be a predictor designed to match the
delta modulation] (CVSD) is a modication of DM in signal spectrum. A nearly perfect Shindler Compander
which the step size is not xed. Rather, when several con- replaced the modied version. It was found the modied
secutive bits have the same direction value, the encoder compander resulted in a less than perfect step size at most
and decoder assume that slope overload is occurring, and signal levels and the fast gain error recovery increased the
the step size becomes progressively larger.
noise as determined by actual listening tests as compared
Otherwise, the step size becomes gradually smaller over to simple signal to noise measurements. The nal comtime. ADM reduces slope error, at the expense of in- pander achieved a very mild gain error recovery due to
creasing quantizing error.This error can be reduced by us- the natural truncation rounding error caused by twelve bit
ing a low-pass lter. ADM provides robust performance arithmetic.
in the presence of bit errors meaning error detection and
correction are not typically used in an ADM radio design,
this allows for a reduction in host processor workload (allowing a low-cost processor to be used).[2]

The complete function of delta modulation, VAC and

Echo Control for six ports was implemented in a single
digital integrated circuit chip with twelve bit arithmetic.
A single digital-to-analog converter (DAC) was shared by

128.10. EXTERNAL LINKS

all six ports providing voltage compare functions for the
modulators and feeding sample and hold circuits for the
demodulator outputs. A single card held the chip, DAC
and all the analog circuits for the phone line interface including transformers.

128.8 See also

Adaptive dierential pulse-code modulation
Analog-to-digital converter (ADC)
Codec
Pulse-code modulation
Pulse-density modulation
Delta-sigma modulation
Direct Stream Digital

128.9 Sources
Steele, R. (1975). Delta Modulation Systems. London: Pentech Press. ISBN 0-470-82104-3.
This article incorporates public domain material
from the General Services Administration document
Federal Standard 1037C (in support of MIL-STD188).
[1] N. S. Jayant and A. E. Rosenberg. The Preference of Slope Overload to Granularity in the Delta
Modulation of Speech.
The Bell System Technical Journal, Volume 50, no. 10, December 1971.
[url=http://bstj.bell-labs.com/BSTJ/images/Vol50/
bstj50-10-3117.pdf]PDF[/url]; [url=http://web.archive.
org/web/20110707222831/http://bstj.bell-labs.com/
BSTJ/images/Vol50/bstj50-10-3117.pdf]Google cached
HTML version</a>)
[2] http://www.cmlmicro.com/
adm-adaptive-delta-modulation/
[3] Olsen, Mikkel Holm. 2011 November 16. Accessed 2013
June 29. http://symlink.dk/nostalgia/dtv/dtvsid/

128.10 External links

Delta Modulator

545

Chapter 129

Delta-sigma modulation
Sigma delta redirects here. For the sorority, see Sigma sigma modulator directly on a disk.
Delta.
Delta-sigma (; or sigma-delta, ) modulation is a
method for encoding analog signals into digital signals as 129.1 Motivation
found in an analog-to-digital converter (ADC). It is also
used to transfer high bit-count low frequency digital signals into lower bit-count higher frequency digital signals 129.1.1 Why convert an analog signal into
a stream of pulses?
as part of the process to convert digital signals into analog
as part of a digital-to-analog converter (DAC).
In a conventional ADC, an analog signal is integrated, In brief, because it is very easy to regenerate pulses at the
or sampled, with a sampling frequency and subsequently receiver into the ideal form transmitted. The only part of
quantized in a multi-level quantizer into a digital signal. the transmitted waveform required at the receiver is the
This process introduces quantization error noise. The rst time at which the pulse occurred. Given the timing instep in a delta-sigma modulation is delta modulation. In formation the transmitted waveform can be reconstructed
delta modulation the change in the signal (its delta) is electronically with great precision. In contrast, without
encoded, rather than the absolute value. The result is a conversion to a pulse stream but simply transmitting the
stream of pulses, as opposed to a stream of numbers as is analog signal directly, all noise in the system is added to
the case with PCM. In delta-sigma modulation, the accu- the analog signal, permanently reducing its quality.
racy of the modulation is improved by passing the digital
output through a 1-bit DAC and adding (sigma) the resulting analog signal to the input signal, thereby reducing
the error introduced by the delta-modulation.

Each pulse is made up of a step up followed after a short

interval by a step down. It is possible, even in the presence
of electronic noise, to recover the timing of these steps
and from that regenerate the transmitted pulse stream alPrimarily because of its cost eciency and reduced cir- most noiselessly. Then the accuracy of the transmission
cuit complexity, this technique has found increasing use process reduces to the accuracy with which the transmitin modern electronic components such as DACs, ADCs, ted pulse stream represents the input waveform.
frequency synthesizers, switched-mode power supplies
and motor controllers.[1]
Both ADCs and DACs can employ delta-sigma modulation. A delta-sigma ADC rst encodes an analog signal using high-frequency delta-sigma modulation, and
then applies a digital lter to form a higher-resolution
but lower sample-frequency digital output. On the other
hand, a delta-sigma DAC encodes a high-resolution digital input signal into a lower-resolution but higher samplefrequency signal that is mapped to voltages, and then
smoothed with an analog lter. In both cases, the temporary use of a lower-resolution signal simplies circuit
design and improves eciency.
The coarsely-quantized output of a delta-sigma modulator is occasionally used directly in signal processing or
as a representation for signal storage. For example, the
Super Audio CD (SACD) stores the output of a delta-

129.1.2 Why delta-sigma modulation?

Delta-sigma modulation converts the analog voltage into a
pulse frequency and is alternatively known as Pulse Density modulation or Pulse Frequency modulation. In general, frequency may vary smoothly in innitesimal steps,
as may voltage, and both may serve as an analog of an
innitesimally varying physical variable such as acoustic pressure, light intensity, etc. The substitution of frequency for voltage is thus entirely natural and carries in
its train the transmission advantages of a pulse stream.
The dierent names for the modulation method are the
result of pulse frequency modulation by dierent electronic implementations, which all produce similar transmitted waveforms.

546

129.2. ANALOG TO DIGITAL CONVERSION

129.1.3

547

Why the delta-sigma analog to digital conversion?

Integrator
1

+-

Counter

Threshold
4

Buer

Impulse

The ADC converts the mean of an analog voltage into the

mean of an analog pulse frequency and counts the pulses
in a known interval so that the pulse count divided by
the interval gives an accurate digital representation of the
mean analog voltage during the interval. This interval can
be chosen to give any desired resolution or accuracy. The
method is cheaply produced by modern methods; and it
is widely used.

2
Summing
Interval

Fig. 1 - Block Diagram Sigma Delta ADC

INPUT

1 = 0.2V

INPUT

1 = 0.4V

0V

0V

1V
2

1V
IMPULSE

IMPULSE

0V

0V
0.4V

0.2V

3
SUM

SUM
- 0.8V

- 0.6V
0V THRESHOLD

0V THRESHOLD
4

INTEGRAL

INTEGRAL

129.2 Analog to digital conversion

5

TRIGGER

129.2.1

Description

TRIGGER

0V THRESHOLD

0V THRESHOLD

INTEGRAL

INTEGRAL

The ADC generates a pulse stream in which the frequency, f , of pulses in the stream is proportional to the
analog voltage input, v , so that f = k v , where k is a
constant for the particular implementation.
A counter sums the number of pulses that occur in a predetermined period, P so that the sum, , is P f =
kP v.
k P is chosen so that a digital display of the count,
, is a display of v with a predetermined scaling factor.
Because P may take any designed value it may be made
large enough to give any desired resolution or accuracy.
Each pulse of the pulse stream has a known, constant
amplitude V and duration d t , and thus has a known
integral V d t but variable separating interval.

Typical Waveforms

Fig. 1: Block diagram and waveforms for a sigma delta ADC.

0V threshold

Integral when impulse occurs at threshold crossing

0V threshold

Integral when impulse occurs at next clock after threshold crossing

clock
Fig. 1a Eect of clocking impulses

In a formal analysis an impulse such as integral V d t is

treated as the Dirac (delta) function and is specied by
the step produced
on integration. Here we indicate that

step as = V d t .
The interval between pulses, p, is determined by a feed1
back loop arranged so that p = f1 = kv
.
The action of the feedback loop is to monitor the integral
of v and when that integral has incremented by , which
is indicated by the integral waveform crossing a threshold,
then subtracting from the integral of v so that the combined waveform sawtooths between the threshold and (
threshold - ). At each step a pulse is added to the pulse
stream.
Between impulses, the slope of the integral is proportional
to v , that is, for some A it equals A v =
p =f =
k v . Whence A = k .
It is the pulse stream which is transmitted for delta-sigma
modulation but the pulses are counted to form sigma in
the case of analogue to digital conversion.

Fig. 1a: Eect of clocking impulses

129.2.2 Analysis
Shown below the block diagram illustrated in Fig. 1 are
waveforms at points designated by numbers 1 to 5 for an
input of 0.2 volts on the left and 0.4 volts on the right.
In most practical applications the summing interval is
large compared with the impulse duration and for signals which are a signicant fraction of full scale the variable separating interval is also small compared with the
summing interval. The NyquistShannon sampling theorem requires two samples to render a varying input signal.
The samples appropriate to this criterion are two successive counts taken in two successive summing intervals.
The summing interval, which must accommodate a large

548
count in order to achieve adequate precision, is inevitably
long so that the converter can only render relatively low
frequencies. Hence it is convenient and fair to represent
the input voltage (1) as constant over a few impulses.
Consider rst the closed feedback loop consisting of the
analogue adder/subtracter, the integrator, the threshold
crossing detector and the impulse generator.
On the left 1 is the input and for this short interval is constant at 0.2 V. The stream of delta impulses generated
at each threshold crossing is shown at 2 and the dierence between 1 and 2 is shown at 3. This dierence is
integrated to produce the waveform 4. The threshold detector generates a pulse 5 which starts as the waveform 4
crosses the threshold and is sustained until the waveform
4 falls below the threshold. Within the loop 5 triggers the
impulse generator to produce a xed strength impulse.
On the right the input is now 0.4 V and the sum during
the impulse is 0.6 V as opposed to 0.8 V on the left.
Thus the negative slope during the impulse is lower on the
right than on the left.
Also the sum is 0.4 V on the right during the interval as
opposed to 0.2 V on the left. Thus the positive slope outside the impulse is higher on the right than on the left.
The resultant eect is that the integral (4) crosses the
threshold more quickly on the right than on the left. A
full analysis would show that in fact the interval between
threshold crossings on the right is half that on the left.
Thus the frequency of impulses is doubled. Hence the
count increments at twice the speed on the right to that
on the left which is consistent with the input voltage being
doubled.The overall eect of the negative feedback loop
is to maintain the running integral of the impulse train
equal to within one impulse to the running integral of the
input analogue signal. Also the frequency of the impulse
train is proportional to the bandwidth limited amplitude
of the input signal.Bandwidth limitation occurs because
the NyquistShannon sampling theorem requires 2 impulses per period to dene the highest frequency passed.

CHAPTER 129. DELTA-SIGMA MODULATION

summing interval to be dened by the same clock with a
suitable arrangement of logic and counters. This has the
advantage that neither interval has to be dened with absolute precision as only the ratio is important. Then to
achieve overall accuracy it is only necessary that the amplitude of the impulse be accurately dened. As stated,
Fig. 1 is a simplied block diagram of the delta-sigma
ADC in which the various functional elements have been
separated out for individual treatment and which tries to
be independent of any particular implementation. Many
particular implementations seek to dene the impulse duration and the summing interval from the same clock as
discussed above but in such a way that the start of the impulse is delayed until the next occurrence of the appropriate clock pulse boundary. The eect of this delay is illustrated in Fig. 1a for a sequence of impulses which occur
at a nominal 2.5 clock intervals, rstly for impulses generated immediately the threshold is crossed as previously
discussed and secondly for impulses delayed by the clock.
The eect of the delay is rstly that the ramp continues
until the onset of the impulse, secondly that the impulse
produces a xed amplitude step so that the integral retains the excess it acquired during the impulse delay and
so the ramp restarts from a higher point and is now on
the same locus as the free running integral. The eect is
that, for this example, the undelayed impulses will occur
at clock points 0, 2.5, 5, 7.5, 10, etc. and the clocked impulses will occur at 0, 3, 5, 8, 10, etc. The maximum
error that can occur due to clocking is marginally less
than one count. Although the Sigma-Delta converter is
generally implemented using a common clock to dene
the impulse duration and the summing interval it is not
absolutely necessary and an implementation in which the
durations are independently dened avoids one source of
noise, the noise generated by waiting for the next common
clock boundary. Where noise is a primary consideration
that overrides the need for absolute amplitude accuracy;
e.g., in bandwidth limited signal transmission, separately
dened intervals may be implemented.

Construction of the waveforms illustrated at (4) is aided 129.2.3 Practical Implementation

by concepts associated with the Dirac delta function in
that all impulses of the same strength produce the same
step when integrated, by denition. Then (4) is con_
_
V
V
structed using an intermediate step (6) in which each inR
impulse
scrap view
tegrated impulse is represented by a step of the assigned
Alternate
(b)
front end
R integrator
R
strength which decays to zero at the rate determined by
C
(c)
(d)
the input voltage. The eect of the nite duration of the
R
R
threshold
V
_
V
in
in
_
impulse is constructed in (4) by drawing a line from the
(a)
+
D Q (f)
(e)
+
base of the impulse step at zero volts to intersect the de_
(g)
Q
cay line from (6) at the full duration of the impulse.
sigma
ref

ref

gate

clock

Now consider the circuit outside the loop. The summing

interval is a prexed time and at its expiry the count is
strobed into the buer and the counter reset. It is necesFig. 1b - Circuit Diagram
sary that the ratio between the impulse interval and the
summing interval is equal to the maximum (full scale)
count. It is then possible for the impulse duration and the Fig. 1b: circuit diagram

summing
interval
counter

count

_
+

buer

129.2. ANALOG TO DIGITAL CONVERSION

549
(b) The impulse waveform. It will be discovered how this
acquires its form as we traverse the feedback loop.

clock

Vin

(a)

1.0V = + Vref
0.4V
0.0V
0.0V

(b)
impulse
-Vref
1.0V
0.4V
(c)

0.0V

R * Ic
-0.6V

-Vref
(d)
integral

0.0V threshold level

(e)
comparator

(f)

Q
negated clock

(c) The current into the capacitor, I , is the linear sum

of the impulse voltage upon R and V upon R. To show
this sum as a voltage the product R I is plotted. The
input impedance of the amplier is regarded as so high
that the current drawn by the input is neglected.The capacitor is connected between the negative input terminal
of the amplier and its output terminal. With this connection it provides a negative feedback path around the
amplier. The input voltage change is equal to the output
voltage change divided by the amplier gain. With very
high amplier gain the change in input voltage can be neglected and so the input voltage is held close to the voltage
on the positive input terminal which in this case is held
at 0V. Because the voltage at the input terminal is 0V the
voltage across R is simply V so that the current into the
capacitor is the input voltage divided by the resistance of
R.

(g)

countstream

Fig. 1c - ADC waveforms

Fig. 1c: ADC waveforms

A circuit diagram for a practical implementation is illustrated, Fig 1b and the associated waveforms Fig. 1c. This
circuit diagram is mainly for illustration purposes, details
of particular manufacturers implementations will usually
be available from the particular manufacturer. A scrap
view of an alternative front end is shown in Fig. 1b which
has the advantage that the voltage at the switch terminals
are relatively constant and close to 0.0 V. Also the current generated through R by V is constant at V /R
so that much less noise is radiated to adjacent parts of
the circuit. Then this would be the preferred front end
in practice but, in order to show the impulse as a voltage
pulse so as to be consistent with previous discussion, the
front end given here, which is an electrical equivalent, is
used.
The waveforms shown in Fig 1c are unusually complex
because they are intended to illustrate the loop behaviour
under extreme conditions,V saturated on at full scale,
1.0V, and saturated o at zero. The intermediate state
is also indicated,V at 0.4V, and is the usual operating
condition between 0 and 1.0v where it is very similar to
the operation of the illustrative block diagram, Fig 1.
From the top of Fig 1c the waveforms, labelled as they
are on the circuit diagram, are:The clock.
(a) V . This is shown as varying from 0.4 V initially to
1.0 V and then to zero volts to show the eect on the
feedback loop.

(d) The negated integral of I . This negation is standard

for the op. amp. implementation of an integrator and
comes about because the current into the capacitor at the
amplier input is the current out of the capacitor at the
amplier output and the voltage is the integral of the current divided by the capacitance of C.
(e) The comparator output. The comparator is a very high
gain amplier with its plus input terminal connected for
reference to 0.0 V. Whenever the negative input terminal is taken negative with respect the positive terminal of
the amplier the output saturates positive and conversely
negative saturation for positive input. Thus the output saturates positive whenever the integral (d) goes below the 0
V reference level and remains there until (d) goes positive
with respect to the reference level.
(f) The impulse timer is a D type positive edge triggered
ip op. Input information applied at D is transferred
to Q on the occurrence of the positive edge of the clock
pulse. thus when the comparator output (e) is positive Q
goes positive or remains positive at the next positive clock
edge. Similarly, when (e) is negative Q goes negative at
the next positive clock edge. Q controls the electronic
switch to generate the current impulse into the integrator. Examination of the waveform (e) during the initial
period illustrated, when V is 0.4 V, shows (e) crossing the threshold well before the trigger edge (positive
edge of the clock pulse) so that there is an appreciable
delay before the impulse starts. After the start of the impulse there is further delay while (e) climbs back past the
threshold. During this time the comparator output remains high but goes low before the next trigger edge. At
that next trigger edge the impulse timer goes low to follow the comparator. Thus the clock determines the duration of the impulse. For the next impulse the threshold is crossed immediately before the trigger edge and so
the comparator is only briey positive. V (a) goes to
full scale, +V , shortly before the end of the next im-

550
pulse. For the remainder of that impulse the capacitor
current (c) goes to zero and hence the integrator slope
briey goes to zero. Following this impulse the full scale
positive current is owing (c) and the integrator sinks at
its maximum rate and so crosses the threshold well before
the next trigger edge. At that edge the impulse starts and
the Vin current is now matched by the reference current
so that the net capacitor current (c) is zero. Then the integration now has zero slope and remains at the negative
value it had at the start of the impulse. This has the eect
that the impulse current remains switched on because Q
is stuck positive because the comparator is stuck positive
at every trigger edge. This is consistent with contiguous,
butting impulses which is required at full scale input.

CHAPTER 129. DELTA-SIGMA MODULATION

assertion consider this.
It is well known that by Fourier analysis techniques the incoming waveform can be represented over the summing
interval by the sum of a constant plus a fundamental and
harmonics each of which has an exact integer number of
cycles over the sampling period. It is also well known
that the integral of a sine wave or cosine wave over one
or more full cycles is zero. Then the integral of the incoming waveform over the summing interval reduces to
the integral of the constant and when that integral is divided by the summing interval it becomes the mean over
that interval. The interval between pulses is proportional
to the inverse of the mean of the input voltage during that
interval and thus over that interval, ts, is a sample of the
mean of the input voltage proportional to V/ts. Thus the
average of the input voltage over the summing period is
V/N and is the mean of means and so subject to little
variance.

Eventually Vin (a) goes to zero which means that the current sum (c) goes fully negative and the integral ramps
up. It shortly thereafter crosses the threshold and this in
turn is followed by Q, thus switching the impulse current
o. The capacitor current (c) is now zero and so the in- Unfortunately the analysis for the transmitted pulse
tegral slope is zero, remaining constant at the value it had stream has, in many cases, been carried over, uncritically,
acquired at the end of the impulse.
to the ADC.
(g) The countstream is generated by gating the negated
It was indicated in section 2.2 Analysis that the eect of
clock with Q to produce this waveform. Thereafter constraining a pulse to only occur on clock boundaries
the summing interval, sigma count and buered count
is to introduce noise, that generated by waiting for the
are produced using appropriate counters and regis- next clock boundary. This will have its most deleterious
ters. The V waveform is approximated by passing the
eect on the high frequency components of a complex
countstream (g) into a low pass lter, however it suers signal. Whilst the case has been made for clocking in the
from the defect discussed in the context of Fig. 1a. One
ADC environment, where it removes one source of error,
possibility for reducing this error is to halve the feed- namely the ratio between the impulse duration and the
back pulse length to half a clock period and double its summing interval, it is deeply unclear what useful purpose
amplitude by halving the impulse dening resistor thus clocking serves in a single channel transmission environproducing an impulse of the same strength but one which ment since it is a source of both noise and complexity but
never butts onto its adjacent impulses. Then there will be it is conceivable that it would be useful in a TDM (time
a threshold crossing for every impulse. In this arrange- division multiplex) environment.
ment a monostable ip op triggered by the comparator
at the threshold crossing will closely follow the threshold A very accurate transmission system with constant samcrossings and thus eliminate one source of error, both in pling rate may be formed using the full arrangement
shown here by transmitting the samples from the buer
the ADC and the sigma delta modulator.
protected with redundancy error correction. In this case
there will be a trade o between bandwidth and N, the
129.2.4 Remarks
size of the buer. The signal recovery system will require redundancy error checking, digital to analog conIn this section we have mainly dealt with the analogue to version, and sample and hold circuitry. A possible further
digital converter as a stand-alone function which achieves enhancement is to include some form of slope regeneraastonishing accuracy with what is now a very simple and tion. This amounts to PCM (pulse code modulation) with
cheap architecture. Initially the Delta-Sigma congura- digitization performed by a sigma-delta ADC.
tion was devised by INOSE et al. to solve problems in
The above description shows why the impulse is called
the accurate transmission of analog signals. In that applidelta. The integral of an impulse is a step. A one bit
cation it was the pulse stream that was transmitted and the
DAC may be expected to produce a step and so must be
original analog signal recovered with a low pass lter afa conation of an impulse and an integration. The analyter the received pulses had been reformed. This low pass
sis which treats the impulse as the output of a 1-bit DAC
lter performed the summation function associated with
hides the structure behind the name (sigma delta) and
. The highly mathematical treatment of transmission ercause confusion and diculty interpreting the name as an
rors was introduced by them and is appropriate when apindication of function. This analysis is very widespread
plied to the pulse stream but these errors are lost in the
but is deprecated.
accumulation process associated with to be replaced
with the errors associated with the mean of means when A modern alternative method for generating voltage to
discussing the ADC. For those uncomfortable with this frequency conversion is discussed in synchronous voltage

129.4. RELATIONSHIP TO -MODULATION

551

to frequency converter (SVFC) which may be followed by

a counter to produce a digital representation in a similar
manner to that described above.[2]

129.3 Digital to analog conversion

129.3.1

Discussion

Delta-sigma modulators are often used in digital to analog

converters (DACs). In general, a DAC converts a digital
number representing some analog value into that analog
value. For example, the analog voltage level into a speaker
may be represented as a 20 bit digital number, and the
DAC converts that number into the desired voltage. To
actually drive a load (like a speaker) a DAC is usually Fig. 2: Derivation of - from -modulation
connected to or integrated with an electronic amplier.
This can be done using a delta-sigma modulator in a Class
which reconstructs the analog signal in the demoduD Amplier. In this case, a multi-bit digital number is
lator section, in front of the -modulator.
input to the delta-sigma modulator, which converts it into
3. Again, the linearity property of the integration ala faster sequence of 0s and 1s. These 0s and 1s are then
lows the two integrators to be combined and a converted into analog voltages. The conversion, usually
modulator/demodulator block diagram is obtained.
with MOSFET drivers, is very ecient in terms of power
because the drivers are usually either fully on or fully o,
However, the quantizer is not homogeneous, and so this
and in these states have low power loss.
explanation is awed. Its true that is inspired by The resulting two-level signal is now like the desired sigmodulation, but the two are distinct in operation. From
nal, but with higher frequency components to change the
the rst block diagram in Fig. 2, the integrator in the
signal so that it only has two levels. These added frefeedback path can be removed if the feedback is taken
quency components arise from the quantization error of
directly from the input of the low-pass lter. Hence, for
the delta-sigma modulator, but can be ltered away by a
delta modulation of input signal u , the low-pass lter sees
simple low-pass lter. The result is a reproduction of the
the signal
original, desired analog signal from the digital values.
The circuit itself is relatively inexpensive. The digital cir
cuit is small, and the MOSFETs used for the power amy = Quantize (u yDM ) .
plication are simple. This is in contrast to a multi-bit DM
DAC which can have very stringent design conditions to
precisely represent digital values with a large number of However, sigma-delta modulation of the same input signal places at the low-pass lter
bits.
The use of a delta-sigma modulator in the digital to analog
(
)
conversion has enabled a cost-eective, low power, and
y
=
Quantize
(u

y
)
.
SDM
SDM
high performance solution.
In other words, SDM and DM swap the position of the in129.4 Relationship
to
- tegrator and quantizer. The net eect is a simpler implementation that has the added benet of shaping the quanmodulation
tization noise away from signals of interest (i.e., signals
of interest are low-pass ltered while quantization noise
modulation (SDM) is inspired by modulation (DM), is high-pass ltered). This eect becomes more dramatic
as shown in Fig. 2. If quantization were homogeneous with increased oversampling, which allows for quantiza(e.g., if it were linear), the following would be a sucient tion noise to be somewhat programmable. On the other
hand, -modulation shapes both noise and signal equally.
derivation of the equivalence of DM and SDM:
Additionally, the quantizer (e.g., comparator) used in DM
has a small output representing a small step up and down
the quantized approximation of the input while the quan

2. The linearity property of integration ( a + b = tizer used in SDM must take values outside of the range

(a + b) ) makes it possible to move the integrator, of the input signal, as shown in Fig. 3.
1. Start with a block
modulator/demodulator.

diagram

of

552

CHAPTER 129. DELTA-SIGMA MODULATION

Integrator
+

Fig. 3: An example of SDM of 100 samples of one period a

sine wave. 1-bit samples (e.g., comparator output) overlaid with
sine wave where logic high (e.g., +VCC ) represented by blue and
logic low (e.g., VCC ) represented by white.

Integrator Quantizer
+

Digital
Filter

1-Bit DAC

Fig. 4: Block diagram of a 2nd order modulator

In general, has some advantages versus modulation: 129.6.2

3-level and higher quantizer

The modulator can also be classied by the number of

bits it has in output, which strictly depends on the out Only one integrator is needed
put of the quantizer. The quantizer can be realized with
The demodulator can be a simple linear lter a N-level comparator, thus the modulator has log2 N-bit
(e.g., RC or LC lter) to reconstruct the signal output. A simple comparator has 2 levels and so is 1 bit
quantizer; a 3-level quantizer is called a 1.5 bit quan The quantizer (e.g., comparator) can have fulltizer; a 4-level quantizer is a 2 bit quantizer; a 5-level
scale outputs
quantizer is called a 2.5 bit quantizer.[4]
The quantized value is the integral of the dierence
signal, which makes it less sensitive to the rate of
129.6.3 Decimation structures
change of the signal.
The whole structure is simpler:

129.5 Principle
The principle of the architecture is explained at length
in section 2. Initially, when a sequence starts, the circuit
will have an arbitrary state which is dependent on the integral of all previous history. In mathematical terms this
corresponds to the arbitrary integration constant of the
indenite integral. This follows from the fact that at the
heart of the method there is an integrator which can have
any arbitrary state dependent on previous input, see Fig.
1c (d). From the occurrence of the rst pulse onward the
frequency of the pulse stream is proportional to the input voltage to be transformed. A demonstration applet is
available online to simulate the whole architecture.[3]

129.6 Variations

The conceptually simplest decimation structure is a

counter that is reset to zero at the beginning of each integration period, then read out at the end of the integration
period.
The multi-stage noise shaping (MASH) structure has a
noise shaping property, and is commonly used in digital
audio and fractional-N frequency synthesizers. It comprises two or more cascaded overowing accumulators,
each of which is equivalent to a rst-order sigma delta
modulator. The carry outputs are combined through summations and delays to produce a binary output, the width
of which depends on the number of stages (order) of
the MASH. Besides its noise shaping function, it has two
more attractive properties:
simple to implement in hardware; only common digital blocks such as accumulators, adders, and D ipops are required
unconditionally stable (there are no feedback loops
outside the accumulators)

There are many kinds of ADC that use this delta-sigma

structure. The above analysis focuses on the simplest
A very popular decimation structure is the sinc lter.
1st-order, 2-level, uniform-decimation sigma-delta ADC.
For 2nd order modulators, the sinc3 lter is close to
Many ADCs use a second-order 5-level sinc3 sigma-delta
optimum.[5][6]
structure.

129.6.1

2nd order and higher order modu- 129.7

lator

The number of integrators, and consequently, the numbers of feedback loops, indicates the order of a modulator; a 2nd order modulator is shown in Fig. 4.
First order modulators are unconditionally stable, but stability analysis must be performed for higher order modulators.

Quantization theory formulas

Main article: Quantization (signal processing)

When a signal is quantized, the resulting signal approximately has the second-order statistics of a signal with independent additive white noise. Assuming that the signal

129.9. NAMING

553

value is in the range of one step of the quantized value where it can be ltered. This technique is known as noise
with an equal distribution, the root mean square value of shaping.
this quantization noise is
For a rst order delta sigma modulator, the noise is shaped
by a lter with transfer function Hn (z) = [1z1 ] . As
suming that the sampling frequency fs f0 , the quanti1 +/2 2

zation noise in the desired signal bandwidth can be aperms =

e de =
proximated as:
/2
2 3
3

n = erms 3 (2f0 ) 2 .
In reality, the quantization noise is of course not indepen- 0
dent of the signal; this dependence is the source of idle Similarly for a second order delta sigma modulator, the
tones and pattern noise in Sigma-Delta converters.
noise is shaped by a lter with transfer function Hn (z) =
1 2
The over-sampling ratio (OSR), where fs is the sampling [1z ] . The in-band quantization noise can be approximated as:
frequency and 2f is Nyquist rate, is dened by
0

n0 = erms
(2f0 ) 2 .
5

OSR =

In general, for a N -order -modulator, the variance of

the in-band quantization noise:

fs
1
=
2f0
2f0

2N +1

n0 = erms 2N
(2f0 ) 2 .
+1
The RMS noise voltage within the band of interest can be
When the sampling frequency is doubled, the signal to
expressed in terms of OSR
quantization noise is improved by 10 log(22N +1 ) dB for a N
-order -modulator. The higher the oversampling raerms
tio, the higher the signal-to-noise ratio and the higher the
n0 =
OSR
resolution in bits.

Another key aspect given by oversampling is the

speed/resolution tradeo. In fact, the decimation lter
put after the modulator not only lters the whole sampled signal in the band of interest (cutting the noise at
higher frequencies), but also reduces the frequency of the
signal increasing its resolution. This is obtained by a sort
of averaging of the higher data rate bitstream.

129.8 Oversampling

129.8.1 Example of decimation

f0

fS

Lets have, for instance, an 8:1 decimation lter and a 1bit bitstream; if we have an input stream like 10010110,
counting the number of ones, we get 4. Then the decimation result is 4/8 = 0.5. We can then represent it with
a 3-bits number 100 (binary), which means half of the
largest possible number. In other words,

Fig. 5: Noise shaping curves and noise spectrum in modulator

the sample frequency is reduced by a factor of eight

Main article: Oversampling

the serial (1-bit) input bus becomes a parallel (3bits) output bus.

Lets consider a signal at frequency f0 and a sampling frequency of fs much higher than Nyquist rate (see g. 5).
modulation is based on the technique of oversampling
to reduce the noise in the band of interest (green), which
also avoids the use of high-precision analog circuits for
the anti-aliasing lter. The quantization noise is the same
both in a Nyquist converter (in yellow) and in an oversampling converter (in blue), but it is distributed over a larger
spectrum. In -converters, noise is further reduced at
low frequencies, which is the band where the signal of
interest is, and it is increased at the higher frequencies,

129.9 Naming
The technique was rst presented in the early 1960s by
professor Haruhiko Yasuda while he was a student at
Waseda University, Tokyo, Japan. The name DeltaSigma comes directly from the presence of a Delta modulator and an integrator, as rstly introduced by Inose et
al. in their patent application.[7] That is, the name comes
from integrating or "summing" dierences, which are

554
operations usually associated with Greek letters Sigma
and Delta respectively. Both names Sigma-Delta and
Delta-Sigma are frequently used.

129.10 See also

Pulse-density modulation
Pulse-width modulation

129.11 References
[1] http://www.numerix-dsp.com/appsnotes/
APR8-sigma-delta.pdf

CHAPTER 129. DELTA-SIGMA MODULATION

129.12 External links

1-bit A/D and D/A Converters
Sigma-delta techniques extend DAC resolution article by Tim Wescott 2004-06-23
Tutorial on Designing Delta-Sigma Modulators:
Part I and Part II by Mingliang (Michael) Liu
Gabor Temes Publications
Simple Sigma Delta Modulator example Contains
Block-diagrams, code, and simple explanations
Example Simulink model & scripts for continuoustime sigma-delta ADC Contains example matlab
code and Simulink model
Bruce Wooleys Delta-Sigma Converter Projects

[2] Voltage-to-Frequency Converters by Walt Kester and

James Bryant 2009. Analog Devices.

An Introduction to Delta Sigma Converters (which

covers both ADCs and DACs sigma-delta)

[3] Analog Devices : Virtual Design Center : Interactive Design Tools : Sigma-Delta ADC Tutorial

Demystifying Sigma-Delta ADCs. This in-depth article covers the theory behind a Delta-Sigma analogto-digital converter.

[4] Sigma-delta class-D amplier and control method for a

sigma-delta class-D amplier by Jwin-Yen Guo and TengHung Chang

Motorola digital signal processors: Principles of

sigma-delta modulation for analog-to-digital converters

[5] A Novel Architecture for DAQ in Multi-channel, Large

Volume, Long Drift Liquid Argon TPC by S. Centro, G.
Meng, F. Pietropaola, S. Ventura 2006

One-Bit Delta Sigma D/A Conversion Part I: Theory article by Randy Yates presented at the 2004
comp.dsp conference

[6] A Low Power Sinc3 Filter for Modulators by A. Lombardi, E. Bonizzoni, P. Malcovati, F. Maloberti 2007

MASH (Multi-stAge noise SHaping) structure with

both theory and a block-level implementation of a
MASH

[7] H. Inose, Y. Yasuda, J. Murakami, A Telemetering System by Code Manipulation -- Modulation, IRE Trans
on Space Electronics and Telemetry, Sep. 1962, pp. 204209.

Walt Kester (October 2008). ADC Architectures

III: Sigma-Delta ADC Basics (PDF). Analog Devices. Retrieved 2010-11-02.
R. Jacob Baker (2009). CMOS Mixed-Signal Circuit
Design (2nd ed.). Wiley-IEEE. ISBN 978-0-47029026-2.
R. Schreier; G. Temes (2005). Understanding
Delta-Sigma Data Converters. ISBN 0-471-465852.
S. Norsworthy; R. Schreier; G. Temes (1997).
Delta-Sigma Data Converters. ISBN 0-7803-10454.
J. Candy; G. Temes (1992). Oversampling Deltasigma Data Converters. ISBN 0-87942-285-8.

Continuous time sigma-delta ADC noise shaping

lter circuit architectures discusses architectural
trade-os for continuous-time sigma-delta noiseshaping lters
Some intuitive motivation for why a Delta Sigma
modulator works
DIGITAL ACCELEROMETER WITH FEEDBACK CONTROL USING SIGMA DELTA
MODULATION

Chapter 130

Continuously variable slope delta

modulation
Continuously variable slope delta modulation (CVSD encoder.
or CVSDM) is a voice coding method. It is a delta
modulation with variable step size (i.e., special case of
adaptive delta modulation), rst proposed by Greefkes 130.1
and Riemens in 1970.

Applications

CVSD encodes at 1 bit per sample, so that audio sampled 12 kbit/s CVSD is used by Motorola's SECURENET line
at 16 kHz is encoded at 16 kbit/s.
of digitally encrypted two-way radio products.
The encoder maintains a reference sample and a step size. 16 and 32 kbit/s CVSD were used by military TRI-TAC
Each input sample is compared to the reference sample. digital telephones (DNVT, DSVT) for use in deployed arIf the input sample is larger, the encoder emits a 1 bit and eas to provide voice recognition quality audio. 16 kbit/s
adds the step size to the reference sample. If the input rates were typically used by US Army forces to conserve
sample is smaller, the encoder emits a 0 bit and subtracts bandwidth over tactical links. 32 kbit/s rates were typthe step size from the reference sample. The encoder also ically used by US Air Force forces for improved voice
keeps the previous N bits of output (N = 3 or N = 4 are quality.
very common) to determine adjustments to the step size;
if the previous N bits are all 1s or 0s, the step size is in- 64 kbit/s CVSD is one of the options to encode voice sigcreased. Otherwise, the step size is decreased (usually nals in telephony-related Bluetooth service proles; e.g.,
in an exponential manner, with being in the range of between mobile phones and wireless headsets. The other
5 ms). The step size is adjusted for every input sample options are PCM with logarithmic a-law or -law quantization.
processed.
To allow for bit errors to fade out and to allow Numerous arcade games, such as Sinistar and Smash TV,
(re)synchronization to an ongoing bitstream, the output and pinball machines, such as Gorgar or Space Shuttle,
speech through an HC-55516 CVSD
register (which keeps the reference sample) is normally play pre-recorded
[1][2]
realized as a leaky integrator with a time constant ( ) of decoder.
about 1 ms.
The decoder reverses this process, starting with the reference sample, and adding or subtracting the step size ac- 130.2 SBS application 24 kbit/s
cording to the bit stream. The sequence of adjusted refdelta modulation
erence samples are the reconstructed waveform, and the
step size is adjusted according to the same all-1s-or-0s
Delta modulation was used by Satellite Business Systems
logic as in the encoder.
or SBS for its voice ports to provide long-distance phone
Adaptation of step size allows one to avoid slope overload service to large domestic corporations with a signicant
(step of quantization increases when the signal rapidly inter-corporation communications need (such as IBM).
changes) and decreases granular noise when the signal is This system was in service throughout the 1980s. The
constant (decrease of step of quantisation).
voice ports used digitally implemented 24 kbit/s delta modCVSD is sometimes called a compromise between sim- ulation with voice activity compression (VAC) and echo
plicity, low bitrate, and quality. Common bitrates are suppressors to control the half second echo path through
the satellite. Listening tests were conducted to verify that
9.6128 kbit/s.
the 24 kbit/s Delta Modulator achieved full voice qualLike other delta-modulation techniques, the output of the ity with no discernible degradation as compared to a
decoder does not exactly match the original input to the high quality phone line or the standard 64 kbit/s -law
555

556

CHAPTER 130. CONTINUOUSLY VARIABLE SLOPE DELTA MODULATION

companded PCM. This provided an 8:3 improvement in

satellite channel capacity. IBM developed the Satellite
Communications Controller and the voice port functions.
The original proposal in 1974 used a state-of-the-art 24
kbit/s Delta Modulator with a single integrator and a
Shindler compander modied for gain error recovery.
This proved to have less than full phone line speech quality. In 1977, one engineer with two assistants in the IBM
Research Triangle Park, NC laboratory was assigned to
improve the quality.
The nal implementation replaced the integrator with
a predictor implemented with a two-pole complex-pair
low-pass lter designed to approximate the long-term average speech spectrum. The theory was that ideally the
integrator should be a predictor designed to match the
signal spectrum. A nearly perfect Shindler compander
replaced the modied version. It was found the modied
compander resulted in a less than perfect step size at most
signal levels and the fast gain error recovery increased the
noise as determined by actual listening tests as compared
to simple signal to noise measurements. The nal compander achieved a very mild gain error recovery due to the
natural truncation rounding error caused by 12-bit arithmetic.
The complete function of delta modulation, VAC, and
echo control for 6 ports was implemented in a single digital integrated circuit chip with 12-bit arithmetic. A single
DAC was shared by all 6 ports providing voltage compare
functions for the modulators and feeding sample and hold
circuits for the demodulator outputs. A single card held
the chip, DAC, and all the analog circuits for the phone
line interface including transformers.

130.3 References
J. A. Greefkes and K. Riemens, Code Modulation
with Digitally Controlled Companding for Speech
Transmission, Philips Tech. Rev., pp. 335-353,
1970.
N.S. Jayant, Digital coding of speech waveforms:
PCM, DPCM, and DM quantizers, Proc. IEEE,
vol. 62, no. 5, pp. 61 1-632, May 1974.
R. Steele, Delta Modulation Systems, Pentech Press,
London, England, 1975.
N. S. Jayant and P. Noll, Digital Coding of Waveforms: Principles and Applications to Speech and
Video, Prentice-Hall, Englewood Clis, N. J., 1984.
A description of the algorithm, plus speech samples
Specication of the Bluetooth System 2.0 + EDR,
Core System Package, Part B Baseband Specication, Section 9 Audio, November 2004
[1] MAME 0.36b7 changelog

[2] Williams/Midway Y-Unit games

Chapter 131

Pulse-density modulation
Pulse-density modulation, or PDM, is a form of
modulation used to represent an analog signal with a
binary signal. In a PDM signal, specic amplitude values are not encoded into codewords of pulses of dierent weight as they would be in pulse-code modulation
(PCM). Instead, it is the relative density of the pulses that
corresponds to the analog signals amplitude. The output
of a 1-bit DAC is the same as the PDM encoding of the
signal. Pulse-width modulation (PWM) is a special case
of PDM where the switching frequency is xed and all the
pulses corresponding to one sample are contiguous in the
digital signal. For a 50% voltage with a resolution of 8bits, a PWM waveform will turn on for 128 clock cycles
and then o for the remaining 128 cycles. With PDM and
the same clock rate the signal would alternate between on
and o every other cycle. The average is 50% for both
waveforms, but the PDM signal switches more often. For
100% or 0% level, they are the same.

131.2 Examples

131.1 Description

A second example of PDM of 100 samples of two periods of a

sine wave of twice the frequency

A single period of the trigonometric sine function,

sampled 100 times and represented as a PDM bitstream,
is:

01010110111101111111111111111111110111111011011010101001001

An example of PDM of 100 samples of one period of a sine wave.

1s represented by blue, 0s represented by white, overlaid with the
sine wave.

Two periods of a higher frequency sine wave would appear as:

01011011111111111111011010100100000000000001000100110111011

In a pulse-density modulation bitstream a 1 corresponds In pulse-density modulation, a high density of 1s occurs

to a pulse of positive polarity (+A) and a 0 corresponds at the peaks of the sine wave, while a low density of 1s
to a pulse of negative polarity (-A). Mathematically, this occurs at the troughs of the sine wave.
can be represented as:

131.3 Analog-to-digital conversion

x[n] = A(1)a[n]
where x[n] is the bipolar bitstream (either -A or
+A) and a[n] is the corresponding binary bitstream (either 0 or 1).
A run consisting of all 1s would correspond to the maximum (positive) amplitude value, all 0s would correspond
to the minimum (negative) amplitude value, and alternating 1s and 0s would correspond to a zero amplitude value.
The continuous amplitude waveform is recovered by lowpass ltering the bipolar PDM bitstream.

A PDM bitstream is encoded from an analog signal

through the process of delta-sigma modulation. This process uses a one bit quantizer that produces either a 1 or 0
depending on the amplitude of the analog signal. A 1 or
0 corresponds to a signal that is all the way up or all the
way down, respectively. Because in the real world, analog
signals are rarely all the way in one direction, there is a
quantization error, the dierence between the 1 or 0 and
the actual amplitude it represents. This error is fed back
negatively in the process loop. In this way, every error
successively inuences every other quantization measurement and its error. This has the eect of averaging out
the quantization error.

557

558

CHAPTER 131. PULSE-DENSITY MODULATION

131.4 Digital-to-analog conversion

Here, E(z) is the frequency-domain quantization error

of the delta-sigma modulator. The factor 1 z 1 represents a high-pass lter, so it is clear that E(z) contributes
less to the output Y (z) at low frequencies, and more at
high frequencies. This demonstrates the noise shaping effect of the delta-sigma modulator: the quantization noise
is pushed out of the low frequencies up into the highfrequency range.

The process of decoding a PDM signal into an analog one

is simple: one only has to pass the PDM signal through a
low-pass lter. This works because the function of a lowpass lter is essentially to average the signal. The average
amplitude of pulses is measured by the density of those
pulses over time, thus a low pass lter is the only step
required in the decoding process.
Using the inverse Z-transform, we may convert this into
a dierence equation relating the input of the delta-sigma
modulator to its output in the discrete time domain,

131.5 Relationship to biology

Notably, one of the ways animal nervous systems represent sensory and other information is through rate coding
whereby the magnitude of the signal is related to the rate
of ring of the sensory neuron. In direct analogy, each
neural event called an action potential represents one
bit (pulse), with the rate of ring of the neuron representing the pulse density.

y[n] = x[n] + e[n] e[n 1]

There are two additional constraints to consider: rst, at
each step the output sample y[n] is chosen so as to minimize the running quantization error e[n] . Second, y[n]
is represented as a single bit, meaning it can take on only
two values. We choose y[n] = 1 for convenience, allowing us to write
y[n] = sgn(x[n] e[n 1])

131.6 Algorithm

{
=

+1 x[n] > e[n 1]

1 x[n] < e[n 1]

= (x[n] e[n 1]) + e[n]

e[n] y[n](x[n]e[n1]) = sgn(x[n]e[n1])(x[n]e[n1])
This, nally, gives a formula for the output sample y[n]
in terms of the input sample x[n] . The quantization error
of each sample is fed back into the input for the following
sample.
The following pseudo-code implements this algorithm to
convert a pulse-code modulation signal into a PDM signal:
Pulse-density modulation of a sine wave using this algorithm.

A digital model of pulse-density modulation can be obtained from a digital model of the delta-sigma modulator.
Consider a signal x[n] in the discrete time domain as the
input to a rst-order delta-sigma modulator, with y[n] the
output. In the discrete frequency domain, the delta-sigma
modulators operation is represented by
(

Y (z) = X(z) + E(z) 1 z

// Encode samples into pulse-density modulation //

using a rst-order sigma-delta modulator function
pdm(real[0..s] x) var int[0..s] y var real[1..s] qe
qe[1] := 0 // initial running error is zero for n from 0
to s if x[n] >= qe[n-1] y[n] := 1 else y[n] := 1 qe[n]
:= y[n] - x[n] + qe[n-1] return y, qe // return output and
running error

131.7 Applications

)
1

Rearranging terms, we obtain

PDM is the encoding used in Sonys Super Audio CD

(SACD) format, under the name Direct Stream Digital.

[
]
Y (z) = E(z) + X(z) Y (z)z 1

Some systems transmit PDM stereo audio over a single

data wire. The rising edge of the master clock indicates
a bit from the left channel, while the falling edge of the
master clock indicates a bit from the right channel.[1][2][3]

1
1 z 1

)
.

131.10. EXTERNAL LINKS

131.8 See also

Delta modulation
Pulse-code modulation
Delta-sigma modulation

131.9 References
[1] Thomas Kite. Understanding PDM Digital Audio
(PDF). 2012. The PDM Microphones section on p. 6.
[2] Maxim Integrated. PDM Input Class D Audio Power
Amplier (PDF). 2013. Figure 1 on p. 5; and the Digital Audio Interface section on p. 13.
[3] Akustica. AKU230 Digital, CMOS MEMS Microphone (PDF). 2012. p. 5.

131.10 External links

1-bit A/D and D/A Converters Discusses delta
modulation, PDM (also known as Sigma-delta modulation or SDM), and relationships to Pulse-code
modulation (PCM)

559

Chapter 132

Morse code
three dots (one dash), and the words are separated by a
space equal to seven dots. The dot duration is the basic
unit of time measurement in code transmission.[1] To increase the speed of the communication, the code was designed so that the length of each character in Morse varies
approximately inversely to its frequency of occurrence in
English. Thus the most common letter in English, the letter E, has the shortest code, a single dot.

International Morse Code

1.
2.
3.
4.
5.

A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T

The length of a dot is one unit.

A dash is three units.
The space between parts of the same letter is one unit.
The space between letters is three units.
The space between words is seven units.

U
V
W
X
Y
Z

Morse code is used by some amateur radio operators, although knowledge of and prociency with it is no longer
required for licensing in most countries. Pilots and air
trac controllers usually need only a cursory understanding. Aeronautical navigational aids, such as VORs and
NDBs, constantly identify in Morse code. Compared to
voice, Morse code is less sensitive to poor signal conditions, yet still comprehensible to humans without a decoding device. Morse is therefore a useful alternative to
synthesized speech for sending automated data to skilled
listeners on voice channels. Many amateur radio repeaters, for example, identify with Morse, even though
they are used for voice communications.

1
2
3
4
5
6
7
8
9
0

Chart of the Morse code letters and numerals.[1]

SOS, the standard emergency signal, is a Morse code prosign

Morse code is a method of transmitting text information as a series of on-o tones, lights, or clicks that can
be directly understood by a skilled listener or observer
without special equipment. It is named for Samuel F.
B. Morse, an inventor of the telegraph. The International Morse Code[1] encodes the ISO basic Latin alphabet, some extra Latin letters, the Arabic numerals and a
small set of punctuation and procedural signals (prosigns)
as standardized sequences of short and long signals called
dots and dashes,[1] or dits and dahs, as in amateur
radio practice. Because many non-English natural languages use more than the 26 Roman letters, extensions to
the Morse alphabet exist for those languages.
Each Morse code symbol represents either a text character (letter or numeral) or a prosign and is represented by
a unique sequence of dots and dashes. The duration of a
dash is three times the duration of a dot. Each dot or dash
is followed by a short silence, equal to the dot duration.
The letters of a word are separated by a space equal to

In an emergency, Morse code can be sent by improvised

methods that can be easily keyed on and o, making it one of the simplest and most versatile methods of
telecommunication. The most common distress signal is
SOS or three dots, three dashes and three dots, internationally recognized by treaty.

132.1 Development and history

Beginning in 1836, the American artist Samuel F. B.
Morse, the American physicist Joseph Henry, and Alfred
Vail developed an electrical telegraph system. This system sent pulses of electric current along wires which controlled an electromagnet that was located at the receiving
end of the telegraph system. A code was needed to transmit natural language using only these pulses, and the silence between them. Morse therefore developed the forerunner to modern International Morse code.

560

132.1. DEVELOPMENT AND HISTORY

561
American
(Morse)

Continental
(Gerke)

International
(ITU)

B
C
CH
D
E
F
G
H
I
J
K
L
M
N
O

P
Q
R
S
T
U

A typical "straight key". This U.S. model, known as the J-38,

was manufactured in huge quantities during World War II, and
remains in widespread use today. In a straight key, the signal
is on when the knob is pressed, and o when it is released.
Length and timing of the dots and dashes are entirely controlled
by the telegraphist.

V
W
X
Y
Z
1
2
3
4
5
6
7

In 1837, William Cooke and Charles Wheatstone in

England began using an electrical telegraph that also used
electromagnets in its receivers. However, in contrast with
any system of making sounds of clicks, their system used
pointing needles that rotated above alphabetical charts to
indicate the letters that were being sent. In 1841, Cooke
and Wheatstone built a telegraph that printed the letters
from a wheel of typefaces struck by a hammer. This machine was based on their 1840 telegraph and worked well;
however, they failed to nd customers for this system and
only two examples were ever built.[2]

8
9
0
0 (alt)

Comparison of historical versions of Morse code with the current

standard. 1. American Morse code as originally dened. 2.
The modied and rationalized version used by Gerke on German
railways. 3. The current ITU standard.

In the original Morse telegraphs, the receivers armature

made a clicking noise as it moved in and out of position to mark the paper tape. The telegraph operators
soon learned that they could translate the clicks directly
into dots and dashes, and write these down by hand, thus
making the paper tape unnecessary. When Morse code
was adapted to radio communication, the dots and dashes
were sent as short and long tone pulses. It was later found
that people become more procient at receiving Morse
code when it is taught as a language that is heard, instead
of one read from a page.[4]

On the other hand, the three Americans system for

telegraphy, which was rst used in about 1844, was designed to make indentations on a paper tape when electric currents were received. Morses original telegraph
receiver used a mechanical clockwork to move a paper
tape. When an electrical current was received, an electromagnet engaged an armature that pushed a stylus onto
the moving paper tape, making an indentation on the tape.
When the current was interrupted, a spring retracted the
stylus, and that portion of the moving tape remained un- To reect the sounds of Morse code receivers, the opmarked.
erators began to vocalize a dot as dit, and a dash as
The Morse code was developed so that operators could dah. Dots which are not the nal element of a characthe letter c
translate the indentations marked on the paper tape into ter became vocalized as di. For example,
[5][6]
Morse code
was
then
vocalized
as
dah-di-dah-dit.
text messages. In his earliest code, Morse had planned
was
sometimes
facetiously
known
as
iddy-umpty,
and
to transmit only numerals, and to use a codebook to look
[7]
a
dash
as
umpty,
leading
to
the
word
"umpteen".
up each word according to the number which had been
sent. However, the code was soon expanded by Alfred
Vail to include letters and special characters, so it could be
used more generally. Vail estimated the frequency of use
of letters in the English language by counting the movable type he found in the type-cases of a local newspaper
in Morristown.[3] The shorter marks were called dots,
and the longer ones dashes, and the letters most commonly used were assigned the shorter sequences of dots
and dashes.

In the 1890s, Morse code began to be used extensively for early radio communication, before it was possible to transmit voice. In the late 19th and early 20th
centuries, most high-speed international communication
used Morse code on telegraph lines, undersea cables and
radio circuits. In aviation, Morse code in radio systems
started to be used on a regular basis in the 1920s. Although previous transmitters were bulky and the spark
gap system of transmission was dicult to use, there

562
had been some earlier attempts. In 1910 the US Navy
experimented with sending Morse from an airplane.[8]
That same year a radio on the airship America had been
instrumental in coordinating the rescue of its crew.[9]
Zeppelin airships equipped with radio were used for
bombing and naval scouting during World War I,[10] and
ground-based radio direction nders were used for airship navigation.[10] Allied airships and military aircraft
also made some use of radiotelegraphy. However, there
was little aeronautical radio in general use during World
War I, and in the 1920s there was no radio system used by
such important ights as that of Charles Lindbergh from
New York to Paris in 1927. Once he and the Spirit of
St. Louis were o the ground, Lindbergh was truly alone
and incommunicado. On the other hand, when the rst
airplane ight was made from California to Australia in
the 1930s on the Southern Cross, one of its four crewmen
was its radio operator who communicated with ground
stations via radio telegraph.

CHAPTER 132. MORSE CODE

As of 2015 the United States Air Force still trains ten people a year in Morse.[13] The United States Coast Guard
has ceased all use of Morse code on the radio, and no
longer monitors any radio frequencies for Morse code
transmissions, including the international medium frequency (MF) distress frequency of 500 kHz.[14] However
the Federal Communications Commission still grants
commercial radiotelegraph operator licenses to applicants who pass its code and written tests.[15] Licensees
have reactivated the old California coastal Morse station
KPH and regularly transmit from the site under either this
Call sign or as KSM. Similarly, a few US Museum ship
stations are operated by Morse enthusiasts.[16]

132.2 User prociency

Beginning in the 1930s, both civilian and military pilots

were required to be able to use Morse code, both for
use with early communications systems and for identication of navigational beacons which transmitted continuous two- or three-letter identiers in Morse code.
Aeronautical charts show the identier of each navigational aid next to its location on the map.
Radio telegraphy using Morse code was vital during
World War II, especially in carrying messages between
the warships and the naval bases of the belligerents.
Long-range ship-to-ship communication was by radio
telegraphy, using encrypted messages, because the voice
radio systems on ships then were quite limited in both
their range and their security. Radiotelegraphy was also
extensively used by warplanes, especially by long-range
patrol planes that were sent out by those navies to scout
for enemy warships, cargo ships, and troop ships.
In addition, rapidly moving armies in the eld could not
have fought eectively without radiotelegraphy, because
they moved more rapidly than telegraph and telephone
lines could be erected. This was seen especially in the
blitzkrieg oensives of the Nazi German Wehrmacht in
Poland, Belgium, France (in 1940), the Soviet Union, and
in North Africa; by the British Army in North Africa,
Italy, and the Netherlands; and by the U.S. Army in
France and Belgium (in 1944), and in southern Germany
in 1945.

A commercially manufactured iambic paddle used in conjunction with an electronic keyer to generate high-speed Morse code,
the timing of which is controlled by the electronic keyer. Manipulation of dual-lever paddles is similar to the Vibroplex, but
pressing the right paddle generates a series of dahs, and squeezing the paddles produces dit-dah-dit-dah sequence. The actions
are reversed for left-handed operators.

Morse code speed is measured in words per minute

(wpm) or characters per minute (cpm). Characters have
diering lengths because they contain diering numbers
of dots and dashes. Consequently words also have different lengths in terms of dot duration, even when they
contain the same number of characters. For this reason,
a standard word is helpful to measure operator transmission speed. PARIS and CODEX are two such standard words.[17] Operators skilled in Morse code can often
Morse code was used as an international standard for
understand (copy) code in their heads at rates in excess
maritime distress until 1999, when it was replaced by
of 40 wpm.
the Global Maritime Distress Safety System. When the
French Navy ceased using Morse code on January 31, In addition to knowing, understanding, and being able
1997, the nal message transmitted was Calling all. This to copy the standard written alpha-numeric and punctuis our last cry before our eternal silence.[11] In the United ation characters or symbols at high speeds, skilled high
States the nal commercial Morse code transmission was speed operators must also be fully knowledgeable of all
on July 12, 1999, signing o with Samuel Morses orig- of the special unwritten Morse code symbols for the
inal 1844 message, "What hath God wrought", and the standard Prosigns for Morse code and the meanings of
these special procedural signals in standard Morse code
prosign SK.[12]
communications protocol.

132.3. INTERNATIONAL MORSE CODE

563

International contests in code copying are still occasionally held. In July 1939 at a contest in Asheville, North
Carolina in the United States Ted R. McElroy set a
still-standing record for Morse copying, 75.2 wpm.[18]
William Pierpont N0HFF also notes that some operators may have passed 100 wpm.[18] By this time they are
hearing phrases and sentences rather than words. The
fastest speed ever sent by a straight key was achieved in
1942 by Harry Turner W9YZE (d. 1992) who reached 35
wpm in a demonstration at a U.S. Army base. To accurately compare code copying speed records of dierent
eras it is useful to keep in mind that dierent standard
words (50 dot durations versus 60 dot durations) and different interword gaps (5 dot durations versus 7 dot durations) may have been used when determining such speed
records. For example, speeds run with the CODEX standard word and the PARIS standard may dier by up to
20%.

viceable, the stations all transmit a short set of identication letters (usually a two-to-ve-letter version of the
station name) in Morse code. Station identication letters are shown on air navigation charts. For example, the
VOR based at Manchester Airport in England is abbreviated as MCT, and MCT in Morse code is transmitted
on its radio frequency. In some countries, during periods of maintenance, the facility may radiate a T-E-S-T
code ( ) or the code may be removed, which
tells pilots and navigators that the station is unreliable. In
Canada, the identication is removed entirely to signify
the navigation aid is not to be used.[20][21] In the aviation service Morse is typically sent at a very slow speed
of about 5 words per minute. In the U.S., pilots do not
actually have to know Morse to identify the transmitter
because the dot/dash sequence is written out next to the
transmitters symbol on aeronautical charts. Some modern navigation receivers automatically translate the code
Today among amateur operators there are several organi- into displayed letters.
zations that recognize high speed code ability, one group
consisting of those who can copy Morse at 60 wpm.[19]
132.3.2 Amateur radio
Also, Certicates of Code Prociency are issued by several amateur radio societies, including the American Radio Relay League. Their basic award starts at 10 wpm
with endorsements as high as 40 wpm, and are available
to anyone who can copy the transmitted text. Members
of the Boy Scouts of America may put a Morse interpreters strip on their uniforms if they meet the standards
for translating code at 5 wpm.

132.3 International Morse Code

Morse code has been in use for more than 160 years
longer than any other electrical coding system. What is
called Morse code today is actually somewhat dierent
from what was originally developed by Vail and Morse.
The Modern International Morse code, or continental
code, was created by Friedrich Clemens Gerke in 1848
and initially used for telegraphy between Hamburg and
Cuxhaven in Germany. Gerke changed nearly half of the
alphabet and all of the numerals, providing the foundation for the modern form of the code. After some minor
changes, International Morse Code was standardized at
the International Telegraphy Congress in 1865 in Paris,
and was later made the standard by the International
Telecommunication Union (ITU). Morses original code
specication, largely limited to use in the United States
and Canada, became known as American Morse code or
railroad code. American Morse code is now seldom used
except in historical re-enactments.

Vibroplex brand semiautomatic key (generically called a bug).

The paddle, when pressed to the right by the thumb, generates a
series of dits, the length and timing of which are controlled by a
sliding weight toward the rear of the unit. When pressed to the left
by the knuckle of the index nger, the paddle generates a single
dah, the length of which is controlled by the operator. Multiple
dahs require multiple presses. Left-handed operators use a key
built as a mirror image of this one.

International Morse code today is most popular among

amateur radio operators, where it is used as the pattern
to key a transmitter on and o in the radio communications mode commonly referred to as "continuous wave"
or CW to distinguish it from spark transmissions, not
because the transmission was continuous. Other keying methods are available in radio telegraphy, such as
frequency shift keying.

The original amateur radio operators used Morse code

exclusively, since voice-capable radio transmitters did not
become commonly available until around 1920. Until
In aviation, instrument pilots use radio navigation aids. 2003 the International Telecommunication Union manTo ensure that the stations the pilots are using are ser- dated Morse code prociency as part of the amateur radio

132.3.1

Aviation

564

CHAPTER 132. MORSE CODE

licensing procedure worldwide. However, the World Radiocommunication Conference of 2003 made the Morse
code requirement for amateur radio licensing optional.[22]
Many countries subsequently removed the Morse requirement from their licence requirements.[23]
Until 1991 a demonstration of the ability to send and receive Morse code at a minimum of ve words per minute
(wpm) was required to receive an amateur radio license
for use in the United States from the Federal Communications Commission. Demonstration of this ability was
still required for the privilege to use the HF bands. Until 2000 prociency at the 20 wpm level was required to
receive the highest level of amateur license (Amateur Extra Class); eective April 15, 2000, the FCC reduced the
Extra Class requirement to ve wpm.[24] Finally, eective on February 23, 2007 the FCC eliminated the Morse
code prociency requirements from all amateur radio licenses.
While voice and data transmissions are limited to specic
amateur radio bands under U.S. rules, Morse code is permitted on all amateur bandsLF, MF, HF, VHF, and
UHF. In some countries, certain portions of the amateur
radio bands are reserved for transmission of Morse code A U.S. Navy signalman sends Morse code signals in 2005.
signals only.
The relatively limited speed at which Morse code can be
sent led to the development of an extensive number of
abbreviations to speed communication. These include
prosigns, Q codes, and a set of Morse code abbreviations for typical message components. For example, CQ
is broadcast to be interpreted as seek you (I'd like to
converse with anyone who can hear my signal). OM (old
man), YL (young lady) and XYL (ex-YL wife) are
common abbreviations. YL or OM is used by an operator when referring to the other operator, XYL or OM is
used by an operator when referring to his or her spouse.
QTH is location (My QTH is My location). The use
of abbreviations for common terms permits conversation
even when the operators speak dierent languages.
Although the traditional telegraph key (straight key) is
still used by some amateurs, the use of mechanical semiautomatic keyers (known as bugs) and of fully automatic electronic keyers is prevalent today. Software is
also frequently employed to produce and decode Morse
code radio signals.

132.3.3

Other uses

pass written tests on operating practice and electronics

theory. A unique additional demand for the First Class
was a requirement of a year of experience for operators
of shipboard and coast stations using Morse. This allowed
the holder to be chief operator on board a passenger ship.
However, since 1999 the use of satellite and very high
frequency maritime communications systems (GMDSS)
has made them obsolete. (By that point meeting experience requirement for the First was very dicult.) Currently only one class of license, the Radiotelegraph Operator Certicate, is issued. This is granted either when the
tests are passed or as the Second and First are renewed
and become this lifetime license. For new applicants it
requires passing a written examination on electronic theory, as well as 16 WPM code and 20 WPM text tests.
However the code exams are currently waived for holders of Amateur Extra Class licenses who obtained their
operating privileges under the old 20 WPM test requirement.
Radio navigation aids such as VORs and NDBs for aeronautical use broadcast identifying information in the form
of Morse Code, though many VOR stations now also provide voice identication.[25] Warships, including those of
the U.S. Navy, have long used signal lamps to exchange
messages in Morse code. Modern use continues, in part,
as a way to communicate while maintaining radio silence.
Submarine periscopes include a signal lamp.

Through May 2013 the First, Second, and Third Class

(commercial) Radiotelegraph Licenses using code tests
based upon the CODEX standard word were still being
issued in the United States by the Federal Communications Commission. The First Class license required 20
WPM code group and 25 WPM text code prociency,
the others 16 WPM code group test (ve letter blocks sent ATIS (Automatic Transmitter Identication System) uses
as simulation of receiving encrypted text) and 20 WPM Morse code to identify uplink sources of analog satellite
code text (plain language) test. It was also necessary to transmissions.

132.4. REPRESENTATION, TIMING AND SPEEDS

132.3.4

565

Applications for the general public 132.4

Representation, timing and

speeds

International Morse code is composed of ve

elements:[1]
Representation of SOS-Morse code.

1. short mark, dot or dit () : dot duration is one

time unit long
An important application is signalling for help through
SOS, " ". This can be sent many ways:
keying a radio on and o, ashing a mirror, toggling a
ashlight and similar methods. SOS is not three separate
characters, rather, it is a prosign SOS, and is keyed without gaps between characters.[26]

2. longer mark, dash or dah () : three time units

long
3. inter-element gap between the dots and dashes
within a character : one dot duration or one unit long

4. short gap (between letters) : three time units long

Some Nokia mobile phones oer an option to alert the
user of an incoming text message with the Morse tone
5. medium gap (between words) : seven time units long
" " (representing SMS or Short Message
Service). In addition, applications are now available for
mobile phones that enable short messages to be input in 132.4.1 Transmission
Morse Code.[27]
Morse code can be transmitted in a number of ways: originally as electrical pulses along a telegraph wire, but also
as an audio tone, a radio signal with short and long tones,
or as a mechanical, audible or visual signal (e.g. a ashing
132.3.5 Morse code as an assistive technol- light) using devices like an Aldis lamp or a heliograph, a
common ashlight, or even a car horn. Some mine resogy
cues have used pulling on a rope - a short pull for a dot
and a long pull for a dash.
Morse code has been employed as an assistive technology, helping people with a variety of disabilities to com- Morse code is transmitted using just two states (on and
municate. Morse can be sent by persons with severe mo- o). Historians have called it the rst digital code. Morse
tion disabilities, as long as they have some minimal motor code may be represented as a binary code, and that is
control. An original solution to the problem that caretak- what telegraph operators do when transmitting messages.
ers have to learn to decode has been an electronic type- Working from the above ITU denition and further denwriter with the codes written on the keys. Codes were ing a bit as a dot time, a Morse code sequence may be
sung by users; see the voice typewriter employing morse made from a combination of the following ve bit strings:
or votem, Newell and Nabarro, 1968.
1. short mark, dot or dit () : 1
Morse code can also be translated by computer and used
in a speaking communication aid. In some cases this
2. longer mark, dash or dah () : 111
means alternately blowing into and sucking on a plastic
3. intra-character gap (between the dots and dashes
tube ("sip-and-pu" interface). An important advantage
within a character) : 0
of Morse code over row column scanning is that, once
learned, it does not require looking at a display. Also, it
4. short gap (between letters) : 000
appears faster than scanning.
5. medium gap (between words) : 0000000
People with severe motion disabilities in addition to sensory disabilities (e.g. people who are also deaf or blind)
Note that the marks and gaps alternate: dots and dashes
can receive Morse through a skin buzzer. .
In one case reported in the radio amateur magazine are always separated by one of the gaps, and that the gaps
QST,[28] an old shipboard radio operator who had a stroke are always separated by a dot or a dash.
and lost the ability to speak or write could communicate with his physician (a radio amateur) by blinking
his eyes in Morse. Another example occurred in 1966
when prisoner of war Jeremiah Denton, brought on television by his North Vietnamese captors, Morse-blinked
the word TORTURE. In these two cases interpreters were
available to understand those series of eye-blinks.

Morse messages are generally transmitted by a handoperated device such as a telegraph key, so there are variations introduced by the skill of the sender and receiver
more experienced operators can send and receive at faster
speeds. In addition, individual operators dier slightly,
for example using slightly longer or shorter dashes or
gaps, perhaps only for particular characters. This is called

566

CHAPTER 132. MORSE CODE

their st, and experienced operators can recognize specic individuals by it alone. A good operator who sends
clearly and is easy to copy is said to have a good st.
A poor st is a characteristic of sloppy or hard to copy
Morse code.

132.4.2

Timing

Some method to standardize the transformation of a word

rate to a dot duration is useful. A simple way to do
this is to choose a dot duration that would send a typical word the desired number of times in one minute. If,
for example, the operator wanted a character speed of 13
words per minute, the operator would choose a dot rate
that would send the typical word 13 times in exactly one
minute.

The typical word thus determines the dot length. It is

common to assume that a word is 5 characters long. There
are two common typical words: PARIS and CODEX.
PARIS mimics a word rate that is typical of natural language words and reects the benets of Morse codes
M O R S E C O D E
shorter code durations for common characters such as e
Next is the exact conventional timing for this phrase, with and t. CODEX oers a word rate that is typical of 5= representing signal on, and . representing signal o, letter code groups (sequences of random letters). Using
the word PARIS as a standard, the number of dot units is
each for the time length of exactly one dit:
50 and a simple calculation shows that the dot length at
1
2
3
4
5
6
7
8
20 words per minute is 60 milliseconds. Using the word
12345678901234567890123456789012345678901234567890123456789012345678901234567890123456789
CODEX with 60 dot units, the dot length at 20 words per
M-----O---------R-----S--minute is 50 milliseconds.
E
C---------O---------D-----E
Because Morse code is usually sent by hand, it is unlikely
===.===...===.===.===...=.===.=...=.=.=...=.......===.=.===.=...===.===.===...===.=.=...=
^ ^ ^ ^ ^ | dah dit | | symbol space letter space word space that an operator could be that precise with the dot length,
and the individual characteristics and preferences of the
operators usually override the standards.
Below is an illustration of timing conventions. The phrase
MORSE CODE, in Morse code format, would normally be written something like this, where represents
dahs and represents dits:

132.4.3

Spoken representation

Morse code is often spoken or written with dah for

dashes, dit for dots located at the end of a character,
and di for dots located at the beginning or internally
within the character. Thus, the following Morse code sequence:
M O R S E C O D E (space)

is orally:

For commercial radiotelegraph licenses in the United

States, the Federal Communications Commission species tests for Morse code prociency in words per minute
and in code groups per minute.[29] The Commission species that a word is 5-characters long. The Commission
species Morse code test elements at 16 code groups per
minute, 20 words per minute, 20 code groups per minute,
and 25 words per minute.[30] The word per minute rate
would be close to the PARIS standard, and the code
groups per minute would be close to the CODEX standard.

Dah-dah dah-dah-dah di-dah-dit di-di-dit dit, Dah-di- While the Federal Communications Commission no
longer requires Morse code for amateur radio licenses,
dah-dit dah-dah-dah dah-di-dit dit.
the old requirements were similar to the requirements for
There is little point in learning to read written Morse as commercial radiotelegraph licenses.[31]
above; rather, the sounds of all of the letters and symbols
A dierence between amateur radio licenses and comneed to be learned, for both sending and receiving.
mercial radiotelegraph licenses is that commercial operators must be able to receive code groups of random characters along with plain language text. For each class of
132.4.4 Speed in words per minute
license, the code group speed requirement is slower than
All Morse code elements depend on the dot length. A the plain language text requirement. For example, for
dash is the length of 3 dots, and spacings are specied in the Radiotelegraph Operator License, the examinee must
number of dot lengths. An unambiguous method of spec- pass a 20 word per minute plain text test and a 16 word
ifying the transmission speed is to specify the dot duration per minute code group test.[15]
as, for example, 50 milliseconds.
Based upon a 50 dot duration standard word such as
Specifying the dot duration is, however, not the common PARIS, the time for one dot duration or one unit can be
practice. Usually, speeds are stated in words per minute. computed by the formula:
That introduces ambiguity because words have dierent
T = 1200 / W
numbers of characters, and characters have dierent dot
lengths. It is not immediately clear how a specic word
Where: T is the unit time, or dot duration in milliseconds,
rate determines the dot duration in milliseconds.

132.5. LEARNING METHODS

and W is the speed in wpm.
High-speed telegraphy contests are held; according to
the Guinness Book of Records in June 2005 at the
International Amateur Radio Union's 6th World Championship in High Speed Telegraphy in Primorsko, Bulgaria,
Andrei Bindasov of Belarus transmitted 230 morse code
marks of mixed text in one minute.[32]

132.4.5

Farnsworth speed

Sometimes, especially while teaching Morse code, the

timing rules above are changed so two dierent speeds
are used: a character speed and a text speed. The character speed is how fast each individual letter is sent. The text
speed is how fast the entire message is sent. For example, individual characters may be sent at a 13 words-perminute rate, but the intercharacter and interword gaps
may be lengthened so the word rate is only 5 words per
minute.

567
Morse Code when transmitted essentially creates an AM
signal (even in on/o keying mode), assumptions about
signal can be made with respect to similarly timed RTTY
signalling. Because Morse code transmissions employ an
on-o keyed radio signal, it requires less complex transmission equipment than other forms of radio communication.
Morse code also requires less signal bandwidth than voice
communication, typically 100150 Hz, compared to the
roughly 2400 Hz used by single-sideband voice, although
at a lower data rate.
Morse code is usually heard at the receiver as a mediumpitched on/o audio tone (6001000 Hz), so transmissions are easier to copy than voice through the noise on
congested frequencies, and it can be used in very high
noise / low signal environments. The transmitted power
is concentrated into a limited bandwidth so narrow receiver lters can be used to suppress interference from
adjacent frequencies. The audio tone is usually created
by use of a beat frequency oscillator.

Using dierent character and text speeds is, in fact, a The narrow signal bandwidth also takes advantage of the
common practice, and is used in the Farnsworth method natural aural selectivity of the human brain, further enof learning Morse code.
hancing weak signal readability. This eciency makes
CW extremely useful for DX (distance) transmissions,
as well as for low-power transmissions (commonly called
132.4.6 Alternative display of common "QRP operation", from the Q-code for reduce power).

characters in International Morse The ARRL has a readability standard for robot encoders
code
called ARRL Farnsworth Spacing [33] that is supposed
See also: Human coding

to have higher readability for both robot and human decoders. Some programs like WinMorse [34] have implemented the standard.

Some methods of teaching Morse code use a dichotomic

search table.

132.5 Learning methods

Graphical representation of the dichotomic search table. The

graph branches left for each dot and right for each dash until
the character representation is exhausted.

132.4.7

Link budget issues

People learning Morse code using the Farnsworth

method are taught to send and receive letters and other
symbols at their full target speed, that is with normal relative timing of the dots, dashes and spaces within each
symbol for that speed. The Farnsworth method is named
for Donald R. Russ Farnsworth, also known by his call
sign, W6TTB. However, initially exaggerated spaces between symbols and words are used, to give thinking
time to make the sound shape of the letters and symbols easier to learn. The spacing can then be reduced with
practice and familiarity.
Another popular teaching method is the Koch method,
named after German psychologist Ludwig Koch, which
uses the full target speed from the outset, but begins with
just two characters. Once strings containing those two
characters can be copied with 90% accuracy, an additional character is added, and so on until the full character
set is mastered.

Morse Code cannot be treated as a classical radioteletype

(RTTY) signal when it comes to calculating a link margin or a link budget for the simple reason of it possessing variable length dots and dashes as well as variant timing between letters and words. For the purposes
of Information Theory and Channel Coding comparisons
the word PARIS is used to determine Morse Codes prop- In North America, many thousands of individuals have
erties because it has an even number of dots and dashes. increased their code recognition speed (after initial mem-

568

CHAPTER 132. MORSE CODE

orization of the characters) by listening to the regu- 132.6.2 Symbol representations

larly scheduled code practice transmissions broadcast by
W1AW, the American Radio Relay Leagues headquar- The symbols !, $ and & are not dened inside the ITU recters station.
ommendation on Morse code, but conventions for them
exist. The @ symbol was formally added in 2004.

132.5.1

Mnemonics

Exclamation mark
There is no standard representation for the exclamation
mark (!), although the KW digraph ( ) was proposed in the 1980s by the Heathkit Company (a vendor
of assembly kits for amateur radio equipment).
While Morse code translation software prefers the
Heathkit version, on-air use is not yet universal as
some amateur radio operators in North America and the
Caribbean continue to prefer the older MN digraph (
) carried over from American landline telegraphy code.
Currency symbols

Scout movement founder Baden-Powells mnemonic chart from

1918

Visual mnemonic charts have been devised over the

ages. Baden-Powell included one in the Girl Guides
handbook[35] in 1918.

The ITU has never codied formal Morse Code representations for currencies as the ISO 4217 Currency Codes are preferred for transmission.
The $ sign code was represented in the Phillips
Code, a huge collection of abbreviations used on
land line telegraphy, as SX.

In the United Kingdom many people learned the Morse

code by means of a series of words or phrases that have
the same rhythm as a Morse character. For instance, Q
in Morse is dah-dah-di-dah, which can be memorized by Ampersand
the phrase God save the Queen, and the Morse for F
is di-di-dah-dit, which can be memorized as Did she like
The representation of the & sign given above, often
it.
shown as AS, is also the Morse prosign for wait. In
A well-known Morse code rhythm from the Second
addition, the American landline representation of an
World War period derives from Beethovens Fifth Symampersand was similar to ES ( ) and hams have
phony, the opening phrase of which was regularly played
carried over this usage as a synonym for and (WX
at the beginning of BBC broadcasts. The timing of the
HR COLD ES RAINY, the weather here is cold &
notes corresponds to the Morse for V"; di-di-di-dah and
rainy).
stood for V for Victory (as well as the Roman numeral
for the number ve).[36][37]
Keyboard AT @

132.6 Letters, numbers, punctuation, prosigns for Morse code

and non-English variants
132.6.1

Prosigns

Main article: Prosigns for Morse code

Prosigns for Morse code are special (usually) unwritten
procedural signals or symbols that are used to indicate
changes in communications protocol status or white space
text formatting actions.

On May 24, 2004 the 160th anniversary of the

rst public Morse telegraph transmission the
Radiocommunication Bureau of the International
Telecommunication Union (ITU-R) formally added
the @ ("commercial at" or commat) character to
the ocial Morse character set, using the sequence
denoted by the AC digraph ( ).
This sequence was reportedly chosen to represent
A[T] C[OMMERCIAL]" or a letter a inside a
swirl represented by a C.[38] The new character facilitates sending email addresses by Morse code and
is notable since it is the rst ocial addition to the
Morse set of characters since World War I.

132.9. REFERENCES

132.6.3

Non-Latin extensions

Main article: Other alphabets in Morse code

569
Hog morse
Instructograph
List of international common standards

For Chinese, Chinese telegraph code is used to map

Chinese characters to four-digit codes and send these digits out using standard Morse code. Korean Morse code
uses the SKATS mapping, originally developed to allow
Korean to be typed on western typewriters. SKATS maps
hangul characters to arbitrary letters of the Latin script
and has no relationship to pronunciation in Korean. For
Russian and Bulgarian, Russian Morse code is used to
map the Cyrillic characters to four-element codes. Many
of the characters are encoded the same way (A, O, E, I, T,
M, N, R, K, etc.). Bulgarian alphabet contains 30 characters, which exactly match all possible combinations of
1, 2, 3 and 4 dots and dashes. Russian requires 1 extra
character, "" , which is encoded with 5 elements.

132.6.4

Unusual variants

During early World War I (19141916) Germany briey

experimented with 'dotty' and 'dashy' Morse, in essence
adding a dot or a dash at the end of each Morse symbol. Each one was quickly broken by Allied SIGINT,
and standard Morse was restored by Spring 1916. Only
a small percentage of Western Front (North Atlantic and
Mediterranean Sea) trac was in 'dotty' or 'dashy' Morse
during the entire war. In popular culture, this is mostly
remembered in the book The Codebreakers by Kahn and
in the national archives of the UK and Australia (whose
SIGINT operators copied most of this Morse variant).
Kahns cited sources come from the popular press and
wireless magazines of the time.[39]
Other forms of 'Fractional Morse' or 'Fractionated Morse'
have emerged.[40]

132.7 Decoding software

Morse code abbreviations

Morse code mnemonics
NATO phonetic alphabet
Tap code
Wabun code
Wireless telegraphy
Theodore Roosevelt McElroy

132.9 References
[1] International Morse code Recommendation ITU-R
M.1677-1. itu.int. International Telecommunication
Union. October 2009. Retrieved 23 December 2011.
[2] Burns 2004, p. 79
[3] Burns 2004, p. 84
[4] ARRLWeb: ARRLWeb: Learning Morse Code (CW)!
[5] L. Peter Carron, Morse Code: The Essential Language,
Radio amateurs library, issue 69, American Radio Relay
League, 1986 ISBN 0-87259-035-6.
[6] R. J. Eckersley, Amateur radio operating manual, Radio
Society of Great Britain, 1985 ISBN 0-900612-69-X.
[7] Iddy-umpty. Oxford English Dictionary. Retrieved 22
October 2016. (available online to subscribers)
[8] History of Communications-Electronics in the United
States Navy
[9] 100 Years ago this airship sailed from Atlantic City. Article is no longer on the page, from the page archives it
appears the information was taken from this video

Decoding software for Morse code ranges from software- [10] How the Zeppelin Raiders Are Guided by Radio Signals. EarlyRadioHistory.us. United States Early Radened wide-band radio receivers coupled to the Re[41]
dio History/Popular Science Monthly (April 1918). Reverse Beacon Network,
which decodes signals and
trieved
January 21, 2015.
detects CQ messages on ham bands, to smartphone
[42]
applications.
[11] An obituary for Morse code, The Economist, January
23, 1999.

132.8 See also

ACP-131
CW Operators Club
Guglielmo Marconi
High-speed telegraphy

[12] The End of Morse - The day the keys in North America
fell silent
[13] Morse code training in the Air Force
[14] Amendments to the International Aeronautical and Maritime Search and Rescue (IAMSAR) Manual
[15] Radiotelegraph Operator License (T)". fcc.gov. Federal
Communications Commission. Retrieved January 21,
2015.

570

CHAPTER 132. MORSE CODE

[16] Maritime Radio Historical Society

[17] Perera, Tom. The Morse Code and the Continental
Code. W1TP Telegraph & Scientic Instruments Museums. Retrieved 23 December 2011.
[18] The Art & Skill of Radio Telegraphy (PDF). 2002. Retrieved 2013-06-14.

[38] International Morse Code Gets a New ITU Home, New

Character. Archived from the original on September 30,
2007. Retrieved February 27, 2007.
[39] Wytho, Grant (July 2014). The Invention of Wireless
Cryptography. The Appendix: Futures of the Past. 2 (3).
Retrieved 2015-01-28.
[40] Fractionated Morse, and Other Oddities.
bloc.com. Retrieved 2013-11-21.

[19] Extremely High Speed Club ocial web page

[20] Chapter 1. Air Navigation. faa.gov. January 3, 2015.
Archived from the original on December 1, 2014. Retrieved January 21, 2015.
[21] COM 3.2, Canadian AIM Archived November 22, 2013,
at the Wayback Machine.
[22] IARUWeb: The International Amateur Radio Union
Archived September 6, 2012, at the Wayback Machine.
[23] Italy Joins No-Code Ranks as FCC Revives Morse Debate in the US. The ARRL Letter. 24 (31). August 12,
2005. Retrieved 2012-04-02.
[24] 1998 Biennial Regulatory Review Amendment of Part
97 of the Commissions Amateur Service Rules (PDF).
Archived from the original (PDF) on October 31, 2005.
Retrieved December 4, 2005.
[25] Aeronautical Information Manual (AIM)". Archived
from the original on September 4, 2009. Retrieved 200712-10.
[26] Prosigns. www.qsl.net. QTH.Com. Retrieved January
21, 2015.
[27] Nokia les patent for Morse Code-generating cellphone,
12 March 2005, Engadget.

Quadi-

[41] http://www.reversebeacon.net/ Reverse Beacon Network

[42] Morse Decoder Test iPhone / iPad | Gerolf Ziegenhain. Gerolfziegenhain.wordpress.com. 2013-05-20.
Retrieved 2016-09-17.

Burns, R. W. (2004), Communications: an international history of the formative years, Institution of

Electrical Engineers, ISBN 0-86341-327-7

132.10 External links

Morse code at DMOZ
Everyone Knows Morse. TV Tropes.. Includes
a list of uses and appearances of Morse Code in
movies, television episodes, and other popular culture.
Morse Code resources
Morse Code Translator at funtranslations.com

[28] Dennis W. Ross, Morse Code: A Place in the Mind,

QST, March, 1992, p. 51.

Morse code MP3 practice les. 200 hours of at increasing speeds plus an ASCII-to-CW le generator
program.

[29] Title 47 Code of Federal Regulations 13.207(c) and Title

47 Code of Federal Regulations 13.209(d)

International Morse Code, Hand Sending US Army

training video 1966.

[30] 47 CFR 13.203(b)

Morse Code Radio Operator Training Technique

of Hand Sending US Navy 1944.

[31] Title 47 Code of Federal Regulations 97.503, 1996 version

[32] Guinness Book of records: Fastest speed for a morse code
transmission, 1 June 2005
[33] http://www.arrl.org/files/file/Technology/x9004008.pdf
[34] Custom Farnsworth Spacing Conguration.
morse.com. Retrieved 2013-11-21.

Win-

[35] Girl Guiding by Lord Baden-Powell (PDF). Pearson.

1938. Retrieved 2015-09-06. Some people nd it easier
to remember the does [sic] and dashes by picturing them
as forming the letters thus: (p61)
[36] Glenn Stanley, The Cambridge Companion to Beethoven,
p.269, Cambridge University Press, 2000 ISBN 0-52158934-7.
[37] William Emmett Studwell, The Americana Song Reader,
p.62, Routledge, 1997 ISBN 0-7890-0150-0.

Codes of the World

132.11. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

571

132.11 Text and image sources, contributors, and licenses

132.11.1

Text

Amplitude modulation Source: https://en.wikipedia.org/wiki/Amplitude_modulation?oldid=747676811 Contributors: AxelBoldt, Mav,

Zundark, The Anome, Ap, Gareth Owen, Ray Van De Walker, Waveguy, Heron, GrahamN, Ram-Man, Edward, Infrogmation, Michael
Hardy, Ixfd64, Delirium, Stw, BAxelrod, GRAHAMUK, Omegatron, Bloodshedder, Robbot, Merovingian, Hadal, Wikibot, BenFrantzDale, MSGJ, Everyking, Ssd, Maroux, Rchandra, Albany45, Pne, Ary29, Bk0, Sonett72, Qef, Freakofnurture, Discospinster, Rich Farmbrough, Guanabot, Bender235, Vicks007, Simon South, R. S. Shaw, Helix84, Jtalledo, Cjthellama, Jftsang, Pkeck, Bluemoose, Isnow,
Eyreland, BD2412, HappyCamper, Ucucha, FlaBot, Margosbot~enwiki, Gurubrahma, Chobot, Krishnavedala, DVdm, Roboto de Ajvol,
YurikBot, Borgx, Mukkakukaku, Splash, Jengelh, Gaius Cornelius, Steven Hepting, Brandon, Mikeblas, Mysid, DeadEyeArrow, Bota47,
Thomas H. White, Petri Krohn, Fram, SmackBot, Eskimbot, Betacommand, Desonia, Cadmium, Coinchon, Oli Filth, Nbarth, Colonies
Chris, Szidomingo, Bob K, Nick Levine, MrRadioGuy, JR98664, Ck lostsword, SashatoBot, Breno, MarkSutton, Rogerbrent, Dicklyon,
Waggers, Kvng, DabMachine, PaulGS, Ximensions, CapitalR, Chetvorno, CmdrObot, Requestion, Myasuda, Cydebot, Thijs!bot, Antidemon, Cool Blue, Mdriver1981, Mack2, JAnDbot, Harryzilber, Quentar~enwiki, .anacondabot, Magioladitis, VoABot II, DerHexer,
Calltech, Jdorwin, Marskang, CommonsDelinker, Gah4, Gomez2002, Vikasmk, Rjf ie, Deadlocke, Diwakarbista, DorganBot, Funandtrvl,
ABF, Pleasantville, Pawinsync, Philip Trueman, TXiKiBoT, Oshwah, The Original Wildbear, Payam09, Martin451, Cuddlyable3, Swagato Barman Roy, Kbrose, Renxa, ToePeu.bot, Hertz1888, Bentogoa, Mdsam2~enwiki, Yerpo, Berserkerus, Miniapolis, Yair rand, Neo.,
Mx. Granger, Dp67, ClueBot, PipepBot, The Thing That Should Not Be, Brews ohare, NuclearWarfare, Aitias, Dspdude, Johnuniq,
SoxBot III, Erodium, Darkicebot, Interferometrist, Dthomsen8, Skarebo, Tanhabot, Leszek Jaczuk, SteveBot, Jan eissfeldt, Legobot,
Luckas-bot, Yobot, AnomieBOT, Rubinbot, Bluerasberry, Materialscientist, Ciudadano001, ArdWar, Xqbot, Capricorn42, DSisyphBot,
Raamaiden, GrouchoBot, Ekkleesia, Nedim Ardoa, Sibian, Pinethicket, I dream of horses, HRoestBot, RedBot, TobeBot, Trappist
the monk, DARTH SIDIOUS 2, Mkmr777, Ripchip Bot, Noommos, Dewritech, RenamedUser01302013, Dcirovic, Werieth, AvicBot,
Mohdabdulwaseem, Mobius Bot, Qwertylurker, TYelliot, Kavya Manohar, ClueBot NG, Leejoe Schar, Widr, Helpful Pixie Bot, LegendofPedro, BG19bot, Roberticus, Morning Sunshine, ChrisGualtieri, YFdyh-bot, Harsh 2580, The.ever.kid, Hamerbro, Ahmad.elkomey,
Vanamonde93, I am One of Many, Herbertweidner~enwiki, JNRSTANLEY, Nijoakim, Ashwini22, Erick Shepherd, Monkbot,
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Modulation Source: https://en.wikipedia.org/wiki/Modulation?oldid=745690754 Contributors: AxelBoldt, The Anome, Bdesham,
Michael Hardy, Ralmin, Stw, Glenn, Smack, Wikiborg, Joy, Denelson83, Robbot, Altenmann, Giftlite, Svenjissom, DavidCary, Qartis,
Inkling, RobertYu, Ssd, Superborsuk, Cihan, Starx, DmitryKo, Danh, Mike Rosoft, EugeneZelenko, Bender235, West London Dweller,
One-dimensional Tangent, Simon South, Photonique, Towel401, Rabarberski, Argilo, DV8 2XL, Mahanga, Meodou, Dandv, Dtwitkowski,
BD2412, Pleiotrop3, HappyCamper, FlaBot, Lmatt, Tedder, Chobot, Hatch68, Krishnavedala, Roboto de Ajvol, YurikBot, RussBot,
Red Slash, Splash, Grafen, BOT-Superzerocool, Mysid, Gadget850, Bota47, Plamka, Yeryry, Light current, Hadipedia, MaratL, Yaco,
Katieh5584, Finell, SmackBot, Bernard Franois, Gilliam, Chris the speller, Oli Filth, MalafayaBot, McNeight, Gutworth, Dreadstar,
Daniel.Cardenas, Muadd, Dicklyon, EEPROM Eagle, Kvng, Lee Carre, Chetvorno, JohnTechnologist, CmdrObot, MC10, Thijs!bot, Siwiak, Nick Number, Dawnseeker2000, Escarbot, Three Laws of Robotics, AntiVandalBot, Seaphoto, Pranav v, Doktor Who, JAnDbot, Harryzilber, VoABot II, Hmo, Wksalar, Read-write-services, Technicolorcavalry, Vanwhistler, Mange01, Yonidebot, Philippe23,
Dave Dial, JClark2906, Atropos235, DorganBot, Idioma-bot, Funandtrvl, Sam Blacketer, VolkovBot, ICE77, Alinja, Cbradiomagazine,
TXiKiBoT, Rei-bot, MichaelStanford, Jpat34721, Canaima, Cuddlyable3, Doc James, Logan, Bluemouse2306, HowardMorland, SieBot,
ToePeu.bot, Gerakibot, Bentogoa, Yerpo, Berserkerus, Smshaner, Unknownx123, Alex.muller, Anchor Link Bot, KLuwak, Tuxa, ClueBot, Binksternet, The Thing That Should Not Be, Pyr0technician, Wispanow, Sepia tone, Aua, Karlhendrikse, Coralmizu, Abrech, Jotterbot, Muro Bot, Berean Hunter, Johnuniq, Tprentice, Analogkidr, Mahamahamaha, Stradivariusis, Rebmertaumer, Ixhotl, Avoided,
Addbot, Grayfell, Fgnievinski, Jpmonroe, Tanhabot, Maziaar83, Leszek Jaczuk, Bfallik, Favonian, Lightbot, Wireless friend, Frehley,
DrFO.Tn.Bot, Snaily, Yobot, Gsmcoupe, Playclever, AnomieBOT, Jim1138, Materialscientist, ArthurBot, MauritsBot, Xqbot, Nasnema,
Almabot, GrouchoBot, Jhbdel, RibotBOT, GliderMaven, Zhouyuanxin, Oalp1003, Z3r0kw3l, RedBot, MastiBot, Bjarkef, TobeBot, Suffusion of Yellow, Alph Bot, Urfriendshailesh, EmausBot, Rw4ni, Solarra, Dcirovic, Thecheesykid, Dweremeichik, Ashwink911, ChuispastonBot, ClueBot NG, Widr, JordoCo, Helpful Pixie Bot, BG19bot, Brian Tomasik, , Frogging101, MatthewIreland, YFdyh-bot,
BrightStarSky, Calumet96, Checkmeleon, Hssaha, Superkronos, Kahtar, JaconaFrere, Tracey1022, Trackteur, Richard Yin, PaulRamone2,
Undolie, Asddfas, CosmicEngineMan, WetNoodles, Billtool, SternDN and Anonymous: 252
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Hardy, Tim Starling, GABaker, Lexor, Liftarn, Ixfd64, Sannse, Paul Benjamin Austin, Karada, Gbleem, Spliced, Pagingmrherman, Tregoweth, Gaz~enwiki, Ahoerstemeier, PJC, Haakon, Mac, ZoeB, Ron Davis, TUF-KAT, Plop, TUF-KAT, Msablic, Aarchiba, Ugen64,
Glenn, Cyan, Nikai, GCarty, Marknew, Mxn, Ilyanep, Arteitle, Hashar, Emperorbma, Ed Cormany, Reddi, Dysprosia, Wik, Tpbradbury,
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Kryptops, Zpb52, Pgosta, Dysepsion, LimoWreck, Kesla, Graham87, Marskell, Qwertyus, Chun-hian, MC MasterChef, Kbdank71, Canderson7, Sj, Rjwilmsi, Koavf, Misternuvistor, Bruce1ee, Vegaswikian, Mbutts, Fred Bradstadt, Sango123, Yamamoto Ichiro, SNIyer12,
Kevmitch, FayssalF, SchuminWeb, RobertG, Musical Linguist, Doc glasgow, Nsjoker, Nihiltres, Fragglet, RexNL, Gurch, Talk1370, Lmatt,
Windharp, Toi, King of Hearts, Frappyjohn, Sharkface217, DVdm, Mhking, Peter Grey, Roboto de Ajvol, Wavelength, Samuel Wiki,

572

CHAPTER 132. MORSE CODE

Phantomsteve, RussBot, J. M., Conscious, Splash, GLaDOS, DanMS, SpuriousQ, Chaser, Chrisjustinparr, Zelmerszoetrop, RadioFan2
(usurped), Stephenb, Gaius Cornelius, Zimbricchio, CambridgeBayWeather, Alvinrune, Rsrikanth05, Dsmouse, Wimt, Willpo~enwiki,
NawlinWiki, Ethan, SEWilcoBot, Wiki alf, Rjensen, Steven Hepting, Irishguy, Malcolma, DAJF, Davidpk212, Alex43223, Flyset, Bucketsofg, Dbrs, DeadEyeArrow, Nescio, Groink, Xedaf, Thomas H. White, Werdna, Djdaedalus, Gohiking, Wknight94, Searchme, FF2010,
Sadistik, Light current, 21655, Deville, Zzuuzz, MaNeMeBasat, ToyoWolf, Nelson50, HereToHelp, Tyrenius, Spliy, Ethan Mitchell,
Crazyquesadilla, Allens, Junglecat, Snaxe920, RG2, Carlosguitar, Mohylek, Cmglee, Linkminer, DVD R W, Kf4bdy, David.hillshafer,
Veinor, SmackBot, MattieTK, Haza-w, Terry1944, KnowledgeOfSelf, Hydrogen Iodide, McGeddon, Pgk, Sea diver, Jagged 85, Davewild,
Thunderboltz, Stephensuleeman, Renesis, Delldot, Fractal3, Jonathanwagner, Kintetsubualo, Alsandro, SmartGuy Old, Gilliam, Ohnoitsjamie, Skizzik, Carl.bunderson, Micwea, Jcarroll, Cabe6403, Kmarinas86, Science3456, Hraefen, Armeria, Schmiteye, Chris the speller,
Kharker, Wuyz, MK8, Miquonranger03, Domthedude001, SchftyThree, Akanemoto, Leoni2, Mark7-2, Whispering, Baronnet, CMYK,
Can't sleep, clown will eat me, Shalom Yechiel, Jennica, Snowmanradio, Ostermana, Darthgriz98, Yidisheryid, WinstonSmith, Rrburke,
Benjamin Mako Hill, ArmitageShanks, Edivorce, Renegade Lisp, Mugaliens, Badbilltucker, Huon, Jmlk17, Ganchelkas, Aldaron, MrRadioGuy, Smooth O, BesselDekker, Quizman1967, Mindraker, Funky Monkey, MisterCharlie, RobHarding, Xagent86, Kleuske, Kalathalan,
Bretonbanquet, Cottingham, Ck lostsword, Kukini, Qmwne235, The undertow, Petr Kopa, Quendus, Kuru, Euchiasmus, Vgy7ujm, Arthuralee, J 1982, Andrewjuren, Kipala, GCW50, Coredesat, Minna Sora no Shita, Gwest1, MonstaPro, Mr. Lefty, Otterman665, A. Parrot,
MarkSutton, Slakr, Beetstra, Kondspi, Bendzh, Waggers, CUTKD, E-Kartoel, Butler david, Dr.K., Peter Horn, Kvng, Hu12, Ginkgo100,
Levineps, DouglasCalvert, OnBeyondZebrax, White Ash, Spark, Cynric~enwiki, IvanLanin, Stereorock, Az1568, Courcelles, Linkspamremover, Bannanas, Waer, Tawkerbot2, Cassamine, Daniel5127, Chetvorno, Dan1679, Jchittoor, Fritz28408, The Haunted Angel, JohnTechnologist, IanWills, Mosaa, JForget, Peter1c, Scohoust, Nczempin, Mig11, MrZap, Birdhurst, McVities, Requestion, Lazulilasher,
Ravensfan5252, Yaris678, Book M, Cahk, Gogo Dodo, B0Rn2bL8, Anonymi, Flowerpotman, Pascal.Tesson, Scott14, Trident13, DumbBOT, Phonemonkey, JodyB, Vanished User jdksfajlasd, Nol888, Gimmetrow, Click23, Ozguy89, Marqmike2, Epbr123, Doct.proloy,
Kussy, Pampas Cat, Mishmash8, Dnyhagen, Spunker540, Picus viridis, X201, Mnemeson, Leon7, Sgaragan, MichaelMaggs, Natalie Erin,
CTZMSC3, Escarbot, Grandin, Mentisto, AntiVandalBot, Seaphoto, Mrshaba, Jbaranao, Epischedda, Venya, Xbox360wraith, Tomgray,
LuckyLouie, Jc3, Chill doubt, Bdean1963, Beachyboy, LegitimateAndEvenCompelling, Myanw, Uusitunnus, JAnDbot, Husond, Harryzilber, Barek, MER-C, Fetchcomms, Andonic, Erpel13, Greensburger, Masked boy~enwiki, Parcemihi~enwiki, Jed S, SiobhanHansa,
Acroterion, Geniac, Magioladitis, Creationlaw, Bongwarrior, VoABot II, AuburnPilot, JNW, Yandman, Paymani, Puddhe, Doug Coldwell,
Jatkins, Robomojo, Recurring dreams, Sgr927, Biokinetica, Cpl Syx, Glen, DerHexer, TheRanger, NatureA16, PhantomS, MartinBot,
Meamvagabond, GM11, Jim.henderson, Rettetast, Rob Lindsey, Kostisl, Sfrandzi~enwiki, CommonsDelinker, AlexiusHoratius, Paulmcdonald, Jmccormac, Gutta Percha, LedgendGamer, Mausy5043, RockMFR, J.delanoy, Trusilver, Anilbg, Wa3frp, Tntdj, Uncle Dick,
Maurice Carbonaro, Jesant13, Jreferee, JA.Davidson, Shawn in Montreal, NX1Z, Listen2myradio, Jigesh, Jayden54, Chalyres, Jackobyte,
AntiSpamBot, RoboMaxCyberSem, GhostPirate, NewEnglandYankee, Fountains of Bryn Mawr, Nwbeeson, Micz.or, SJP, Gregtzy,
Ontarioboy, Liliana-60, BigHairRef, Smitty, Prhartcom, 2help, Cometstyles, Jamesontai, Znx, Davidezell, Bonadea, Useight, Eduardo
Mendona de Lima, CardinalDan, Idioma-bot, Funandtrvl, X!, Deor, VolkovBot, ABF, Almazi, Rclocher3, Chienlit, Philip Trueman,
Majorxp, Jhon montes24, Oshwah, Mercy, Ldonna, The Original Wildbear, Pachayachachic, Mr Percy, Drestros power, SteveStrummer, Arnon Chan, Pjdd2, Qxz, Monkey Bounce, Anna Lincoln, Clarince63, Dendodge, HorusHawkX, Corvus cornix, DocteurCosmos, Martin451, Slysplace, Person324, Abdullais4u, Eatabullet, Jackfork, LeaveSleaves, Raymondwinn, Arthurs1212, Uannis~enwiki,
Greswik, Andy Dingley, Wasted Sapience, Synthebot, Falcon8765, Enviroboy, Burntsauce, GlassFET, Thor12x, Ka6s, Symane, Logan,
DigitalC, Tesla4life, EJF, Blue borg, Smobri, Romeodesign, Millars, Tiddly Tom, Scarian, WereSpielChequers, NB-NB, Hertz1888, Dawn
Bard, Viskonsas, Caltas, Matthew Yeager, Command5, Thyroe, Yintan, M.thoriyan, MyNickname, Best 24, Dochdododo, Keilana, Bentogoa, Happysailor, Sletfsak2, Oda Mari, ScAvenger lv, Faradayplank, AngelOfSadness, Joydrop, Stoneygirl45, Katecummings, Lightmouse, Manway, Rafamachine, Svick, Datadrainacidblast, Jongleur100, Kristine.clara, Dust Filter, Mr. Stradivarius, Ascidian, PerryTachett, Denisarona, Jons63, Asher196, Troy 07, Valiant11, Serialdownloader, Elassint, Rhyshuw1~enwiki, ClueBot, SummerWithMorons,
LAX, Michael Gary Scott, Fspade, Deviator13, GorillaWarfare, Jackollie, Snigbrook, Foxj, The Thing That Should Not Be, Littlekorea34,
FLAHAM, Leonard 280, Drmies, Frmorrison, DanielDeibler, Wikijens, CounterVandalismBot, Skeeball93, Niceguyedc, EconomicsGuy,
Gointv, Mayawi, Bob bobato, Neverquick, Nseidule, Chelseax3rose, Excirial, Jusdafax, Anquiliquest, Moreau1, Rcooley~enwiki, Wikitumnus, Eeekster, Conical Johnson, Samx0x0x0, Abrech, Dropsore, Atomicfro, Vinhchaule, Arjayay, Jotterbot, Tinje, 7&6=thirteen,
Razorame, Dekisugi, Deviljin21, SchreiberBike, Mlas, Safreeman, Q1w2e88, Calor, Girtyzg, Thingg, Maczad, Aitias, Footballfan190,
500million, Versus22, Sleddog71, Superherogirl7, Johnuniq, Egmontaz, Vanished user uih38riiw4hjlsd, Vanished User 1004, DumZiBoT, Qwertyqwertqwert, Aristokrata, Willem103, XLinkBot, Hotcrocodile, Spitre, Bar uurum, Gnowor, Andyl620, Vividenblem,
Stickee, Rror, Bradv, Ed1234ab, 21stCenturyGreenstu, Avoided, WikHead, SilvonenBot, Badgernet, Noctibus, Artaxerxes, Subversive.sound, JinJian, S TiZzL3, Radiodata researcher, Milos Stevanovic, Addbot, Mortense, Manuel Trujillo Berges, Fyrael, Captain-tucker,
Kingjames528, Otisjimmy1, Friginator, Fgnievinski, Swampre, Bob sagget jr., Fieldday-sunday, Laurinavicius, Kman543210, Aashleynj, Ka Faraq Gatri, Vrray people107, MrOllie, XRK, Dylanrules123456789, LinkFA-Bot, 84user, Tide rolls, Lightbot, OlEnglish,
Helt, Serge Lachinov, Gail, David0811, Albeiror24, Gursis11, Luckas-bot, Vedran12, Yobot, Fraggle81, II MusLiM HyBRiD II, Aldebaran66, Melvalevis, Joetaras, Troymacgill, Washburnmav, SwisterTwister, Knownot, Axel22, MacTire02, OregonD00d, AnomieBOT,
Stears81, Quangbao, Sertion, Jim1138, Galoubet, Eating Tomatoes, Piano non troppo, Kingpin13, RandomAct, Materialscientist, Citation bot, Anthonypunk1, Beenturns23, Crimsonmargarine, Kirchsw, TinucherianBot II, Timir2, LeX4051, The sock that should not be,
Capricorn42, Drilnoth, Tex-linke, Jerey Mall, Rainshower, Batesmas214, Teamitem, Crabman90210, AbigailAbernathy, TheIntersect,
DjbFire, Ab1, Brandon5485, DaleDe, Yoganate79, EMDavidson, Astatine-210, Fotaun, GliderMaven, FrescoBot, Magnagr, Tangent747,
Tobby72, A.Abdel-Rahim, Sky Attacker, HJ Mitchell, Audemat, Blacky111, Jamesooders, Cannolis, HamburgerRadio, Citation bot 1,
Connerandtom, MacMed, Pinethicket, I dream of horses, Hard Sin, PrincessofLlyr, Pillo, Skyerise, Jschnur, Tesladeservescredit, Serols,
SpaceFlight89, Meaghan, D1tempo, Hyater, Pankaj2211, EdoDodo, Cnwilliams, Postdeleter, Gryllida, Hsnmoom, Thrissel, Discographer, MAS10, Francis E Williams, Vrenator, Davish Krail, Gold Five, Wiki-Updater 2.0, Everyone Dies In the End, Mttcmbs, Brian
the Editor, Suusion of Yellow, Tbhotch, Reach Out to the Truth, Sideways713, Marie Poise, Mean as custard, Qwerky0o0, Jonathan
Levy, Johnjones5278, Slon02, EmausBot, Nebabc11, Thetofuseezall, Yuhter, Ken95, Immunize, Gfoley4, Jorge c2010, Yaleshen, Ajraddatz, TLPA2004, Dewritech, Courcelles is travelling, GoingBatty, RA0808, Robert376, CaptRik, Smappy, Cherrybear101, Slightsmile,
Tommy2010, Hagis5555550, Wikipelli, K6ka, Hagisman, Thecheesykid, Kkm010, 15turnsm, 88frog88, Susfele, Chuck Baggett, F,
A930913, H3llBot, Wayne Slam, Rcsprinter123, TechWriterNJ, Gsarwa, Adbatson, ChuispastonBot, Teapeat, 28bot, Superdehound,
Halfbreed m, Cgt, ClueBot NG, Smtchahal, Winsladed08, CocuBot, This lousy T-shirt, BarrelProof, Jayanthkrishna, DobriAtanassovBatovski, Jocelyncarrasco, Snotbot, Crossreradio, Mesoderm, Widr, Reify-tech, Theopolisme, Oddbodz, Helpful Pixie Bot, Ghostshock,
Kiwitunza3, Strike Eagle, Titodutta, Wbm1058, Lowercase sigmabot, BG19bot, Stupidguy24, TCN7JM, Spoons14, Northamerica1000,
ISTB351, Commandochris, MusikAnimal, Planetary Chaos Redux, Mark Arsten, JHobson2, Robert the Devil, Soerfm, 17morria, Loriendrew, Klilidiplomus, Tucci mayne, Happenstancial, Cqdx, Miszatomic, Jamecons, MartinBoudreault, Embrittled, Diyanah satariah,

132.11. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

573

Total-MAdMaN, Epicwo, Nikeboy175, Adias13, Elddup11, Rahulradio, Hmainsbot1, Webclient101, Boby9952, SFK2, Reatlas, Iturbe Online, Fycafterpro, Faizan, Aftabbanoori, Baconatorsforall, JamesMoose, Jakec, DetroitSeattle, Do Thang, Syamsunders, DavidLeighEllis,
Kavithasri362, Liquid Lime18, Sirwalterdouglas, Comp.arch, Finnusertop, Ginsuloft, George8211, Noyster, Mrman21, UY Scuti, Meteor
sandwich yum, Bballer123456789321, Esl555666, TrekkieSpeller, Mortierr, HHubi, Crookedy0ungg, Superdragonmonster, Monkbot,
Nemasdia5673, Patient Zero, Sssredg, Phemmyjohnson, Golf, Meep876, 3primetime3, HMSLavender, Idunnowhat, Himisterpie, Beeshal Khadka, Craig Leo Johnson, Scientistmangesh, REDIRECT, SQMeaner, KasparBot, Chand3994, Blamheadshot11, Agricola123,
ProprioMe OW, Pulltea, Swissinator, Filpro, Bigmike88, Bigboombox, Goose121, CLCStudent, Duraka Radio, Jekson Bim, Wobblytabletop, Mariusrobin1981, Westofawesome, Radio batista ide, Su69, Stuthings1234567891011121314151617181920, On the ceiling, Electivo000, Zorgate, Marc5989, CODbacon20 and Anonymous: 1512
Carrier wave Source: https://en.wikipedia.org/wiki/Carrier_wave?oldid=749806239 Contributors: The Anome, Christian List, Waveguy,
Angela, Radiojon, Jakenelson, Furrykef, Itai, Omegatron, Robbot, Graeme Bartlett, Rchandra, Edcolins, PACO~enwiki, Geof, ArnoldReinhold, *drew, PWilkinson, Poweroid, Wtshymanski, Stephan Leeds, Nuno Tavares, Alvis, Nuggetboy, Eyreland, Geimas5~enwiki,
Srleer, DVdm, YurikBot, MMuzammils, , Rsrikanth05, Deville, Fernblatt, Rikimaru~enwiki, SmackBot, Xaosux, Oli
Filth, Sputtups, Cybercobra, RomanSpa, 16@r, SlayerK, Tawkerbot2, Chetvorno, Mattisse, Dawnseeker2000, Harryzilber, Jim.henderson,
J.delanoy, Athaenara, TomyDuby, Dorftrottel, Mlewis000, Idioma-bot, VolkovBot, Amikake3, TXiKiBoT, SieBot, Hertz1888, Miniapolis, Dravecky, ElectronicsEnthusiast, ClueBot, PipepBot, MystBot, Deineka, NjardarBot, OlEnglish, Legobot, Luckas-bot, RibotBOT,
GliderMaven, D'ohBot, MastiBot, Jimys salonika, EmausBot, WikitanvirBot, ClueBot NG, O.Koslowski, Joeplex, KasparBot, Gaelan,
InternetArchiveBot and Anonymous: 39
Frequency modulation Source: https://en.wikipedia.org/wiki/Frequency_modulation?oldid=752099783 Contributors: Mav, The Anome,
Hannes Hirzel, Waveguy, Ram-Man, Michael Hardy, Pit~enwiki, Nixdorf, Karada, Stw, Ahoerstemeier, Stevenj, Docu, Glenn, Lee M,
Smack, Bemoeial, Radiojon, Furrykef, Saltine, Omegatron, Phoebe, Olathe, Robbot, Pibwl, Blainster, Giftlite, DavidCary, BenFrantzDale, Lee J Haywood, Ssd, Siroxo, Albany45, Matt Crypto, Stevietheman, Antandrus, Rdsmith4, Sonett72, Jakro64, CALR, Rich Farmbrough, Lion, Ibagli, Bender235, MBisanz, Jarl, Cacophony, Simon South, Bobo192, Ntmatter, Rbj, Cohesion, Sparkgap, Andrewpmk,
Fritz Saalfeld, Chivalry, Atomicthumbs, Wtmitchell, Wtshymanski, Paul1337, Cburnett, RainbowOfLight, DV8 2XL, Redvers, Ringbang,
TomTheHand, Hdante, Zilog Jones, Eyreland, Junes, Graham87, BD2412, Eteq, Zoz, MZMcBride, Vegaswikian, MapsMan, Titoxd,
FlaBot, RexNL, Lmatt, Srleer, Chobot, Jpkotta, YurikBot, Borgx, RussBot, Splash, Akamad, Dogcow, Sangwine, Joelhalbert, Brandon,
Mikeblas, Tachs, Happyharris, Plamka, Daniel C, Pb30, SmackBot, TalezShin, Eskimbot, Commander Keane bot, Yamaguchi , Phillipbeynon, Skizzik, Oli Filth, EncMstr, Bob K, Harumphy, JonHarder, Kukini, Ysoldak, Soumyasch, MonsieurET, Magicmat, Makyen, JustinSmith, Rogerbrent, Dicklyon, Larrymcp, Kvng, Tawkerbot2, Chetvorno, SkyWalker, CmdrObot, JohnCD, Lark ascending, Casper2k3,
Necrat, Mblumber, Scissorhands1203, Quibik, Thijs!bot, N5iln, Gerry Ashton, Brichcja, Magicscott, KrakatoaKatie, Luna Santin, HyperDrive, JAnDbot, Harryzilber, CosineKitty, Quentar~enwiki, Magioladitis, KyleAndMelissa22, VoABot II, Email4mobile, Kaifeng,
Phmonopoly, Tercer, Kayau, Hemidemisemiquaver, MartinBot, Haner, Wa3frp, FreshBreeze, Reedy Bot, McSly, Samtheboy, KylieTastic, Ampsys, David.lecomte, Funandtrvl, VolkovBot, Wikipedita, Alinja, TXiKiBoT, Vsarank, Serrano24, LeaveSleaves, Cuddlyable3,
Robert1947, Spinningspark, Daviddoria, AlleborgoBot, ConnTorrodon, Renxa, Vladimir Stalin, SieBot, Interselector, YourEyesOnly, Smsarmad, Flyer22 Reborn, Justinperkins, Berserkerus, Miniapolis, Lisatwo, BlackOrestes, Svick, Joelster, ElectronicsEnthusiast, Dp67,
ClueBot, Binksternet, Muhandes, Umair ajmal01, Johnuniq, BodhisattvaBot, SilvonenBot, DOI bot, Chamal N, AndersBot, CodySupermarketSweep, Tassedethe, Romanskolduns, Snaily, Legobot, , Luckas-bot, Yobot, Ptbotgourou, DemocraticLuntz, Ciudadano001, Mofelix2, LilHelpa, Xqbot, Jhbdel, Nedim Ardoa, Chase.chapman, Prari, Citation bot 1, Pinethicket, MondalorBot, Gehilfen,
Vrenator, Inferior Olive, Reaper Eternal, Suusion of Yellow, Paulipu, Minimac, Cryptochromatologist, Ripchip Bot, Becritical, EmausBot,
Hhhippo, ZroBot, Chanli44, Caspertheghost, Boashash, Burhem, ChuispastonBot, Mjean-njitwill, ClueBot NG, MelbourneStar, Raghith,
Engradio, Helpful Pixie Bot, Vagobot, Northamerica1000, Collins20V2, Frogging101, Loriendrew, ChrisGualtieri, Pradku2, The.ever.kid,
Lugia2453, ASJoshi, Neerajguptanew, EG16, MitchRandall, Lgunther1, Kavya l, Rijoan and Anonymous: 252
Frequency Source: https://en.wikipedia.org/wiki/Frequency?oldid=748783259 Contributors: AxelBoldt, Mav, Tarquin, Tbackstr, AstroNomer, Andre Engels, Ben-Zin~enwiki, DrBob, TomCerul, Heron, Youandme, Spi~enwiki, Lir, Patrick, Chinju, Dgrant, Ellywa,
Ahoerstemeier, Stevenj, , Glenn, Nikai, Andres, Mxn, HolIgor, Reddi, Hyacinth, Tero~enwiki, Omegatron, Aliekens, Denelson83, Maheshkale, Robbot, Sverdrup, Pifactorial, HaeB, Tea2min, Psb777, Giftlite, Djinn112, BenFrantzDale, Everyking, Niteowlneils,
Tom-, Sundar, Jackol, SWAdair, LucasVB, Pcarbonn, Noe, Antandrus, Radman, PricklyPear, MacGyverMagic, Icairns, Parakalo~enwiki,
Ta bu shi da yu, Heryu~enwiki, A-giau, Discospinster, Vsmith, Pie4all88, Bender235, Andrejj, Evice, Nabla, Quinobi, Alberto Orlandini,
Bobo192, Smalljim, .:Ajvol:., Helix84, Haham hanuka, Jason One, Ranveig, Arthena, Ricky81682, Melaen, Wildstar2501, Wtshymanski, Cburnett, Endersdouble, RainbowOfLight, Kusma, HenryLi, Dan100, Oleg Alexandrov, Brookie, Roland2~enwiki, Firsfron, OwenX,
Woohookitty, MONGO, Macaddct1984, Waldir, SeventyThree, Erl, BD2412, Josh Parris, Sjakkalle, Amitparikh, The wub, FlaBot, VKokielov, Nihiltres, Sanbeg, RexNL, Ayla, Alvin-cs, Srleer, Chobot, DVdm, Bgwhite, Cactus.man, Digitalme, YurikBot, RobotE, Sceptre,
Gavrilis, Jimp, Phantomsteve, RussBot, Chuck Carroll, KSmrq, Stephenb, Polluxian, CambridgeBayWeather, Rsrikanth05, Msoos, Int 80h,
ZacBowling, Yahya Abdal-Aziz, Holon, Dhollm, Pele Merengue, WolFox, BOT-Superzerocool, PrimeCupEevee, Wknight94, Searchme,
Light current, Deville, Zzuuzz, Lt-wiki-bot, JoanneB, HereToHelp, Ethan Mitchell, Mejor Los Indios, Sbyrnes321, Marquez~enwiki,
NetRolller 3D, Sardanaphalus, KnightRider~enwiki, SmackBot, MattieTK, Blue520, Bomac, Scubbo, Cessator, Hudd, Gilliam, Bluebot, Bre Dun, SlimJim, Kernigh, Complexica, Metacomet, Nbarth, Bob K, Tsca.bot, Can't sleep, clown will eat me, Nick Levine,
Tschwenn, Chlewbot, JesseRafe, Computer guy57, Nakon, GoldenBoar, Cockneyite, BinaryTed, Acdx, Daniel.Cardenas, Kukini, Ged
UK, SashatoBot, BorisFromStockdale, Kuru, RTejedor, Accurizer, 16@r, Alma Teao Wilson, Mr Stephen, Dicklyon, Optakeover, Oreos
are crack, SirPavlova , ShakingSpirit, Shadow Puppet, Levineps, Iridescent, Amakuru, Tawkerbot2, Chetvorno, Slmader, Lnatan25, JForget, Cynical Jawa, Irwangatot, Suls, Jsd, McVities, Skoch3, Cydebot, Editor at Large, Omicronpersei8, JodyB, Doomooman, Epbr123,
HoodenHen, JNighthawk, Atillidie13, Marek69, SGGH, Yettie0711, Greg L, Escarbot, Mentisto, Porqin, Nervature, AntiVandalBot,
UnivEducator, Tomasr, JAnDbot, MER-C, Aka042, Catgut, EagleFan, Madmoomix, Vssun, PatPeter, Colithium, RisingStick, Thompson.matthew, Leyo, Cyrus Andiron, Ooga Booga, J.delanoy, Trusilver, Igorls1~enwiki, Mike V, Izno, Idioma-bot, Xenonice, VolkovBot,
ABF, VasilievVV, Constant314, Philip Trueman, TXiKiBoT, Zidonuke, Sankalpdravid, Don4of4, Trevorcox, Dprust, Chaotic cultist,
Houtlijm~enwiki, Lerdthenerd, Mattazzer, Yk Yk Yk, Ageyban, AlleborgoBot, Nagy, EmxBot, SieBot, Moonriddengirl, Malcolmxl5,
Paradoctor, Danielsb7676, GrooveDog, Jerryobject, Christopherwrong, Flyer22 Reborn, Oda Mari, Faradayplank, Alex.muller, Dravecky,
C'est moi, Cyfal, Mike2vil, Anchor Link Bot, Kortaggio, Francvs, Mx. Granger, Elassint, ClueBot, Binksternet, GorillaWarfare, PipepBot, The Thing That Should Not Be, Ventusa, Niceguyedc, DragonBot, Abdullah Krolu~enwiki, Quercus basaseachicensis, Jusdafax,
SpikeToronto, Brews ohare, PhySusie, JamieS93, Thingg, Scalhotrod, SoxBot III, Crowsnest, Gonzonoir, Stickee, Rror, Little Mountain
5, NellieBly, Jbeans, ElMeBot, Thatguyint, Mwstyles2002, Stephen Poppitt, Tayste, Kraaiennest, Addbot, Queenmomcat, Friginator, Fgnievinski, Ronhjones, Fieldday-sunday, Laurinavicius, Leszek Jaczuk, LaaknorBot, CarsracBot, Redheylin, Favonian, Tyw7, Ehrenkater,

574

CHAPTER 132. MORSE CODE

QuadrivialMind, Teles, Zorrobot, David0811, Luckas-bot, Yobot, VengeancePrime, Ptbotgourou, Wikipedian Penguin, Ayrton Prost, EricWester, AnomieBOT, Sunlight123, Jim1138, Galoubet, Aditya, Ulric1313, Materialscientist, Citation bot, Akilaa, Klij, Pinapple man, Jock
Boy, LilHelpa, Xqbot, Ssola, Xax12345, Capricorn42, Jsharpminor, Anna Frodesiak, NOrbeck, GrouchoBot, AVBOT, Frosted14, RibotBOT, Logger9, Hkhk59333, Shadowjams, WaysToEscape, A. di M., Krj373, Vicharam, Dger, Steve Quinn, InternetFoundation, Xhaoz,
Citation bot 1, Pinethicket, I dream of horses, Jonesey95, Martinvl, TobeBot, Trappist the monk, Callanecc, LilyKitty, Jerome pic, PeterFlannery, Suusion of Yellow, Bonebreaker1238, Marie Poise, DARTH SIDIOUS 2, TjBot, Bento00, DexDor, Skamecrazy123, EmausBot, Dewritech, Robert376, Antodges, Spiderbill, Enggdrive, Wikipelli, ZroBot, John Cline, Dondervogel 2, SporkBot, Wayne Slam,
Frigotoni, Cmathio, Arman Cagle, Boashash, Atlantictire, RockMagnetist, TYelliot, DASHBotAV, MicahJonson, ClueBot NG, Matthiaspaul, This lousy T-shirt, Chester Markel, AeroPsico, Widr, EmilyGirl003, Pluma, Diyar se, Helpful Pixie Bot, Doorknob747, Rijinatwiki,
Cyberpower678, TheGeneralUser, MusikAnimal, Snow Blizzard, Glacialfox, Loriendrew, BillBucket, TheInfernoX, Cyberbot II, Mediran, Corn cheese, Reatlas, Faizan, Praveenskpillai, ElHef, Babitaarora, Monkbot, Horseless Headman, Silas69696969, Justin15w, Thewikichanger666, MatthewS1999, 115.241.241.2d, Zppix, Stillmorepeople, Cyrej, Cncunjn, Priyanksoni9713, Jaysilver075, RunnyAmiga,
Dranoelpnairb, Jimli536, Mr.Mohel, Kulia91 and Anonymous: 559
Radiotelephone Source: https://en.wikipedia.org/wiki/Radiotelephone?oldid=745512940 Contributors: Heron, Tedernst, Patrick, Pnm,
Glenn, Wfeidt, GRAHAMUK, Radiojon, Fvw, Sewing, Donreed, BigHaz, Bumm13, MementoVivere, ChrisRuvolo, Rich Farmbrough,
RoySmith, Wtshymanski, Richard Weil, Linas, Cbdorsett, Vegaswikian, Krash, Margosbot~enwiki, RobyWayne, Wongm, Mikeblas, Deville, Closedmouth, David Jordan, Ekeb, MrWilly, Airodyssey, Jmchu, DCDuring, Mauls, Commander Keane bot, Kharker, Thumperward, SchftyThree, IronGargoyle, Ckatz, 16@r, Chetvorno, WeggeBot, Cydebot, LuckyLouie, Alphachimpbot, Harryzilber, MERC, CosineKitty, Magioladitis, MartinBot, Jim.henderson, Geoweb54, VolkovBot, Cireshoe, Jamelan, Logan, Fanatix, SieBot, Addbot,
CarsracBot, Yobot, Soldarat, Poiyiop1, Omnipaedista, Pinethicket, Yunshui, Itu, RjwilmsiBot, Jackehammond, Dewritech, Udvarias,
Forbin1, ClueBot NG, Gossesol, Helpful Pixie Bot, Alan, David Spil, 32RB17, Filedelinkerbot, KasparBot, CLCStudent and Anonymous: 30
Two-way radio Source: https://en.wikipedia.org/wiki/Two-way_radio?oldid=751689462 Contributors: William Avery, Ubiquity, Glenn,
Warofdreams, Denelson83, Bearcat, DocWatson42, N1zyy, MementoVivere, Rich Farmbrough, Blue Wizard, Hooperbloob, Fordan, Wtshymanski, Sciurin, Computerjoe, RxS, Jorunn, Misternuvistor, Vegaswikian, Kolbasz, Wavelength, Kencaesi, Winnie-MD, Brandon,
Mysid, Jory Plummer, David Jordan, Heterodyne~enwiki, SmackBot, Arny, Frymaster, Movementarian, Mixmatch, Deli nk, Rrburke,
Gschadow, Kc2idf, Mike1901, Levineps, Sigil VII, Simon12, Iridescent, EPO, Adhawan, Chetvorno, CmdrObot, Cydebot, Gogo Dodo,
Shimada22~enwiki, Widefox, Alphachimpbot, Harryzilber, MER-C, Andonic, Appraiser, Jufam44, DoorsAjar, Kdbailey, Fanatix, Faradayplank, ImageRemovalBot, SiriusPro, Timbrux, Cfsenel, Sv1xv, Sin Harvest, Addbot, Fgnievinski, Lightbot, Zorrobot, Yobot, Hwardsil,
Karanne, Iroony, AnomieBOT, Jim1138, Joewood33, J04n, Kuppa.soop, Surv1v4l1st, Gonzosft, Serelektronik, Dunkson, Yunshui, Fox
Wilson, Batternut, Mean as custard, EmausBot, MrFawwaz, HenryHayes, ClueBot NG, Nispio, Helveteshunden, Helpful Pixie Bot, Zuixo,
BG19bot, Nen, Daki72, Fylbecatulous, Jionpedia, Lemnaminor, Osbournehutch, JasonBrady55, Nionman442, Candy 2016 and Anonymous: 116
Airband Source: https://en.wikipedia.org/wiki/Airband?oldid=748426596 Contributors: Arpingstone, GRAHAMUK, Radiojon, Flauto
Dolce, Ericg, Cacycle, ArnoldReinhold, Smyth, Sparkgap, Krellis, Wtshymanski, Armando, Tabletop, Ahunt, Schoen, Change1211, David
Jordan, SmackBot, Elonka, Tantivy, Chris the speller, Erzahler, KevM, Cottingham, MilborneOne, Fnlayson, Altaphon, Oosoom, Epbr123,
Blair Bonnett, Harryzilber, CosineKitty, Charlene.c, Sgeureka, Je G., Mr.hogi, Markmc, Dfwilt, Explicit, SchreiberBike, Davgrps,
Addbot, Yobot, AnomieBOT, Francis E Williams, Miracle Pen, F1jmm, Obankston, John of Reading, Smsmonster, SporkBot, ClueBot
NG, Rezabot, Nen, Dkgibson, Ices2Csharp, JakeWi, Monkbot, COMPACTY, Bender the Bot and Anonymous: 22
Citizens band radio Source: https://en.wikipedia.org/wiki/Citizens_band_radio?oldid=750926673 Contributors: WojPob, Tarquin,
Gorm, William Avery, GABaker, Tango, Gbleem, Tregoweth, F1lby, BAxelrod, Dj ansi, Mulad, WhisperToMe, Steinsky, IceKarma,
Kierant, Fibonacci, Bevo, AnonMoos, Eckzow, Denelson83, Astronautics~enwiki, KeithH, Moriori, Cyrius, DocWatson42, Nichalp, ZackDude, Karn, Mboverload, Rchandra, Bobblewik, R. end, Rdsmith4, Jesster79, Bumm13, Phil1988, Paul99, Neutrality, Ukexpat, Jakro64,
ChrisRuvolo, DanielCD, Discospinster, Rich Farmbrough, Yipper, Bender235, Kms, Kbh3rd, Ylee, CanisRufus, The King Of Gondor,
Huntster, Lunaverse, Rpresser, Func, BalooUrsidae, Csl77, Guidod, Sparkgap, Kjkolb, Towel401, Ociallyover, Danski14, Alansohn,
Anthony Appleyard, Wtshymanski, Nholland~enwiki, Kaibabsquirrel, Zxcvbnm, BDD, DV8 2XL, Gene Nygaard, Bastin, Unixxx, Optimusnauta, Roboshed, Woohookitty, Lifung, Plaws, Tabletop, SDC, Jonnabuz, Btyner, Mandarax, Graham87, Villager57, Haikupoet, RadioActive~enwiki, Linuxbeak, Vegaswikian, Makaristos, Gg630504, VidTheKid, Kornbelt, Ground Zero, Mga, TheAnarcat, Anonym1ty,
RobyWayne, Windharp, Hatch68, Bgwhite, Uvaduck, YurikBot, Crazytales, Pleonic, Deerslayer, Akamad, Gaius Cornelius, Chick Bowen,
ONEder Boy, Fixedd, Voidxor, Mad Max, Ma3nocum, Elizabeyth, Sandman1142, Bota47, Jeh, Mrtea, J. Van Meter, Mike Selinker,
Arthur Rubin, David Jordan, Rearden9, PMHauge, Junglecat, Mdwyer, Kingboyk, Elliskev, Borisbaran, SmackBot, Reedy, Argyll Lassie,
Yvesdesprit, Arny, Commander Keane bot, Oscarthecat, Bazonka, Rolypolyman, A. B., Beatgr, Dethme0w, Can't sleep, clown will eat me,
Tim Messer, Duncancumming, DJboutit, Mulder416, Ashawley, Jwilkers, KaiserbBot, Luno.org, TenPoundHammer, Lambiam, JzG, Jadedoto, Adavidw, KenFehling, Euchiasmus, Epicam, Kythri, Dicklyon, Twalls, Arkrishna, E-Kartoel, Lenn0r, Kvng, PaulGS, Potashnik,
*brew~enwiki, Joseph Solis in Australia, MaxHarmony, Stereorock, BKmetic, DJGB, Sohebbasharat, CmdrObot, Picaroon, Requestion,
NE Ent, Anklepants, Wingman358, Cydebot, Khatru2, Dragomilo, Epbr123, Btball, Qwyrxian, WillMak050389, Big Bird, Porqin, AntiVandalBot, ReviewDude, Widefox, Seaphoto, Malvineous, Heavensblade23, Up4017, JAnDbot, Harryzilber, Supersparks, Awien, Greensburger, MegX, SiobhanHansa, VoABot II, SHCarter, Think outside the box, Benglines, Ebowdish, Woodieq, Coeepusher, Cascadia,
Oroso, XXxPigeonKickerxXx, Kf4yfd, Rhinestone K, Maurice Carbonaro, Sc00baSteve, TheHurtProcces, Gwyth, SpigotMap, Interscan,
Toneythetiger, Gregtzy, Runt, Squidfryerchef, KylieTastic, Leawoodcops, Random Passer-by, Joeinwap, VolkovBot, Cbradiomagazine,
DoorsAjar, Xhantar, G4led, Rei-bot, DerGolgo, Drew2000, Drappel, Ttennebkram, Greswik, Rhvanwinkle, Falcon8765, Earl Marischal,
Truthanado, Ron McCracken, Michaelsbll, Memo232, Daveh4h, Tyrwh, Spur, The Parsnip!, Igor.grigorov, Not LTD, Happysailor, Marmotdan, Pedalboard, Shioda, Miniapolis, Lightmouse, Callidior, Manway, Diego Grez-Caete, RedBlade7, Anchor Link Bot, TheRealJohnMcClane, Atif.t2, ClueBot, Phoobahr, Gophi, EoGuy, RNKCHICAGO1963, Joni Ellen, 9urges, Auntof6, BOBNEIL60657, Rek4385,
John Nevard, Arjayay, ChrisHodgesUK, Bjdehut, DumZiBoT, XLinkBot, Roxy the dog, Moline670, NellieBly, QRZ11~enwiki, KE6LYU,
Addbot, Willowcb, LP, Some jerk on the Internet, Fyrael, Non-dropframe, TutterMouse, Sattmaster, Keithatncd, Rocketradio, Quercus
solaris, Kb3pxr, 2H2UZ, Tassedethe, Numbo3-bot, Lightbot, Ivanov id, Gail, The Bushranger, Luckas-bot, Yobot, AnomieBOT, Flewis,
Citation bot, Neurolysis, LilHelpa, Ekconklin, Spike-from-NH, Khajidha, Roctober, FrescoBot, Surv1v4l1st, Firstwords, DigbyDalton,
DrilBot, Vk3pjb, Yfcb, RedBot, 46percent, TobeBot, Mercy11, Raytk12, Nathan34t, Dinamik-bot, F1jmm, Bubrahma, PaulHammond2,
Stegop, Wb2kqg, Obankston, Ripchip Bot, Hoopylove, EmausBot, Davejohnsan, Dewritech, Ihucker, Wikipelli, Mobilewi, ZroBot,
ToiletAssassin, Dondervogel 2, Rockclaw1030, Kindzmarauli, Tony Ling, Daus w2nri, AKeenEye, BornonJune8, Senator2029, ClueBot
NG, Chester Markel, Widr, 29hn001, Helpful Pixie Bot, Captain Klystron, TRDunne, 911cops, BG19bot, AsciiWolf, Steven19at066,

132.11. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

575

Callharr123, Several Pending, Mdann52, SpitFireFarely, ChrisGualtieri, Lucy34bell, Khazar2, 313 TUxedo, Mogism, Goodtiming8871,
A320tech, JakeWi, Rybec, Georeyknight, Pancake Johnny, 32RB17, Citizenfane, Namscout, KasparBot, YesPretense, Chris.wingrave,
Linux STAIN, Scan911, Steven066 and Anonymous: 439
Quadrature amplitude modulation Source: https://en.wikipedia.org/wiki/Quadrature_amplitude_modulation?oldid=751024769 Contributors: Damian Yerrick, The Anome, Etu, Michael Hardy, Ahoerstemeier, Glenn, Grin, HPA, Charles Matthews, Radiojon, Jake Nelson, Omegatron, FlyByPC, Boy b, Sbisolo, Magnicat, DocWatson42, Ssd, Mboverload, Rchandra, Bumm13, Kevin Rector, Solitude,
Guanabot, Qutezuce, Tgies, Kwamikagami, Alereon, Simon South, Foobaz, Bobbis, Karlthegreat, Arthena, Lord Pistachio, Adamgoldberg, Dtcdthingy, Bcombee, Lerdsuwa, MartinVillafuerte85, SeventyThree, BD2412, Tangotango, Ddawson, HappyCamper, Drbrain,
Alejo2083, Srleer, Stevep001, Roboto de Ajvol, YurikBot, RussBot, Splash, Gaius Cornelius, Willpo~enwiki, Poetatoe, Robertvan1,
Byj2000, Dogcow, Brandon, Voidxor, Semperf, Zwobot, Rdmoore6, JLaTondre, Rathfelder, SmackBot, Delphi00, Eskimbot, Sam8,
Gilliam, Bluebot, DStoykov, Oli Filth, Nbarth, Colonies Chris, Hongooi, Zirconscot, Dcamp314, Romanski, Salamurai, Dave314159,
Littleman TAMU, Notmicro, Abolen, Dicklyon, AxG, Kvng, Siebrand, Harold f, Sakurambo, Requestion, Meno25, Thijs!bot, MadProcessor, Grayshi, Dawnseeker2000, Deective, Harryzilber, Drizzd~enwiki, .anacondabot, Markhahn, MartinBot, R'n'B, Mange01, DorganBot, Bonadea, Alinja, Philip Trueman, Colmanian, Ann Stouter, Thunderbird2, SieBot, Henry Delforn (old), Lenz1105, Anchor Link
Bot, Melcombe, PrinceGaz, Hongthay, Poterxu, Bbb2007, PixelBot, Ykhwong, 1ForTheMoney, Johnuniq, Life of Riley, Salam32, Addbot, Fgnievinski, Boss756, MrVanBot, Ozob, Ben Ben, Legobot, Luckas-bot, Yobot, AnomieBOT, Ciudadano001, Munozdj, Nedim
Ardoa, Shadowjams, Green Cardamom, FrescoBot, Voxii, Itusg15q4user, Zhouyuanxin, I dream of horses, Adam Anderson CIT, Bugybunny, FoxBot, Dinamik-bot, Miracle Pen, J. in Jerusalem, Alcapwned86, EmausBot, Bongoramsey, Myth318, Mocks9, Edgar.bonet,
Petrb, ClueBot NG, Widr, BG19bot, Ceradon, Testkylia, Srinathkr3, Cyberbot II, YFdyh-bot, Babitaarora, Spyglasses, ErRied, Bernael,
Cdma2k, Qzd, InternetArchiveBot, GreenC bot and Anonymous: 187
Medium wave Source: https://en.wikipedia.org/wiki/Medium_wave?oldid=751767278 Contributors: Timo Honkasalo, The Anome,
RTC, GABaker, Spliced, Ellywa, Glenn, Palmpilot900, Wfeidt, Mulad, Radiojon, Jerzy, Twang, RedWolf, Baldhur, Phil1988, JTN,
ArnoldReinhold, Ericamick, Gerry Lynch, ZeroOne, Evice, Nigelj, ProhibitOnions, Wtshymanski, Rugxulo, Stephan Leeds, DV8 2XL,
Gene Nygaard, Jakes18, KelisFan2K5, Jpers36, Pol098, BD2412, Squideshi, RexNL, Chobot, 121a0012, YurikBot, SpuriousQ, Dddstone, Thomas H. White, Daniel C, IslandHopper973, SmackBot, Eskimbot, Kharker, Tghe-retford, A. B., AKMask, Suicidalhamster,
Harumphy, Quizman1967, Danikayser84, Zonk43, Mattdp, Bucksburg, Metre01, Stereorock, Dani 7C3, Chetvorno, Wa2ise, Flowerpotman, Dawnseeker2000, JAnDbot, Harryzilber, Rothorpe, JMyrleFuller, Ashishbhatnagar72, Glrx, Kostisl, R'n'B, CommonsDelinker,
J.delanoy, Ohms law, Liveinthewire, RingtailedFox, TXiKiBoT, Sankalpdravid, Qxz, Cuddlyable3, SteveSTFA, SieBot, Hertz1888, Purbo
T, Callidior, Rcooley~enwiki, Dxinginfo, Iohannes Animosus, Mlas, DumZiBoT, Thebestofall007, Addbot, M.nelson, Lightbot, Luckasbot, Yobot, Dellant, GrouchoBot, Omnipaedista, RibotBOT, Maitchy, Sibian, DABenji, RedBot, Cnwilliams, FoxBot, Unbitwise, Zumbooruk2, Rssbro, A930913, Peterh5322, ChuispastonBot, Matthiaspaul, PoqVaUSA, Danim, MerlIwBot, Helpful Pixie Bot, Cqdx,
Justincheng12345-bot, Hasenburg, 313 TUxedo, FellowesCarl, Corn cheese, One Of Seven Billion, Monkbot, DXFinder, InternetArchiveBot and Anonymous: 91
AM broadcasting Source: https://en.wikipedia.org/wiki/AM_broadcasting?oldid=742780152 Contributors: Bryan Derksen, Aldie, SimonP, GrahamN, Fonzy, Ericd, Rbrwr, Lir, Patrick, Infrogmation, GABaker, Egil, Mdebets, Glenn, Rossami, Deisenbe, Wfeidt, Mulad, Dysprosia, Snickerdo, Will, Hajor, Bearcat, Academic Challenger, Blainster, Neckro, DocWatson42, Ike~enwiki, Digital innity,
Mboverload, Wmahan, Antandrus, HorsePunchKid, Mako098765, MacGyverMagic, Mydotnet, Bumm13, B.d.mills, McCart42, Trilobite,
Abdull, Thorwald, Imroy, JTN, Rich Farmbrough, Guanabot, Ericamick, Bender235, Kbh3rd, Jnestorius, Evice, Kiand, Simon South,
Chbarts, Ociallyover, Wtshymanski, Jakes18, KelisFan2K5, Armando, RPharazon, WikianJim, Andromeda321, Eyreland, Gimboid13,
Graham87, BD2412, Haikupoet, Koavf, XP1, Reactor, Yamamoto Ichiro, SchuminWeb, Rune.welsh, RexNL, Ewlyahoocom, Leslie Mateus, Chobot, 121a0012, UkPaolo, Wavelength, Sceptre, Charles Gaudette, Raccoon Fox, Pigman, Epolk, RandallJones, Anomalocaris,
Mipadi, Harksaw, Retired username, Jpbowen, Mysid, Thomas H. White, Light current, Dposse, SmackBot, TBH, Video99, Antifumo,
Commander Keane bot, Hmains, Cabe6403, Coinchon, Colonies Chris, Can't sleep, clown will eat me, Harumphy, BNutzer, Mattdp, Zahid
Abdassabur, Khazar, Vgy7ujm, Masciare, Sectumsempra, Dicklyon, Esoltas, Iridescent, Igoldste, Stereorock, Az1568, Chetvorno, DangerousPanda, Fedir, CompRhetoric, Peripitus, A Softer Answer, Epbr123, Crockspot, Danbonsai, Seaphoto, Sion8, Jayron32, LuckyLouie,
Elaragirl, Milonica, Husond, Harryzilber, Erpel13, Steveprutz, Penubag, Magioladitis, Bongwarrior, CodeCat, Olsonist, YUiCiUS, Pekaje,
Mrceleb2007, Gaussgauss, Jamesofur, Gwen Gale, RingtailedFox, Philip Trueman, The Original Wildbear, Piperh, Ferengi, Liquid77,
SieBot, Hertz1888, Lightmouse, Callidior, Manway, Blake, Loren.wilton, ClueBot, The Thing That Should Not Be, EoGuy, FLAHAM,
Mild Bill Hiccup, Skeeball93, Blanchardb, Mayawi, Sepia tone, Excirial, Jusdafax, Rcooley~enwiki, Dxinginfo, Andy80586, Arjayay, Hans
Adler, Mlas, SoxBot III, Miami33139, Ascher15, BarretB, XLinkBot, Emmette Hernandez Coleman, Addbot, Mortense, Willking1979,
Non-dropframe, Vrray people107, Tassedethe, Tide rolls, Lightbot, Yobot, AnomieBOT, Mare420, NAC, Mahmudmasri, Materialscientist, Jagwar, Xqbot, Ringopox555, FrescoBot, Everlasting Winner, Jonesey95, 1m y0ur targ, Trappist the monk, FrankDev, Suusion of
Yellow, Dexter Nextnumber, Sean13zz, Teravolt, Dewritech, 1980fast, Bmmxc damo, Petrb, ClueBot NG, Widr, Antiqueight, BG19bot,
Zedshort, Loriendrew, Starsky135, Spray787, Jamesx12345, Heartanatomy, JakeWi, Ugog Nizdast, Stamptrader, SnoozeKing, HHubi,
Wyn.junior, Monkbot, CV9933, TBob2, RIT RAJARSHI, JenniferMari-Gardner, Gzkefpro and Anonymous: 181
Heterodyne Source: https://en.wikipedia.org/wiki/Heterodyne?oldid=748697532 Contributors: Waveguy, Heron, Michael Hardy, Julesd,
Glenn, Tonsofpcs, Tzf, Graeme Bartlett, Inkling, AJim, Foobar, Bobblewik, Hutschi, DragonySixtyseven, AmarChandra, Gary D,
Deglr6328, Danh, Blanchette, Unixplumber, JustinWick, Nigelj, Army1987, Hooperbloob, Keenan Pepper, Wtshymanski, Drbreznjev,
Aerowolf, Rnt20, Vegaswikian, Gisho, Lmatt, Srleer, Vidkun, Jschultz, Tole, Lavenderbunny, Bovineone, Dsmouse, Aler, Mysid,
Kkmurray, Petri Krohn, KNHaw, Nekura, SmackBot, PEHowland, Fulldecent, Ckerr, MonteChristof, Chris the speller, Kira nerrice, Oli
Filth, Onceler, Spiritia, Noahspurrier, Rainwarrior, Kvng, Chetvorno, VPliousnine, Sobreira, Northumbrian, Justyn, Danroa, MikeLynch,
JAnDbot, Uunter, CosineKitty, Talon Artaine, Glrx, BigrTex, Fountains of Bryn Mawr, Potatoswatter, VolkovBot, TXiKiBoT, GLPeterson, Jamelan, Eskovan, Spinningspark, Hertz1888, Nancy, Jadvinia, TypoBoy, Jacques.boudreau, The-tenth-zdog, Dspdude, Life of Riley,
SilvonenBot, Addbot, Download, Care, Luckas-bot, Jim1138, Omnipaedista, RibotBOT, FrescoBot, Atomtech, TheKing2200, RjwilmsiBot, DexDor, Hpfeil, Nobelium, Mohdabdulwaseem, ChuispastonBot, Helpful Pixie Bot, Themichaud, CitationCleanerBot, Zedshort,
Khazar2, Edinburghglasgow, Monkbot, CitrusEllipsis, Rfrobenius, Bender the Bot and Anonymous: 71
Detector (radio) Source: https://en.wikipedia.org/wiki/Detector_(radio)?oldid=738242421 Contributors: Michael Hardy, Reddi, Rholton,
DavidCary, Rchandra, M1ss1ontomars2k4, Peter B., Wtshymanski, Flayked, DV8 2XL, Rjwilmsi, Srleer, Krishnavedala, DVdm, Light
current, SmackBot, Steve carlson, Sam8, Bluebot, Nakon, Kvng, Chetvorno, Neelix, Slazenger, Bobblehead, Esmond.pitt, Harryzilber,
Nikevich, Jim.henderson, Glrx, JA.Davidson, TomyDuby, SJP, Cuddlyable3, Cwkmail, GreenSpigot, Sv1xv, Addbot, HatlessAtlas, Bae
gab1978, Yobot, LilHelpa, Xqbot, Maitchy, Wiki white owl, FrescoBot, Element98, Thinking of England, John Elson, Dcirovic, Ego White
Tray, ClueBot NG, Cyberbot II, Superdragonmonster, GreenC bot and Anonymous: 30

576

CHAPTER 132. MORSE CODE

Rectier Source: https://en.wikipedia.org/wiki/Rectifier?oldid=751542356 Contributors: The Anome, Tim Starling, Modster, Delirium,
Mac, Glenn, Andres, Dcoetzee, Reddi, Furrykef, Omegatron, Robbot, ZimZalaBim, Blainster, Timvasquez, Dinomite, Leonard G.,
LennartBolks~enwiki, Vadmium, PenguiN42, Andycjp, Mako098765, Lesgles, Glogger, PACO~enwiki, B.d.mills, ShortBus, Mike Rosoft,
CALR, Discospinster, Rich Farmbrough, Smyth, MAlvis, Mani1, Plugwash, MBisanz, SpeedyGonsales, PiccoloNamek, Hooperbloob,
Alansohn, Atlant, Wtmitchell, Wtshymanski, Danhash, DV8 2XL, Aempirei, Kenyon, Unixxx, David Haslam, Pol098, Arru, SCEhardt,
BD2412, Nanite, Ketiltrout, Rjwilmsi, Kazrak, Dennyboy34, Dinosaurdarrell, Arnero, Margosbot~enwiki, Nihiltres, RexNL, Fresheneesz, Geimas5~enwiki, Lmatt, Srleer, Wrightbus, Chobot, Krishnavedala, Wavelength, Oliviosu~enwiki, DMahalko, Hydrargyrum,
Stephenb, Shaddack, NawlinWiki, Bjf, Anetode, Dbrs, Scottsher, Barjazz, Petr.adamek, Light current, Super Rad!, Tabby, Fang Aili,
Petri Krohn, Anclation~enwiki, Poulpy, Anthony717, SmackBot, Sue Anne, Bmearns, Arny, Swerdnaneb, Bromskloss, Gilliam, Chris the
speller, Bluebot, EncMstr, AndrewBuck, DHN-bot~enwiki, Sbharris, Chrislewis.au, Audriusa, JustUser, OrphanBot, Addshore, SundarBot, Salamurai, Pilotguy, Kukini, Rigadoun, JorisvS, Minna Sora no Shita, CyrilB, Beetstra, Kvng, Jon barden, Majora4, Audiosmurf,
Chetvorno, Nczempin, Drinibot, Zureks, WeggeBot, Cydebot, A876, Gogo Dodo, ST47, Underpants, Arcayne, Click23, Thijs!bot, HappyInGeneral, Talyene, Antiekeradio, John254, Gerry Ashton, Dgies, Urdutext, Pie Man 360, AntiVandalBot, Luna Santin, Widefox, Guy
Macon, Rico402, JAnDbot, B3organ, Photodude, VoABot II, Swpb, Email4mobile, Deepdive217, JJ Harrison, AstroHurricane001, Silverxxx, DarkFalls, Suckindiesel, Simon the Dragon, DorganBot, Mlewis000, Pleasantville, ICE77, VasilievVV, Af648, Msdaif, Ulfbastel,
Wiae, Andy Dingley, Falcon8765, Spinningspark, !dea4u, Biscuittin, SieBot, Triwbe, Happysailor, Flyer22 Reborn, MinorContributor,
Csloomis, Anupriya9, Steven Crossin, Nancy, StaticGull, Treekids, ClueBot, Trojancowboy, Cyril42e, EoGuy, Compellingelegance, Drmies, Mild Bill Hiccup, Powersys, Versus22, SoxBot III, Makemewish, DumZiBoT, Rror, Little Mountain 5, TFOWR, Alexius08, Gggh,
Osarius, Nikhilb239, Addbot, Willking1979, Ki162, CanadianLinuxUser, Numbo3-bot, Luckas Blade, Snaily, Luckas-bot, Yobot, Kartano, Fraggle81, Legobot II, Amirobot, Andrew Pullen, AnomieBOT, Kristen Eriksen, Rubinbot, Jim1138, Fahadsadah, Poetman22,
, Materialscientist, Akilaa, ArthurBot, Xqbot, TracyMcClark, Armstrong1113149, Sellyme, NobelBot, Retsnom 2, Okras, Kitsune
Taiyal, GliderMaven, Dunks1, Jc3s5h, Jamesooders, Black.je, Citation bot 1, AstaBOTh15, Pinethicket, Serols, SpaceFlight89, Chryseus,
Orenburg1, Lee A. Hart, Reaper Eternal, Tbhotch, DARTH SIDIOUS 2, Onel5969, RjwilmsiBot, MagnInd, Asheek555, EmausBot, GoingBatty, Wikipelli, K6ka, Daonguyen95, Lindseyrose, AManWithNoPlan, Sirpentagon, Sbmeirow, Zosonr, Passenger2010, The beings,
Dllu, ClueBot NG, ClaretAsh, Swapppawar, Matthiaspaul, CocuBot, Historikeren, Eruditechamp, Clampower, Geo2011, Helpful Pixie Bot,
Wbm1058, BG19bot, Arnavchaudhary, Hz.tiang, JohnChrysostom, Poushag, Nav0817, BattyBot, Srivalli Kavuri, David.moreno72, Cyberbot II, ChrisGualtieri, Mdu7078, Dexbot, CaSJer, Bbexigo, Narenait, Spyglasses, Ubidefeo, Jianhui67, Jdx, KasparBot, Imran335534,
Chakhuu, Chand3994, IRaa1, , Leatherbrenn darby, Elektrik Fanne, GreenC bot, Bender the Bot, Bakertom and Anonymous:
487
Fleming valve Source: https://en.wikipedia.org/wiki/Fleming_valve?oldid=731971150 Contributors: Heron, Reddi, Alan Liefting, Giraedata, Daderot, SmackBot, Slashme, Valfontis, Chetvorno, Guy Macon, Rico402, VoABot II, Fountains of Bryn Mawr, GlassFET,
Moletrouser, ClueBot, Redheylin, Bae gab1978, Lightbot, Helpful Pixie Bot, Wbm1058, PearlSt82, KasparBot, Doulph88, Ka7tur and
Anonymous: 8
Continuous wave Source: https://en.wikipedia.org/wiki/Continuous_wave?oldid=738943238 Contributors: DrBob, Olrick, Michael
Hardy, Liftarn, Docu, Glenn, Nikai, Wfeidt, Mulad, Charles Matthews, Radiojon, Jvangorp, DavidCary, Micru, Decoy, Gzuckier, Kubieziel, Sam Hocevar, Kevin Rector, Deglr6328, Rich Farmbrough, Closeapple, Petersam, Edward Z. Yang, Simon South, Nigelj, Lectonar, Wtshymanski, Dan100, Kotoviski, FlaBot, FredK~enwiki, Srleer, YurikBot, Wavelength, Arado, Brandon, Mysid, SmackBot,
Fireworks, Hmains, Kharker, Cadmium, McNeight, Nakon, JoeBot, Chetvorno, ShelfSkewed, Gogo Dodo, Christian75, Epbr123, N5iln,
Gerry Ashton, Malvineous, N6KB, Nikevich, Kf4yfd, Hans W, Rexlint, Robertgreer, Geekdiva, RedBlade7, ClueBot, Michael.Urban,
XLinkBot, Addbot, LaaknorBot, SpBot, GrouchoBot, Surv1v4l1st, EmausBot, Nachosan, ZroBot, Helpful Pixie Bot, Mogism, N9ysq,
KasparBot and Anonymous: 36
Alexanderson alternator Source: https://en.wikipedia.org/wiki/Alexanderson_alternator?oldid=752180398 Contributors: The Anome,
Glenn, Reddi, Cleduc, Blainster, Wjbeaty, Giftlite, ElectraFlarere, Rchandra, Davewjessup, Aranel, Physicistjedi, Hooperbloob, Alansohn, Atlant, Wtshymanski, DV8 2XL, Gene Nygaard, Alai, Ma Baker, Mbutts, Daderot, Ian Pitchford, GreyCat, Aghost, Hellbus, Caerwine, Light current, Petri Krohn, Mais oui!, SmackBot, Bluebot, Thumperward, Dethme0w, Chetvorno, Rico402, Yahel Guhan, Nikevich,
Stzge308, LorenzoB, Read-write-services, TXiKiBoT, GLPeterson, IPSOS, Andy Dingley, P1h3r1e3d13, Moonriddengirl, Sjmelhuish,
Alan Larson, DavidBlackwell, Alexbot, XLinkBot, Alchaemist, Addbot, Lightbot, PaulT, Luckas-bot, MinorProphet, TechBot, David W
Jessup, Jwntr, Grepman, John of Reading, Mikhail Ryazanov, Widr, PearlSt82, Pas s maslom, SJ Defender and Anonymous: 36
Lee de Forest Source: https://en.wikipedia.org/wiki/Lee_de_Forest?oldid=751586109 Contributors: Mav, Aldie, Edward, Infrogmation,
Paul Benjamin Austin, Delirium, DavidWBrooks, Stan Shebs, Bluelion, Ugen64, Glenn, Evercat, Lommer, Adam Bishop, Reddi, Wik,
Zoicon5, Wernher, Bevo, Twang, Riddley, AlexPlank, Blainster, St3vo, AlistairMcMillan, JillandJack, Wmahan, SarekOfVulcan, 1297,
Fuper, Neutrality, Flyhighplato, D6, RossPatterson, Moverton, Eb.hoop, Brianhe, JPX7, Bender235, CanisRufus, Dgorsline, Fenevad,
Rgdboer, Sherurcij, Ransak, Orelstrigo, Bbsrock, Tony Sidaway, Gene Nygaard, Gmaxwell, Richard Arthur Norton (1958- ), Scjessey,
Kosher Fan, Stefanomione, Graham87, BD2412, Ted Wilkes, Ketiltrout, Sjakkalle, MarnetteD, FlaBot, Margosbot~enwiki, RMc, Srlefer, Dsc~enwiki, Jaraalbe, DVdm, Gwernol, YurikBot, Wavelength, Oliviosu~enwiki, Raccoon Fox, RussBot, WAvegetarian, Conscious,
NawlinWiki, Cryptoid, Padawer, Albedo, ThrashedParanoid, MaxVeers, Thomas H. White, Homagetocatalonia, Rms125a@hotmail.com,
GraemeL, Scrabbler, JLaTondre, RenamedUser jaskldjslak904, Lamat~enwiki, SmackBot, Arniep, Duncanr, Gilliam, Qonox, Bluebot,
Jprg1966, Z herbert, Ryan Roos, Nishkid64, Ser Amantio di Nicolao, JKBrooks85, Khazar, Notmicro, Jperrylsu, Dale101usa, Doczilla,
Norm mit, Yves-Laurent, Stereorock, Chetvorno, Vanisaac, Cydebot, Fnlayson, Scooteristi, Protious, JamesAM, Leondegrance, Mojo
Hand, Bolman Deal, Marek69, EdJohnston, AntiVandalBot, Steveokeefe, Guy Macon, Tjmayerinsf, Harryzilber, DuncanHill, Postcard Cathy, JeromeParr, Authorviews, Dapsv~enwiki, Magioladitis, Staib, Pedro, Faizhaider, Doug Coldwell, Waacstats, Schily, GeoFan49, CliC, Jim.henderson, Keith D, Glrx, Kostisl, CommonsDelinker, Jiuguang Wang, Eliz81, WFinch, Ryan Postlethwaite, Allreet,
Fountains of Bryn Mawr, Jrcla2, Joshmt, Kolja21, Typometer, Sam Blacketer, BillyMassie, ABF, Rikster2, Amikake3, Instantiayion,
Davidwr, The Original Wildbear, Hqb, GcSwRhIc, IPSOS, Calbookaddict, Grimne, Pleroma, Softlavender, GlassFET, Spinningspark, FlyingLeopard2014, Maralex334, Norhelt, SE7, Flyer22 Reborn, Lisatwo, Lightmouse, ClueBot, Binksternet, All Hallows Wraith, Sabbah67,
Zabadu~enwiki, FLAHAM, Jack231, Mmarsh, Masterpiece2000, Alexbot, Steamroller Assault, Sun Creator, Draggleduck, Arjayay, Nobody of Consequence, Mlas, SoxBot III, SilvonenBot, Zwinglisjubilee, Kbdankbot, Broke Back Records, Addbot, Fluernutter, Pnerger,
LaaknorBot, Vega2, Bguras puppy, Lightbot, Pdd3517, Luckas-bot, Yobot, TaBOT-zerem, Jan Arkesteijn, THEN WHO WAS PHONE?,
Gongshow, Ningauble, AnomieBOT, Diderot08, Rubinbot, Yachtsman1, Bob Burkhardt, V35b, Xqbot, Ethics2med, J JMesserly, RibotBOT, Rat2, Lagelspeil, I dream of horses, Tom.Reding, Tinton5, Moonraker, Jauhienij, Kgrad, Firstfoxbat, Minimac, RjwilmsiBot,
Jackehammond, EmausBot, John of Reading, Donald 24, Dewritech, PBS-AWB, Lemeza Kosugi, , Lew4vrv, Askrich, Computergeek125, ClueBot NG, Engradio, Kn, Helpful Pixie Bot, Johnny C. Morse, Bekah725, Kaltenmeyer, PearlSt82, CitationCleanerBot,

132.11. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

577

Wannabemodel, Comfr, BattyBot, Justincheng12345-bot, David.moreno72, ~riley, Vanished user lt94ma34le12, Ninmacer20, Cyberbot II,
Soulbust, EuroCarGT, Dobie80, Mogism, VIAFbot, Theguyfromthere, Froglich, ArmbrustBot, OliviaSvetich, Ben Rapoza, BethNaught,
Jonarnold1985, Gareld Gareld, Unician, NilubonT, KasparBot and Anonymous: 159
Amplier Source: https://en.wikipedia.org/wiki/Amplifier?oldid=751885984 Contributors: AxelBoldt, Eloquence, Mav, Ray Van De
Walker, SimonP, Waveguy, Heron, Kku, Ixfd64, Delirium, Docu, Kingturtle, Glenn, Nikai, GRAHAMUK, Jengod, Ww, Wik, Jessel,
Maximus Rex, Omegatron, Bevo, Raul654, Lumos3, Friedo, RedWolf, Donreed, Dave Bass, Hcheney, David Gerard, Centrx, Giftlite,
DocWatson42, Lunkwill, DavidCary, Laudaka, Lupin, Vk2tds, Markus Kuhn, Jcobb, AJim, Maroux, Jason Quinn, Rchandra, Nayuki,
Wmahan, Chowbok, Sam Hocevar, Jcorgan, BrianWilloughby, Abdull, Rich Farmbrough, TedPavlic, Guanabot, Pmsyyz, Pt, Dennis Brown,
Meggar, Timl, Hooperbloob, Watsonladd, Malo, Osmodiar, Wtshymanski, Twisp, Crosbiesmith, Woohookitty, Uncle G, Pol098, Peter
Beard, DaveApter, BD2412, FreplySpang, Snaekid, Koavf, Amire80, Quiddity, Oblivious, Brighterorange, RobertG, Arnero, Margosbot~enwiki, Alfred Centauri, Kolbasz, Krishnavedala, 121a0012, Bgwhite, Ahpook, The Rambling Man, Nol Aders, Matt512, Epolk,
Bergsten, Chaser, Rohitbd, Bjf, Bou, Welsh, Howcheng, Thiseye, Dhollm, Speedevil, DeadEyeArrow, Searchme, Light current, Mattg2k4,
Deville, Kungfuadam, Mebden, Jer ome, Kf4bdy, Kimdino, SmackBot, Reedy, Unyoyega, Freestyle~enwiki, Daviddavid, Lindosland,
Anachronist, Chris the speller, Bluebot, TimBentley, Cadmium, Jprg1966, Thumperward, Papa November, Szidomingo, Sajendra, OrphanBot, Seduisant, Evilspoons, SnappingTurtle, DMacks, Pilotguy, Bn, Shields020, J 1982, Breno, Minna Sora no Shita, CyrilB, Rogerbrent,
Dicklyon, 2006mba, Kvng, Politepunk, OnBeyondZebrax, Iridescent, Walton One, Mihitha, Yves-Laurent, Chetvorno, JohnTechnologist,
Xcentaur, CmdrObot, Chrumps, Nczempin, Lenilucho, Anoneditor, Doctormatt, Tubenutdave, Red Director, HermanFinster, Australian
audio guy, FredYork, Gionnico, Editor at Large, Enter The Crypt, Pjvpjv, Saimhe, Guy Macon, Mccartyp, Lovibond, CPMartin, Lbecque,
Esmond.pitt, CombatWombat42, CosineKitty, TAnthony, MegX, Jahoe, Xoneca, Magioladitis, VoABot II, Askari Mark, JNW, JamesBWatson, Faizhaider, MichaelSHoman, The Real Marauder, Black Stripe, Ngwill, MartinBot, Sigmundg, Jim.henderson, Anaxial, Nono64,
Masisnr1, M samadi, DrKay, AntiSpamBot, SophieCat, Vspengen, Colorbow, Ale2006, Mlewis000, Funandtrvl, Joeinwap, Meiskam,
ICE77, Philip Trueman, Oshwah, The Original Wildbear, Zuperman~enwiki, Smcreator, Henrydask~enwiki, Anonymous Dissident, Auent Rider, Someguy1221, Monkey Bounce, Don4of4, Jackfork, Billinghurst, Kilmer-san, Dragonkillernz, Spinningspark, Internetexploder,
Biscuittin, Audioamp, Jokullmusic, Krawi, Kotabatubara, Hiddenfromview, Henry Delforn (old), Lightmouse, Nitram cero, StaticGull,
Hamiltondaniel, Denisarona, Asher196, Thinkingatoms, ClueBot, Binksternet, The Thing That Should Not Be, GeoreyHale, Jan1nad,
Wysprgr2005, GreenSpigot, AnnArborRick, Niceguyedc, Blanchardb, Linan0827, Gtstricky, Brews ohare, Arjayay, Versus22, Johnuniq,
XLinkBot, Alexius08, Revancher, Srcloutier, Pedro magalhaes86, Addbot, Mortense, Olli Niemitalo, Fgnievinski, Avobert, Yobot, Jordsan,
Bestiasonica, Dleger, P1ayer, Sarukum, AnomieBOT, Piano non troppo, B137, Materialscientist, Citation bot, LilHelpa, Justanothervisitor, Harikrishna69, Ubcule, Maitchy, Uusijani, GliderMaven, FrescoBot, Gog182, Jc3s5h, Nickw2066, Nojiratz, Gdje je nestala dua
svijeta, Icontech, I dream of horses, TechnoDanny, Anooshg, Jujutacular, Hessamnia, Orenburg1, Theo10011, Minimac, Belledonne,
Qianchq, John of Reading, Kodabmx, Cmavr8, Dewritech, TuomTuo, GoingBatty, Solarra, JohnFLand, AnonymousNarrator, The Nut,
ChunkyPastaSauce, Namoroka, Tuborama, Peterh5322, Lowkyalur, Donner60, Jefolly, Lakkasuo, Nikolas Ojala, Antiguru, Petrb, ClueBot NG, Jaanus.kalde, MelbourneStar, This lousy T-shirt, Piast93, Andreas.Persson, Historikeren, Robsuper, Primergrey, MerlIwBot,
Helpful Pixie Bot, HMSSolent, Bibcode Bot, Supersam654, CitationCleanerBot, Crh23, 1292simon, Braun walter, ChrisGualtieri, Ajv39,
Dexbot, SoledadKabocha, Farmer Brown, Frosty, Mark viking, Epicgenius, Acrislg, I am One of Many, Jamesmcmahon0, Brzydalski,
Spyglasses, Rewa, AddWittyNameHere, Stamptrader, Poponuro, JaconaFrere, Jbolton07, Gerbenvaneerten, Barefootwhistler, MasterTriangle12, Grsh90, Kennellm, Mario Casteln Castro, Anupambharti1995, Paulinaacuna, Sweepy, Santoshjain000, G-dac, Mar11, InternetArchiveBot, PedantEngineer, Lou45654, Bender the Bot, Musicalst and Anonymous: 458
Transmitter Source: https://en.wikipedia.org/wiki/Transmitter?oldid=750683340 Contributors: Timo Honkasalo, Danny, Fredbauder,
Aldie, Karen Johnson, Heron, D, Kku, Ixfd64, Prefect, Spliced, Glenn, Palfrey, BAxelrod, GRAHAMUK, Radiojon, K1Bond007,
GarnetRChaney, Cutler, Marnanel, Mintleaf~enwiki, COMPATT, Everyking, Karl-Henner, CALR, Chairboy, Bobo192, Cmdrjameson, Hooperbloob, Jumbuck, Zachlipton, Alansohn, Atlant, Wtshymanski, Tycho, Gpvos, RainbowOfLight, Gene Nygaard, Axeman89,
JeremyA, Je3000, GregorB, SCEhardt, Obersachse, BD2412, Dpv, Edison, Vegaswikian, Nneonneo, UsagiM, Ground Zero, Margosbot~enwiki, Ewlyahoocom, Goudzovski, Mrschimpf, RobotE, , Tresckow, Mikeblas, Ma3nocum, Samir, Engineer Bob, Daniel C,
Deville, RickReinckens, BorgQueen, SmackBot, Hydrogen Iodide, KocjoBot~enwiki, Gilliam, Hmains, Kmarinas86, Chris the speller,
Bidgee, Shalom Yechiel, Erzahler, J 1982, Hlucho, 16@r, JustinSmith, Mets501, Kvng, Levineps, Igoldste, Chetvorno, Slazenger, Tubenutdave, Flowerpotman, TheM62Manchester, Tawkerbot4, Biblbroks, ManN, Dtgriscom, Pjvpjv, Dfrg.msc, Chillysnow, MichaelMaggs,
KrakatoaKatie, AntiVandalBot, E-s-B, LuckyLouie, JAnDbot, Harryzilber, Jahoe, Magioladitis, Njiro, R'n'B, CommonsDelinker, Mikael
Hggstrm, Deor, ICE77, DoorsAjar, TXiKiBoT, Zidonuke, Anna Lincoln, Jackfork, Perfectajay, Kbrose, Oldphella, Matthew Yeager,
Tawglobal, Stoneygirl45, Lightmouse, Iain99, Callidior, Martarius, ClueBot, The Thing That Should Not Be, Rjd0060, Hornet35, Wikijens, Sv1xv, Brews ohare, Hakware, Thingg, DumZiBoT, Roxy the dog, Addbot, Fgnievinski, Luckas-bot, TaBOT-zerem, KamikazeBot,
Materialscientist, RadioBroadcast, ArthurBot, Geac, Ponticalibus, RibotBOT, Nedim Ardoa, FrescoBot, Jc3s5h, Louperibot, HamburgerRadio, Broadcasttransmitter, Footwarrior, FoxBot, Lotje, EmausBot, Siddhartha 90, Gfoley4, RA0808, Lssg124, Josve05a, Ebrambot,
Bamyers99, ClueBot NG, Rtucker913, Floatjon, Wikishotaro, Rezabot, JordoCo, Kangaroopower, AvocatoBot, Dropbuilt1234, Fylbecatulous, Millennium bug, A Certain Lack of Grandeur, Pakozm, JaconaFrere, Preston2335, KH-1, CAPTAIN RAJU and Anonymous:
146
Arc converter Source: https://en.wikipedia.org/wiki/Arc_converter?oldid=745452951 Contributors: Michael Hardy, Glenn, Wtshymanski, DV8 2XL, BD2412, Josh Parris, Daderot, Bgwhite, Ospalh, Light current, Chetvorno, CRGreathouse, Cydebot, Khatru2, Martin
Hogbin, Guy Macon, CosineKitty, Foroa, Glrx, Fountains of Bryn Mawr, Alexbot, Addbot, Lightbot, Zorrobot, Yobot, AnomieBOT,
Xqbot, Tom.Reding, Codwiki, Neptune1969, Sehateld, MadManMarkAu,
, PearlSt82, Bender the Bot and Anonymous: 13
Microphone Source: https://en.wikipedia.org/wiki/Microphone?oldid=752078972 Contributors: Mav, Dachshund, SimonP, Peterlin~enwiki, Robin726, Waveguy, Heron, Ryguasu, Chas zzz brown, Michael Hardy, Tim Starling, Fwappler, CG, Ellywa, Ahoerstemeier, Ronz, CatherineMunro, Andrewa, Mark Foskey, Iain, Nikai, Smack, Schneelocke, Ww, Dmdwiggi, Alpdpedia, Pheon, Furrykef,
Omegatron, David.Monniaux, Shantavira, Twang, Rogper~enwiki, Robbot, Hankwang, Pigsonthewing, Chris 73, RedWolf, Modulatum, Nerval, Mjscud, Enz1, Wjbeaty, Giftlite, SnackAdmiral, DocWatson42, Palapala, BenFrantzDale, Everyking, Tom-, Jackol, Bobblewik, Tagishsimon, Wmahan, LiDaobing, Antandrus, OverlordQ, Rdsmith4, Burgundavia, Grimey, Ukexpat, Klemen Kocjancic, Fabrcio Kury, Caquia, Mike Rosoft, Quirk, Kmccoy, Andy Smith, Andrewferrier, Dour High Arch, Paul August, Bender235, Jnestorius, Yvolution, Mdf, Kwamikagami, Aude, Shanes, Jpgordon, Bobo192, Smalljim, Cmdrjameson, Ultramancool, .:Ajvol:., Jjk, Timl,
Alphax, Pschemp, PJ, Hooperbloob, Alansohn, Anthony Appleyard, Eleland, LtNOWIS, Atanamir, Fraslet, Samaritan, Mysdaao, Hohum, Snowolf, Wtshymanski, Cburnett, Danhash, Bsadowski1, Gene Nygaard, DSatz, Tm1000, Dismas, Issk, Gmaxwell, Googleaseerch,
Starblind, Woohookitty, Etf, RHaworth, Thorpe, Scjessey, Polyparadigm, Ma Baker, Pol098, Tabletop, Kmg90, Hotshot977, GregorB, SCEhardt, Wayward, Stefanomione, Dysepsion, Deltabeignet, BD2412, Tlroche, Avochelm, Tangotango, Keoka, Pualiaz, JP

578

CHAPTER 132. MORSE CODE

Godfrey, Bubba73, Brighterorange, Bensin, Burris, AlisonW, Timothybb, Ekimdrachir, FlaBot, Ianthegecko, SchuminWeb, Margosbot~enwiki, Nihiltres, Nivix, Phatmonkey, RexNL, Gurch, KFP, Brianmacian, Chninkel, Jxr~enwiki, WikiWikiPhil, Startaq, King of
Hearts, DVdm, Bgwhite, YurikBot, Wavelength, Charles Gaudette, General Bison, RussBot, Peter S., TimNelson, Hydrargyrum, CambridgeBayWeather, Rsrikanth05, Irk, Janke, Cquan, Circumspect, Irishguy, Retired username, Mikeblas, Voidxor, Adicarlo, Oliverdl,
Ksg-88, Nlu, Nick123, Searchme, ClaesWallin, FF2010, Light current, Bloud, Cpswarrior, NHSavage, Toddgee, Petri Krohn, GraemeL,
Alias Flood, Chrishmt0423, JLaTondre, Gorgan almighty, F. Cosoleto, Katieh5584, One, Crystallina, Errickfoxy, SmackBot, Markyoshi,
Fireworks, Kellen, CompuHacker, Ze miguel, Speight, Atomota, Brossow, Edgar181, Evanreyes, Commander Keane bot, Gilliam,
Ohnoitsjamie, Hmains, ERcheck, Lindosland, KD5TVI, Bluebot, Thumperward, MalafayaBot, Victorgrigas, Rediahs, IIXII, Charles
Nguyen, A. B., Gracenotes, Onceler, Quaque, Dethme0w, Audioholic, Harumphy, Alphathon, Jjhjjh, Dwerneck, Rrburke, Clements, Flyguy649, Big Swifty, Jwy, Nakon, EVula, PetesGuide, Wikicrusader, HarisM, LapTop006, Weregerbil, ILike2BeAnonymous, Mbandgeek,
Wg0867~enwiki, SashatoBot, Dudecon, SilverStar, J 1982, Tim bates, Nux, Bjankuloski06en~enwiki, Chrisch, Bags~enwiki, Silvarbullet1,
Werdan7, Dicklyon, TerryKing, Waggers, Ace Frahm, Ryulong, Chickencha, H, Kvng, Levineps, OnBeyondZebrax, Clarityend, Joseph
Solis in Australia, Splitpeasoup, J Di, Newyorkbrad, Majora4, Ziusudra, Tawkerbot2, Chetvorno, Wolfdog, CmdrObot, Wafulz, Sir Vicious, Picaroon, Nczempin, Drinibot, Jamoche, McVities, TheUnremorsefulZork, WeggeBot, Lenilucho, MrFish, Whereizben, Pewwer42,
Cydebot, W.F.Galway, PeterPan23, Peytonio, Altaphon, Corpx, Llort, Sempai, Jabal bob, Trent 900, Editor at Large, CJ King, Collesano,
Omicronpersei8, UberScienceNerd, Satori Son, Thijs!bot, Qwyrxian, N5iln, Headbomb, Peter Deer, Pjvpjv, Marek69, Gerry Ashton,
Tellyaddict, Mikesongli, SusanLesch, Uruiamme, Mentisto, AntiVandalBot, Clf23, Opelio, SummerPhD, Matias.Reccius, Prolog, Iarnell,
LuckyLouie, Leevclarke, Dougher, Labongo, JAnDbot, Deective, Husond, Danielchoo, MER-C, Instinct, Ccrrccrr, Greensburger, LittleOldMe, Bencherlite, Pedro, Walloper69, Bongwarrior, VoABot II, Rhwawn, JNW, J.P.Lon, Kaivosukeltaja, Tomhannen, Think outside
the box, TARBOT, Dulciana, Ramtronik, Rap-Royalty.Com, Asaspades, Otivaeey, WhatamIdoing, Bryson430, Nposs, Noodle snacks,
Adrian J. Hunter, Cisum.ili.dilm, Mcfar54, DerHexer, JaGa, Chrismarx85, InvertRect, MartinBot, STBot, Poeloq, APT, Notmyhandle, Giano II, Anaxial, Zouavman Le Zouave, Mschel, Blue Dinosaur Jr, Squeezeweasel, Gzkn, Merqury5, DarkFalls, Gurchzilla, Jodakai, AntiSpamBot, Harrje233, Fountains of Bryn Mawr, Tarsaucer, Potatoswatter, KylieTastic, Senmgalopp, Dpamic, Moondoll, Vinsfan368, Mlewis000, Funandtrvl, ACSE, Lights, Deor, Thedjatclubrock, Cbilinski, Meaningful Username, Je G., Jmrowland, Jingshen,
Bovineboy2008, Rclocher3, Davidwr, DaRaeMan, WarddrBOT, Philip Trueman, Refsworldlee, TXiKiBoT, Oshwah, Jdcrutch, Arnon
Chan, Qxz, Sloggerbum, Sintaku, Cootiequits, LeaveSleaves, BotKung, E.P.Y. Foundation, PrinzPH, Madhero88, Andy Dingley, Altermike, Falcon8765, Enviroboy, TML, Imon 2nd, Symane, Annasam, SvNH, EmxBot, Cbshah, SieBot, YonaBot, Euryalus, Da Joe,
Classicstruggle4, 1836311903, Keilana, Flyer22 Reborn, Faradayplank, 4d0lf H17l3r, Fbarw, Gunmetal Angel, Svick, Onlyonen, HairyWombat, ImageRemovalBot, Martarius, ClueBot, Djsc00by, Compdude47, Binksternet, Nasoeng, RonBeeCNC, Fyyer, The Thing That
Should Not Be, MIDI, Nsk92, Razimantv, DrFO.Jr.Tn~enwiki, Jmn100, Ridge Runner, The Watusi, DragonBot, Excirial, Jusdafax, Mcglynn, Saltmiser, La Pianista, Thingg, Tuzi, Aitias, Webbbbbbber, Cryptk, Apparition11, DumZiBoT, XLinkBot, Pichpich, Roxy the dog,
Wikiuser100, Nicoguaro, Svadhisthana, Hullo909, UkiahBass, NellieBly, Badgernet, Noctibus, ZooFari, Sweetmusic999, Chipm4, Tomisgood123, Addbot, Olli Niemitalo, DaughterofSun, Older and ... well older, Jaymesuk, Fbfree, Psylabs, CanadianLinuxUser, Cst17, RTG,
Redheylin, Robert.Harker, CUSENZA Mario, Oldmountains, Favonian, SeymourSycamore, Andrus Kallastu, Krano, ZeTaByTe, Margin1522, Luckas-bot, Vikom, Legobot II, Donfbreed, RobertoBozzi, THEN WHO WAS PHONE?, AnomieBOT, Jim1138, JackieBot,
AdjustShift, Crecy99, B137, Materialscientist, Likeyah64, Citation bot, OllieFury, ArthurBot, Xqbot, Chicken2112, Capricorn42, Justanothervisitor, GrouchoBot, AlSweigart, Newshound7, Amaury, Tankymorgan, Aandroyd, Yoganate79, Maitchy, Canned Soul, Shadowjams, Vanished user giiw8u4ikmfw823foinc2, Vaxquis, SchnitzelMannGreek, Dougofborg, FrescoBot, Tobby72, Jc3s5h, Alexsten, Bballmonster26, Outback the koala, HamburgerRadio, OgreBot, Citation bot 1, AstaBOTh15, Pinethicket, I dream of horses, Tom.Reding,
Canistabbats, Kuyamarco123, SpaceFlight89, Bua1234, Firdaush, Brycecohan, LogAntiLog, Nataev, Unbitwise, Minimac, Mmarroquin,
Onel5969, NameIsRon, NerdyScienceDude, Forenti, WildBot, Jpgtg101, DASHBot, John of Reading, TheClerksWell, Immunize, Astromici, Dewritech, 4Petesake, Ttdashc2, Winner 42, ParagonTomWaits, Wikipelli, Dcirovic, Zachrcks, Mz7, Listmeister, CLI, Susfele,
A2soup, Bryce Carmony, HawkMcCain, Christian R N Baker, Wayne Slam, Diabeticwalrus1, L Kensington, Hurpyderple, AVarchaeologist, Noodleki, Enjarcher, Gearhead1972, Anonimski, Atlantictire, Evan-Amos, DASHBotAV, Waistcoattubs, Lewisrooney93, ClueBot
NG, MelbourneStar, Jasono4407, Dhruvie54321, BroderickAU, AeroPsico, DieSwartzPunkt, Spikehall1234, Kasirbot, Burley001, Widr,
Scottonsocks, WikiPuppies, JordoCo, Helpful Pixie Bot, ChrisEngelsma, Lowercase sigmabot, BG19bot, Barthcox, Lucasbosch, BattyBot,
Jimw338, Cyberbot II, Dexbot, SoledadKabocha, Brees Block, Me, Myself, and I are Here, Acousticator, Nonsenseferret, Wifsy, Flat
Out, RzSHI, L Manju, Monkbot, Justin15w, JaunJimenez, DaveeBlahBlah, Audionutcase, Bbygirl6738, HMSLavender, Andwellneverberoyals999, Upshawjj11, Jason Wiston, Tardis218, ChamithN, AidanD1011, CV9933, User name 42, KasparBot, The Footstool Empire,
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Michael Hardy, Chris-martin, Dcljr, Spliced, Glenn, Deisenbe, Radiojon, LMB, Twang, Bearcat, Blainster, Tzf, Markus Kuhn, Mboverload, Albany45, Beland, Imroy, Yaoleilei, Rich Farmbrough, Evice, Cap'n Refsmmat, Art LaPella, Sparkgap, Sasquatch, Boredzo,
Musiphil, Alansohn, JYolkowski, Rosenzweig, PopUpPirate, Atlant, Jeltz, Gareld226, Dhartung, SidP, ClockworkSoul, Evil Monkey,
Tony Sidaway, Thryduulf, Aerowolf, Eyreland, Tobb, Zpb52, Graham87, BD2412, Haikupoet, Rjwilmsi, Erebus555, Platypus222, Algebra, FlaBot, Ian Pitchford, Leslie Mateus, Ndoble, Mrschimpf, Acett, Scoops, UkPaolo, Huw Powell, Raccoon Fox, Ytrottier, Hydrargyrum, Gcapp1959, Howcheng, Robert Moore, Rson-W, Jpbowen, Voidxor, Mysid, Caerwine, Typer 525, Daniel C, Deville, The
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Deepred6502, Martync84, Mattdp, John, Dr Greg, JustinSmith, Dicklyon, AxG, Arkrishna, Sharcho, Kvng, Iridescent, Pegasus1138,
Stereorock, Chetvorno, Nutster, CmdrObot, Matthieu Houriet, BeauGiles, Shahinaz, Nczempin, The i factor, Kd5npf, Gogo Dodo, Elximo, DangApricot, PKT, Numen, Paul Fisher, Marek69, Turkeyphant, Nick Number, Dugwiki, Psythik, Rainonwood, Yellowdesk, Alphachimpbot, Abunet, Chriscornwell982, Esmond.pitt, Kaini, Harryzilber, MikeBC, Byeee, Erpel13, Sspeirs, Denimadept, Lisaggg, Magioladitis, Bongwarrior, Jpmaurya, J.P.Lon, Northofdc, CS46, Gabriel Bouvigne, Hbent, Gwern, Stephenchou0722, R'n'B, Gah4, Tikiwont,
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FrescoBot, Lonaowna, RodolfoMita, GardenInlet, Burzyn, DigbyDalton, I dream of horses, Fox Wilson, Jfmantis, RjwilmsiBot, Djwole,
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579

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Kramho, CAPTAIN RAJU, LavenderAlice, RIT RAJARSHI, JenniferMari-Gardner, Sghost1 and Anonymous: 256
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ZetorT, Trygve Leo, Dtfgjgcjxgh, Joen223, Monkbot, Get-a-pair-of-goggles, SantiLak, Chsau2, Whitey Westside, Tressargentos, Corrinagentry, PGBen, John685, Wikiuttam, TyScienceGuy, Paewiki, Qwertyoiplin, MMoreno18, GhostOfNoMeme and Anonymous: 241
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Anome, Maury Markowitz, Edward, Michael Hardy, David Martland, Spliced, CesarB, Aarchiba, Glenn, Radiojon, Hyacinth, Omegatron, Phoebe, Adam Carr, Ckape, Naddy, Alexwcovington, Karn, Bensaccount, Ssd, Bobblewik, Pgan002, Mako098765, Mamizou, Anythingyouwant, Barrettam, Kevin Rector, Jakro64, Rich Farmbrough, ArnoldReinhold, Alistair1978, BonzoESC, Billlion, Bobo192, Nigelj,
Wikinaut, Hooperbloob, G Colyer, Atlant, Wtshymanski, Kenyon, Jannex, Kgrr, Eyreland, Jonnabuz, Mandarax, Graham87, Rjwilmsi,
HappyCamper, FlaBot, Daderot, CiaPan, Korg, Mcneight, Palladinus, Jengelh, Stephenb, Gaius Cornelius, Yrithinnd, Brandon, Ninly,
SmackBot, Capnquackenbush, Hydrogen Iodide, KelleyCook, Bluebot, Kharker, Oli Filth, Bob K, Kevinpurcell, Moenada, Vgy7ujm,
Rogerbrent, Dicklyon, Arkrishna, Kvng, G-W, Jesse Viviano, CuriousEric, ST47, N8vi, Electron9, N7bsn, LuckyLouie, Harryzilber,
CosineKitty, OllyH, VoABot II, Hmo, Nikevich, CodeCat, Jim.henderson, QofASpiewak, Cometstyles, 28bytes, VolkovBot, RingtailedFox, Akld guy, Serrano24, Jackfork, Spinningspark, Bpringlemeir, Kbrose, SieBot, VVVBot, Revent, Fratrep, Dodger67, Dp67, Arjayay,
Dthomsen8, SilvonenBot, Addbot, Sillyfolkboy, CuteHappyBrute, Lightbot, Luckas-bot, Yobot, Optomist1, Cepheiden, Ciudadano001,
Eumolpo, GrouchoBot, Omnipaedista, Nedim Ardoa, CaZeRillo, Sristykrishnaprasad, RedBot, Crcwiki, TobeBot, Mir09, EmausBot,
John of Reading, GoingBatty, ZroBot, Ida Shaw, Cymru.lass, , Tolly4bolly, Petrb, ClueBot NG, ChristophE, Helpful Pixie
Bot, Woutgg, Codeh, Jacksonps4, SFK2, The Quirky Kitty, ARuseToCruise, Waczze, Wipur, Spyglasses, Finnusertop, WildyLion, SasaIv,
Arcknet, Kavya l, Boehm and Anonymous: 65
Longwave Source: https://en.wikipedia.org/wiki/Longwave?oldid=748608480 Contributors: The Anome, SimonP, GrahamN, GABaker,
Liftarn, Spliced, Glenn, Kwekubo, Lee M, Mulad, MatrixFrog, Reddi, Radiojon, Jerzy, Hajor, Denelson83, Sjorford, Bearcat, Josh Cherry,
Altenmann, Modulatum, Lowellian, Rhombus, Alexwcovington, Markus Kuhn, Sca, ConradPino, Kar98, Trilobite, Picapica, Guanabot,
Ericamick, Gerry Lynch, Pavel Vozenilek, Jnestorius, Kiand, Sole Soul, Nigelj, AndreyMavlyanov~enwiki, Sparkgap, QVanillaQ, Atlant,
Wtshymanski, Paul1337, Gpvos, Woohookitty, GVOLTT, Armando, Eyreland, Matturn, Graham87, Grammarbot, Scrouds, Tlitic, Weichbrodt, TSamuel, Chobot, Travis Wells, RussBot, Groogle, Johantheghost, Dddstone, Thomas H. White, Alureiter, KnightRider~enwiki,
SmackBot, Jereykopp, Tom Lougheed, Nethency, HeartofaDog, Yamaguchi , WikiFlier, Bazonka, Colonies Chris, Harumphy, Hoof
Hearted, Treki, Zonk43, TenPoundHammer, Ohconfucius, Trounce, Dicklyon, AxG, Dl2000, Hetar, Stereorock, Chetvorno, Vakarel, CmdrObot, Mattbr, Chrumps, Moefuzz, DanielRigal, AndrewHowse, A876, C2r, Msebast~enwiki, Biruitorul, Martin Hogbin, Nick Number,
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Hertz1888, Wikifex, Purbo T, Becalmed, Curang, Hal8999, Niceguyedc, Sv1xv, Ost316, Camoz87, Arturo57, Addbot, CF1V8, Kicior99, Yobot, Bestiasonica, Echtner, AnomieBOT, Rubinbot, Mahmudmasri, Citation bot, Carlsotr, Nikolaus2, Waihorace, Dellant,
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transmission?oldid=733372577 Contributors: Imran, Grendelkhan, Kevin Rector, Scott5114, Ketiltrout, Brandon, SmackBot, Bluebot,
Redhatter, Dicklyon, Kvng, Waihung, Eastlaw, CmdrObot, Alaibot, Jim.henderson, R'n'B, Pbroks13, Hertz1888, Flyer22 Reborn,
Aspects, Dodger67, Capitalismojo, Metiscus, Johnuniq, EjsBot, Legobot, Yobot, Blackknight12, Materialscientist, Ciudadano001,
Recognizance, BenzolBot, Keysem, PancakesMan, Alpha Quadrant, Alexander Misel, Sven Manguard, Kavya Manohar, ClueBot NG,
Nen, Italicus84, WikiSavesLives, Naveengouda, Fematich, Shipandreceive, Bilorv, Rohan1395, Patoshjul, Learncontribute, Joecarjoe,
KerimF and Anonymous: 40

580

CHAPTER 132. MORSE CODE

Product detector Source: https://en.wikipedia.org/wiki/Product_detector?oldid=653843479 Contributors: Michael Hardy, Egil, Glenn,

Ckape, Naddy, Albany45, Mat cross, Hooperbloob, DV8 2XL, StradivariusTV, Jxr~enwiki, SmackBot, Sam8, Bluebot, Amikake3, Wdwd,
Sv1xv, Addbot, LilHelpa, Erik9bot and Anonymous: 11
Envelope detector Source: https://en.wikipedia.org/wiki/Envelope_detector?oldid=727254782 Contributors: Zundark, Heron, Hephaestos, Michael Hardy, Glenn, Radiojon, Hyacinth, Omegatron, Ckape, Alan Liefting, DavidCary, Erics, PrisonerOfPain, Hooperbloob,
QVanillaQ, DV8 2XL, SteinbDJ, Jonnabuz, Vegaswikian, Srleer, Jxr~enwiki, Krishnavedala, Steven Hepting, BirgitteSB, Bakkster Man,
Tevildo, Eenu, SmackBot, The Photon, Ignacioerrico, Ankitgoel mail17, Bluebot, Papa November, N.MacInnes, Dicklyon, Kvng, Shoez,
Cydebot, Sluzzelin, H1voltage, Indomaster, Gmoose1, Amikake3, The Original Wildbear, Spinningspark, Gladiool, Sfan00 IMG, Sv1xv,
Brews ohare, Addbot, Olli Niemitalo, Fgnievinski, Luckas-bot, Xqbot, GrouchoBot, MondalorBot, Maaks, Eekh.eu, RaptureBot, ClueBot
NG, Wbm1058, Khazar2, Dough34 and Anonymous: 31
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oldid=693282839 Contributors: Radiojon, Big Bob the Finder, Grendelkhan, Aaronhill, SimonMayer, Kevin Rector, Scott5114, SmackBot,
Bluebot, Nakon, Kvng, Eastlaw, Alaibot, Jim.henderson, Dodger67, Chamal N and Anonymous: 5
Automatic gain control Source: https://en.wikipedia.org/wiki/Automatic_gain_control?oldid=746814428 Contributors: Brion VIBBER,
Eloquence, The Anome, HelgeStenstrom, Waveguy, Glenn, GRAHAMUK, Saltine, Omegatron, Owen, Chris Roy, Rchandra, R-Joe,
Cab88, Mormegil, Altmany, Meggar, Hooperbloob, Pinar, Wtshymanski, Pol098, ABot, RussBot, Yahya Abdal-Aziz, Mikeblas, Eli lilly,
Light current, SmackBot, PEHowland, Commander Keane bot, Oli Filth, Mwtoews, Cmh, Belugaperson, Dicklyon, Chetvorno, LeetHaxor,
Ddrane, Yomangani, MER-C, Cpl Syx, R'n'B, DorganBot, TXiKiBoT, Oshwah, Lechatjaune, Jamelan, A. Carty, Binksternet, ChrisHodgesUK, Qwfp, Fastily, Spitre, Addbot, Oldmountains, Semiwiki, Rubinbot, TechBot, GrouchoBot, Green Cardamom, FrescoBot, RjwilmsiBot, Piyush035, Klbrain, ClueBot NG, AeroPsico, Rapisu, BattyBot, Mejbp, Wadhwaabhishek, Ginsuloft, Monkbot, Bender the Bot and
Anonymous: 40
Broadcasting Source: https://en.wikipedia.org/wiki/Broadcasting?oldid=746199595 Contributors: JeLuF, Christian List, Mintguy,
Patrick, Nommonomanac, GABaker, Paul Barlow, Willsmith, Paul Benjamin Austin, Minesweeper, MichaelJanich, Spliced, CatherineMunro, TUF-KAT, Angela, Glenn, Lee M, Mxn, Schneelocke, Mulad, Guaka, Krwells, Wik, Zoicon5, Radiojon, Bhuston, Thue, Jerzy,
Denelson83, Ckape, Robbot, Dale Arnett, ComicMasta, TMillerCA, RedWolf, Altenmann, Naddy, Saforrest, GarnetRChaney, Mushroom, Wayland, Bob cat, Enochlau, Julianp, DocWatson42, Robin Patterson, BenFrantzDale, Peoplesyak, Angmering, Everyking, Monaco
Kati~enwiki, D2s, Bobblewik, Wmahan, Gadum, SebastianBreier~enwiki, Catdude, CharlieZeb, Gscshoyru, Tomwalden, Cab88, Janneok~enwiki, Picapica, Zondor, Adashiel, TheObtuseAngleOfDoom, Jakro64, Noisy, Rich Farmbrough, Bender235, Goplat, Violetriga,
Brian0918, Mwanner, Art LaPella, Cacophony, Keno, Allyn, BarkingFish, Giraedata, Jerryseinfeld, Idleguy, Pearle, Alansohn, JoaoRicardo, Walkerma, Spangineer, Gavin Starks, Alai, Redvers, Prattora~enwiki, Woohookitty, Yansa, Pichu0102, Thruston, Wikiklrsc,
Toussaint, Darren Jowalsen, RichardWeiss, BD2412, Pigmingo, Edison, Rjwilmsi, Fahrenheit451, Martin-C, Kallemax, DDerby, RexNL,
Czar, KFP, TeaDrinker, Srleer, Bgwhite, Hairy Dude, MMuzammils, RussBot, Rocketgoat, Gaius Cornelius, CambridgeBayWeather,
Pelago, Thane, NawlinWiki, Cocoloco, Rjensen, Raven4x4x, Mssetiadi, Mikeblas, IslandGyrl, Deville, Alasdair, Vicarious, SIGURD42,
Junglecat, Thomas Blomberg, Paul Erik, SpLoT, SmackBot, David Kernow, Ashley thomas80, Wcquidditch, Cavenba, Iandstanley, KiloLima, Klokie, Yamaguchi , Ohnoitsjamie, Hmains, Skizzik, Anwar saadat, Sinblox, Chris the speller, Bluebot, Coinchon, Oli Filth,
Hallenrm, A. B., Nintendude, Yanksox, Harumphy, Shalom Yechiel, Erzahler, Khoikhoi, Wp, Sigma 7, Euchiasmus, MonstaPro, 16@r,
AxG, Optakeover, Butler david, Kvng, Levineps, OnBeyondZebrax, Iridescent, Triktrak~enwiki, Joseph Solis in Australia, Twas Now,
Igoldste, MGlosenger, Shoreranger, Blehfu, Momet, Mattimeeleo, Bobby131313, Chetvorno, Zealotgi, Alexv7255, CmdrObot, Mattbr,
Yarnalgo, Requestion, Mike Russell, Pro bug catcher, Pit-yacker, Chasingsol, Swalker2000, Bdragon, Sagaciousuk, Andyjsmith, Dnyhagen,
Bobblehead, Rob.au, Escarbot, Ssr, AntiVandalBot, Gioto, Luna Santin, Wayiran, Bluedisk, JAnDbot, Harryzilber, Lauramartz, Erpel13,
VoABot II, JamesBWatson, Boob, Hamiltonstone, LorenzoB, Hbent, Oicumayberight, BowmanJason, Dennis Kussinich 08, R'n'B, CommonsDelinker, Smokizzy, Gladys j cortez, Mange01, FrummerThanThou, Belovedfreak, Fountains of Bryn Mawr, JHeinonen, Kolja21,
S.M.Latif Shahid, DASonnenfeld, Funandtrvl, VolkovBot, ABF, Rtdixon86, Clegs, Ask123, Qxz, Anna Lincoln, Rumiton, Falcon8765,
Crispy park, AlleborgoBot, Kbrose, SieBot, Colleenthegreat, Ryan1 walker, Hertz1888, Neutralhomer, Cindy141, Miniapolis, Dailyvoid,
Mx. Granger, Dp67, ClueBot, Binksternet, Fyyer, The Thing That Should Not Be, Ilyarmas214, Tsomas214, EoGuy, Wysprgr2005,
Tomas e, Winger84, Skeeball93, Niceguyedc, Mayawi, Kashi0341, Enterpoint, Edwina Storie, Olisssr, Mas214Kapinga, Chuenprayothmas214, Chotisornmas214, Bartolomas214, McDonaldmas214, Mclaughlinmas214, Milenkovic214, Ismailmas214, Arjayay, Sfeagles5,
SchreiberBike, Harris-Grad, Johnuniq, DumZiBoT, XLinkBot, Cowpip, Bernelis~enwiki, Pichpich, Stickee, Rror, TFOWR, Aunt Entropy, Birtitia, Addbot, Fgnievinski, Nath1991, MrOllie, Chamal N, Glane23, FiriBot, Tide rolls, OlEnglish, Ben Ben, Luckas-bot, Yobot,
, Wiki Roxor, AnomieBOT, Blackwellmas229, Healy229, Pattersonmas229, Materialscientist, Almostsorted, Caggegi229,
Dzulkk, Xqbot, Synergy radio, MoarNoir-Mas229, Capricorn42, Tcooling, HardyMAS229, Taylormas229, Laycockmas229, Leimas229,
Jacobmas229, Vidshow, Raja229, Nedim Ardoa, Drakes are abound, Shadowjams, Tiwifey1, FrescoBot, GEBStgo, A.Abdel-Rahim,
Creator-bz, BenzolBot, OgreBot, Redrose64, Pinethicket, Jonesey95, MDGx, Reconsider the static, Elmoro, Lotje, Aoidh, WikiTome,
Mean as custard, DASHBot, EmausBot, JustinTime55, Jmv2009, N24p, Xtzou, Unreal7, Grammar conquistador, ChuispastonBot, Peter Karlsen, Mandylyn, SamuelFreli, Rocketrod1960, ClueBot NG, JordoCo, Helpful Pixie Bot, Trepier, BG19bot, Northamerica1000,
Lesterxyz, Bing98748109347, MrBill3, Dropbuilt1234, KGun10, BattyBot, ChrisGualtieri, GoShow, Coster34, Yarrowworks, FoCuSandLeArN, Gblack505, Aymankamelwiki, Andranik.Aslanyan, Amethyst1234, Ugog Nizdast, Quenhitran, Wyn.junior, Corrinagentry, TerryAlex, KH-1, Ak4oojoe, KasparBot, 3 of Diamonds, Kbhanuprakash7 and Anonymous: 278
Linear amplier Source: https://en.wikipedia.org/wiki/Linear_amplifier?oldid=744941901 Contributors: Heron, Andrewman327, DavidCary, Ssd, Albany45, Bobblewik, Mysidia, Hooperbloob, Woohookitty, SCEhardt, JamesBurns, Ian Pitchford, Welsh, Mysid, Light current,
Deville, SmackBot, Mcld, Chris the speller, Cadmium, R.F.La Fontaine, Completesentence, Fuhghettaboutit, Beetstra, Dicklyon, Kvng,
Iridescent, Skapur, Nczempin, WillMak050389, Electron9, LuckyLouie, 7severn7, Magioladitis, Pavium, R'n'B, Drake Redcrest, Andy
Dingley, Spinningspark, FusionNow, Sv1xv, Brews ohare, SchreiberBike, Ekconklin, FrescoBot, I dream of horses, Klbrain, Helpful Pixie
Bot, BG19bot, Cqdx, Bender the Bot and Anonymous: 29
Pulse-width modulation Source: https://en.wikipedia.org/wiki/Pulse-width_modulation?oldid=749922571 Contributors: Damian Yerrick, PierreAbbat, SimonP, Heron, Lumpbucket, Michael Hardy, Tim Starling, Ixfd64, Glenn, GRAHAMUK, Selket, EpiVictor, Pingveno,
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Bhny, Kibbitzer, Dforest, Johantheghost, Matticus78, Voidxor, Mysid, Bota47, Dddstone, Caerwine, Maddog Battie, Ninly, Arthur Rubin,
Junglecat, Groyolo, DocendoDiscimus, SmackBot, Fireworks, Jereykopp, Reedy, TBH, Sea diver, Gilliam, Carl.bunderson, Cabe6403,
Chris the speller, Bidgee, Bazonka, Colonies Chris, A. B., Beatgr, OrphanBot, Kevinpurcell, Adamantios, Hateless, EdGl, Harryboyles,
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CosineKitty, Boguslinks, Ggugvunt, Jahoe, No more bongos, Dsergeant, Jerome Kohl, Steve Hosgood, CodeCat, Ashishbhatnagar72, 0612,
Burgh House, Maurice Carbonaro, 8hhaggis, Mrceleb2007, Plasticup, Americandxer, Fluteboy, RJASE1, VolkovBot, RingtailedFox, Athletes Foot, Ai4ijoel, Adrian two, Bobbetts, The Original Wildbear, Trashbag, Sankalpdravid, Argument~enwiki, Cabezon-raven, NW7US,
Cosprings, WereSpielChequers, Coati123, Miniapolis, Gregory.hand, Iceman63976, Altzinn, Dlrohrer2003, Serialdownloader, ClueBot,
Trojancowboy, Binksternet, Badger Drink, Jelf64, Kathleen.wright5, Kotalampi, Sv1xv, Nobidicus, Kitsunegami, Rcooley~enwiki, Eeekster, Dxinginfo, Ysrc, Arjayay, Cexycy, XLinkBot, Twitherspoon, Rio de oro, Addbot, Quantock, Riadismet, Avobert, Vchorozopoulos, Damiens.rf, Download, Kicior99, Angrense, Lightbot, Dellium, Luckas-bot, Yobot, Rccoms, Donfbreed, Alfonso Mrquez, ShrtWave, AnomieBOT, Andrewrp, Erud, JFY, Light,Love and Law, Kernel.package, Demigodgodd, Eugene-elgato, GliderMaven, FrescoBot, Surv1v4l1st, Riventree, Jc3s5h, Citation bot 1, PigFlu Oink, Sibian, AstaBOTh15, DrilBot, Broadcasttransmitter, GrapedApe,
AAT17, Hsnmoom, Mjs1991, PhillyDelphia, Mickeylove73, NameIsRon, Jackehammond, Steve03Mills, Graeme 2, John of Reading,
Duncan952, GoingBatty, Ovidcaput, G7cnf, Dreamer26, 1980fast, Alpha Quadrant (alt), Noodleki, Bryanmaupin, ChuispastonBot, Mongoosander, A120068020, Ivolocy, ClueBot NG, Reify-tech, Danim, Billgrove, Helpful Pixie Bot, Jyg1093, BG19bot, Nen, Michael Barera,
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744599151 Contributors: Glenn, ChrisJ, Eyreland, SeventyThree, BD2412, Rjwilmsi, Splash, Coinchon, Stereorock, CmdrObot, Miniapolis, Arjayay, MystBot, Addbot, Andimik, Xqbot, FrescoBot, Wearealmosthere, Veso266, H3llBot, Timdog13, Monkbot, SopaXorzTaker
and Anonymous: 3
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Emperorbma, Radiojon, Jwpurple, Fredrik, Karn, Everyking, Kevin Rector, Jccooper, Wtshymanski, SDC, Jonnabuz, BD2412, Vegaswikian, FlaBot, RobyWayne, Mcneight, Mikeblas, Mysid, Jeh, Morpheios Melas, Deville, Fernblatt, SmackBot, Mitchan, Hydrogen
Iodide, Kharker, TripleF, Rebelguys6, Harumphy, Nakon, Kvng, Eastlaw, CmdrObot, Thijs!bot, Electron9, Dfrg.msc, Widefox, Harryzilber, CosineKitty, Meredyth, R'n'B, Softguyus, AndrewBolt, Ginsengbomb, RingtailedFox, Spinningspark, Avenged Eightfold, The Thing
That Should Not Be, Ramaratnam, Addbot, Nedim Ardoa, Pinethicket, ClueBot NG, Bped1985, ArchaeC14, KasparBot and Anonymous:
24
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Heron, Denelson83, Bearcat, Alexwcovington, Ssd, Whitis, Rchandra, Peter Ellis, Ebear422, ChrisRuvolo, Nigelj, Wtshymanski, Gene
Nygaard, Plaws, Rjwilmsi, Gg630504, 121a0012, Moe Epsilon, SmackBot, McNeight, Frap, Samuel.dellit, Ryt, CmdrObot, Dfrg.msc,
WinBot, CosineKitty, Magioladitis, Jsadur, Read-write-services, Kf4yfd, Ibn Battuta, Geekdiva, RingtailedFox, Sv1xv, Alexbot, Mlas,
Addbot, Lightbot, Ivanov id, Jonkerz, EmausBot, Traxs7, Frietjes, Awoolford, Faizan and Anonymous: 20

582

CHAPTER 132. MORSE CODE

Modulation (disambiguation) Source: https://en.wikipedia.org/wiki/Modulation_(disambiguation)?oldid=738384207 Contributors: Hyacinth, Altenmann, Wafry, BD2412, Stormwatch, Tedder, Haroldarmitage, Royalbroil, Agradman, Soulbot, Vanwhistler, H1voltage, Addbot, SpBot, John Smi, Alpinwolf, Tassedethe, Bwrs, -, Luckas-bot, In ictu oculi, WikitanvirBot, GoingBatty, ClueBot NG,
Jerey Scott Maxwell, Sleeping is fun and Anonymous: 4
Electronics Source: https://en.wikipedia.org/wiki/Electronics?oldid=750550790 Contributors: Bryan Derksen, Zundark, Ap, Perry Bebbington, Jkominek, Aldie, Mudlock, Ray Van De Walker, SimonP, Waveguy, Heron, K.lee, Patrick, RTC, Michael Hardy, Tim Starling,
Fred Bauder, Mahjongg, Kku, Liftarn, Skysmith, Ahoerstemeier, Mac, Docu, Julesd, Glenn, Nikai, Netsnipe, Rob Hooft, Smack, GRAHAMUK, Hashar, Crusadeonilliteracy, Wikiborg, RickK, Reddi, Tpbradbury, Tero~enwiki, Omegatron, Jusjih, Archivist~enwiki, AnthonyQBachler, Branddobbe, Robbot, Fredrik, Kizor, Vespristiano, RedWolf, Altenmann, Rholton, Gidonb, DHN, Hadal, Fuelbottle, Pengo,
Alan Liefting, Cedars, Ancheta Wis, Alf Boggis, Giftlite, DavidCary, 0x0077BE, Greyengine5, Tom harrison, Ferkelparade, Everyking,
Henry Flower, Robert Southworth, Micru, Guanaco, Yekrats, Solipsist, Anoop t, Knutux, OverlordQ, Mako098765, Aulis Eskola, Zfr,
Corti, Discospinster, Vsmith, Brandon.irwin, VT hawkeye, Dmeranda, Bender235, JoeSmack, Plugwash, BjarteSorensen, CanisRufus, El
C, Miraceti, Mwanner, Edward Z. Yang, Art LaPella, RoyBoy, Bookofjude, Adambro, Bobo192, Smalljim, Matt Britt, SpeedyGonsales,
Jojit fb, Obradovic Goran, Nsaa, Jumbuck, Mduvekot, Atlant, PatrickFisher, Rclindia, Riana, Samohyl Jan, Wtmitchell, Here, Siskin1, Wtshymanski, Cburnett, Docboat, Cal 1234, LFaraone, Versageek, DV8 2XL, SteinbDJ, Gene Nygaard, Mindmatrix, BillC, Kokoriko, Ruud
Koot, Tabletop, Kglavin, Cbdorsett, Hard Raspy Sci, The Lightning Stalker, Allen3, Dysepsion, Graham87, Dwward, BD2412, Commander, Vary, JoshuacUK, Crazynas, Chebbs, ABot, SeanMack, The wub, Twerbrou, Flarn2006, Moskvax, RobertG, RexNL, Gurch,
A.K.Karthikeyan, Intgr, Srleer, Mongreilf, Chobot, Antilived, Krishnavedala, WriterHound, CaseKid, YurikBot, Wavelength, RobotE,
Trainthh, GLaDOS, Admiral Roo, Chaser, Stephenb, Shaddack, NawlinWiki, Wiki alf, Madcoverboy, Grafen, Srinivasasha, Xdenizen,
Jpbowen, Speedevil, Dbrs, Scottsher, PrimeCupEevee, Kkmurray, Wknight94, Searchme, Light current, Mickpc, Cbennyi, Zzuuzz,
Lt-wiki-bot, Magiluke, Closedmouth, Tabby, Nkendrick, Tevildo, GraemeL, GrinBot~enwiki, CrniBombarder!!!, Nippoo, Tom Morris,
SmackBot, Abcfox, Reedy, Hydrogen Iodide, The Photon, Bomac, Cwmccabe, Eupedia, Jwestbrook, Mad hatter, Brad2006, Nyckname,
Skizzik, Vercalos, Lindosland, Schmiteye, Saros136, JRSP, Kurykh, NCurse, Bduke, Oli Filth, Pitix, A. B., Suicidalhamster, Can't sleep,
clown will eat me, TheGerm, Frap, Sephiroth BCR, NoahElhardt, JonHarder, Rrburke, RedHillian, Edivorce, Dharmabum420, BostonMA,
Nakon, Jiddisch~enwiki, DylanW, Doodle77, Bidabadi~enwiki, FlyHigh, ArglebargleIV, Kuru, KenFehling, J 1982, Soumyasch, Breno,
Goodnightmush, Invsoigne, Capmo, CyrilB, Randomtime, Willy turner, Stupid Corn, TerryKing, Waggers, Jam01, Anonymous anonymous, P199, Jose77, Levineps, Iridescent, Casull, Linkspamremover, Tawkerbot2, JohnTechnologist, JForget, Biscay, Van helsing, Ilikefood, JohnCD, Nczempin, Jamoche, Michael J. Mullany, Myasuda, MaxEnt, Gogo Dodo, Odie5533, Tawkerbot4, Dynaow, Energetic
is francine@yahoo.com, Jrgetsin, Editor at Large, SpK, Aerielle 7@yahoo.com, BetacommandBot, Epbr123, Barticus88, LaGrange, Linioaxerist, Bulansarkar, Michagal, Almonit, Headbomb, Marek69, John254, Sodaboy1138, Leon7, Sanglap, Silver Edge, Escarbot, I already forgot, Hmrox, Austin Maxwell, AntiVandalBot, KP Botany, Khin007, Ste4k, Myanw, JAnDbot, Barek, MER-C, The Transhumanist, BenB4, Heathert87, PhilKnight, Sparky451, Nicolaasuni, Magioladitis, Bongwarrior, VoABot II, JamesBWatson, Sam.yates, Father
Goose, Ecksemmess, Pixel ;-), Sidneyhuber, Catgut, Theroadislong, Gabriel Kielland, 28421u2232nfenfcenc, Allstarecho, M 3bdelqader,
Clipjoint, Glen, Patrick Denny, Philg 124, Black Stripe, Hdt83, MartinBot, Vigyani, Manavbhardwaj, BetBot~enwiki, Jim.henderson,
AlexiusHoratius, Brinkie, Mausy5043, J.delanoy, Pharaoh of the Wizards, Mange01, Trusilver, Uncle Dick, G. Campbell, It Is Me Here,
Minime72706, Touch Of Light, Mirithing, Evb-wiki, Jamesofur, Vanished user 39948282, Treisijs, Marstronix, Microcon, Cinnagingercat, DASonnenfeld, Squids and Chips, Ikalogic, Wikieditor06, Irdam, Katy,Girl, F458, Hellosezoo, TXiKiBoT, Oshwah, The Original
Wildbear, Porkrind, Sankalpdravid, Qxz, Vanished user ikijeirw34iuaeolaseric, Anna Lincoln, Franko234, Bibijee, Leafyplant, ^demonBot2, DesmondW, Seek202, Madhero88, Improve~enwiki, Elliot hoste, Meters, Synthebot, Strangerer, Spinningspark, Atreusk, Brianga,
AlleborgoBot, Symane, Jimmi Hugh, Eloc Jcg, Neparis, Wildelectronics, SieBot, IronGarb, Defparadox, Mikebar, Dawn Bard, Viskonsas, RJaguar3, Kumudh, Aillema, Flyer22 Reborn, Topher385, Oxymoron83, Lightmouse, Urquhart1, Felizdenovo, Denisarona, Dalyman,
Tuxa, Dp67, Tanvir Ahmmed, De728631, ClueBot, Kl4m, The Thing That Should Not Be, Vertigoa, Wolfch, Meisterkoch, Dxnlmb,
Uncle Milty, Blanchardb, Trivialist, Drew335, Excirial, 12spacejk1, Abrech, Gtstricky, Lihmwiki, Esbboston, Jotterbot, Skaapgif, Tnxman307, Singhalawap, Dekisugi, MilesAgain, DerBorg, Sergio15, SoxBot III, Bcherwrmlein, Prasanna gandhiraj, XLinkBot, Gwandoya, Megtec, Frood, Manorwiki504, Addbot, Xp54321, Jordowney, Pjezzy, Willking1979, Twaz, Betterusername, Landon1980, Dimosvki, Marx01, Fieldday-sunday, GyroMagician, Yangandjiao, Ravindra 20, Stan Sykora, NjardarBot, Asaurabh, Download, CarsracBot,
Norman21, Laynelagasse, CuteHappyBrute, Mukulanandsrivastava, Eagle999, Tide rolls, BetoVinci, Lightbot, YJoosshhiuea101, B1u
SkR33N, Jim, Legobot, Luckas-bot, Yobot, OrgasGirl, Fraggle81, Pcap, THEN WHO WAS PHONE?, AmeliorationBot, ArcticREPtilia, Wonder, , Thabonch, AnomieBOT, DemocraticLuntz, Rubinbot, Jim1138, Galoubet, Kingpin13, Earizon, NickK,
Thefuzzmaster24, Materialscientist, Carl086, ArthurBot, Xqbot, Zad68, Capricorn42, Drilnoth, Creativesoul8, Praraj99, JimBeam251,
Cyphoidbomb, IntellectToday, Magnus0re, Dpro369, Coty0816, Secondwatch, Pistol980, Smallman12q, Krrish23, Plusspace pcc, Shadowjams, Remshad, Qasim9, RuslanBer, Paine Ellsworth, Raissazhou, Nageh, Foxthor11, Steve Quinn, Ganesh.fc, Tintenschlein, Pinethicket,
Leogertrudemsc, MJ94, Bzlcs, Calmer Waters, BigDwiki, Noel Streateld, Craig Lyd, Serols, SpaceFlight89, Killergod129, Abhishekchavan79, FoxBot, TobeBot, Trappist the monk, SchreyP, DixonDBot, Jordanbeneld, Bandasuppan, Lotje, Electriedpete, GeeZ, Vrenator, Electorial, RobotQuistnix, Canuckian89, Stroppolo, Derild4921, Mean as custard, TjBot, Alph Bot, Arunr.in, Example111, Midhunnageswaram, EmausBot, Beatnik8983, Korbman, GoingBatty, MICROTECHINDIA, K6ka, Kxiz, Lamb99, Edmundred, AvicBot,
Kkm010, ZroBot, Tonyton101, Shuipzv3, Arpit.withu, Inamleapord, JackieBM, Access Denied, Fifa10pro, EWikist, Lion789, Shakti
singh 789, Nick007p, Tomsdearg92, Abby1028, GrayFullbuster, Goatboy22, ClueBot NG, Matthiaspaul, This lousy T-shirt, L284363829,
Millermk, Floatjon, O.Koslowski, Widr, WikiPuppies, Nender14, Fahadraza007, Meniv, Almasimagorwa, Harishgvk, Wbm1058, Shwetamahajan, Neptunes Trident, Dsajga, Pine, Gokulmaba, Raysylvester, Jprbtech, Mahmodsamy, Sleeping is fun, MusikAnimal, Amp71,
Mitesh1401, Snow Blizzard, Will Gladstone, Psindt1, Glacialfox, Lgmobilephone, David.moreno72, Spcyoutlaw, Mdann52, Embrittled,
Andres shasta, Hksuj91, Underoi, BrightStarSky, Dexbot, Webclient101, Mysterious Whisper, CuriousMind01, Numbermaniac, Lugia2453, Frosty, Jamesx12345, FletcherV, Super86, The Anonymouse, M.Ahmad Blooch, Reatlas, ArslanAlvi, Alexwho314, IliyaKovac,
Africanssuckaids, GamerMan7799, , CensoredScribe, Ugog Nizdast, Melody Lavender, YiFeiBot, Jojosyjohn, Keithraymondgriths, Shamim apee, 2electronic, HiYahhFriend, SpanglishArmado, , Welcome1To1The1Jungle, Dcoptimum, Universe DNA, Pavankumarchenna, Thingmaker, KH-1, Lohithjavali, ChamithN, Julietdeltalima, Weegeerunner, MarkyNToby, Buhari500,
Ibukharix, KasparBot, Kittykatken, CAPTAIN RAJU, MBlaze Lightning, CLCStudent, Nicole stormsword, Boombiwed, Qzd, Boishakhi
Mridha, Chrisdayle, Fmadd, Sopan Kotbagi, Swarankargaurav, VYSHNAV and Anonymous: 829
Telecommunication Source: https://en.wikipedia.org/wiki/Telecommunication?oldid=750174296 Contributors: The Cunctator, Mav,
Bryan Derksen, The Anome, Ap, Rjstott, Aldie, Heron, Olivier, Edward, Michael Hardy, Mahjongg, Dan Koehl, Kku, Ixfd64, Dcljr,
Sannse, Tregoweth, Card~enwiki, Ahoerstemeier, DavidWBrooks, Haakon, Bluelion, Glenn, Nikai, Tristanb, Raven in Orbit, Guaka,
Ralesk, Reddi, Hydnjo, Will, Wik, Tpbradbury, Munford, Maximus Rex, SEWilco, Topbanana, Fvw, Chuunen Baka, Robbot, Chrism,
Vespristiano, RedWolf, Romanm, Modulatum, Richardpitt, Stewartadcock, Rfc1394, Steeev, Rasmus Faber, Hadal, Borislav, Betsumei,

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Rwwww, GrinBot~enwiki, Sbyrnes321, Veinor, SmackBot, InverseHypercube, Unyoyega, CyclePat, Blue520, Misto, Eskimbot, KelleyCook, Lakhim, Gilliam, Ohnoitsjamie, Hmains, Ppntori, Chris the speller, Persian Poet Gal, Payxystaxna, Oli Filth, Jeysaba, Silly rabbit,
Vasu99a, Telecom.portal, Colonies Chris, A. B., Stenson jack, , Mitsuhirato, Rrburke, Addshore, DR04, A5b, Mion,
Ugur Basak Bot~enwiki, SashatoBot, Rory096, Harryboyles, Demicx, Mike1901, Smasafy, Bushsf, GothCabbage, Aden Scott, IronGargoyle, 16@r, Special-T, Shangrilaista, Beetstra, Milesdowsett, Mr Stephen, Dicklyon, InedibleHulk, SandyGeorgia, TastyPoutine, Totel,
Ffxaddict899, Jose77, Kvng, ShakingSpirit, SansSanity, OnBeyondZebrax, Iridescent, Joseph Solis in Australia, Ohad.cohen, Courcelles,
Tawkerbot2, JohnTechnologist, JForget, CRGreathouse, CmdrObot, Wafulz, JohnCD, N2e, SkylineEvo, Thomasmeeks, Penbat, Cydebot,
Obornp, Gogo Dodo, Hughdbrown, Studerby, Kraky, Tawkerbot4, Ethan01, Kozuch, Lxdbsn, Malleus Fatuorum, Thijs!bot, Hcberkowitz,
John254, Tellyaddict, Solveforce, Dawnseeker2000, Escarbot, Mentisto, KrakatoaKatie, AntiVandalBot, Majorly, Luna Santin, Grammargal, Venya, Qsa5kn, PJY, Juzaily, Julie Deanna, Lperez2029, Once in a Blue Moon, JAnDbot, Harryzilber, MER-C, CosineKitty,
PhilKnight, Kerotan, Magioladitis, VoABot II, Appraiser, Verkhovensky, Bwhack, ClovisPt, LorenzoB, DerHexer, Oicumayberight, Kayau,
Gwern, Europaandio, MartinBot, Jim.henderson, R'n'B, CommonsDelinker, Erkan Yilmaz, J.delanoy, Pharaoh of the Wizards, Trusilver,
Wa3frp, Jesant13, A New Nation, It Is Me Here, McSly, Brolsma, Skier Dude, Zedh, The Transhumanist (AWB), Fountains of Bryn Mawr,
KylieTastic, DASonnenfeld, Mlewis000, Idioma-bot, Funandtrvl, Remi0o, Sam Blacketer, VolkovBot, DMcMPO11AAUK, AlnoktaBOT,
Coreyxbs, Gaianauta, Sdsds, Philip Trueman, TXiKiBoT, Chimpex, GcSwRhIc, Bogatabeav, Saligron, Canaima, From-cary, Mezzaluna,
PDFbot, Bhavin105, Wiae, ARUNKUMAR P.R, SpecMode, Madhero88, Kjoseph7777, Mohan0704, Aulman, Meters, IdleUser, Synthebot, Spinningspark, Insanity Incarnate, Symane, Logan, Kbrose, SieBot, Moonriddengirl, Scarian, Gerakibot, Keilana, JD554, Andrew
Hartford, Matthewedwards, SPACKlick, WannabeAmatureHistorian, Ioverka, Nazi 2007, Lightmouse, RW Marloe, Ngrieth, OKBot,
Svick, Spitre19, Kristine.clara, Rapaporta, Jayeshtula, WikiLaurent, Asocall, Denisarona, Ossguy, Tuxa, Twinsday, Church, Martarius, Elassint, ClueBot, Valeria70, GorillaWarfare, PipepBot, Qedu, Pvineet131, The Thing That Should Not Be, WaltBusterkeys, SyntaxBlitz, Wutsje, Businessphonesystems, Bbb2007, Excirial, Hadiyana, Hugsforsale, Sun Creator, Georgiamonet, Arjayay, Razorame,
Muro Bot, Pwarrior, BOTarate, Hdorren, Murali intl, Carlroddam, Johnuniq, SoxBot III, Vanished user uih38riiw4hjlsd, Skunkboy74,
XLinkBot, NocturnalA6 2.7, Setherson, Sweetpoet, Gggh, Addbot, DOI bot, Fgnievinski, Bkmays, Leszek Jaczuk, Fluernutter, Kutulus, MrOllie, Download, Favonian, 5 albert square, Tyw7, Lightbot, OlEnglish, Gail, Zorrobot, MuZemike, -, Solidice190,
Luckas-bot, Yobot, OrgasGirl, TaBOT-zerem, Samsam.yh, THEN WHO WAS PHONE?, KamikazeBot, Nyat, AnomieBOT, Srobak,
Rsayles, Bsimmons666, Bowmanmas229, Jim1138, Galoubet, Gaga.vaa, Piano non troppo, Kjkarthikmaddy, AdjustShift, Materialscientist, Whiskers9, Citation bot, Jeremyjf22, Freeness, Elm-39, Schproject, DynamoDegsy, Readiwip, ArthurBot, MauritsBot, Xqbot, Capricorn42, 4twenty42o, IMarc89, LoKiLeCh, DSofa, Ched, Srich32977, Coretheapple, Wiki2contrib, Nasa-verve, GrouchoBot, Wizardist,
Omnipaedista, Smartishkindaguy, Bo98, Shadowjams, 11cookeaw1, SD5, Gururaju, A.amitkumar, Anth12, Tsiuser09, FrescoBot, GEBStgo, Alarics, Mthrandir, Finalius, Citation bot 1, XxTimberlakexx, Biker Biker, MacMed, I dream of horses, Lars Washington, MastiBot,
Ezhuttukari, Bridget Huntley, Serols, Blycroft, 123, Crusoe8181, Thrissel, V4nd3r, TobeBot, Trappist the monk, SchreyP, Paul
J Wayman, Lotje, Callanecc, Vrenator, Aoidh, TheGrimReaper NS, Merlinsorca, Minimac, Sideways713, DARTH SIDIOUS 2, Mean
as custard, Onfopt, Basangbur, Haylstorms, EmausBot, John of Reading, Orphan Wiki, WikitanvirBot, Gfoley4, Katherine, Pugliavi,
Primefac, GoingBatty, RA0808, MCI telcomm, Telecomman, Wikipelli, Sprinklezz, Kkm010, Vihar7, Cogiati, F, H3llBot, Marc Spoddle, LIVPAT, Alrino, IGeMiNix, Kaeh4, Donner60, Rifasj123, Rangoon11, Chris857, ChuispastonBot, ThePowerofX, Philippe BINANT,
Teapeat, Sepersann, 28bot, ClueBot NG, JetBlast, This lousy T-shirt, Draksis314, Satellizer, DobriAtanassovBatovski, Mrgates, Mr Myson,
Muon, Widr, Glauki, Helpful Pixie Bot, BG19bot, Hittman627, Brittanyab, Northamerica1000, Ashishkulshreshtha, Graham11, Colbry53,
Axis Research Mind, Joydeep, Swamynathan007, Elagoutova, HelinaZ, Achowat, Fylbecatulous, Pratyya Ghosh, Oreileao, Khazar2, Mnativesacl, Mhughes38, Katiewiltshire, FoCuSandLeArN, Opensourceyk, Thermocycler, PeacefulPlanet3, Lugia2453, Perep80, Me, Myself,
and I are Here, Reatlas, Joeinwiki, Phamnhatkhanh, Faizan, Anawesomeeditor, Rizwaanahamed3, Chriyu, DavidLeighEllis, Daideep patel,
Ugog Nizdast, Melody Lavender, NottNott, Ginsuloft, Jianhui67, Danieltele, Joancdocyogen, Mendisar Esarimar Desktrwaimar, Iamandrewg, 7Sidz, HHubi, Salton Finneger, Monkbot, Dsprc, Trackteur, Wikijuanjo1514, Chicken butt0192, MRD2014, Vkryla, ChamithN,
Prinzpopo, Esquivalience, NekoKatsun, MarkyNToby, JaDam, Aman.singh5317, Deborah Chiaravalloti, Unibateman, KasparBot, Dinnypaul, Kiprorodri, Srednuas Lenoroc, Salwati6, SamWolves23, Jhansiranim, Kate A. Steel, GSS-1987, Yazebi, JMBeggs74, Rajram123,
GreenC bot, Fmadd, Monvoip, Bender the Bot and Anonymous: 765
Waveform Source: https://en.wikipedia.org/wiki/Waveform?oldid=749266315 Contributors: Damian Yerrick, Derek Ross, The Anome,
Tbackstr, SimonP, Heron, Michael Hardy, Fwappler, ZoeB, Mxn, Omegatron, Fredrik, Romanm, No Guru, Bender235, Cmdrjameson, Alansohn, Patrick Bernier, Riana, Ayrshire-77, Pol098, Vegaswikian, SeanMack, Ahabel, Barrykas, Geimas5~enwiki, Ozzykhan,
Deville, DVD R W, Marquez~enwiki, SmackBot, FocalPoint, Prodego, BiT, Oli Filth, Kalatix, Adrigon, JzG, Bjankuloski06en~enwiki,
Teadrinker, Unisouth, Dicklyon, Doceddi, A Softer Answer, Daniel Olsen, Thijs!bot, Mutiny, Myanw, Hekerui, Black Stripe, MartinBot, NewEnglandYankee, ^demonBot2, Pigslookfunny, Inductiveload, Beardy123, Kylemew, ClueBot, Binksternet, Hwyengineer47,
Eeinfo2008, ChrisHodgesUK, Versus22, Dextreme~enwiki, Mitrg, Wyatt915, Fgnievinski, Aykantspel, Debresser, Legobot, Yobot,
AnomieBOT, Manda.L.Isch, Akilaa, Groovenstein, Jhbdel, MINITEK, Raniero Supremo, Haeinous, Udalov, DexDor, AndyHe829,
ZroBot, Caspertheghost, Kirill Borisenko, Kharlos84, Radiodef, Wikigeek244, Xzolo990, Nj46k534l5675, Davy2016 and Anonymous:
45
Analog signal Source: https://en.wikipedia.org/wiki/Analog_signal?oldid=741200823 Contributors: Derek Ross, The Anome, Peterlin~enwiki, TomCerul, Waveguy, Edward, Patrick, Michael Hardy, Tim Starling, SGBailey, Ixfd64, Stevan White, HarmonicSphere,
Mac, Glenn, Cimon Avaro, Alex756, Rob Hooft, Smack, Reddi, Jitse Niesen, Zoicon5, Maximus Rex, Jni, Robbot, Altenmann, Ojigiri~enwiki, Blainster, Hadal, Wikibot, Wereon, Lupo, Ancheta Wis, Matt Gies, Alerante, Alf Boggis, Niteowlneils, Ptk~enwiki, Vina,
MacGyverMagic, Bumm13, Marc Mongenet, Klemen Kocjancic, Discospinster, Rich Farmbrough, Hydrox, Slipstream, Notinasnaid, ZeroOne, Bobo192, Longhair, Maurreen, Hooperbloob, Alansohn, Hackwrench, Zippanova, Cburnett, Kusma, Ceyockey, Jakes18, Doctorkb, Knuckles, JRHorse, SDC, Prashanthns, Taestell, SpNeo, Heah, RexNL, Guanxi, The Rambling Man, Ugha, Borgx, Tole, Nawl-

584

CHAPTER 132. MORSE CODE

inWiki, E2mb0t~enwiki, Relayer250, SkepticMuhs, Juanscott, Jwissick, Josh3580, JLaTondre, CIreland, KnightRider~enwiki, SmackBot, Ashenai, The0208, KelleyCook, Timotheus Canens, Master of Puppets, Can't sleep, clown will eat me, Jwillbur, MHoerich, Just
plain Bill, Rockvee, Rory096, BurnDownBabylon, Breno, Hvn0413, Girmitya, Kvng, Dl2000, Pejman47, OnBeyondZebrax, Tawkerbot2,
Chetvorno, JimKandol, CRGreathouse, CmdrObot, Ale jrb, Mathsgeek, Peripitus, Thijs!bot, CoronadoII, Leon7, Dzubint, AntiVandalBot,
Seaphoto, Alphachimpbot, Elaragirl, JAnDbot, Harryzilber, MER-C, Bahar, PhilKnight, Bwhack, Drondent, Avicennasis, Oicumayberight,
I B Wright, FisherQueen, Jackson Peebles, Rettetast, Trusilver, AAA!, Bogey97, Bakkouz, 01livesp, Century0, Biglovinb, Juliancolton,
VolkovBot, Sankalpdravid, Anna Lincoln, LeaveSleaves, BotKung, ARUNKUMAR P.R, SQL, Logan, Kuroanei, SieBot, Steorra, Jauerback, Hertz1888, Dillard421, Hippie Metalhead, ClueBot, Binksternet, Mexican Sponge, Mild Bill Hiccup, Basketball110, Bradderz90, 7,
AmusedRepose, Johnuniq, SoxBot III, Vanished user uih38riiw4hjlsd, DumZiBoT, WikHead, SilvonenBot, MystBot, B2thak, Numbo3bot, Issyl0, Zorrobot, WikiDreamer Bot, Quantumobserver, HerculeBot, Legobot, Yobot, Ajh16, Sarrus, AnomieBOT, Barking Mad42,
Justme89, Xqbot, GrouchoBot, RibotBOT, SassoBot, Dougofborg, Fooziedog, ShashClp, GliderMaven, Amplitude101, SaturdayNightSpecial, TobeBot, Dinamik-bot, Asb.iluvu, Tbhotch, Showbiz9, Nil Spaar, John of Reading, Kueller1, Sp33dyphil, Tommy2010, Wayne
Slam, TYelliot, ClueBot NG, Lord Chamberlain, the Renowned, Totalporch2, JordoCo, ChrisGualtieri, BrightStarSky, Tayyabmanzoor,
Crystallizedcarbon, Qweqweqwett, KasparBot, JJMC89, Elektrik Fanne, Expurgation, Novel12, Viswanadhgarimella and Anonymous: 220
Baseband Source: https://en.wikipedia.org/wiki/Baseband?oldid=747942754 Contributors: Imran, Pde, Glenn, Med, Omegatron, Bearcat,
Fredrik, Spamhog, Bbx, Alan Liefting, Giftlite, David Johnson, Mboverload, Fys, Peter bertok, Kevin Rector, Qef, Art LaPella, JYolkowski,
Pspealman, Fritzpoll, Evil Monkey, Gene Nygaard, Unixxx, Tangotango, Chobot, YurikBot, Bhny, Splash, Voidxor, Yudiweb, Ninly,
LeonardoRob0t, Rwwww, SmackBot, Thumperward, Snori, Oli Filth, Dcamp314, DylanW, Zac67, Anlace, Dicklyon, Kvng, Tawkerbot2,
Dlohcierekim, Chetvorno, Le savoir et le savoir-faire, Alaibot, Scepia, MER-C, CosineKitty, Dcooper, Bongwarrior, 28421u2232nfenfcenc,
Mange01, Chungw74, DorganBot, CardinalDan, Oshwah, Spinningspark, BOTijo, Biscuittin, WereSpielChequers, Flyer22 Reborn, ClueBot, The Thing That Should Not Be, Sepia tone, PixelBot, Johnuniq, Addbot, Fgnievinski, Ettrig, Legobot, Luckas-bot, Yobot, C5813,
Materialscientist, Xqbot, Etoombs, Jhbdel, Angelus Delapsus, GerbilSoft, WhackTheWiki, Suusion of Yellow, Ripchip Bot, EmausBot,
Morbidkokos, Alle, ChuispastonBot, ClueBot NG, Helpful Pixie Bot, Johnny C. Morse, PhnomPencil, CitationCleanerBot, Epicgenius,
Jamesmcmahon0, *thing goes, KasparBot, GSS-1987, Phoenix Gill, Bender the Bot and Anonymous: 85
Demodulation Source: https://en.wikipedia.org/wiki/Demodulation?oldid=732601229 Contributors: PierreAbbat, Europrobe, Egil, Ellywa, Kh7, Jondel, BrianWilloughby, Alansohn, Anthony Appleyard, Fred Bradstadt, FlaBot, King of Hearts, YurikBot, Anuran, Steven
Hepting, FlyingPenguins, SmackBot, Slashme, Gilliam, Kvng, Chetvorno, BrainStain, CmdrObot, Kairotic, Thijs!bot, Harryzilber,
Labroid, Jim.henderson, Mange01, TomyDuby, ICE77, Amikake3, Alinja, Colmanian, Synthebot, AHMartin, ClueBot, GreenSpigot,
LizardJr8, Sv1xv, Razorame, Jonverve, DumZiBoT, Kat-roxx, Addbot, Vintage Dave, Tanhabot, Limitio, Luckas-bot, Gsmcoupe, CvetanPetrov1940, DemocraticLuntz, A More Perfect Onion, Nishantjr, Ammubhave, Maitchy, Wireless Keyboard, Eden garrett, Dinamik-bot,
JeepdaySock, EmausBot, Dgd, Ego White Tray, ClueBot NG, Wbm1058, BG19bot, Amindayo2, Jestoph, MRFYPTS and Anonymous:
48
Low-pass lter Source: https://en.wikipedia.org/wiki/Low-pass_filter?oldid=743278659 Contributors: Mav, The Anome, Rjstott, Heron,
Patrick, JohnOwens, Lexor, David Martland, Glenn, Palfrey, Dysprosia, Furrykef, Omegatron, ThereIsNoSteve, Giftlite, DavidCary, Wolfkeeper, BenFrantzDale, Bensaccount, Vadmium, LucasVB, Antandrus, BrianWilloughby, Moxfyre, R, Rich Farmbrough, TedPavlic,
Mecanismo, ESkog, Teorth, Foobaz, Cavrdg, Hangjian, Hooperbloob, Dragoljub, Wtshymanski, Cburnett, Flying sh, Davidkazuhiro,
Pol098, Akavel~enwiki, Pfalstad, Torquil~enwiki, Mikm, Alfred Centauri, Kri, Krishnavedala, Borgx, PinothyJ, Tole, Gaius Cornelius,
Brandon, Mikeblas, Searchme, Light current, Mickpc, Deville, Petri Krohn, LeonardoRob0t, Phil Holmes, RG2, Mejor Los Indios, EXonyte, KnightRider~enwiki, Mitchan, Steve carlson, Pgk, Niehaus~enwiki, ASarnat, Yamaguchi , Chris the speller, Nbarth, RoysonBobson, Zvar, Soundsop, IE, P.o.h, Elzair, Dog Eat Dog World, Minna Sora no Shita, Rogerbrent, Dicklyon, Kvng, Ss181292, Unmitigated
Success, Myasuda, Paddles, Editor at Large, Epbr123, Sobreira, Bobblehead, Brichcja, Majorly, Danroa, Lovibond, Ekkanant, JAnDbot,
Xhienne, Drizzd~enwiki, Time3000, Bongwarrior, VoABot II, Dics, Eus Kevin, Parijata, Kayau, MartinBot, Renski, Tgeairn, RockMFR,
Mange01, Slamedsilver, LLcopp, VolkovBot, Inductiveload, Ahmedsaieed, Spinningspark, Anoko moonlight, Kbrose, Tetos~enwiki,
Tugjob, Dp67, ClueBot, Binksternet, Brews ohare, Thingg, 7, Monstrim, Dusen189, Johnuniq, XLinkBot, Mm40, ZooFari, Addbot,
Howard Landman, Jojhutton, Redheylin, Parvejkhan, Nocal, Tide rolls, Gail, Legobot, Bdb112, Yobot, AnomieBOT, Floquenbeam,
Jim1138, B137, Materialscientist, Citation bot, Xqbot, Armstrong1113149, Ponticalibus, Christopherley, RibotBOT, Rb88guy, Hlovatt,
GliderMaven, ICEAGE, Jonesey95, RedBot, Piandcompany, December21st2012Freak, Trappist the monk, The Utahraptor, Mgclap,
Astro89, WikitanvirBot, Immunize, Dewritech, Catshome2000, Clusternote, Zueignung, Teapeat, Dweymouth, ClueBot NG, Satellizer,
Widr, BG19bot, Varun varshney12, OceanEngineerRI, Kizzlebot, JYBot, Kroq-gar78, CsDix, Babitaarora, My name is not dave, Quenhitran, Meteor sandwich yum, Monkbot, Andars97 and Anonymous: 241
Digital data Source: https://en.wikipedia.org/wiki/Digital_data?oldid=751894758 Contributors: Damian Yerrick, Dave McKee, Eclecticology, Heron, Patrick, Nixdorf, Kku, Ixfd64, Karada, Ahoerstemeier, Mac, Nanshu, Angela, Glenn, Rob Hooft, Smack, Iseeaboar, Ww,
Gutza, Wik, DJ Clayworth, Mackensen, Aleph4, Donarreiskoer, Robbot, Jimdundereld, RedWolf, Nurg, Academic Challenger, Jondel,
Mushroom, Mandel, SoLando, Tea2min, Matt Gies, Rs2, Ssd, Ptk~enwiki, Mboverload, Cyber-It, Vanished user 1234567890, CesarFelipe,
Zfr, Fg2, Damieng, Zaf, D6, Discospinster, Evice, Hayabusa future, Jpgordon, Longhair, Matt Britt, Maurreen, SpeedyGonsales, DCEdwards1966, Jakew, HasharBot~enwiki, Guy Harris, Fourthords, Rick Sidwell, Cburnett, SteinbDJ, Ceyockey, Forderud, Feezo, Jerey O.
Gustafson, Woohookitty, Myleslong, CharlesC, Skoban, Haikupoet, Sjakkalle, Theye, Tangotango, Oblivious, ABot, KirkEN, Mortice,
FlaBot, Nivix, TheDJ, Imnotminkus, Chobot, Occidens~enwiki, Bgwhite, StopSineMan, YurikBot, Wavelength, RussBot, Hydrargyrum,
Manop, Ugur Basak, David R. Ingham, Shanel, Jpbowen, Jwissick, Petri Krohn, Nothlit, Pursin1, Royalguard11, Gigs, Yrdy, Jab843,
Gilliam, Ohnoitsjamie, Hmains, MK8, Can't sleep, clown will eat me, Frap, Cybercobra, DMacks, LeoNomis, JHunterJ, Slakr, George
The Dragon, Dicklyon, Optakeover, Ryulong, Kvng, Xionbox, Igoldste, Tawkerbot2, Dan1679, DBooth, JForget, Captmog, Tawkerbot4,
Malleus Fatuorum, Thijs!bot, Epbr123, JustAGal, EdJohnston, AntiVandalBot, Guy Macon, AnAj, Once in a Blue Moon, Storkk, JAnDbot, MER-C, Hello32020, IIIIIIIII, Bongwarrior, Tedickey, Allstarecho, Lord mrazon, Oicumayberight, MartinBot, R'n'B, Jmccormac,
HEL, Johnbod, AntiSpamBot, Warut, SmilesALot, Doctoroxenbriery, Czarbender, Pdcook, VolkovBot, ABF, Indubitably, Alexandria,
Philip Trueman, TXiKiBoT, Mamidanna, Qxz, Poo1000, A7a neez, Don4of4, LeaveSleaves, Melissa komunikasiUI, Kbrose, SieBot, Savorie, Nopetro, Faradayplank, KPH2293, Hippie Metalhead, WikipedianMarlith, ClueBot, The Thing That Should Not Be, Supertouch,
Wysprgr2005, Drmies, Mild Bill Hiccup, Shinpah1, Kingrattus, Brewcrewer, Sun Creator, Iohannes Animosus, Razorame, SchreiberBike, Bald Zebra, Kezoce, Aitias, Cantor, Johnuniq, XLinkBot, Fgnievinski, Nintenutts, NjardarBot, Mjr162006, Tassedethe, Tide rolls,
Homo Computeris, Jarble, Insider, Legobot, Math Champion, Yobot, Cc2po, Eric-Wester, AnomieBOT, Jim1138, Photorepetto, Ubcule,
AV3000, JeKnight, GrouchoBot, RibotBOT, Sahehco, Shadowjams, Pritamd20, ShashClp, Prari, Altg20April2nd, GEBStgo, Raziaar,
Zero Thrust, Igor233, DrilBot, Pinethicket, HRoestBot, Noel Streateld, Nickyus, Overjive, Brian the Editor, Reach Out to the Truth, Sideways713, Alph Bot, WikitanvirBot, Dken, ChuispastonBot, 28bot, ClueBot NG, BarrelProof, Go Phightins!, Widr, MerlIwBot, Helpful

132.11. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

585

Pixie Bot, Snaevar-bot, Solomon7968, Atomician, DigitalDev, Dissonus, Guess016, Ducknish, Interlude65, Eransgran, The Anonymouse,
Njjklp, Rockbreath79, Chriyu, Sodaha, Microchip2013, Yikkayaya, JackHoang, MusikVarmint, Wuel.co, DmiGurk, RainFall, Hdhugdd
and Anonymous: 261
Public switched telephone network Source: https://en.wikipedia.org/wiki/Public_switched_telephone_network?oldid=751058328 Contributors: The Anome, Andre Engels, Gsl, Aldie, William Avery, SteveDay, MikkoM, Youandme, Steverapaport, Patrick, JohnOwens,
Michael Hardy, Darkaddress, Cameron Dewe, Looxix~enwiki, Tusixoh, Glenn, Crissov, Dysprosia, Radiojon, SEWilco, Robbot, Rfc1394,
DavidCary, Markus Kuhn, Niteowlneils, Leonard G., Rchandra, Falcon Kirtaran, Tagishsimon, Gloop, Chowbok, JeremiahOeltjen, Adrian
Sampson, Hugh Mason, JTN, Richardelainechambers, MBisanz, Fourpointsix, Bobo192, MarkWahl, Redlentil, Espoo, Disneyfreak96,
Poweroid, ChrisUK, Rohaq, Guy Harris, Wtmitchell, HenryLi, OwenX, ^demon, Ruud Koot, Graham87, BD2412, Yurik, Snaekid,
Pmj, Rjwilmsi, Makru, FlaBot, Ian Georey Kennedy, Polaralex, Chobot, YurikBot, Rsrikanth05, Cryptic, Hm2k, NickBush24, Adamn,
Jpbowen, Tony1, Nethgirb, Mysid, Elkman, Max Schwarz, Sharkb, Closedmouth, Petri Krohn, Hirudo, SmackBot, MerlinMM, JMiall,
Rick7425, Oli Filth, MalafayaBot, Duckbill, AmiDaniel, -ramz-, Nobodyinpart, Dicklyon, H, Kvng, Iridescent, BobbyLee, Joseph Solis in Australia, Az1568, Chetvorno, JohnTechnologist, CmdrObot, Ale jrb, BeenAroundAWhile, Yukoba~enwiki, Alaibot, Dragont,
Thijs!bot, Simeon H, Escarbot, Agnvoip, Alphachimpbot, JAnDbot, Harryzilber, Jan Friberg, Sln3412, Albany NY, Bellhead, Verkhovensky, AlephGamma, Kgeischmann, Calltech, I-baLL, Zahakiel, MartinBot, DrDorkus, Jim.henderson, Nono64, J.delanoy, Peter Chastain, NewEnglandYankee, Manassehkatz, Ishanbhanu, Birczanin, Netmonger, PNG crusade bot, TXiKiBoT, Vipinhari, Abtinb, Rei-bot,
Monkey Bounce, Doug, Isdnip, AlleborgoBot, Kbrose, Quietbritishjim, SieBot, Dwandelt, Gerakibot, Yunghkim, Mahehere, Jojalozzo,
Ebernat, Machina.sapiens, WordyGirl90, ClueBot, EoGuy, Taroaldo, Trivialist, Mlas, XLinkBot, Deadlyturtletank, WikHead, SilvonenBot, Dgtsyb, Addbot, AkhtaBot, Download, Numbo3-bot, Lightbot, Loupeter, Zorrobot, , Luckas-bot, Bunnyhop11, KamikazeBot, Vini 17bot5, AnomieBOT, New2way, Rubinbot, Kingpin13, Abdulraheemsidz, Obersachsebot, Xqbot, Ranjandutta, Toetoetoetoe,
GrouchoBot, SimonInns, FrescoBot, Nageh, Haeinous, Austria156, Ezhuttukari, EmausBot, WikitanvirBot, Super48paul, Boundarylayer,
Rkononenko, Midas02, Anthony.selby, Miguelito2010, ClueBot NG, Widr, ZombieRamen, Bmbaker88, Voipsatellite, Rlegends, Earaps,
Rp8083, Mogism, Ptuttle123, Me, Myself, and I are Here, Slumberbus, Haminoon, Tc.guho, Spasticsociety, Rajuarya125, Dinnypaul,
Zupotachyon and Anonymous: 242
Channel (communications) Source: https://en.wikipedia.org/wiki/Channel_(communications)?oldid=750727476 Contributors: Little
guru, Michael Hardy, Chris~enwiki, Kku, Cameron Dewe, Ellywa, Technopilgrim, Rholton, Giftlite, Ferkelparade, Mboverload, D3,
Beland, Lucanos, ArnoldReinhold, Giraedata, Suruena, RJFJR, Woohookitty, Rocastelo, Burgher, Jonnabuz, Marudubshinki, RichardWeiss, BD2412, Amire80, Gsp, FlaBot, Margosbot~enwiki, Lmatt, John Dalton, Gene.arboit, RussBot, Grubber, CarlHewitt, Grafen,
Mikeblas, Light current, Deville, Cynicism addict, Asterion, SmackBot, Commander Keane bot, AussieLegend, Cybercobra, Ryan Roos,
Molerat, Cuddy Wifter, Arialblack, Dicklyon, Kvng, Chetvorno, Argon233, Penbat, Maxxicum, Viridae, Vmadeira, Nick Number, Widefox, Dougher, Gkhan, JAnDbot, Harryzilber, Drizzd~enwiki, Leolaursen, Jim.henderson, Mange01, Arnastya, Alinja, Jamelan, Ponyo,
Gerakibot, Flyer22 Reborn, Kielhofer, Troy 07, ClueBot, The Thing That Should Not Be, Uncle Milty, Trivialist, DragonBot, Johnuniq,
Feinoha, Addbot, Blacksosis, Legobot, Yobot, Themfromspace, AnomieBOT, Materialscientist, LilHelpa, Isheden, Johnnie Rico, Dougofborg, Nageh, I dream of horses, LittleWink, CobraBot, EmausBot, John of Reading, Dewritech, Wikipelli, Survivor1126, Rmashhadi,
ClueBot NG, Rtucker913, Dkmmheng, JordoCo, Wbm1058, BG19bot, Shaysom09, AvocatoBot, Justincheng12345-bot, Me, Myself, and
I are Here, Jessica.English30, Melcrum - Connecting Communicators, Kethrus, CAPTAIN RAJU, Greenward567 and Anonymous: 90
Band-pass lter Source: https://en.wikipedia.org/wiki/Band-pass_filter?oldid=748657225 Contributors: The Anome, Maury Markowitz,
Patrick, Angela, Nanobug, Glenn, Poor Yorick, BAxelrod, Emmjade, Guaka, Omegatron, ThereIsNoSteve, Giftlite, Sword~enwiki, Zowie,
R, CALR, Billlion, Shanes, Hooperbloob, SidP, Cburnett, OwenX, Cbdorsett, Pfalstad, Zbxgscqf, Sango123, Ianthegecko, Arnero,
Antikon, DVdm, Martin Hinks, YurikBot, Splash, PinothyJ, Tole, Brandon, Hakeem.gadi, Deville, KNfLrPnKNsT, LeonardoRob0t,
Poulpy, Machtzu, RG2, Henrikb4, Binarypower, Commander Keane bot, Oli Filth, Vina-iwbot~enwiki, Clicketyclack, Robosh, Mofomojo, Dicklyon, Tawkerbot2, Nalvage, Sobreira, AlienBlancmange, CosineKitty, Email4mobile, RisingStick, STBot, Mange01, Acalamari,
VolkovBot, Cuddlyable3, Inductiveload, Spinningspark, Benjwgarner, Dp67, Binksternet, PipepBot, ChrisHodgesUK, Johnuniq, Addbot,
Alexandra Goncharik, Redheylin, OlEnglish, B137, Citation bot, GrouchoBot, GliderMaven, Ebrambot, Lorem Ip, ClueBot NG, Rezabot, Helpful Pixie Bot, Flyguy53, Ankitd.elec, Chetan.meshram, Omegaoptical, Forestrf, CsDix, Ugog Nizdast, Trackteur, Wikigeek244,
Joshua Mahesh Inayathullah, CAPTAIN RAJU, Bender the Bot and Anonymous: 70
Frequency-division multiplexing Source: https://en.wikipedia.org/wiki/Frequency-division_multiplexing?oldid=744817802 Contributors: Bryan Derksen, The Anome, Spliced, Bearcat, VikOlliver, Tagishsimon, Khalid, Cmdrjameson, Nsaa, Guy Harris, Andrewpmk,
Rcbarnes, Markaci, MassimilianoC, Palica, Rjwilmsi, Joe Decker, Arnero, Gwernol, YurikBot, Arado, Sparky132, Rsrikanth05, GrinBot~enwiki, Unyoyega, Zhukun~enwiki, Oli Filth, Tripledot, Steveo1544, A5b, Jan.Smolik, Robosh, MonsieurET, Kvng, Phoenixrod,
Chetvorno, Thijs!bot, Dawnseeker2000, Widefox, JAnDbot, Harryzilber, Pedro, Canyouhearmenow, Jim.henderson, John Millikin,
Mange01, Derekbd, TXiKiBoT, Hobartimus, Wdwd, Prohlep, Sillyfolkboy, West.andrew.g, , Yobot, Fraggle81, TaBOTzerem, Backslash Forwardslash, 0majortom0, Imveracious, Nageh, BenzolBot, Dr.buznakovich, RjwilmsiBot, RainyShadow, Tastalian,
Openstrings, Learns visits aw, ClueBot NG, MerlIwBot, Jhoyossanchez, Kavya l, Eno Lirpa and Anonymous: 74
Line code Source: https://en.wikipedia.org/wiki/Line_code?oldid=751874684 Contributors: The Anome, Danny, SimonP, Twilsonb,
Ronz, Charles Matthews, Colin Marquardt, Itai, Omegatron, Robbot, Ktims, Tea2min, DavidCary, BenFrantzDale, Wwoods, Falcon
Kirtaran, DRE, Kevin Rector, Rich Farmbrough, Sladen, West London Dweller, Foobaz, Courtarro, Geraldshields11, Kusma, SeventyThree, Kimchi.sg, Mmccalpin, PrologFan, Brandon, RichG, Thumperward, Eesa, Kvng, Hu12, Nczempin, Msebast~enwiki, Hazmat2,
Bushra09, Magioladitis, Hmo, Swpb, Glrx, CommonsDelinker, Mange01, Robzle, STBotD, Dorftrottel, Wrev, Elicohn, Durnitz, Jackfork, SieBot, Commodore Gu, WimdeValk, Explicit, Johnuniq, Jugandi, Dsimic, Addbot, SpBot,
, Luckas-bot, Gsmcoupe, Ptbotgourou, AnomieBOT, Rubinbot, , ArthurBot, Udreilly, 4twenty42o, Nasa-verve, Thehelpfulbot, GliderMaven, Mjesfahani, Dcirovic, ZroBot, Ashima oberoi, ClueBot NG, Zelpld, PanaceaLai, Millermk, FinFihlman, Wannabemodel, Camthetechboy,
Sadashivakamath, Horseless Headman, Ritwik.m07 and Anonymous: 58
Local area network Source: https://en.wikipedia.org/wiki/Local_area_network?oldid=752093630 Contributors: AxelBoldt, Bryan Derksen, Zundark, The Anome, Rjstott, Brovnik, Aldie, Ben-Zin~enwiki, Hannes Hirzel, Chuq, Frecklefoot, Patrick, PhilipMW, Norm,
Mahjongg, Liftarn, Dave Farquhar, Sannse, Delirium, Alo, Pcb21, Tregoweth, Ahoerstemeier, Nanshu, Snoyes, Angela, Glenn,
Panoramix, Greenrd, Wernher, Pigsonthewing, Psychonaut, Academic Challenger, Jondel, Hadal, HaeB, Giftlite, DavidCary, Wikilibrarian, Lupin, AlistairMcMillan, Solipsist, VampWillow, Matthus Wander, Bobblewik, Antandrus, Beland, Sam Hocevar, Biot, Jcw69,
Quester~enwiki, Cy0x~enwiki, Mr Bound, Monkeyman, Discospinster, FiP, Mjpieters, Closeapple, Plugwash, Violetriga, Evice, Shanes,
Perfecto, Robotje, Wipe, BrokenSegue, Ricsi, Roy Baty, Zachlipton, Poweroid, Alansohn, Arthena, Atlant, Comrade009, Jvano~enwiki,
Wtmitchell, Peter McGinley, Rick Sidwell, Aka, 2mcm, RainbowOfLight, MIT Trekkie, KTC, CONFIQ, Woohookitty, Mindmatrix,

586

CHAPTER 132. MORSE CODE

Camw, Rocastelo, Tripodics, Skor, Ilario, Commander Keane, Wayward, Prashanthns, Hovea, Radiant!, Mandarax, Tslocum, Graham87,
Stefan h~enwiki, Snaekid, Pmj, Canderson7, Jorunn, Commander, Feydey, The wub, AlisonW, Aapo Laitinen, SanGatiche, Yamamoto
Ichiro, FlaBot, Born2cycle, Hall Monitor, Anrie Nord, Roboto de Ajvol, Wavelength, Daverocks, Phantomsteve, J. M., The Adventurer,
SpuriousQ, Dotancohen, Stephenb, Manop, Gaius Cornelius, Rsrikanth05, Ibc111, Abarry, Bovineone, Grafen, Exir Kamalabadi, Irishguy,
Mortein, Raven4x4x, SixSix, DeadEyeArrow, Bota47, Jeh, Yudiweb, Haon, Emijrp, Zzuuzz, Closedmouth, KGasso, JLaTondre, Spliy,
Caballero1967, Katieh5584, Joebediah, SmackBot, KnowledgeOfSelf, McGeddon, Grey Shadow, Delldot, KelleyCook, KennethJ, PeterSymonds, Gilliam, Ohnoitsjamie, Hmains, Savio mit electronics, Chris the speller, Bluebot, Taelus, DStoykov, Thumperward, Snori,
MalafayaBot, Villarinho, Dawd, Darth Panda, Exer 505, Quaque, Can't sleep, clown will eat me, Frap, Onorem, KevM, JonHarder, DonConquistador, TheKMan, Iricigor, Rsm99833, SundarBot, Soosed, Cybercobra, IrisKawling, HarisM, Sigma 7, Jna runn, Zac67,
Thejerm, SashatoBot, Ocee, Xaldafax, Hope(N Forever), Akhilsharma86, IronGargoyle, PseudoSudo, Melody Concerto, Ckatz, 16@r,
Waggers, Citicat, Peyre, Lorany21k, Kvng, Mdanh2002, Dead3y3, JoeBot, Skapur, CapitalR, Astral9, Fullerene~enwiki, Mzub, Tawkerbot2, Ossworks, SkyWalker, ShakespeareFan00, GHe, Requestion, Nmacu, Phatom87, Rajubanka, Mashby, Gogo Dodo, Tkynerd, Skittleys, Tawkerbot4, Quibik, Colorprobe, Ameliorate!, NMChico24, LarryQ, Joowwww, Thijs!bot, Epbr123, Pajz, Headbomb, Aray,
Dawnseeker2000, Rees11, AntiVandalBot, Luna Santin, Widefox, Chico75, Seaphoto, Turlo Lomon, Shirt58, ArmondoSC, Coolmaxi898,
Mbbs, Barry26, Pdicanio1986, Exposit, Dougher, Husond, Daz 90, Harryzilber, MER-C, Sitethief, Magioladitis, Bongwarrior, VoABot II,
JamesBWatson, Stuart Morrow, Willy on Wheels over Ethernet, JRamlow, Cipher text, MaestroX, Twsx, Lonewolf BC, Animum, JoeDaStudd, Stdazi, Cpl Syx, DerHexer, InvertRect, Koki.s~enwiki, JediLofty, Patstuart, MartinBot, Arjun01, CommonsDelinker, Haner,
PrestonH, MerlinYoda, Ceros, Pierre-Yves Schtz, J.delanoy, Bthebest, Trusilver, Rgoodermote, Catmoongirl, Athaenara, Neon white,
Ignatzmice, Naniwako, Abresas, Chriswiki, Hennessey, Patrick, Kondody, Cmichael, KylieTastic, Juliancolton, DorganBot, Bonadea,
Wikieditor06, MTurpin, Philomathoholic, Farchand, Amaraiel, Scorwin, Alexandria, Fagiolonero, London2012, DoorsAjar, TXiKiBoT,
Oshwah, Sylvanwulf, Vipinhari, Rei-bot, CharlieGalik, Lradrama, Monopolyisgreat, Jackfork, Mannafredo, KennyRogerz, Wtt, Synthebot, Falcon8765, Enviroboy, Owchowch, Brianga, HiDrNick, Pjoef, AlleborgoBot, Jakolu, C0N6R355, Demize, Kbrose, SieBot, Nubiatech, Laoris, Jason Patton, Gcorbaz, Windowsvistafan, Chris jones the man, Oxymoron83, J wood hail, Smilesfozwood, Bagatelle, Steven
Crossin, Darkeekt, Danelo, Qxl32, Spartan-James, Myri fan, Yair rand, Escape Orbit, Troy 07, ClueBot, The Thing That Should Not
Be, 1johnny 1269, Mild Bill Hiccup, Niceguyedc, DragonBot, Takeaway, Excirial, Eeekster, Rhododendrites, Ice Cold Beer, Jotterbot,
Polly, Micky140391, Vybr8, Johnuniq, Vaidyanathparli, DumZiBoT, Davismargaret, XLinkBot, Roxy the dog, Wertuose, BodhisattvaBot, Libcub, WikHead, StubbyT, PL290, Dgtsyb, ZooFari, Mozillar, Networkingguy, Addbot, Kcufuoyokifyounowwhtim, Jjensen347,
Ohyassie, Rawrxmimi, NjardarBot, Cst17, CarsracBot, Lemcmaster, Numbo3-bot, Tide rolls, Teles, Gail, Legobot, Luckas-bot, Ptbotgourou, Fraggle81, Karanne, THEN WHO WAS PHONE?, Slipmikeknot, Marshall Williams2, Wadamja, AnomieBOT, Jim1138, JackieBot, Kingpin13, Ulric1313, Materialscientist, Aneah, Frankenpuppy, ArthurBot, Sdowg, Gsmgm, Xqbot, I Feel Tired, DSisyphBot,
Wizardist, Omnipaedista, RibotBOT, Wikicrazier2011, Mathonius, SD5, GliderMaven, Bingo-101a, Urgos, Itusg15q4user, Luke111000,
I dream of horses, Monkeyfox, SurreyGaming, RedBot, Reconsider the static, A beast with claws, Weylinp, FoxBot, TobeBot, Trollingftw,
TBloemink, Theslapandwack, Driftkid92, Tiger xox, Reach Out to the Truth, DARTH SIDIOUS 2, Hbk cmd, TjBot, EmausBot, Immunize,
Povtula, Syncategoremata, Active Banana, Mogulu, Wikipelli, F, Klavierspieler, L Kensington, Mayur, Mentibot, MessiFCB, Ianmillner,
Anguskywong, RowanQuigley, Rocketrod1960, Petrb, ClueBot NG, Gareth Grith-Jones, MelbourneStar, Satellizer, ScottSteiner, Widr,
Lcsrns, Anupmehra, Mtking, nanmu, HMSSolent, Brt100, Vagobot, Northamerica1000, Metricopolus, 13magilj, Tony6ty4ur, CitationCleanerBot, NNU-1-05100211, Qzwxeccexwzq, REP93, Camjam2312, Anbu121, Aleksandar Bulovic', T.seppelt, BattyBot, MahdiBot,
GoShow, Gertjanmeteenboomstam, Khazar2, JYBot, Obtund, Kushalbiswas777, Lugia2453, Frosty, Fox2k11, Robertviews, Telfordbuck,
Reatlas, Passengerpigeon, Epicgenius, Ialdreadyknow, Maura Driscoll, Ugog Nizdast, SpiderRider3, Ginsuloft, KALPESH2607, AddWittyNameHere, Rogerio25, Ulhas shenoy, Imran farooq beigh, PapaJeckloy, Qwertyxp2000, NMJFC14, Thebookman2, Victor Lesyk, Anik
Chanda, Cherdchai Iamwongsrikul, FaizanSid, Neemanee, Deunanknute, XTWDSR, KasparBot, Maksudul Hasan, Isaadadam, ThatGuyyyyyyyyyyyyyyyyyyyyyyy, CLCStudent, Peterdeng200111, Tee lim, Marianna251, Chrissymad, Proteq11801, Incontintuity, Marlon
brandnew, Bender the Bot, Bhatughshsgdhdhhd and Anonymous: 683
Narrowband Source: https://en.wikipedia.org/wiki/Narrowband?oldid=729684673 Contributors: Waveguy, Dysprosia, Radiojon, Itai,
Tlotoxl, Robbot, Yosri, Orangemike, Bobo192, Viriditas, Wtshymanski, Gene Nygaard, Vegaswikian, Ground Zero, RobyWayne, Frappyjohn, Splash, Cleared as led, Deville, SmackBot, Mattbr, Cydebot, Kozuch, Sobreira, CosineKitty, Magioladitis, Davace, Jamelan,
Anitanesbitt, Justbridge, Wikijens, Nukeless, Eik Corell, XLinkBot, Addbot, Guoguo12, Yobot, BentleyCoon, Xqbot, Wladek92, Landmobile, GoingBatty, ZroBot, DBigXray, Hanthoec, Mmpozulp and Anonymous: 23
Wideband Source: https://en.wikipedia.org/wiki/Wideband?oldid=749393486 Contributors: Gbleem, Radiojon, Itai, Bearcat, Everyking,
Quadell, Gdoten, Zondor, Johnteslade, Maurreen, Hooperbloob, Vegaswikian, Krash, NSR, Aeusoes1, Voidxor, SmackBot, PEHowland,
Chris the speller, Oli Filth, A5b, Ale jrb, Cydebot, Sobreira, Bobblehead, Dfrg.msc, Networktech, Jim.henderson, Adavidb, Bogatabeav,
MichaelStanford, Tigereye7, Addbot, Golover, Haeinous, AmgadASalama, Britannic124, BG19bot, Nen, Spilton, Alishirmoradi, SaraWong001 and Anonymous: 23
Data transmission Source: https://en.wikipedia.org/wiki/Data_transmission?oldid=748676662 Contributors: Anders Trlind, Aldie, SimonP, Imran, Edward, Kku, Ixfd64, Theresa knott, Chuunen Baka, Robbot, Centrx, Giftlite, DavidCary, Mboverload, Oscar, D6, Xezbeth, CanisRufus, Hooperbloob, Walter Grlitz, Wtshymanski, Computerjoe, Nuno Tavares, ^demon, Btyner, Mandarax, BD2412, Vegaswikian, Gsp, Srleer, DVdm, Algebraist, Borgx, Daverocks, Hydrargyrum, Rsrikanth05, Welsh, Anetode, JPMcGrath, Tachs, Covington, Trickstar, Luk, SmackBot, Gilliam, Chris the speller, Persian Poet Gal, Can't sleep, clown will eat me, JonHarder, Sljaxon, Bushsf,
Robosh, JorisvS, Boky, Kvng, CmdrObot, No1lakersfan, Phatom87, AndrewHowse, Gogo Dodo, Thijs!bot, JustAGal, Knighttp01,
Dawnseeker2000, AntiVandalBot, Luna Santin, Once in a Blue Moon, Bukharin, Harryzilber, MER-C, PhilKnight, 28421u2232nfenfcenc,
Oicumayberight, MartinBot, Infrangible, BetBot~enwiki, Jim.henderson, Rettetast, Mange01, KazakhPol, Theo Mark, Cspan64, MartinEm, Acalamari, St.daniel, Shoessss, Sukkoth Qulmos, DorganBot, Inwind, Funandtrvl, VolkovBot, Xanucia, Philip Trueman, Oshwah,
Klower, Madhero88, MrChupon, Kbrose, Gerakibot, Taemyr, ErelOnline, Iain99, Nancy, Mario ami, ClueBot, Snigbrook, Alexbot, Jusdafax, Fc02dcurtis, Lambtron, Johnuniq, Carl Ponder, XLinkBot, Stickee, Jovianeye, Dgtsyb, Badgernet, Addbot, Poco a poco, AkhtaBot,
Download, LaaknorBot, SpBot, Quercus solaris, Numbo3-bot, Legobot, Blah28948, Luckas-bot, Yobot, AnomieBOT, Ciphers, Cunchem,
Materialscientist, Obersachsebot, Almabot, Backpackadam, N419BH, FrescoBot, A.Abdel-Rahim, Pinethicket, Arlo.Clauser, LittleWink,
FoxBot, SchreyP, Vrenator, Aoidh, DARTH SIDIOUS 2, Mean as custard, TjBot, Ripchip Bot, Onlinediscuss, John of Reading, Immunize, VladaPUB, Primefac, GoingBatty, K6ka, GeorgeBarnick, DRSPORTY, ClueBot NG, Widr, CJdamaster, JordoCo, Oddbodz, Helpful
Pixie Bot, Dannydan93, Megalibgwilia, Jasonvaidya123, YFdyh-bot, Webclient101, Me, Myself, and I are Here, Phamnhatkhanh, Faizan,
Liamsallur, Anitmadhani96, Ginsuloft, Dull Dreams, Sweepy and Anonymous: 153
Carrier frequency Source: https://en.wikipedia.org/wiki/Carrier_frequency?oldid=704438323 Contributors: SimonP, Poor Yorick, Emperorbma, Dysprosia, Modulatum, Geimas5~enwiki, Srleer, YurikBot, MCB, Fernblatt, JonHarder, Nakon, Hazza401, Peter Horn, Kvng,

132.11. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

587

ALM scientist, Joshtrick, Dfrg.msc, Dawnseeker2000, Widefox, Chill doubt, CombatWombat42, Schmloof, Jim.henderson, Mange01,
Funandtrvl, VolkovBot, Alinja, Rhesusminus, Deineka, Yobot and Anonymous: 3
Frequency modulation synthesis Source: https://en.wikipedia.org/wiki/Frequency_modulation_synthesis?oldid=752074285 Contributors: Zundark, The Anome, Tarquin, Michael Hardy, Furrykef, Hyacinth, Omegatron, Tlotoxl, Mintleaf~enwiki, Ds13, Zzo38, UgenBot,
Karol Langner, Johnpmahoney, Freundlich~enwiki, Muijz, Ardonik, Femto, Rbj, Wtshymanski, Woohookitty, Timharwoodx, Sega381,
Graham87, JoshuacUK, Nivix, GreyCat, YurikBot, Gaius Cornelius, Voidxor, Ninly, SmackBot, Jagged 85, Monz, ERcheck, Bluebot,
EncMstr, HeavyD14, Captnapalm, HenningThielemann, Chrislk02, Alaibot, Timopie, Michael Tiemann, MartinBot, Gzkn, AntiSpamBot, TXiKiBoT, Jalwikip, Don4of4, Dragana666, Krisnick, ClueBot, Binksternet, Shape84, Boleyn, Midnightsleazy, Grayfell, MrOllie,
Download, Redheylin, Yala0, Lightbot, Legobot, Yobot, AnomieBOT, Citation bot, Ekkleesia, FrescoBot, DelphinidaeZeta, Clusternote,
Dcirovic, Mjbmrbot, Popcorndu, FuFoFuEd, Meatsgains, ChrisGualtieri, Timaeus222, Monkbot, Lukeme9X, Ra227, Prove It, REDIRECT, Mmalizola, Cameronwjones, Bender the Bot and Anonymous: 81
Constant envelope Source: https://en.wikipedia.org/wiki/Constant_envelope?oldid=724847576 Contributors: Berek, QuiteUnusual, Postcard Cathy, AnomieBOT, I dream of horses, Trinity11726 and Fouett rond de jambe en tournant
Angle modulation Source: https://en.wikipedia.org/wiki/Angle_modulation?oldid=711225474 Contributors: Klemen Kocjancic, Xezbeth,
Oli Filth, Lazylaces, Kvng, Alaibot, V.petcu, Mange01, TXiKiBoT, Andy Dingley, JWhiteheadcc, Mx. Granger, Tuxa, PixelBot, Addbot,
AnomieBOT, Rubinbot, Wabbott9, Pawansalunke57 and Anonymous: 13
Phase modulation Source: https://en.wikipedia.org/wiki/Phase_modulation?oldid=747311279 Contributors: CYD, The Anome, Glenn,
Bemoeial, Omegatron, Giftlite, Ssd, Ablewisuk, Cacophony, La goutte de pluie, Nsaa, Redvers, Ringbang, Prashanthns, Akubhai, HappyCamper, Krash, Gurch, Antikon, Chobot, Roboto de Ajvol, YurikBot, Splash, Yyy, Willpo~enwiki, Islamsalah, Rhodekyll, Edin1,
SmackBot, Bromskloss, Harumphy, Hadmack, Dejudicibus, Dicklyon, Belizefan, Owen214, Chrumps, Doctormatt, Devanatha, Doktor
Who, CosineKitty, Quentar~enwiki, Email4mobile, Mange01, Stmiller, Skier Dude, Jerry Safranek, Deadlocke, Cuddlyable3, Daviddoria, Renxa, SieBot, Phe-bot, Rogermx, WingkeeLEE, Binksternet, Addbot, Fgnievinski, AndersBot, AdjustShift, Ciudadano001,
Mghansen256~enwiki, WikiMix, Omnipaedista, Erik9bot, Vhann, Pinethicket, Ventril2009, EmausBot, John of Reading, WikitanvirBot,
Dewritech, ZroBot, Bollyje, Potasmic, ClueBot NG, Widr, Vanished user lt94ma34le12, Makecat-bot, The.ever.kid and Anonymous:
60
Bit rate Source: https://en.wikipedia.org/wiki/Bit_rate?oldid=741393680 Contributors: Tarquin, SimonP, Edward, Kku, SebastianHelm,
Ellywa, Julesd, Habj, Andres, Ehn, Adam Conover, Crissov, Dysprosia, Radiojon, Furrykef, Omegatron, Topbanana, Nnh, Robbot, Vespristiano, P0lyglut, Mattaschen, Giftlite, DavidCary, BenFrantzDale, AssetBurned~enwiki, Bobblewik, LucasVB, OverlordQ, Aulis Eskola,
Maximaximax, Icairns, Quota, Chrisbolt, Alkivar, Rich Farmbrough, Smyth, Alistair1978, Kjoonlee, Evice, Syp, West London Dweller,
Grue, Longhair, SickTwist, Jerryseinfeld, Larryv, Hooperbloob, Jumbuck, Eleland, Pforret, DariuszT, Kocio, Hu, Cgmusselman, Rebroad, Cburnett, Gene Nygaard, Saxifrage, Joke dst, Woohookitty, Mindmatrix, LOL, Nuggetboy, Jersyko, Commander Keane, LinkTiger,
Magister Mathematicae, Teknic, Kbdank71, Mulligatawny, Ketiltrout, Pangolin, Traut, Kchoboter, RexNL, DVdm, Quicksilvre, Wavelength, Timeheater, RussBot, Palladinus, DanMS, Gaius Cornelius, Brandon, Mditto, NorsemanII, Bdell555, Dposse, SmackBot, QuantumShadow, Humble226, Phaehe, Flux.books, Durova, Unbreakable MJ, Sur3, Oli Filth, Nbarth, A. B., Can't sleep, clown will eat me,
Radagast83, Cybercobra, Duckbill, Lus Felipe Braga, Jidanni, Don't give an Ameriag, Misteror, Trounce, Kvng, Jynx980, Vanisaac,
GFellows, AndrewHowse, Cydebot, Mjoyce, Kubanczyk, Ultimus, Dingbats, Marek69, MilesPark, Nezzadar, Tirk, Kuteni, TuvicBot,
MikeLynch, JAnDbot, CosineKitty, Instinct, Roleplayer, Annie May, Acroterion, VoABot II, RMN, Antipodean Contributor, Nyttend,
CS46, Cooleric1234, JMyrleFuller, Jim.henderson, Mschel, R'n'B, Nono64, Mange01, Peh-Jota, Felixcollins, Jesant13, WikiBone, McSly,
Joeinwap, Valeriana~enwiki, TXiKiBoT, A4bot, Tim9798, Mrdvt92, WinTakeAll, Are1981, Mastersquirrel3, Thunderbird2, Meatytebah,
Lightmouse, Mbabane, OKBot, Colvin11, M2Ys4U, Nikuda, ClueBot, The Thing That Should Not Be, Tomas e, Peter-ZA, Muhandes,
Squid tamer, Burner0718, Johnuniq, Dthomsen8, Galzigler, Matma Rex, MystBot, Dsimic, Cistus~enwiki, Fgnievinski, Download, Debresser, Getmoreatp, Guydrawers, KaiKemmann, Tide rolls, Zorrobot, Arsenalboi21, Yobot, TaBOT-zerem, AnomieBOT, Gtz, Piano
non troppo, Lockem, Xqbot, Grantgw, FrescoBot, Nageh, W Nowicki, MichaelBueker, RedBot, Saadisaadsaadi, Vrenator, Amiodarone,
Skc7, Colingum, DARTH SIDIOUS 2, EmausBot, John of Reading, Scgtrp, Honziczech85, Dondervogel 2, Beber29, Music Sorter, Sasajak, BioPupil, Emzed, ChuispastonBot, Diamondland, ClueBot NG, Jack Greenmaven, Awesomeness95, Titodutta, Wbm1058, Op47,
EmadIV, Altar, RscprinterBot, Kiewbra, Jimw338, Phillipfrancis, 48xgamil, Makecat-bot, Radiodef, Lolo Lympian, Hinekyle, NightShadow23, Victor sila, Tentinator, Comp.arch, Konveyor Belt, Brainfrandell, GreenC bot, Bender the Bot and Anonymous: 246
Symbol rate Source: https://en.wikipedia.org/wiki/Symbol_rate?oldid=728398784 Contributors: Rjstott, Peak, Unfree, Markus Kuhn, Dziban303, Teque5, Vegaswikian, FlaBot, Splash, Kyle Barbour, SmackBot, Colonies Chris, Radagast83, P199, Kvng, GFellows, Sakurambo,
CmdrObot, Harej bot, Gregbard, Cydebot, Ring0, Alphachimpbot, JAnDbot, CosineKitty, Tarif Ezaz, GrahamDavies, Mange01, Cigreen,
Thunderbird2, Timewatcher, Kbrose, Lightmouse, Wdwd, ClueBot, Kurt.smolderen, Rwestafer, Johnuniq, XLinkBot, Addbot, Fgnievinski, Download, Debresser, AnomieBOT, Citation bot, Isheden, Goles, Onlinediscuss, Hhhippo, Dondervogel 2, Sbmeirow, Donner60,
ClueBot NG, Zelpld, Snotbot, BG19bot, SkateTier, Pinus27, De la Marck and Anonymous: 55
Digital signal Source: https://en.wikipedia.org/wiki/Digital_signal?oldid=734332464 Contributors: Damian Yerrick, The Anome, Andres,
Smack, Tea2min, Giftlite, DavidCary, Golbez, Bishonen, Evice, Longhair, Cburnett, Bsadowski1, Mwilde, Cbhiii, Uncle G, BD2412,
Sjakkalle, Exeunt, Gurch, King of Hearts, Adoniscik, YurikBot, SpuriousQ, Stephenb, Pseudomonas, NawlinWiki, Catamorphism, Phgao,
Spliy, Alexan es, Rmosler2100, Nbarth, Bob K, Khukri, MHoerich, DMacks, Kukini, Dicklyon, Kvng, Iridescent, Lahiru k, Ronaldvd,
Iokseng, Penbat, Ermija, Sturm55, Dawnseeker2000, Mentisto, AntiVandalBot, Harryzilber, MER-C, FisherQueen, MartinBot, Mschel,
R'n'B, Mange01, Jesant13, Matthardingu, Signalhead, WarddrBOT, Philip Trueman, Oshwah, Sankalpdravid, Jamelan, Viewcloth, Biasoli, SieBot, RatnimSnave, Lightmouse, ImageRemovalBot, Twinsday, ClueBot, The Thing That Should Not Be, LeoFrank, Sushi1726,
Alexbot, Bradderz90, BOTarate, Aitias, 7, Egmontaz, Addbot, Mortense, Fgnievinski, Ronhjones, CanadianLinuxUser, Download, Tide
rolls, Fraggle81, Grebaldar, Crispmuncher, Kamran engineer, Backslash Forwardslash, AnomieBOT, Kingpin13, Materialscientist, Maddie!, GliderMaven, Pinethicket, Notedgrant, RobinK, Tbhotch, Minimac, Onel5969, Nil Spaar, Stryn, Kueller1, MonoAV, Petrb, ClueBot NG, Totalporch2, JordoCo, Razputrocks, Wbm1058, BG19bot, Hellothere37612, FoCuSandLeArN, Sumedh Tayade, BourkeM and
Anonymous: 103
Digital-to-analog converter Source: https://en.wikipedia.org/wiki/Digital-to-analog_converter?oldid=751234746 Contributors: Damian
Yerrick, The Anome, PierreAbbat, Waveguy, Mjb, Heron, Michael Hardy, TakuyaMurata, ZoeB, Glenn, GRAHAMUK, Bemoeial,
Reddi, Zoicon5, Maximus Rex, Omegatron, Wernher, Thue, Topbanana, Robbot, Kizor, Ojigiri~enwiki, Lupo, Giftlite, Wolfkeeper,
BenFrantzDale, Bradeos Graphon, Ssd, SWAdair, CryptoDerk, Stevenalex, Hellisp, Hugh Mason, BrianWilloughby, DJS~enwiki,
Chmod007, Chepry, Imroy, TedPavlic, Paul August, Ht1848, CanisRufus, Meestaplu, Rbj, Johnteslade, Giraedata, Photonique, Timecop,

588

CHAPTER 132. MORSE CODE

Hooperbloob, Alansohn, Jannev~enwiki, Cburnett, Algocu, Bookandcoee, Kenyon, Bobrayner, Woohookitty, StradivariusTV, Je3000,
Gradulov, CPES, Mandarax, BD2412, Joe Decker, FlaBot, Arnero, Mcleodm, Lsu, Chobot, RobotE, Thane, Tharanath1981, Garion96, Yoshm, SmackBot, Fnfd, Tex23, Andy M. Wang, EncMstr, Southcaltree, RProgrammer, JonHarder, Adamantios, Sturm, UVnet,
Kvng, Lee Carre, Nczempin, HenkeB, Dept of Alchemy, Thijs!bot, Ecclaim, AntiVandalBot, Salgueiro~enwiki, Father Goose, Rivertorch,
Soulbot, Calltech, Sicaspi, MartinBot, Anaxial, Glrx, Abuthayar, R'n'B, Nono64, J.delanoy, Boodidha sampath, Ontarioboy, VolkovBot,
ICE77, TXiKiBoT, Neildmartin, Spinningspark, Mahira75249, Crm123, Masgatotkaca, Travelingseth, Binksternet, VQuakr, Pointillist, ChardonnayNimeque, Arjayay, Andrebragareis, DanteLectro, DumZiBoT, Analogkidr, XLinkBot, StormtrooperTK421, Addbot,
Mortense, Xx521xx, Cst17, MrOllie, Redheylin, Semiwiki, Tide rolls, Lightbot, Legobot, Luckas-bot, Yobot, AnomieBOT, Materialscientist, Danno uk, Xqbot, TheAMmollusc, RibotBOT, Louperibot, HRoestBot, 10metreh, RedBot, Serols, RobinK, Overjive, Brainmedley,
Suusion of Yellow, Ravenmewtwo, Incminister, Karkat-H-NJITWILL, John Siau, Lexusuns, Chad.Farmer, Rpal143, Wsko.ko, ClueBot
NG, Blitzmut, Chester Markel, Helpful Pixie Bot, Bpromo7, Josvanehv, Binglau, Me, Myself, and I are Here, Camyoung54, Glaisher,
ScotXW, Mohammadali Aghakhani, KasparBot, Adam9007, Idahoprogrammer, Abhijeetabhi0442 and Anonymous: 211
Analog transmission Source: https://en.wikipedia.org/wiki/Analog_transmission?oldid=748332435 Contributors: Mushroom, Giftlite,
DavidCary, Jared Preston, Tole, Welsh, Jeh, Davepape, Gilliam, Kvng, No1lakersfan, Dawnseeker2000, Elaragirl, Twsx, Jodi.a.schneider,
Mange01, Nmorales435, SchreiberBike, AmusedRepose, DumZiBoT, Sillyfolkboy, Yobot, LilHelpa, Tlonca, Jopisjop2, ClueBot NG,
JordoCo, Helpful Pixie Bot, AmaryllisGardener, Sweepy and Anonymous: 17
Phase-shift keying Source: https://en.wikipedia.org/wiki/Phase-shift_keying?oldid=750063105 Contributors: CYD, Bryan Derksen,
Heron, Michael Hardy, Glenn, Grendelkhan, Lensi, Johnleemk, Cedars, DavidCary, Karn, Fleminra, Ssd, Rchandra, Bobblewik, Edcolins, Pgan002, Ary29, Qef, DmitryKo, Danh, Pt, R. S. Shaw, Neonumbers, Marudubshinki, BD2412, Sjakkalle, HappyCamper, Ligulem,
Alejo2083, King of Hearts, Bgwhite, Roboto de Ajvol, The Rambling Man, Wavelength, RussBot, Splash, Gaius Cornelius, Rsrikanth05,
Willpo~enwiki, Welsh, Brandon, Mhasabel, Spondoolicks, GrinBot~enwiki, That Guy, From That Show!, SmackBot, KnowledgeOfSelf,
Eskimbot, KelleyCook, Lacbil, Oli Filth, OrphanBot, Adamantios, Radagast83, Dreadstar, Rspanton, Anttipng, Lvazquez, Ksn, JoshuaZ,
Bjankuloski06en~enwiki, RomanSpa, Vanished user 8ij3r8jwe, Rogerbrent, Dicklyon, David e cooper, Hu12, Sakurambo, Chrumps, Requestion, Cahk, MC10, Tshb, Luispic, Ring0, CynicalMe, Gioto, Esromneb, Fiberware, Anarchyson, CosineKitty, Jheiv, Animum, Kf4yfd,
Jim.henderson, Haner, Mange01, It Is Me Here, Dtneilson, Djodjo~enwiki, Tiggerjay, Mathuranathan, Scls19fr, Hqb, Colmanian, Leonardomio, Gekritzl, Warddr, Squam, Mahira75249, Henrikholm, Thunderbird2, DaHeik, Spartan-James, Kittani, Denisarona, Jd185152,
ClueBot, Falkonry, Scottydog010, Johnuniq, Max613, Cerireid, Mitch Ames, Addbot, Joshgu, Fgnievinski, MrOllie, ,
Legobot, Yobot, Gsmcoupe, Simard, AnomieBOT, Materialscientist, Ciudadano001, Citation bot, TheAMmollusc, Omnipaedista, Shadowjams, FrescoBot, Geek2003, OgreBot, I dream of horses, Sohaibafzal, RCHenningsgard, WildBot, Acather96, Timtempleton, Seikku
Kaita, Chandankuila, EWikist, Wiki contributor 21, Ramjar, Mikhail Ryazanov, Teaktl17, ClueBot NG, Kazemita1, JackieTW, Maratyv,
MerlIwBot, BG19bot, Nen, Cyberbot II, Dexbot, FoCuSandLeArN, Tshuva, Mrtrandaithang, Acsinuk, Ol Spanky, Gaurav647, Zycxm,
Jlogue01, Raven Onthill, SaltyOrange, GreenC bot, NNIyyii and Anonymous: 204
Frequency-shift keying Source: https://en.wikipedia.org/wiki/Frequency-shift_keying?oldid=749308057 Contributors: The Anome,
Michael Hardy, Ellywa, CatherineMunro, Glenn, Robbot, Ktims, DavidCary, Karn, Ssd, Ary29, Vishahu, Sonett72, Xezbeth, ChrisJ,
Mcpusc, Smalljim, Bsadowski1, Dan100, Camw, Jonnabuz, Murat40, BD2412, HappyCamper, Bubba73, FlaBot, Fresheneesz, Roboto de
Ajvol, Willpo~enwiki, Klaun, Deville, David Biddulph, SDS, SmackBot, Moeron, KelleyCook, Oli Filth, Liebeskind, Harumphy, Dougmc,
Dicklyon, Kvng, Tawkerbot2, Xcentaur, Wafulz, Chrumps, Tawkerbot4, Kozuch, Thijs!bot, Epbr123, Electron9, Tarnjp, Kauczuk, Alphachimpbot, Jim.henderson, Microsloth, Glrx, Haner, J.delanoy, Dhaluza, Brianonn, CanOfWorms, LeaveSleaves, Stoneygirl45, Sv1xv,
RFdave007, Djkryptyk, Addbot, Cuaxdon, Ramkumarvecsrv, , Legobot, Yobot, AnomieBOT, Materialscientist, Ciudadano001, Jerey Mall, Omnipaedista, FrescoBot, 2A4Fh56OSA, Yahia.barie, DARTH SIDIOUS 2, RjwilmsiBot, Timtempleton, RenamedUser01302013, F, , Pun, ClueBot NG, MerlIwBot, Wbm1058, BG19bot, Mbpaz, Srinathkr3, ChrisGualtieri,
Frosty, Tentinator, Ginsuloft, MitchRandall, Raven Onthill, Bender the Bot and Anonymous: 98
Amplitude-shift keying Source: https://en.wikipedia.org/wiki/Amplitude-shift_keying?oldid=749489839 Contributors: Michael Hardy,
Tim Starling, Glenn, Ary29, Fg2, Simon South, Towel401, Mrio, Woohookitty, Murat40, BD2412, Alejo2083, Toresbe, YurikBot,
Rsrikanth05, Springbokmarine, SmackBot, Unyoyega, Oli Filth, Beetstra, Dicklyon, Stotr~enwiki, OS2Warp, CmdrObot, Wsmarz,
No1lakersfan, Hoemaco, MadProcessor, Bobblehead, Phopon, Seaphoto, Jayron32, Jim.henderson, Haner, Justin Z, TheChrisD, KylieTastic, STBotD, Daisydaisy, Dangernude, Pirround, Falcon8765, SieBot, ToePeu.bot, Stoneygirl45, Melcombe, Rhododendrites, Addbot, Luckas-bot, Ciudadano001, ArdWar, 4twenty42o, Galessandroni, Omnipaedista, RibotBOT, FrescoBot, Sohaibafzal, EmausBot,
Ankurnnd, Alexander Misel, ClueBot NG, Graphium, Nijoakim, Ankit011 and Anonymous: 65
Binary number Source:
https://en.wikipedia.org/wiki/Binary_number?oldid=752023951 Contributors:
Zundark, MarXidad,
Charleschuck, Ed Poor, Christian List, SimonP, Valhalla, Karl Palmen, Edward, Michael Hardy, Pit~enwiki, Sorw, Nixdorf,
Wapcaplet, Dcljr, TakuyaMurata, Delirium, Ahoerstemeier, Haakon, Snoyes, Suisui, Poor Yorick, Evercat, Rl, Rob Hooft, Jonik,
GRAHAMUK, Speuler, Charles Matthews, Dcoetzee, Dysprosia, Daniel Quinlan, Patrick0Moran, AndrewKepert, SEWilco, Omegatron,
Wernher, Robbot, Fredrik, Chris 73, Jmabel, Gandalf61, Rorro, Mendalus~enwiki, JesseW, Wikibot, Mushroom, Lupo, Mattaschen,
Tea2min, Jimpaz, Giftlite, Gwalla, DavidCary, Kim Bruning, Tom harrison, LLarson, Luigi30, Jaan513, SWAdair, Vadmium, Utcursch,
Alexf, CryptoDerk, LiDaobing, Noe, Antandrus, ALE!, Supaari, Quarl, R-Joe, Wzwz, SimonArlott, Jacob grace, CaribDigita, Yayay,
Amesville, Mschlindwein, Adashiel, Mike Rosoft, The demiurge, R, Poccil, DanielCD, Discospinster, NrDg, Rama, Florian Blaschke,
Smyth, Dbachmann, Paul August, Bender235, ESkog, ZeroOne, Andrejj, Martinman11, Kbh3rd, Violetriga, El C, Kwamikagami,
Shanes, RoyBoy, Causa sui, Bobo192, Iamunknown, Jonatan Lindstrom, Marco Polo, Smalljim, Shenme, R. S. Shaw, Spug, Dungodung,
Kappa, Giraedata, Samadam, Helix84, Haham hanuka, Nsaa, Jumbuck, Alansohn, Interiot, Spangineer, Scottcraig, Malo, Bart133,
Wtmitchell, Amorymeltzer, Sciurin, Mikeo, Bookandcoee, Dryman, Oleg Alexandrov, Linas, RHaworth, TigerShark, Camw, Yansa,
Jonathan de Boyne Pollard, Robert K S, WadeSimMiser, I64s, Noetica, Wayward, Gimboid13, Yegorm, Marudubshinki, Dysepsion,
MassGalactusUniversum, Magister Mathematicae, Kbdank71, Dkleeman, Jshadias, Josh Parris, Sjakkalle, Rjwilmsi, Peter 2005,
Daganboy, GregAsche, Sango123, Platypus222, Titoxd, MatthewMastracci, RobertG, Mathbot, JiFish, Lost~enwiki, Nivix, Krackpipe,
RexNL, Gurch, Fresheneesz, Viznut, Chobot, DVdm, Gwernol, The Rambling Man, Siddhant, Wavelength, Deeptrivia, Jimp, Blackworm,
Phantomsteve, RussBot, Anonymous editor, SpuriousQ, Kirill Lokshin, Stephenb, Anomie, Mipadi, Astral, Grafen, Arichnad, Trovatore,
Keka, SCZenz, Dogcow, Retired username, D. F. Schmidt, Daniel Mietchen, Ruhrsch, Superiority, Ninly, Closedmouth, Arthur Rubin,
6a4fe8aa039615ebd9ddb83d6acf9a1dc1b684f7, Jogers, MathsIsFun, CWenger, GinaDana, Junglecat, MarkKB, Innity0, Auroranorth,
Capitalist, SmackBot, Adam majewski, Incnis Mrsi, Honza Zruba, InverseHypercube, KnowledgeOfSelf, Bigbluesh, Blue520, Jagged
85, Chairman S., David n m bond, HalfShadow, Yamaguchi , Peace keeper, Gilliam, Ohnoitsjamie, Kevinalewis, Psiphiorg, Zinc2005,
Kurykh, Da nuke, EncMstr, Miquonranger03, MalafayaBot, Baa, DHN-bot~enwiki, Darth Panda, Rlevse, Jereyarcand, Kotra, Can't
sleep, clown will eat me, Pooresd, Rsm99833, Addshore, Iridescence, Kleuske, Jon Awbrey, AlexJ, The PIPE, Sigma 7, Kukini,

132.11. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

589

Ohconfucius, The undertow, SashatoBot, Lambiam, Doug Bell, Mouse Nightshirt, Kuru, CharlesDexterWard, General Ization, Vgy7ujm,
Cronholm144, Sir Nicholas de Mimsy-Porpington, Bjankuloski06en~enwiki, Jim.belk, Ben Kidwell, Zippokovich, Slakr, Stwalkerster, Tasc, Dante Shamest, Beetstra, SQGibbon, Mr Stephen, Dicklyon, Mhdc2003~enwiki, Meco, Waggers, Mets501, Ravi12346,
EdC~enwiki, Avant Guard, Dodo bird, GorillazFanAdam, BranStark, Aursani, HallwayGiant, Iridescent, UncleDouggie, SohanDsouza,
Courcelles, Tawkerbot2, Gav89, Gco, Andy120, Jafet, Psychotic Midget, JForget, Insanephantom, Maniaque27, Scohoust, Dodgerdave,
Arabic Pilot, Baiji, Gregbard, HexenX, Sopoforic, Mblumber, Johnsmitzerhoven, Meno25, Gogo Dodo, Vwollan, Travelbird, Tawkerbot4,
DumbBOT, Chrislk02, FastLizard4, LinkWalker, Edmarriner, Thijs!bot, Epbr123, N5iln, Mojo Hand, Headbomb, Newton2, Asdfg1234,
Escarbot, AntiVandalBot, Majorly, Abu-Fool Danyal ibn Amir al-Makhiri, Seaphoto, Opelio, SummerPhD, Prolog, Farosdaughter, Fritz
Jrn, Gdo01, Derouch, Fireice, AubreyEllenShomo, Myanw, JAnDbot, MER-C, PhilKnight, .Absolution., Michaeldadmum, Snehalbhai,
VoABot II, AtticusX, JNW, JamesBWatson, Swpb, Aerographer1981, Twsx, WODUP, Catgut, 28421u2232nfenfcenc, David Eppstein,
Wikipop~enwiki, DerHexer, JaGa, Ishan.beckham, Patstuart, Wyzzard~enwiki, Violinbecky76543, Naohiro19, Keith D, Jorgepblank,
Zouavman Le Zouave, Zackfox, Linuxwikiuser, EdBever, Erkan Yilmaz, J.delanoy, Naki, Trusilver, Numbo3, Jstew87, OKeh~enwiki,
Bot-Schafter, Katalaveno, Hakufu Sonsaku, AntiSpamBot, Midnight Madness, Belovedfreak, NewEnglandYankee, Xander756, Kraftlos,
Milogardner, Juliancolton, Cometstyles, STBotD, Nitomatik, Gwen Gale, VoidLurker, Pedalist, Nedge123, RJASE1, Idioma-bot,
CWii, Dejan Jovanovi, JohnBlackburne, LokiClock, Philip Trueman, TXiKiBoT, Oshwah, Waterbender kara, GroveGuy, Vipinhari,
Anonymous Dissident, Crohnie, Someguy1221, Oxfordwang, Mckoch, PaulTanenbaum, Brusinsky, Jackfork, Wiae, Bcharles, Billinghurst,
RandomXYZb, Andy Dingley, Synthebot, Falcon8765, Purgatory Fubar, TrippingTroubadour, Spinningspark, DeniabilityPlausible,
WatermelonPotion, Dmcq, Mike4ty4, Monty845, Sue Rangell, AlleborgoBot, Sorisos, Logan, Scottywong, EmxBot, Kbrose, Arjun024,
Legalboard~enwiki, SieBot, Tiddly Tom, Scarian, Citizen, Euryalus, ToePeu.bot, Winchelsea, Caltas, Shanken, RJaguar3, Vanished
User 8a9b4725f8376, Fabio479, Ham Pastrami, Renato91~enwiki, Chromaticity, Aztects, Antonio Lopez, Tombomp, IdreamofJeanie,
Anchor Link Bot, Dorkenhavvon, Jacob.jose, Mr. Stradivarius, WikiLaurent, WimdeValk, VanishedUser sdu9aya9fs787sads, R00m c,
Velvetron, The sunder king, Polpolpol4, Lochlomond, Loren.wilton, Martarius, ClueBot, Cutiepie17881, Justin W Smith, The Thing
That Should Not Be, Wolfch, Meisterkoch, Rjd0060, Supertouch, Poopship75, Martinap98, Meekywiki, Drmies, Mild Bill Hiccup,
Raf1qu3, , LizardJr8, Liempt, Arunsingh16, Quatrinauta~enwiki, Infaredz, Netralized, Kingo1234, Excirial, Jusdafax,
Watchduck, Zac439, Carsrac, Brews ohare, Jotterbot, Jarek Duda, Hans Adler, Acabashi, BlaenkDenum, Aitias, Buzzlite101, SoxBot
III, Egmontaz, LightAnkh, SpacePirate59, Deggert, C. A. Russell, SilvonenBot, Airplaneman, EEng, Elegost5555, Addbot, Blanche of
Kings Lynn, Willking1979, Twaz, Thelazyleo, Azreal Umbra, Pikujs, CanadianLinuxUser, MrOllie, Glane23, Avazelda13, Debresser,
Favonian, LinkFA-Bot, Jasper Deng, Tide rolls, Apteva, MuZemike, Z1nk666, JSR, Margin1522, Yobot, WikiDan61, 2D, Ptbotgourou,
Senator Palpatine, TaBOT-zerem, II MusLiM HyBRiD II, THEN WHO WAS PHONE?, MetroMan4, Azcolvin429, AnomieBOT,
Vanished user x10, Rubinbot, 1exec1, A.kamburov, Rjanag, Jim1138, Piano non troppo, Hatredto, AdjustShift, Grolltech, Kingpin13,
Ubergeekguy, Flewis, Bluerasberry, Materialscientist, ArthurBot, Cureden, Capricorn42, Drilnoth, 4twenty42o, TheWeakWilled,
RJGray, Mlpearc, Gap9551, Reno171, Trurle, RibotBOT, PoojanWagh, Controls.freq, Superfrowny, Adavis444, Shadowjams, E0steven,
Techbeats123, Jugdev, Dan6hell66, Queen Spiral, Frozenevolution, Rohanpol, Krishnaupas, Tobby72, SpAwNaGeZ, 999retard,
Michael93555, Tomislavlac, Macjohn2, Majopius, Machine Elf 1735, Aleniko17, Citation bot 1, Amplitude101, Tintenschlein,
Pinethicket, I dream of horses, HRoestBot, Tanweer Morshed, Calmer Waters, Nerd272, Bulletd, Includeiostream, JoeliusCeasar, Serols,
ContinueWithCaution, Full-date unlinking bot, Shanmugamp7, Qwerty112233, Abc518, WoollyMind, FoxBot, , Sweet
xx, HelenOnline, Catinator, Zvn, 4, Math MisterY, Tbhotch, Reach Out to the Truth, Onel5969, Mean as custard, TjBot, Regancy42,
Dstone66, Castedo, DASHBot, Sandor rawks, EmausBot, NoobTheShow24, N, Heymid, Britannic124, Winner 42, Soupystar, K6ka,
Thecheesykid, John Cline, F, Josve05a, 2andrewknyazev, Tuminure, Wayne Slam, Donner60, Orange Suede Sofa, RockMagnetist,
TYelliot, Bbourne20, Mannix Chan, Assassin15, ClueBot NG, Proz, Matthiaspaul, MelbourneStar, Baseball Watcher, Snotbot, Delusion23,
Jiri 1984, Smith14333, Joel B. Lewis, Widr, Rurik the Varangian, Wipeoutman, , Helpful Pixie Bot, Westnest, Ephert,
Gurt Posh, CityOfSilver, MusikAnimal, GKFX, Tomtad, Cncmaster, Jdk42, David McIlvenna, Justincheng12345-bot, Cimorcus,
Toploftical, The Illusive Man, Dustin Dewynne, Dexbot, FoCuSandLeArN, Peri eljko, Uquiqui, Webclient101, PeacefulPlanet3,
Fuebar, Sandeep Kalshaniya, Frosty, Graphium, Jochen Burghardt, Hrishikesh0111, Andypandyjay, The Anonymouse, The Mol
Man, Technical math, Ssassddd, Orienomesh-w, Faizan, FallingGravity, Ruby Murray, Acetotyce, JPaestpreornJeolhlna, Eyesnore,
Jaq2013, WIKIWIZDOM, Syntaxerrorz, LieutenantLatvia, Jianhui67, Jajahada, Monkbot, Jose2027, Joeleoj123, Abc 123 def 456, Trax
support, Lich counter, Soa Koutsouveli, Kd5gua, Sam-walker1999, JoeHebda, Hamlet33111, Jthistle38, Zunarshh, Orduin, Hunty101,
NekoKatsun, Minecraftwizard, BoxOfChickens, A normal guy who goes to wiki, Rainierroitayam, Ezracollier7, Yagki, KasparBot,
Sweepy, Arrakis, Akresben2016 4, Patrickomeara, Twiceyoucoont, BU Rob13, CAPTAIN RAJU, Aaditya Mohanty, Seminyoon2,
Luis150902, Scott12344444, CLCStudent, Idliekde, Notfruit, Gabuab, Captchadener, Omni Flames, Tranngocnhatminh, P3truss,
Jjetgaming, Anon6022, 011010010110010001101001011011110111010001110011a, SrikanthPs6, KarinePaegon, Yinf, Deacon Vorbis,
Proesor Chinky, 0000, Zrod, AstaRasta01, Stupidwikipediass and Anonymous: 1252
Bit Source: https://en.wikipedia.org/wiki/Bit?oldid=749626391 Contributors: Derek Ross, Uriyan, Bryan Derksen, Tarquin, Stephen
Gilbert, Andre Engels, Fritzlein, Christian List, Aldie, PierreAbbat, SimonP, Boleslav Bobcik, Imran, Mjb, Heron, Hirzel, B4hand,
Dwheeler, Frecklefoot, Edward, Michael Hardy, Lousyd, Liftarn, SGBailey, Ixfd64, Fruge~enwiki, Anders Feder, Mac, Docu, Basswulf, Andres, Kaihsu, Jonik, Mxn, Iseeaboar, Hashar, Ralesk, Gutza, DJ Clayworth, Jcajacob, Omegatron, Spikey, Vaceituno, Indefatigable, Dbabbitt, Robbot, Fredrik, Schutz, Jmabel, Altenmann, Naddy, Mdrejhon, Centrx, Giftlite, DocWatson42, Harp, Fleminra, Markus
Kuhn, Frencheigh, Jorge Stol, Siroxo, AlistairMcMillan, VampWillow, Bobblewik, Vadmium, Stevietheman, Bact, Quadell, Rdsmith4,
Icairns, Marc Mongenet, Lev, Troels Arvin, Urhixidur, Ukexpat, Andreas Kaufmann, Random account 47, NathanHurst, Guanabot, Smyth,
Paul August, Sietse Snel, Art LaPella, Aaronbrick, Longhair, Viriditas, StoatBringer, R. S. Shaw, Johnteslade, SpeedyGonsales, Toh,
Boredzo, Towel401, Gsklee, Jumbuck, Karlthegreat, CyberSkull, PoptartKing, PAR, Wanderingstan, Dirac1933, TenOfAllTrades, Duplode, Tariqabjotu, Woohookitty, Shreevatsa, Armando, Marudubshinki, Mandarax, Graham87, Kbdank71, Rjwilmsi, Geimas5~enwiki,
Srleer, Glenn L, Physchim62, Bgwhite, E Pluribus Anthony, YurikBot, Sceptre, FrenchIsAwesome, Gunblade~enwiki, Splash, Stephenb,
Archelon, Yyy, Wimt, NawlinWiki, Grafen, Nick, Cholmes75, LaraCroft NYC, E rulez, Mikeblas, RL0919, Zwobot, Ospalh, Jeh,
Alan Millar, Light current, Lt-wiki-bot, Sharkb, Dspradau, JLaTondre, Rwwww, Dkasak, Groyolo, SmackBot, Monkeyblue, Bomac,
KocjoBot~enwiki, Thunderboltz, Eskimbot, Mgreenbe, BiT, Ohnoitsjamie, Tennekis, Rmosler2100, Anwar saadat, TimBentley, MK8, Oli
Filth, Deli nk, Jerome Charles Potts, Nbarth, Discharger12, JonHarder, Juandev, VMS Mosaic, SundarBot, Calbaer, BostonMA, Cybercobra, Mwtoews, Demicx, PanBK, Ex nihil, George The Dragon, Vagary, Bobamnertiopsis, Vaughan Pratt, Aubrey Jaer, Neelix, Chrisahn,
NE Ent, Gregbard, Sopoforic, Mblumber, Kallerdis, Hendrib, Dusty relic, Ameliorate!, Omicronpersei8, Epbr123, Shmaltz, Michagal,
N5iln, Mojo Hand, Sobreira, Neil916, JustAGal, Philippe, AlefZet, Escarbot, AntiVandalBot, Luna Santin, Widefox, Guy Macon, Opelio,
Samsbc12, Ozzieboy, Quintote, Leuko, BrotherE, Bongwarrior, VoABot II, JamesBWatson, Animum, Dan Pelleg, 0612, Holistic~enwiki,
MartinBot, Flexdream, R'n'B, Nono64, J.delanoy, Hrollins, Ten-K, NerdyNSK, , VolkovBot, DagnyB, Tesscass, Philip
Trueman, Charleca, TXiKiBoT, Oshwah, PaulTanenbaum, RiverStyx23, Jesin, Synthebot, Spinningspark, YordanGeorgiev, Thunderbird2,

590

CHAPTER 132. MORSE CODE

EmxBot, Neparis, Kbrose, Bill Riojas Mclemore, SieBot, JoeyLJ, Mar(c), Happysailor, Flyer22 Reborn, E.shijir, Harry-, Lightmouse,
SimonTrew, Ericjul, BenoniBot~enwiki, OKBot, Paulinho28, Troy 07, ClueBot, Quadstrike, The Thing That Should Not Be, Mild Bill Hiccup, ChandlerMapBot, LeoFrank, Excirial, Jusdafax, NotSarenne, Jiemurat, Thehelpfulone, MpMadhuranga, Aitias, Johnuniq, SoxBot III,
DumZiBoT, Williams.daryl, Freakinewirddawg, GSMR, CarsracBot, RTG, AnnaFrance, 5 albert square, Tide rolls, Ale66, Luckas-bot,
Synapses12, Yobot, Synapses13, OrgasGirl, The Earwig, Terryblack, Ayrton Prost, Franois Melchior, Naderra, AnomieBOT, Wikifane12,
1exec1, Whittlepedia, 9258fahskh917fas, Zangar, Citation bot, Kuwaity26, Quebec99, TechControl, Almabot, RibotBOT, Shadowjams,
GiacomoV, FrescoBot, Nicolas Perrault III, LucienBOT, GEBStgo, MathFacts, Weetoddid, Big threatening button, MacMed, Pinethicket,
Vicenarian, HRoestBot, Brad Polard, MastiBot, TobeBot, Dinamik-bot, Vrenator, Bluest, Sabisteven, Suusion of Yellow, Unbitwise, Tbhotch, Marie Poise, DARTH SIDIOUS 2, EmausBot, Lanceallenhall, Wikipelli, BigMattyO, Josve05a, Quondum, Poisock, Jay-Sebastos,
, ChuispastonBot, DASHBotAV, ClueBot NG, Matthiaspaul, Satellizer, HonestIntelligence, Mightymights, Clij123,
Calabe1992, Wbm1058, Doorknob747, BG19bot, Vagobot, Umais Bin Sajjad, Klilidiplomus, Tagremover, Dschryver, JYBot, Bitso, Audakhan, Frosty, DavidLeighEllis, Comp.arch, Wikiuser13, Ugog Nizdast, Textcheese, Aleks000, Textcheese pro, Ethically Yours, SwaManBra, MarkiPoli, Amortias, Asdfugil, Vineshgowda, Sro23, InternetArchiveBot, AZ1199, Gulumeemee and Anonymous: 321
Baud Source: https://en.wikipedia.org/wiki/Baud?oldid=745179676 Contributors: Damian Yerrick, Mav, The Anome, Tarquin, TomCerul,
Olivier, Bdesham, Looxix~enwiki, Snoyes, Mxn, Smack, Emperorbma, Crissov, Mrand, E23~enwiki, Indefatigable, Robbot, Goethean,
Tea2min, SimonMayer, DocWatson42, Mintleaf~enwiki, BenFrantzDale, Markus Kuhn, Skagedal, Bobblewik, Maximaximax, Alotau,
Adashiel, Mike Rosoft, KneeLess, YUL89YYZ, Pt, Kwamikagami, West London Dweller, Bobo192, Shlomital, Rabarberski, Stephan
Leeds, Mixer, Nuno Tavares, Palica, BD2412, Teque5, JHMM13, FlaBot, Margosbot~enwiki, RexNL, Bgwhite, The Rambling Man,
YurikBot, RussBot, Stephenb, Gaius Cornelius, Nick, Kyle Barbour, Bota47, Ms2ger, Darrel francis, SmackBot, Mountainlogic, Aksi
great, Bluebot, Colonies Chris, Nakon, JanCeuleers, Ligulembot, SashatoBot, Morten, Markharris, Dicklyon, Sharcho, P199, Lee Carre,
Yinyang94, Twas Now, Ossworks, Conrad.Irwin, Sakurambo, Harej bot, Cydebot, Hebrides, Biblbroks, LGReed, CynicalMe, Bradhyatt, AntiVandalBot, Luna Santin, Prolog, Once in a Blue Moon, JAnDbot, Deective, TimidGuy, Jim.henderson, Mange01, Trusilver,
PhoenixofMT, Thomas Larsen, Wa3pxx, Cometstyles, STBotD, MVLPbear, Squids and Chips, VolkovBot, Jonwilloughby, QuackGuru,
Dwight666, A4bot, Raverinnigeria, BotKung, Vskgopu, Thunderbird2, Kbrose, YonaBot, Phe-bot, Dynamitecow, Oxymoron83, KoshVorlon, Int21h, Dillard421, XU-engineer, ClueBot, Jeshan, Boing! said Zebedee, Erudecorp, Passargea, Alexbot, Stepheng3, MelonBot, Johnuniq, Addbot, Fgnievinski, Lad1984, Zorrobot, Legobot, Luckas-bot, Yobot, Amirobot, AnomieBOT, ArthurBot, Capricorn42, Vicenarian, MastiBot, Footwarrior, FoxBot, altay, EmausBot, Chricho, Hhhippo, Dondervogel 2, Sbmeirow, ClueBot NG, IfYouDoIfYouDon't,
Wbm1058, Op47, Caypartisbot, JYBot, Aymankamelwiki, Nrbray, Werddemer and Anonymous: 128
Constellation diagram Source: https://en.wikipedia.org/wiki/Constellation_diagram?oldid=751233482 Contributors: Michael Hardy,
Glenn, Conti, DavidCary, Whosasking, YurikBot, Splash, KSchutte, Mazer, Sam8, Lacbil, Oli Filth, Vina-iwbot~enwiki, Sakurambo,
Nyq, Rod57, KylieTastic, Scls19fr, Alinja, Leonardomio, McM.bot, Ronald S. Davis, Muhandes, Addbot, OlEnglish, Ptbotgourou, Shadowjams, LucienBOT, ZroBot, ClueBot NG, BG19bot, Alishan786, YFdyh-bot, Kishore407, Elasticninja, Allthefoxes and Anonymous:
26
Complex number Source: https://en.wikipedia.org/wiki/Complex_number?oldid=750494559 Contributors: AxelBoldt, Brion VIBBER,
Bryan Derksen, Zundark, The Anome, Tarquin, Taw, Ap, Gareth Owen, Dragon Dave, BenBaker, Josh Grosse, Christian List, Matusz,
Enchanter, PierreAbbat, Miguel~enwiki, Roadrunner, Maria Renee Jenkins, Stevertigo, Patrick, Boud, Michael Hardy, Wshun, Dominus,
Nixdorf, Ixfd64, TakuyaMurata, GTBacchus, Flamurai, Card~enwiki, Looxix~enwiki, Stevenj, Nanshu, Strebe, Snoyes, ,
Ciphergoth, AugPi, Poor Yorick, Rossami, Andres, Dod1, Dlo1986, Hashar, HolIgor, Revolver, Charles Matthews, Dcoetzee, Dino,
Wikiborg, Dysprosia, Jitse Niesen, Zoicon5, Furrykef, Hyacinth, Saltine, Taxman, Fibonacci, Thue, Bevo, Shizhao, JensMueller, Finlay McWalter, Denelson83, Jni, Robbot, Fredrik, Huppybanny, Romanm, Gandalf61, MathMartin, P0lyglut, Sverdrup, Henrygb, Rasmus
Faber, Bkell, Matty j, Intangir, Robinh, Chris-gore, Aetheling, Fuelbottle, Seth Ilys, Tea2min, Tosha, Matthew Stannard, Centrx, Giftlite,
Rs2, Elf, Recentchanges, Wolfkeeper, var Arnfjr Bjarmason, MSGJ, Herbee, Fropu, Wwoods, Georgesawyer, Brona, Fleminra,
Alison, Waltpohl, Rookkey, Jason Quinn, Jackol, Pne, Ato, Chowbok, MarkSweep, Kaldari, Gauss, Pmanderson, LHOON, Trevor MacInnis, Mh, Flex, Cypa, Freakofnurture, Rcog, Guanabot, Pj.de.bruin, Pjacobi, MeltBanana, Eric Shalov, Paul August, Bender235, Zaslav,
ReallyNiceGuy, Plugwash, Pt, Rgdboer, Kine, Shoujun, Harley peters, Gunark, C S, L33tminion, Scentoni, Obradovic Goran, Haham
hanuka, Crust, Mdd, Zachlipton, Red Winged Duck, Msh210, ChristopherWillis, Guy Harris, Keenan Pepper, Krischik, Sligocki, Snowolf,
Saga City, Fiedorow, Wtshymanski, RainbowOfLight, HenryLi, Kenyon, Tentoes, Oleg Alexandrov, Bobrayner, Joriki, Linas, Mindmatrix, StradivariusTV, DanBishop, Oliphaunt, Jimbryho, OdedSchramm, Keta, Wurzel~enwiki, SeventyThree, Calrfa Wn, Graham87,
BD2412, Qwertyus, Chun-hian, Kbdank71, Raymond Hill, Ketiltrout, Commander, Bob A, MarSch, Omnieiunium, Salix alba, HappyCamper, SeanMack, Virga, Marozols, Watcharakorn, Streyeder, FlaBot, VKokielov, Mathbot, RexNL, Ewlyahoocom, ChongDae, Nivaca,
Fresheneesz, BitterMilton, Lmatt, Kri, Zodino, Chobot, DVdm, Wavelength, Angus Lepper, Hairy Dude, Deeptrivia, X42bn6, Loom91,
Stephenb, Argentino, David R. Ingham, Wiki alf, MathMan64, Trovatore, Jamesg, Zwobot, Zirland, RyanJones, User27091, Ms2ger,
Googl, Pegship, Igin, Saric, Zzuuzz, Netrapt, Arundhati bakshi, Gesslein, Sidonath~enwiki, Paul D. Anderson, RG2, Bo Jacoby, Cmglee, DVD R W, Matt Heard, SmackBot, RDBury, FocalPoint, Incnis Mrsi, Jagged 85, PizzaMargherita, Nmulder, Nejko, Spireguy, GraemeMcRae, HalfShadow, Bromskloss, Gilliam, Betacommand, Isaac Dupree, Da nuke, Ncrfgs, Oli Filth, Raja Hussain, Silly rabbit, Papa
November, Octahedron80, Nbarth, Sbharris, Dual Freq, Szidomingo, Darth Panda, Bob K, AdamSmithee, Armend, Grover cleveland, Alanius, Opticyclic, Cybercobra, Taggart Transcontinental, Bidabadi~enwiki, Tesseran, Lambiam, Chrisandtaund, Scottie 000, Soap, Khazar,
MvH, Andymc, Nijdam, Michael Kinyon, Loadmaster, Grasyop, Mr Stephen, SirFozzie, Waggers, Mets501, Elb2000, Dl2000, Asyndeton,
Quaeler, Nicoli nicolivich, Iridescent, Quantum Burrito, Laurens-af, Madmath789, Newone, Catherineyronwode, Ivysaur, RJChapman,
Igoldste, Happy-melon, Courcelles, Profjohn, Tawkerbot2, JRSpriggs, Eastlaw, Nutster, JForget, Yellowstone6, CRGreathouse, Wafulz,
Barno uk, CBM, KyraVixen, Guru6969, MarsRover, HenningThielemann, Bwe203, Myasuda, SuperMidget, Mct mht, Adhanali, FilipeS, Pablogrb, Goldencako, Inkington, Abtract, Xantharius, Epbr123, Barticus88, Koeplinger, Pstanton, Noneofyourbusiness, Marek69,
Itsmejudith, Pemboid, Dgies, Urdutext, BigJohnHenry, Mentisto, AntiVandalBot, Tariqhada, Majorly, Lovibond, Tyco.skinner, Hannes
Eder, Emmelie, Storkk, JAnDbot, Onkel Tuca~enwiki, Oxinabox, Ricardo sandoval, Thenub314, JRocketeer, Hut 8.5, Kerotan, 7severn7,
.anacondabot, Pablothegreat85, VoABot II, JamesBWatson, Jakob.scholbach, Aka042, 2.718281828459..., First Harmonic, Thalesfernandes, Khalid Mahmood, Qe2eqe, Matqkks, Jfredrickson, Dima373, Twigletmac, Rohan Ghatak, JaimeLesMaths, TechnoFaye, Yjwong,
Mange01, Tikiwont, Jol123, Wayp123, P0807670, Trumpet marietta 45750, Raise exception, Policron, Dissimul, Thisma, Shoessss, Juliancolton, Cometstyles, DavidCBryant, Prietol, Micro01, Treisijs, Ale2006, Mlewis000, Idioma-bot, Spellcast, VolkovBot, Pleasantville,
JohnBlackburne, Soliloquial, TXiKiBoT, Vipinhari, Nxavar, Anonymous Dissident, Voorlandt, Mogmiester, Leafyplant, LeaveSleaves,
Lambyte, UnitedStatesian, Madhero88, Jesin, Rabkid15, Wolfrock, Philmac, Falcon8765, Brianga, Dmcq, Twooars, Symane, Iapetusuk,
Lagrange123, Pitel, Rhanekom, SieBot, Ivan tambuk, Tiddly Tom, Steorra, Jasondet, Paolo.dL, Polymath618, SimonTrew, Kudret abi,
DesolateReality, Stfg, Monroetransfer, Anchor Link Bot, Randomblue, Nic bor, Felizdenovo, Denisarona, ClueBot, Bobathon71, Kotniski,

132.11. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

591

The Thing That Should Not Be, Blogeswar, Mild Bill Hiccup, TheOldJacobite, Niceguyedc, UKoch, Wesaq, M4gnum0n, Crywalt, Bender2k14, Kenneth Brookes, EBY3221, Rhododendrites, VTBushyTail, Cenarium, Livius3, Rsmuruga, Jotterbot, Jarek Duda, ChrisHodgesUK, Qwfp, Crowsnest, Kiensvay, Marc van Leeuwen, Rror, Nicoguaro, Patrick.ar, SilvonenBot, Virginia-American, Som subhra, WikiDao, AllTheThings, Truthnlove, Ttimespan, Wyatt915, Tayste, Manuel Trujillo Berges, Olli Niemitalo, Fgnievinski, KarlJacobi, Fielddaysunday, Favonian, LinkFA-Bot, DE logics, Fireaxe888, Ehrenkater, Lightbot, JDSperling, MuZemike, Balabiot, Jarble, Santosga, Ben Ben,
Legobot, Luckas-bot, Finbob83, Yobot, Kan8eDie, KamikazeBot, AnakngAraw, AnomieBOT, Jim1138, Haroldco, Materialscientist, Citation bot, LilHelpa, Phlembowper99, Xqbot, Dert34, Timir2, Capricorn42, Fern 24, Br77rino, Isheden, Gap9551, Ferran Mir, Bigrafo,
ProtectionTaggingBot, Nios, Aaron Kauppi, COVIZAPIBETEFOKY, FrescoBot, Sawomir Biay, Raphaelsss, Haein45, Citation bot
1, Xxglennxx, Petecrawford, Tkuvho, GlenShennan, Pinethicket, Boulaur, Sergiacid, Hard Sin, Jujutacular, Ravisingh57547, Janisozaur,
Graemeb1967, FoxBot, Double sharp, TobeBot, Trappist the monk, Ale And Quail, Remyrem1, Dinamik-bot, LilyKitty, Inferior Olive,
Duoduoduo, Diannaa, CeNobiteElf, Terry2012~enwiki, Laurent MAYER, Momo kiki, LibertyDodzo, EmausBot, Skysmurf, Lessbread,
Tommy2010, ObserverFromAbove, Brandon Brunner, Dcirovic, Slawekb, Werieth, AvicBot, ZroBot, Gsokolov, Akashkumarrath, Bruno
Simes, Brazmyth, Quondum, L Kensington, Maschen, Chewings72, Takatodigi, Christopherkennedy1994,
, Tcha216, Eliah
Kagan, Mobower, Readysoaper, Whommighter, Modelpanicer, Moralshearer, Basispoeter, ClueBot NG, Wcherowi, CocuBot, Satellizer, Movses-bot, DieSwartzPunkt, Lifeonahilltop, Widr, Antiqueight, Jashaszun, FightingMac, Helpful Pixie Bot, Atongmy, BG19bot,
Jmvicent~enwiki, Evnis, ServiceAT, Amp71, Onewhohelps, F=q(E+v^B), Steven Windsor, Supergeek22, Brad7777, Minsbot, BattyBot, IkamusumeFan, OceanEngineerRI, ChrisGualtieri, Gdfusion, Khazar2, EuroCarGT, Waepudding, KunjanK, , AHusain314,
Lambda Fairy, Russell157, Meghas, Mmitchell10, The Mol Man, Franois Robere, Soumya Mittal, Tango303, Smwolfe, DavidLeighEllis,
Anant.sogani, Blackbombchu, Ugog Nizdast, Mcse, GiantPeachTime, Zoydb2, Prakalpparadox765, Gareth.eming15, Vieque, Suraj 967,
Mario Casteln Castro, WillemienH, Loraof, Zppix, Lilkennnn, User000name, Kavya l, Peterkos, KasparBot, Rhermanrherman, CAPTAIN
RAJU, Marianna251, Fmadd, -glove- and Anonymous: 664
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Delirium, Theresa knott, Andres, Mxn, Agtx, Revolver, Charles Matthews, Nohat, Dysprosia, Furrykef, SirJective, Fredrik, Bkell, PrimeFan, Lzur, Jleedev, Alan Liefting, Giftlite, Gene Ward Smith, Philwelch, Lethe, Fropu, Guanaco, Nayuki, Noe, Bob.v.R, Gauss, Simoneau, TreyHarris, Mschlindwein, Gazpacho, Mormegil, Ardonik, Paul August, Bender235, Andrejj, Plugwash, Rgdboer, EmilJ, Viames,
Cje~enwiki, Rbj, DG~enwiki, Haham hanuka, Ricky81682, RoySmith, Burn, EvenT, Dirac1933, MIT Trekkie, Algocu, Oleg Alexandrov, Joriki, Mindmatrix, Justinlebar, LeonWhite, Lkjhgfdsa, MFH, Wurzel~enwiki, Philbarker, Bobmilkman, Sj, Bob A, Volfy, Antimatt, RobertG, Mathbot, Intersoa, Born2cycle, Kri, Chobot, Nylex, DVdm, Algebraist, EamonnPKeane, UkPaolo, Wavelength, PiAndWhippedCream, Prometheus235, RussBot, Kauner, Rick Norwood, Trovatore, Amakuha, Kyle Barbour, Light current, Arthur Rubin,
StealthFox, Gesslein, Ghazer~enwiki, Finell, Matikkapoika~enwiki, That Guy, From That Show!, Eykanal, Dash77, SmackBot, PizzaMargherita, DTM, Gilliam, Skizzik, Silly rabbit, Octahedron80, Bob K, Hgrosser, Modest Genius, Can't sleep, clown will eat me, Tamfang,
Taggart Transcontinental, Nmnogueira, Zchenyu, Lambiam, Loadmaster, Xiaphias, Mets501, Elb2000, JDAWiseman, Macwiki, Quaeler,
Chris53516, Majora4, Phoenixrod, Courcelles, Bstepp99, CmdrObot, Wafulz, FilipeS, Yaris678, Cydebot, Benzi455, KarolS, Dadofsam,
Cario24, Vinyanov, Janlo, Mungomba, Ati7, Duncan McB, AntiVandalBot, Majorly, Luna Santin, Edokter, JAnDbot, Carmicheal99, Andonic, Fourchannel, Penubag, Magioladitis, Vanish2, JamesBWatson, SHCarter, Usien6, Sullivan.t.j, Rajpaj, Gwern, Tentacles, MartinBot,
Themania, Paulnwatts, M samadi, Prokoev2, Icefall5, Gene Ray (Cubic), Pope Nigel the porter, KylieTastic, Adamd1008, 28bytes, Je
G., JohnBlackburne, Fxrbds, Thurth, Philip Trueman, Reagar, SveinHarris, Anonymous Dissident, Lou.weird, TBond, Maxno, Synthebot,
Dmcq, MaCRoEco, Jorge C.Al, SieBot, X-Fi6, This, that and the other, MikeGogulski, Fan Railer, Essap, Masgatotkaca, 888Xristos,
Vhomet, Classicalmasta, Drjjgonzalez, Nic bor, Kortaggio, SallyForth123, Twelvepack, ClueBot, Maymay, Alexbot, Frozen4322, Bentu,
Darkicebot, MystBot, DominoSonic, Kbdankbot, Addbot, Jkasd, Fgnievinski, Ronhjones, SamatBot, Tide rolls, Yobot, AnomieBOT, Materialscientist, Beerockxs, ArthurBot, Xqbot, Sionus, The Evil IP address, Isheden, Jeremymwest, Phillofantiock, Shadowjams, Datakid1100,
X7q, Majopius, Prosaicpat, William915, DrilBot, Goalsonly23, 10metreh, Number Googol, , Robo Cop, Willmea, Konstantin Pest,
Duoduoduo, Aa42john, Qaedtgujol, Netheril96, K6ka, JSquish, 1e+a2e, StringTheory11, Quondum, Hunocsi, ChuispastonBot, ClueBot
NG, LutherVinci, BarrelProof, Jpenedones, Helpful Pixie Bot, Wbm1058, Theoldsparkle, HMman, B3stb33stm4n, SarahLZ, SergeantHippyZombie, ChrisGualtieri, Collingwood, Pokajanje, Thirteenthreefourteen, Ambyjkl, SkateTier, Originalmiles, BrianPansky, Loraof,
Vmwwiikkiivm, Lemondoge, Fromrajeev, InternetArchiveBot, GreenC bot and Anonymous: 224
Passband Source: https://en.wikipedia.org/wiki/Passband?oldid=740939415 Contributors: SimonP, Hephaestos, Omegatron, Giftlite,
MylesCallum, Zowie, Cmdrjameson, Hooperbloob, Rsholmes, Rabarberski, Cburnett, Forderud, Kenyon, Marudubshinki, BD2412, Grammarbot, Ketiltrout, Srleer, YurikBot, Muchness, Brandon, Light current, Juliano, SmackBot, Cybercobra, Dicklyon, Kvng, Chetvorno,
CosineKitty, Tswsl1989, Mange01, Al.locke, Milan Kerlger, Jamelan, Spinningspark, Tasnet, Mild Bill Hiccup, Johnuniq, Addbot, Fgnievinski, Laurinavicius, Redheylin, Skippy le Grand Gourou, Yobot, Citation bot, Jhbdel, Steve Quinn, I dream of horses, Widr, Helpful
Pixie Bot, BG19bot, CitationCleanerBot, Fjmvieira, JaconaFrere, Trackteur, BD2412bot, Bender the Bot and Anonymous: 16
Radio frequency Source: https://en.wikipedia.org/wiki/Radio_frequency?oldid=752236472 Contributors: WojPob, Zundark, The Anome,
Fredbauder, Aldie, SimonP, Waveguy, Rcingham, Heron, Mintguy, Stevertigo, Kku, Prefect, Bogdangiusca, Palmpilot900, Wfeidt, Conti,
Mulad, RadarCzar, Emperorbma, Reddi, Radiojon, Tero~enwiki, SEWilco, Jerzy, Denelson83, Robbot, Moriori, RedWolf, Arkuat, Stewartadcock, Blainster, Hadal, Danceswithzerglings, DocWatson42, Average Earthman, Fleminra, Cantus, Jfdwol, Bobblewik, Utcursch,
Beland, Ary29, Ukexpat, Klemen Kocjancic, Deglr6328, Jakro64, Discospinster, Guanabot, LindsayH, Harriv, Bender235, El C, PhilHibbs, Bobo192, Sparkgap, MARQUIS111, Haham hanuka, ClementSeveillac, Atlant, Wtmitchell, Wtshymanski, Cburnett, Suruena,
DV8 2XL, Gene Nygaard, WojciechSwiderski~enwiki, Kenyon, Alex.g, Camw, Pol098, Plaws, Zilog Jones, Ch'marr, Isnow, MarkPos,
Zpb52, LimoWreck, Kotukunui, Koavf, Misternuvistor, Mike Peel, Vegaswikian, Fred Bradstadt, Ground Zero, RexNL, Smileyrepublic,
Alvin-cs, Srleer, King of Hearts, Wavelength, Fabartus, Anonymous editor, Yyy, Giro720, Teb728, Wiki alf, Retired username, Mortein,
Anetode, Hyandat, Voidxor, Shadowblade, Kermi3, User27091, Jules.LT, Aparna82, GraemeL, Alureiter, SmackBot, Rutja76, Aim Here,
C.Fred, Tbonnie, Yamaguchi , Gilliam, Bluebot, Avin, EncMstr, Bazonka, Can't sleep, clown will eat me, Harumphy, Frap, JustUser,
Adamantios, Khoikhoi, NoIdeaNick, A.R., Anlace, Stattouk, Jcoy, Dicklyon, Stijak, NetBMC, Dsongman, Chetvorno, JohnTechnologist, Daggerstab, Chrumps, Requestion, Cydebot, Kanags, The Ultimate Koopa, Tsenapathy, L7HOMAS, Jstuby, Epbr123, Headbomb,
Rosarinagazo, John254, Dawnseeker2000, AntiVandalBot, Orionus, Nitrous231, Myanw, MagiMaster, JAnDbot, Harryzilber, Ph.eyes,
Ccrrccrr, Erpel13, .anacondabot, Bubba hotep, Benmcgraw, DonVincenzo, Rettetast, Lcabanel, PrestonH, Cpiral, JA.Davidson, Osndok,
Coppertwig, NewEnglandYankee, DAID, Ibrahimyu, , Radioactivebloke, Steel1943, Deor, ICE77, Metroccfd, Mill haru,
Anonymous Dissident, Anna Lincoln, Onevim, BwDraco, BotKung, Spinningspark, Hertz1888, Caltas, Bentogoa, Hovev~enwiki, Callidior,
OP8, Lucyjuice, Regushee, Vcaeken, ClueBot, Noabar, Dean Wormer, CounterVandalismBot, Duane-light, Auntof6, PhySusie, M.O.X,
Cexycy, Elizium23, Therm96, Jonverve, HumphreyW, InternetMeme, Ean5533, BarretB, Hotcrocodile, Jytdog, TopherGZ, Mitch Ames,
Tvargy, Alexius08, Addbot, Yoenit, Zhipengye, Fgnievinski, Thaejas, Ronhjones, GyroMagician, Redheylin, Xicer9, Tide rolls, -
, Bssquirrel, Neilforcier, Dede2008, Cm001, Galoubet, Bluerasberry, Materialscientist, Limideen, 45Factoid44, Madjar, DSisyphBot,

592

CHAPTER 132. MORSE CODE

Barkinfool, RadiX, Mathonius, Nedim Ardoa, Fotaun, Darwinius, Prari, Jc3s5h, Nojiratz, Vhann, Drew R. Smith, Hawkpride3000,
-jem-, Esar100, Tbhotch, RHC3, RjwilmsiBot, Paulmasters, Orphan Wiki, Wikipelli, Dcirovic, OnePt618, Milliemchi, Mohsen.1987,
Coasterlover1994, Vietcuong1212, Doris Camire, Taylor10897, RockMagnetist, Weisspiloti, ClueBot NG, AeroPsico, Mclinch, AlagrecoNJITWILL, Solanki.3108, JordoCo, MerlIwBot, Helpful Pixie Bot, BG19bot, Dragon2531, Shaun, Jeanlyhautyetienne, MeanMotherJr,
NPSao, Theos Little Bot, EstonianMan, DetroitSeattle, Shivansh Chaudhary, Soham, Spyglasses, Hanthoec, Tshuva, Airwoz, Symphero,
JaconaFrere, Monkbot, Thadlooms32, Ff9473, Hafsa1982, SrihariThalla, Mcstacheattack, KasparBot, Gorkhaliyuvraj and Anonymous:
386
Pulse shaping Source: https://en.wikipedia.org/wiki/Pulse_shaping?oldid=656122059 Contributors: Hankwang, Pol098, Krishnavedala,
Eatcacti, SmackBot, Oli Filth, Wazronk, Rogerbrent, CosineKitty, Mange01, H1voltage, Alinja, Spinningspark, TreeSmiler, Hoplon,
Wdwd, Sepia tone, Dthomsen8, Isheden, EmausBot and Anonymous: 15
Digital signal processing Source: https://en.wikipedia.org/wiki/Digital_signal_processing?oldid=750390248 Contributors: AxelBoldt,
Tobias Hoevekamp, Brion VIBBER, The Anome, Tbackstr, Ap, HelgeStenstrom, Wayne Hardman, Rade Kutil, Ben-Zin~enwiki, Boleslav
Bobcik, Olivier, Patrick, Yaroslavvb, Michael Hardy, Nixdorf, Kku, Easterbrook, MightCould, Loisel, Mac, Ronz, Glenn, Smack, Ww,
Dysprosia, Omeomi, Furrykef, Hyacinth, Greglocock, Omegatron, Phoebe, Ldo, Finlay McWalter, Jondel, Lzur, Giftlite, Wolfkeeper,
Ds13, Mcapdevila, SWAdair, Pgan002, Bact, Togo~enwiki, Ukexpat, DJS~enwiki, Abdull, Moxfyre, Discospinster, Style, Y(J)S, Martpol, Violetriga, Alberto Orlandini, .:Ajvol:., Rbj, Matt Britt, Hooperbloob, Vizcarra, Ryanmcdaniel, Atlant, Jnothman, Bart133, Cburnett,
Tony Sidaway, Mwilde, Tertiary7, Gimboid13, Essjay, Graham87, Jshadias, Coneslayer, Jehochman, Cyberparam~enwiki, Wknight8111,
Jeremyp1988, RexNL, Turbotron, Tomer Ish Shalom, Alphachimp, Webshared, Adoniscik, YurikBot, Mysid, Tachs, CLW, Vanished
user 34958, JPushkarH, Nvd, Johnpseudo, GrinBot~enwiki, Zvika, Trolleymusic, SmackBot, PEHowland, The Photon, KocjoBot~enwiki,
Mdd4696, Ohnoitsjamie, Betacommand, Andy M. Wang, Reza1615, Kurykh, Landen99, Bob K, Can't sleep, clown will eat me, Gbuett,
Spectrogram, Cybercobra, Savidan, Dreadstar, Rekh, Soumyasch, RomanSpa, Dicklyon, Belizefan, Caiaa, Kvng, Hu12, CapitalR, Vermolaev, Van helsing, Rohan2kool, Penbat, Jefchip, Indeterminate, DumbBOT, ErrantX, Briantw, Thijs!bot, Epbr123, Muaddeeb, Trlkly,
Gkhan, MER-C, Raanoo, Bongwarrior, Recurring dreams, Whoop whoop, Yewyew66, Allstarecho, Ged Davies, SamShearman, MartinBot, Glrx, JohnPritchard, 3dB dar, Dr Alan Hewitt, Rickyrazz, Chinneeb, King Lopez, Jmrowland, Alinja, Ctmt, Mistman123, One
half 3544, Inductiveload, Swagato Barman Roy, Turgan, Pdfpdf, Iquinnm, Travelingseth, Yswismer, Joaopchagas2, Cgrislin, Dspanalyst,
Pinkadelica, OSP Editor, ClueBot, Binksternet, Dawdler, Yangjy0113, Niceguyedc, TypoBoy, Abdul muqeet, Drew335, Mutaza~enwiki,
Excirial, Mohammed hameed, Hezarfenn, Moberg, Versus22, Pantech solutions, Johnuniq, Semitransgenic, Sandeeppasala, Skarebo, Stillastillsfan, Siddharth raw, Thebestofall007, Captain-tucker, Fgnievinski, TutterMouse, Fieldday-sunday, Stan Sykora, Cst17, Je8080,
Shekure, WikiDreamer Bot, Frmatt, Legobot, OrgasGirl, TaBOT-zerem, AnomieBOT, Jim1138, Eart4493, Materialscientist, Thisara.d.m,
LilHelpa, Agasta, SkiAustria, Kesaloma, A.amitkumar, ShashClp, GliderMaven, Prari, SpaceFlight89, Allen4names, DARTH SIDIOUS 2,
Helwr, Primefac, K6ka, ZroBot, Josve05a, GeorgeBarnick, Orange Suede Sofa, Tot12, Paileboat, TYelliot, Rememberway, ClueBot NG,
Vinras, Jack Greenmaven, AeroPsico, Frietjes, Mesoderm, Rezabot, Helpful Pixie Bot, Gfoltz9, AvocatoBot, EmadIV, CitationCleanerBot,
Jeancey, Humourmind, Physicsch, Rogueleaderr, BattyBot, ChrisGualtieri, YFdyh-bot, VladimirDsp, Tcs az, Webclient101, Jogfalls1947,
Evotopid, Striznauss, Stevebillings, Radiodef, Sisyphus110, Isarra (HG), Phamnhatkhanh, David Lloyd-Jones, LCS check, Ugog Nizdast,
AndyThe, ScotXW, Arta1365, DiscantX, CV9933, KasparBot, H.dryad, Bender the Bot and Anonymous: 285
Direct digital synthesizer Source: https://en.wikipedia.org/wiki/Direct_digital_synthesizer?oldid=715974066 Contributors: Heron,
Glenn, Radiojon, HaeB, Mako098765, Lankiveil, Rbj, Chirag, Hooperbloob, Gene Nygaard, BD2412, Nihiltres, Speedevil, Chris the
speller, Radagast83, Nmnogueira, Wmattis, David s gra, My2jia, Thijs!bot, WinBot, Alphachimpbot, RebelRobot, Glrx, STBotD, TXiKiBoT, B Pete, Jpat34721, Spinningspark, Svick, JL-Bot, Bob1960evens, Sv1xv, RexxS, Cvniras, Addbot, Agrophobe, Yobot, Lupin3362,
Simonjohndoherty, RobinK, Clusternote, Danuggster, Me, Myself, and I are Here and Anonymous: 30
Fading Source: https://en.wikipedia.org/wiki/Fading?oldid=749041322 Contributors: The Anome, Rgamble, Michael Hardy, Karada,
Notheruser, Glenn, Willem, Alvestrand, Karol Langner, Cihan, Giraedata, Guy Harris, Atlant, Riana, Wtshymanski, Woohookitty,
MONGO, Kgrr, Eyreland, Mandarax, BD2412, Vegaswikian, HappyCamper, FlaBot, Wesley Biggs, TexasAndroid, LogIntuit, Splash,
Cryptic, ALoopingIcon, Mmccalpin, Mysid, Tachs, Posix4e, Manfreeed, Chris the speller, Bluebot, Devvyn, Vina-iwbot~enwiki, Kvng,
JoeBot, JohnTechnologist, ShelfSkewed, Cydebot, Skittleys, Stanislav87, Mas2265, Bobblehead, Nick Number, Porqin, Dougher, Gatemansgc, JamesBWatson, STBot, R'n'B, Matyos1, Mange01, McLaurin, Foobarian, Indubitably, Amikake3, TXiKiBoT, Serrano24,
Aasi007onre, SieBot, Flyer22 Reborn, Elch Yenn, ClueBot, Ark2120, Fleem, Pot, Jonathan Laventhol, Kiwux, Gregdurgin, Addbot,
Me Three, LaaknorBot, SpBot, Yobot, Jim1138, Ivan.wy, Xqbot, Capricorn42, Isheden, LucienBOT, Pmokeefe, Smitaaqua, Or michael,
Lotje, Mohan Patra, EmausBot, Bharath K Asrani, SunnyBingoMe, Mittgaurav, 28bot, Northcamel, BG19bot, Millennium bug, Several
Pending, E273b773, Kevin.mille, Lugia2453, Ammar.elfalou, Gburd, Monkbot, Enigmatore, Zamaster4536 and Anonymous: 66
Attenuation Source: https://en.wikipedia.org/wiki/Attenuation?oldid=747036645 Contributors: AlexWasFirst, SimonP, Hephaestos,
Patrick, Michael Hardy, Tobias Conradi, Mxn, Marshman, Omegatron, Tonderai, Hemanshu, Wikibot, Saaga, OldakQuill, Zantolak,
Bumm13, Sonett72, Frau Holle, Vsmith, Alansohn, Falsian, Keenan Pepper, PAR, Blaxthos, Tabletop, Joel D. Reid, SeanMack, JanSuchy, Preslethe, Terrx, Goudzovski, Srleer, YurikBot, Wavelength, RussBot, SpuriousQ, Holon, THB, Allegrorondo, Closedmouth,
Reyk, Petri Krohn, Profero, SmackBot, Elonka, EliF, Berland, Drphilharmonic, Angela26, Fingew, DO11.10, Rafert, Lee Carre, DabMachine, Capacitor, Rrten00, David s gra, Chrumps, Cydebot, PlanetCoder, Andyjsmith, Pjvpjv, JAnDbot, Magioladitis, Parsecboy, Jarekt,
MichaelSHoman, EagleFan, DerHexer, Mad macs, PhysicsPat, MartinBot, Jim.henderson, Rettetast, R'n'B, Smokizzy, Lantonov, ARTE,
Dhaluza, Yecril, Jehan60188, Xerxesnine, Wideload30, Saligron, Oikos-team, Jestar, Synthebot, Spinningspark, ClueBot, Binksternet,
Ideal gas equation, Bigly, Polyamorph, AndreiDukhin, Crywalt, Chininazu12, Al.arodob, Johnuniq, Crowsnest, Superbirk, Addbot, Caden, Fyrael, Fgnievinski, NjardarBot, LaaknorBot, TStein, Yobot, Worldbruce, Piano non troppo, Materialscientist, DCStrain, Nedim
Ardoa, Logger9, Mnmngb, Kwinkunks, BlaueEliese, Paisiello2, Steve Quinn, Kwiki, Chasingmytail, Citation bot 1, Maggyero, DrilBot,
HRoestBot, Merlion444, Fastilysock, Marie Poise, Wikiborg4711, EmausBot, H3llBot, Quondum, Djmerthe, ChuispastonBot, George
Makepeace, ClueBot NG, Jack Greenmaven, RupyTN, Widr, Imgaril, Ssocg561, Kgraghav, Themulticaster, Jliller91, CAPTAIN RAJU,
InternetArchiveBot, GreenC bot and Anonymous: 122
Superheterodyne receiver Source: https://en.wikipedia.org/wiki/Superheterodyne_receiver?oldid=751401102 Contributors: Carey
Evans, Maury Markowitz, Panairjdde~enwiki, Hfastedge, Michael Hardy, Breakpoint, Julesd, Glenn, GRAHAMUK, Omegatron, KeithH, PBS, Dina, DavidCary, Fleminra, Markus Kuhn, Mamizou, Kesac, Yuriz, Blanchette, Bender235, Nigelj, Cmacd123, Hooperbloob,
Hackwrench, Wtshymanski, DV8 2XL, Gmaxwell, Jonnabuz, Gisling, Dweekly, Graham87, BD2412, FayssalF, Ground Zero, Margosbot~enwiki, Nihiltres, Karch, Bgwhite, YurikBot, RussBot, Tole, Gaius Cornelius, Dsmouse, Anomalocaris, Brandon, Bota47, Ninly,
Whaa?, PVSpud, SmackBot, Hmains, Russvdw, Colonies Chris, Bob K, Audriusa, Tim Pierce, Ryan Roos, Jwelby, Romanski, A5b,
Alejandro Exojo, Euchiasmus, Kvng, Freyyr890, Iridescent, Chetvorno, Emote, Elekas, VoxLuna, Requestion, Kairotic, Thijs!bot, Electron9, Phu, Jasen betts, JAnDbot, Harryzilber, CosineKitty, Magioladitis, JaGa, VetPsychWars, Cerium136, Jim.henderson, Glrx, Wylve,

132.11. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

593

CommonsDelinker, Cdamama, TomyDuby, Fountains of Bryn Mawr, Gonzalo M. Garcia, Pawinsync, TXiKiBoT, GLPeterson, Wikisc84,
Jack1993jack, Raymondwinn, DesmondW, Cuddlyable3, Hotuan87, Spinningspark, Rep07, Abcdwiki, AHMartin, SieBot, Hertz1888,
Flyer22 Reborn, Smshaner, PhilSalkie, Dp67, Martarius, ClueBot, EoGuy, Wwheaton, Mild Bill Hiccup, Sv1xv, Skaapgif, Drrdf, BOTarate, The-tenth-zdog, Camboxer, Ultramince, Interferometrist, Angelxmod3, Khindjal, Addbot, Mercyjhansi, Jpchevreau~enwiki, Lightbot, Zorrobot, Luckas-bot, Yobot, CvetanPetrov1940, AnomieBOT, BentleyCoon, Materialscientist, LilHelpa, Xqbot, Nedim Ardoa,
Shadowjams, Hyju, Ranger27, I dream of horses, Strenshon, Lissajous, Md naveed, Francis E Williams, PleaseStand, Fuzy2K, EmausBot, John of Reading, WikitanvirBot, Dewritech, GoingBatty, Mkratz, Zueignung, ClueBot NG, Velo Vrbata, Engradio, Anmcca, Kevin
Gorman, Helpful Pixie Bot, LegendofPedro, CitationCleanerBot, Oran tru, Khazar2, Dexbot, Camyoung54, Melonkelon, Jajohns1, Mr.
Smart LION, AlbertACJeerson, Driftvelocity, KasparBot, Ashker2710 and Anonymous: 129
Undersampling Source: https://en.wikipedia.org/wiki/Undersampling?oldid=745273318 Contributors: Psychonaut, Hooperbloob,
Amire80, Nbarth, Bob K, Dicklyon, J.delanoy, Mange01, Pawinsync, Addbot, ANDROBETA, Helpful Pixie Bot, CitationCleanerBot,
Bender the Bot and Anonymous: 9
Matched lter Source: https://en.wikipedia.org/wiki/Matched_filter?oldid=750254845 Contributors: Michael Hardy, Carnildo, BenFrantzDale, Glogger, Pearle, Flambe, Forderud, Bratsche, Gaius Cornelius, Zerodamage, Maryhit, PEHowland, Oli Filth, CmdrObot,
Synergy, El pak, Rabbanis, Alunwyn, Steve8675309, Alinja, Pronuncer, Mikeblew, Altzinn, Sepia tone, Alexbot, SchreiberBike, TimothyRias, Addbot, SpBot, Luckas-bot, RibotBOT, EeX2, OgreBot, AManWithNoPlan, Mjbmrbot, Kavya Manohar, Newyorkadam,
BG19bot, DrunkSquirrel, Marcocapelle, S Larctia, Mrt3366, ChrisGualtieri, Derekdoth, NoiseLTD, JMike93, Schnafte, Ncasale, Kohlbr
and Anonymous: 52
Intersymbol interference Source: https://en.wikipedia.org/wiki/Intersymbol_interference?oldid=725271732 Contributors: The Anome,
Imran, Edward, DavidCary, Xezbeth, Bobo192, Woohookitty, Masterjamie, Uncle G, Marudubshinki, Grammarbot, N0YKG, Alejo2083,
Ground Zero, Nihiltres, Intgr, Deville, KnightRider~enwiki, SmackBot, Wjmallard, Jab843, Oli Filth, TripleF, Dicklyon, EBorisch,
Sakurambo, MrZap, Tirk, Dawnseeker2000, Blair Bonnett, Skarkkai, WordSurd, CosineKitty, Magioladitis, Tedickey, CarlFeynman,
R'n'B, Idunno271828, Alinja, Spinningspark, SieBot, Loren.wilton, Sepia tone, Avoided, Addbot, Luckas-bot, Yobot, Materialscientist,
Pradeepthundiyil, Kyng, Chris828, Thehelpfulbot, Jonesey95, Tom.Reding, Sohaibafzal, Fox Wilson, Bahamakyle, Alfaisanomega, Kevinpk, AvicAWB, Donner60, ClueBot NG, JordoCo, Helpful Pixie Bot, Touchthelife, Silvrous, Lmsedares, Ajraymond, JakeWi, Sharinjf
and Anonymous: 46
Phase synchronization Source: https://en.wikipedia.org/wiki/Phase_synchronization?oldid=735603697 Contributors: Wolfkeeper, Pucicu, Bluemoose, Dannya222, Dmharvey, Bluebot, Pjvpjv, Radagast3, Sphilbrick, Addbot, TobeBot, Khazar2, Minksk and Anonymous:
9
Asynchronous communication Source: https://en.wikipedia.org/wiki/Asynchronous_communication?oldid=747831113 Contributors:
Infrogmation, Pnm, LittleDan, Altenmann, Cyrius, Tea2min, McDutchie, Vadmium, Stevietheman, Trivial0921, Grue, NetBot, AllyUnion, Maurreen, Grobertson, Wtshymanski, Cburnett, Allen3, BD2412, Ketiltrout, Srleer, YurikBot, RussBot, Hellbus, Finell, SmackBot, MalafayaBot, Radagast83, Igor Markov, Kvng, Lenoxus, Cyborgelph, Grahamec, Kubanczyk, Meredyth, David gv ray, Mange01,
Lights, 28bytes, TXiKiBoT, Tfdb, ClueBot, Fyyer, SchreiberBike, WikHead, Dgtsyb, Leszek Jaczuk, Legobot, Yobot, Erik9bot, Truth
through the lense, Sae1962, , Jandalhandler, DASHBot, EmausBot, ClueBot NG, Widr, Baby' qiRl 03, UAwiki, Cqdx, ProtossPylon,
Mohamed-Ahmed-FG, GreenC bot, Bender the Bot and Anonymous: 49
Multiple frequency-shift keying Source: https://en.wikipedia.org/wiki/Multiple_frequency-shift_keying?oldid=737858325 Contributors: Glenn, Merovingian, DavidCary, Karn, Frencheigh, Sonett72, One-dimensional Tangent, Smalljim, Eyreland, Graham87, Phatmonkey, Brandon, NielsenGW, SmackBot, John Lunney, Oli Filth, Adamantios, Dicklyon, Tawkerbot2, Lovibond, Jim.henderson, R'n'B, CommonsDelinker, AlleborgoBot, Thunderbird2, KathrynLybarger, Sv1xv, Addbot, DOI bot, Vyom25, Lightbot, Citation bot, Omnipaedista,
MastiBot, Jonkerz, Dcirovic, Secret ant, H3llBot, Cyberbot II, Ajv39, 32RB17, Monkbot, GreenC bot and Anonymous: 17
Dual-tone multi-frequency signaling Source: https://en.wikipedia.org/wiki/Dual-tone_multi-frequency_signaling?oldid=751207738
Contributors: Damian Yerrick, AxelBoldt, Derek Ross, WojPob, The Anome, Aldie, PierreAbbat, Ray Van De Walker, Maury Markowitz,
GrahamN, Michael Hardy, Mahjongg, Karada, Minesweeper, Ahoerstemeier, Rboatright, Alex756, Chuljin, Timc, Radiojon, Joy, Bloodshedder, AnonMoos, Denelson83, Rfc1394, Litefantastic, Auric, Xanzzibar, DocWatson42, Frencheigh, Chowbok, Beland, DragonySixtyseven, Betaguy9000, Finog, Chmod007, Davidbod, JTN, Discospinster, Xezbeth, Dmeranda, Brian0918, Femto, Bobo192, Guido
del Confuso, Celada, HasharBot~enwiki, Shawn K. Quinn, Arthena, Ricky81682, Raymond, RoySmith, ProhibitOnions, Cburnett, Gene
Nygaard, Klparrot, Martian, Alvis, Woohookitty, Borb, Pol098, Plaws, Graham87, BD2412, Vegaswikian, FlaBot, Mrschimpf, YurikBot,
Hairy Dude, RussBot, Alyourpal, Hellbus, Hydrargyrum, Bovineone, NormanGray, Mysid, Elkman, Codell, Closedmouth, David Jordan,
Wrobertson, SmackBot, Avanatt, KelleyCook, Jory, Jibjibjib, Optikos, Kurykh, Oli Filth, MartynDavies, Lexlex, Samanathon, Dethme0w,
Jwilkers, Mshook, Redhatter, JanCeuleers, PetesGuide, NickPenguin, Stepheneming, Mike Richardson, ManiacK, Tomhubbard, Dicklyon, Interlingua, Hu12, FairuseBot, Paulmlieberman, Ale jrb, Charles dye, MeekMark, Sahrin, Thijs!bot, Headbomb, Smsmith0223,
Kainino, Harryzilber, Greensburger, Jahoe, VoABot II, Xb2u7Zjzc32, Upholder, ChrisSmol, J. D. Pfa, LorenzoB, Jim.henderson, Glrx,
R'n'B, JonnyH, Piercetheorganist, Barts1a, Zedmelon, Atropos235, RoseTech, TXiKiBoT, DISEman, Rei-bot, Don4of4, Zep-45, Nicodeamuz, Madhero88, Scottywong, Kbrose, BotMultichill, Jan Nilsen, D4 user, Crimethinker, Svick, ClueBot, Logicaluser, Uncle Milty, Adrian
dakota, Northernhenge, LevelTubes, Johnuniq, Dgtsyb, Sweetpoet, Lost on Belmont, Arbitrarily0, Legobot, Yobot, Fraggle81, Citation bot,
Xqbot, An805Guy, Capricorn42, Sampayu, Drkossvet, Some standardized rigour, FrescoBot, Mistakender, Tinton5, Tim1357, Jptmoore,
Tokaino, NameIsRon, Rkbowen, DASHBot, EmausBot, WikitanvirBot, Jim Barry, F, Dolovis, Askedonty, S1312, TheUberOverLord,
Abo rao3a, Petrb, ClueBot NG, Lyla1205, Widr, Lincoln Josh, Danielraerty, 23W, ChrisGualtieri, Jamesmcmahon0, Rajdiplaha, Osbournehutch, wpeditcc, , NgYShung and Anonymous: 179
On-o keying Source: https://en.wikipedia.org/wiki/On-off_keying?oldid=744223275 Contributors: The Anome, Glenn, IceKarma, Simon South, Frodet, The RedBurn, BD2412, FlaBot, Mirror Vax, Srleer, Jpkotta, GSchjetne, Daedalus-Prime, McNeight, Nbarth,
Dicklyon, Flowerpotman, Nikevich, Mange01, Daisydaisy, Stoneygirl45, Addbot, Luckas-bot, AnomieBOT, Ciudadano001, Nasa-verve,
Surv1v4l1st, Zero Thrust, , Heywood J2, ChuispastonBot, 28bot, Berberisb, Helpful Pixie Bot, Mmahdim, Nitinpawade5,
CyanoTex, The Voidwalker and Anonymous: 11
8VSB Source: https://en.wikipedia.org/wiki/8VSB?oldid=737009019 Contributors: Bryan Derksen, Maury Markowitz, David Martland,
Angela, Rossami, Mulad, Radiojon, Riddley, Robbot, Karn, Markus Kuhn, Wmahan, Guanabot, Evice, Cmdrjameson, Guy Harris, Algocu,
GregorB, Eyreland, Mulligatawny, Rjwilmsi, Alan J Shea, Srleer, Nick, Voidxor, SmackBot, Nsayer, KelleyCook, Farry, Microfrost,
Metageek, Notmicro, Jesse Viviano, Smallpond, Jimj wpg, Acug, KJRehberg, Justin Z, Mange01, Funandtrvl, Joeinwap, Mezzaluna, Lightbot, Legobot, AnomieBOT, Drilnoth, Stairstep24, RjwilmsiBot, DASHBot, SlowByte, Dondervogel 2, Floatjon, Frosty, Nicceg, GreenC
bot and Anonymous: 49

594

CHAPTER 132. MORSE CODE

Polar modulation Source: https://en.wikipedia.org/wiki/Polar_modulation?oldid=726487750 Contributors: DavidCary, Gene Nygaard,

Dtwitkowski, SmackBot, Bluebot, Nbarth, Bob K, Ttiotsw, Mange01, Aeris-chan, Dewritech, Jakuzem, Hmainsbot1 and Anonymous: 6
Continuous phase modulation Source: https://en.wikipedia.org/wiki/Continuous_phase_modulation?oldid=695807066 Contributors:
Piels, DavidCary, Xezbeth, Superninja, Slambo, Cburnett, BD2412, SmackBot, Sam8, Chris the speller, Bluebot, Can't sleep, clown will eat
me, Kvng, Dawnseeker2000, Jim.henderson, R'n'B, Mange01, SchreiberBike, Addbot, Gsmcoupe, Xqbot, Omnipaedista and Anonymous:
14
Minimum-shift keying Source: https://en.wikipedia.org/wiki/Minimum-shift_keying?oldid=738064454 Contributors: The Anome,
Glenn, Munford, Piels, DavidCary, Karn, One-dimensional Tangent, Atlant, Eyreland, BD2412, Alejo2083, SmackBot, Oli Filth, TripleF,
Memming, Radagast83, Dicklyon, Kvng, Glrx, Mange01, Rod57, AntiSpamBot, The Original Wildbear, Serrano24, Jamelan, Mild Bill
Hiccup, WikHead, Addbot, Braithwa, Gsmcoupe, Rswanca, Ciudadano001, Doojsdad, Omnipaedista, FrescoBot, 2A4Fh56OSA, Mir09,
GoingBatty, ClueBot NG, LaurentianShield, YiFeiBot, Ericcc65, MSheshera, MitchRandall and Anonymous: 47
Orthogonal frequency-division multiplexing Source: https://en.wikipedia.org/wiki/Orthogonal_frequency-division_multiplexing?
oldid=750201537 Contributors: The Anome, Malcolm Farmer, Ray Van De Walker, DrBob, Edward, David Martland, Nixdorf, Deadstar, Gbleem, Spliced, Ronz, Glenn, Mulad, Wik, Zoicon5, Omegatron, Rohan Jayasekera, Mordomo, JorgeGG, Denelson83, Pakcw,
Giftlite, Ryanrs, DavidCary, Ssd, Niteowlneils, Leonard G., Zoney, Rchandra, Bobblewik, Tagishsimon, Neilc, Utcursch, Pearcedh, Thincat, Shotwell, Brianhe, Unixplumber, R6144, Flynns32547, Flib0, Lankiveil, Sietse Snel, Narym~enwiki, Bastique, Oyz, Giraedata,
Podo, Towel401, Japsu, Guy Harris, Andrew Gray, Jiing, Mavros, Garzo, Brholden, ReubenGarrett, Algocu, Ceyockey, Timharwoodx,
Tabletop, Yueh, Eyreland, Plrk, BD2412, Mulligatawny, Josh Parris, Rjwilmsi, Gamesmasterg9, Pessi~enwiki, Vegaswikian, SystemBuilder, Alejo2083, FlaBot, Ian Pitchford, Lmatt, Nehalem, 121a0012, Bgwhite, YurikBot, Borgx, RobotE, MMuzammils, Bhny, Stewartjohnson, Stephenb, Gaius Cornelius, Txuspe, ENeville, Net~enwiki, Nad, Thiseye, Debot~enwiki, Diotti, Valkyra3~enwiki, Voidxor,
Ma3nocum, Mysid, Plamka, Petri Krohn, Phil Holmes, Whaa?, Rathfelder, Gavinito, Jkpjkp, Ctut, SmackBot, Estoy Aqu, KelleyCook,
Lindosland, Chris the speller, Kurykh, Coinchon, Parkamark, Oli Filth, Russvdw, Krallja, Southcaltree, Cantalamessa, Steveo1544, BevanFindlay, FilippoSidoti, Palopt, The2ndood, Dicklyon, Koweja, Kvng, Hu12, JoeBot, Paul Foxworthy, GDallimore, CmdrObot, Originofsymmetry, Chrumps, Loopkid, Wattyirl, Requestion, Meowsqueak, Kumar Appaiah, Equendil, Tsenapathy, Jamie Lokier, Djg2006, Gogo
Dodo, NigelKing, Dleeper47, Dbraun1234, Thijs!bot, Barticus88, Sagaciousuk, Electron9, Hcobb, OrenBochman, Dawnseeker2000, WinBot, Widefox, Abram1977~enwiki, Maksud, Mlcastellanos, JAnDbot, Helcat, Nikevich, KJRehberg, SandStone, Retroneo, Yawe, Conquerist, Zzdario, Dima373, Jim.henderson, R'n'B, J.delanoy, Mange01, Ironphoenix, Uncle Dick, Cupid143, JA.Davidson, Titeuf~enwiki,
Digitalradiotech, Mathuranathan, Llorenzi, Funandtrvl, Sam Blacketer, VolkovBot, ABF, Vrac, Alinja, C3stlavi3, Rsteinmetz, Jpat34721,
Heegard, Azimout, AlleborgoBot, Thunderbird2, Vswrman, Leon.debruxelles, Jedufa, MC-CDMA, SieBot, VVVBot, Figomac, Avnjay,
Nuttycoconut, Lightmouse, Galoiserdos, Anchor Link Bot, TreeSmiler, Tuxa, ClueBot, Aquegg, Snigbrook, The Thing That Should Not
Be, Jstarr, Fakahi, Niceguyedc, Mel aad, Rcooley~enwiki, Sun Creator, BOTarate, Stlman, DumZiBoT, XLinkBot, Dthomsen8, RyanCross, Addbot, Shafqatz, MrOllie, Download, RTG, Glane23, Waveletrules, Tide rolls, Rjaf29, OlEnglish, AntiWhilst, Luckas-bot, Yobot,
Colin R Wright, AnomieBOT, Wikisire, Materialscientist, ArthurBot, Xqbot, , Evandroroncatto, Miym, J04n, RibotBOT, Kyng, FrescoBot, Nageh, W Nowicki, Itusg15q4user, Bsuperkid, Misumi~enwiki, Netcruise, Raul lacerda, Pmokeefe, Fentlehan, Jujutacular, Fulldate unlinking bot, Trappist the monk, Cyberwizzard, RjwilmsiBot, EmausBot, John of Reading, WikitanvirBot, Wikfr, Mankomal, Wiki
contributor 21, Patchingwiki, Ivanpeter5o, ClueBot NG, Helpful Pixie Bot, Ejder.bastug, KLBot2, BG19bot, Mark Arsten, Caypartisbot,
BattyBot, User 99 119, Lee yunjong, Captain Conundrum, LCS check, Techeditor001, Pravindrakumar iit, Stamptrader, CrasherX, Gspatwardhan, Melcous, Monkbot, ErRied, Plarry87, Jstevenson32, Rubbish computer, Teowey, Rfwireless, InternetArchiveBot, GreenC bot,
Bender the Bot and Anonymous: 382
Wavelet modulation Source: https://en.wikipedia.org/wiki/Wavelet_modulation?oldid=715588570 Contributors: Glenn, AJR, Majromax, Brandon, SmackBot, Wundermac, Dabis~enwiki, Alaibot, Magioladitis, Hmo, Mange01, Erik9bot, EmausBot, Bulwersator, Dexbot,
CLCStudent and Anonymous: 4
Trellis modulation Source: https://en.wikipedia.org/wiki/Trellis_modulation?oldid=735663611 Contributors: AxelBoldt, Maury
Markowitz, Waveguy, Omegatron, Raul654, RobertYu, Finn-Zoltan, Bobblewik, Yayay, Forbsey, Jheald, Teque5, Jamsignal, Ian Pitchford,
Crazycomputers, Ewlyahoocom, Gaius Cornelius, Voidxor, Bruyninc~enwiki, Marra, SmackBot, Oli Filth, Jlpayton, Spiritia, Cydebot, Invitatious, Arch dude, Nikevich, Conquerist, Mange01, Lights, VolkovBot, Theaveng, Unbuttered Parsnip, Mumiemonstret, SchreiberBike,
Asafshelly, EEng, Addbot, Lightbot, AnomieBOT, Xqbot, Isheden, BenzolBot, PigFlu Oink, Full-date unlinking bot, Trappist the monk,
Abckookooman, WikitanvirBot, DnaX, Ramjar, Mikhail Ryazanov, ClueBot NG, Snotbot, ChrisGualtieri, The Quirky Kitty, FrigidNinja,
Comp.arch, Hampton11235 and Anonymous: 25
Spread spectrum Source: https://en.wikipedia.org/wiki/Spread_spectrum?oldid=751310866 Contributors: Europrobe, Heron, Michael
Hardy, Gbleem, Rossami, Samw, Novum, Dying, Patrick0Moran, Omegatron, Twice25, Fredrik, Merovingian, Giftlite, DavidCary,
Curps, Ssd, HorsePunchKid, N328KF, R6144, Wk muriithi, Bobo192, Johnteslade, Savvo, AndrewRH, Photonique, Carr, EvanGrim,
Jiing, Rabarberski, Schapel, Carlos Quesada, Algocu, Martian, Cryo~enwiki, Vndas, Ae7ux, Snaekid, Orangehatbrune, Vegaswikian,
Nneonneo, Heptor, King of Hearts, Roboto de Ajvol, YurikBot, Ksyrie, MonMan, Brandon, Shot, Arastcp, RUL3R, Asbl, Hobit, Deville, Closedmouth, Rdschwarz, SmackBot, Folajimi, Kmarinas86, QEDquid, Snori, Oli Filth, Roya ALkamil, Droll, Torzsmokus, TripleF,
Royboycrashfan, Bentobias, Adamantios, Easwarno1, Wuzzy, The PIPE, TJJFV, Lambiam, Kevin k, MonsieurET, Dicklyon, Dammit,
Clocker, Chetvorno, Eastlaw, JohnTechnologist, Requestion, W.F.Galway, Rwalters, Mjmarcus, Martin Hogbin, Rotundo, Widefox, Tjmayerinsf, Darklilac, Harryzilber, WordSurd, CosineKitty, Lawilkin, Jim.henderson, R'n'B, Haner, Mange01, Tarotcards, Fountains of
Bryn Mawr, STBotD, Idioma-bot, GLPeterson, Rei-bot, Mistman123, Modal Jig, Calibann, Mr. PIM, The Random Editor, Bfpage, Nihil
novi, Hertz1888, Miniapolis, Scottpett, Goodone121, Professor Jim Bob, Jonverve, Siberx, Vybr8, Kornjaca, Rror, Dthomsen8, Pgallert,
SilvonenBot, Addbot, Debresser, Numbo3-bot, OlEnglish, Luckas-bot, Yobot, Ptbotgourou, AnomieBOT, Sunlight123, Jim1138, Unara,
The High Fin Sperm Whale, Srwalden, Nasa-verve, Dead Mary, GWS EE, Ralphmrm1, Chenopodiaceous, PrincessofLlyr, Jonesey95,
Aliottaj, EmausBot, Orphan Wiki, Raj kariya, F, ClueBot NG, MKA667, Widr, Twoborg, Helpful Pixie Bot, BG19bot, Charon77, Bondaruk85, Srinathkr3, Aous.younis, Klilidiplomus, Thorachu, Lugia2453, Franois Robere, Ginsuloft, Ashwini27031991, Aro88, Thethumb
and Anonymous: 146
Direct-sequence spread spectrum Source: https://en.wikipedia.org/wiki/Direct-sequence_spread_spectrum?oldid=748944584 Contributors: PierreAbbat, Europrobe, Waveguy, Heron, Glenn, Charles Matthews, Omegatron, Karn, Rchandra, Udo.bellack, Cihan, DmitryKo,
Ste~enwiki, Kms, MarkWahl, Jiing, Carlos Quesada, MIT Trekkie, Algocu, Kelly Martin, FlaBot, FrancisDrake, YurikBot, Mikeblas,
Bota47, Rdschwarz, Liquidcable, KelleyCook, Vassgergely, Trebor, Agateller, Oli Filth, Fredvanner, Chlewbot, Richard0612, Breno, Dr
Greg, Kvng, TherstM, Esposimi, Eastlaw, Kansas Sam, Msebast~enwiki, Thijs!bot, Dawnseeker2000, CosineKitty, Utilitysupplies, DAGwyn, Jim.henderson, Lihui912, Mange01, Cspan64, TXiKiBoT, BwDraco, Vitz-RS, Amerkn, Vsabio, Paul Ashcroft, Suradnik13, Jonverve,

132.11. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

595

Addbot, Fgnievinski, Jamesinc87, Luckas-bot, Yobot, Ptbotgourou, Mmxx, AnomieBOT, Materialscientist, Xqbot, Leon3289, 10metreh,
Sideways713, Guikipedia, TeleComNasSprVen, Josve05a, Zalnas, Petrb, ClueBot NG, Fauzan,
, Mdapjack, Spyglasses, SJ Defender,
MSheshera, CV9933, AllBestFaith, Gouzmalix and Anonymous: 69
Chirp spread spectrum Source: https://en.wikipedia.org/wiki/Chirp_spread_spectrum?oldid=655010993 Contributors: Karn, Bender235, Stuartyeates, RHaworth, Physchim62, Coderzombie, SmackBot, Mcld, Georg-Johann, Legis, Dawnseeker2000, Dougher,
Jim.henderson, Funandtrvl, Lightmouse, Wdwd, Niemeyerstein en, Jonverve, Addbot, Rhoisington, Wireless friend, AnomieBOT, Kylemanel and Anonymous: 6
Frequency-hopping spread spectrum Source: https://en.wikipedia.org/wiki/Frequency-hopping_spread_spectrum?oldid=746079894
Contributors: AxelBoldt, PierreAbbat, Europrobe, Waveguy, David Martland, LenBudney, Gbleem, Qfwfq, Glenn, Technopilgrim, Radiojon, Jeq, Blainster, Anthony, DavidCary, Ssd, Gyrofrog, Sam Hocevar, ArnoldReinhold, Quistnix, Kms, MyNameIsNotBob, Guy Harris,
Wtmitchell, Stephan Leeds, Axeman89, Woohookitty, MarcelloBasie, Robert K S, Isnow, Eyreland, Graham87, Vegaswikian, FlaBot,
Ground Zero, JdforresterBot, RobyWayne, DVdm, Wavelength, Mikeblas, Cadillac, Arthur Rubin, Alain r, Eskimbot, Oli Filth, Mark7-2,
Adamc83, Nakon, Bigmantonyd, Lambiam, Krashlandon, Kuru, Optakeover, PRRfan, Ryulong, Kvng, VoxLuna, Mjmarcus, Christian75,
Thijs!bot, Dawnseeker2000, Escarbot, Widefox, Pro crast in a tor, Fritz Jrn, Dougher, .anacondabot, Nikevich, AlephGamma, Lihui912,
R'n'B, Mange01, Mojodaddy, TyrS, Arms & Hearts, Nwbeeson, Funandtrvl, Lasombra bg, Falcon8765, Nihil novi, Mwaisberg, A. Carty,
Oxymoron83, ClueBot, Binksternet, Wysprgr2005, Kingrattus, Petarpopovski, Carriearchdale, Jonverve, Kruusamgi, Addbot, Veekippedia, CarsracBot, Luckas-bot, Yobot, AnomieBOT, Unara, Materialscientist, Capricorn42, FrescoBot, Humichael, Trappist the monk, Sohaibafzal, Subsumee, EmausBot, Ajraddatz, Heracles31, Daonguyen95, Emily Jensen, ClueBot NG, LukaszKatlewa,
, Tristanseifert,
Voltaicsca, 220 of Borg, Aznkirby001, Dexbot, Nbeaver, Nhergert, Red-eyed demon, Johnls7424, Noyster, Monkbot, HMSLavender,
Fraubalance, InTheUniversal, Mariah isabella m, Dot11q and Anonymous: 118
Channel access method Source: https://en.wikipedia.org/wiki/Channel_access_method?oldid=747987731 Contributors: AxelBoldt, Palfrey, Radiojon, Robbot, Tea2min, Everyking, Tagishsimon, MementoVivere, Casey Abell, Ewlyahoocom, Intgr, RussBot, Splash,
Net~enwiki, Welsh, Brandon, Deville, Extraordinary, SmackBot, Snori, Robosh, Morten, Slakr, Kvng, Elinav, Danhannan, Cydebot,
Mblumber, Travelbird, Qwyrxian, Opare, Dawnseeker2000, Harryzilber, Jim.henderson, Lihui912, R'n'B, Mange01, Mojodaddy, VitzRS, AlleborgoBot, Kbrose, Malcolmxl5, Muhandes, Estirabot, Sun Creator, InternetMeme, Tprentice, Addbot, Paddor~enwiki, Wireless
friend, Biezl, Piano non troppo, LilHelpa, Xqbot, Jhbdel, FrescoBot, Itusg15q4user, BenzolBot, Pinethicket, Orenburg1, , ClueBot
NG, Helpful Pixie Bot, K.e.elsayed, Flat Out, Johnbwaterhole, Burgessbrian88, Bender the Bot and Anonymous: 56
Multi-carrier code division multiple access Source: https://en.wikipedia.org/wiki/Multi-carrier_code_division_multiple_access?oldid=
745495160 Contributors: Jitse Niesen, Giftlite, Rich Farmbrough, R6144, Chbarts, Gene Nygaard, Vegaswikian, Gaius Cornelius, Rbarreira, Nuwankumara, Bluebot, Thiagomacieira, Alaibot, Wikih 66, Widefox, Hbent, Mange01, Mojodaddy, Digitalradiotech, Linnartz,
MC-CDMA, Flyer22 Reborn, Editore99, Jonverve, BG19bot, Greg.warnes, Hafsa1982, ABDELFATTAH Amr and Anonymous: 8
Orthogonal frequency-division multiple access Source: https://en.wikipedia.org/wiki/Orthogonal_frequency-division_multiple_access?
oldid=752252675 Contributors: Ryuch, Vipintm, R6144, Neonumbers, Jiing, Kenyon, Mud4t, Frv, Nevsan, SmackBot, Jupix, Bluebot,
Oli Filth, Lloyd Wood, FilippoSidoti, Harryboyles, Jwyrwas, Kvng, Gnfnrf, Xwas, Dawnseeker2000, Loveshack1, Kgeischmann, Lihui912, Mange01, Mojodaddy, Hgmyung, Chenzw, M7ammad, MC-CDMA, NPalmius, Ariksa, Subrawiki, Mustafaerg, Estirabot, Muro
Bot, BOTarate, Addbot, DOI bot, LaaknorBot, Luckas-bot, Yobot, AnomieBOT, Materialscientist, Citation bot, Xqbot, Omnipaedista,
RibotBOT, Nageh, Trappist the monk, Chronulator, DuineSidhe, Dmw3580, EmausBot, John of Reading, Gdcastel, Wikfr, ClueBot NG,
KLBot2, Mehdi111111, Mypslim, Borishill, Water tends, LCS check, Melcous, Monkbot, Rfwireless, InternetArchiveBot and Anonymous:
52
Class-D amplier Source: https://en.wikipedia.org/wiki/Class-D_amplifier?oldid=745834352 Contributors: Omegatron, Cholling,
Rchandra, Bobblewik, MacGyverMagic, Imroy, TedPavlic, Pjacobi, Aaronbrick, Richi, Giraedata, Hooperbloob, Dtcdthingy, Lkinkade,
BD2412, Vegaswikian, Ian Pitchford, WriterHound, Koeyahoo, Rohitbd, Light current, Majoran~enwiki, That Guy, From That Show!,
SmackBot, Steve carlson, Javalenok, Frap, Je DLB, Radagast83, CyrilB, Rogerbrent, Dicklyon, OnBeyondZebrax, Chetvorno, Esobocinski, CmdrObot, Dycedarg, Rsutherland, HermanFinster, FrederikSchack, Mbell, Electron9, Nick Number, Alphachimpbot, Verkhovensky,
Carl0s, Gwern, Read-write-services, Nalorin, Janislaw, Homer Landskirty, Audiosh, Joeinwap, Nburden, HiraV, Andy Dingley, Peter
Karam, Jdaloner, PabloStraub, Trojancowboy, Binksternet, GreenSpigot, Cyrilgermond~enwiki, Tommyo333, Thom Delaney, Johnuniq,
MarmotteNZ, Addbot, Robert.Harker, Numbo3-bot, Luckas-bot, Yobot, B137, Xqbot, GrouchoBot, FengRail, BenzolBot, Kgynkisd,
Orenburg1, Rockermatc, Rpulham, Classedhaie, Wheelerdealer55, ClueBot NG, David C Bailey, Ontist, Sonic7406, Widr, Da5id403,
D.plomat, Bgoswami2k1, Easleydp, MPuhakka, Kogmaw, JaconaFrere, Patient Zero, MikeSynnott, Viam Ferream, CAPTAIN RAJU and
Anonymous: 111
RF power amplier Source: https://en.wikipedia.org/wiki/RF_power_amplifier?oldid=749312030 Contributors: Glenn, Carlossuarez46,
Trevj, Guthrie, GregorB, BD2412, Brandon, SmackBot, Tom Lougheed, Paxse, Kharker, Can't sleep, clown will eat me, Dicklyon, Kvng,
Dlohcierekim, Picaroon, MarshBot, Widefox, CosineKitty, Askari Mark, Swpb, Heyyotyson, Jim.henderson, Glrx, ICE77, LeaveSleaves,
Logan, Biscuittin, Bozafaca, TypoBoy, Addbot, Mortense, Yobot, AnomieBOT, Materialscientist, Deepak K Sharma, Fumitol, Mean as
custard, Sinestro322, K6ka, Ebrambot, DPL bot, Reatlas, JaconaFrere, GeorgeV73GT, SageGreenRider and Anonymous: 27
Code division multiple access Source: https://en.wikipedia.org/wiki/Code_division_multiple_access?oldid=749265449 Contributors:
Mav, Maury Markowitz, Edward, Michael Hardy, Goatasaur, Ahoerstemeier, Ronz, Jpatokal, Salsa Shark, Ka9q, Kaihsu, Dysprosia, Andrewman327, Furrykef, Thue, Hemanshu, Baloo rch, Hadal, Eliashedberg, Dave6, Giftlite, BenFrantzDale, Fleminra, Goofrider, Bookcat,
Pgan002, Beland, OverlordQ, Oneiros, Yohsuke, Canterbury Tail, Mike Rosoft, Markalex, Mormegil, Rich Farmbrough, Sladen, Pak21,
Wk muriithi, Pavel Vozenilek, Gauge, Lankiveil, Art LaPella, .:Ajvol:., A-Day, Citruswinter, Sasquatch, Ascheinberg, Towel401, Vanished user lkjsdkf34ij48fjhk4, Apatterno, Guy Harris, Jiing, Wdfarmer, VladimirKorablin, BRW, Cburnett, Dan100, Hyfen, Tournesol,
Toyoda, Poppafuze, Eras-mus, Sega381, Graham87, Kbdank71, FreplySpang, Dananderson, Rjwilmsi, Lars T., Jake Wartenberg, Golden
Eternity, HappyCamper, Ligulem, Brighterorange, Makru, SystemBuilder, Alejo2083, FlaBot, Gurch, Fresheneesz, Pevernagie, Kbrams,
Srleer, Chobot, Bgwhite, Gridlock Joe, Sparky132, DanMS, CambridgeBayWeather, Grafen, Dugosz, MonMan, Thiseye, PrologFan,
Zwobot, BOT-Superzerocool, Asbl, Zzuuzz, Wsiegmund, Chriswaterguy, Kevin, Rdschwarz, Whaa?, Erudy, Jarrodchambers, Shepard,
PeterBrett, KnightRider~enwiki, SmackBot, Jasonuhl, Prodego, Deon Steyn, Wjmallard, ProveIt, Relaxing, Unforgettableid, Gilliam, Eug,
Desonia, Hugo-cs, Thumperward, Oli Filth, Repetition, DHN-bot~enwiki, Glloq, JonHarder, Nakon, DylanW, Kuru, Ocee, Ksn, Dicklyon, Mariersteve, LPH, Aditi.nsit, George100, JohnTechnologist, Errandir, Requestion, Cydebot, Mblumber, Christian75, Starionwolf,
Ameliorate!, Kozuch, Omicronpersei8, TAG.Odessa, Wernight, DmitTrix, Khottorp, Marcotulio, Qarel, Philippe, Dawnseeker2000, AntiVandalBot, Davido, Nisselua, EarthPerson, Isilanes, AlekseyFy, Storkk, Randy549, JAnDbot, PopsHunsinger, Tc-engineer, MER-C,

596

CHAPTER 132. MORSE CODE

Jonashart, Methgon, RBBrittain, Fusionmix, Malcolmst, Sanoj1234, Email4mobile, Aka042, Recurring dreams, Boob, DerHexer, JaGa,
Bayboy4, MartinBot, Mschel, Smokizzy, RockMFR, Mange01, Mojodaddy, Euku, Sigmundpetersen, P0p-s3cr37, Ellisbjohns, McSly,
GS3, Subedisan, Halmstad, Plasm980, VolkovBot, TXiKiBoT, Orie0505, BotKung, Richard Kervin, Bugone, Dirkbb, SieBot, Ytoledano,
Vijrohit, Jim77742, Sara Aab, Theaveng, Galib.cse, Dlindqui, Guycalledryan, Svick, Telecomwave, Timeastor, C0nanPayne, ClueBot,
Tamelion, Scottstensland, Mild Bill Hiccup, Vidhyardhi, DragonBot, LeoFrank, Mohit677, Pearmaster, BOTarate, Jonverve, 7, Berean
Hunter, Sylvestersteele, Samdamsam~enwiki, InternetMeme, XLinkBot, Jovianeye, WikHead, Wca08, PL290, Dsimic, Addbot, Speer320,
Some jerk on the Internet, Robaston, John Chamberlain, Download, Corey21, Marcos vicente, AndersBot, Doniago, LemmeyBOT, Semiwiki, Tavenger5, Cjerrells, Legobot, , The.Nth, Yobot, Tohd8BohaithuGh1, Ptbotgourou, THEN WHO WAS PHONE?,
AnomieBOT, Materialscientist, Theoprakt, Xqbot, JimVC3, TechBot, Shulini, Nasa-verve, GrouchoBot, Jhbdel, Mdhivya, Karghazini,
Mathonius, Shadowjams, Frumphammer, Dave3457, RetiredWikipedian789, GliderMaven, FrescoBot, Janolabs, PorkchopLarue, Syedkamran1988, I dream of horses, Adlerbot, Delan006, Jschnur, Cupid1889, Aoidh, The Utahraptor, RjwilmsiBot, Mield, Bento00, Hardikvasa, NerdyScienceDude, Indianw200i, EmausBot, MrFawwaz, ScottyBerg, Dcirovic, Gurmeetluvteddy, Wieralee, H3llBot, Netknowle,
Learns visits aw, John Smith 104668, ChuispastonBot, Cimp3, Shi Hou, Gwen-chan, ClueBot NG, CocuBot, Cyberbisson, Michael-stanton,
Clearlyfakeusername, Snotbot, Dan.aboimov, Vendrizi, Helpful Pixie Bot, Shlyopa, Truesnder, Your Trusted Friend In Science, Ils20,
Tetrapole, Wikih101, Raphael cendrillon, Poppopsun, Marty Crabneck, Osama7ssn, Dhani.sahani, Darth Sitges, Sandip.dalvi, Cdmaware,
Brian Giiligan, BenefactorDubsta, Supdiop, TheoriginalGeorgeW and Anonymous: 458
Software-dened radio Source: https://en.wikipedia.org/wiki/Software-defined_radio?oldid=738021161 Contributors: Derek Ross,
Nealmcb, Breakpoint, CesarB, CatherineMunro, Julesd, Glenn, Smack, Radiojon, Jeq, Bearcat, Robbot, Fredrik, Roddeg, DavidCary, Inkling, Marcika, Fleminra, Albany45, Khalid hassani, Decoy, Quadell, Mako098765, Abdull, Trevor MacInnis, D6, N328KF,
Pmsyyz, ArnoldReinhold, Ht1848, CanisRufus, Keno, Nigelj, MaxHund, AndrewRH, Hooperbloob, Wendell, DrDeke, Garzo, Notjim,
MIT Trekkie, BryanHolland, Armando, Je3000, Tmassey, Rjwilmsi, Pdelong, Vegaswikian, Jehochman, LjL, Krash, The wub, WriterHound, YurikBot, Wierdy1024, Hydrargyrum, Albedo, Brandon, Mikeblas, Voidxor, Mysid, Ninly, Mark hermeling, SmackBot, Bggoldie~enwiki, KD5TVI, Kharker, Thumperward, IanBailey, WikiFlier, Modest Genius, Frap, Rhodesh, Zkac050, Metageek, G-J, Romanski, A5b, Vina-iwbot~enwiki, Superdosh, Feedme, Dicklyon, DabMachine, Jerrybtaylor, Iridescent, CapitalR, Balexis~enwiki, CmdrObot,
Requestion, Joelholdsworth, Inzy, Cydebot, Rwmcgwier, Mike65535, Urlass, Kozuch, Leendert, BetacommandBot, Mattisse, Thijs!bot,
N5iln, Grange65, Electron9, Rfrtxs, Hcobb, Dawnseeker2000, JurgenG, STK~enwiki, Spencer, DOSGuy, Jahoe, Sanoj1234, Buckshot06,
DerHexer, G1MFG, Jim.henderson, Glrx, Blubber2, EdBever, Mojodaddy, MooresLaw, Ptsullivan79, Rjf ie, Warut, Whitethunder79, Mister Pe, Jennifersteinberg, VolkovBot, TXiKiBoT, The Original Wildbear, Jpat34721, Viridiangold, Turletti, Hertz1888, Triwbe, Mmuckfr,
Sphilbrick, The Thing That Should Not Be, R in remacr, HughesLAWBL, Sv1xv, Mumiemonstret, Ik2wqi, Versus22, DumZiBoT, N5ac,
XLinkBot, Roxy the dog, Ariconte, Dsimic, Tommy spumoni, Addbot, Fgnievinski, Bfallik, Fditore, Lightbot, Loupeter, Legobot, Yobot,
Redcrown01, AnomieBOT, VeroAraujo, Adam Zbransk, Simon the Likable, Peterpan73, Xqbot, Danielcamara, JeremyTraub, SassoBot, Kmiki87, FrescoBot, Nageh, Gaborheja, Citation bot 1, Redrose64, Zyxw9875, 2A4Fh56OSA, Diannaa, Nickhacko, EmausBot,
WikitanvirBot, Sgemeny, Noah976, Wingman4l7, Lokpest, Laid2, SBaker43, Circuit hacker, Cainwil7, ClueBot NG, Chester Markel,
Sonic7406, Amr.rs, Helpful Pixie Bot, Peter Wisner, Ejder.bastug, Titodutta, Wbm1058, BG19bot, Jor.langneh, BattyBot, BobDohse,
Joeinwiki, Benoit Fricaudet, Elliot530, Akhil Lawrence, ArtfulDodger42, AusTechEditor, Monkbot, Engineering Physicist Martin, Delar303, Berteged, KasparBot, NgYShung and Anonymous: 205
Cognitive radio Source: https://en.wikipedia.org/wiki/Cognitive_radio?oldid=750972463 Contributors: Michael Hardy, Ronz, Julesd,
Jerey Smith, Omegatron, Joy, Bearcat, Auric, Unfree, DavidCary, Mboverload, Wipe, John Vandenberg, Voxadam, Armando, Kgrr,
Rjwilmsi, Vegaswikian, Ian Pitchford, Gurch, RobyWayne, Splash, Idfubar, Przemyslaw Pawelczak, Allens, Honamos, SmackBot, KelleyCook, Chris the speller, Bluebot, Oli Filth, JonHarder, G-J, JoeBot, Harej bot, Requestion, Vprasad, A n k u r, Aray, Dawnseeker2000,
AntiVandalBot, Smartantennas, Prolog, Magioladitis, DerHexer, EdBever, Wadiogeek, Mange01, Alan381, Maxim, Inductiveload, Azimout, Derek96969, Jamessungjin.kim, Akai945, Bentogoa, Flyer22 Reborn, Tiptoety, Miniapolis, JL-Bot, Kl4m, Auntof6, Alexbot,
Mlas, DumZiBoT, XLinkBot, Addbot, Fluernutter, LaaknorBot, Ettrig, Yobot, AnomieBOT, Whitespacespectrum, Jmjornet, TechBot,
Shulini, Truguers, GrouchoBot, FrescoBot, Oita2001, Citation bot 1, Je monster, Sambarutan, BRUTE, Samedina, Cristeab, Trappist the
monk, Chronulator, RjwilmsiBot, WikitanvirBot, AManWithNoPlan, CoralUser, ChuispastonBot, ClueBot NG, Vaclav1~enwiki, WW82,
Emailrag, Amedeisis, BG19bot, BattyBot, Cyberbot II, ChrisGualtieri, Feirichardyu, Wirelessfan, Shashenka, Dexbot, Me, Myself, and
I are Here, Mark viking, Schwigi, Cable97, Shjjj, FBAsia, DrBoris1, Youmeng19910821, Andmariani, Vahid.Esmaeelzadeh, Ncasale,
GreenC bot, Mathematicalice and Anonymous: 102
Manchester code Source: https://en.wikipedia.org/wiki/Manchester_code?oldid=735264892 Contributors: The Anome, Maury
Markowitz, Michael Hardy, Julesd, AugPi, Oakad, Magnus.de, Dysprosia, Saltine, Itai, Omegatron, Ktims, R3m0t, DavidCary, Nadavspi, BenFrantzDale, Simson~enwiki, Boism, Trevor MacInnis, Natrij, ESkog, Plugwash, Billlion, Foobaz, Gargaj, Oz1cz, Caesura,
Voxadam, Ilario, Jake Wartenberg, FayssalF, Chobot, Aluvus, CecilWard, Dibujon, Frv, Deville, SmackBot, Mauls, Gilliam, Bluebot, Oli Filth, Nbarth, Nakon, Wirbelwind, ILike2BeAnonymous, Titaniumcranium, Bjankuloski06en~enwiki, MarkSutton, Dicklyon,
Optakeover, Kvng, Rfwebster, Cxw, Loopkid, Lo2u, Mbell, Michagal, Pjvpjv, Invitatious, Pikachy, JAnDbot, CosineKitty, Dilane, Cpl
Syx, Matt B., CommonsDelinker, Palomdude, HEL, Javawizard, Asymmetric, Dattasubramanya, Duncan.Hull, Spinningspark, SieBot,
Mustafaturan~enwiki, Smithderek2000, Mike Shepherd, Tombomp, PipepBot, The Thing That Should Not Be, IlliniFlag, Ali Esfandiari,
Addbot, Jojhutton, Fgnievinski, Download, Tide rolls, Luckas-bot, Yobot, Simard, II MusLiM HyBRiD II, Crispmuncher, AnomieBOT,
Ciudadano001, Citation bot, DynamoDegsy, ArthurBot, Xqbot, Nasa-verve, Jangirke, PikkuHiirri98, I dream of horses, RjwilmsiBot,
EmausBot, 2nd47, ClueBot NG, Widr, Nen, Snow Blizzard, Mrt3366, Dexbot, SoledadKabocha and Anonymous: 91
Non-return-to-zero Source: https://en.wikipedia.org/wiki/Non-return-to-zero?oldid=748344503 Contributors: Heron, Twilsonb, Michael
Hardy, Colin Marquardt, Itai, Omegatron, BenFrantzDale, HangingCurve, Alvestrand, Uzume, Edcolins, Justzisguy, Phe, Klemen Kocjancic, YUL89YYZ, Photonique, Frodet, Alansohn, Andrewpmk, Quuxplusone, Mancini, Chobot, YurikBot, RobotE, RussBot, Cholmes75,
Closedmouth, Cenk, Radagast83, Shushruth, Rait, Aquadisco, Dicklyon, Kvng, Rob.desbois, Pyrilium, Invitatious, Gadget1700, Jasen
betts, Alphachimpbot, JAnDbot, Xhienne, CosineKitty, Austinmurphy, A.M.R., JamesBWatson, Jim.henderson, R'n'B, Mojodaddy, JonShops, Philip Trueman, Wireless router, Jetforme, Pyker, WRK, OsamaBinLogin, Svick, ToBarc, Asafshelly, Spitre, Dsimic, Addbot,
Electron, Luckas-bot, Yobot, Jordsan, AnomieBOT, Materialscientist, Ciudadano001, Xqbot, DSisyphBot, Shulini, Nasa-verve, Jusses2,
EmausBot, Tolly4bolly, Rcsprinter123, Vladkpone, ClueBot NG, Satellizer, Eoppetit, Jimw338, AbuJazar, Deltahedron, DrBungle, Jackmcbarn, Mik81, Codedbilk3 and Anonymous: 97
Unipolar encoding Source: https://en.wikipedia.org/wiki/Unipolar_encoding?oldid=741782539 Contributors: GPHemsley, Rich Farmbrough, Antaeus Feldspar, Craigy144, Ahruman, RJFJR, Alai, Adoniscik, Welsh, Theda, Back ache, SmackBot, Nbarth, ShelfSkewed,
Pyrilium, Invitatious, VoABot II, Joeinwap, Materialscientist, Nasa-verve, Ankur140290, ClueBot NG and Anonymous: 19

132.11. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

597

Bipolar encoding Source: https://en.wikipedia.org/wiki/Bipolar_encoding?oldid=750141096 Contributors: Ktims, Giftlite, DavidCary,

DemonThing, Antaeus Feldspar, Helix84, Guy Harris, Stillnotelf, A D Monroe III, Tabletop, Schzmo, YurikBot, Mmccalpin, Moe Epsilon,
Mikeblas, Tony1, Kungfuadam, SmackBot, Radagast83, Fwaggle, Dicklyon, DabMachine, CmdrObot, Thijs!bot, Invitatious, Bellhead,
Hbent, STBot, Jim.henderson, LoopTel, Biscuittin, SieBot, Editore99, Alexbot, SilvonenBot, Kurniasan, Addbot, Electron, Luckas-bot,
Yobot, Ciudadano001, Nasa-verve, MastiBot, EmausBot, WikitanvirBot, ZroBot, Jack Greenmaven, InternetArchiveBot, GreenC bot,
Codedbilk3 and Anonymous: 29
Pulse wave Source: https://en.wikipedia.org/wiki/Pulse_wave?oldid=731602333 Contributors: Zundark, D, Bearcat, Xezbeth, Eleassar777, Davetron5000, Krishnavedala, Tole, SamuelRiv, SmackBot, Teadrinker, Amalas, Linus M., Magioladitis, Nagy, Berean Hunter,
Jewikiedit, Fgnievinski, Jncraton, Yobot, MINITEK, Erik9bot, Josve05a, WPcorrector, Khazar2, FiredanceThroughTheNight, Dough34,
DatGuy and Anonymous: 11
Discrete-time signal Source: https://en.wikipedia.org/wiki/Discrete-time_signal?oldid=732693517 Contributors: Michael Hardy, Smack,
Omegatron, Robbot, Rs2, Marius~enwiki, Fjarlq, Vina, Xezbeth, Longhair, Rbj, Cburnett, Pol098, Chobot, Krishnavedala, Bota47,
Petr.adamek, Unschool, Shoy, Bluebot, Bob K, Dreadstar, Lambiam, Dicklyon, Kvng, Walton One, Ring0, Steel1943, TXiKiBoT, Spinningspark, SieBot, Rinconsoleao, Wdwd, Artyom, Alexbot, Johnuniq, Addbot, Olli Niemitalo, Fgnievinski, AkhtaBot, Vasi, Luckas-bot,
AnomieBOT, Hamamelis, ShashClp, Duoduoduo, Soun0786, ClueBot NG, Axel.hallinder, Widr, Sourabh.khot, AK456, Tow, Radiodef,
YiFeiBot, Meteor sandwich yum, Some Gadget Geek and Anonymous: 28
Forward error correction Source: https://en.wikipedia.org/wiki/Forward_error_correction?oldid=722922772 Contributors: The Anome,
Imran, Michael Hardy, Kku, Ixfd64, Technopilgrim, Denelson83, Mjscud, DocWatson42, DavidCary, Karn, Frau Holle, Abdull, Discospinster, Rich Farmbrough, ESkog, ZeroOne, West London Dweller, MaxHund, A-Day, Jumbuck, Guy Harris, Culix, Linas, Eyreland,
BD2412, Raymond Hill, Ciroa, Rjwilmsi, Bruce1ee, Planetneutral, The Rambling Man, YurikBot, Gaius Cornelius, Bovineone, Aryaniae,
Robertvan1, SmackBot, Unyoyega, Skizzik, Bluebot, RDBrown, Oli Filth, Nbarth, Frap, Ghiraddje, Chrylis, DylanW, A5b, Ligulembot,
Novangelis, Kvng, JoeBot, Chetvorno, Ylloh, Requestion, Nilfanion, Widefox, Em3ryguy, .anacondabot, Upholder, First Harmonic, Edurant, Bugtrio, CliC, Mange01, Warut, Xavier Gir, Davecrosby uk, 28bytes, Spongecat, CanOfWorms, Cuddlyable3, Jamelan, Wykypydya, Synthebot, Yczheng, Snarkosis, Mkjo, PixelBot, Jakarr, Callinus, Subversive.sound, Addbot, Hunting dog, Arsenalboi22, Happyclayton, Legobot, Yobot, TaBOT-zerem, AnomieBOT, Xqbot, Agasta, TechBot, Isheden, Omnipaedista, Nageh, Caprisan, Itusg15q4user,
UteFan16, BenzolBot, I dream of horses, Full-date unlinking bot, EmausBot, John of Reading, Pugliavi, Dewritech, Dcirovic, Fred
Gandt, Quondum, BillHart93, Petrb, ClueBot NG, JordoCo, Curb Chain, Hartlojl, Adamroyce, Camlf, Informationist1, Alarbus, BattyBot,
Mabokham, ChrisGualtieri, Aymankamelwiki, Ajraymond, SImedioP, Snookerr, James timberly, Monkbot, Samyelgendy89, Wurtemberg
and Anonymous: 94
Pulse-amplitude modulation Source: https://en.wikipedia.org/wiki/Pulse-amplitude_modulation?oldid=746311628 Contributors:
Damian Yerrick, Derek Ross, PierreAbbat, Maury Markowitz, Michael Hardy, Kku, Ronz, Glenn, Reddi, Oakad, Giftlite, Dbenbenn, DavidCary, Bobblewik, Amitj79, Starx, Brandon.irwin, Guy Harris, Wtshymanski, Suruena, Gene Nygaard, Kanenas, YurikBot,
The1physicist, Voidxor, Fram, Mebden, SmackBot, Oli Filth, UNHchabo, L337p4wn, Uweschwoebel, Kvng, Alaibot, Electron9, Escarbot, Dcorzine, Dougher, Opello, R'n'B, Mange01, Upaplc, AlleborgoBot, Lightmouse, ImageRemovalBot, Mild Bill Hiccup, Niceguyedc,
ResidueOfDesign, PixelBot, Ra2007, Orbital fox, DumZiBoT, Life of Riley, Skarebo, MystBot, Addbot, Download, Luckas-bot, Fraggle81, C5813, Materialscientist, Xqbot, Omnipaedista, Erik9bot, 802geek, Bitlab, EmausBot, Sven Manguard, Mikhail Ryazanov, ClueBot NG, BG19bot, MusikAnimal, Chandu17 2 91, Repentsinner, Potatomeng, Jochen Burghardt, GeeF, Crystallizedcarbon, My Chemistry
romantic, Aklimaj, Alvinezonda, Akpanditji, SASANK and Anonymous: 63
Pulse-position modulation Source: https://en.wikipedia.org/wiki/Pulse-position_modulation?oldid=729556054 Contributors: Bryan
Derksen, Edward, Michael Hardy, Wapcaplet, Ronz, Snoyes, Glenn, Cimon Avaro, GRAHAMUK, DavidCary, Rchandra, Starx, Frenchwhale, Geof, RPaschotta, Interiot, Suruena, RJFJR, Rjwilmsi, YurikBot, The1physicist, SmackBot, Sam8, Chris the speller, The PIPE,
Jklin, InedibleHulk, Tawkerbot4, Aaron LUFC, Headbomb, Luna Santin, Time3000, R'n'B, AlleborgoBot, Pplecke, Oxymoron83, Bloodholds, Mild Bill Hiccup, Rippey574, Zootboy, Mythdon, Mitch Ames, Addbot, Omnipaedista, Erik9bot, FrescoBot, Obankston, John of
Reading, SlowByte, DnaX, ClueBot NG, Lyla1205, Srbullock, Ajv39, YiFeiBot, MatthieuCastet, Avinashambre and Anonymous: 40
Pulse-code modulation Source: https://en.wikipedia.org/wiki/Pulse-code_modulation?oldid=751185170 Contributors: Damian Yerrick,
Bryan Derksen, Zundark, The Anome, Ap, Amillar, Aldie, Waveguy, Mjb, Heron, Bobdobbs1723, Michael Hardy, Chris-martin, Tannin,
Ixfd64, Karada, MichaelJanich, Ahoerstemeier, Muriel Gottrop~enwiki, CatherineMunro, Kragen, Glenn, Coren, Jdstroy, Dysprosia, Furrykef, AnthonyQBachler, Lumos3, Ktims, Dittaeva, Jleedev, Giftlite, Ssd, Tom-, Matt Crypto, Adam McMaster, SWAdair, Bobblewik,
Neilc, Alexf, DRE, Mikko Paananen, Starx, Kelson, Abdull, Discospinster, Lovelac7, Khalid, Lankiveil, SickTwist, .:Ajvol:., Giraedata,
Unused0022, Mote, Gerweck, Andrewpmk, Hu, 25or6to4, MRB, Tslocum, Graham87, BD2412, SudoMonas, MordredKLB, KamasamaK,
Nneonneo, Miserlou, KirkEN, FlaBot, Margosbot~enwiki, Ewlyahoocom, Kolbasz, Sstrader, Intgr, Lmatt, GreyCat, Chobot, Bgwhite,
YurikBot, Spacepotato, Kymacpherson, RussBot, Bjoern.thalheim~enwiki, Gaius Cornelius, Retired username, Malcolma, Brandon, Shepazu, Mysid, Thetrilogy, ReCover, Deville, Pb30, Dan Kee, Dystopianray, Zvika, Emanuel.munteanu, Qoqnous, SmackBot, Haza-w, Jagged
85, Stuarta, Jcarroll, JorgePeixoto, Alias777, Jerome Charles Potts, Chendy, Kalatix, Chlewbot, Daniel.Cardenas, Vina-iwbot~enwiki,
L337p4wn, SashatoBot, IronGargoyle, Vanished user 8ij3r8jwe, Frango com Nata, Dicklyon, Kvng, Lee Carre, OnBeyondZebrax,
LethargicParasite, Shoaib Meenai, Emote, Lid2000, Lanma726, Sorn67, Mblumber, Qwyrxian, Phy1729, Escarbot, Barneyg, Prolog,
Davidbrucesmith, AlexOvShaolin, Oddity-, JAnDbot, Harryzilber, Dobbse, Asnac, Gloomba, Magioladitis, LorenzoB, Oicumayberight,
Ariel., Jim.henderson, Pharaoh of the Wizards, Alexwright, Acalamari, Dispenser, Skullers, Gerstman ny, Je G., TXiKiBoT, A4bot,
Broadbot, Nicodeamuz, Eubulides, The Seventh Taylor, VanishedUserABC, Abhishekdevra, EgbertE, SieBot, Bill Waggener, Callistussj,
Jmjanssen, Fishnet37222, ClueBot, Aquegg, Binksternet, Lawrence Cohen, Ndenison, Mild Bill Hiccup, Boing! said Zebedee, Rcooley~enwiki, SchreiberBike, ChrisHodgesUK, Rachelfenn, Ulyssix, The Zig, DumZiBoT, Stratsve, Addbot, Klane11, DOI bot, KitchM,
GyroMagician, OlEnglish, Matj Grabovsk, Luckas-bot, Yobot, OrgasGirl, Iranvijay, Nyat, Armchair info guy, Gtz, Jim1138, Sz-iwbot,
Materialscientist, Citation bot, Xqbot, Sirgorpster, Albert.guiteras, Nasa-verve, Shadowjams, Kernaazti, FrescoBot, Mfwitten, Citation
bot 1, Hondootedly, Jandalhandler, AXRL, Jfmantis, Salvio giuliano, EmausBot, Acather96, Wikipelli, Dcirovic, Kokken Tor, L Kensington, Eigenbanana, Donner60, Gmt2001, ClueBot NG, Chester Markel, Helpful Pixie Bot, IWPAG, Pfeerz, HMSSolent, BG19bot,
Klilidiplomus, Anbu121, BattyBot, Pratyya Ghosh, TheJJJunk, Jochen Burghardt, Epicgenius, Boulbik, Babitaarora, Spyglasses, YasiuMody, Monkbot, KasparBot, Eido95, GreenC bot, Elaareessex and Anonymous: 236
Dierential pulse-code modulation Source: https://en.wikipedia.org/wiki/Differential_pulse-code_modulation?oldid=732694172 Contributors: Damian Yerrick, Beland, KeithTyler, Derbeth, RHaworth, FlaBot, Lmatt, Malcolma, Rory096, Dicklyon, Kvng, Rayt~enwiki,
Jherm, Mange01, Hawk777, Wdwd, UnCatBot, MystBot, Addbot, Omnipaedista, , GenaroEnriqueMiguel, Widr, GMachine,
Temp12345789, Prof. Mc and Anonymous: 6

598

CHAPTER 132. MORSE CODE

Adaptive dierential pulse-code modulation Source: https://en.wikipedia.org/wiki/Adaptive_differential_pulse-code_modulation?

oldid=746401407 Contributors: Furrykef, Discospinster, Lmatt, Bgwhite, Dicklyon, Kvng, Thijs!bot, Pinkadelica, ClueBot, Addbot,
Vopap, Piano non troppo, Albert.guiteras, Ashematian, Trappist the monk, RjwilmsiBot, John of Reading, ZroBot, ClueBot NG, Kyonzuken, Prash317, Bender the Bot and Anonymous: 13
Delta modulation Source: https://en.wikipedia.org/wiki/Delta_modulation?oldid=742252285 Contributors: Damian Yerrick, Imran, Furrykef, Discospinster, TedPavlic, Scott5114, GregorB, Marudubshinki, Lmatt, Chobot, Krishnavedala, Hydrargyrum, Hakeem.gadi, Attilios, SmackBot, Katanzag, Gilliam, Oli Filth, EncMstr, Dicklyon, Eastlaw, Alice Mudgarden, CmdrObot, Mbell, Jim.henderson, Justin Z,
Huzzlet the bot, Mange01, Itemirus, SieBot, Caltas, Flyer22 Reborn, Oxymoron83, Pinkadelica, Mild Bill Hiccup, DragonBot, Addbot,
LatitudeBot, , KamikazeBot, Materialscientist, LilHelpa, Xqbot, GliderMaven, Vrenator, Jitendra drona, Rjabate, Rahulnairhari24, ClueBot NG, Widr, Helpful Pixie Bot, Pawan23391, Morrisrx, David.moreno72, Khazar2, RotlinkBot, Comp.arch, Shaq
Ahmad Chohan, Shwekoto and Anonymous: 62
Delta-sigma modulation Source: https://en.wikipedia.org/wiki/Delta-sigma_modulation?oldid=733924406 Contributors: Damian Yerrick, The Anome, Charles Matthews, Markhurd, Omegatron, Hankwang, DavidCary, Qdr, Jkl, Rich Farmbrough, TedPavlic, Alistair1978,
Ociallyover, Gerweck, Atlant, Jwinius, RJFJR, StradivariusTV, Bratsche, GregorB, Ketiltrout, Rjwilmsi, SchuminWeb, Chobot, Krishnavedala, 121a0012, Bgwhite, Roboto de Ajvol, YurikBot, Sanjosanjo, Gaius Cornelius, Snood1, Epugachev, Voidxor, Cojoco, Alain
r, SmackBot, Jab843, Sam8, Katanzag, MalafayaBot, Southcaltree, DHeyward, S Roper, Ohconfucius, NOW, Yates, CyrilB, Optimale,
Onionmon, Kvng, CapitalR, CmdrObot, Hanspi, Requestion, HenningThielemann, Wsmarz, Cydebot, Mblumber, DmitTrix, Edokter,
Mwarren us, Jim.henderson, Sgeo-BOT, Huzzlet the bot, Rjf ie, Bob Bermani, Lulo.it, Icarus4586, Serrano24, Lm317t, Tetvesdugo, Andy
Dingley, Mahira75249, Beetelbug, Altzinn, Denisarona, Mx. Granger, Pungbilly, Mild Bill Hiccup, Ozfest, Tchai, Theking2, Addbot,
Mortense, MrOllie, CountryBot, Margin1522, Yobot, Lanugo, Nummify, Materialscientist, Xqbot, FrescoBot, , I dream of
horses, Bappi48, GoingBatty, Dcirovic, Druzhnik, RaptureBot, Lv131, Muon, Bpromo7, Jd8837, BattyBot, Gruauder, Raj.rlb, ReidWender, Sandro cello, , Skpreddy, Nimadavidson, 2opremio, Eric Houg and Anonymous: 123
Continuously variable slope delta modulation Source: https://en.wikipedia.org/wiki/Continuously_variable_slope_delta_modulation?
oldid=737316931 Contributors: Damian Yerrick, William M. Connolley, Julesd, Charles Matthews, Topbanana, Bobblewik, Trixter,
Woohookitty, Daderot, Tole, Potterra, Stickyfox, M jurrens, Vanished user 8ij3r8jwe, CmdrObot, Pfagerburg~enwiki, Reywas92, Nick
Number, Jim.henderson, UPCMaker, RatherJovialTim, SoledadKabocha, GreenC bot and Anonymous: 14
Pulse-density modulation Source: https://en.wikipedia.org/wiki/Pulse-density_modulation?oldid=749413922 Contributors: Damian
Yerrick, Mjb, Hephaestos, Michael Hardy, Smack, Dcoetzee, Maximus Rex, Dpbsmith, DavidCary, Nunh-huh, Andux, EBB, Starx,
Jbinder, Moxfyre, TedPavlic, Kghose, Rbj, ABCD, Oleg Alexandrov, Graham87, Jengelh, Jaxl, SmackBot, Dicklyon, Reywas92, Kaldosh,
WinBot, Adavidb, Rjf ie, Xavier Gir, Ross Fraser, Serrano24, SieBot, Oxymoron83, Wdwd, Sylvain Leroux, SchreiberBike, NicholasKinar, Addbot, Chzz, Pcap, Keithbob, Xqbot, RibotBOT, MastiBot, Wsko.ko and Anonymous: 32
Morse code Source: https://en.wikipedia.org/wiki/Morse_code?oldid=752242065 Contributors: Damian Yerrick, Tobias Hoevekamp,
WojPob, Mav, Bryan Derksen, 0, The Anome, Koyaanis Qatsi, Ed Poor, Christian List, Ben-Zin~enwiki, Mjb, Heron, Arj, Xoder,
PhilipMW, Michael Hardy, Tim Starling, Ixfd64, Dcljr, Cyde, Delirium, Altailji, CruciedChrist, Gbleem, Ducker, Ahoerstemeier, Rboatright, Rossami, Kwekubo, HPA, Wfeidt, Denny, Mulad, Dysprosia, Lou Sander, Geary, Fuzheado, Bjh21, Timc, Radiojon, Furrykef,
Tero~enwiki, Omegatron, Bevo, Xyb, Topbanana, Joy, Dcsohl, Pakaran, Johnleemk, Denelson83, Phil Boswell, Robbot, Noldoaran,
Friedo, Fredrik, Chris 73, Scriptwriter, RedWolf, Altenmann, Romanm, Lowellian, YBeayf, Wikibot, Wereon, Vikreykja, Pifactorial,
Tea2min, Alan Liefting, David Gerard, Giftlite, JamesMLane, Thorne, Laudaka, Nichalp, BenFrantzDale, Lee J Haywood, Lupin, RealGrouchy, Hagedis, Karn, Ds13, Everyking, Gus Polly, Lussmu~enwiki, Ssa, Ssd, Filceolaire, Sdsher, AJim, Tom-, Macrakis, Jackol,
Pne, Bobblewik, Ragib, Celerityfm, DavidBrooks, Gazibara, Slowking Man, Sonjaaa, Cyber-It, Rdsmith4, Glogger, AndrewTheLott,
Xeroc, Jagnor, ArthurDenture, Mschlindwein, Demiurge, Lacrimosus, Grstain, ChrisRuvolo, Ultratomio, Spiko-carpediem~enwiki, Discospinster, Brianhe, PeterJerde, ArnoldReinhold, Smyth, R.123, Mani1, SpookyMulder, Bender235, ZeroOne, Kjoonlee, Violetriga,
Pt, Kwamikagami, Shanes, RoyBoy, Mdonken, Orlady, Gdt, Femto, One-dimensional Tangent, Causa sui, Bobo192, Nigelj, Vervin,
MaxHund, Elipongo, Slugguitar, Acjelen, Slambo, David Gale, MPerel, Haham hanuka, Hooperbloob, Leifern, Xideum, TobyRush,
Ranveig, Alansohn, Andrewpmk, Verdlanco, Yamla, Lectonar, Zippanova, ScooterSES, SlimVirgin, Gblaz, Bart133, DreamGuy, Wtmitchell, BRW, Wtshymanski, RainbowOfLight, John5008, Joeva3eo, DV8 2XL, Mattbrundage, Mosesofmason, Richard Weil, DrDaveHPP, Jerey O. Gustafson, Oxling, Daira Hopwood, Pol098, MONGO, Beastmaster, Rjairam, Kelisi, Frungi, Eyreland, Waldir,
Jonnabuz, CPES, Gimboid13, Essjay, Waterboy12, Palica, Kotoviski, MrSomeone, Mandarax, Kesla, RichardWeiss, Graham87, Magister Mathematicae, BD2412, Li-sung, Reisio, Josh Parris, Ketiltrout, Rjwilmsi, Seidenstud, Koavf, Syndicate, Binkowski, Jivecat, Leeyc0, Tangotango, Goldfndr, SMC, NeonMerlin, Bubba73, Bhadani, Dermeister, Sango123, N0YKG, FlaBot, Wars, Anonym1ty, TeaDrinker, Sderose, Vidkun, Butros, Jarubel, Chobot, DVdm, Bgwhite, YurikBot, Wavelength, Borgx, RobotE, Sceptre, Kencaesi, Kniveton, FrenchIsAwesome, Me and, Cougarwalk, Bergsten, Hydrargyrum, Akamad, Stephenb, Grubber, Gaius Cornelius, CambridgeBayWeather, Wimt, NatureBoy~enwiki, Den68cube, SEWilcoBot, Wiki alf, Astral, Kemkerj, ONEder Boy, Maikeru Go, Robchurch, Waterguy, Ke4djt, Brandon, Jpbowen, Mikeblas, Ospalh, RussHolsclaw, Scottsher, DeadEyeArrow, Jeh, Graham Jones, Nescio, Thomas
H. White, Cstaa, Poochy, Slicing, EAderhold, Blueyoshi321, Orchid Righteous, Emijrp, Sagsaw, Ninly, Zeppelin4life, Theda, Xorx,
Skittle, Yaco, PMHauge, Moomoomoo, GrinBot~enwiki, Elliskev, DVD R W, That Guy, From That Show!, Mawa, Sava chankov, Crystallina, SmackBot, MattieTK, Timrb, Mmernex, Hydrogen Iodide, Dminott, Pgk, C.Fred, Blue520, Jagged 85, Michael Dorosh, Jab843,
Xaosux, Cool3, PeterSymonds, Gilliam, Hmains, Betacommand, Skizzik, Leighklotz, LeighKlotz, Durova, KD5TVI, Chris the speller,
Bluebot, Kharker, W8IMP, Ian13, Jordanhurley, Miquonranger03, McNeight, Wtroopwept, DHN-bot~enwiki, Audriusa, Royboycrashfan,
Dethme0w, NYKevin, Chlewbot, OrphanBot, Nixeagle, Kindall, TheKMan, Rrburke, Sidious1701, Gragox, Nakon, PetesGuide, Derek R
Bullamore, Weregerbil, The PIPE, Fagstein, Pilotguy, NeoVampTrunks, Blahm, SashatoBot, EMan32x, Xdamr, Michael Thomas Ryan,
Mouse Nightshirt, Ringmaster j, Buchanan-Hermit, Minna Sora no Shita, Gahs, Peterlewis, Mr. Lefty, IronGargoyle, A. Parrot, SpecialT, Beetstra, SQGibbon, KHAAAAAAAAAAN, SlayerK, Rizome~enwiki, Warder, Es330td, Mets501, Texas Dervish, MTSbot~enwiki,
Zapvet, Twinpinesmall, Klimot, Paul Koning, Lathrop1885, Grblomerth, Wikited, Rangi42, JayHenry, Tawkerbot2, Vanisaac, Aplonis,
JForget, Dkazdan, Washi, Nczempin, MnSteve, W1tgf, Trocisp, Requestion, Moreschi, MeekMark, Smoove Z, HiFlyChick, Cydebot,
Abeg92, Future Perfect at Sunrise, Mike65535, MC10, Gogo Dodo, Palmiped, Numnuz, Tawkerbot4, Dinnerbone, Briantw, Thijs!bot,
Epbr123, Daa89563, N5iln, Mojo Hand, Berria, A3RO, LarsJensen, Siwiak, Miller17CU94, Nick Number, Big Bird, Dawnseeker2000,
Natalie Erin, Nivek1385, Escarbot, Mentisto, AntiVandalBot, Yonatan, JurgenG, Seaphoto, Czj, Doc Tropics, Sconklin, LuckyLouie,
North Shoreman, Spencer, Wolf grey, Lklundin, Ingolfson, Sluzzelin, JAnDbot, Harryzilber, MER-C, CosineKitty, Aris00, MegX, Magioladitis, Bakilas, Hkiernan, Bongwarrior, VoABot II, Nyq, Benimatt, JNW, Yakushima, Dsergeant, Doug Coldwell, Aka042, Avicennasis,
Bubba hotep, Catgut, WikiTraveller, ChrisSmol, DonVincenzo, LindaKaySmith, Glen, DerHexer, 1549bcp, Eeera, Dadrados, Hdt83,

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Evb-wiki, Spiesr, Vanished user 39948282, Pekster, Gtg204y, Zomgpwnagedeath, OmgIRox0rz, Finley Breese, Vilem l., PeaceNT, Deor,
VolkovBot, TreasuryTag, Lordmontu, Kriplozoik~enwiki, Leebo, JoeDeRose, Cullaloe, Ai4ijoel, DancingMan, Philip Trueman, TXiKiBoT, Oshwah, Erik the Red 2, Jalwikip, Muro de Aguas, Alsaf, Miranda, Spence598, Anonymous Dissident, HS2JFW, Qxz, Anna Lincoln,
Seraphim, Mars12343, Dapet123456, Wizzkid11, Liberal Classic, Ruzmutuz, Teh romaoer, Rhopkins8, GerdLivJalla, Spinningspark,
Kaori, Magiclite, Sue Rangell, AlleborgoBot, Quantpole, Aducore, EmxBot, Willy on Waterloo, Kbrose, K7DFA, SieBot, Junh1024, Tiddly Tom, WereSpielChequers, Caltas, Joeames, Happysailor, Flyer22 Reborn, Ts15210~enwiki, Oxymoron83, Nuttycoconut, KoshVorlon,
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builder211, Bludmir6, Ashur2003, Nemoanon, Lantolar, Chopper12123, Reece2305, H.dryad, GreenC bot, Bender the Bot and Anonymous: 988

132.11.2

Images

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File:2008-07-28_Mast_radiator.jpg Source: https://upload.wikimedia.org/wikipedia/commons/7/72/2008-07-28_Mast_radiator.jpg

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132.11. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

601

File:A_plus_bi.svg Source: https://upload.wikimedia.org/wikipedia/commons/5/50/A_plus_bi.svg License: CC BY-SA 4.0 Contributors:

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jpg License: Public domain Contributors: Retrieved on 7 October 2013 from <a data-x-rel='nofollow' class='external text' href='http:
//books.google.com/books?id=2RRLAAAAMAAJ,<span>,&,</span>,pg=PA14'>John Ambrose Fleming 1916 The Principles of Electric
Wave Telegraphy and Telephony, 3rd Ed., Longmans Green and Co., New York, p. 14, g. 13</a> on Google Books Original artist: John
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27s_observation_tower%2C_1904_Saint_Louis_Louisiana_Purchase_Exposition.JPG License: Public domain Contributors: Appears in
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Armstrong_FM_radio_station_W2XMN_Alpine_NJ_1940.jpg License: Public domain Contributors: Retrieved October 3, 2015 from <a
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602

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File:Armstrong_prototype_FM_transmitter_1935.jpg
Source:
https://upload.wikimedia.org/wikipedia/commons/
8/86/Armstrong_prototype_FM_transmitter_1935.jpg
License:
Public
domain
Contributors:
Retrieved
October
26,
2015
from
<a
data-x-rel='nofollow'
class='external
text'
href='https://books.google.com/books?id=
ySUDAAAAMBAJ,<span>,&,</span>,pg=PA16,<span>,&,</span>,dq=armstrong+%22frequency+modulation%22'>"New
Radio
System Eliminates Static in Popular Science magazine, Popular Science Publishing Co., New York, Vol. 127, No. 1, July 1935, p. 16</a>
on Google Books Original artist: Unknown<a href='//www.wikidata.org/wiki/Q4233718' title='wikidata:Q4233718'><img alt='wikidata:
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page 228. This page was scanned by Swtpc6800 on an Epson Perfection 1240U at 300 dpi with half-tone de-screening enabled, and stored
as an TIFF. The image was cropped and touched up in Adobe Photo Elements 5.0. This copy was saved as a 150-dpi PNG le. Original
artist: Published by Experimenter Publishing Company Inc,. 233 Fulton Street, New York, N.Y. Hugo Gernsback, President; Sidney
Gernsback, Treasurer; Milton Hymes, Secretary.
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License:
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Retrieved March 4, 2014 from <a data-x-rel='nofollow' class='external text'
href='http://books.google.com/books?id=vd7mAAAAMAAJ,<span>,&,</span>,pg=RA5-PA28'>The
Wireless
Age
magazine, The Wireless Publishing Co., New York, Vol.
10, No.
6, March 1923, p.
28</a> on Google Books Original artist:
Unknown<a href='//www.wikidata.org/wiki/Q4233718' title='wikidata:Q4233718'><img alt='wikidata:Q4233718'
src='https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png'
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data-le-height='590' /></a>
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132.11.3

CHAPTER 132. MORSE CODE

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