AN APPROACH TO IMPLEMENT KAHN'S TECHNIQUE WITH …

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AN APPROACH TO IMPLEMENT KAHN'S TECHNIQUE WITH AN APPROACH TO IMPLEMENT KAHN'S TECHNIQUE WITH

DYNAMIC POWER SUPPLY DYNAMIC POWER SUPPLY

Sowjanya Kommu Wright State University

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AN APPROACH TO IMPLEMENT KAHN’STECHNIQUE WITH DYNAMIC POWER

SUPPLY

A thesis submitted in partial fulfillment

of the requirements for the degree of

Master of Science in Electrical Engineering

By

Sowjanya Kommu

B. Tech., Vishnu Institute of Technology, Bhimavaram, Andhra Pradesh India, 2012

2016Wright State University

WRIGHT STATE UNIVERSITYGRADUATE SCHOOL

July 22, 2016

I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SU-PERVISION BY Sowjanya Kommu ENTITLED AN APPROACH TO IMPLEMENTKAHN’S TECHNIQUE WITH DYNAMIC POWER SUPPLY BE ACCEPTED INPARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OFMaster of Science in Electrical Engineering.

Marian K. Kazimierczuk, Ph.D.Thesis Director

Brian Rigling, Ph.D.

ChairDepartment of Electrical Engineering

College of Engineering andComputer Science

Committee onFinal Examination

Marian K. Kazimierczuk, Ph.D.

Yan Zhuang, Ph.D.

Saiyu Ren, Ph.D.

Robert E. W. Fyffe, Ph.D.Vice President for Research andDean of the Graduate School

Abstract

Kommu, Sowjanya. M.S.Egr, Department of Electrical Engineering, Wright State

University, 2016. An Approach to Implement Kahn’s Technique with Dynamic Power

Supply.

Radio-frequency power amplifiers are an integral part of today’s communication

systems. Primary importance is given to improve its efficiency and linearity, which

are required for the effective signal transmission. Three main architectures on which,

the efficiency of communication systems are based on are: (a) Kahn’s technique,

(b) Doherty’s power amplifiers, and (c) Cheireix out-phasing modulation. Several

schemes to implement these techniques exist in literature and their study is very

diverse. In this thesis, a detailed literature survey on these techniques is presented,

which includes their operation, properties, advantages, disadvantages, and areas of

potential applications. This main objective of this thesis is to adopt the Kahn’s

architecture and implement the various electrical blocks using the latest technology.

The main building blocks of the described architecture are: AM/PM signal generator,

amplitude detector, dynamic power supply, and a radio-frequency power amplifier.

The circuit operation, properties, and circuit-level implementation of all these blocks

are presented. The design of a pulse-width modulated buck dc-ac converter used as

a dynamic power supply is given. The amplitude-modulated Class-D radio-frequency

power amplifier is designed and its performance is evaluated. Each of the circuit-level

implementations of the various blocks were designed, built, and simulated on SABER

circuit simulator. A test audio signal with frequency 2.5 kHz is generated in the

AM/PM signal generator block. A buck dynamic power supply operates at a fixed

supply voltage of 25 V with its output voltage varying between 3 V to 23 V. The

Class-D radio-frequency power amplifier is designed to generate a carrier frequency

of 250 kHz. The efficiency of each stage was determined.

iii

Contents

1 Introduction 2

1.1 Power Amplifiers with Dynamic Power Supply for Efficient

Communication Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Operating Modes of Dynamic Power Supply . . . . . . . . . . . . . . . 4

1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Literature Survey 8

2.1 Process of Communication . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.1 Base-band Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.2 Digital Signal Processing . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.3 Process of Modulation . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.4 Amplitude Modulation . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1.5 Phase Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.6 Local Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.1.7 Radio-Frequency Power Amplifier . . . . . . . . . . . . . . . . . . 16

2.1.8 Classification of Linear Radio Frequency Power Amplifiers . . . . 17

2.2 Linearity-Efficiency Trade-offs . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Non-Linear Radio Frequency Power Amplifiers for Efficiency Improvement 18

2.4 Classification of Non-Linear Radio Frequency Power Amplifiers . . . . . 19

2.5 Evolution of Data Transmission from 1st Generation to 5th Generation 20

3 Classical Techniques in Communication 22

3.1 Classical Techniques of Communication for Efficiency Improvement . . 22

3.1.1 Cheirix Out-phasing Modulation . . . . . . . . . . . . . . . . . . 22

3.1.2 Doherty’s Power Amplifiers . . . . . . . . . . . . . . . . . . . . . 23

iv

3.1.3 Kahn’s Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4 An approach to implement Kahn’s Technique with Dynamic

Power Supply 27

4.1 AM/PM Signal Generator . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1.1 Circuit Description . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.1.2 Operation of AM/PM Signal Generator . . . . . . . . . . . . . . . 29

4.2 Amplitude Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.2.1 Circuit Description . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2.2 Operation of Amplitude Detector . . . . . . . . . . . . . . . . . . 31

4.2.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.3 Dynamic Power Supply to Class D RF Power Amplifier . . . . . . . . . 33

4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.3.2 Circuit Description . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3.3 DC-AC Buck Converter . . . . . . . . . . . . . . . . . . . . . . . 36

4.3.4 Operation dc-ac Buck Converter . . . . . . . . . . . . . . . . . . . 37

4.3.5 Steady-State Analysis . . . . . . . . . . . . . . . . . . . . . . . . 38

4.3.6 Design Example of dc-ac Buck Converter in CCM . . . . . . . . . 39

4.4 Class D RF Power Amplifier . . . . . . . . . . . . . . . . . . . . . . . . 46

4.4.1 Operation of Class D RF Power Amplifier . . . . . . . . . . . . . 47

4.4.2 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.4.3 Steady-State Analysis . . . . . . . . . . . . . . . . . . . . . . . . 48

4.4.4 Design of Class D RFPA . . . . . . . . . . . . . . . . . . . . . . . 49

4.5 Operation of Dynamic Power Supply to Class D RF Power Amplifier . 54

4.6 Class D RF Power Amplifier as a Mixer . . . . . . . . . . . . . . . . . . 57

5 Conclusions 66

5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

v

5.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.4 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6 Bibliography 69

vi

List of Figures

1.1 Topology of dynamic power supply to linear power amplifiers for

efficiency improvement. 3

1.2 Topology of dynamic power supply to switch mode power amplifiers

for amplitude modulation. 3

1.3 Operating modes of dynamic power supply power amplifiers based on

Booth chart. 5

2.1 Evolution of telecommunication system. 8

2.2 Block diagram of communication system. 9

2.3 Block diagram of process of communication. 10

2.4 Block diagram of digital signal processing. 11

2.5 MATLAB plot showing modulating signal,carrier signal and

amplitude modulated signal. 13

2.6 MATLAB plot showing modulating signal,carrier signal and phase

modulated signal. 14

2.7 Block diagram showing relation between phase and frequency

modulations. 15

2.8 MATLAB plot showing the slight difference in the phase and

frequency modulations. 15

2.9 Radio frequency power amplifier. 17

vii

3.1 Simplified block diagram of Cheireix out-phasing system 23

3.2 Doherty’s power amplifier. 24

3.3 Block diagram of Khan’s technique. 25

3.4 Detailed block diagram of Kahn’s technique. 26

4.1 Block diagram of dynamic power supply to RF power amplifier

implemented in Kahn’s technique. 27

4.2 Circuit diagram of an AM/PM signal generator. 28

4.3 Output of an envelope generator. 30

4.4 Circuit diagram of an envelope detector. 31

4.5 Envelope detection from the envelope. 33

4.6 Sinusoidal pulse width modulation converter waveforms. 34

4.7 Buck converter as DPS to class D RF power amplifier. 35

4.8 Circuit diagram of dc-ac buck converter. 36

4.9 Waveforms of vGS,vL,iL of sinusoidal voltage driven dc-ac buck

converter. 39

4.10 Vsaw,Vsin and vGS of pulse width modulator of dc-ac buck converter. 45

4.11 Inductor current iL, output voltage vO waveforms of sinusoidal

voltage driven dc-ac buck converter. 45

4.12 Circuit diagram for class D RF power amplifier. 46

viii

4.13 Waveforms of class D RF power amplifier. 49

4.14 vGS1,vGS2 of class D RF power amplifier. 53

4.15 vO of class D RF power amplifier. 53

4.16 Equivalent circuit of dynamic power supplied class D RF power

amplifier. 54

4.17 Waveforms of vGS1, vGS2, vGS3, iL, i1, i2 dynamic power supplied class

D RF power amplifier. 55

4.18 vGS1, vGS2, vGS3 of dynamic power supplied class D RF power amplifier. 56

4.19 vObuck,vOclassD of dynamic power supplied class D RF power amplifier. 56

4.20 Circuit diagram of envelope elimination and amplitude modulation

based on Kahn’s technique. 58

4.21 Saber circuit for Amplitude detection and amplification. 59

4.22 AM/PM signal generation and amplitude detection. 60

4.23 PWM output of dc-ac buck converter. 60

4.24 iL, vO of of dc-ac buck converter. 61

4.25 PWM output for phase modulation at Q2 to class D RF power amplifier. 61

4.26 PWM output for phase modulation at Q3 to class D RF power amplifier. 62

4.27 Output of DPS to class D RF power amplifier of the design. 62

4.28 MATLAB validation for AM/PM signal generation. 63

ix

4.29 MATLAB validation for change in efficiency w.r.t the change in input

voltage of class D RF power amplifier. 64

4.30 MATLAB validation for change in efficiency w.r.t the change in

output of dc-ac buck converter. 64

4.31 MATLAB validation for change in efficiency w.r.t the change in

duty-cycle of dc-ac buck converter. 65

4.32 MATLAB validation for duty cycle variation w.r.t. PWM. 65

x

Acknowledgement

First and foremost, I would like to express my sincerest gratitude to my advisor

Dr. Marian K. Kazimierczuk, whose support, patience, and kindness has helped me

benefit the most out of this thesis. My heartfelt thank you to him.

I would also like to thank my thesis committee members Dr. Yan Zhuang and Dr.

Saiyu Ren sincerely for their insightful comments and suggestions. I am greateful to

the Department of Electrical Engineering and the Department Chair, for giving me

this opportunity to obtain my MS degree at Wright State University.

The present research met its pace with constant guidance and motivation by my

fellow colleagues, Agasthya Ayachit and Dalvir Saini. My heartfelt thanks and best

wishes to them.

I owe my thanks much more than words can express to my parents and brother

whose sacrifice in all respects from time to time with love and affection has made

me to reach this goal. My special thanks to all my friends for their constructive

criticism,which made me to work hard produce better report.

1

1 Introduction

1.1 Power Amplifiers with Dynamic Power Supply for Effi-cient Communication Systems

In most of the portable wireless systems, Radio Frequency Power Amplifier (RFPA)

is the most power consuming component [1]-[3]. Modern communication systems are

focused on improving the linearity and efficiency of the transceiver [3],[4]. Use of

pulse width modulated power converters helps to improve the efficiency for low to

medium power transmitters [1]-[12]. Recent advancements in the integrated circuit

design reduced the size and cost of the communication systems [11]. Envelope elimi-

nation and restoration, Doherty’s power amplifiers, Cheireix out phasing modulation,

linearization, linear amplification with non-linear components and Dynamic Power

Supply(DPS) to the radio frequency power amplifiers are some of the techniques to

mitigate the efficiency versus linearity tradeoffs [3].

The high amount of power consumption in radio frequency power amplifier is due

to the modulated signal with high peak-peak average power ratio and wide band-width

[12]. The overall efficiency of the power amplifier depends on the drain efficiency and

power added efficiency. The drain efficiency is the ratio of RF output to RF input

of the MOSFET ηD = (PO

PI). The power added efficiency is the ratio of drain power

subtracted from the output power to the input power (PAE) ηPAE = (PO−PDr)PI

. The

overall efficiency is the ratio of output power to the drain power added to the input

power of the radio frequency power amplifier [14]. The dynamic control of the power

supply to the radio frequency power amplifier improves the efficiency of the linear

power amplifiers. It gives the amplitude modulated signal with non-linear power

amplifiers [3].

2

Figures 1.1 and 1.2 shows the topology of dynamic power supply to linear radio

frequency power amplifiers and switched mode power amplifier.

!

Figure 1.1: Topology of dynamic power supply to linear power amplifiers for efficiencyimprovement.

Figure 1.2: Topology of dynamic power supply to switch mode power amplifiers foramplitude modulation.

3

The efficiency of linear power amplifiers is less. The large amount of power is

dissipated in the form of heat for lower inputs to the radio frequency power amplifier

shown in the Figure 1.3. The dynamic power supply to the linear power amplifier

improves the efficiency by dynamically varying the input. The output voltage/power

tracks the input voltage/power. Hence it is also called as ’supply on demand’ voltage

source. The dynamic power supply to switch mode power amplifiers gives the ampli-

tude modulated output. The dc-ac buck converter acts as a dynamic power supply.

The frequency of the output voltage of the dc-ac buck converter is the modulating

frequency of the amplitude modulated output. The switching frequency of the switch

mode power amplifier is the carrier frequency of the amplitude modulated output.

1.2 Operating Modes of Dynamic Power Supply

Several techniques are implemented to improve the efficiency of RF power amplifier.

The use of dynamic power supply changes the power supply from the fixed value to

the variable value makes the RF power amplifier from the conventional 2-port to 3-

port circuit. All the power amplifiers are actually 3-port circuits with two inputs such

as supply voltage and the RF input and one output i.e., RF output. Generally, the

power supply port is ignored with the DPS in the design which is no longer practical.

The operation of DPS can be classified in to three operating modes, namely

• L-mode: The output power depends on the input power and not on the power

supply.

• C-mode: The output power depends on the supply voltage and not on the input

power.

• P-mode: The output power depends on both input power and supply voltage.

Figure 1.3 shows the three operating modes based on the transistor characteristics

taken from the Booth chart.

4

Figure 1.3: Operating modes of dynamic power supply power amplifiers based onBooth chart.

L-mode is the linear operation of an amplifier. RF output power is not dependent

on the value of the power supply for any particular value of RF input power.

In C-mode, the sensitivities and non-sensitivities are swapped from L-mode. In

L-mode the output power sensitivity is only with the power supply and not with the

input power. This operating mode is very nonlinear.

In P-mode the output power is a product of the power supply value and the input

RF power. It only appears when the power supply has a very small value to be

sensitive to both input power and power supply variations. In P-mode the transistor

operates as a controlled variable resistance [9, 10].

5

1.3 Motivation

Efficiency management of radio frequency power amplifiers with the good linearity is

a challenging task. Several architectures are developed to mitigate the linearity versus

efficiency tradeoffs. The band-width, distortion, interference etc. has a great impact

on efficiency. The literature survey on the communication systems, impact of power on

the wireless communication, classical techniques for efficiency improvement, different

designs motivated me to develop a design based on Khan’s technique. The study

on envelope tracking and the different amplitude modulation techniques motivated

me to implement dynamic power supply to radio frequency power amplifiers. The

combined design and the output generated lead to the study on different parameters

that are responsible for power losses.

1.4 Thesis Objectives

• To perform a rigorous literature survey on efficiency vs. linearity trade-offs of

RF power amplifiers.

• Current state-of-the-art circuits to enhance RF power amplifier efficiency and

to determine their advantages, disadvantages, and applications.

• To study the different topologies of dynamic power supplies used in amplitude

modulation systems and determine their impact on current technologies.

• To understand the features, design, benefits, and applications of Kahn’s tech-

nique.

• To design and simulate a pulse-width modulated dc-ac buck power converter

used as a dynamic power supply.

• To design and simulate a basic Class-D RF power amplifier and an amplitude-

modulated Class-D RF power amplifier.

6

• To design envelope generation and envelope detection circuits required for im-

plementation of Kahn’s technique.

• To propose the use of Class-D RFPA as a mixer for both amplitude and phase

modulation schemes.

7

2 Literature Survey

Communication at a distance is called telecommunication [14]. The telecommunica-

tion is a process of transmission and reception of information over a distance. The

process of telecommunication started with beacons and pigeons. Modern telecom-

munication systems make use of electrical and electromagnetic technologies. The

evolution of communication is shown in the below Figure 2.1. The main objective of

this paper is to discuss the impact of power on the evolution of telecommunication

[14].

Figure 2.1: Evolution of telecommunication system.

Vacuum tubes are the electronic devices that are used to control the electric cur-

rent between the electrodes in electronic and communication systems. Vacuum tubes

are bulky with high operating voltages and high power consumption. The discovery

of electromagnetic induction by Faraday, the development of telegraph systems using

wires, transmission of information using radio-waves, and finally the invention of tran-

sistor and subsequent developments as integrated circuit are the main key features

of the above mentioned evolution [15]. The process of communication is discussed in

8

this thesis to better understand the efficiency.

Electronic communication plays a very important role in day-to-day life. The

purpose of communication is to either convey or to transfer the information from

one point to another. Instant communication over long distances become a reality.

Invention of radio made the information transfer efficient. The communication system

mainly consists of a transmitter, receiver and a channel. The basic block diagram of

communication system is as shown in the Figure 2.2 [16].

Figure 2.2: Block diagram of communication system.

The basic modes of communication are two types.

• Broadcasting.

• Point - Point communication.

Broadcasting is the process of communication from one transmitter to multiple

receivers. The point to point communication is a bi-directional process of commu-

nication from one point to another and vice-verse. The main parameters of the

communication system are transmission power, speed and band-width. The signal

speed is measured in number of bits per second and the bandwidth is the width of

the band of frequencies. Bandwidth is the range of frequencies in which, the signal

is allowed to transmit. Transmitted power is the average power of the transmitted

signal.

9

The reproduction of an input message signal at the receiver end in the original

form (same amplitude and frequency) is impractical. This is due to distortion, noise

and power loss of the signal. Noise is the unwanted signals that interfere with the

message signals reception. Distortion is due to the non-ideal channel characteristics.

The detailed description of each block is explained below. The complete block diagram

of process of communication system is shown in the Figure 2.3 [14],[16].

!"

#

Figure 2.3: Block diagram of process of communication.

2.1 Process of Communication

2.1.1 Base-band Signal

Un-modulated signal or the basic signal is called a Base-band signal. Generally, the

base-band signals are low frequency signals with some magnitude in the vicinity of

10

origin and can be neglected elsewhere. For example, a simple voice signal is said to a

base-band signal. The frequency range of base-band signal is 1-3 MHz [17].

2.1.2 Digital Signal Processing

Base-band signals are supposed to be modulated for transmission purposes. These

signals are properly shaped with the help of digital signal processing. This is shown

as frequency up convert and intermediate frequency amplifier in the Figure 2.3. The

modulation of a base band signal takes place in this block. The signal is converted

from analog to digital using Analog to Digital Converter(ADC) and is processed and

again converted back from digital to analog using Digital to Analog Converter(DAC)

as shown in the Figure below 2.4 [17].

Figure 2.4: Block diagram of digital signal processing.

2.1.3 Process of Modulation

The signal with the lower frequencies cannot be transmitted in the communication

system. Hence the signals are modulated. Modulation is the continuous reversible

change that is made to RF current or voltage signal. The variation is applied by

mixing this base-band signal with the high frequency signal [17]. A basic sinusoidal

signal will be mainly having three parameters namely amplitude, phase and frequency.

It is mathematically represented as

V = Vm sin(ωt+ φ), (2.1)

where

11

Vmis the amplitude of the message signal,

f is the frequency of the signal, and

φ is the phase of the signal.

The three types of modulations are

1. Amplitude Modulation.

2. Phase Modulation.

3. Frequency Modulation.

2.1.4 Amplitude Modulation

”In accordance to the amplitude of low frequency modulating signal, the amplitude of

high frequency carrier signal is varied by keeping phase and frequency constant”[18].

The carrier signal, modulating signal and the amplitude modulated signal are as

shown in the Figure 2.5 below. The carrier signal is the high frequency signal used

for transmission purposes. The modulating signal is the message signal that has to

be transmitted. The modulating signal and the carrier signal are mathematically

represented as

Vm = Am sin(ωmt) (2.2)

Vc = Ac sin(ωct) (2.3)

The amplitude modulation can be mathematically represented as

VAM = Ac[1 +m sin(ωmt)] sin(ωct), (2.4)

where

m is the modulation index.

12

0 0.5 1 1.5 2 2.5 3

time(sec) ×10-3

-2

0

2

Am

plitu

de(v

olt)

Modulating Signal

0 0.5 1 1.5 2 2.5 3

time(sec) ×10-3

-5

0

5

Am

plitu

de(v

olt)

Carrier Signal

0 0.5 1 1.5 2 2.5 3

time(sec) ×10-3

-10

0

10

Am

plitu

de(v

olt)

Amplitude Modulated signal

Figure 2.5: MATLAB plot showing modulating signal,carrier signal and amplitudemodulated signal.

Vm is the modulating signal.

Vc is the carrier signal.

VAM is the amplitude modulated signal.

The modulation index is the ratio of Vm to Vc. The modulation index gives the

degree of modulation.

2.1.5 Phase Modulation

Phase Modulation is defined as the rate of change of the point moves around the circle

[18]. Frequency and phase modulations are inter-related. The frequency modulation

and the phase modulation are mathematically represented as follows. The phase

modulation with the modulating and the carrier frequencies is shown in the Figure

2.6.

VFM = Ac sin[ωct+m cos(ωmt)], (2.5)

13

VPM = Ac sin[ωct+m sin(ωmt)], (2.6)

where Vm is the modulating signal,

Vc is the carrier signal,

VFM is the frequency modulated signal,

VPM is the phase modulated signal.

0 200 400 600 800 1000

time(sec)

-5

0

5

Am

plitu

de(v

olt)

Modulating Signal

0 200 400 600 800 1000

time(sec)

-5

0

5

Am

plitu

de(v

olt)

Carrier Signal

0 200 400 600 800 1000

time(sec)

-5

0

5

Am

plitu

de(v

olt)

Phase Modulated signal

Figure 2.6: MATLAB plot showing modulating signal,carrier signal and phase mod-ulated signal.

The inter-relation of phase modulation and frequency modulation is depicted in

the Figure 2.7. Integral of frequency modulation gives phase modulation. In the figure

2.7 f is the instantaneous radial frequency. The frequency and phase modulations

from the above equations is shown in the Figure 2.8. The slight difference of phase

and frequency modulation can be observed from the Figure 2.8 [17].

m(t) is the modulating signal.

14

Figure 2.7: Block diagram showing relation between phase and frequency modula-tions.

v(t) is the modulated signal.

dΦ(t)dt

= 2π(f − fc) (2.7)

0 200 400 600 800 1000

time(sec)

-5

0

5

Am

plitu

de(V

)

Phase Modulated signal

0 200 400 600 800 1000

time(sec)

-5

0

5

Am

plitu

de(V

)

Frequency Modulated signal

Figure 2.8: MATLAB plot showing the slight difference in the phase and frequencymodulations.

Modulation of a signal sets the range of frequency, which helps to transmit multiple

signals over a single channel. Modulation also helps to reduce the height of the

15

antenna. The height of antenna should be 1/10th of the wavelength of the signal [13].

The height of the quarter wave antenna is

Ha = λ

4 = c

4f , (2.8)

where

λ is the wave-length,

c is the speed of light and

f is the frequency of electromagnetic waves.

Modulation helps to identify the signal with the help of frequency. Amplitude

modulation is the variation that is made with respect to the amplitude of a signal.

The phase modulation is the modulation with respect to an angle. The frequency

modulation is equivalent to a phase modulation where the shift in the phase is in-

versely proportional to the audio frequency.

2.1.6 Local Oscillator

An oscillator is a circuit that produces a periodic output signal without any ac input

signal. An electronic oscillator is a nonlinear circuit with at least two energy storage

components. It establishes the transmitter carrier frequency and drive the mixer

stages that convert signals from one frequency to another. Frequency conversion

plays an important role in the process of communication. It is the circuit that is

helpful in adjusting the frequency of the signal which generally produces the sum or

difference of the frequencies [17].

2.1.7 Radio-Frequency Power Amplifier

Radio frequency power amplifier is a circuit that amplifies the power of the transmit-

ter. Generally, filter circuit will be available along with the power amplifier, which

filters out the unwanted noise or the disturbance in the transmitter circuit. The basic

16

diagram of RF power amplifier is as shown in the Figure 2.9 [13].

Figure 2.9: Radio frequency power amplifier.

Coupling capacitor is used in the RF power amplifier circuits in order to block DC

(Direct Current) and to allow only AC (Alternate Current) into the circuit whereas,

RF choke helps the circuit to block high frequency components i.e. harmonics.

2.1.8 Classification of Linear Radio Frequency Power Amplifiers

Relation of conduction angle of the drain current of the transistor (used as dependent

current source) to the linearity and the power efficiency leads to different classes of

RF power amplifiers.

Table 1: Classification of Linear Radio Frequency Power Amplifiers.

RFPA Conduction Angle vGS Efficiency Harmonics

Class A θ = 360 vGS < vt 50% Absent

Class B θ = 180 vGS = vt 78.5% Present

Class C θ < 180 vGS > vt 85% Higher Harmonics

Class AB θ > 180 < 360 vGS > vt < 85% Higher Harmonics

17

Conduction angle is the amount of wave period in which the active device is

conducting. The Table 1 gives different classes of linear RF power amplifiers with

their respective conduction angles.

2.2 Linearity-Efficiency Trade-offs

Linearity versus Efficiency is the main problem in RF power amplifiers, where linearity

refers to the quality of the signal (distortion free signal) and efficiency refers to the

power efficiency i.e. ratio of output power to input power. Class A, B, C and AB

RF power amplifiers are called linear power amplifiers. The design of RF amplifier

with good linearity and power efficiency is a challenging task. Linearity is inversely

proportional to power efficiency. The radio frequency power amplifier is a circuit

that amplifies the power level of the circuit with the given input voltage [5]. The

amplification done should be linear in order to get a good reproduction of the amplified

signal at the receiving end. Thus both amplitude and phase modulations are required

for linear amplification.

2.3 Non-Linear Radio Frequency Power Amplifiers for Effi-ciency Improvement

The transistor can be used as a switch, or dependent voltage source,or dependent

current source based on the application. The transistor is operated as an amplifier

according to the operating point. The transistor is operated as dependent voltage or

current source for linear power amplification. The drain current and drain to source

voltage vary linearly with change in gate to source voltage, where the power efficiency

has to be compromised. The transistor is operated as a switch, where drain current

and drain to source voltage are independent of the gate to source voltage [13]. The

operation of a transistor as a switch draws high amount of current and low voltage

that results in high power efficiency.

18

2.4 Classification of Non-Linear Radio Frequency Power Am-plifiers

Alternating current is a sinusoidal wave with respect to the time, where the entire

cycle is mathematically represented as 2θ i.e. 360. The other classification of power

amplifiers such as Class D,E and F RF power amplifiers is based on switching opera-

tion of MOSFET. Class D RF power amplifier makes use of two MOSFETs produces

a half sinusoidal waveform and a square voltage alternatively. During the first half of

the cycle the upper transistor is ON and the lower transistor is OFF and vice verse.

The current through the second transistor and voltage through the first transistor

will be zero constitutes the generation of half sine and half square waves. The main

drawback of Class D RF power amplifier it is hard to drive the upper MOSFET in

the topology. The internal parasitic capacitance and resistances of the MOSFET pro-

duces losses in each cycle. Efficiency of class D is theoretically 100 %, but cannot be

achieved practically due to the presence of parasitic capacitance and lead inductance.

Class E RF power amplifier uses only one MOSFET, which operates as a switch in

the RF power amplifier. Class E RF power amplifier uses shunt capacitance in order

to operate power amplifier at higher frequencies efficiently. Filter circuits are used

in RF power amplifiers in order to output only the fundamental component of the

waveform and to suppress harmonics. Resonant circuit is placed at the output stage

of RF power amplifier, which is generally a parallel resonant circuit that gives maxi-

mum gain due to high impedance [13]. Class E RF power amplifiers are classified in

to two types

• Class E Zero Voltage Switching.

• Class E Zero Current Switching.

The values of the resonant circuit are to be chosen correctly such that the power

dissipation of the transistor will be less. Class F RF power amplifiers use multiple

19

harmonic resonators to reduce power dissipation. The efficiency of the power amplifier

is improved by shaping the drain to source voltage to be flat or low such that the

current is high or the drain to source voltage is high, when the drain current is zero.

The class F RF power amplifiers are classified in to two types

• Odd harmonic class F RF power amplifier.

• Even harmonic class F RF power amplifier.

2.5 Evolution of Data Transmission from 1st Generation to5th Generation

The invention of transistor made the communication easy. The use of transistor as

a switch improved the power efficiency of RF power amplifiers. The developments

in the communication can be clearly seen by the miniaturization of transistor and

improved power efficiency. These two factors lead to the vast developments in wireless

communication systems. The first generation of wireless telephone technology is called

1G. Analog radio signals were used for transmission purposes. The frequency of 1G

system is 150MHz and above. The second generation of wireless telephone technology

is called 2G.

Analog radio signals were replaced with the digital signals. The main advantages

of 2G networks over 1G is digital encryption of telephone conversations, provided

various networks for text messages and picture messages. The third generation (3G)

wireless telephone technology sets high standards for International Mobile Telecom-

munication which, allows the features such as mobile internet access, video calls

mobile TV etc. The fourth generation (4G) wireless technology that is developed

with the higher speeds to provide various features such as mobile web access, gaming,

video conferencing etc. The evolution of data transmission from first generation to

fifth generation is clearly shown in the below Table 1.2.

20

Table 2: Evolution of Wire-less Technology.

First Generation(1980’s)

The communica-tion is throughAnalog phones

Limited capabili-ties due to sizeand weight

1%Americanswith mobilesubscriptions

2nd Generation(1991)

The communica-tion became Digi-tal enabling us touse digital dataservices

Text and Email 3%Americanswith mobilesubscriptions

3rd Generation(2001)

Fast data trans-fer via digital net-work and enabledGPS and multime-dia

GPS and Multi-media for photosand videos

45%Americanswith mobilesubscription

4th Genera-tion/LTE (2009)

Even fast trans-fer of data withhigh speeds andmore informationcan be accessedeasily

Streaming movieswith high defini-tion

85%Americanswith mobilesubscription

LTE Advanced(2014)

Enables multipleradio frequencychannels toquicker in gather-ing and sendingthe data

Carrier Aggrega-tion (use of band-width more effec-tively)

96%Americanswith mobilesubscription

Fifth Generation Several hundredsof thousands con-nections are sup-ported simultane-ously

Research is goingon

-

21

3 Classical Techniques in Communication

3.1 Classical Techniques of Communication for Efficiency Im-provement

The power efficiency of RF power amplifiers was less in early 1920’s. There are

three main classical techniques to reduce the efficiency versus linearity problems.

They are Chireix out phasing amplifier, Doherty’s Power amplifier, Kahn’s technique.

In earlier days transistor is used as a dependent source. The efficiency of the linear

amplifier is less. These are the techniques that are used to improve the efficiency of

linear power amplifiers and are still in existence due to their advantages and improved

efficiency [13].

3.1.1 Cheirix Out-phasing Modulation

The cheirix out-phasing modulation is used to improve both the linearity and effi-

ciency, where the linear amplification is achieved with non-linear components to get

good efficiency at high peak to average signals. In conventional out phasing, a de-

sired output signal is decomposed into two constant-amplitude signals, which can be

summed to provide the desired output. Figure 3.1 shows the simplified block diagram

of Cheireix out-phasing system [19].

Min is the input signal to an amplifier and M1 and M2 are the two signals decom-

posed. The decomposed signals are given to power amplifier and amplified signals are

represented as M ′1 and M ′

2. The amplifiers have the non-linear input-output charac-

teristics. Hence obtained signals are linearly combined with power combiner. As the

two signals are of constant amplitude, they can be synthesized with highly efficient

power amplifiers including partially and fully-switched-mode designs. Combining the

22

Figure 3.1: Simplified block diagram of Cheireix out-phasing system

two constant-amplitude outputs in a power combining network enables the net output

amplitude to be controlled via the relative phase of the two constituent components.

The topology and working of a this technique is similar to that of phase modulated

resonant dc-ac inverter and dc-dc converters [20].

3.1.2 Doherty’s Power Amplifiers

Doherty’s Technique is used to improve the average efficiency of power amplifier

with the help of an auxiliary amplifier according to the required power. The main

amplifier is called carrier power amplifier and the other is called peaking power am-

plifier with 90 phase shift. The power is directly sent to the carrier amplifier such

that the overall efficiency is improved. The topology of Doherty’s Power amplifier to

improve the power efficiency is as shown in the Figure 3.2 [21].

Generally, a class B power amplifier is used in basic Doherty’s model. The appli-

cation of basic Doherty’s power amplifiers is mainly in medium and high-power, low

frequency and medium frequency AM transmitters. The main disadvantage of this

scheme is non-linearity and it requires envelope correction and feed-back linearization

23

Figure 3.2: Doherty’s power amplifier.

circuits to be used. The basic Doherty’s topology is changed by replacing the class

B RF power amplifer with class C RF power amplifier. This gives 100% modulation

and very little drive power that results in improved efficiency. The revised Doherty’s

power amplifiers are used to improve the linearity, optimal biasing of carrier and peak

cells for inter-modulation cancellation and optimized uneven power splitting for load

modulation. This architecture is important in energy efficiency transmitters of variety

of wireless communication applications [22].

3.1.3 Kahn’s Technique

Kahn’s technique is a technique in which, the amplitude and phase of single sideband

are separated, modulated and then combined to improve the power efficiency. As

the envelope is eliminated and restored it is also called as Envelope Elimination and

Restoration technique. The block diagram of Kahn’s technique is shown in the Figure

3.3.

Generation of single sideband is highly complex. The conventional system pro-

24

Figure 3.3: Block diagram of Khan’s technique.

duces the desired single sideband at very low power. This low power single sideband

is amplified with the help of cascaded series of linear power amplifiers. As the effi-

ciency of the above system is very low, a new technique was proposed to improve the

efficiency of power amplifier called Kahn’s technique. The efficiency of linear power

amplifiers such as class A, B, C and AB is improved with this technique. Single

sideband is used in this technique is to improve bandwidth efficiency. The ampli-

tudes of single sideband signal and the carrier wave are considered to be equal. The

amplitude and phase are separated from a small portion of single sideband signal.

The amplitude is separated by an amplitude detector. The phase was detected by a

limiter circuit. As the amplitude and phase are separated from the single sideband,

the envelope is said to be eliminated. Thus separated amplitude is amplified with

an audio power amplifier and phase is separately amplified with the linear RF power

amplifier as shown in the Figure 3.3. The amplified output was then given to the

modulator equipment where, the eliminated envelope is restored at the output of the

modulator. The output of the modulator is given to the antenna for transmission.

Practical implementation of this technique consists of other blocks such as phase

25

equalizer, mixer, XTAL oscillator and output level control shown in the Figure 3.4

[24].

!"

#$

%

%

&

Figure 3.4: Detailed block diagram of Kahn’s technique.

The mixer and XTAL oscillator are used to regulate the frequency of single side

band generator according to the required output frequency. Phase equalizer is used

to equalize the time delay between the amplitude modulation channel and phase

modulation channel. Output level control is used for transmitting variable average

amplitude signal, if the amplitudes of the single sideband and the carrier wave are

not of same amplitudes. The main advantages of this system are as follows:

• Performance of the circuit is equal or better than conventional linear power

amplifier.

• Overall efficiency is equal to double side band amplitude modulated transmitter.

• Distortion and spurious frequency is independent of the power level transmitted.

The practical implementation of Kahn’s technique was done with 1 KW telephone

transmitter by producing 2.5 KW peak power single sideband [24].

26

4 An approach to implement Kahn’s Techniquewith Dynamic Power Supply

The main motto of this thesis is to implement dynamic power supply to radio

frequency power amplifier in Kahn’s technique to improve the efficiency. The block

diagram of Kahn’s technique with dynamic power supply is shown in the Figure 4.1.

It mainly consists of the blocks AM/PM signal generator, amplitude detector, dc-ac

buck converter as dynamic power supply, class D RF power amplifier, phase detector.

In this chapter each block is explained along with design of the respective electrical

circuitry.

Figure 4.1: Block diagram of dynamic power supply to RF power amplifier imple-mented in Kahn’s technique.

4.1 AM/PM Signal Generator

The AM/PM signal generator is the circuit that combines the amplitude modulation

and phase modulation together to form an envelope. The amplitude modulation is

achieved using the operational amplifier in inverting configuration with negative feed-

27

back and a switch [25]. Phase modulation is achieved with the pulse width modulator

set up. The AM/PM signal generator circuit is shown in the Figure 4.2.

Figure 4.2: Circuit diagram of an AM/PM signal generator.

4.1.1 Circuit Description

The AM/PM signal generator circuit consists of two op-amps U4 and U5 and a MOS-

FET Q4 and resistors. Q4 is the MOSFET used as a switch. The amplitude modu-

lation uses the inverting configuration of an op-amp U4. The phase modulation uses

the op-amp U5 as comparator. In inverting operation of an op-amp the non-inverting

28

terminal is given to the switch, where the source terminal of MOSFET is grounded

as shown in the Figure 4.3. The inverting terminal of an op-amp U4 consists of two

resistors Rf and R1. R1 is the input resistor and the Rf is the feed back resistance.

The op-amp U5 consists of two voltage sources Vtri and Vsin as in the pulse width

modulator.

4.1.2 Operation of AM/PM Signal Generator

Both the Op-amps U4 and U5 are assumed as ideal op-amps. The triangular input

Vtri is given to the inverting terminal of op amp U5. The sinusoidal input Vsin to

the non-inverting terminal of op-amp U5. The U5 op amp acts as a comparator that

compares the triangular input to the sinusoidal input and gives the pulse output. The

duty cycle of the MOSFET is varied by the pulse width modulator. The change in

the frequency of the sinusoidal input changes the turn ON and turn OFF times of

the MOSFET. The frequency and the phase are inter related in the angular plane,

where the integral of the phase gives the frequency. The inverse of the time period is

the frequency. The resistor Rf is the negative feedback resistor. The voltage at the

inverting terminal of an op-amp U4 is the output of the potential divider formed with

the input resistor R1 and the feedback resistor Rf . The resistor R2 and the MOSFET

forms another potential divider circuit. The resistances are chosen in such a way that

the voltages at the inverting and non-inverting terminals to be equal. The output of

pulse width modulator is a pulse that varies according to the sinusoidal input given

to it. The values of resistors are chosen in such a way that the input voltage at the

comparator terminals are maintained to be the same. The values of R1 and Rf are

chosen to be the same, such that the voltage gain is equal to unity.

Vs = R1

(R1 +Rf )VO (4.1)

29

Vs = R2VO (4.2)

Figure 4.3: Output of an envelope generator.

The envelope generated has two frequencies. The modulating frequency and the

carrier frequency. The outer sinusoid is due to the carrier frequency and the inner

pulsed sinusoid is of modulating frequency shown in the Figure 4.3.

4.2 Amplitude Detector

The amplitude detector circuit detects the amplitude of the signal. The obtained out-

put of the amplitude detector should be able to detect the outer sinusoid of AM/PM

signal.

30

4.2.1 Circuit Description

The circuit of the amplitude detector is shown in the Figure 4.4. The main aim of the

amplitude detector is to detect the amplitude above x-axis. A simple op-amp with

RC filter circuit and diode serves this function. The diode helps the unidirectional

flow of current. The RC filter setup detects the signal i.e. peak values in every cycle

above the ground. This circuit gives good results for the large signals even without

the Op-amp.The use of op-amp with the negative feedback gives the best results of

peak detection with good linearity. The output of the AM/PM signal generator is

given to the input of the AM/PM signal detector.

Figure 4.4: Circuit diagram of an envelope detector.

4.2.2 Operation of Amplitude Detector

Initially the amount of current will be equal to zero, hence the output of amplitude

detector will be zero. As the amount of current flow increases, the diode turns ON

31

after it crosses the diode turn-on voltage and follows the input and charges up the

capacitor. Whenever the diode crosses the peak value, the voltage at the capacitor

drops, where the current can lead it. As the diode allows unidirectional flow of current,

the current goes in to the resistor. So the resistor is also called as bleeding resistor.

The value of the resistance is made to be high such that the capacitor discharges

the current slowly. During the time t RC time constant τ of the capacitor slowly

discharges and moves to the next cycle. The negative feedback of op-amp helps to

get rid of the diode turn-on voltage by making the input voltage difference equal to

zero. The output of the amplitude detector is shown in the Figure 4.5.

4.2.3 Analysis

RC time constant

τ = RC (4.3)

cut-off frequency is given by

fc = 12πRC (4.4)

The frequency of the generated signal is

R = 10, 000 Ω. (4.5)

pick

fc = 50, 434 Hz. (4.6)

C = 31.5 nF3. (4.7)

32

Figure 4.5: Envelope detection from the envelope.

The amplitude detector along with dc-ac buck converter together is the dynamic

power supply to this design.

4.3 Dynamic Power Supply to Class D RF Power Amplifier4.3.1 Introduction

The dynamic supply to power amplifier is also called as class S amplifier. The

dynamic power supply from sinusoidal voltage driven buck converter to RF power

amplifiers is efficient. The dynamic power supply to linear power amplifiers improves

the efficiency, whereas it gives the amplitude modulated wave, when given to the

non-linear power amplifiers. Sinusoidal Pulse Width Modulation (SPWM) is widely

used in power electronic applications to digitize the power [26]. The width of the

33

pulses are modulated to get the inverter output, which reduces the harmonic content.

The triangular wave as a carrier signal is compared with the sinusoidal wave of the

desired frequency. The op-amp acts as a comparator and the waveforms are shown

in the Figure 4.6. The efficiency of a system with a certain input and output can

be improved by the external supplement of power to the circuit through input of

the controllable switches. The pulse width modulator and sinusoidal pulse width

modulator circuits are employed according to the application.

Figure 4.6: Sinusoidal pulse width modulation converter waveforms.

The dc-ac buck converter converts the dc power to ac power at desired output

voltage and frequency. The dynamic action of the converter is due to the filter

capacitor present in the converter, which provides the constant dc link voltage. The

dc-ac converters are mainly classified into two types.

• Voltage fed dc-ac converter.

• Current fed dc-ac converter.

34

The variation of duty cycle means managing the turn ON and turn OFF times

of the MOSFETs with a control. The amplitude and the frequency of the sinusoidal

input to the pulse width modulator plays a key role to vary the duty cycle. The ampli-

tude modulation is the process of mixing two sinusoidal waves of different frequencies.

The output of the dynamic power supply is a varying sinusoidal wave, which varies

the input of the radio frequency power amplifier. The sinusoidal signal that varies

according to the given frequency combines with the input given to the MOSFET in

radio frequency power amplifier and gives amplitude modulated wave. The dynamic

power supply is provided by the dc-ac buck converter. Figure 4.7 shows the class D

radio frequency power amplifier supplied with dc-ac buck converter.

!

!

!

Figure 4.7: Buck converter as DPS to class D RF power amplifier.

4.3.2 Circuit Description

The circuit consists of three MOSFETs Q1, Q2, Q3, a diode D1, a second order

low pass filter, three pulse width modulators, impedance matching circuit and a load

resistor RL. All the three MOSFETs are used a switches. All the MOSFETs are

driven using pulse width modulators. The low pass filter in the buck converter allows

only low frequency components. The dc-ac buck converter and class D power amplifier

are briefly described to better understand the combined system.

35

4.3.3 DC-AC Buck Converter

Buck converter is a circuit that is generally used as a chopper, as it chops the given

input. A buck converter mainly consists of a controllable a switch Q1, a diode D1,

an inductor L1 a capacitor C1 and a load resistor RL. The circuit diagram of buck

converter is shown in the Figure 4.8.

Figure 4.8: Circuit diagram of dc-ac buck converter.

The output voltage of the buck converter is lower than that of input voltage.

The MOSFET or the controllable switch used in the buck converter is not referenced

to the ground, so it is hard to drive the MOSFET. Hence,the dc-dc transformer

with the pulse width modulation setup is used to drive the upper MOSFET. The

MOSFET always requires the constant input to operate, as it requires the certain

charge formation across the internal capacitor present in it, which is responsible for

the switching action. The pulse width modulator is a set of an operational amplifiers

with two sources such as a triangular voltage source Vtri and a sinusoidal voltage

source Vsin through which pulses are generated with the varying duty cycle according

to the switching frequency as discussed above. The duty cycle is the ratio of the

36

time for which the switch is ON to the total time period. It can also be expressed as

the product of switching frequency and the time for which the MOSFET is ON. The

switch Q1 is controlled by a pulse-width modulator and is turned on and off at the

switching frequency fs = 1T

and the duty cycle D defined asD = tonT

.

4.3.4 Operation dc-ac Buck Converter

The operation of dc-ac buck converter with fixed input to variable output is similar

to the operation classical dc-dc buck converter. The MOSFET is turned ON and

OFF using gate driver circuit. The MOSFET Q1 is ON for a time DT where D is

the duty cycle and T is the switching period. The duty cycle of the gate to source

voltage of the MOSFET is governed according to the sinusoidal frequency given to

the pulse width modulator. When the MOSFET of the buck converter is turned ON

the diode is in reverse biased condition and the current flow across the diode will be

zero. The inductor gets charged with the slope of (VI−VO)L

.

where,

VI is the dc input voltage of buck converter. VO is the ac Output voltage of buck

converter.

When the MOSFET is turned OFF the inductor acts as the current source and

makes the diode to turn ON. And hence the inductor discharges with the slope −VO

L.

The complementary action of the diode and the MOSFET forms the voltage and cur-

rent loops. The assumptions made for the steady-state analysis of the buck-converter

are as follows:

• The power MOSFET and the diode are ideal switches.

• The transistor output capacitance, the diode capacitance, and the lead induc-

tances are zero, and thereby switching losses are neglected.

• Passive components are linear, time invariant, and frequency independent.

37

• The output impedance of the input voltage source VI is zero for both dc and

ac components.

• The converter operates in a steady state.

• The switching period T = 1fs

is much shorter than the time constants of reactive

components.

• The dc input voltage Vi and the load resistance RL are constant, but the dc

output voltage VO is variable.

• The converter is loss-less.

The equations governing the sinusoidal voltage driven dc-ac buck converter are

considered under the following assumptions.

4.3.5 Steady-State Analysis

The volt-second balance to inductor current waveform gives

(VI − VO)DT = VOD′T. (4.8)

The input to output voltage transfer function MV DC is given by

MV DC = VOVI

= D (4.9)

The inductor peak current is given

∆iL = (VI − VO)DTL

= VO(1−D)fsL

(4.10)

,

where fs is the switching frequency. The minimum inductance required

38

Lmin =VO(( 1

ηmin)−Dmin)

2fsIOmin(4.11)

Cmin = 14fsrcmax

(4.12)

Figure 4.9: Waveforms of vGS,vL,iL of sinusoidal voltage driven dc-ac buck converter.

The converter is said to be in continuous conduction mode, if the inductor current

is continuous, and said to be in dis-continuous conduction mode if the inductor current

not continuous. For the buck converter with variable voltage, the maximum ripple

current occurs at the duty cycle D = 0.5. The gate-source voltage, inductor voltage

and inductor current are shown in the Figure 4.9.

4.3.6 Design Example of dc-ac Buck Converter in CCM

Specifications of the buck converter in continuous conduction mode are VI = 25V,

VO = (3− 23)V, POmax = 7W, fs = 100 KHz, Vr/VO = 1% [13]

The load resistance is

RL = V 2Omax

POmax= 232

7 = 75.5714 Ω. (4.13)

39

Nominal output power at nominal output voltage will be

POnom = V 2Onom

RL

= 132

75 = 2.2363W. (4.14)

The output power at VO = 3V is

POmin = V 2Omin

RL

= 32

75.5714 = 0.1191W. (4.15)

The maximum load current

IOmax =√

(POmaxRL

) =√

( 775.5714) = 0.3043A. (4.16)

The nominal load current

IOnom =√

(POnomRL

) =√

(2.2575 ) = 0.1720 A. (4.17)

The maximum load current

IOmin =√

(POmaxRL

) =√

(0.1275 ) = 0.0397 A. (4.18)

The maximum, nominal and minimum values of DC voltage transfer function are

MV DCmin = VOminVI

= 325 = 0.1200. (4.19)

MV DCnom = VOnomVI

= 1325 = 0.5200. (4.20)

MV DCmax = VOmaxVI

= 2325 = 0.9200. (4.21)

Assume efficiency η = 90% at VO = 23V, η = 85% at VO = 10V, η = 30% at

VO = 3V .

The minimum nominal and maximum values of duty cycle are

40

Dmin = MV DCmin

ηmin= 0.12

0.3 = 0.400. (4.22)

Dnom = MV DCnom

ηnom= 0.52

0.85 = 0.6118. (4.23)

Dmax = MV DCmax

ηmax= 0.92

0.95 = 0.9684. (4.24)

The minimum inductance required to maintain the converter in continuous con-

duction mode is

Lmin = RLmax

8× fs= 75

8× 100× 1000 = 94.464 mH. (4.25)

[27]

Pick L = 95 µH.

The maximum inductor ripple current is

∆iLmax= VI

4× fs × L= 25

4× 100× 1000× 95× 10−6 = 1.3158 A. (4.26)

The inductor ripple voltage is

Vr = VO100 = 13

100 = 130 mV. (4.27)

The maximum ESR value of the filter capacitance is

rcmax = Vr∆iLmax

= 0.0131.3198 = 0.0988 Ω. (4.28)

Pick rcmax = 500 mΩ.

The minimum value of filter capacitance is

41

Cmin = 14× fs × rC

= 14× 100× 1000× 500× 10−3 = 5 µF. (4.29)

Pick C = 6 µF.

The corner frequency of the low pass filter fO is

fO = 12× π ×

√L× C

= 12× π ×

√95× 10−6× 6× 10−6

= 6666.3 Hz. (4.30)

The voltage and current stresses are

VSM = VDM = VI = 25 V (4.31)

ISMmax = IDMmax = IOmax + ∆iLmax

2 = 0.305 + 1.31982 = 0.9622 A (4.32)

The International Rectifier IRF150 MOSFET is selected [28]. The specifications

are VDss = 100 V, ISM = 40 A, rDS = 55mΩ, Qg = 69 nC, CO = 100pF . Schottky

diode is chosen, which has IDM = 25A, VDM = 45V, VF = 0.3V, and RF = 20mΩ.

The MOSFET gate power is given by

PG = fs ×Qg × VGSPP = 100× 1000× 63× 10−9× 4 = 0.0276 W. (4.33)

The conduction power loss in the MOSFET is

PrDS= Dmax × rDS × I2

Omax = 0.9684× 0.055× 0.3052 = 0.0049 W. (4.34)

The switching power loss in the MOSFET is

Psw = fs × CO × V 2I = 100× 103 × 100× 10−12× 252 = 0.0016 W. (4.35)

42

The total power loss in the MOSFET is

PFET = PrDS + Psw2 = 0.0049 + 0.0016

2 = 0.0057 W. (4.36)

The diode power loss is

PV F = (1−Dmax)× VF × IOmax = (1− 0.9684)× 0.3× 0.3052 = 0.0029 W (4.37)

The diode loss due to RF is

PRF = (1−Dmax)×RF × I2Omax = (1− 0.9684)× 20× 10−3× 0.3052 = 58.508 µW.

(4.38)

The total diode loss is

PD = PV F + PRF = 2.8914× 10−3 + 58.7918× 10−6 = 0.0029 W. (4.39)

The power loss in the inductor rL = 0.005Ω is

PrL = rL × I2Omax = 0.2× 0.3052 = 0.0185 W. (4.40)

The peak to peak inductor ripple current at Dmax = 0.9684 is

∆iL = VOmax × (1−Dmax)fs × L

= 23× (1− 0.9684)100× 1000× 95× 10−6 = 0.0765 mA. (4.41)

The power loss in the capacitor ESR is

PrC = rc ×∆i2Lmax12 = 0.5× (0.0765)2

12 = 0.24355 mW. (4.42)

The total power loss is

43

PLS = PrDS+Psw+PD+PrL+Prc = 0.0049+0.0016+0.0029+0.0185+0.24355×10−3 = 0.0282 W.

(4.43)

The minimum efficiency of the buck converter is

ηmin = POPO + PLS

= 0.120.12 + 0.03276 = 0.8085. (4.44)

The nominal efficiency of the buck converter is

ηnom = POPO + PLS

= 2.252.25 + 0.03276 = 0.9875. (4.45)

The maximum efficiency of the buck converter is

ηmax = POPO + PLS

= 77 + 0.03276 = 0.996. (4.46)

The theoretical efficiency of sinusoidal voltage driven dc-ac buck converter for the

minimum maximum and nominal values are calculated. The buck converter has a

second order low pass filter which allows only the low frequency components. The

PWM inverter circuit waveforms are shown in the Figure 4.10. The converter design

is taken in CCM and the inductor current and dc-ac buck output voltage is shown in

the Figure 4.11.

The buck converter outputs the varying sinusoidal signal according to the switch-

ing frequency. The efficiency of dc-ac buck converter varies with respect to varying

output power. The distortion in due to the gate driver circuit. The power losses of

due to the non-linear components of the circuits such as MOSFET and a diode are

calculated.

44

(V

)

−2.0

0.0

2.0

4.0

6.0

t(s)

4.65m 4.7m 4.75m 4.8m

(V

)

−5.0

0.0

5.0

(V) : t(s)

vgs

(V) : t(s)

v_sin

v_saw

Figure 4.10: Vsaw,Vsin and vGS of pulse width modulator of dc-ac buck converter.

t(s)

4.78m 4.8m 4.82m 4.84m

(V

)

16.0

17.0

18.0

19.0

20.0

(A

)

−0.2

0.0

0.2

0.4

0.6

0.8

(V) : t(s)

v_O

(A) : t(s)

i_L

Figure 4.11: Inductor current iL, output voltage vO waveforms of sinusoidal voltagedriven dc-ac buck converter.

45

4.4 Class D RF Power Amplifier

The topology of class D RF power amplifier consists of two MOSFETs Q2 and Q3,

which are operated as switches and a filter circuit. The circuit of class D RFPA is

shown in the Figure 4.13 The class D RF power amplifiers are mainly classified into

two types.

• Voltage-Switching Class D RF power amplifier.

• Current-Switching Class D RF power amplifier.

The main difference between the mentioned two different class D power amplifiers

is the voltage switching class D RF power amplifier is fed with the dc voltage source

and current switching class D RF power amplifier is fed with the dc current source

(done through RF choke, and dc voltage source). The voltage switching class D RF

power amplifier makes use of series resonant circuit and the current switching class

D RF power amplifier makes use of parallel resonant circuit.

Figure 4.12: Circuit diagram for class D RF power amplifier.

The main advantage of voltage switching class D RF power amplifier is the voltage

across each transistor in class D topology is low i.e. almost equal to supply voltage

46

because of which, these amplifiers can be used for high-voltage applications. The

challenging task in class D RF power amplifier comes with driving the upper MOSFET

called a driver circuit (Example: pulse transformer). The two n-channel MOSFETs

are operated as switches and a series resonant circuit is used to provide necessary

impedance that improves the gain of an amplifier. The range of voltages in application

of class D RF power amplifier mainly depends on gate side driver used in the circuit

that drives the upper MOSFET. Voltage mirror circuit as the gate driver circuit is

used for high voltage applications. Gate driver circuit plays a very important role

when the MOSFET is used as a switch, which requires constant input power to turn

ON and turn OFF the MOSFET. Internal capacitor called gate capacitor in the

MOSFET charges when the constant power i.e. gate to source voltage is given to it

and gets discharged when the input is low. Due to charge and discharge of a gate

capacitor in MOSFET increases the power losses.

4.4.1 Operation of Class D RF Power Amplifier

The main function of class D RF power amplifier is to convert low frequency sine wave

to a high frequency square wave, which in turn is filtered to obtain high frequency

sine wave. The frequency of the input signal is responsible for the change in the pulse

width of the square wave obtained i.e. duty cycle which is 0.5. D=0.5 means that

the transistor is turned ON half the time and OFF for half the time.

The filter that is present in class D power amplifier allows only ac to obtain

amplified output. When Q2 is ON, Q3 is OFF and the current flows through the

filter circuit via Q2 and When Q2 is OFF, Q3 is ON and the current flows through

the filter via switch Q3. The gate to source voltages and the current waveforms are

as shown in the Figure 4.13. At resonant condition (i.e. the frequency at which the

amplitude of output is maximum) the switching action of MOSFET takes place at

zero current, which is responsible for high efficiency. The assumptions made for the

47

steady-state analysis of class D RF power amplifier are

4.4.2 Assumptions

• The transistor and the diode form a resistive switch whose on-resistance is

linear, the parasitic capacitance of the switch are neglected, and the switching

times are zero.

• The elements of the series-resonant circuit are passive, linear, time invariant,

and do not have parasitic reactive components.

• The loaded quality factor QLof the series-resonant circuit is high enough so that

the current i through the resonant circuit is sinusoidal.

4.4.3 Steady-State Analysis

The inductance of class D RFPA is

L = QLRt

ωO(4.47)

The capacitance of class D RFPA is

C = 1ωOQLRt

(4.48)

The resonant frequency of the circuit is

ωO = 12π√

(LC) (4.49)

48

Figure 4.13: Waveforms of class D RF power amplifier.

4.4.4 Design of Class D RFPA

Specifications of the Class D RF power amplifier are VI = 12 V, PO = 10 W, fs = 250

KHz, rDS = 0.1Ω , QL = 5.5, QL0 = 200, η = 0.9, D = 0.5 Assume efficiency ηIr = 0.9

and neglecting switching losses [13].

Hence,DC input power is

PI = POη

= 100.9 = 11.1111 W. (4.50)

The total resistance is

Rt = 2× V 2I

π2 × PI= 2× 122

π2 × 11.1111 = 2.6262 Ω. (4.51)

The load resistance is

RL = η ×Rt = 0.9× 2.6262 = 2.3636 Ω. (4.52)

The maximum parasitic resistance is

rmax = Rt −R = 2.6262− 2.3636 = 0.2626 Ω. (4.53)

49

The inductance is

L = QL ×Rt

ω0= 5.5× 2.6262

2× π × 250× 1000 = 9.1956 µH. (4.54)

The capacitance is

C = 1ω0 ×QL ×Rt

= 12× π × 250× 1000× 5.5× 2.6262 = 44.074 nF. (4.55)

The voltage stresses are

VDSM = VI = 12V .

The amplitude of output current is

IS = ISM =√

2× POR

=√

2× 102.3636 = 2.9088 A. (4.56)

Assuming Kn = µnO × COx = 0.142 × 10−3 AV 2 , Vt = 0.3V , L = 0.18µm, a = 2 ,

IDsat = a× IDM . The aspect ratio of N-channel Si transistor is

(WL

)N = 2× IDsatKn × (VGSH − Vt)2 = 2× 1.057

0.142× 10−3× (3.3− 0.3)2 = 3308. (4.57)

Pick (WL

)N = 3400

The peak voltages across resonant components L and C

VCm = ImωO × C

= 2.90882× π × 250× 1000× 44.07× 10−9 = 42.020 V. (4.58)

VLm = Im × L× ωO = 2× 250× 1000× 9.19× 10−9× 2.9088 = 0.04199 V. (4.59)

The conduction power loss in each MOSFET

50

PrDS = rDS × I2m

4 = 0.1× (2.9088)2

4 = 0.2115 W. (4.60)

The switching power loss in each MOSFET

PswQ1 = 12 × f × CO × V

2I = 1

2 × 250× 1000× 10× 10−9× 122 = 0.18 W. (4.61)

The power loss in each MOSFET

PMOS = PrDS + PswQ1 = 0.2115 + 0.18 = 0.3915 W. (4.62)

The total switching loss in amplifier

Psw = 2× f × CO × V 2I = 2× 250× 1000× 10× 10−9× 122 = 0.72 W. (4.63)

The drain efficiency

ηD = PDSPI

= (PI − 2× PMOS)PI

= (11.111− 2× 0.39151)11.111 = 0.9295 (4.64)

The ESR of the inductor is

rL = ωO × LQLO

= 2× π × 250000× 9.19× 10−6200 = 0.07217 Ω. (4.65)

The ESR of the capacitor is

rC = 1ωO × C ×QLO

= 12× π × 250× 1000× 44.07× 10−6× 1000 = 14.44 µΩ.

(4.66)

The power loss in the inductor ESR is

51

PrL = (rL × I2m)

2 = (0.07217× 2.90882)2 = 61.11 mW. (4.67)

The power loss in the capacitor ESR is

PrL = (rC × I2m)

2 = (0.0144× 2.90882)2 = 60.92 mW. (4.68)

The efficiency of resonant circuit is

ηr = POPO + PrL + Prc

= 1010 + 0.06111 + 0.06092 = 0.987 = 98% (4.69)

The total losses PLS

PLS = 2×PrDS+PrL+PrC +Psw = 2×0.2115+0.06111+0.0609+0.72 = 1.26501 W.

(4.70)

The efficiency of Class D RFPA is

η = POPO + PLS

= 1010 + 1.26501 = 0.8877 = 88.770% (4.71)

The theoretical efficiency of Class D RFPA is 88.07%

The efficiency of class D RF power amplifier is

η = Average(PO)Average(PI)

× 100η = 8.7010.72 × 100η = 81.15% (4.72)

The practical efficiency is

The class D RF power has a filter which allows only ac. The gate-source voltages

of two MOSFETs and the output voltage class D RF power amplifier is shown in the

Figure 4.14. The practical efficiency of class D RF power amplifier is shown in the

Figure 4.15. The distortion in due to the gate driver circuit used to help the upper

MOSFET.

52

Figure 4.14: vGS1,vGS2 of class D RF power amplifier.

Figure 4.15: vO of class D RF power amplifier.

53

4.5 Operation of Dynamic Power Supply to Class D RF PowerAmplifier

The operation of class D RF power amplifier supplied with dc-ac buck converter is

explained below. The complementary action of the diode and MOSFET of the buck

converter varies the input voltage of the class D RF power amplifier. The equivalent

circuit is shown in the Figure 4.16. The inductor in the buck converter acts as an

energy storage element. The inductor gets charged and discharged according to the

turn ON and turn OFF times of the MOSFETs. The inductor acts as a current source

during the second half of the cycle.

Figure 4.16: Equivalent circuit of dynamic power supplied class D RF power amplifier.

The filter circuit of class D RF power amplifier allows only the ac component and

amplifiers the input. The equivalent circuit shown in the Figure 4.17 forms two loops

according to the turn ON and turn OFF times of the MOSFETs in sinusoidal voltage

driven class D RF power amplifier. It is the combination of the buck converter and

class D RFPA. Class D RF power amplifier acts as a load to the dc-ac buck converter.

The waveforms from the steady-state analysis of dynamic power supplied class D RF

power amplifier are shown in the Figure 4.17.

The replacement of dc voltage source with the sinusoidal voltage gives in PWM is

the other sinusoidal wave along with the output of buck converter that is responsible

for the amplitude modulated wave. These two sinusoidal signals i.e., the two inputs

of class D RF power amplifier are combined to get an amplitude modulated wave.

54

Figure 4.17: Waveforms of vGS1, vGS2, vGS3, iL, i1, i2 dynamic power supplied classD RF power amplifier.

55

t(s)

1.97m 1.98m 1.99m 2.0m

(V

)

−10.0

0.0

10.0

20.0

(V

)

−10.0

0.0

10.0

20.0

(V

)

−5.0

0.0

5.0

10.0

(V) : t(s)

vgs_Q3

(V) : t(s)

vgs_Q2

(V) : t(s)

vgs_Q1

Figure 4.18: vGS1, vGS2, vGS3 of dynamic power supplied class D RF power amplifier.

(V

)

−10.0

−5.0

0.0

5.0

10.0

t(s)

2.0m 2.5m 3.0m 3.5m

(V

)

14.0

16.0

18.0

20.0

22.0

(V) : t(s)

V_O_classD

(V) : t(s)

V_O_buck

Figure 4.19: vObuck,vOclassD of dynamic power supplied class D RF power amplifier.

The design of the dc-ac buck converter and class D power amplifier are combined

to get amplitude modulated wave. The gate-source voltages of the MOSFETs Q1, Q2,

Q3 are shown in the Figure 4.18. The output voltages of dc-ac buck converter and

56

class D RF power amplifier are shown in the Figure 4.19. The degree of modulation

depends on the modulation index. The duty cycle of the buck converter and the duty

cycle of the two MOSFETs in class D RF power amplifier are regulated with the pulse

width modulator. The percentage of amplitude modulation is given by modulation

index. The modulation index is the ratio of amplitude of the modulating wave to the

amplitude of the carrier wave.

4.6 Class D RF Power Amplifier as a Mixer

The pulse width modulation varies the duty cycle of the amplifier provides the phase

modulation. The amplitude modulation by the two sinusoidal signals and the phase

modulation through duty cycle variation produces AM/PM signal. As the amplitude

modulation and phase modulation are combined through class D power amplifier it

works as the mixer. The frequency of the two sinusoidal waves are the switching

frequencies of the buck converter and class D RFPA. The frequency of sine buck is

the modulating frequency and the frequency of class D RFPA is the carrier frequency.

The complete circuit diagram of dynamic power supply to RF power amplifier

implemented in Kahn’s technique is shown in the Figure 4.20. The AM/PM sig-

nal generator generates AM/PM signal. The amplitude detector circuit detects an

amplitude. The amplitude detector along with dc-ac buck converter is the dynamic

power supply. Phase modulation is provided by the pulse width modulator circuit

that drives two MOSFETs in class D RF power amplifier. The amplitude modulation

is achieved through dynamic power supply to class D RF power amplifier and phase

modulation introduced through the PWM circuit. Class D RF power amplifier gives

the amplified AM/PM signal.

The complete circuit is simulated using the SABER simulator shown in the Figure

4.21. Figure 4.22 shows the AM/PM signal generation and amplitude detection.

Figure 4.23 shows PWM output of dc-ac buck converter. Figure 4.24 shows the

57

Figure 4.20: Circuit diagram of envelope elimination and amplitude modulation basedon Kahn’s technique.

58

Gate

vcc4

vcc4

VCC3

VEE3

VEE1

VCC2

VEE

VCC

VEE

VCC

v_si

n

ampl

itude

:0.6

75fr

eque

ncy:

5000

0

offs

et:2

.5

v_si

n

ampl

itude

:1.2

5fr

eque

ncy:

2500

offs

et:2

.5

2.5k

1.25

k

2.5k

vee

vcc

op1

v_dc

5

v_dc

−5

vee

vcc

op1

VEE1

VCC2

v_dc 5

v_dc

−5

vtri pe

riod:

4u

ampl

:5

offs

et:0

31n

10k

idea

lmos

sd

vee

vcc

op1

VEE3

VCC3

v_dc

6

v_dc

−6

93.7

5u

6u

v_dc

25

Gate

DC

/DC

n1:1

n2:1

pp pm

sp sm

Env_Det

v_dc

8

n_121

vee

vcc

op1

vtri

perio

d:10

u

G2

S1

9.19

u

G1

irf51

0_sl

d s

44.0

7n

2.36

36

irf51

0_sl

d s

S1

vtri

perio

d:4u

vee

vcc

op1

DC

/DC

n1:1

n2:1

pp pm

sp sm

G1

n_555

v_dc

12

n_555

vtri

perio

d:4u

vee

vcc

op1

n_564

v_dc

12

G2

n_564

v_si

n

ampl

itude

:0.6

75fr

eque

ncy:

2500

v_si

n

ampl

itude

:0.6

75fr

eque

ncy:

2500

irf150

s

d

mbr2545ct

Figure 4.21: Saber circuit for Amplitude detection and amplification.

59

inductor current and dc-ac buck output voltage.

t(s)

1.0m 1.5m 2.0m 2.5m 3.0m

(V

)

−5.0

0.0

5.0

(V) : t(s)

Amp_det

AM/PM signal

Figure 4.22: AM/PM signal generation and amplitude detection.

t(s)

1.58m 1.6m 1.62m 1.64m

(V

)

−2.0

0.0

2.0

4.0

6.0

8.0

10.0

(V

)

−2.0

0.0

2.0

4.0

6.0

(V) : t(s)

vgs_Buck

(V) : t(s)

V_saw

Amp_det

Figure 4.23: PWM output of dc-ac buck converter.

60

t(s)

1.62m 1.64m 1.66m 1.68m

(V

)

0.0

10.0

20.0

30.0

(A

)

−1.0

0.0

1.0

2.0

3.0

4.0

(V) : t(s)

VO_Buck

(A) : t(s)

i_L_buck

Figure 4.24: iL, vO of of dc-ac buck converter.

(V

)

−10.0

0.0

10.0

20.0

t(s)

1.43m 1.44m 1.45m 1.46m

(V

)

−5.0

0.0

5.0

(V) : t(s)

vgs_Q2

(V) : t(s)

v_sin_PM

v_saw_PM

Figure 4.25: PWM output for phase modulation at Q2 to class D RF power amplifier.

61

(V

)

−10.0

0.0

10.0

20.0

t(s)

1.99m 2.0m 2.01m

(V

)

−5.0

0.0

5.0

(V) : t(s)

vgs_Q3

(V) : t(s)

v_sin_PM2

v_saw_PM2

Figure 4.26: PWM output for phase modulation at Q3 to class D RF power amplifier.

(V

)

−10.0

−5.0

0.0

5.0

10.0

t(s)

2.0m 3.0m

(V) : t(s)

V_O_Design

Figure 4.27: Output of DPS to class D RF power amplifier of the design.

62

Figure 4.25 shows the PWM output for phase modulation at Q2 to class D RF

power amplifier. Figure 4.26 shows the PWM output for phase modulation at Q3 to

class D RF power amplifier. Figure 4.27 shows the output voltage of DPS class D

RF power amplifier. Figure 4.28 shows the MATLAB validation for AM/PM signal

generation. Figure 4.29 shows the MATLAB validation for change in efficiency w.r.t

the change in input voltage of class D RF power amplifier. Figure 4.30 shows the

MATLAB validation for change in efficiency w.r.t the change in output of dc-ac buck

converter. Figure 4.31 shows the MATLAB validation for change in efficiency w.r.t

the change in duty cycle of dc-ac buck converter. Figure 4.32 shows the MATLAB

validation for duty cycle variation w.r.t. PWM.

0 1 2 3 4 5 6 7 8

time(sec)

-10

0

10

Am

plitu

de(v

olt)

Modulating Signal from the output of buck converter

0 1 2 3 4 5 6 7 8

time(sec)

-1

0

1

Am

plitu

de(v

olt)

Carrier Signal from the PWM circuit

0 1 2 3 4 5 6 7 8

time(sec)

-1

0

1

Am

plitu

de(v

olt)

AM signal at the output of class D RF power amplifer

Figure 4.28: MATLAB validation for AM/PM signal generation.

63

4 6 8 10 12 14 16 18 20 22 V

I(V)

55

60

65

70

75

80

85

90

95

η(%

)

Figure 4.29: MATLAB validation for change in efficiency w.r.t the change in inputvoltage of class D RF power amplifier.

4 6 8 10 12 14 16 18 20 22 V

0(V)

88

90

92

94

96

98

100

η(%

)

RLmin

RLnom

RLmax

Figure 4.30: MATLAB validation for change in efficiency w.r.t the change in outputof dc-ac buck converter.

64

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 D

80

82

84

86

88

90

92

94

96

98

100

η(%

) RLmin

RLnom

RLmax

Figure 4.31: MATLAB validation for change in efficiency w.r.t the change in duty-cycle of dc-ac buck converter.

0 0.2 0.4 0.6 0.8 1

Time (sec)

-5

0

5

Am

plitu

de(V

olt)

Sawtooth and Sinusoidal Signals of PWM

0 0.2 0.4 0.6 0.8 1

Time (sec)

0

0.5

1

Am

plitu

de (

Vol

t)

Duty Cycle Regulation

Figure 4.32: MATLAB validation for duty cycle variation w.r.t. PWM.

65

5 Conclusions

5.1 Summary

The work presented in this thesis can be summarized as follows:

1. A rigorous literature survey on three main efficiency enhancement topologies

in communication systems related to the transmission of a signal has been per-

formed. The techniques are (a) Kahn’s technique, (b) Doherty’s power amplifier,

and (c) Cheireix out-phasing. Their operation, features, advantages, disadvan-

tages, and areas of application have been provided.

2. The usage of a dynamic power supply for linear power amplifiers and switching

power amplifiers have been discussed. The different modes of operation of the

dynamic power supplies have been presented.

3. A modified Kahn’s architecture has been developed, which comprises the AM/PM

signal generator, amplitude detector, dynamic power supply, and switching

power amplifier.

4. The circuit-level implementation of all the aforementioned stages have been

shown.

5. The procedure to design the various stages have been presented.

6. Performance of analysis of each stage has been performed using MATLAB.

7. The steady-state waveforms have been analyzed for the overall system and the

total efficiency of the complete design has been determined.

66

5.2 Conclusions

1. It has been shown that the Kahn’s technique can be implemented using a dy-

namic power supply and a Class-D switching power amplifier.

2. It was shown that the pulse-width modulated buck dc-ac converter is a reliable

circuit required for amplitude modulation.

3. The cutoff frequency of the diode rectifier in the amplitude detector circuit must

be chosen such that its value is higher than the modulating frequency.

4. The cutoff frequency of the low-pass filter in the buck dc-ac converter must be

chosen such that its value is higher than the modulating frequency.

5. The linearity in signal transmission is compromised in the dynamic power supply

due to the presence of the nonlinear switching network.

6. The designed dynamic power supply for Class-D switching power amplifier op-

erates in the P-mode.

7. The efficiency of the buck dynamic power supply is low at low modulating signal

amplitudes and increases with the amplitude of the modulating signal.

8. It has been shown that the power transistor is the most “energy-hungry” com-

ponent in the transmission system. Thus, careful attention must be given for

proper heat dissipation mechanisms.

5.3 Contributions

1. This thesis forms a one-stop literature survey about the three main efficiency

enhancement topologies in communication systems related to signal transmis-

sion.

67

2. The phase modulation was achieved through duty cycle regulation techniques.

3. The circuit required to generate an amplitude and phase modulated signal has

been proposed.

4. It has been shown that the Class-D radio-frequency power amplifier can be used

an AM and PM signal mixer.

5.4 Future Work

1. The intermediate circuitry between the phase detector and phase modulator

must be designed.

2. The total harmonic distortion and signal-to-noise ratio must be calculated.

3. High bandwidth dynamic power supply must be designed to accommodate signal

over wide range of frequencies.

68

6 Bibliography

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