analysis of a radio frequency class d amplifier architecture with bandpass sigma-delta modulation

184 Pages·2007·2.63 MB·English

ANALYSIS OF A RADIO FREQUENCY CLASS D
AMPLIFIER ARCHITECTURE WITH BANDPASS
SIGMA-DELTA MODULATION
Thomas Johnson
B.A.Sc., University of British Columbia, 1987
M.A.Sc., Simon Fraser University, 2001
A THESIS SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTORO F PHILOSOPHY
in the School
of
Engineering Science
@ Thomas Johnson 2006
SIMON FRASER UNIVERSITY
Fall 2006
All rights reserved. This work may not be
reproduced in whole or in part, by photocopy
or other means, without the permission of the author.
APPROVAL
Name: Thomas Johnson
Degree: Doctor of Philosophy
Title of thesis: Analysis of a Radio Frequency Class D Amplifier Architecture
with Bandpass Sigma-Delta Modulation
Examining Committee: Dr. Albert Leung, Chair
Professor of Engineering Science
Dr. Shawn Stapleton, Senior Supervisor
Professor of Engineering Science
Dr. James Cavers, Supervisor
Professor of Engineering Science
Dr. Rodney Vaughan, Supervisor
Professor of Engineering Science
Dr. Daniel Lee, SFU Examiner
Associate Professor of Engineering Science
Dr. Yuanxun Wang, External Examiner
Professor of Electrical Engineering,
University of California, Los Angeles
Date Approved:
'
SIMON FRASER brary
I
UNWEEKY~
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Revised: Fall 2006
Abstract
This thesis analyzes an amplifier architecture that combines a RF class D amplifier with a
bandpass sigma-delta modulator, broadening the utility of class D amplification to include
signals with envelope variation. An integrated design methodology is presented that incor-
porates the coding efficiency and average pulse transition frequency of the encoded pulse
train into classical RF class D amplifier design equations. The equations are used to pre-
dict the power efficiency of a complementary voltage switched class D amplifier design with
CMOS, pHEMT, and MESFET switches. Simulated results are compared with the analysis
and verify the design methodology.
The power efficiency analysis shows a direct link between modulator coding efficiency
and the output power of the amplifier; therefore, a modulator with high coding efficiency is
desirable. It is shown that coding efficiency depends significantly on the order of the modu-
lator loop filter as well as the carrier oversample ratio employed in the design. The variation
with carrier oversample ratio is not monotonic for second and fourth order modulators, and
some oversample ratios are more optimal than others.
Bandpass CA modulation synthesizes a pulse train with synchronous zero-crossings, and
the coding efficiency limitations of encoding a binary amplitude pulse train with constrained
zero-crossings is analyzed. The analysis and characterization of other encoder designs shows
that bandpass CA modulation is remarkably efficient. The analysis is extended to pulse
train upconversion employing Manchester encoding. Upconversion reduces the difficulty of
implementing highly selective noise shaping resonators at RF frequencies, and the impact
of upconversion in terms of coding efficiency and average transition frequency is shown.
Dedicated to my mother, Gwendolyn Johnson
1929-2005
We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.
T. S. Eliot ''Little Gidding"
Acknowledgments
My senior supervisor, Dr. Shawn Stapleton, has been visionary in terms of promoting
switching RF amplifier technology for wireless system applications starting in the mid-
1990's. He has said that there will be many opportunities in this emerging research area,
and I agree. My journey over the last four years has lead to the discovery of many interesting
problems, and this thesis is a summary of the insights I have gained. I sincerely thank Shawn
for supporting this research, and giving me this opportunity to gain experience in what I
am sure will continue to be an active research area.
I would also like to thank my other two supervisors, Dr. James Cavers and Dr. Rodney
Vaughan. My meetings with them have been infrequent over the years, but their support
has been invaluable and assisted me on my journey.
The Ph.D. is an enormous commitment, and without a doubt I have had unwavering
support from my family as I have traveled the ups and downs of research. I have an incredible
family, and I have had the loving support of a wife, mother, father, and brother. My two
boys have also traveled with me on my journey through graduate school, and I look forward
to the new adventures which lie ahead.
Finally, I would like to thank my friends, colleagues in the wireless lab, and funding
sponsors for supporting my work. Telus Mobility has been the primary sponsor for this
research, and I am grateful for a scholarship from the Canadian Wireless and Telecom-
munications Association, as well as graduate fellowships, and stipends from Simon F'raser
University. The funding has provided a unique opportunity for me, and I expect to continue
the research which they have sponsored.
Contents
Approval ii
Abstract iii
Dedication iv
Quotation v
Acknowledgments vi
Contents vii
List of Tables xii
List of Figures xiii
List of Abbreviations xviii
List of Symbols xx
1 Introduction 1
. . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Amplifier Architecture Overview 2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Source Encoder 2
1.1.2 RF Class D Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.3 Driver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Definitions. 6
1.2.1 Drain Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Overall Power Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 7
. . . . . . . . . . . . . . . .
1.2.3 Envelope and Carrier Oversample Ratios 7
1.2.4 Coding Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
vii
1.2.5 Average Transition Frequency . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.1 RF Class D Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.2 Audio Class D Power Amplifiers . . . . . . . . . . . . . . . . . . . . . 13
1.4.3 Bandpass CA Modulation . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.4 RF Class D Amplifiers With Bandpass CA Modulation . . . . . . . . 14
1.5 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.6 Supporting Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.7 Organization of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 Bandpass Sigma-Delta Modulation 20
2.1 Bandpass CA Modulator Models . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.1 Continuous-Time Model . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.2 Discrete-Time Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1.3 Signal and Noise Transfer Functions . . . . . . . . . . . . . . . . . . . 23
2.2 Bandpass CA Modulator Designs . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.1 Discrete-time Second Order Bandpass Modulator . . . . . . . . . . . . 24
2.2.2 Discrete-time Fourth Order Bandpass Modulator . . . . . . . . . . . . 26
2.2.3 Discrete-time Bandpass Modulators Spread Zeros . . . . . . . . . . 26
-
2.2.4 Continuous-time Bandpass Modulators . . . . . . . . . . . . . . . . . . 27
2.3 Modulator Pulse Train Power Spectral Density . . . . . . . . . . . . . . . . . 28
2.3.1 Signal and Noise Power Spectrums . . . . . . . . . . . . . . . . . . . . 28
2.3.2 Power Spectral Density Measurements . . . . . . . . . . . . . . . . . . 31
2.4 Signal-to-Noise Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.1 SNR With An Ideal Bandpass Reconstruction Filter . . . . . . . . . . 32
2.4.2 SNR With An Optimum Reconstruction Filter . . . . . . . . . . . . . 34
2.4.3 Sinusoidal Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.4 W-CDMA Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.5 Narrowband Gaussian Source . . . . . . . . . . . . . . . . . . . . . . . 39
2.5 Coding Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.5.1 Coding Efficiency and SNR Trade-offs . . . . . . . . . . . . . . . . . . 42
2.5.2 Coding Efficiency and Carrier Oversample Ratio Trade-offs . . . . . . 42
...
Vlll
2.5.2.1 Coding Efficiency with a Sinusoidal Source . . . . . . . . . . 43
2.5.2.2 Coding Efficiency with a W-CDMA Source . . . . . . . . . . 46
2.6 Average Transition Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3 RF Class D Amplifier Power Efficiency 51
3.1 Complementary Voltage Switched Class D Amplifier . . . . . . . . . . . . . . 51
3.1.1 Ideal Circuit Analysis - Zero Switch Resistance . . . . . . . . . . . . . 54
3.1.2 Compensation for Switch Resistance . . . . . . . . . . . . . . . . . . . 55
3.1.3 Current Utilization Margin . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2 Conduction Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3 Capacitive Switching Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3.1 Charge and Discharge Current Paths . . . . . . . . . . . . . . . . . . . 60
3.3.2 pHEMT/MESFET Capacitance Models . . . . . . . . . . . . . . . . . 62
3.3.3 Stored Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4 pHEMT/MESFET Amplifier Design . . . . . . . . . . . . . . . . . . . . . . . 65
3.4.1 Modulator Operating Point . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4.2 Optimum Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4.3 Reconstruction Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.4.4 Analytic and Simulated Results . . . . . . . . . . . . . . . . . . . . . . 68
3.4.5 Power Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.4.5.1 Low Peak-to-Average Power Ratio W-CDMA . . . . . . . . . 71
3.4.5.2 Comparison of pHEMT and MESFET Switches . . . . . . . 71
3.5 CMOS Amplifier Design with Driver . . . . . . . . . . . . . . . . . . . . . . . 73
3.5.1 CMOS Amplifier Overview . . . . . . . . . . . . . . . . . . . . . . . . 73
3.5.2 Switch Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.5.3 Capacitive Switching Losses . . . . . . . . . . . . . . . . . . . . . . . . 78
3.5.4 Power Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4 Coding Efficiency of a Periodic Signal Model 81
4.1 Periodic Binary Amplitude Pulse Trains . . . . . . . . . . . . . . . . . . . . . 82
4.1.1 Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.1.2 Signal Reconstruction Space Examples . . . . . . . . . . . . . . . . . . 85