EC-222 Analog Communication

Dr. J.RAVINDRANADH
Professor
E-mail : jrnadh@gmail.com

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 1

 Test Books & Reference Books
 Text Books
 Simon Haykin, Introduction to Analog and Digital
Communication Systems, 2rd Edition, John Wiley & S
ons,
 George Kennedy - Communication Systems, 3rd
Edition, TMH Publishing.
 Reference Books
 Sam Shanmugam - Analog and Digital
Communication Systems, John Wiley, 1992.
 B.P.Lathi - Communication Systems, BS
Publications, 2006.
2
 Syllabus
Unit-I
AMPLITUDE MODULATION
Time domain description, Frequency domain description , Single
tone modulation , Power Relations in AM Waves , Generation of
AM wave ,Square law modulator , Switching Modulator ,
Detection of AM waves , Square law detector , Envelope detector
DSB-SC Modulation, Time-domain and frequency domain
indescriptions of DSB-SC , Generation of DSB-SC : Balanced
modulator , Ring modulator , Coherent detection of DSB-SC
modulated waves , Costas loop, Quadrature-Carrier
multiplexing
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 3
SSB & VSB MODULATION

Band-pass transmission, Complex lowpass representation

of Narrow-band signals, Concepts of pre-envelope,
Complex envelope and Natural envelope, Equivalent
low-pass transmission model, Single side band
modulation: Frequency domain description, Generation of
SSB-SC wave, Frequency-discrimination method, Phase
discrimination method, Demodulation of
SSB-SC wave.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 4

 Unit-II
ANGLE MODULATION :
Introduction to Angle modulation, Relation between
frequency Modulation and phase modulation, Single tone
frequency modulation, Spectrum analysis of sinusoidal FM
wave, Narrow Band FM and Wide Band FM, Transmission
bandwidth of FM waves, Carson's Rule, Generation of FM
waves, Indirect FM (Armstrong Method), Direct FM,
Demodulation of FM waves, Balanced frequency
discriminator - Zero-crossing detector, Linearized model of
PLL.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 5

Unit-III
RADIO TRANSMITTERS & RECEIVERS

RADIO TRANSMITTERS :

Frequency allocation for radio communication systems,

Block diagrams and functions of radio transmitters for AM
and FM systems.

RADIO RECEIVERS :

TRF and super heterodyne receivers, RF, Mixer and IF

stages, Choice of IF, Image frequency, Alignment and
tracking of radio receivers, AGC, Tone and volume controls,
Receiver characteristics and their measurements, FM
receivers, Communication receivers.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 6

Unit-IV
DISCRETE MODULATION :

Generation and Demodulation of PAM, PWM and PPM

NOISE IN ANALOG MODULATION :

AM Receiver model, Signal to noise ratios for coherent

reception. DSB-SC receiver, SSC-SC receive, Noise in
AM receivers using envelope detection. AM threshold
effect, FM receiver model, Noise in FM reception,
Capture effect in FM, Threshold effect, FM threshold
reduction, Pre-emphasis and De-emphasis in FM.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 7

COURSE OBJECTIVES:

1. To analyze the AM, different versions in AM i.e.

AMSC, DSB, SSB, and VSB in the time domain and
frequency domain, and its generation and
demodulation techniques.
2. To analyze Angle modulation, versions of FM (NBFM,
WBFM) and modulation and demodulation
techniques for FM.
3. To understand the concepts of Radio Transmitter and
Radio receiver.
4. To analyze the effect of noise on the performance of
AM and FM receivers and understand the principles
of PAM, PWM, and PPM, TDM, and FDM techniques.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 8

COURSE OUTCOMES:
After successful completion of the course, the students
will be able to:
1. Demonstrate knowledge in Elements of
communication systems, Amplitude, Frequency,
and Phase Modulations and De-Modulations,
Radio Transmission & reception and Noise
2. Maintain standards while designing radio
transmitters and receivers
3. Analyze Noise Performance in different
modulation systems, calculation of total power
and bandwidth
4. Solve problems pertaining to modulation
schemes, transmitters and receivers considering
noise effects. 9
 Communication is a process of conveying message at a
distance
 Two types transmission media
1. Line communication 2. Radio communication
 Line communication
 In Line communication the media of transmission is a

pair of conductors called transmission line. In this

technique signals are directly transmitted through
the transmission lines. The installation and
maintenance of a transmission line is not only costly
and complex, but also overcrowds the open space.
 Radio communication
 In radio communication transmission media is open

space or free space. In this technique signals are

transmitted by using antenna through the free space
in the form of EM waves.
10
 Block diagram of communication
 Message source
 Information source contain non electrical things
data, music, picture , voice
 Transmitter
 Transmitter is the equipment which converts
physical message, such as sound, words, pictures
etc., into corresponding electrical signal.
 Channel
 Channel may be either transmission line or free
space, which provides transmission path between
transmitter and receiver.
 Receiver: Receiver is equipment which converts
electrical signal back to the physical message. 11
Band Name Freq. range Common Use

Very Low Frequency 3 to 30 kHz (Sub-)Marine communications,

(VLF) , heart rate monitors, geophysics

Low Frequency (LF) 30 to 30 0kHz Long distance communication

AM (medium-wave) broadcasts,
Medium Frequency (MF) 300 to 3000KHz amateur radio,
Long-distance aircraft/ship
High Frequency (HF) 3 to 30 MHz communication
Very High Frequency FM, television broadcasts,
30 to 300 MHz
(VHF) aircraft communication
Television broadcasts, microwave
Ultra High Frequency 300 to 3000MHz links, mobile phones, wireless LAN,
(UHF)
Bluetooth, Zigbee, GPS, …

Super High Frequency Satellite communications,

3 to 30 GHz microwave links, radars
(SHF)
satellite TV, radio astronomy…
Extremely High …
Radio astronomy, microwave radio
Frequency (EHF) 30 to 300 GHz relay, microwave remote sensing

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 12

L-Band:
L bands are having the frequency range between 1 GHz
to 2 GHz and their wavelength in free space is 15cm to
30cm. These ranges of waves are used in navigations,
GSM mobile phones, and in military
Dr. J. Ravindranadh/ applications.
Professor
/ ECE Dept / Analog
Communication 13
S-Band:
S-band microwaves are having the frequency range
between 2 GHz to 4 GHz and their wavelength range is
7.5cm to 15 cm. These waves can be used in navigation
beacons, optical communications, and wireless networks.
C-Band:
C band waves are having the range between 4 GHz to 8
GHz and their wavelength is between 3.75 cm to 7.5 cm.
C band microwaves penetrate clods, dust, smoke, snow,
and rain to reveal the earth’s surface. These microwaves
can be used in long-distance radio telecommunications.
X-Band:
The frequency range for S-band microwaves is 8 GHz to
12 GHz having the wavelength between 25 mm to 37.5
mm. These waves are used in satellite communications,
broadband communications, radars, space
communications, and amateur radio signals. 14
Ku-Band
These waves are occupying the frequency range between
12 GHz to 18 GHz and having the wavelength in between
16.7 mm to 25 mm. “Ku” refers to Quartz-under. These
waves are used in satellite communications for measuring
the changes in the energy of the microwave pulses and
they can determine the speed and direction of wind near
coastal areas.
K-Band and Ka-Band:
The frequency range for K band waves in between 18 GHz
to 26.5 GHz. These waves are having a wavelength
between 11.3 mm to 16.7 mm.
For the Ka-band the frequency range is 26.5 GHz to 40
GHz and they are occupying the wavelength in between 5
mm to 11.3 mm. These waves are used in satellite
communications, astronomical observations, and radars.
Radars in this frequency range provide short-range, high
resolution, and high amounts of data at the renewing 15
rate.
 Modulation

CW Wave Modulation Pulse Modulation

Amplitude Modulation Angle Modulation Pulse Analog Modulation

SSB-SC VSB PAM PWM PPM

DSB-FC DSB-SC

Frequency Modulation Phase Modulation

NBFM WBFM
16
 Modulation
 Modulation is defined as the process by which some
characteristics (i.e. amplitude, frequency, and
phase) of a carrier are varied in accordance with a
modulating wave
 Demodulation
 It is the reverse process of modulation, which is
used to get back the original message signal.
Modulation is performed at the transmitting end
whereas demodulation is performed at the receiving
end.
 In analog modulation sinusoidal signal is used as
carrier where as in digital modulation pulse train is
used as carrier.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 17

 Need for Modulation
 Reduces the height of the Antenna
 Avoiding the mixing of the signal
 Increase the operating range
 Allows Multiplexing of the signal
 Allows adjustment of Bandwidth
 Improving the quality of reception

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 18

 Reduces the height of the Antenna
In order to transmit a wave effectively the length
of transmitting antenna should be approximately
equal to the wavelength of the wave.
Velocity
Wavelength=
Frequency
If audio frequency are transmitted directly into
space, length of transmitting antenna required is
very large 8
3  10
  15km
20k
This is too long to construct practically.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 19

 For this reason it is impracticable to radiate audio
signal directly into space. On other hand if a carrier
wave is high frequency to carry the signal, we need
antenna length small and it can be easily
constructed.
 Avoiding the mixing of the signal
If the baseband sound signals are transmitted
without using the modulation by more than one
transmitter, then all the signals will be in the same
frequency range i.e. 0 to 20 kHz . Therefore, all
the signals get mixed together and a receiver can
not separate them from each other.
Hence, if each baseband sound signal is used to
modulate a different carrier then they will occupy
different slots in the frequency domain. Thus,
modulation avoids mixing of signals.
20
 Increase the operating range
The frequency of baseband signal is low, and the low
frequency signals can not travel long distance when
they are transmitted . They get heavily attenuated.
The attenuation reduces with increase in frequency
of the transmitted signal, and they travel longer
distance.
The modulation process increases the frequency of
the signal to be transmitted. Therefore, it increases
the operating range.
 Allows Multiplexing of the signal
Multiplexing is a process in which two or more signals
can be transmitted over the same communication
channel simultaneously. This is possible only with
modulation.
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 21
 The multiplexing allows the same channel to be used
by many signals . Hence, many TV channels can use
the same frequency range, without getting mixed with
each other or different frequency signals can be
transmitted at the same time.
 Allows adjustment of Bandwidth
Bandwidth modulated signal may be made smaller or
larger.
 Improving the quality of reception
With frequency modulation (FM) and the digital
communication techniques such as PCM, the effect of
noise is reduced to a great extent . This improves
quality of reception.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 22

 Amplitude modulation (AM):
 Amplitude modulation is defined as the process in
which the amplitude of the carrier signal is varied
in accordance with the modulating signal or message
signal.
 In India Amplitude Modulation occurs in radio
transmission. In television amplitude modulation is
used for picture and for sound purpose frequency
modulation is used.
Consider a sinusoidal carrier signal C (t) is defined as

C (t )  Ac cos(2f c t )
Where Ac= Amplitude of the carrier signal
fc= frequency of the carrier signal
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 23
Consider a m(t) as base band or message signal or
Modulating signal is defined as

m(t )  Am cos(2f m t )
The combination of c(t) and m(t) is called modulated
signal.
An amplitude-modulated (AM) wave S(t) can be
described as function of time is given by

s (t )  [ Ac  m(t )] cos(2f c t )
m(t )
s (t )  Ac [1  ] cos( 2f c t )
Ac
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 24
 s (t )  Ac [1  k a m(t )] cos(2f c t )
1
ka  =Amplitude sensitivity factor
Ac
There are two requirements to maintain the envelope of
AM signal is same as the shape of base band signal.
1. The amplitude of the ka m(t) is always less than unity
i.e., |kam(t)|<1 for all t
2. Carrier frequency fc is far greater than highest
frequency W component of message signal or base
band signal m(t) i.e., fc>>W

s (t )  Ac [1  k a Am cos 2f mt ] cos(2f c t )

s (t )  Ac [1   cos 2f mt ] cos(2f c t )
µ is called modulation index 25
m(t) Message signal

c(t) Carrier wave

s(t) AM wave

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 26

Critical Modulation
When the modulation index µ is 100% is called Critical
Modulation. Under these circumstances the signal level
falls to zero and rises to twice the value with no
modulation. In this case the voltage rises to a maximum
of twice the normal level – this means that the power
will be four times that of the quiescent value.

27
Under Modulation
Modulation index lies between 0<µ <1 is called under
modulation. then the carrier will not fall to zero, no will
it rise to twice the level, but the deviation will be less
than this from the quiescent level. The diagram below
shows a level of 50% modulation, but the principle holds
good for any value between 0 and 100% modulation.

Dr. J. Ravindranadh/ Professor

/ ECE Dept / Analog
Communication 28
Over modulation
The modulation index is µ is greater than the 100% is
called over modulation. The carrier experiences 180°
phase reversals where the carrier level would try to go
below the zero point. These phase reversals cause
serious interference to other users.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 29

Spectrum of Amplitude Modulation wave
Time domain Modulating signal m(t )  Am cos(2f m t )
Am
Taking Fourier transform M ( f )   ( f  f m )   ( f  f m )
2
Time domain carrier signal c(t )  Ac cos(2f c t )
Ac
Taking Fourier transform C ( f )   ( f  f c )   ( f  f c )
2
Time domain description of convention AM wave is by

s (t )  Ac [1  k a m(t )] cos(2f c t )
s (t )  Ac cos(2f c t )  Ac k a m(t ) cos(2f c t )]
Taking Fourier transform both sides
Ac Ac k a
S( f )   ( f  f c )   ( f  f c )  M ( f  f c )  M ( f  30f c 
2 2
 C(f)

-fc +fc

31
 The spectrum of AM signal consists of two impulse
functions weighted by a factor Ac/2 occurring at ±
fc

 Two version of the baseband spectrum translated

by ± fc and scaled amplitude by kaAc/2.

 For positive frequencies the portion of spectrum of

AM wave lying above carrier frequency fc has a
upper side band where as symmetrical portion below
fc is referred as lower side band.

 For positive frequencies the highest frequency of AM

wave is fc + W and the lowest frequency component
is fc-W.
32
Transmission Bandwidth
The difference between upper side and lower side
define the transmission bandwidth

BT  f USB  f LSB

 fc  W  ( fc W )

 fc  W  fc  W
BT  2W
The transmission bandwidth AM wave is twice the base
band signal frequency.
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 33
Single tone modulation

In single-tone modulation modulating signal consists of

only one frequency component where as in multi-tone
modulation modulating signal consists of more than one
frequency component.

Let us consider the AM wave is

s (t )  Ac [1  k a m(t )] cos(2f c t ) (1)

consider message signal m(t) which consists a single tone
frequency component.

m(t )  Am cos(2f m t )
Substitute m (t) in equation (1)
34
 s (t )  Ac [1  k a Am cos(2f m t ] cos(2f c t )
s (t )  Ac [1   cos(2f m t ] cos(2f c t )

  k a Am

µ which is known as modulation index or modulator factor

Modulation index is defined as the ratio of amplitude

of message signal to the amplitude of carrier signal.

Am

Ac
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 35
let us consider the AM wave
Amax

Amin

Amax  Ac 1    Amin  Ac 1   

Amax 1    Amax  Amin

 
Amin 1    Amax  Amin

Modulation index µ exists only between o<µ<1

36
µ =1 Amin=0 and Amax=2Ac as Amin=0 it has 100%
modulation

µ =0 Amin= Amax ,0% modulation

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 37

Frequency domain description of AM wave

s (t )  Ac [1   cos(2f m t ] cos(2f c t )
s (t )  Ac cos( 2f c t )  Ac cos( 2f c t ) cos( 2f m t )
Ac
s (t )  Ac cos(2f c t )  cos 2 ( f c  f m )t  cos 2 ( f c  f m )t 
2
Taking Fourier transform both sides
Ac
S( f )   ( f  f c )   ( f  f c ) 
2
Ac 
  ( f  ( f c  f m )   ( f  ( f c  f m ) 
4
Ac 
  ( f  ( f c  f m )   ( f  ( f c  f m ) 
4
38
 Ac/2 S(f) Ac/2

µAc/4 µAc/4 µAc/4 µAc/4

-fc-fm -fc -fc+fm fc-fm fc fc+fm

Spectrum of Single tone AM signal

Power calculations of single-tone AM signal

The standard time domain equation for single-tone
AM signal is given by
Ac
s (t )  Ac cos(2f c t )  cos 2 ( f c  f m )t  cos 2 ( f c  f m )t 
2

carrier USB LSB 39

 2
Carrier power
A
Pc  c
2  2 Ac2
Upper Side Band power PUSB 
8
 2 Ac2
Lower Side Band power PLSB 
82
Total power PT = Pc + PUSB + PLSB
Ac  2 Ac2  2 Ac2
  
2 8 8
2 2
 Pc  Pc  Pc
4 4
2  2 
 Pc  Pc Pt  Pc 1  
2  2 

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 40

Current calculations
It is often more convenient to measure transmitting
current than power. Ic is rms value of un-modulated
current and It is total rms value after modulation of an
AM transmitter.

Pt I t2 R 2
 2  1
Pc I c R 2
  2

I t  I c 1  
2 2

 2 
 2 
I t  I c 1  
 2 
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 41
Transmission efficiency η
The transmission efficiency is defined as the ratio of
power carried by the sidebands to the total transmitted
power is called transmission efficiency η

 A2 2
 A
2 2

PUSB  PLSB c
 c

  8 8
Pt  2 
Pc 1  
 2 
2
Pc
 2
   2 2
Pc 1   
2  2 2

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 42
Multi-tone modulation
In multi-tone modulation modulating signal consists of
more than one frequency component where as in single-
tone modulation modulating signal consists of only one
frequency component.

Let us consider the AM wave is

s (t )  Ac [1  k a m(t )] cos(2f c t ) (1)

consider message signal m(t) which consists a multi tone
frequency component.
m(t )  Am1 cos(2f m1 t )  Am 2 cos(2f m 2 t )
Substitute m (t) in equation (1)
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 43
s (t )  Ac [1  k a Am1 cos(2f m1t )  k a Am 2 cos(2f m 2 t )] cos(2f c t )

s (t )  Ac [cos( 2f c t )  k a Am1 cos( 2f m1t ) cos( 2f c t )

 k a Am 2 cos( 2f m 2 t ) cos( 2f c t ) ]

1  k a Am1  2  k a Am 2

s (t )  Ac cos( 2f c t )  1 Ac cos( 2f c t ) cos( 2f m1 ) t

  2 Ac cos( 2f c t ) cos( 2f m 2 t )

1 Ac
s(t )  Ac cos(2f c t )  cos 2 ( f c  f m1 )t  cos 2 ( f c  f m1 )t 
2
 2 Ac
 cos 2 ( f c  f m 2 )t  cos 2 ( f c  f m 2 )t 
2
44
 Taking Fourier transform both sides
Ac Ac 1
S ( f )   ( f  f c )   ( f  f c )   ( f  ( f c  f m1 )   ( f  ( f c  f m1 )
2 4
Ac 1 Ac  2  ( f  ( f c  f m 2 ) 
  ( f  ( f c  f m1 )   ( f  ( f c  f m1 )   
4 4   ( f  ( f c  f m 2 )
Ac  2
  ( f  ( f c  f m 2 )   ( f  ( f c  f m 2 )
4

Ac/2 S(f) Ac/2

µ2Ac/4 µ1Ac/4 µ1Ac/4 µ2Ac/4 µ2Ac/4 µ1Ac/4 µ1Ac/4 µ2Ac/4

-fc-fm2 -fc-fm1-fc -fc+fm1-fc+fm2 fc-fm2 fc-fm1 fc fc+fm1 fc+fm2

Spectrum of Multi tone AM signal
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 45
Total Power of Multi-tone AM signal is given by
  12  22 
Pt  Pc 1    .... 
 2 2 

  t2 
Pt  Pc 1  
 2 

 t 2   12   2
2  ....

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 46

A carrier frequency of 16k Hz is modulated by audio
frequency range from 300 to 2700. What will be the
range of upper and lower side side.

If fm= 300 Hz
USB= 16k+300=16.3k

LSB= 16k-300=15.7k

If fm= 2700 Hz
USB= 16k+2700=18700

LSB= 16k-2700=13300
Upper side band range 16.3k to 18.7k

Lower side band range 13.3k to 15.7k

47
A sinusoidal carrier voltage of frequency 1200kHz is
amplitude modulated by a sinusoidal value of frequency
20k Hz resulting in max and min, modulated carrier
amplitude of 100V and 80V respectively. Calculate
(a) Frequency of LSB and USB (b) Modulation index
(c) Un-modulated carrier amplitude
(a)
(b)

USB= 1200k+20k=1220k Amax  Amin 20

   0.11
LSB= 1200k-20k=1180k Amax  Amin 180

Amax  Ac 1    100  Ac 1  0.11 Ac  90

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 48

A 400 W carrier is modulated to a depth of 75%.
Calculate total power in modulating wave.

 2   0.752   512.5W
Pt  Pc 1   Pt  4001  
 2   2 
A Broadcast radio transmitter radiate 5KW when the
modulation index is 60% how much is carrier power.

 2   0.60 2 
Pt  Pc 1   5k  Pc 1  
 2   2 

Pc  4237.28W
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 49
The antenna current of an AM Transmitter is 8A. Then
only carrier is sent but it is increases to 8.96A when
the carrier is modulated by single tone sinusoidal Find
% of modulation index

   2
   2
I t  I c 1   8.96  8 1  
 2   2 
  0.713
Amplitude modulation signal is given by
s AM (t )  10 cos(2  10 6 ) t  5 cos(2  10 6 ) t cos(4  10 3 )t
Find the modulation index, amplitude of carrier
frequency, total side band power and bandwidth.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 50

  
s AM (t )  10 1  0.5 cos(4  10 3 )t cos(2  10 6 ) t

Modulation index=0.5
Amplitude of carrier =10V

Total Side Band power =  A  6.25W

2 2
c

4
Band width = 2fm = 4k Hz
How many AM broad casting stations can be
accommodated in a 100KHz bandwidth if highest
frequency modulating carrier is 5kHz.

Total bandwidth 100k

  10
Single station bandwidth 2  5k

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 51

A 300W carrier is simultaneously modulated by two
audio waves with modulation % of 50 and 60
respectively. What is total side band power radiated.

1 Pc
2
 2 Pc
2

PSB    91.5W
2 2
A 75M Hz carrier having amplitude of 50V is modulated
by a 3kHz audio signal having amplitude of 20V, Sketch
audio, carrier and Amplitude modulated signal.
Determine the modulated index. Write the spectrum of
modulated wave.

m(t )  20 cos(2  3  10 t )
3

c(t )  50 cos(2  75  10 t ) 6

52
s (t )  50[1  0.4 cos( 2  3  10 t ] cos( 2  75  10 t )
3 6
20

-20

50

-50

70

30

-30

-70
53
s (t )  50[1  0.4 cos( 2  3  10 3 t ] cos( 2  75  10 6 t )

s (t )  50 cos(2  75  10 6 t )  20 cos(2  75  10 6 t ) cos(2  3  103 t )

s (t )  50 cos(2  75  10 6 t ) 

10 cos 2 (75.003  10 6 )t  cos 2 (74.997  10 6 )t 
Taking Fourier transform both sides

 
S ( f )  25  ( f  75  10 6 )   ( f  75  10 6 )
 5 ( f  (75.003  10 )   ( f  (75.003  10 )
6 6

 5 ( f  (74.997  10 )   ( f  (74.997  10 )

6 6

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 54

 25 S(f) 25

5 5 5 5

-75.003M -75M -74.993M 74.993M 75M 75.003M

Spectrum of Single tone AM signal

An audio signal is given as 15 sin(2πx1500t) amplitude
modulated carrier is given as 60sin(2πx10000t). Sketch
audio, carrier and Amplitude modulated signal.
Determine the modulated index. Write the spectrum of
modulated wave.

s (t )  60[1  0.25 sin( 2  1500t ] sin( 2  10  10 t ) 3

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 55

15

-15

60

60

75
45

-45
-75

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 56

 s (t )  60[1  0.25 sin( 2  1500t ] sin( 2  10  10 3 t )

s (t )  60 sin( 2  10  103 t )  15 sin( 2  10  103 t ) sin( 2  1500t )

s ( t )  60 sin( 2  10  10 3 t ) 

7 . 5 cos 2 (8 . 5  10 3 ) t  cos 2 (11 . 5  10 3 ) t 
Taking Fourier transform both sides

S( f ) 
30
j

 ( f  10  10 3 )   ( f  10  10 3 ) 

 3 . 75  ( f  ( 8 . 5  10 3 )   ( f  ( 8 . 5  10 3 ) 
 3 . 75  ( f  (11 . 5  10 3 )   ( f  (11 . 5  10 3 ) 
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 57
 S(f)
30/j

3.75 3.75

-11.5k -10k -8.5k 8.5k -10k 11.5k

3.75 3.75

30/j

Spectrum of Single tone AM signal

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 58

Generation of AM Wave
There are two methods to generate AM waves
1. Square-law modulator
2. Switching modulator
Square- law modulator

Block diagram of Square- law modulator 59

A Square-law modulator requires three features: a
means of summing the carrier and modulating waves, a
nonlinear element, and a band pass filter for extracting
the desired modulation products. Semi-conductor diodes
and transistors are the most common nonlinear devices
used for implementing square law modulators. The
filtering requirement is usually satisfied by using a
single or double tuned filters.

When a nonlinear element such as a diode is suitably

biased and operated in a restricted portion of its
characteristic curve, that is ,the signal applied to the
diode is relatively weak, we find that transfer
characteristic of diode-load resistor combination can
be represented closely by a square law.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 60

 V2 (t )  a1 V1 (t )  a 2 V12 (t ) (i)

Where a1, a2 are constants

Now, the input voltage V1 (t) is the sum of both

carrier and message signals

V1 (t )  Ac cos 2f c t  m(t ) (ii)

Substitute equation (ii) in equation (i) we get

V2 (t )  a1  Ac cos 2f c t  m(t )  a 2  Ac cos 2f c t  m(t )

2

V2 (t )  a1  Ac cos 2f c t  m(t )  a 2 Ac cos 2 2f c t  a 2 m(t ) 2

2

 2a 2 Ac cos 2f c t m(t )

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 61
 V2 (t )  a1 Ac cos 2f c t  a1 m(t )  a 2 Ac cos 2 ( 2f c t )
2

 a 2 m(t ) 2  2a 2 Ac cos 2f c t m(t )

 2a2 
V2 (t )  a1 Ac 1  m(t ) cos 2f c t  a1m(t )  a2 m(t ) 2
 a1 
 a2 Ac cos 2 (2f c t )
2

V2 (t )  a1 Ac 1  k a m(t )cos 2f c t  a1 m(t )  a 2 m(t ) 2

 a 2 Ac cos(f c t )
2 2

2a 2
where k a 
a1
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 62
Now design the tuned filter /Band pass filter with center
frequency fc and pass band frequency width 2W.We can
remove the unwanted terms by passing this output voltage
V2(t) through the band pass filter and finally we will get
required AM signal.

V0 (t )  a1 Ac 1  k a m(t )cos 2f c t

V0 (t )  a1 Ac cos(2f c t )  2 Ac a 2 m(t ) cos(2f c t )]

Taking Fourier transform both sides

a1 Ac
V0 ( f )   ( f  f c )   ( f  f c )  Ac a 2 M ( f  f c )  M ( f  f c 
2

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 63

 M(f)

-W 0 W
C(f)

-fc S(f) +fc

a1Ac/2 a1Ac/2

a2AcM(0)

-fc-W -fc -fc+W 0 fc-W fc fc+W

64
The AM spectrum consists of two impulse functions
which are located at fc & -fc and weighted by Aca1/2
& a2Ac/2, two USBs, band of frequencies from fc to
fc+W and band of frequencies from -fc-W to –fc,
and two LSBs, band of frequencies from fc-W to fc
& -fc to-fc+W.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 65

 Switching modulator
Block diagram of switching modulator shown in figure

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 66

Assume that carrier wave C(t) applied to the diode is
large in amplitude, so that it swings right across the
characteristic curve of the diode .we assume that the
diode acts as an ideal switch, that is, it presents zero
impedance when it is forward-biased and infinite
impedance when it is reverse-biased. We may thus
approximate the transfer characteristic of the diode-
load resistor combination by a piecewise-linear
characteristic.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 67

The input voltage applied Vi(t) applied to the diode is
the sum of both carrier and message signals

V1 (t )  Ac cos 2f c t  m(t )

During the positive half cycle of the carrier signal i.e. if

C(t)>0, the diode is forward biased, and then the diode
acts as a closed switch. Now the output voltage V2(t) is
same as the input voltage V1(t) .

During the negative half cycle of the carrier signal

i.e. if C(t) <0, the diode is reverse biased, and then
the diode acts as a open switch. Now the output
voltage V2(t) is zero i.e. the output voltage varies
periodically between the values input voltage V1(t) and
zero at a rate equal to the carrier frequency fc.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 68

 1

T/2
The output of the diode will be

V2 (t )  V1 (t )
V2 (t )  g p (t )V1 (t )

V2 (t )  Ac cos 2f c t  m(t )g p (t )

Rectangle pulse train with period equal to T=1/fc

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 69

Representing gp(t) of its Fourier series
1 2 2 2
g p (t )   cos( 2f c t )  cos(3f c t )  cos(5f c t )  .......
2  3 5
1 2 
V2 (t )  Ac cos 2f c t  m(t )  cos(2f c t )  .........
2  

1 1 2 Ac 2
V2 (t )  Ac cos 2f c t  m(t )  cos (2f c t )  m(t ) cos 2f c t
2

2 2  

1 1 Ac Ac 2
V2 (t )  Ac cos 2f c t  m(t )   cos(4f c t )  m(t ) cos 2f c t
2 2   

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 70

The required AM wave centered at fc is obtained by
passing V2(t) through an ideal BPF having a centre
frequency fc and bandwidth 2W

Output of the Band pass filter is

1 2
V0 (t )  Ac cos 2f c t  m(t ) cos 2f c t
2 
Ac  4 
V0 (t )  1  m(t ) cos 2f c t
2  Ac 
Ac
V0 (t )  1  k a m(t )cos 2f c t
2
4
Where k a 
Ac
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 71
 1

-T/2 -T/4 T/4 T/2

Fourier series of even symmetry bn=0

T
g t (t )  1 0  t 
4
T T
0 t 
4 2
2 
T /4 T /2
1
a 0    1dt   0dt  
T0 T /4  2

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 72

 4 2 2 
T /4 T /2
an  
T 
0
cos n
T
tdt   0 cos n
T /4
T
tdt 

T /4
 2 
sin(n t) 
4 T 2 n
    sin
T 2  n 2
n
 T  0

1  2 n
g p (t )    sin cos n 2f c t
2 n 1 n 2

1 2 2 2
g p (t )   cos 2f c t  cos 3f c t  cos 5f c t  .......
2  3 5

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 73

Demodulation of AM Wave
There are two methods to demodulated AM waves
1. Square-law detector
2. Envelope detector
Square- law detector

Block diagram of Square- law detector 74

A Square-law demodulator requires nonlinear element
and a low pass filter for extracting the desired
message signal. Semi-conductor diodes and transistors
are the most common nonlinear devices used for
implementing square law demodulators. The filtering
requirement is usually satisfied by using a single or
double tuned filters.

When a nonlinear element such as a diode is suitably

biased and operated in a restricted portion of its
characteristic curve, that is ,the signal applied to the
diode is relatively weak, we find that transfer
characteristic of diode-load resistor combination can
be represented closely by a square law.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 75

 V2 (t )  a1 V1 (t )  a 2 V12 (t ) (i)
Where a1, a2 are constants
Now, the input voltage V1 (t) is the AM wave

V1 (t )  Ac 1  k a m(t )cos 2f c t (ii)

Substitute equation (ii) in equation (i) we get

V2 (t )  a1 Ac 1  k a m(t )cos 2f c t  a 2  Ac 1  k a m (t )cos 2f c t 

2

V2 (t )  a1 Ac 1  k a m(t )cos 2f c t

2

 a 2 Ac cos 2 2πf c t 1  k a2(t)m 2(t)  2k a (t)m(t) 
V2 (t )  a1 Ac 1  k a m(t )cos 2f c t
2


a 2 Ac
2

1  cos(4f c t )1  k a2(t)m 2(t)  2k a(t)m(t) 
76
The desired signal is a2Ac2kam(t) is due to a2V12(t)term
hence the description is square law detector. This
component can be extracted by means of LPF.

V0 (t )  a 2 Ac2 k a m(t )
However the term ½ a2Ac2ka2m2(t) will give the
distorted base band signal. A square law detector can
not provide distortion less AM detector.
The ratio of wanted signal to the distortion is 2/kam(t)
so that distortionless recovery of base band signal m(t)
is possible only if applied AM is weak and % modulation
is very small. M(f)
a2Ac2kaM(0)

-fm 0 fm 77
 Envelope Detector
Block diagram of envelope detector shown in figure

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 78

The operation of the envelope detector. On a positive
half cycle of the input signal, the diode is forward
biased and the capacitor C charges up rapidly to the
peak value of the input signal. When the input signal
falls below this value, the diode becomes reverse
biased and the capacitor C discharges slowly through
the load resistor RL . The discharging process continues
until the next positive half cycle. When the input signal
becomes greater than the voltage across the capacitor,
the diode conducts again and the process is repeated.
The charging time constant RsC is very small when
compared to the carrier period 1/fc

1
R s C 
fc
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 79
The capacitor C charges rapidly to the peak value of
the signal. The discharging time constant RLC is very
large when compared to the charging time constant.

1 1
 R L C 
fc W

The result to detect peak value of envelope and

produce original baseband signal. The detector output
usually has a small ripple at carrier frequency. These
ripple can be eliminated by using a low pass filter.

Envelope detector is used to detect high level modulated

signal, whereas square-law detector is used to detect
low level modulated signals

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 80

 Advantages of Amplitude modulation
 Generation and detection of AM signals are very
easy
 It is very cheap to build, due to this reason it is
most commonly used in AM radio broad casting
 Disadvantages of Amplitude modulation
 Amplitude modulation is wasteful of power.
 Amplitude modulation is wasteful of band width
 Application of Amplitude modulation
 AM Radio Broadcasting
 In television amplitude modulation is used for
picture

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 81

Double Sideband Suppressed Carrier (DSB-
(DSB-SC)

s (t )  Ac [1   cos(2f m t ] cos(2f c t )
Ac
s (t )  Ac cos( 2f c t )  cos 2 ( f c  f m )t  cos 2 ( f c  f m )t 
2

Carrier USB LSB

67% 33%
AM wave consists of carrier and two sidebands. The
carrier of amplitude modulated wave does not contain
any information and total power is required for
transmitting carrier is about 67%.
Hence carrier is suppressed only sideband remains and
in this way saving of 2/3 rd power achieved 100%
modulation.
82
This type of suppression of carrier does not effect base
band signal. The result is obtained the transmitted wave
consists of only the upper and lower sidebands.
Double sideband-suppressed carrier (DSB-SC)
modulation consists of the product of both the message
signal m (t) and the carrier signal c(t)

Antenna
m(t) Product
modulator
m(t) Ac cos2Πfct

c(t)=Ac cos2Πfct

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 83

 Time domain description
s (t )  m(t ) Ac cos(2f c t )
 Am cos(2f m t ) Ac cos(2f c t )
Am Ac
 cos ( 2π(f c  f m )t  cos ( 2π(f c  f m )t 
2
Frequency domain description

s (t )  m(t ) Ac cos(2f c t )

Ac
S( f )  M ( f  f c )  M ( f  f c )
2
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 84
85
 M(f)

-W 0 W
C(f)

-fc +fc
S(f)
Ac/2

-fc-W -fc -fc+W fc-W fc fc+W

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 86

 The DSB-SC signal exhibits phase reversal whenever
base band signal crosses zero, because of this the
envelope of DSB-SC modulated signal is different from
message signal.
 It is clear that the impulse at ± fc are missing which
means that the carrier term is suppressed in the
spectrum and only two side band terms are present.
Therefore it is called DSB-SC.
 Considering the positive side the Upper side band
frequency is fc +fm and Lower side band frequency is
fc-fm. The difference of these two frequency is equal
to the transmission band width of DSB-SC signal.
 Bandwidth of a DSB-SC signal is 2fm. It is same as
that of general AM Wave.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 87

 Generation of DSB-
DSB-SC signal
 There are two methods to Generated
DSB-SC signal

 Balanced Modulator
 Ring Modulator

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 88

Balanced Modulator
m(t ) s1 (t )  Ac [1  k a m(t )] cos( 2f c t )
AM
Modulator
Message
signal
Ac cos(2f c t )
+
S(t)
Oscillator 
Ac cos( 2f c t ) -

 m(t ) AM
Modulator
Message s 2 (t )  Ac [1  k a m(t )] cos(2f c t )
signal
Block diagram of Balanced modulator 89
One possible scheme for generating a DSBSC wave is to
use two AM modulators arranged in a balanced
configuration so as to suppress the carrier wave.
Assume that two AM modulators are identical, except
for the sign reversal of the modulating signal applied to
the input of one of the modulators
Thus the outputs of the two AM modulators can be
expressed as
s1 (t )  Ac [1  k a m(t )] cos( 2f c t )
s 2 (t )  Ac [1  k a m(t )] cos( 2f c t )
s (t )  s1 (t )  s 2 (t )  2 Ac k a m(t ) cos( 2f c t )

Hence, except for the scaling factor 2ka the balanced

modulator output is equal to product of the modulating
signal and the carrier signal
90
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 91
The DSB-SC signal is

s (t )  2 Ac k a m(t ) cos 2 a f c t
Apply Fourier transform both side

S ( f )  Ac k a M ( f  f c )  M ( f  f c 
Spectrum of the DSB-SC signal is
S(f)

Acka M(0)

-fc-W -fc -fc+W fc-W fc fc+W

92
 Ring Modulator

It consists of input transformer T1 output transformer

T2, and four diodes connected in bridge circuit. Diodes
are controlled by square wave carrier.
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 93
If the transformers are perfectly balanced and the
diodes are identical, there is no leakage of the modulation
frequency into the modulator output.
When the carrier supply is positive, the outer diodes are
switched ON and the inner diodes are switched OFF, so
that the modulator multiplies the message signal by +1
When the carrier supply is negative, the outer diodes are
switched OFF and the inner diodes are switched ON, so
that the modulator multiplies the message signal by -1.
The square wave carrier c(t) shown in figure

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 94

The square wave carrier c(t) can be represented by a
Fourier series
Even symmetry, half wave/quarter symmetry a0=bn=0
T /4
 2 
8
T /4
2  8 
sin( n t)  4 n
a n    cos n tdt    T

 sin
T0 T  T  2  n 2
n 
 T  0


4  n 
c(t )   sin  cos n  t
n 1 n  2 
4 4 4
c(t )  cos t  cos 3t  cos 5t  ...........
 3 5
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 95
The ring modulator output is s(t)= c(t) m(t)

4 4 4 
s (t )   cos t  cos 3t  cos 5t  ........... m(t )
 3 5 

4 4 4
s (t )  m(t ) cos t  m(t ) cos 3t  m(t ) cos 5t 
 3 5
The output of Band pass filter is

4
s (t )  m(t ) cos 2f c t


Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 96

 Message signal

Carrier signal

DSB-SC signal

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 97

 4
The DSB-SC signal is s (t )  m(t ) cos 2f c t

Apply Fourier transform both side
2
S( f )  M ( f  fc )  M ( f  fc 

Spectrum of the DSB-SC signal is
S(f)

2/Π M(0)

-fc-W -fc -fc+W fc-W fc fc+W

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 98

Coherent detector of DSB-SC wave
Block diagram of coherent detector of DSB-SC wave

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication

99
 The base band signal m (t) can be recovered from a
DSB-SC wave s (t) by multiplying s(t) with a locally
generated sinusoidal signal and then low pass filtering
the product.
 It is assumed that local oscillator signal is coherent or
synchronized, in both frequency and phase ,with the
carrier signal c(t) used in the product modulator to
generate s(t).
 This method of demodulation is know as coherent
detection or synchronous demodulation.
 The product modulator produces the product of both
input signal and local oscillator and the output of the
product modulator v (t) is given by

v (t )  Ac/ cos( 2f c   )t s(t)

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 100

 v(t )  Ac/ cos( 2f c   )t m(t) Ac cos( 2f c )t
Ac/ Ac Ac/ Ac
v(t )  m(t) cos( 4f c t   )  m(t) cos 
2 2

message
Unwanted term
The 1st term representing a DSB-SC wave with a carrier
frequency 2fc where 2nd term is proportional to baseband
signal m(t).
As the low pass signal remove the unwanted term provided
that bandwidth greater than W but less than 2fc-W.
Then we get demodulated output as
/
A Ac
v0 (t )  c
m(t) cos 
2 101
The demodulated signal is proportional to the message
signal m (t) when the phase error is constant.

Amplitude of demodulated signal is maximum when ø=0

and is minimum when=±Π/2 and it represents quadrature
null effect of coherent detector.
Ac/ Ac
The output of demodulated is v(t )  m(t) cos 
2
Apply Fourier transform both side
/
A Ac
S( f )  c
cos  M(f)
4 M(f)
A’cAc/4 cosø M(0)

-W 0 W 102
Costas Loop

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 103

 Costas receiver main purpose is to demodulate DSB-
SC signal at receiver end.
 This system consists of two coherent detector
supplied with same DSB-SC input signal wave but the
individual local oscillator is adjusted to be same as
carrier frequency.
 The detector in upper part is referred as in-phase
coherent detector or I-Channel and lower part is
referred as quadrature phase coherent detector or
Q-Channel.
 These two detectors are coupled to each other to
form negative feedback system designed in such a way
has to maintain local oscillator synchronous with
carrier wave.
Output of I-Chanel ½ Ac’Ac cosø m(t)
Q-Chanel ½ Ac’Ac sinø m(t)
104
Let us assume that local carrier signal is synchronized
with incoming DSB-SC wave at ø=0 output of Q-Channel
is zero because of quadrature null effect and output of
I-channel is desired signal that is ½ A’cAc m(t)
Let us assume that local oscillators frequency drifts
slightly i.e ø is very small non zero quantity and I
channel output is almost unchanged but Q-Channel output
is proportional to sinø.
I Chanel and Q Channel both are applied to phase
discriminator. It provides DC Control signal which may be
used to correct local oscillator phase error.

Pilot carrier Small amount of carrier signal is transmitted

along with modulated signal from transmitter. A small
amount of carrier signal is known as pilot carrier.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 105

Band pass signals
We say that a signal g(t) is a band-pass signal if its
Fourier transform G(f)
G(f)

G( f c )

-fc fc
2W 2W

We refer to fc as the carrier frequency and the

bandwidth is 2W is small compared with fc and so we
refer to such a signal as a narrow band signal.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 106

 Band Pass transmission
 Pass band transmission is the transmission
after shifting the baseband frequencies to
some higher frequency range using
modulation.
 If modulated signal is transmission over the
channel, it is known as band pass
transmission.
 It is used for long distances.
 Less noise as signals is modulated
107
 Hilbert Transform
 The device which produces a phase shift of -90ᵒ for
all positive frequencies and a phase shift of +90 for
all negative frequencies.
 The amplitude of all frequency components of the
input signal are unaffected by transmission through
device. Such an ideal device is called a Hilbert
transform. H(f)
90
Hilbert
g(t) Transform g˄(t)
h(t)= 1/Πt f
 1 -90
g (t )  g (t )  h(t )  g (t ) 
t 108
Hilbert transform of g(t) denoted as g˄(t). it is
defined as

 1 g ( )
g (t )   d
  t  
Original signal can be recover by using the inverse
Hilbert transform


1 g ( )
g (t )    d
  t  
Interpretation of Hilbert transform

The Fourier transform of g(t) and 1/πt are

g (t )  G ( f ) 1
  jSgn( f )
t
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 109
Signum function define as it equals +1 for positive
frequency and -1 for negative frequency.
+1
1 f  0

Sgn( f )  0 f  0 f
 1 f  0
 -1
 1
g (t )  g (t ) 
t
Taking Fourier transform both side
 
G ( f )  G ( f ) jSgn( f ) G ( f )   jSgn( f )G ( f )
The Hilbert transform g^(t) of signal g(t) is obtained
by passing g(t) through a linear two port device whose
transfer function is equal to –jSgn(f).
110
Properties of Hilbert Transform
Property1: A signal g(t) and its Hilbert transform g˄(t)
have same amplitude spectrum.

Fourier transform of g˄(t)= G˄(f)=-jSgn(f). G(f)

The magnitude of-jSgn(f) is equal to 1 for all values
of f

G( f )  G( f )

The magnitude spectrum of g˄(t) is equal to g(t)

Property2: If g˄(t) is Hilbert transform of g(t) then

Hilbert transform of g˄(t) is –g(t)

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 111

 H ' ( f )  H ( f )  H ( f )   jSgn ( f )   jSgn ( f )
 j 2 Sgn 2 ( f )
but  Sgn 2 ( f )  1 and j 2  1
 H ' ( f )  1 for all values of f

Hence Fourier transform of output is G ( f ) H ' ( f )  G ( f )

Thus the Hilbert transform of g˄(t) is equal to -g(t)
Property3: A signal g(t) and its Hilbert transform g˄(t)
are orthogonal
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 112
Pre-envelope
The pre-envelope of the signal g(t) is define as the
complex valued function can be given as

g  (t )  g (t )  j g (t )
Where g(t) is the real part of the pre-envelope or
base band signal and g˄(t) represent the imaginary
part of pre-envelope or the Hilbert transform of g(t).
Taking Fourier transform of the g+(t) is

G ( f )  G ( f )  j G ( f )

We know that G ( f )   jSgn ( f )G ( f )

G  ( f )  G ( f )  j  jSgn ( f )G ( f )
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 113
 G  ( f )  G ( f )1  Sgn ( f )
Substituting the Signum function value in above equation

2G ( f ) f 0

G ( f )  G (0) f 0
0 f 0

G(0) is zero frequency value of G(f). The pre envelope
of Fourier transformable signal has no frequency
component for negative frequencies as shown.
G(f)

G( f c )

fc
2W 114
Complex Envelope
Pre-envelope of narrow band signal g(t) expressed in
the form of
g  (t )  g~ (t ) exp( j 2f c t )
g~(t) is a complex envelope of the signal. Definition of
the complex envelope interms of pre- envelope

The spectrum of g+(t) is limited the frequency band

fc-W≤f≤ fc+w.
Applying frequency shifting property of the Fourier
transform to above equation , we find the spectrum of
complex envelope g~(t) is limited to –W≤f≤W and
centered at origin.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 115

 Amplitude Spectrum of Complex-envelope

G+(f)

2 G( f c )

-W W

g (t )  Reg~ (t ) exp( j 2f c t )

g~(t) is a complex quantity

g~ (t )  g I (t )  jg Q (t )

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 116

Using Euler’s identity

 
g (t )  Re g I (t )  jg Q (t ) cos( 2f c t )  j sin( 2f c t )

hence g (t )  g I (t ) cos( 2f c t )  g Q (t ) sin( 2f c t )

g(t) is called canonical representation of narrow band
signal in terms of In-phase components gI(t) and
Quadrature components gQ(t).

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 117

Natural Envelope
Alternatively we may express the complex envelope
g~(t) in the form

g~ (t )  a (t ) exp j (t )

Where a(t) and ø(t) are both real valued low-pass

functions. Based on this representation, the band pass
signal g(t) is defined by

g (t )  a (t )Cos (2f c t   (t ))
We refer to a(t) as the natural envelope or the
envelope of the band pass signal g(t) and to ø(t) as
the phase of the signal.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 118

Single Side Band Modulation SSB
Standard amplitude modulation and DSB-SC are
wasteful of bandwidth because they both require a
transmission bandwidth equal to twice the message
Bandwidth.
Neither case one of transmission bandwidth occupies
by upper side band of modulating wave where as the
other occupies by the lower side band.
The transmission of information is concerned only if
one sideband is necessary and both other carrier and
sideband are suppressed at transmitter. .
So no information is lost. Thus the channel needs to
provide only the same bandwidth as the message signal
When only one sideband is transmitted modulation is
referred as single side band modulation.
119
Frequency domain description
The frequency domain description of SSB wave depends
on which side band is transmitted.
Consider a message signal m(t) with a spectrum M(f)
limited to band –W≤f≤W as show in figure

M(f)
M(0)

-w 0 W

The spectrum of DSB-SC modulated wave obtained by

multiplying m(t) with carrier Ac cos(2Πfct) as shown
120
 S(f)

LSB LSB

-fc-W -fc -fc+W fc-W fc fc+W

The LSB is represented in duplicate by frequency below

fc for positive frequencies and those above –fc for
negative frequencies and only lower sideband is
transmitted spectrum of corresponding SSB modulating
wave as shown in figure
½ AcM(0)

LSB LSB

-fc -fc+W fc-W fc 121

LSB frequencies of SSB Modulation
The SSB wave equation only LSB transmitted

Ac  

sL (t ) 
2 m(t ) cos(2f c t )  m(t ) sin(2f c t )
 
Let modulated signal m(t) represented as

m(t )  A m Cos (2f m t )

The Hilbert transform of the modulating signal m(t) is

obtained by passing it through a -90 phase shifter.
So that the Hilbert transform is given by

m(t )  A m sin(2f m t )
122
Substitute the m(t) and m^(t) in the above equation

Ac  
s L (t )  A
 m cos( 2f m t ) cos( 2f c t )  Am sin( 2f m t ) sin( 2f t
c )
2  
Ac Am
s L (t )  cos 2 ( f c  f m )t )
2
Apply Fourier transform both side
Ac Am
SL ( f )   ( f  ( f c  f m )   ( f  ( f c  f m )
4
AcAm/2

-fc+fm fc-fm

123
Like wise upper side band is located in duplicate by
frequency above fc and those below –fc and when only
USB is transmitted the resulting SSB wave obtained as
spectrum is shown in below

USB USB

-fc-W -fc fc fc+W

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 124

USB frequencies of SSB Modulation
The SSB wave equation only USB transmitted

Ac  

sU (t ) 
2 m(t ) cos(2f c t )  m(t ) sin(2f c t )
 

Let modulated signal m(t) represented as

m(t )  A m Cos (2f m t )

The Hilbert transform of the modulating signal m(t) is
obtained by passing it through a -90 phase shifter.
So that the Hilbert transform is given by

m(t )  A m sin(2f m t )
125
Substitute the m(t) and m^(t) in the above equation

Ac  
sU (t )  A
 m cos( 2f c t ) cos( 2f m t )  Am sin( 2f c t ) sin( 2f t
m )
2  
Ac Am
sU (t )  cos 2 ( f c  f m )t )
2
Apply Fourier transform both side
Ac Am
SU ( f )   ( f  ( f c  f m )   ( f  ( f c  f m )
4
AcAm/4

-fc-fm fc+fm

126
Time domain description of SSB wave
Idea of a complex envelope in the time domain description
of an SSB s(t) in the canonical form is given by

s (t )  s I (t ) cos( 2f c t )  s Q (t ) sin( 2f c t )

sI(t) In-phase components of the SSB wave and sQ(t)
is its Quadrature components
The in-phase component except for a scaling factor
may be derived from s(t) by first multiply s(t) by
cos(2Πfct) and the passing through a LPF.

similarly quadrature component except for a scaling

factor may be derived from s(t) by first multiply s(t)
by sin(2Πfct) and the passing through a LPF.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 127

Fourier transform of SI(t) and SQ(t) are related to
that of SSB wave as follows, respectively

SI ( f )  S( f  fc )  S( f  fc ) -W  f  W
S Q ( f )  jS ( f  f c )  S ( f  f c ) -W  f  W

where –W≤f≤W define frequency band occupied by the

message signal

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 128

 Spectrum of SSB -USB

-W-fc -fc fc fc +W
Spectrum of SSB –USB shifted right by fc S( f  fc )

W 0 2fc 2fc +W
Spectrum of SSB –USB shifted left by fc S( f  fc )

-W-2fc -2fc 1 0 W
2
Ac M (0 ) S I (f)
Spectrum of SSB
In-phase component
-W 0 W 129
The in-phase component of spectrum equation

1
S I (f)  Ac M ( f )
2
The in-phase component in time domain

1
s I (t)  Ac m(t )
2

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 130

 Spectrum of SSB -USB

-W-fc -fc fc fc +W

Spectrum of SSB –USB shifted right by fc jS ( f  f c )

W 0 2fc 2fc +W

Spectrum of SSB –USB shifted left by fc  jS ( f  f c )

-W-2fc -2f 0 W
c

131
Spectrum of quadrature component of SSB-USB

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 132

From spectrum of quadrature component we may write

 j
 2 Ac M ( f ) f 0

S Q (f)   0 f 0
 j
 Ac M ( f ) f 0
 2

 j
S Q (f)  Ac Sgn( f ) M ( f )
2
M^(f) Fourier transform of Hilbert transform
Ac 
 S Q (f)  M(f )
2
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 133
The quadrature component of spectrum equation
Ac 
S Q (f)  M(f )
2
The quadrature component in time domain
1 
s Q (t)  Ac m(t )
2
Substituting in-phase and quadrature component in
canonical form of s(t)

1 1 
s (t )  Ac m(t ) cos( 2f c t )  Ac m(t ) sin( 2f c t )
2 2

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 134

Generation of SSB wave
1. Frequency discrimination method
2. Phase Discrimination method
3. Third method or weavers method

1. Frequency discrimination method

Frequency discrimination method may be used to
generate as SSB wave when m(t) satisfy two condition.
1. The message signal m(t) has little or no frequency
content. Example Speech audio and Music signal.

2. The highest frequency component W of the message

signal m(t) is much less than the carrier frequency.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 135

Under these condition the desired sideband will appear
in a non over lapping interval in the spectrum in such a
way that it may be selected by appropriated filter.
The frequency discrimination method of SSB generation
consists of a product modulator which produces DSBSC
signal and a band pass filter to extract the desired
side band and reject the other and is shown in the
figure below.

Product DSB SSB wave

m(t) Band
modulator pass filter

c(t)=Ac cos2Πfct

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 136

In designing the band pass filter, the following
requirement should be satisfied.
1. The pass band of the filter occupies the same
frequency range as the spectrum of the desired
SSB modulated wave,
2.The width of the guard band of the filter separating
the pass and form the stop band, where the
unwanted sideband of the filter input lies is twice
the lowest frequency component of the message
signal.
the center frequency of BPF decide whether USB
signal is generated or LSB signal is generated
suppose we want to transmit USB, then using an
ideal BSP with center frequency fc+W/2, we can
obtain desired result as shown in spectrum. 137
 m(t)

-W 0 W

SDSB

-fc-W fc -fc+W fc-W fc fc+W

BPF
-fc-W fc fc fc+W

SSSB

-fc-W fc fc 138
fc+W
 The draw back of frequency discrimination method

1. Since ideal BPF is not available in the result SSB

signal some additional frequency component will be
present. Because of this drawback SSB modulation is
limited for the transmission of voice signal only

2. When it is necessary to generate an SSB modulated

wave occupying a frequency band that is much higher
than that of the message signal it become very
difficult to design an appropriate filter that will pass
the desired side band and reject the other
.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 139

In such situation it is necessary to resort to a multiple
modulation process so as to ease the filtering
requirement. This approach is illustrated in the
following figure involving two stages of modulation.

m(t) SSB
Product Band Product Band
Modulator pass filter Modulat pass wave
or filter

Ac cos( 2f 1t ) Ac cos( 2f 2 t )

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 140

The SSB modulated wave at the first filter output is
used as the modulating wave for the second product
modulator, which produces a DSBSC modulated wave
with a spectrum that is symmetrically spaced about the
second carrier frequency f2.

The frequency separation between the side bands of

this DSBSC modulated wave is effectively twice the
first carrier frequency f1, there by permitting the
second filter to remove the unwanted side band.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 141

Phase Discrimination method
The block diagram of phase discrimination method of
generation of SSB wave In-phase path
SSB wave
m (t) Product
+ S(t)
Modulator
I

+
_
Wide band Ac cos(2fc t)
90 phase
90ᵒ Phase shift
shift
Ac sin(2fc t)

m(t) Product
Modulator
Q
Quadrature path
142
 The SSB modulator uses two product modulators In-
phase and Quadrature supplied with carrier waves in-
phase quadrature to each other
 The message signal m(t) and a carrier signal Ac
cos(2Πfct) is directly applied to the product
modulator I, producing a DSB-SC wave.
 The hilbert transform m^(t) of m(t) and carrier signal
shifted by 90 are applied to the product modulator Q,
producing DSB-SC wave.
 The output of product modulator I is

s I (t )  m(t ) Ac cos( 2f c t )

 The output of product modulator Q is

sQ (t )  m(t ) Ac sin( 2f c t )
143
These signals sI(t) and sQ(t) are fed to a summer

The output of the summer is

s (t )  s I (t )  s Q (t )

s (t )  Ac m(t ) cos(2f c t )  Ac m(t ) sin( 2f c t )
Merits
Bulkier filters are replaced by small filters
Low audio frequencies may be used for modulation
It can generate SSB at any frequency
Easy switching from one sideband to other sideband is
possible
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 144
 Demerits

1. The output of two balanced modulators must be

exactly same otherwise cancellation will be incomplete

2. If the phase shifter provides a phase change other

than 90ᵒ at any audio frequency, that particular
frequency will not be completely removed from the
unwanted sideband.

Demodulation of SSB

s(t) Product v(t) Low pass v0(t)

Modulator Filter
SSB-SC


Ac cos( 2f c t )
145
The base band signal m(t) can be recovered from a
SSB-SC wave s(t) by multiplying s(t) with a locally
generated carrier signal and then passing through low
pass filtering.
Product modulator output is v (t )  s (t ) Ac cos( 2f c t )
where s(t) is

Ac  

s (t ) 
2 m(t ) cos( 2f c t )  m(t ) sin( 2f c t 
Substitute s(t) in v(t)

Ac  
 
v(t )   m (t ) cos( 2f c t )  m (t ) sin( 2f c t  Ac cos( 2f c t )
2
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 146
  ˆ
Ac Ac m(t ) Ac Ac m(t )
v(t )  cos(4f c t )  1  sin(4f c t 
4 4
 
Ac Ac m(t ) Ac Ac
v(t )   m(t ) cos(4f c t )  mˆ (t ) sin(4f c t 
4 4
Spectrum of the product modulator output v(t)

V(t)

-2fc-W -2fc -W 0 W 2fc 2fc+W

The first term is the wanted signal and the second

term is unwanted signal represent as SSB modulating
wave with carrier frequency 2fc.
147
When v(t) is passed through the LPF the high
frequency components are removed and thereby
yielding the desired baseband signal.

Thus at the output of the Low pass filter we get the

demodulated signal v0(t)

Ac Ac m(t )
v0 (t ) 
4
The spectrum of demodulated signal V0(f)

V0(t)

-W 0 W

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 148

The method of coherent detection is based on the
assumption that there is perfect synchronization
between local carrier and that in the transmitter both
in frequency and phase.

Any error in the frequency or the phase of the local

oscillator gives rise to distortion in the demodulated
signal. Assume a frequency error Δf so that the local
oscillator signal is Ac cos(2Π(fc+Δf)). The effect of
frequency error is
1. If the incoming SSB wave contains the lower sideband
and the frequency error Δf is positive or if SSB wave
contains the upper sideband and Δf is negative then
the frequency components of the demodulated signal
are shifted outwards by Δf compare with baseband
signal
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 149
2. If the incoming SSB wave contains the lower sideband
and the frequency error Δf is negative or if SSB
wave contains the upper sideband and Δf is positive
then the frequency components of the demodulated
signal are shifted inwards by Δf compare with
baseband signal

But in practice there is phase error ø in the locally

generated carrier wave which distorts the output V0(t)


Ac Ac
v0 (t )  m(t ) cos   mˆ (t ) sin 
4

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 150

Above equation tells us that due to the phase error,
the output consists of not only the desired message
signal m(t) but also its Hilbert transform. Thus the
output has a phase distortion.
This phase distortion is usually not serious with voice
communications because the human ear is relatively
insensitive to phase distortion. But presence of such
phase distortion gives the effect called as “ Donald
Duck voice effect”
Such distortion cannot be tolerable in the transmission
of music and video signals.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 151

Advantage of SSB Modulation
 SSB required the bandwidth same as
message bandwidth.( half of the
bandwidth of AM and DSB-SC).
 Due to suppression of carrier and one
sideband power is saved.
 Reduced interference of noise.
 Fading does not occur in SSB
transmission.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 152

 Disadvantage of SSB
 The generation and reception of SSB signal is a
complex process.
 Since carrier is absent, the SSB transmitter and
receiver need to have an excellent frequency
stability
 The SSB Modulation is expensive and highly
complex to implement.
 Application of SSB
 SSB transmission is used in the applications where
the power saving is required in mobile system
 SSB is also used where bandwidth requirement are
low

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 153

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162
 Vestigial sideband modulation
 VSB modulated wave containing Fully one
sideband and vestige of the other sideband is
transmitted.
 The band width of VSB is W+fv
 VSB modulation technique is used in TV signal
transmission

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 163

Generation of VSB modulation wave
To generate a VSB modulating wave passing a DSB-SC
modulating wave through a sideband sharping filter as
shown in fig. the exact design of this filter depends on
desired spectrum of VSB modulating wave.

Side band VSB wave

m(t) Product DSB s(t)
Sharping
Modulator Filter H(f)

Ac cos( 2f c t )
The filter will pass the wanted sideband as it is and
the vestige of the unwanted sideband.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 164

Let the transfer function of the filter be H(f). Hence
the spectrum of the VSB modulated wave is given by

Ac
S( f )  M ( f  f c )  M ( f  f c )H ( f )
2
Where M(f) is message spectrum and S(f) defines the
spectrum of desired VSB wave.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 165

Time Domain Description of VSB
 Let us consider that s(t) as a VSB modulated wave
containing Full upper sideband and vestige of the lower
sideband.
 S(t) is viewed as an output of sideband shaping filter
in response to the input DSB-SC modulated wave.
 The sideband shaping filter can be represented by its
transfer function H(f) and we express H~(f) as the
difference between two components H~u(f) and H~v(f).
~ ~ ~
H( f )  Hu ( f )  Hv ( f ) (1)
 H~u(f) pertains to a complex low pass filter equivalent
to band pass filter designed to reject the lower
sideband completely.
 H~v(f) accounts for both the generation of a vestige of
the LSB and the removal of USB.
J. Ravindranadh/ Professor/EC
316 Analog Communication 166
J. Ravindranadh/ Professor/EC 316 Analog Communication 167
Mathematically it can be expressed USB H~(f)
~ 1
H u ( f )  1  sgn( f ) 0  f W
2
0 otherwise
Substituting the above equation in equation (1)
~ 1
2
 ~
H ( f )  1  sgn( f )  2 H v ( f )   f v  f  W (2)

0 otherwise
The signum function sgn(f) and the transfer function
H~v(f) are both odd functions of the function f.

Hence they both have purely imaginary inverse Fourier

transforms.

J. Ravindranadh/ Professor/EC 316 Analog Communication 168

Accordingly it is possible to produce new transfer function

1
 ~
H S ( f )  sgn( f )  2 H ( f )
j

Substituting the above equation in equation (2)
~ 1
H ( f )  1  jH S ( f )  fv  f  W
2
0 otherwise
Let us now determine the VSB modulated wave s(t)
s (t )  Re ~
s (t ) exp( j 2f c t ) (3)

s~(t) is the complex envelope of s(t)

J. Ravindranadh/ Professor/EC 316 Analog Communication 169

We can define spectrum of s~(t) as

~ ~ ~
s ( f )  H ( f ) S DSBSC ( f )

The complex envelope of the S~ DSBSC(f) wave is

~
S DSBSC ( f )  Ac M ( f )
Substitute the H~(f) and S~ DSBSC(f)

~ Ac
S( f )  1  jH S ( f ) M(f)
2
By taking inverse Fourier transform of S~(f)

Ac
~
s (t )  m(t )  jm s (t )
2
J. Ravindranadh/ Professor/EC 316 Analog Communication 170
Where ms(t) is the output of a lowpass filter of impulse
response hs(t) when input to the lowpass filter is the
message signal m(t).

Substituting s~(t) in equation (3) we get

 Ac 
s (t )  Re  m(t )  jm s (t )cos(2f c t )  j sin(2f c t )
2 
Ac Ac
s (t )  m(t ) cos(2f c t )  m s (t ) sin( 2f c t )
2 2

J. Ravindranadh/ Professor/EC 316 Analog Communication 171

Demodulation of VSB
Low pass V0(t)
s(t) Product V(t)
Filter
Modulator

Ac cos( 2f c t )
The demodulation of VSB modulated wave can be
achieved by passing VSB wave s(t) through a coherent
detector.
Thus multiplying s(t) by a locally generated carrier
wave which is synchronous with in incoming wave in both
frequency and phase , we will get

v (t )  Ac cos 2f c t  s (t )
172
Taking Fourier transform on both side

Ac
V(f)  S ( f  f c )  S ( f  f c ) 
2
Ac
Where S ( f )  M ( f  f c )  M ( f  f c ) H ( f )
2
Ac
S ( f  fc )  M ( f  f c  f c )  M ( f  f c  f c ) H ( f  f c )
2
Ac
S ( f  fc )  M ( f )  M ( f  2 f c ) H ( f  f c )
2
Similarly
Ac
S ( f  fc )  M ( f  2 f c )  M ( f ) H ( f  f c )
2
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 173
 Ac
V(f) M ( f ) H ( f  f c )  H ( f  f c ) 
4
A
 c M ( f  2 f c ) H ( f  f c )  M ( f  2 f c ) H ( f  f c ) 
4
Spectrum of the product modulator output

The above equation passing through LPF eliminates the

unwanted term and passing only wanted term
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 174
 Ac
V0 ( f )  M ( f ) H ( f  f c )  H ( f  f c ) 
4
The spectrum of the demodulated signal

For getting distortion less reproduction of original base

band signal at coherent detector output. The transfer
function H(f) must satisfy the condition

H ( f  fc )  H ( f  fc )  2 H ( fc )
Where H(fc) is constant with message spectrum M(f)
Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 175
Envelope Detection of a VSB plus carrier
VSB modulation is used in the commercial TV
broadcasting in which along with VSB transmission a
carrier signal of substantial size is transmitted.
The modulated wave can be demodulated by using
envelope detector. The VSB modulated wave with full
USB and a vestige of LSB is given by

s (t )USB 
Ac
2

m I (t ) cos(2f c t )  mQ (t ) sin( 2f c t ) 
Adding carrier component scaled by a factor ka,
modified modulated wave applied to the envelope
detector input as

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 176

 s (t )  Ac cos(2f c t )  k a s (t )USB

s (t )  Ac cos( 2f c t )  k a
Ac
2

m I (t ) cos( 2f c t )  mQ (t ) sin( 2f c t ) 
 ka  k a Ac
s (t )  1  mI (t ) Ac cos(2f c t )  mQ (t ) sin( 2f c t )
 2  2

s(t) the first term represent the in-phase component

and second term represent the quadrature phase
component. Where ka is the modulation index, it
determines the percentage modulation.

When the above signal s(t) is passed through the

envelope detector, the detector output is

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 177

 2 2
 ka  2  k a Ac 
a (t )  1  mI (t ) Ac   mQ (t )
 2   2 
2
 ka 
 mQ (t ) 
 k   2
a (t )  Ac 1  a mI (t ) 1  2
 2   ka 
1  2 m(t )

2 1/ 2
  ka  
 m (t ) 
 ka   2 Q  
a (t )  Ac 1  mI (t ) 1   
 2   k 
  1  a
m(t )  
 2  

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 178

The detector output is distorted by the quadrature
component mQ(t)

Methods to reduce distortion

1. Distortion can be reduced by reducing percentage

modulation ka
2. Distortion can be reduced by reducing mQ(t) by
increasing the width of the vestigial sideband.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 179

 Comparison of Amplitude Modulation Techniques
1. In standard AM system, sideband and carrier are
transmitted, demodulation is accomplish by using
envelope or square law detector. On other hand in
suppressed carrier system, receiver is more complex
because additional circuitry must be provided for the
purpose of carrier recovery. For this reason we use
standard AM in commercial broadcast systems, which
involve one transmitter and numerous receivers.
2. Suppressed carrier modulation system has an
advantage over AM system. They require much less
power to transmit same amount of information and
less expensive than those required for standard AM.
Suppressed carrier systems are well suited for point
to point communication, involving one transmitter and
one receiver.
180
3. The single sideband modulation required minimum
transmission power and minimum transmission
bandwidth possible for conveying a message signal
from one point to another. SSB modulation is
preferred for long-distance transmission of voice
signals over metallic circuits.
4. VSB modulation requires a transmission bandwidth
that is intermediate between that required for SSB
and DSBSC modulation. If modulating wave of large
bandwidth are handled in case of TV signals and wide
band data.
5. DSB-SC and SSB-SC, VSB are example of linear
modulation. The output of a linear modulator can be
expressed in the canonical form.

s (t )  s I (t ) cos(2f c t  s Q (t ) sin( 2f c t )

181
Type of Modulation In-phase Quadrature
component component
DSBSC m(t) 0 m(t) message signal
SSB
(a) USB Transmitted ½ m(t) ½ m^(t) m^(t) Hilbert
(b) LSB Transmitted ½ m(t) -½ m^(t) transform

VSB
(a) Vestige of LSB ½ m(t) ½ ms(t) ms(t)=output of
Transmitted filter of transfer
(b) Vestige of VSB ½ m(t) -½ ms(t) function Hs(f)
Transmitted

6. In both SSB and VSB modulation role of quadrature

component is mainly to interfere with inphase
component so as to eliminate power in one of side
band.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 182

When the modulation percentage is 75%, an AM
transmitter radiates 10KW Power. How much of this is
carrier Power?

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 183

An AM transmitter radiates 20KW. If the modulation
Index is 0.7. Find the carrier Power

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 184

The total Power content of an AM signal is 1000W.
Determine the power being transmitted at carrier
frequency and at each side bands when modulation
percentage is 100%.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 185

A500W, 100KHz carrier is modulated to a depth of 60%
by modulating frequency of 1KHz. Calculate the total
power transmitted. What are the sideband components of
AM Wave?

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 186

A 400W, 1MHz carrier is amplitude-modulated with a
sinusoidal signal 0f 2500Hz. The depth of modulation is
75%. Calculate the sideband frequencies, bandwidth, and
power in sidebands and the total power in modulated wave.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 187

Calculate the percentage power saving when one side band
and carrier is suppressed in an AM signal if percentage of
modulation is 50%.

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 188

189
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The AM wave 10[ 1+0.5 cos(2Π500t)]cos(2Π106t is
demodulated by an envelope detector. Find the time
constant Г and the resistor if capacitor used is 100pF

Dr. J. Ravindranadh/ Professor / ECE Dept / Analog Communication 192