Electronics Circuits for

Communications
Total periods: 42 Theory: 30 Practice: 12 Group Assignment: 27
Final exam: 60% Practice: 20% Group Assignment: 20%

1
Learning Resources
[1] Hoàng Đình Chiến, “Mạch Điện Tử Thông Tin”, Nhà xuất bản ĐHQG, 2004.
[2] Hoàng Đình Chiến, “Thông Tin vô tuyến – Nguyên lý và tính toán, ứng dụng”, Nhà
xuất bản ĐHQG, 2008.
[3] Ulrich. L. Rohde, David. P. Newkirk, “RF/Microwave Circuit Design for Wireless
Applications”, John Wiley & Sons, 2000.
[4] Steve C. Cripps, “RF Power Amplifiers for Wireless Communications”, second edition,
Artech House, 2006.
[5] Jeffrey S. Beasley, Gary M.Miller, “Modern Electronic Communication”, 9th edition,
Pearson, 2014.
[6] Wayne Tomachi, “Advanced Electronic Communication Systems”, Prentice Hall, 2000.
…

2
 Chapter 1
Introduction of Communication
Systems and Elements

3
Radio Frequency Bands
International Telecommunication Union (ITU)

4
Radio Frequency Bands
US Institute of Electrical and Electronics Engineers (IEEE)

5
Basic View on Modulation

Angle modulation with

higher immunity to noise
and interference
6
Elements of RF Communication Systems
1st Gen.

8st Gen.

Example of evolution of Electronics Circuits for Communications

7
Elements of traditional RF Communication Systems

8
Elements of traditional RF Communication Systems
1. The source of the message, may be analogue or digital information,
transformed into an electrical signal.
2. The signal is amplified and often passed through a low-pass filter to
limit the bandwidth.
3. The RF oscillator establishes the carrier frequency. Frequency stability
is required to keep the transmitter on its assigned frequency, the
oscillator is often controlled by a quartz crystal (Chapter 7).
4. One or more amplifier (and/or frequency multiplier) stages increase the
power level (and/or frequency) of the signal from the oscillator to that
needed for input to the modulator.
5. The modulator combines/mixes the message signal and carrier signal
(radio frequency) to produce the modulated signal (in the radio
transmitting band) (Chapter 8, 9).
6. Power amplifier required after the modulator to gain the power of the
transmitting signal (Chapter 3).
7. The transmitting antenna radiates the RF energy into electromagnetic
waves propagating in the space and a part of this energy is toward the
receiving antenna.

9
Elements of traditional RF Communication Systems
8. The receiving antenna may be omni-directional for general service or highly
directional for point-to-point communication. Due to the path loss in the
transmitting, the amplitudes at the receiving antenna port may be less than 1µV.
9. The RF low noise amplifier increases the signal power to a suitable level for the
mixer because of a high degree of noise introduced in the mixer stage. This
stage often includes a channel filter to reject undesired frequencies components
in the channel.
10. The local oscillator in the receiver generates a signal - frequency fLO that is
mixed to the received signal - frequency fRF to produce the signal - intermediate
frequency fIF that is equal to fLO – fRF or fRF – fLO.
11. The mixer is a nonlinear device that shifts the received signal at fRF to the
intermediate frequency fIF. The modulated message information in fRF band is
also shifted to the fIF band.
12. The IF amplifier increases the signal to a level suitable for detection. This stage
is often with good frequency selectivity at the fixed fIF band (ceramic or crystal
filters) to filter out undesired signals.
13. The detector or demodulator recovers the message signal from the modulated
signal in fIF band (Chapter 8).
14. The audio or video amplifier increases the level of the recovered message signal
to a suitable level to drive a loudspeaker, a television tube, or others.
15. The output device converts the signal information back to its original physic
form (sound waves, picture, etc.).
10
Problems and Solutions in Practical RF Systems

▪ Radio Channel Division and Multiplexing

Time, Frequency, Code, Space

TDM, FDM, CDMA, Smart Antennas, MIMO

11
Problems and Solutions in Practical RF Systems

▪ Propagation Effects
Path Loss, Antenna Directivity Gain, External Noise, Interference

Multi-Path, Fading

12
Problems and Solutions in Practical RF Systems

▪ Image frequency and Image reject filter

Super-heterodyne receiver
BP: Band pass,
LNA: Low Noise Amplifier,
VCO: Voltage Controlled Oscillator,
ADC: Analogue Digital Converter,
DSP: Digital Signal Processor

13
Problems and Solutions in Practical RF Systems

▪ Image frequency and Image reject filter

Super-heterodyne receiver with double down-conversion

14
Problems and Solutions in Practical RF Systems

▪ Image frequency and Image reject filter

Hartley and Weaver Image reject techniques

15
Problems in Practical RF Systems
▪ Distortion

Nonlinear
LNA

with fundamental and the higher order harmonics

16
 Problems in Practical RF Systems
▪ Intermodulation (IM)

Response of a Nonlinear LNA: Nonlinear

LNA

17
Problems in Practical RF Systems
▪ Intermodulation (IM)

Input signal with f1 and f2 Nonlinear

component

18
Metrics for RF Elements and Systems
▪ Signal amplitude and Power
In RF and microwave techniques, power is usually used to describe
signals, noise level, or distortion degree with the typical unit of decibels
above 1 milliwatt (dBm). Voltage and current are expressed as peak,
peak-to-peak, or root-mean-square (rms).

19
Metrics for RF Elements and Systems
▪ Signal amplitude and Power

20
Metrics for RF Elements and Systems
▪ Total Harmonic Distortion (THD)
Harmonic distortion factors (HDi) provide a measure for a distortion introduced by
each harmonic for a given input signal level (using a single tone at a given
frequency)

HDi is defined as the ratio of the output signal level of the i-th harmonic to that of
the fundamental.

21
Metrics for RF Elements and Systems
▪ 1-dB Compression Point
1-dB compression point is defined as the point where the fundamental gain
deviates from the ideal gain (small signal) by 1 dB (using a single tone at a given
frequency)

22
Metrics for RF Elements and Systems
▪ Third-order Intercept Point (IP3)
IP3 point is defined as the intercept point of the fundamental component with
third-order intermodulation component (using dual tone)

23
Metrics for RF Elements and Systems
▪ Third-order Intercept Point (IP3)

4 𝛼1
֜ 𝐴𝐼𝐼𝑃3 ≅
3 𝛼3

▪ Third-order Intermodulation Distortion (IM3)

3 𝛼3 2
𝐼𝑀3 ≅ 𝐴
4 𝛼1

24
Metrics for RF Elements and Systems
▪ Dynamic Range
➢ Linearity determines how large a signal a receiver can handle
➢ Noise determines how small a signal a receiver can handle
1. Dynamic Range: the minimum detectable signal to the 1-dB compression point
2. Intermodulation Free Dynamic Range

25
Modern RF Transceiver Architectures
A Transceiver consists of a transmitter and a receiver
Example of Half Duplex Super-Heterodyne Transceiver

2
1

26
Modern RF Transceiver Architectures
Full Duplex Transceiver with Circulator and Self-Interference Canceller

2
1

SIC: Self-Interference Canceller

LO: Local Oscillator

27
Modern RF Transceiver Architectures
Impulse Radio Transmitter and Receiver

PPM: Pulse Position Modulation

BBSP: Baseband Signal Processing

Impulse based radios for short range, low power and high speed applications.
UWB (Ultra-Wideband) standards have already been published by the FCC (Federal
Communications Commission - US) employing impulse transmission within a
frequency band between 3.1 GHz and 10.6 GHz.

28
Modern RF Transceiver Architectures
Smart Antenna, MIMO Transceivers

29
Software-Defined Radios (SDR)

Multi-mode handset featuring separate radios

30
Software-Defined Radios (SDR)
▪ SDR is a radio communication technology that is based on software
defined wireless communication protocols instead of hardwired
implementations. In other words, frequency band, air interface protocol
and functionality can be upgraded with software download and update
instead of a complete hardware replacement. SDR provides an efficient
and secure solution to the problems of building multi-mode, multi-band
and multifunctional wireless communication devices.
▪ A SDR is capable of being re-programmed or reconfigured to operate
with different waveforms and protocols through dynamic loading of
new waveforms and protocols. These waveforms and protocols can
contain a number of different parts, including modulation techniques,
security and performance characteristics defined in software as part of
the waveform itself.

Source: http://focus.ti.com/docs/solution/folders/print/357.html

31
Software-Defined Radios (SDR)
▪ SDR Evolution – stage 2: Quadruple-band (800, 900,1800, and 1900 MHz),
quadruple-mode (AMPS, TDMA, GSM, CDMA), multi-band, multi-mode handset.

32
Software-Defined Radios (SDR)
▪ SDR Evolution – stage 3: A/D, D/A and signal processing chips at that stage had
the capacity to perform IF and baseband processing.

33
Software-Defined Radios (SDR)
▪ SDR Evolution – stage 4: Current and Future products.

▪ System on Chip

34
 Chapter 2
Fundamentals in Radio Frequency

1
Lumped Elements
Ideal elements

2
Lumped Elements
Lossy elements

3
Lumped Elements
Series to parallel conversions

Assuming that Xs and Xp are similar type, either capacitance (X<0) or inductance (X>0)

Series to parallel
conversion:

Parallel to series
conversion:

4
 Maximum Power Transfer
RS
2
2
𝑉𝑆
𝑝 = 𝑖 𝑅𝐿 = 𝑅𝐿
VS 𝑅𝑆 + 𝑅𝐿
RL

The derivative of p :
𝑑𝑝 𝑑 𝑉𝑆 2 𝑅𝑆 −𝑅𝐿
= 𝑖 2 𝑅𝐿 = 𝑅𝐿 =𝑉𝑆2
𝑑𝑅𝐿 𝑑𝑅𝐿 𝑅𝑆 +𝑅𝐿 𝑅𝑆 +𝑅𝐿 3

The power p is maximum if RS

𝑑𝑝 𝑅𝑆 − 𝑅𝐿
= 𝑉𝑆2 3
=0 ⟹ 𝑅𝐿 = 𝑅𝑆
𝑑𝑅𝐿 𝑅𝑆 + 𝑅𝐿

𝑉𝑆2
𝑝𝑚𝑎𝑥 =
4𝑅𝑆
5
 Maximum Power Transfer

ZS 𝑍𝐿 plane (𝑍𝐿 =R+jX)

with 𝑍𝑆 =50+j50 Ω
VS ZL
Max Power

(Ω)
Power contours
Condition for maximum Power Transfer:
𝑍𝐿 = 𝑍𝑆∗

(Ω)

6
Impedance Matching
Impedance matching to transform a load impedance
ZL to the optimal working impedance of the source
with Zs

𝑍 = 𝑍𝑆∗

7
 Impedance Matching
▪ High Q-factor resonant circuits

R’

L R’

R’

R’
C R’

8
R’
Impedance Matching
▪ Two reactance matching network - Γ and

9
Impedance Matching
▪ Two reactance matching network - Γ and

At resonant frequency, the

imaginary part is eliminated:

10
Impedance Matching
▪ Two reactance matching network - Γ and

Condition at resonant frequency:

11
Impedance Matching
▪ Π matching network

Recommended values of Q from 1 to 10

12
Impedance Matching
▪ T matching network 1

13
Impedance Matching
▪ T matching network 2

14
Impedance Matching
▪ three-reactance matching network

15
Resonant Circuits
▪ Parallel resonant circuit

Impedance:

Resonance frequency:
Q factor:
Vout drop 3dB value:

3dB frequency cut off:

3dB bandwidth: 16
 Impedance Matching Examples

R’

L R’

R’ 𝐶𝑒𝑞
𝑄 ≈ 𝑅′
f=1GHz, R=10Ω, R’=50Ω, Q=100. Find C1, C2 and L 𝐿

17
Impedance Matching Examples
Impedance
40 Z(1,1) Swp Max

Impedance Matching 1 5000 MHz

20
m1:
946 MHz
L Re 25.45
Im 25.43

X
0 m3:
1000 MHz
m2:
Re 50
1044 MHz
Im -6.18
Re 25.56
Im -25.35
-20

R’ Swp Min
0 MHz
-40
Smith Chart 0 10 20 30 40 50 60
1.0

Swp Max
0.8

5000MHz R
Z(1,1)
6

Abs Impedance
0.

|Z(1,1)|
0
2.

60
4 Impedance Matching 1 Impedance Matching 1
0.
0
3.

4.
0 50 m2:
m1:
1000 MHz
5.0 994 MHz
0.2 m2: 50.38
50.77
993.9 MHz
r 1.01545 10.0
40
x -0.000279299
10.0
0.2

0.4

0.6

0.8

1.0

2.0

3.0

4.0
5.0
0

30

m1: -10.0
1000 MHz 20
-0.
2 r 0.998194 0
x -0.130371 -5.
.0
-4
10
.0
.4
-3
-0
.0

0
-2

18
.6
-0

0 1000 2000 3000 4000 5000

-0.8

Swp Min
-1.0

0MHz Frequency (MHz)

Impedance Matching Examples

f=1GHz, R=10Ω, R’=50Ω. Find C and L

19
 Impedance Matching Examples
Impedance
40 Z(1,1) Swp Max

Impedance Matching 2 5000 MHz

20

m1: m3:
788 MHz 1000 MHz

X
0 Re 50
Re 28.36
Im 13.55 Im -3.553e-14

m2:
-20 1286 MHz
Re 27.1
Im -36.46

Swp Min
0 MHz

Smith Chart -40

0 20 40 60 80
1.0

Swp Max
0.8

5000MHz R
6
0.

Z(1,1) Abs Impedance

0
2.

60 |Z(1,1)|
0.
4
Impedance Matching 2 0 Impedance Matching 2
3.
m1:
4.
0 1000 MHz
50 50 m2:
5.0
0.2 1109 MHz
54.81
10.0 40
m1:
10.0
0.2

0.4

0.6

0.8

1.0

2.0

3.0

4.0
5.0

1000 MHz
0

r1 30
x -7.65404e-06
-10.0

2
20
-0. 0
-5.
4 .0
-

.0
10 m3:
.4
-3
0 MHz
-0
10
.0

0
-2

20
.6
-0

0 1000 2000 3000 4000 5000

-0.8

Swp Min
-1.0

0MHz Frequency (MHz)

 Impedance Matching Examples
▪ Π matching network

f=1GHz, RL=10Ω, R=50Ω, Q=5. Find C1, C2 and L

21
 Impedance Matching Examples
Impedance
30 Z(1,1) Swp Max

Impedance Matching 1 5000 MHz

20

10 m1:
934 MHz m3:
Re 26.67 1000 MHz
0 Im 16.02 Re 50
Im -9.237e-14

X
-10

m2:
-20 1080 MHz
Re 26.28
Smith Chart Im -34.53
-30
1.0

Swp Max
0.8

5000MHz Swp Min

Z(1,1)
6

0 MHz
0.

-40
0
2.

4 Impedance Matching 1 0 10 20 30 40 50 60
0.
0 R
3.

4.
0 Abs Impedance
60 |Z(1,1)|
5.0
0.2 Impedance Matching 1
10.0 50 m2:
1000 MHz m1:
m1: 50 1026 MHz
10.0
0.2

0.4

0.6

0.8

1.0

2.0

3.0

4.0
5.0

1000 MHz 53.26

40
0

r 1.0016
x -0.00421079
-10.0 30
2
-0. 0
-5.
20
.0
-4

.0
.4
-3 10
-0
.0
-2
.6

0
22
-0

-0.8

Swp Min 0 1000 2000 3000 4000 5000

-1.0

0MHz Frequency (MHz)

 Chapter 3
RF Power Amplifiers

1
RF Power Amplifier Efficiency

Efficiency is a • High cost of high power, high

crucial parameter frequency active devices
of a RF power • Limitation in battery-power of
mobile equipment
amplifier due to

2
RF Power Amplifier Efficiency
Collector efficiency for
amplifier using bipolar 𝑃𝑂
transistors (BJTs) or drain 𝜂=
𝑃𝑑𝑐
efficiency for amplifiers
using MOSFETs

P0 usually
includes both RF
𝑃𝑑𝑐 = 𝑉𝑑𝑐 𝐼𝑑𝑐 fundamental
and harmonic
powers

3
RF Power Amplifier Efficiency

Overall efficiency 𝑃𝑂
also accounts for 𝜂𝑜𝑣𝑒𝑟𝑎𝑙𝑙 =
𝑃𝑑𝑐 + 𝑃𝐼𝑁
the driving power

𝜂𝑜𝑣𝑒𝑟𝑎𝑙𝑙
Power gain
𝑃𝑂
𝑃𝑂 =
𝐺𝑃 = 𝑃
𝑃𝐼𝑁 𝑃𝑑𝑐 + 𝑂
𝐺𝑃

4
Power Output Capability

When N power devices of a Power Output Capability

amplifier are expected to use in 𝑃𝑂𝑚𝑎𝑥
their maximum voltage and 𝐶𝑃 =
𝑁𝑉𝐶,𝑝𝑘 𝐼𝐶,𝑝𝑘
current ranges

5
Operating Classes
When BE junction is forward-biased
and CB junction is reverse-biased: 𝑖𝐶 ≈ 𝛽𝑖𝐵
𝑉𝑏 > 𝑉𝑇
When BE junction is reverse-biased
and CB junction is reverse-biased: 𝑖𝐶 ≈ 0
𝑉𝑏 < 𝑉𝑇

Control
Changing
the bias
continuity
voltage
of 𝑖𝐶
𝑉𝐵𝐵

RFC RFC

DC Block

DC Block
6
Operating Classes
Portion per a RF cycle,
• Class A, if 2𝜃𝐶 = 360𝑜
in which amplifying
• Class AB, if 360𝑜 < 2𝜃𝐶 < 360𝑜
device is in its active • Class B, if 2𝜃𝐶 = 180𝑜
region - conduction • Class C, if 2𝜃𝐶 < 180𝑜
angle 2𝜃𝐶

7
 Waveform Harmonics
Waveform:
𝑖 𝜃
• DC harmonic 𝑛 = 0
𝐼𝑀 𝑐𝑜𝑠𝜃 − 𝑐𝑜𝑠𝜃𝑐 𝑠𝑖𝑛𝜃𝑐 −𝜃𝑐 𝑐𝑜𝑠𝜃𝑐
, −𝜃𝑐 ≤ 𝜃 − 2𝑘𝜋 ≤ 𝜃𝑐 , 𝑘 ∈ 𝑍 𝐼0 𝜃𝑐 = 𝐼𝑀 𝛼0 𝜃𝑐 = 𝐼𝑀
=൞ 1 − 𝑐𝑜𝑠𝜃𝑐 𝜋 1−𝑐𝑜𝑠𝜃𝑐
0 , otherwise • Fundamental harmonic 𝑛 = 1
𝜃 −𝑠𝑖𝑛𝜃𝑐 𝑐𝑜𝑠𝜃𝑐
𝐼1 𝜃𝑐 = 𝐼𝑀 𝛼1 𝜃𝑐 = 𝐼𝑀 𝑐
𝜋 1−𝑐𝑜𝑠𝜃𝑐
Fourier transform of the waveform • n-order harmonics 𝑛 = 2, 3, …
∞ 𝑠𝑖𝑛(𝑛−1)𝜃𝑐 𝑠𝑖𝑛(𝑛+1)𝜃𝑐
−
𝑛−1 𝑛+1
𝑖 𝜃 = ෍ 𝐼𝑛 (𝜃𝑐 )cos 𝑛𝜃 𝐼𝑛 𝜃𝑐 = 𝐼𝑀 𝛼𝑛 𝜃𝑐 = 𝐼𝑀
𝑛𝜋 1−𝑐𝑜𝑠𝜃𝑐
𝑛=0

8
 Waveform Harmonics
Waveform:
𝑖 𝜃
𝐼𝑀 𝑐𝑜𝑠𝜃 − 𝑐𝑜𝑠𝜃𝑐 • DC harmonic 𝑛 = 0
, −𝜃𝑐 ≤ 𝜃 − 2𝑘𝜋 ≤ 𝜃𝑐 , 𝑘 ∈ 𝑍 𝑠𝑖𝑛𝜃𝑐 −𝜃𝑐 𝑐𝑜𝑠𝜃𝑐
=൞ 1 − 𝑐𝑜𝑠𝜃𝑐 𝐼0 𝜃𝑐 = 𝐼𝑃 𝛾0 𝜃𝑐 = 𝐼𝑃
𝜋
0 , otherwise • Fundamental harmonic 𝑛 = 1
𝜃 −𝑠𝑖𝑛𝜃𝑐 𝑐𝑜𝑠𝜃𝑐
𝐼1 𝜃𝑐 = 𝐼𝑃 𝛾1 𝜃𝑐 = 𝐼𝑃 𝑐
𝜋
Fourier transform of the waveform • n-order harmonics 𝑛 = 2, 3, …
∞ 𝑠𝑖𝑛(𝑛−1)𝜃𝑐 𝑠𝑖𝑛(𝑛+1)𝜃𝑐
−
𝑛−1 𝑛+1
𝑖 𝜃 = ෍ 𝐼𝑛 (𝜃𝑐 )cos 𝑛𝜃 𝐼𝑛 𝜃𝑐 = 𝐼𝑃 𝛾𝑛 𝜃𝑐 = 𝐼𝑃
𝑛𝜋
𝑛=0

9
 Waveform Harmonics

𝛼𝑛 of the harmonics versus conduction angle 2𝜃𝑐

10
𝛾𝑛 of the harmonics versus conduction angle 2𝜃𝑐
 RF Class C Power Amplifier
▪ Common emitter (CE) single-end amplifier
(collector circuit)
✓ Operating class controlled by the base-bias
circuits
✓ RF choke (RFC) that provides a DC
current, Idc
✓ DC blocking capacitor, Cd
✓ Load resistor, R
✓ Parallel resonant LC circuit allows only the
fundamental harmonic frequency ω0 for
the load suppressing all other harmonics

𝑣 𝑡 = 𝑉𝑑𝑐 + 𝑉0 cos 𝜔0 𝑡 = 𝑉𝑑𝑐 + 𝑅𝐼𝑀 𝛼1 (𝜃𝑐 ) cos 𝜔0 𝑡

11
 RF Class C Power Amplifier

The maximum power and efficiency obtained if

2
𝑉𝑑𝑐
𝑃0𝑚𝑎𝑥 =
2𝑅

The peak collector voltage if

𝐼𝑂 𝑉𝑑𝑐
The peak collector current 𝑖𝑚𝑎𝑥 = 𝐼𝑀 = =
𝛼1 (𝜃𝑐 ) 𝑅𝛼1 (𝜃𝑐 )
𝑃𝑂𝑚𝑎𝑥 𝛼1 (𝜃𝑐 )
The power output capability 𝐶𝑃 = =
𝑣𝑚𝑎𝑥 𝑖𝑚𝑎𝑥 4 12
 RF Class C Power Amplifier
▪ The choice of conduction angle is a
tradeoff among efficiency, power output
capability, peak values of voltage and
current and power gain.

13
 RF Class C Power Amplifier
▪ Common emitter (CE) single-end amplifier
(Base circuit)
𝐼𝑑𝑐 𝐼𝑃 𝛾0 (𝜃𝑐 )
𝐼𝐵0 = =
𝛽0 𝛽0
𝐼𝑃 𝐼0
𝐼𝑏 = =
𝛽 𝛽𝛾1 (𝜃𝑐 )

For -θc < θ < θc , the transistor is in its active

region. Consequently, the voltage across its BE
junction is VBE(on) ≈ 0.7V

14
 RF Class C Power Amplifier
▪ Bias circuit

15
 RF Class C Power Amplifier Example
▪ Design a class C amplifier delivers P0=8W to a RL=50-Ohm load with 85%
efficiency. The operating frequency is 1GHz, the DC power supply is
VDC=12V.
Assuming, the base input impedance
𝑅𝑏 = 10Ω, 𝛽 = 25, VBE(on) ≈ 0.7V.
Design the bias base circuit

16
RF Class C Power Amplifier Example

17
 RF Class C Frequency Multiplier
▪ Class C frequency multiplier has the same
schematic as Class C power amplifier and
operates in much the same way. The only
difference is that the collector resonant
circuit is tuned to the desired harmonic,
suppressing all other harmonics.
The parallel LC output circuit is ideal, tuned to the
n-th harmonic

𝑃𝑂𝑚𝑎𝑥 𝛼𝑛 (𝜃𝑐 )
𝐶𝑃 = = 18
𝑣𝑚𝑎𝑥 𝐼𝑀 4
 RF Class D Power Amplifier
▪ Class D amplifier is a switching-mode amplifier that uses two active
devices driven in a way that they are alternately switched ON (saturation)
and OFF to define either a rectangular voltage or rectangular current
waveform.
▪ The load circuit contains a band- or low-pass filter that removes the high-
order harmonics of the rectangular waveform and results in a sinusoidal
output.

19
 RF Class D Power Amplifier
Assuming a 50 percent duty cycle.

The output current and output voltage are sinusoidal:

The output current amplitude:

20
 RF Class D Power Amplifier
The output power:

The DC input current:

The DC power:

The collector efficiency:

The power output capability:

21
 Chapter 4
Noise and Low-Noise Amplifiers

1
 Spectral Density of Thermal Noise (Johnson Noise)
Two approaches can be used to derive the spectral distribution of thermal noise:
1. The thermal velocity distribution of the charge carriers is used to calculate the time
dependence of the induced current, which is then transformed into the frequency domain.
2. Application of Planck’s theory of black body radiation.
The first approach clearly shows the underlying physics, whereas the second “hides” the physics by
applying a general result of statistical mechanics. However, the first requires some advanced concepts
that go well beyond the standard curriculum, so the “black body” approach will be used.
In Planck’s theory of black body radiation the energy per mode
So at low frequencies the
spectral density is independent
of frequency and for a total
and the spectral density of the radiated power bandwidth B the noise power
that can be transferred to an
external device

This is the power that can be extracted in equilibrium

2
 Thermal Noise in Resistors
To apply this result to the noise of a resistor, consider a resistor R whose thermal noise gives rise
to a noise voltage Vn . To determine the power transferred to an external device consider the
circuit
Spectral noise voltage density:

The power dissipated

in the load resistor RL:

The maximum power

transfer occurs when
RL = R, so Spectral noise current density:

Since the maximum power

that can be transferred to RL is kTB ,

Power of the noise source: 3

Shot noise
A common example of noise due to number fluctuations is “shot noise”, which occurs
whenever carriers are injected into a sample volume independently of one another.
Example: current flow in a pn junction of a semiconductor diode (emission over a barrier)

Spectral noise current density:

Shot noise does not occur in “ohmic” conductors. Since the number of available charges is not
limited, the fields caused by local fluctuations in the charge density draw in additional carriers to
equalize the total number.

Shot noise plays an important role in BJTs since they consist of pn junctions (especially for the
forward biased base emitter junction). Usually, the shot noise of FETs is very small since there
are no relevant pn-junctions.

4
Flicker noise or 1/f noise
Flicker noise or 1/f noise or excess is a kind of number fluctuations in carriers. Charge can be
trapped and then released after a characteristic lifetime 𝜏. Typically, the power spectral density
of 1/f noise is inversely proportional to frequency:
𝑑𝑃𝑛𝑜𝑖𝑠𝑒 1
∝ 𝛼 typically 𝛼 = 0.5 – 2
𝑑𝑓 𝑓
The 1/f noise is dominant at low
frequencies, beyond a certain frequency
(corner frequency) thermal noise is
dominant. The effect of 1/f noise can usually
be ignored in RF band. An exception is in
the oscillators, where 1/f noise can
modulate the output signal, producing or
increasing phase noise. The 1/f noise is also
important in direct down-conversion
receivers, as the output signal is close to
DC.

5
Noise Modeling for Bipolar Transistors
Small-signal equivalent circuit of BJT at high frequencies (without noise):

𝑟𝑏 = 𝑟𝑏𝑏′ , 𝑟𝜋 = 𝑟𝑏′ 𝑒 , 𝐶𝜋 = 𝐶𝑏′ 𝑒 , 𝐶𝜇 = 𝐶𝑏′ 𝑐

BJT with base shot noise, collector shot noise, and thermal noise at 𝑟𝑏 :

6
Noise Modeling for Bipolar Transistors

Small-signal equivalent circuit of BJT with noises:

7
Noise Figure
Considering an amplifier with power gain G: Si S0
G

where Si is the input signal power, S0 is the output signal power

Noise factor definition:

This factor shows how much the signal-to-noise ratio is degraded through the system
where N0(total) is the total noise at the output. If N0(source) is the noise at the output originating at the
source, and N0(added) is the noise at the output added by the electronic circuitry, then we can write:

Noise figure (dB):

8
Noise Figure of An Amplifier

All internal noise sources in the circuit are modeled into a series noise voltage source vn and a
parallel current noise source in placed in front of a noiseless amplifier with current gain Ai.
Input current is split between the input impedance and the source admittance YS with a ratio α.

Noise factor:
9
 Noise Figure of An Amplifier
In general, in and vn will not be correlated
with each other, the current in will be
partially correlated with vn and partially
uncorrelated. We can expand both the
current and voltage into these two explicit
parts:
𝑖𝑛 = 𝑖𝑐 + 𝑖𝑢 , 𝑣𝑛 = 𝑣𝑐 + 𝑣𝑢
The correlated components : 𝑖𝑐 = 𝑌𝑐 𝑣𝑐
YC is the correlation admittance
The noise factor can now be written as:

Noise figure is not only dependent on the internal noise parameters, but it also depend the external
source impedance ZS or YS (GS , BS) 10
Minimizing Noise Figure for Amplifier

GS and BS can be chosen to the following conditions for minimum noise

11
 Noise Figure of An Amplifier (simplified)
If 𝑣𝑢 is ignored:

𝑖𝑛 = 𝑖𝑐 + 𝑖𝑢 , 𝑣𝑛 = 𝑣𝑛

The correlated components : 𝑖𝑐 = 𝑌𝑐 𝑣𝑛

YC is the correlation admittance

𝑖𝑢2 + 𝑌𝑐 + 𝑌𝑠 2 𝑣𝑛2
𝐹 =1+ 2
𝑖𝑛𝑠

2 2
𝐺𝑢 + 𝐺𝑐 + 𝐺𝑠 + 𝐵𝑐 + 𝐵𝑠 𝑅𝑛
𝐹 =1+
𝐺𝑠

12
 Example: Noise Parameters of An Amplifier
! NEC710
# GHZ S MA R 50
2 .95 -26 3.57 157 .04 76 .66 -14
22 .60 -144 1.30 40 .14 40 .56 -85
! NOISE PARAMETERS
# FREQ NFmin dB |Gammaopt| Ang(Gammaopt) rn
4 .7 .64 69 .38
18 2.7 .46 -33 .40
Zs = 50 Ohm

13
 Equivalent Input Referred Noise Model for BJTs

≈
𝑟𝑏 ≪ 1

Short Base circuit:

Thermal noise in 𝑟𝑏 :

Base shot noise:

Open Base circuit:
Collector shot noise:

14
Equivalent Input Referred Noise Model for BJTs

𝐼𝐵 2 𝑉𝑇 + 𝑌 2 𝑟
+ 𝑌𝑐 + 𝑌𝑠 𝑠 𝑏
2𝑉𝑇 2𝐼𝐶
𝐹 =1+ 15
𝐺𝑠
 Noise Figure and Bias Current in BJTs

𝐼𝐵 2 𝑉𝑇 2
+ 𝑌𝑐 + 𝑌𝑠 + 𝑌𝑠 𝑟𝑏
2𝑉𝑇 2𝐼𝐶
𝐹 =1+
𝐺𝑠

At low currents, collector shot noise will

dominate and noise figure will improve
with increasing current. However, the
effect of base shot noise also increases
and will eventually dominate. Thus, there
will be some optimum level.

16
Example: Noise Model of an BJT
f = 1e9;
Ic = 50e-3;
VT = 25e-3;
beta = 100;
rb = 0;
Cpi = 20e-12;
rpi = beta*VT/Ic

17
 Noise Figure of a Multi-Stage System

The output signal S0 is given by:

The total output noise is:

The output noise due to the source is:

The formula shows how the gain of preceding stage causes the reduction in noise figure effect for a
stage. For this reason, only one low-noise stage is often designed at the front of the system.

18
Example: Noise Figure of a Multi-Stage System

G1_dB = 10dB
G2_dB = 5dB
G3_dB = 20dB

NF1_dB = 2dB
NF2_dB = 5dB
NF3_dB = 5dB

19
Chapter 5
RF Mixers

1
 Introduction of Mixers (frequency converters)
Mixer is a three-port element including two ports for the input signals at two
different frequencies and produces at the third port a signal that is the summation
or subtraction of the two input frequencies:

Upconverter mixer: Downconverter mixer:

Local oscillator (pump) frequency (LO): fp Local oscillator (pump) frequency (LO): fp
Intermediate frequency (IF): f1 Input signal frequency (RF): f1
Output signal frequency (RF): f0 = f1 + fp Intermediate frequency (IF): f0 = fp − f1

2
Nonlinear Characteristic of Devices
Diodes and BJTs:
The nonlinear function of a p-n junction diode or BJT: 𝑰 𝒕 = 𝑰𝑺 𝒆𝒒𝑽(𝒕)/𝒌𝑻

The excitation signal:

The device current:

3
 Nonlinear Characteristic of Devices
The basic result is a set of frequencies nωp + mω1 where n and m can take on any integer.
The usual desired output for a receiver is the intermediate frequency (IF), ω0. The
frequencies of primary interest are given the following names:

4
Nonlinear Characteristic of Devices
FETs:
The nonlinear function of a FET: 𝑰 𝒕 = 𝑰𝑫𝑺𝑺 𝟏 − 𝑽(𝒕)/𝑽𝑻 𝟐

The excitation signal:

The output current:

5
 Merit Parameters of a Mixer
Conversion Loss is the ratio of the input available power to the delivered output power:

Available RF input power, 𝑃1

𝐿=
Ouput IF power, 𝑃0

The conversion loss for a typical diode mixer is between 4 and 7 dB. The conversion loss
is dependent on the local oscillator power and the impedance matching of the ports.

Isolation is the inverse of the degree of LO power that leaks into either the IF or the RF
ports. For double-balanced mixers this value typically lies in the 15 to 25 dB range.
Conversion compression: for example, the 1-dB compression point occurs when the
conversion loss increases by 1 dB above the conversion loss in the low-power linear
range. A typical value of 1.0 dB compression occurs when the RF power is +7 dBm and
the LO is +13 dBm.
LO drive power is the required LO power level needed to make the mixer operates in
optimum. For a double-balanced mixer, this is typically +6 dBm to +20 dBm.

6
 Merit Parameters of a Mixer
Noise figure is a measure of the noise added by the mixer itself to the RF input signal as
it gets converted to the output IF.
Dynamic range is the maximum RF input power range for the mixer. The maximum
amplitude is limited by the conversion compression, and the minimum amplitude is limited
by the noise figure.
Input intercept point is the RF input power at which the output power levels of the
undesired intermodulation products (e.g. IM3) and the desired IF output would be equal.
It conducts to the definition of spurious free dynamic range (SFDR)

7
 Single-Ended Diode Mixer
The single-ended mixer in below figure shows that the RF input signal and the local
oscillator signal enter the mixer at the same point.
Some degree of isolation between the two is achieved by using a directional coupler in which
the RF signal enters the direct port and the local oscillator enters through the coupled port.

The amplitude of the LO is large enough to turn the diode on and off during each cycle. The
LO power is so large as to cause clipping of the LO voltage, thereby approximating a square
wave. The small RF signal is then presented with alternately a short or open circuit at the LO
rate. It is this turning on and off of the RF frequency that produces the set of frequencies:

The one of most interest in the standard receiver is f0 = fp - f1

8
Single-Ended Diode Mixer

The disadvantages of the single-ended mixer are a high-noise figure, a large number of
frequencies generated because of the nonlinear diode, a lack of isolation between the RF and LO
signals, and large LO currents in the IF circuit. The RF to LO isolation problem can be very
important, since the LO can leak back out of the RF port and be radiated through the receiver
antenna. The LO currents in the IF circuit would have to be filtered out with a low-pass filter that
has sufficient attenuation at the LO frequency to meet system specifications.

The advantage is that requiring lower LO power than the other types of mixers.

9
Single-Balanced Diode Mixers

10
Single-Balanced Diode Mixers
It is assumed that the LO voltage is much greater than the RF voltage, so Vp>> V1.
The LO voltage can be approximated as a square wave with period T = 1/fp

Fourier analysis of the square wave

If the input RF signal is expressed as V1 cos ω1t, then the output voltage is this multiplied
by the switching function:

Only the odd harmonics of the local oscillator voltage will effect the IF load. Thus the
spurious voltages appearing in the IF circuit are:

11
and all even harmonics of fp are suppressed (or balanced out).
Example: Single-Balanced Diode Mixers
Delte_F=100
F2=F1+Delta_F

PRF=-30 PLO=10
PRF2=PRF-900 PLO1=PLO-900

PORT2 DIODE1 DIODE1

P=1 ID=D2 ID=D1
Z=50 Ohm Nu=1.2 Nu=1.2
Fdelt=Delte_F MHz T=21.85 DegC T=21.85 DegC
V_METER
Pwr1=PRF dBm Io=1e-06 mA Io=1e-06 mA
ID=V_LO
Pwr2=PRF2 dBm

RF IF
PORT
DIODE1 DIODE1 P=3
ID=D4 ID=D3 Z=50 Ohm
Nu=1.2 Nu=1.2
T=21.85 DegC T=21.85 DegC
Io=1e-06 mA Io=1e-06 mA

3 4 5

SUBCKT
ID=S2
NET="Transformer Three Coils"

1 2
PORT2
P=2
Z=50 Ohm
Fdelt=Delte_F MHz
Pwr1=PLO1 dBm
Pwr2=PLO dBm

LO 12
 Example: Single-Balanced Diode Mixers
Vtime(PORT_3,1)[*] (V)
Single
SBMixer Balance
Multitone TimeMixer
Signal V_IF
DB(|Pharm(PORT_3)|)[*] (dBm)
SBMixer Multitone Spectrum
0.01 -10 Single Balance Mixer
m2:
100 MHz m4:
-40.44 dBm m1: 2100 MHz
-30 1000 MHz -40.44 dBm
-35.43 dBm
0.005 m6:
-50 m3: 2300 MHz
1200 MHz -52.14 dBm

Power (dBm)
-56.32 dBm
V_IF (V)

-70
0
-90

-110
-0.005

-130

-0.01 -150
0 5 10 15 20 0 1000 2000 3000 4000 5000
Time (ns) Frequency (MHz)

Vtime(V_METER.V_LO,1)[*] (V)
Single
SBMixer Balance
Multitone Mixer
Time Signal Diode V_RF V_LO
1

V_LO (V)
-1

-2

-3
0 5 10 15 20
Time (ns)
13
 Double-Balanced Diode Mixers

The double-balanced mixer is capable of isolating both the RF input voltage and the
LO voltage from the IF load. The slight additional cost of some extra diodes and a balun
is usually outweighed by the improved intermodulation suppression, improved dynamic
range, low conversion loss, and low noise.
Two most widely used double balanced mixers for the RF and microwave band are the
“ring” mixer and the “star” mixer
14
 Double-Balanced Diode Mixers

In both these cases (ring and star mixers) the switching function is shown as:

There is no RF signal nor LO voltage seen in the IF circuit, nor any even harmonics of
the LO voltage.

15
Example: Double-Balanced Diode Mixers
V_METER
Delte_F=100 ID=V_RF
F2=F1+Delta_F

PRF=-30 PLO=10
PRF2=PRF-900 PLO1=PLO-900

PORT2
P=2
Z=50 Ohm
Fdelt=Delte_F MHz DIODE1
DIODE1
Pwr1=PLO1 dBm ID=D2
ID=D1
Pwr2=PLO dBm Nu=1.2
Nu=1.2
T=21.85 DegC
1 3 T=21.85 DegC
LO Io=1e-06 mA
Io=1e-06 mA

4 V_METER
ID=V_LO

2 5 DIODE1
DIODE1
ID=D4
SUBCKT ID=D3
Nu=1.2
ID=S1 Nu=1.2
T=21.85 DegC
NET="Transformer Three Coils" Io=1e-06 mA T=21.85 DegC
Io=1e-06 mA

IF
PORT
3 4 5 P=3
Z=50 Ohm

SUBCKT
ID=S2
NET="Transformer Three Coils"

PORT2 1 2
P=1
Z=50 Ohm
Fdelt=Delte_F MHz
Pwr1=PRF dBm
Pwr2=PRF2 dBm

RF 16
 Example: Double-Balanced Diode Mixers
DBMixer Multitone Time Signal DB(|Pharm(PORT_3)|)[*]
DBMixer Multitone Spectrum (dBm)
0.02
Vtime(PORT_3,1)[*] (V)V_IF -10 Double Balance Mixer
Double Balance Mixer
m1: m2:
-30 100 MHz 2100 MHz m3:
-34.18 dBm -34.18 dBm 2300 MHz
0.01 -44.86 dBm
-50

Power (dBm)
V_IF (V)

-70
0
-90

-110
-0.01

-130

-0.02 -150
0 5 10 15 20 0 1000 2000 3000 4000 5000
Time (ns) Frequency (MHz)

Vtime(V_METER.V_LO,1)[*] (R, V) DB(|Pcomp(PORT_3,-1_1)|)[1,X] (dBm)

Double Balance Mixer Sweep Power Double Balance Mixer
DBMixer Multitone Time Signal Diode V_RF V_LO
0.04 Vtime(V_METER.V_RF,1)[*] (L, V) 2
DB(|Pcomp(PORT_3,-3_3)|)[1,X]
Sweep Power (dBm)
20 Sweep Power Double Balance Mixer
Double Balance Mixer

0.02 1 IF Har. Comp. Power (dBm) -30

V_LO (V)
V_RF (V)

0 0 -80

-0.02 -1 -130

-0.04 -2 -180
0 5 10 15 20 -40 -20 0 17 20
Time (ns) RF Input Power (dBm)
Single-Ended Transistor Mixers

Using transistor, these are called active mixers because they provide the possibility of
conversion gain that the diode mixers are not capable of doing.

18
Double-Balanced Transistor Mixers
Gilbert cell multiplier:

19
Double-Balanced Transistor Mixers

20
 Example: Gilbert Cell Mixer

Vcc

Vcc

Vcc

Vcc

Vcc

Vcc

Vcc
Vcc

3V 3V 3V 3V 3V 3V 3V
3V

RES RES RES RES RES

DCVS ID=R1 ID=R2 ID=R7 ID=R8 ID=R9
ID=VCC R=Rv44 Ohm R=Rv44 Ohm R=Rv11 Ohm R=Rv55 Ohm R=Rv55 Ohm
V=3 V

0V
CAP
GBJT3
ID=GP16
GBJT3
ID=GP18
ID=C1
C=100 pF
NN3=4.1

XFMR
IF
PORT
ID=XF5 P=3
2.63 V 2.52 V 0V Z=50 Ohm
RES 2 C C 2 2 C C 2 RES 2 C 2 C N=NN3
4 2
ID=R3 ID=R16 RES
R=1000 Ohm R=1000 Ohm ID=R14
1 1 1 1 1 1 0V
PORT2 R=Rv22 Ohm o o
P=1 3 n1:1 1
B V
2.62 B 2.62 V B B B V
2.41 B V
2.41
Z=50 Ohm
Fdelt=100 MHz NN1=2.5 GBJT3
GBJT3 GBJT3 2.52 V 0V
XFMR E E 3 E E 3GBJT3 3 E 3 E
Pwr1=Pin1 dBm ID=GP1 3 3 ID=GP2 ID=GP3 ID=GP4 CAP
Pwr2=Pinn2 dBm ID=XF1
N=NN1 ID=C2
1 3 1.84 V 1.84 V 1.75 V 1.59 V 1.59 V C=100 pF
1:n1
0V
o o

RF 2 4

2 C C 2
RES
PORT2 ID=R4 1 1
P=2 R=1250 Ohm RES RES
Z=50 Ohm ID=R18 ID=R15 B B
Fdelt=100 MHz NN2=2.7
2 C C 2 R=1250 Ohm R=Rv33 Ohm
Pwr1=-900 dBm XFMR
GBJT3 GBJT3
Pwr2=-30 dBm ID=XF3 3 E E 3
N=NN2 ID=GP19 ID=GP21
1 3 1 1
1:n1 0.791 V 0.791 V
o o
0V B V
1.73 B 1.73 V

LO
LO
2 4 GBJT3
ID=GP5
3 E E 3 GBJT3
ID=GP6
RES
ID=R12
RES
ID=R13
R=50 Ohm
0.931 V R=50 Ohm

C 2 2 C 2 C 2 C 2 C0.698 V

1 1 1 1 1
GBJT3
GBJT3 B B V
0.825 B B B ID=GP20
GBJT3 GBJT3 GBJT3
ID=GP7
ID=GP14 ID=GP17 ID=GP22
E 3 3 E 3 E 3 E 3 E

21
 Example: Gilbert Cell Mixer
DB(|Pcomp(PORT_3,-1_1)|)[1,X] (dBm)
Different Amplifier and Gilbert Miixer.AP_HB
DB(|Pcomp(PORT_3,-3_3)|)[1,X] (dBm)
DB(|LSSnm(PORT_3,PORT_1,-1_1,1_0)|)[*,X]
Conversion Gain Different Amplifier andOut_In
Power Gilbert Miixer.AP_HB
20 Different Amplifier and Gilbert Miixer.AP_HB 0

m2:
-20.56 m1:
10.52 dB -20
10 -50
Conversion Gain (dB)

-9.698 dBm
m1: Freq = 1000 MHz
-27.79

Pout (dBm)
11.54 dB

0 -100

-10 -150

-20 -200
-100 -80 -60 -40 -20 0 -100 -80 -60 -40 -20 0
P_RF (dBm) Pin (dBm)

Vtime(PORT_3,1)[*] DB(|Pharm(PORT_3)|)[*] (dBm)

Output (V)
Time Signal 0
Output Spectrum
Different Amplifier and Gilbert Miixer.AP_HB
0.02 Different Amplifier and Gilbert Miixer.AP_HB
m2:
m1: 2100 MHz
100 MHz -37.4 dBm
0.01 -28.48 dBm

-50
m5: m4:
Voltage (V)

300 MHz 2300 MHz

-103.7 dBm m3:
1900 MHz -83 dBm
0
-100.1 dBm

-100
-0.01

-0.02 -150
0 5 10 15 20 0 2000 4000 6000
Time (ns) Frequency (MHz) 22
 Chapter 7
Oscillators & Frequency Synthesisers

1
Oscillators Analysis with Feedback Theory

Closed- loop voltage gain:

Barkhausen criterion for oscillation: a𝛽 = 1

2
Oscillators Analysis with Feedback Theory
𝑖𝑖

shunt – shunt connection

𝛽 = 𝑦12𝑓

3
 LC Tank Transistor Oscillators
𝐶
At resonant frequency of a high Q resonant tank:
𝑋1 + 𝑋2 + 𝑋3 = 0 𝑋3
𝐵 𝐼𝑇 𝑋2 𝑉𝐶𝐸
𝑉𝐵𝐸 𝐼𝑇 . 𝑗𝑋1 −𝑋1 𝑋1
𝛽= ≈ = =
𝑉𝐶𝐸 −𝐼𝑇 . 𝑗𝑋2 𝑋2 𝑋1 + 𝑋3 𝑉𝐵𝐸 𝑋1

𝑋1 , 𝑋2 > 0 (inductors) and 𝑋3 < 0 (capacitor) ⇒ Hartley oscillator

or
𝑋1 , 𝑋2 < 0 capacitors and 𝑋3 > 0 (inductor) ⇒ Colpitts oscillator

4
 EC Hartley Oscillator
C

C L C 𝐿1 L
Cb
Q1 Q1
𝐼𝑇 E

𝐿2
Rb VCC Rb

B
RE CE
VBB

Check phase condition of the tank: 𝑀 = 𝑘 𝐿1 𝐿2

𝑋1 = 𝑋𝐵𝐸 = 𝜔𝐿2 > 0

𝑉𝐵𝐸 𝐼𝑇 𝑗𝜔(𝐿2 + 𝑀) 𝐿2 + 𝑀
𝑋2 = 𝑋𝐶𝐸 = 𝜔𝐿1 > 0 𝛽= ≈ =−
1 𝑉𝐶𝐸 −𝐼𝑇 𝑗𝜔(𝐿1 + 𝑀) 𝐿1 + 𝑀
𝑋3 = 𝑋𝐶𝐵 = − <0
𝜔𝐶

5
 EC Hartley Oscillator: Transformer
▪ L1 and L2 are coupling (on the same inducting core):
C
𝑉𝐵𝐸 𝐿2 + 𝑀
𝛽= ≈− 𝑀 = 𝑘 𝐿1 𝐿2
𝑉𝐶𝐸 𝐿1 + 𝑀 C 𝐿1 L
Q1
𝐼𝑇 E

𝐿2
𝐿1 = 𝛼. 𝑛12 ; 𝐿2 = 𝛼. 𝑛22 Rb

B
𝛼.𝑛22 +𝑘.𝛼.𝑛1 .𝑛2 𝑛2 (𝑛2 +𝑘𝑛1 )
⇒𝛽≈− =−
𝛼.𝑛12 +𝑘.𝛼.𝑛1 .𝑛2 𝑛1 (𝑛1 +𝑘𝑛2 )

𝑛2 (𝑛2 + 𝑘𝑛1 ) 𝑉𝐵𝐸

⇒𝛽=− =
𝑛1 (𝑛1 + 𝑘𝑛2 ) 𝑉𝐶𝐸

𝑛2
In case of close coupling: 𝑘 = 1 ⇒𝛽≈−
𝑛1

▪ L1 and L2 are not coupling (different inducting cores):

𝐿2
𝛽≈−
𝐿1
6
EC Hartley Oscillator: Small Signal Model
B C 𝑅𝐶
𝐶

L1 L
Rb hie hfe.ib L1
C 𝐸
L2 C
E E L2
Rb hie

𝑉𝐶𝐸 −ℎ𝑓𝑒 . 𝑖𝑏 . 𝑅𝐶 −ℎ𝑓𝑒 𝑅𝑏 //ℎ𝑖𝑒

𝑎= = = 𝑅 𝑅𝐶 =
𝑉𝐵𝐸 𝑖𝑏 . ℎ𝑖𝑒 ℎ𝑖𝑒 𝐶 𝑛2

𝑉𝐸𝐵 𝑛2 (𝑛2 + 𝑘𝑛1 )

𝛽= ≈ =𝑛
𝑉𝐶𝐸 𝑛1 (𝑛1 + 𝑘𝑛2 )

ℎ𝑓𝑒 𝑅𝑏 //ℎ𝑖𝑒
𝛽𝑎 = 1 ⇒ 𝑛. =1
ℎ𝑖𝑒 𝑛2

ℎ𝑓𝑒
𝑛= (𝑅 //ℎ𝑖𝑒 )
ℎ𝑖𝑒 𝑏 7
BC Hartley Oscillator

Cng L1
Q C

L2

CB R1 R2 Re

VCC

𝑖𝑒
E C

Re hib hfb.(-ie) L1
C4

B B L2

8
 Colpitts Oscillator
VCC

𝑉𝐵𝐸 𝐶1
R2 Lch
𝛽= ≈ − = −𝑛
𝑉𝐶𝐸 𝐶2
Q
Cng C1
L B C

C1
C2
R1
Rb hie hfe.ib L

RE CE
E E C2

VCC VCC

R2 L Rb

Q
Cng
E C
Q
C1
C1 Re hib hfb.(-ie) C1
L L
B B
C2
CB R1 Re
C2
Re C2

9
Clapp Oscillator
VCC

R2 Lch
𝐶0 ≪ 𝐶1 , 𝐶2

Q
Cng
1 1 L
𝑓0 = ≈ C1
2𝜋 𝐿𝐶 2𝜋 𝐿𝐶0
R1
C2 Co
RE CE

10
 Phase Noise

H(s) can be written as a truncated Taylor series:

The conditions of stable oscillation must be satisfied, 𝐻 𝑗𝜔0 = 1

Noise power is of interest here

the two terms on the right are orthogonal:

𝐻 ≈ 1 near the resonance frequency

11
 Phase Noise

In the special case, the feedback path is unity,

H1 = H, and |H | = 1 near resonance.

Phase noise is usually quoted as an absolute noise

referenced to the carrier power, 𝑃𝑆

12
 Phase Noise
Total resonator losses has an available noise power of
kT, int is the noise current injected into the oscillator
from the biasing network, the collector shot noise icn
from the transistors.

where Rp is the equivalent parallel resistance of the tank, 𝜌 is the fraction of a cycle for which
the transistors are completely switched.
Noise figure:

Flicker noise is insignificant at the frequencies

of interest

13
Example: BC Colpits Oscillator Design
VCC

R2 L Re = 500
RL = 50
f = 100e6
Q Q = 50
C1 Ic = 1.0e-03
Beta =100
CB R1
alpha = 3
Re C2

E C

C1
Re hib hfb.(-ie)
L
B B
C2

14
Example: BC Colpits Oscillator Design
VCC

R2 L

C1

CB R1 Magnitude
OSC Test (dB)

Open loop gain (dB) Open loop phase (deg.)

100 BC Oscillator Small Signal
Re C2 m2:
100 MHz
0.2695 Deg
Angle (deg.) (Deg)
50 BC Oscillator Small Signal

-50
10 m1:
100 MHz
5 9.544 dB

-5

-10
50 100 150 200
Frequency (MHz) 15
 Vtime(PORT_1,1)[*] (V)
BC Oscillator Large Signal.AP_HB
Vtime(V_METER.Vce,1)[*] (V)
Example: BC Colpits Oscillator Design
BC Oscillator Large Signal.AP_HB
DB(|Pharm(PORT_1)|)[*] (dBm)
BC Oscillator Large Signal.AP_HB

Time Signal Spectrum

40 20
30 m1:
Ic (mA)

100 MHz
20 0 7.912 dBm
10
0 -20
-10 m2:
1 -40 200 MHz
-51.46 dBm

Po (dBm)
Port1 (V)

0.5 -60
0
-0.5 -80
-1 -100
12
10
Vce (V)

-120
8
-140
6
4 -160
0 5 10 15 20 0 500 1000 1500 2000
DB(PH_NOISE(PORT_1,1,1))[*,X]
Time (ns) Frequency (MHz)
BC Oscillator Large Signal

Phase Noise
-100
m1:
0.0001 MHz
-102.26 dB
FREQ = 1000 MHz
-120
PN (dBc/Hz)

-140

-160 p1

-180
0.0001 0.0201 0.0401 0.0601 0.0801 0.1
Frequency (MHz)
16
Voltage-Controlled Oscillator with Varactors

Colpitts CB oscillator with varactors Colpitts CC oscillator with varactors

17
Phase Locked Loop
Integer-N PLL Synthesisers

Step size= 𝑓𝑟
18
 VCO
𝜔0 = 𝜔𝑛𝑜𝑚 + 𝐾𝑉𝐶𝑂 𝑣𝑐

Remove the “dc” part of the equation

and only consider the part that is
changing

Relate frequency w to phase q:

𝑡
𝜃𝑉𝐶𝑂 = න 𝜔𝑉𝐶𝑂 𝑑𝑡 = 𝐾𝑉𝐶𝑂 න 𝑣𝑐 𝜏 𝑑𝜏
0

In the Laplace domain

The output phase after the divider is simply

19
 Phase Detectors
Phase-Frequency Detector (PFD)

The current flows for the length of time t between the output edge and the reference
edge. If the period is T, the average output current is:
𝜏 𝐼
𝐼𝑜𝑢𝑡 = 𝐼 = 𝜃 − 𝜃𝑜
𝑇 2𝜋 𝑅 20
Loop Filter

21
Simplified Loop Equations

22
 Fractional-N PLL Frequency Synthesisers
Fractional-N Synthesizer with a Dual Modulus Pre-scaler

It is called a dual modulus pre-scaler because it can be programmed to two division

ratios. The fractionality can be achieved by toggling the divisor value between two
values, P and P + 1.
23
Fractional-N PLL Frequency Synthesisers
Fractional-N Synthesizer with a Dual Modulus Pre-scaler
Ex: Describe the operation of a 3-bit accumulator with input K = 1 and K = 3, assuming
the accumulator seed value (i.e., the initial accumulator output value) is equal to 0.
If the accumulator has 3 bits, the size of the accumulator is 23 = 8, or F = 8, even
though the largest value which can be stored is 111, corresponding to 7

If the dual modulus prescaler divides by P when Cout is low and divides by P + 1 when
Cout is high, the average VCO output frequency is:

24
 Chapter 8
Analog Modulation & Demodulation

1
Analog Modulation Methods
➢Amplitude Modulation:
• Standard amplitude modulation (AM) with carrier.
• Suppressed-carrier double-sideband modulation (DSB).
• Single-sideband modulation (SSB).
• Vestige-sideband modulation (VSB).
➢Frequency Modulation
➢Phase Modulation

2
Amplitude Modulation Signals

3
Amplitude Modulation Signals

Message spectrum with bandwidth W

AM spectrum: AM bandwidth is 2W
𝑓𝑚𝑖𝑛 𝑓𝑚𝑎𝑥 𝑓𝐶 𝑓
𝑓𝐶 − 𝑓𝑚𝑎𝑥 𝑓𝐶 − 𝑓𝑚𝑖𝑛 𝑓𝐶 + 𝑓𝑚𝑖𝑛 𝑓𝐶 + 𝑓𝑚𝑎𝑥

AM transmitted power:

where Pc represents unmodulated carrier power:

and Psb represents power per sideband:

where Sx is average message power.

If fc >>W and µ ≤ 1, then the message can be extracted from xc(t) by a

simple envelope detector.

4
AM Modulators
❑ Using Multiplier:

5
AM Modulators
❑ Using square-law element:

❑ High-level modulation
using class C amplifier:

6
AM Demodulation
❑ Synchronous detection (coherent detection): The oscillator of demodulator is
exactly synchronized (both phase and frequency) with the transmitting carrier.

Using PLL for carrier synchronization.

❑ Envelop detection:

7
Double-SideBand - DSB (Suppressed-Carrier AM)
DSB signal and spectra: The wasted carrier power in AM can be eliminated by setting
µ = 1 and suppressing the carrier-frequency component. The resulting DSB signal is:


m1 m2 c

DSB power:

8
AM balanced modulator Balanced Mixer
DSB Demodulation
❑ Synchronous detection (coherent detection): As AM demodulator. Required
carrier synchronization.

Using PLL for carrier synchronization.

❑ DSB using pilot carrier.


c

9
Single-SideBand - SSB
SSB spectra: one wasted sideband in DSB is removed:


m1 m2 c

SSB bandwidth and power:

10
 SSB Modulation

Based on DSB modulator and filter Two-step SSB modulator

HQ(f): 90o
phase shifter

Phase-shift method Weaver method

11
Carrier Synchronization
❑ Squaring loop

❑ Costas loop

12
Phase and Frequency Modulations
❑ Angle Modulation Signals:

If θc(t) contains the message information x(t), then it is exponential

modulation (or angle modulation).

❑ Phase modulation (PM) is defined by

The constant φ∆ (φ∆ ≤ 180o) represents the maximum phase shift (or PM index, or
phase deviation) produced by x(t).

13
Phase and Frequency Modulations
❑ Frequency modulation (FM) is defined by

The constant frequency f∆ called frequency deviation, represents the maximum

shift of f(t) relative to the carrier frequency fc

By definition:

If t0 is selected such that φ(t0) = 0, then

The FM signal is written as:

14
Phase and Frequency Modulations

15
FM, PM Spectra
❑ Average transmitted power (for PM and FM): regardless of message x(t):

❑ Narrowband PM and FM: Representing the exponential modulation and using

Euler’s identity :

If

The spectrum of xc(t) in term of the message spectrum is:

Therefore, we conclude that if the message has bandwidth of W << fc, then
the bandwidth of the signal after narrowband modulation is 2W. 16
FM, PM Spectra
❑ Single tone modulation

The parameter β is the modulation index for PM and FM in the case of tone modulation.
▪ Narrowband PM/FM requires β << 1:

17
FM, PM Spectra
▪ Wideband PM/FM single tone modulation

Using Bessel function:

▪ Bandwidth of PM/FM single tone modulation: According to Carson’s rule:

18
FM, PM Spectra
Jn(β)

19
FM, PM Modulators
❑ Direct FM -VCO

20
FM, PM Modulators
❑ Narrowband phase modulator:

❑ Indirect FM transmitter:

21
FM, PM Demodulator
❑ FM/PM demodulator (detector) using PLL:

22