John Hoverston (Ph.D. 2010),
Efficient and Linear Microwave Transmitters
for High Peak-to-Average Ratio Signals
by
John Hoversten
B.S., Embry-Riddle Aeronautical University, 2005
M.S., University of Colorado, 2008
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Department of Electrical and Computer Engineering
May 2010
This thesis entitled:
Efficient and Linear Microwave Transmitters
for High Peak-to-Average Ratio Signals
written by John Hoversten
has been approved for the Department of Electrical and Computer Engineering
The final copy of this thesis has been examined by the signatories, and we
find that both the content and the form meet acceptable presentation standards
of scholarly work in the above mentioned discipline.
Hoversten, John (Ph.D., Electrical Engineering)
Efficient and Linear Microwave Transmitters
for High Peak-to-Average Ratio Signals
Thesis directed by Professor Zoya Popović
Current wireless communication systems use spectrally efficient modulation of microwavefrequency carriers (e.g. W-CDMA, OFDM). The base-station downlink signal is characterized by high peak-to-average power ratio (PAR) and a Rayleigh amplitude distribution and requires highly linear microwave transmitters. Traditional power amplifiers
(PAs) can have high efficiency near peak output power and, as a result, have low average efficiencies for high-PAR signals. This thesis addresses the challenge of maintaining
linearity and high efficiency over a broad output power range in high-power microwave
communication transmitters.
PA efficiency is addressed with an improved load pull characterization method for
high-power transistors in the 2-GHz range, in which fundamental frequency load pull
is extended to include harmonic impedance termination and full-wave electromagnetic
discontinuity analysis. The method is validated for harmonic-tuned and switched-mode
high-efficiency PA topologies reaching 81% efficiency at 2.14GHz with 36 W peak output
power and 14.5 dB gain from a class-F−1 prototype.
The high-efficiency operation is extended to reduced output power levels using an
envelope tracking (ET) transmitter architecture implementing both drain and drive
modulation. Drain modulation is achieved using an analog dynamic supply designed
in close collaboration with colleagues in analog and power electronics. A variety of
signal processing techniques (e.g. digital pre-distortion) addressing specific distortion
mechanisms are used to fully restore transmitter linearity. A methodology for system
design and integration is developed which relies on a new measurement-based ET system
iii
simulation tool. The simulation merges aspects of digital baseband, signal processing,
digital-to-analog conversion, up-conversion, envelope-bandwidth analog circuits, and RF
components.
The integrated ET demonstration transmitter measures 50.6% total system PAE
with over 7 dB adjacent channel power linearity margin for a 40-W peak power 7 dB
PAR W-CDMA downlink signal at 2.14 GHz. The ET transmitter dissipates 61% less
total heat than the standard drive-modulated solution, operating more than 74% longer
from an equivalent fixed energy supply, while exceeding W-CDMA 3GPP linearity specifications.
iv
Dedication
To Kate.
Personal Acknowledgments
It has been my great pleasure to share the graduate school experience with the
present and past members of the research group. For their invaluable technical expertise
and comradery I extend my sincere thanks to Dr. Patrick Bell, Dr. Jason Breitbarth,
Evan Cullens, Erez Falkenstein, Dan Kuester, Dr. Hung Loui, Dr. Qianli Mu, John
O’Brien, Dr. Mabel Ramı́rez, Dr. Leonardo Ranzani, Dr. Sébastien Rondineau, Rob
Scheeler, Jason Shin, Thomas Thalmann, Dr. Kenneth Vanhille, Christi Walsh, and Dr.
Narisi Wang. I am especially grateful to Dr. Alan Brannon for dispensing sage advice
about graduate student life; to Jonathon Chisum for time spent discussing so many
topics unrelated to microwave microscopy; to Dr. Charles Dietlein for an introduction
to beautifully type-set documents and for eagerness to share his knowledge of nearly
everything; to Dr. Negar Ehsan for solidarity in studying for the qualifying exam; to
Dr. Mike Elsbury, Dr. Luke Sankey, and Dr. Aaron Scher for esprit de corps as we
spent our first years at CU; to Nicola Kinzie for proof-reading this entire thesis; to Dr.
Néstor López for his patience while working with a new graduate student; to the Pepsi
Cola Corporation for faithfully distributing a light, crisp, and refreshing beverage; and
to Michael Roberg for being a great collaborator and friend. I am also grateful to Phil
Bonzell, Rev. Daniel Burhop, Prof. Milton Cone, Dr. Kyle Lampe, Lisa Lampe, Chan
La-o-vorakiat, Joseph McCalley, and Dr. Karl Siebold for their friendship, support, and
encouragement. I could not have asked for better colleagues, teachers, or friends.
I would like also to thank my family for their prayers, love, and support throughout
vi
my life. I am grateful to my parents for providing opportunities and encouragement
to pursue this goal. I learned the value of hard work and dedication by their example.
Finally, thank you Kate for your unwavering love, patience, and reassurance. You put
life into perspective, and help me to focus on the things that really matter.
Soli Deo Gloria
vii
Professional Acknowledgments
I am sincerely grateful to Prof. Zoya Popović for serving as my advisor. She has
worked tirelessly to provide exciting research projects, technical direction, funding, an
impressively-equipped lab, and an outstanding group of colleagues. My graduate school
experience has been punctuated by numerous collaborations, internships, and travel
experiences that she made possible. I am honored to have studied with her.
I very much appreciate the efforts of my thesis committee: Prof. Zoya Popović, Prof.
Ken Baker, Prof. Tim Brown, Prof. Dejan Filipović, Prof. José Angel Garcı́a, Dr. Cole
Howard, and Prof. Dragan Maksimović who took time to discuss, read, evaluate, and
make valuable suggestions.
Several others have contributed critical pieces to my graduate education and to the
work presented in this thesis, and must be acknowledged:
• Researchers in the group who did excellent work in the field of power amplifiers,
and so freely share their time, knowledge, and experience - especially my predecessor Dr. Néstor López, and successor Michael Roberg.
• Jarka Hladisova, Adam Sadoff, and Wayne Gardener for handling many of the
administrative aspects of graduate research with professionalism and efficiency.
• Prof. Dragan Maksimović and Mark Norris of the Colorado Power Electronics
Center for collaboration throughout most of my graduate work, but especially in
the envelope tracking research.
viii
• Rob Woolf at National Semiconductor for research funding, internship and employment opportunities, words of advice and wisdom, and for being a good friend.
• Steve Berg, Dr. Sandeep Dhar, Mark Kagey, Yushan Li, Kevin Vannorsdel, Prof.
Vahid Yousefzadeh, and Art Zirger at the National Semiconductor Longmont
Design Center, for contributing further analog and power electronics expertise.
Envelope tracking transmitter research without their input, collaboration, and
prototype circuitry would have been impossible.
• The U.S. Department of Education, for funding Prof. Popović’s Graduate Assistance In Areas of National Need (GAANN) fellowship proposal, which funded my
first year of graduate research.
• Dan Hornung of Roydan Enterprises, Mark Klatt of Motorola, and Mark Bloom
formerly of Freescale Semiconductor for internship experiences early in my collegiate education which provided a valuable real-world perspective.
• Bill McCalpin, Bob Crispell, Dr. Joe Hagerty, Dr. Srdjan Pajić, and several others
at TriQuint Semiconductor for collaboration, discussion, and use of equipment.
• Tim Driver with RF Micro Devices, Dr. David Choi formerly with RF Micro
Devices, Randy Cochran with Nitronex, and Dr. Todd Nichols formerly with
Nitronex for collaboration, practical advice, and providing sample transistors.
• Dr. Cole Howard at Science Applications International Corporation for funding
research, and for the opportunity to spend a summer in Washington D.C. exploring
digital predistortion techniques.
• Dr. Michael Forman at Sandia National Labs for funding research, the opportunity
to speak at Sandia, and also the opportunity to gain experience using harmonic
load pull tuners.
ix
• Prof. José Angel Garcı́a at the University of Santander for the invitation to give
a course with Prof. Popović, the opportunity to travel to Spain, for providing
comprehensive feedback on this thesis, and for traveling to the Colorado to attend
my defense.
x
Contents
1 Introduction
1.1
1.2
1.3
1
Microwave Transmitters . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.1.1
Power Amplifier Efficiency . . . . . . . . . . . . . . . . . . . . . .
3
1.1.2
High-PAR Transmitter Efficiency . . . . . . . . . . . . . . . . . .
7
1.1.3
Envelope Tracking Transmitter . . . . . . . . . . . . . . . . . . .
13
High-PAR Signals
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
1.2.1
Signal Characteristics . . . . . . . . . . . . . . . . . . . . . . . .
16
1.2.2
Linearity Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
1.2.3
Test Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
Thesis Organization and Contributions . . . . . . . . . . . . . . . . . . .
23
2 High-Efficiency PA Theory
27
2.1
High-Power Microwave Transistors . . . . . . . . . . . . . . . . . . . . .
28
2.2
Load Line and Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
2.3
Reduced Conduction Angle PAs . . . . . . . . . . . . . . . . . . . . . . .
33
2.3.1
Class AB, B, and C Operation . . . . . . . . . . . . . . . . . . .
33
2.3.2
Overdriven PAs . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.3.3
Practical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
Harmonic-Tuned PAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
2.4.1
41
2.4
Wave Shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
2.5
2.6
2.4.2
Class-F and -F−1 . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
2.4.3
Practical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
Switched-Mode PAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
2.5.1
Class E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
2.5.2
Practical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
3 High-Efficiency PA Design
3.1
3.2
3.3
3.4
3.5
55
Load Pull Characterization . . . . . . . . . . . . . . . . . . . . . . . . .
57
3.1.1
Mechanical Tuners and Prematching Circuits . . . . . . . . . . .
59
3.1.2
Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
3.1.3
Power Measurement . . . . . . . . . . . . . . . . . . . . . . . . .
66
3.1.4
General Measurement Procedure . . . . . . . . . . . . . . . . . .
69
UHF Class E Load Pull and PA Design . . . . . . . . . . . . . . . . . .
70
3.2.1
Class E Load Pull . . . . . . . . . . . . . . . . . . . . . . . . . .
71
3.2.2
Prototype Design . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
3.2.3
Prototype Performance . . . . . . . . . . . . . . . . . . . . . . .
76
S-Band Transistors and Packaging . . . . . . . . . . . . . . . . . . . . .
78
3.3.1
GaN HEMT Transistor Technology . . . . . . . . . . . . . . . . .
78
3.3.2
Traditional High-Power Transistor Packaging . . . . . . . . . . .
82
S-Band Class F−1 Load Pull and PA Design . . . . . . . . . . . . . . . .
84
3.4.1
Feasibility of Harmonic Termination . . . . . . . . . . . . . . . .
86
3.4.2
Swept Harmonic Load Pull Method . . . . . . . . . . . . . . . .
90
3.4.3
Load Pull and PA Prototype Results . . . . . . . . . . . . . . . .
93
Conclusion
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Envelope Tracking Components and Simulation
4.1
97
99
Supply Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
xii
4.2
4.3
Envelope Modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2.1
EM Requirements for Linearity . . . . . . . . . . . . . . . . . . . 104
4.2.2
EM Architecture for Efficiency . . . . . . . . . . . . . . . . . . . 109
4.2.3
EM-PA Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Power Amplifiers for Envelope Tracking . . . . . . . . . . . . . . . . . . 113
4.3.1
ET PA Theory and Design . . . . . . . . . . . . . . . . . . . . . 114
4.3.2
ET PA Bias Network . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.3.3
ET PA Characterization . . . . . . . . . . . . . . . . . . . . . . . 118
4.4
Signal Split . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.5
System Analysis Tool
4.6
Conclusion
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5 Envelope Tracking System Integration
5.1
5.2
5.3
137
System Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.1.1
Signal Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.1.2
Peripheral Hardware . . . . . . . . . . . . . . . . . . . . . . . . . 142
System Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.2.1
Distortion Mechanism Investigation . . . . . . . . . . . . . . . . 145
5.2.2
EM Gain, Offset, and Equalization . . . . . . . . . . . . . . . . . 146
5.2.3
Signal Split . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.2.4
Delay Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.2.5
Digital Pre-Distortion . . . . . . . . . . . . . . . . . . . . . . . . 154
5.2.6
Circular Signal Generation and Time Alignment . . . . . . . . . 158
5.2.7
Order of Adaptions . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Final Proof of Concept ET System . . . . . . . . . . . . . . . . . . . . . 159
5.3.1
PA and EM Prototype Hardware . . . . . . . . . . . . . . . . . . 160
5.3.2
Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
xiii
5.3.3
5.4
Power and Efficiency Measurements . . . . . . . . . . . . . . . . 163
Conclusion
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6 Conclusion
169
6.1
Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.2
Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.3
Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
Bibliography
181
xiv
List of Tables
1.1
Impact of PA efficiency on total transmitter power consumption. . . . .
9
3.1
Material properties of Si and GaN. . . . . . . . . . . . . . . . . . . . . .
80
3.2
Characteristics of two GaN HEMT transistors. . . . . . . . . . . . . . .
86
4.1
Expected average PA efficiency for three signal split trajectories. . . . . 124
4.2
Simulated ET system PA performance and EM requirements. . . . . . . 132
5.1
Simulated and measured ηd,P A for ET and constant-Vdd operation. . . . 164
5.2
Summary of four milestone ET transmitter measurement results. . . . . 168
6.1
Transmitter power budget in traditional and ET configurations using a
high-efficiency class-F−1 PA. . . . . . . . . . . . . . . . . . . . . . . . . . 172
xv
xvi
List of Figures
1.1
Block diagram of a general RF transmitter. . . . . . . . . . . . . . . . .
2
1.2
Block diagram of a general PA. . . . . . . . . . . . . . . . . . . . . . . .
5
1.3
Typical PA efficiency and gain over output power. . . . . . . . . . . . .
9
1.4
Block diagram of an envelope tracking transmitter. . . . . . . . . . . . .
13
1.5
Complex IQ trajectory for a 10-msec segment of a downlink W-CDMA
signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6
16
Amplitude/phase and in-phase/quadrature representations of a downlink
W-CDMA signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
1.7
PSD and PDF of a W-CDMA downlink signal. . . . . . . . . . . . . . .
20
1.8
PSD of a W-CDMA downlink signal showing adjacent and alternate channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2.1
First order model of a FET. . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.2
Cross section of a high-power LDMOS microwave transistor. . . . . . . .
29
2.3
PA block diagram showing bias, matching, and important reference planes. 31
2.4
Idealized IV curves for a FET transistor showing a class A bias point and
load line.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
2.5
Class A drain voltage and current waveforms. . . . . . . . . . . . . . . .
32
2.6
Class AB, B, and C drain voltage and current waveforms. . . . . . . . .
35
xvii
2.7
Theoretical efficiency and output power for reduced conduction angle
modes of operation.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.8
Overdriven class B drain voltage and current waveforms. . . . . . . . . .
37
2.9
Class B drain voltage and current waveforms assuming realistic knee behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
2.10 Photograph of a packaged LDMOS transistor with internal prematching.
40
2.11 Ideal class F drain voltage and current waveforms. . . . . . . . . . . . .
42
2.12 Sine wave with addition of a 3rd harmonic component of various relative
amplitudes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
2.13 Class F drain voltage and current waveforms assuming only 2nd and 3rd
harmonic termination. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
2.14 Schematic representation of a simple switching amplifier. . . . . . . . . .
47
2.15 Drain voltage and current waveforms for a simple switching amplifier. .
47
2.16 Schematic representation of an ideal class E amplifier. . . . . . . . . . .
49
2.17 Drain waveforms for an ideal class E amplifier. . . . . . . . . . . . . . .
51
3.1
Load-pull system photographs and block diagram. . . . . . . . . . . . .
58
3.2
Single-slug mechanical load-pull tuner schematic. . . . . . . . . . . . . .
59
3.3
Impedance constellations at load-pull plane P4, P3, and P2. . . . . . . .
60
3.4
Output prematch circuit and impedance verification circuit. . . . . . . .
61
3.5
Input, line, and output line standards for a break-apart microstrip TRL
calibration kit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
3.6
Thru gain contours used for load-pull system verification. . . . . . . . .
65
3.7
Drain efficiency for varying Idd and Pout with constant Vdd . . . . . . . .
66
3.8
Drain bias circuit schematic for a pulsed-RF measurement. . . . . . . .
67
3.9
Peak power limit analysis for load-pull tuners. . . . . . . . . . . . . . . .
69
3.10 Photograph of a break-apart fixture for class E load-pull. . . . . . . . .
72
xviii
3.11 Source-pull gain contours. . . . . . . . . . . . . . . . . . . . . . . . . . .
72
3.12 Load-pull power and efficiency contours in class E configuration. . . . .
73
3.13 Fractional drain efficiency reduction due to output loss. . . . . . . . . .
74
3.14 Low-loss output matching and bias network for the UHF class E PA
prototype. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
3.15 Measured impedance of the UHF class E PA output matching and bias
network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
3.16 Photograph of the 110 W class E UHF PA prototype. . . . . . . . . . . .
77
3.17 Measured power sweep for the UHF class E PA. . . . . . . . . . . . . . .
79
3.18 Measured frequency sweep for the UHF class E PA.
79
. . . . . . . . . . .
3.19 Photograph and HFSS simulation of the transformation between a transistor and microstrip circuit edge through bond wires and the RF705
package. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
3.20 Radiating Q-factor for microstrip transmission lines of varying Zo . . . .
84
3.21 Block diagram of load-pull system including device and package parasitic
effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
3.22 Photographs and FEM models for transistor packaging and for chip/wire
construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
3.23 Impedance transformation for DUT1 in three packaging configurations.
88
3.24 Impedance transformation for DUT2 in three packaging configurations.
89
3.25 Photograph of the swept-harmonic load-pull setup and prematch circuit.
91
3.26 Swept-harmonic load-pull impedance constellations at reference planes
P3, P2 and P1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
3.27 Small signal load-pull gain contours used to validate load-pull calibration
after harmonic tuning. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
3.28 Load-pull efficiency contours for six different 2nd harmonic terminations.
94
xix
3.29 Load-pull power and efficiency contours for the 2nd harmonic termination
condition and for the 2nd and 3rd harmonic termination condition. . . .
95
3.30 Simulated and measured S-band PA prototype output impedance. . . .
96
3.31 Photographs of the class F−1 PA prototype and enlargement of diemicrostrip interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
4.1
Simplified block diagram of the ET transmitter system. . . . . . . . . . 100
4.2
PAE vs. Pout for varying Vdd measured for a 120-W class AB GaN HEMT
PA at 2.14 GHz.
4.3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
PSD of the in-phase, quadrature, and amplitude components of a fourtone signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.4
PSD of the in-phase, quadrature, and amplitude components of a WCDMA downlink signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.5
Measured small-signal frequency response for an EM prototype under
varying DC loads.
4.6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Block diagram of an EM architecture using a SMPS supplemented by a
linear amplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.7
Ideal W-CDMA envelope and simulation of SMPS and linear amplifier
components considering three different SMPS bandwidths. . . . . . . . . 111
4.8
Load lines notionally corresponding to varying drain voltage and input
drive levels of Fig. 4.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.9
Summary of load-pull contours used to design a PA for ET applications
measured for the Nitronex NPT25100 GaN HEMT. . . . . . . . . . . . . 116
4.10 Photograph of a 120 W class AB PA prototype designed for ET applications.117
4.11 Gain and insertion phase for the NPT25100-based PA prototype measured over a matrix of input and drain voltage measured in pulsed-RF
mode biased with 600 mA quiescent current. . . . . . . . . . . . . . . . . 120
xx
4.12 Drain current and PAE for the NPT25100-based PA prototype measured
over a matrix of input and drain voltage measured in pulsed-RF mode
biased with 600 mA quiescent current. . . . . . . . . . . . . . . . . . . . 120
4.13 Comparison of simulated PA output power and efficiency over drain voltage with and without self-heating effects. . . . . . . . . . . . . . . . . . 122
4.14 Measured PAE and output voltage for the 120-W class AB PA prototype
and three possible signal split Vdd trajectories. . . . . . . . . . . . . . . . 123
4.15 Projected ṽin and Rdd trajectories based on measured PA data for three
signal split Vdd trajectories. . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.16 Projected Vdd , |ṽin |, and Rdd time domain waveforms resulting from the
three signal split trajectories of Fig. 4.14 based on measured PA data. . 126
4.17 Sensitivity of the gain and phase to variation in Vdd and ṽin . . . . . . . . 127
4.18 Ideal drain voltage waveform and the same waveform impaired by a 6MHz bandwidth limit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.19 Ideal drain voltage waveform and the same waveform impaired by a 100V/µsec slew limit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.20 Simulated ET system output PSD for a W-CDMA waveform for two
non-ideal EM models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.21 EM bandwidth and slew rate required to meet ET system linearity requirements, shown for three signal split trajectories. . . . . . . . . . . . 131
4.22 Degradation in ET system ACP1 due to EM-PA interface resistance. . . 133
4.23 Degradation in ET system ACP1 due to EM-PA interface inductance. . 133
5.1
Block diagram of the ET transmitter system. . . . . . . . . . . . . . . . 140
5.2
Simulated |ỹ| and |ṽout | with a small Vdd path delay error. . . . . . . . . 145
5.3
Vdd path frequency response before and after equalization. . . . . . . . . 147
xxi
5.4
Measured instantaneous transmitter gain and insertion phase (g̃) after
the first signal split adaptation. . . . . . . . . . . . . . . . . . . . . . . . 150
5.5
Adapted |ỹ| → β̃ transfer function after each of six signal split iterations. 151
5.6
ET system ACP given varying τEM value. . . . . . . . . . . . . . . . . . 153
5.7
Digital pre-distortion conceptual block diagram and transfer functions. . 154
5.8
General polynomial predistorter with indirect learning. . . . . . . . . . . 155
5.9
Threshold decomposition of an amplitude-only signal into two components.157
5.10 Summary of load-pull contours for ET applications measured using the
TGF2023-10 GaN HEMT with class F−1 harmonic terminations. . . . . 160
5.11 Photograph of the final PA prototype connected to the proprietary EM
hardware. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.12 Three Vdd trajectories and ṽin trajectories expected based on PA characterization data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
5.13 ET system output PSD at various stages of linearity correction. . . . . . 163
6.1
PA efficiency vs. output power in ET and traditional operation, WCDMA signal PDF, and PA power dissipation PDF in ET and traditional
operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.2
Transmitter power dissipation in traditional and ET configurations.
xxii
. . 173
List of Abbreviations
2DEG
2D electron gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3GPP
3rd Generation Partnership Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
ACLR
adjacent channel leakage ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
ACP
adjacent channel power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
AuSn
gold tin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
AWG
arbitrary waveform generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
BJT
bipolar junction transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
CAD
computer aided design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
CCDF
complementary cumulative distribution function . . . . . . . . . . . . . . . . . . . . . . 17
CF
crest factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
CFR
crest factor reduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
CuMo
copper molybdenum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
CW
continuous wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
DDR
dynamic deviation reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
DPD
digital pre-distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
DSP
digital signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
DUT
device under test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
xxiii
EDGE
Enhanced Data rates for GSM Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
EER
envelope elimination and restoration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
EM
envelope modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
EVM
error vector magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
FEM
finite element method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
FET
field effect transistor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
FIR
finite impulse response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
GaN
gallium nitride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
GMSK
Gaussian multiple shift keying. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105
GSM
Global System for Mobile Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
HBT
heterojunction bipolar transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
HEMT
high electron mobility transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
HFSS
High Frequency Surface Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
HVHBT
high-voltage heterojunction bipolar transistor . . . . . . . . . . . . . . . . . . . . . . . . 11
IPD
integrated passive device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
LDMOS
laterally-diffused metal oxide semiconductor . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
LINC
linear amplification using nonlinear components . . . . . . . . . . . . . . . . . . . . . . 11
LUT
look-up table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
MESFET
metal semiconductor field effect transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
MIMO
multiple input multiple output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
MMIC
monolithic microwave integrated circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
MOS
metal oxide semiconductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
MOSFET
metal oxide semiconductor field effect transistor . . . . . . . . . . . . . . . . . . . . . . 81
xxiv
MP
memory polynomial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
OFDM
orthogonal frequency division multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
OBW
occupied bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
OPB
output power back-off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
PA
power amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
PAE
power added efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
PAR
peak-to-average power ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
PCDE
peak code domain error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
PDF
probability density function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
PEP
peak envelope power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
PSD
power spectral density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
RS
Rohde and Schwarz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
RF
radio frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
RMS
root mean squared . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
RRC
root raised cosine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
RSPC
repeated scaled peak cancelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
SC-FDMA
single-carrier frequency division multiple access . . . . . . . . . . . . . . . . . . . . . . 178
Si
silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
SiC
silicon carbide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
SMPS
switched-mode power supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
SNR
signal to noise ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
SPDT
single pole double throw. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
TM
test and measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
xxv
TRL
thru reflect line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
UAV
unmanned arial vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
UHF
ultra high frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
VNA
vector network analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
VSA
vector signal analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
VSWR
voltage standing wave ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
W-CDMA
Wideband Code Division Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
ZVS
zero voltage switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
xxvi
Chapter 1
Introduction
Contents
1.1
Microwave Transmitters . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2
High-PAR Signals
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
1.3
Thesis Organization and Contributions . . . . . . . . . . . . . . . . . .
23
This thesis addresses the problem of efficient amplification of RF1 signals with high
PAR2 . Such signals have come into widespread use as communication links demand
more data throughput with limited spectrum. The single-channel W-CDMA3 downlink
signal is used throughout this work as a representative high-PAR signal, though concepts
presented here apply to a wide variety of similar signals.
The first portion of this chapter discusses general RF transmitters, PA4 efficiency
enhancement, and high-PAR transmitter efficiency enhancement techniques. Next a
brief overview of W-CDMA modulation and linearity requirements is presented, followed
by an outline of the thesis.
1
radio frequency
2
peak-to-average power ratio
3
Wideband Code Division Multiple Access
4
power amplifier
1.1
Microwave Transmitters
A general RF transmitter block diagram is shown in Fig. 1.1. The PA (also called the
power stage) is the dominant source of power dissipation and nonlinearity in the transmitter, so this work focuses on that key component. Therefore, in this work “transmitter” performance will reflect the contribution of only the PA, assuming other transmitter
components are ideal. Center frequency, output power, gain, and modulation type are
the main parameters that impact PA design.
This thesis focuses on design of transmitters producing peak output power levels
from 5 W to 250 W at frequencies ranging from 300 MHz to 2.5 GHz and with gain from
10 dB to 18 dB. Modulation types can be divided into two classes: constant envelope
and varying envelope.
The following general definitions will be used throughout this work, referring to
Fig. 1.1:
Fundamental and Harmonic Frequencies – fo is the fundamental, or carrier frequency, of the transmitter. fn is used to denote frequencies which are an integer
multiple of the fundamental. A frequency f2 = 2fo is referred to as the second
harmonic.
RF Input and Output Power – Pin and Pout are average input and output RF
Power
Converter
Prime
Power Source
Vdd
Idd
Pdd
Upconverter
Baseband
Processing
D/A
I+jQ
Pin
Driver Amplifiers
fo
Power
Amp
Pout
Isolator
LO
Figure 1.1: Block diagram of a general RF transmitter. The PA is the primary contributor to transmitter power dissipation and nonlinearity, and is the focus of this work.
2
power, always referenced to a 50Ω termination, and expressed in units of watts
unless otherwise noted. The decibel-milliwatt (dBm) scale is also used with the
following conversion:
PdBm = 10 log (PW ∗ 1000)
(1.1)
Conversion between RF power and the peak value of the RF voltage (also called
envelope voltage or modulation amplitude) is achieved using the following:
|Vpk | 2
√
2
|Vpk |2
|Vrms |
2
=
=
P =
R
R
2R
(1.2)
In this work these quantities will be used with reference to the power stage PA
only. Only power at fo is included in this definition, as harmonic power delivered
to the load is not useful.
Drive and Drain Modulation – Traditionally PA output power is controlled by variation of RF input power (drive modulation). Techniques discussed in this work will
also include variation of drain supply voltage Vdd as a means of output power control
(drain modulation).
Gain – G is the ratio of output power to input power for a stage or series of stages.
Gain of RF components in this work is always with reference to the power stage
PA, and always expressed in decibels:
G = 10 log
1.1.1
Pout
Pin
(1.3)
Power Amplifier Efficiency
Constant envelope waveforms, such as those used in the GSM5 communications standard
and most radar applications, have constant output power; they do not rely on precise
amplitude variation to convey information. As a result these signals can make use of
a PA operating in a highly non-linear, gain compression region. As a result of the
5
Global System for Mobile Communications
3
gain compressed operation, the PA operates with improved efficiency. Even so, a 50%efficient PA producing 100 W requires 200 W input power, generating 100 W waste heat.
Active thermal management is frequently required to ensure high reliability, adding
to energy requirements. In mobile applications, PA efficiency has a direct impact on
battery life.
The following additional definitions will be used throughout this work:
Amplifiers and Transmitters – An amplifier is distinct from a transmitter in that
both its input and output are RF signals. Modern transmitters have digital inputs
and may incorporate many amplifiers.
Drain Efficiency – ηd is the ratio of output RF power to drain supply power:
ηd =
Pout
Pdd
(1.4)
Note that no consideration is given to the amount of RF input power consumed.
When gain is low (and input power is an appreciable fraction of output power)
it becomes important to state both drain efficiency and gain or use a different
efficiency metric. Measurement of drain efficiency is very straightforward because
it involves measurement of only two quantities.
Power Added Efficiency – PAE6 takes into account the required input power:
P AE =
Pout (1 −
Pout − Pin
=
Pdd
Pdd
1
G)
1
= ηd 1 −
G
(1.5)
PAE is always less than ηd , but as gain rises ηd and PAE begin to converge to the
same value.
Fig. 1.2 is a general block diagram of a PA using a FET7 . Input power, output
power, and drain supply voltage and current are the same quantities defined for the
power stage in Fig. 1.1. Additional terminology includes the following:
6
power added efficiency
7
field effect transistor
4
Vgg
Vdd
Igg
Idd
drain
Pin
gate
matching
network
50Ω
Zsource
+
vds
- ids
matching
network
Z load
Pout
50Ω
source
Figure 1.2: Block diagram of a general PA.
Gate, Drain, and Source – FETs are used throughout this work, with corresponding
gate, drain, and source nomenclature. A BJT8 transistor has equivalent terminal
names: base, collector, and emitter, respectively.
Source and Load Impedance – Zsource and Zload are the impedances seen by the
transistor. Note that these impedances are defined at not only the fundamental,
but all frequencies.
Gate Supply Voltage and Current – Vgg is the DC value of the gate bias voltage.
Some types of transistors draw a small amount of gate current Igg under saturated
operation.
Drain Supply Voltage and Current Vdd and Idd are isolated from the FET drain
by an RF choke, and are thus constant for a constant value of Pout .
Drain Voltage and Current vds and ids are the instantaneous voltage across and
current through the transistor drain and source terminals. Simultaneously nonzero drain voltage and current create power dissipation in the transistor. This is
the dominant cause of dissipation in traditional PAs. Note that vds is not equal to
the voltage across the 50Ω PA output terminal due to the presence of a matching
8
bipolar junction transistor
5
network.
High-efficiency harmonic-tuned and switched-mode PA operation can dramatically
reduce PA power dissipation as compared to traditional classes of operation (A, AB, B,
C) [1]. Both methods increase PA efficiency by shaping vds and ids to reduce overlap,
avoiding loss in the transistor. This wave shaping is achieved by, for example, summing
odd-harmonic voltage components to produce a square vds waveform rather than the
class AB sinusoidal shape. High-efficiency modes of operation are more complex to
design, demand higher-performance transistors than traditional PA designs, and require
design of specific fundamental and harmonic load impedances.
High-power transistor packages are often an obstacle to high-efficiency design [2].
Though designed for adequate electrical performance at the fundamental frequency,
commercial packaging frequently presents a high-Q network at harmonic frequencies,
making harmonic impedance control difficult. Ansoft HFSS9 is used in this work for
FEM10 simulation of the package transformation. In cases where packaging makes
high-efficiency design impractical, alternative packaging methods are pursued, including
modification of the package and use of un-packaged (chip) devices. In this method the
die is wire-bonded directly to the microstrip PA circuit, reducing parasitic effects but
adding significant time and complication in prototype assembly.
Traditional amplifier design methods using S-parameters are not useful for inherently
nonlinear high-efficiency design. Furthermore, existing non-linear models have been
found inadequate for high-power high-efficiency designs [3] in which the well-modeled
transistor active region is largely avoided. Instead, empirical design methods supplement approximate analytical designs. In a load pull system mechanical tuners are used
to present varying source and load impedance to the transistor via pre-matching circuitry, resulting in mapping of device performance over a range of impedances [4]. A
9
10
High Frequency Surface Simulator
finite element method
6
specialized load-pull method is described in this work which includes the impact of
harmonic impedance control in the measurement [5].
A 110-W class E PA [6] at 360 MHz achieving 83% drain efficiency with 16 dB gain
and a 36-W class F−1 PA [2] at 2.14 GHz achieving 81% drain efficiency with 14.5 dB
gain are presented to illustrate the high-efficiency design methods described in this work.
1.1.2
High-PAR Transmitter Efficiency
The following definitions related to modulated signals will be used throughout this work
(consistent with [7]):
Envelope, or Amplitude – Amplitude modulation results in slow variations of the
peak RF voltage of the carrier. This level is referred to as the envelope, or amplitude, of the modulated signal.
Baseband Representation – Vector modulation of an RF carrier can be expressed in
terms of amplitude and phase or as the sum of orthogonal in-phase and quadrature
carrier components:
v(t) = A(t) cos(ωt + φ(t)) = (I(t) cos ωt − Q(t) sin ωt) = < ṽ(t)ejωt
(1.6)
When analyzing signals in the modulation domain it is useful to eliminate the timeharmonic variation of the RF carrier, leaving a baseband representation using either
“IQ” (I(t) and Q(t)) or “Aφ” (A(t) and φ(t)) forms. Both forms are equivalent and
useful in different contexts. Throughout this work complex baseband modulation
signals are indicated by lower-case variables beneath a tilde (e.g. ṽ).
Peak Envelope Power – PEP11 is the maximum instantaneous value of the RF output power. Envelope voltage magnitude and PEP are related by the power-voltage
relationship of Eqn. 1.2.
11
peak envelope power
7
Average Power – Pavg is the time-averaged RF output power.
Modulated, or Average, Efficiency – Because efficiency varies with output power
level it becomes critical to distinguish between efficiency with constant output
power and with modulated output power. Average efficiency is not equal to the
average of the time-varying efficiency but is instead defined as:
ηavg = Pout,avg /Pdd,avg
(1.7)
Average efficiency is assumed when discussing efficiency of modulated signals.
Output Power Backoff – OPB12 is the amount by which maximum transmitter power
is reduced to avoid gain compression non-linearity.
Driven by demand for increased spectral efficiency, waveforms with varying amplitude and phase such as EDGE13 and W-CDMA have time-average power significantly
lower than the PEP. The PAR of these waveforms ranges from 3 dB to more than 10 dB.
The efficiency of the high-efficiency modes of operation described previously degrades
quickly with reduced output power, resulting in a low time-average efficiency.
Amplitude modulated signals require input-output power linearity and can withstand only limited distortion due to gain compression. Such distortion is traditionally
limited by avoiding very high output power levels at which PA gain is compressed. OPB
causes the PA to operate in the linear region, further reducing the average output power
and average efficiency.
Notional curves representing typical PA efficiency and gain behavior with decreasing
output power are shown in Fig. 1.3 along with the amplitude probability density function for a high-PAR signal. Note that the highest-probability output power levels are
produced with low efficiency, and that output power back-off exaggerates the problem.
12
output power back-off
13
Enhanced Data rates for GSM Evolution
8
Gain [dB], Efficiency [%], Probability [%]
Amplitude
Probability
Density
Function
PA Efficiency
Gain
PDF under OPB
Output Power [dBm]
Output Power
Backoff (OPB)
Figure 1.3: Typical PA efficiency and gain behavior over output power. Probability
density functions for a high-PAR signal at two average output power levels are overlaid.
The impact of high-PAR signals is apparent when examining power consumption of
high-power cellular base stations in the 2.14 GHz downlink band, in which power stage
PA efficiency is typically on the order of 9% for an LDMOS14 class AB transmitter power
stage [8]. Average output power of 50 W therefore requires more than 550 W DC power,
resulting in 505 W heat dissipation. Dissipation due to air conditioning systems and
DC power converter systems result in a further penalty of 1.41 W per watt dissipated
[9]. Table 1.1 illustrates this impact for three PA power stage efficiencies.
Improving PA efficiency from 9% to 50% reduces PA input power requirements from
555 W to only 100 W. Total power required including peripheral equipment drops from
Table 1.1: Impact of PA efficiency on total transmitter power consumption.
PA Efficiency
PA Output Power
PA Input Power
PA Dissipated Power
Peripheral Losses (e.g. Cooling, Power Distribution)
Total Power Dissipation
Transmitter Efficiency Including Peripheral Losses
14
laterally-diffused metal oxide semiconductor
9
9%
30%
50%
50 W
555 W
505 W
712 W
1217 W
50 W
167 W
117 W
165 W
282 W
50 W
100 W
50 W
71 W
121 W
4.0%
15.1%
29.2%
1,267 W to only 171 W - an 86.5% reduction in power stage energy consumption. This
type of improvement has a large impact on systems operating from a limited energy
supply, such as mobile applications. The impact is also significant in terms of energy
cost.
Transmitter efficiency for high-PAR signals has been previously addressed with a
number of methods [10]. DPD15 techniques [11] account for the non-linearity gain
compression in high-efficiency class AB operation by modifying the digital baseband
input signal. The ability to operate closer to maximum PEP with reduced OPB allows
increased average output power and higher average efficiency.
The baseband signal can be pre-processed using CFR16 techniques to reduce PAR
[12]. Infrequently-occurring high-power peaks are clipped to a lower power level. PAR
can be significantly reduced with acceptable increase in distortion, resulting in increased
PA efficiency.
Invented many decades ago [13], Doherty power amplifiers make use of a main amplifier biased class AB and a peaking amplifier biased class C and connected via a special
impedance transformation network. At low output power levels the main amplifier operates linearly and the peaking amplifier is inactive, dissipating no power. As power
increases the main amplifier becomes compressed and operates efficiently as the peaking
amplifier turns on. Operation of the peaking amplifier changes the load impedance seen
by the main amplifier, which is adjusted with output power level to achieve improved
efficiency at low input power and improved output power at high input power. A variety
of permutations have evolved from this basic concept [14] varying the size and number of
peaking amplifiers. These techniques improve efficiency at reduced output power levels
and, therefore, average efficiency of high-PAR modulated signals.
15
digital pre-distortion
16
crest factor reduction
10
In [15] an LDMOS-based Doherty PA designed for W-CDMA downlink modulation
with 9.8 dB PAR at 2.14 GHz achieved 41% PAE average efficiency at 46 dBm average
power. This performance is an increase of 15% over class AB operation with the same
device. A similar design using cutting-edge HVHBT17 device technology from Triquint
[16] resulted in 57% average collector efficiency for a W-CDMA downlink signal with
6.5 dB PAR at 47 dBm average output power, an increase of 25% efficiency over class
AB operation. This record result comes largely from the application of cutting-edge
device technology, shown by the fact that the main PA exhibited an impressive 72%
collector efficiency at PEP.
Though very significant in terms of efficiency enhancement, the Doherty solution
is not without disadvantages. Linearity is necessarily degraded as compared to class
AB operation and requires the use of DPD linearization. Though not always active,
both amplifiers are always driven with RF input power, reducing gain by at least 3 dB.
Furthermore, the output transformation network has bandwidth typically less than 10%.
Chiriex, outphasing, and LINC18 architectures (discussed in detail in [17] and [18])
also utilize two high-efficiency PAs to maintain high efficiency over a range of output
power levels. The input to both PAs is a constant envelope signal, maintaining highefficiency compressed operation continuously. Peak power is achieved by feeding both
PAs with an identical signal. A phase offset of equal magnitude and opposite sign can be
applied to the input signal of each PA resulting in out-of-phase output power combining,
and consequently reduced output amplitude.
Supply modulation techniques all involve variation of the PA drain supply voltage
with desired output power. Reduced drain supply voltage changes the PA operating
point and consequently reduces output power capability. Gain compression, and thus
efficient operation, occurs at reduced output power. This fundamental idea has been
17
high-voltage heterojunction bipolar transistor
18
linear amplification using nonlinear components
11
implemented in the literature in many ways and with varying terminology.
EER19 was originally conceived in 1952 by Kahn [19]. An amplitude detector is
used to determine the RF input modulation amplitude, and a drain supply modulator
applies a linearly related PA drain supply voltage. A limiter at the PA input eliminates
envelope variation, applying a constant input power level to the PA. Gain changes with
drain supply variation and imposes amplitude modulation on the PA output signal.
The constant input power to a Kahn EER PA must be large enough to produce
high efficiency and output power, resulting in excessive gain compression at average
output power leading to reduced PAE especially in the case of high-PAR signals. Power
coupling from PA input to PA output, even in the absence of drain supply voltage, is
also a problem for signals which must instantaneously reach zero output power. Authors
have since realized the advantage of drive modulation [20] in EER systems to produce
required output power with high efficiency and the minimum required drive power.
Cripps describes such systems as “Polar” or “Envelope Restoration” systems lacking
the input RF limiter [21].
Digital implementations of EER are also frequently described in literature as polar
transmitters [22] [23]. A variety of terms have appeared to describe drain- and drivemodulated transmitter power stages, including Hybrid EER [24] [25], Wideband EER
[26], Hybrid Quadrature Polar Modulated [27], and Wideband Envelope Tracking [28].
These methods vary among each other in the type of PA used (switched mode or linear),
in the degree of gain compression created in the PA, and in implementation.
The family of supply modulation techniques most closely related to the work in
this thesis are encompassed by “Envelope Tracking”. This term most frequently refers
to a digitally controlled system driving a class AB biased PA into heavy saturation. A
number of ET implementations have been described addressing the W-CDMA downlink
application with a power level and center frequency similar to systems in this work [29]
19
envelope elimination and restoration
12
[30] [31]. The primary distinctions between these references and this thesis lie in the PA
design (discussed in Chapters 2 and 3), ET system simulation (Chapter 4), and specific
signal processing techniques used for linearization (Chapter 5).
1.1.3
Envelope Tracking Transmitter
An ET system block diagram is shown in Fig. 1.4. The ET architecture makes use of
analog circuitry to vary the PA drain supply voltage with respect to the instantaneous
output power. In this work the drain supply modulation circuitry is called an EM20 .
Supply variation results in gain compressed, high-efficiency PA operation for both peak
and average output power levels. Efficiencies must be re-defined when discussing ET
transmitters:
System, or Transmitter, Efficiency – PAE and drain efficiency of envelope tracking
systems must consider losses in the EM:
ηd =
Prime
Power Source
α’
~
y
Baseband
Processing
D/A
~
β’
(1.8)
PDC
Vdd,in
D/A
Pout
PDC
Envelope
Modulator
Upconverter
~v
in
Vdd
Idd
re( v~in e jωt ) Power
Pin Amp
Driver Amplifiers
fo
Pdd
re( ~
vout e jωt )
Pout
Isolator
LO
A/D
Feedback Path
Figure 1.4: Block diagram of an envelope tracking transmitter. Note the addition of
a supply modulation circuit and a down-conversion feedback path from the PA output
used to correct transmitter linearity.
20
envelope modulator
13
P AE =
Pout − Pin
PDC
(1.9)
Component Efficiency – Individual EM and PA efficiencies are also defined:
ηd,P A =
P AEP A =
Pout
Pdd
Pout − Pin
Pdd
ηEM =
Pdd
PDC
(1.10)
(1.11)
(1.12)
Unlike the PA, the EM has a high-impedance input which consumes no input power.
Therefore power-added efficiency of an EM is undefined.
The baseband representation of complex PA input and output signals are labeled with
ṽin and ṽout , while transmitter input (a digital baseband signal) is labeled ỹ.
Complex PA and Transmitter Gain – Magnitude and phase of the complex gain
are also called “insertion gain” and “insertion phase.” Complex gain can be defined
at the PA and transmitter reference planes:
g̃P A = ṽout /ṽin
(1.13)
g̃ = ṽout /ỹ
(1.14)
The complex PA gain g̃P A varies with drain supply voltage, and the complex transmitter gain g̃ defines transmitter linearity.
Many signal processing techniques are used in the baseband processing block to
achieve transmitter linearity: (1) the modulated input signal ṽin must be adjusted for
the time-varying complex PA gain g̃ using a look-up table filled with gain and phase
correction factors, (2) EM frequency response is corrected through the use of a linear
equalizer, (3) a delay adjustment algorithm ensures that drain supply variation and
PA input modulation occur in synchrony, and (4) dynamic distortion in the PA is
14
accounted for through the use of a polynomial-based digital pre-distortion algorithm.
These techniques are discussed in detail in Chapters 4 and 5.
ET system efficiency is the product of the efficiencies of PA and EM components.
Placing certain demands on the EM to achieve PA efficiency can dramatically reduce
EM efficiency, leading to reduced overall system efficiency. This tradeoff is made by
carefully shaping the drain supply as a function of the instantaneous desired output
power, dictating the waveform that the EM must reproduce. The relationship between
drain supply voltage and instantaneous desired output power also impacts PA efficiency.
Thus the EM waveform can be made easier to reproduce, increasing EM efficiency at
the expense of PA efficiency.
An ET system proof-of-concept test bed has been designed and implemented to
enable this research. Well suited to a wide variety of high-PAR signals, the ET demonstration is cast as a W-CDMA downlink transmitter. Test and measurement equipment and extensive Matlab computer control are used to generate modulated RF and
analog signals, down-convert and capture waveforms, and realize the signal processing
algorithms described above. A number of previously unforseen challenges in PA, EM,
and system design are only uncovered after integration on the test bench.
This work presents measured results from many pieces of the ET proof-of-concept
system. ET system PAE above 50% is demonstrated at 8.5 W average power for a 7 dB
PAR W-CDMA signal with excellent linearity. This represents more than 20% efficiency
improvement over the traditional drive-modulated final PA stage, and a reduction in
dissipated power of 12.1 W, or 38.9%. Dissipated power in the RF transistor is reduced
from 19.8 W to only 2.7 W, a reduction of 86.4%. The high level of system complexity
of the ET system is offset by significant performance improvements.
15
1.2
High-PAR Signals
Throughout this work the W-CDMA downlink modulation signal is used as a representative high-PAR signal. Large amplitude peaks and a Rayleigh amplitude distribution
result from the summation of many statistically independent signals. In fact, most all
spectrally efficient modulation types, such as OFDM21 , exhibit similar characteristics.
The concepts and results shown in this work can thus be generalized to other modulation
schemes sharing certain important features.
1.2.1
Signal Characteristics
The complex IQ trajectory for a 10-msec segment of a downlink W-CDMA signal is
shown in Fig. 1.5. Note that the amplitude reaches a very high peak value only once
during the segment.
Normalized Quadrature Component
1
0.8
0.6
0.4
0.2
0
−0 2
−0.4
−0.6
−0.8
−1
−1
−0 5
0
0.5
Normalized In−Phase Component
1
Figure 1.5: Complex IQ trajectory for a 10-msec segment of a downlink W-CDMA signal
shown in black. The blue portion is a 5-µsec segment used in the plots of Fig. 1.6, and
connects the chipping instances which are shown by red stars.
21
orthogonal frequency division multiplexing
16
The 5-µsec blue segment of Fig. 1.5 is shown projected into amplitude/phase (Fig. 1.6(a))
and in-phase/quadrature (Fig. 1.6(b)) components. Note from Fig. 1.6(a) that the amplitude, and thus the output power, of the signal value changes (slews) from minimum
to maximum in only 250 nsec. This feature, coupled with sharp amplitude nulls such as
the one occurring at 2.5 µsec, are of great importance in an ET system. Ideally the EM
would track this wide-bandwidth amplitude profile exactly.
The salient features of any modulated signal can be described using the following
metrics and plots:
Power Spectral Density – The PSD22 for an ideal W-CDMA downlink signal is
shown in Fig. 1.7(a). Note that the signal under analysis is the baseband representation – the carrier has been removed. The ideal modulated RF signal can be
instead shown by shifting the PSD x-axis from DC to the carrier frequency.
Output Power Back-off – OBW23 is the bandwidth required to encompass 99% of
the power in the signal. In the case of the case of the signal shown in Fig. 1.7(a)
the OBW is 4.165 MHz.
Probability Density Function – The PDF24 for an ideal W-CDMA downlink signal
is shown in Fig. 1.7(b), and indicates the likelihood of a given instantaneous modulated output power level. Technically the amplitude distribution of a quantized
variable is called a probability mass function, but PDF is used in this work for
consistency with literature.
Complementary Cumulative Distribution Function – The CCDF25 for an ideal
W-CDMA downlink signal is shown in Fig. 1.7(b), and indicates the likelihood that
the instantaneous modulated output power will be higher than a given value.
22
power spectral density
23
occupied bandwidth
24
probability density function
25
complementary cumulative distribution function
17
Amplitude [Normalized]
1
0.8
0.6
0.4
0.2
0
0
1
2
3
Time [usec]
4
5
1
2
3
Time [usec]
4
5
Phase [deg]
200
100
0
−100
−200
0
(a)
In-Phase [V]
0.5
0
−0 5
0
1
2
3
Time [usec]
4
5
1
2
3
Time [usec]
4
5
Quadrature [V]
1
0.5
0
−0 5
0
(b)
Figure 1.6: Amplitude and phase (a), and in-phase and quadrature (b) components of
a 5-µsec segment of a W-CDMA downlink signal.
18
Peak-to-Average Ratio and Crest Factor – PAR was previously described based
on the ratio of a single peak power value to the average power. In reality this
value occurs very infrequently and can be difficult to measure with high precision.
Instead PAR is defined henceforth as the ratio of power occurring at 0.01% CCDF
to average power. CF26 will retain the previous definition of PAR: absolute peak
power to average power. Both metrics find distinct and important application in
this work, but are elsewhere used interchangeably.
1.2.2
Linearity Metrics
Performance specifications for W-CDMA base station transmitters are outlined by the
3GPP27 standards organization in [32]. EVM28 and ACP29 are two linearity specifications which especially concern the power stage of a transmitter. These metrics define
transmitter in-band and out-of-band linearity. Testing and limits for these metrics are
precisely defined in [33], and [34] is an excellent high-level reference.
Error Vector Magnitude – EVM is a measure of the difference between the desired
and transmitted IQ trajectory at each symbol time (red stars shown in Fig. 1.5).
Before comparison, the transmitted waveform is first passed through a 3.84 MHz
RRC30 receive filter and processed using the same means available to a receiver:
frequency, absolute phase, absolute amplitude, and chip clock timing adjustments
to minimize EVM. Final EVM calculation consists of the ratio of RMS31 error
magnitude at each chipping instant to the RMS modulation amplitude. Limits in
[32] set maximum EVM for W-CDMA base station transmitters at 17.5%.
26
crest factor
27
3rd Generation Partnership Project
28
error vector magnitude
29
adjacent channel power
30
root raised cosine
31
root mean squared
19
Power Spectral Density [dB/Hz]
0
−10
−20
−30
−40
−50
−60
−70
−80
−20
−15
−10
−5
0
5
Frequency [MHz]
10
15
20
(a)
100
10
9
Probability [%]
8
7
6
10−1
CCDF
PDF
PAR= 9.62dB at 0.01% CCDF
CF=10.89dB
10−2
5
10−3
4
3
10−4
2
1
−30
−25
−20
−15
−10
−5
0
5
Power Relative to Average [dB]
10
10−5
15
(b)
Figure 1.7: PSD (a) and PDF (b) of an ideal W-CDMA downlink signal. Note the
distinction between CF (10.9 dB) and PAR at 0.01% CCDF (9.6 dB).
20
Adjacent Channel Power – ACP, also sometimes referred to as ACLR32 , is the ratio
of RRC filtered power centered on an adjacent channel relative to that in the
desired channel. Power in adjacent channels can interfere with operation of other
RF systems. Two adjacent channels are typically measured at offsets 5 MHz and
10 MHz above and below the desired carrier with a specified resolution bandwidth.
Absolute maximum levels for the W-CDMA bases station application are set by
[32] at 45 dBc and 50 dBc for a 5 MHz and 10 MHz offsets, respectively. The 5-MHz
band can be called ACP1, or the adjacent channel, and the 10-MHz band can be
called ACP2, or the alternate channel. Fig. 1.8 shows these channels overlaid on a
W-CDMA PSD. The PSD is computed without spectral averaging to prevent main
channel energy from bleeding into the adjacent channel.
0
PSD
Desired Channel
ACP1
ACP2
−10
PSD [dB/Hz ]
−20
−30
−40
−50
−60
−70
−80
−20
−15
−10
−5
0
5
Frequency [MHz]
10
15
20
Figure 1.8: PSD computed with very little spectral averaging, providing the best estimate of ACP. Desired, adjacent (ACP1), and alternate (ACP2) channel bands are
shown with green, red, and black bars.
32
adjacent channel leakage ratio
21
Other transmitter-level linearity metrics, such as PCDE33 , are not relevant to performance of the power stage, or are easily met when the power stage achieves ACP
requirements [35]. The reference also shows that, if the power stage meets ACP requirements it will also meet EVM requirements assuming typical PA distortion mechanisms
(e.g. gain compression).
1.2.3
Test Signals
The W-CDMA downlink is highly reconfigurable, allowing transmission at varying datarates to varying numbers of users. To standardize test conditions a set of six test models
are defined in [33], each to be used for different base station conformance tests. Test
Model 1 specifies spreading codes, relative power levels, and timing offsets for 64 user
channels, representing a typical base station operating condition. This test model was
used to generate the plots of Section 1.2.1 and will be used throughout this work.
Recall that average PA efficiency is a strong function of modulation PAR. As a
result, significant work has been devoted to reducing the PAR of modulated signals
while maintaining acceptable linearity. CFR algorithms add band-limited distortion to
the original signal to reduce peak amplitude levels, and thus PAR, while maintaining
acceptable linearity. Some degradation of linearity is expected, typically most evident
in increased EVM.
The CFR algorithm used in this work is called RSPC34 [36]. This algorithm was
chosen for its relatively simple implementation and ability to be extended to multicarrier modulation. PAR for the single-carrier W-CDMA Test Model 1 signal is reduced
using RSPC from 9.8 dB PAR to 7.0 dB PAR with no increase in ACP and less than 5%
increase in EVM. This increase in EVM is an acceptable degradation, as the decrease in
PAR will allow increased average power and efficiency. In some cases a 2-3 dB reduction
33
peak code domain error
34
repeated scaled peak cancelation
22
of PAR can lead to reduced DC power consumption of 50% [10].
Because EVM at a certain PAR varies depending upon the CFR algorithm in use
and its implementation, the impact of CFR on EVM measurements will be removed
from transmitter linearity performance. Additive EVM is thus defined as the difference
between EVM measured at the transmitter output and EVM of the desired signal.
Throughout this work additive EVM will be assumed.
1.3
Thesis Organization and Contributions
The remainder of the thesis is divided into the following chapters. Original publications,
workshop segments, courses, and disclosures concerning the material in each chapter are
noted. A topical summary of contributions is presented in Chapter 6, along with a thesis
summary and directions for future work.
Chapter 2: High-efficiency PA theory in this chapter provides a foundation for
discussions of method and results in Chapters 3 and 4. Load line theory and reduce
conduction angle operation are reviewed, providing context for two distinctly different
high-efficiency PA techniques: (1) harmonic-tuned operation, in which harmonic energy
is used to shape drain waveforms, and (2) switched-mode operation, a time-domain
technique based on the approximation of the RF transistor as an ideal switch. Theory of
operation, idealized performance, and practical pitfalls of each technique are discussed.
Chapter 3: Design methods for harmonic-tuned and switched-mode PA prototypes
are discussed and developed with measured results. The non-ideality of high-power
devices and lack of accurate nonlinear models forces the use of empirically-driven design
to realize prototypes based on the theory of Chapter 2. Harmonic load pull is used to
demonstrate a switched-mode class E 110-W LDMOS PA design at UHF35 with 83%
drain efficiency. A method involving analysis of package and device parasitic effects
35
ultra high frequency
23
is presented to determine feasibility of high-efficiency operation at higher frequencies.
Demonstration of the method results in a harmonic-tuned class F−1 36-W GaN36 PA
design at S-band with 81% drain efficiency. Original contributions in the area of highefficiency PA design techniques include the following:
• [37] An invited short course describing high-efficiency PA theory and load pull
techniques. Results were also presented for a 6-W class E GaN HEMT PA prototype at 2.14 GHz achieving over 79% PAE.
• [38] [39] An invited workshop segment describing high-efficiency class E PA design
and linearization techniques, and presenting a variety of prototypes from UHF to
X-band.
• [40] A conference paper discussing characterization of a 65-W class E GaN HEMT
transistor and measurements from a PA prototype at 370 MHz achieving 82%
PAE.
• [6] A conference presentation discussing design of a 110 W class E LDMOS PA prototype at 360 MHz with 83% drain efficiency and 16 dB gain. A power combining
strategy is presented for greater than 5 kW total power.
• [41] A conference presentation discussing class E PA design for a 449 MHz wind
profiler radar system.
• [5] A conference paper and presentation discussing a oad-pull-based design method
for UHF class E PAs utilizing a power-efficiency optimization metric. Results are
presented for four different prototypes of varying device technology.
• [2] A conference paper and presentation discussing a new methodology for highefficiency design at S-band using fundamental-frequency tuners and including analysis of high-efficiency feasibility for a given transistor and microwave package. A
36
gallium nitride
24
example 36-W GaN HEMT class F−1 design is presented with 81% drain efficiency
and 14.5 dB gain at 2.14 GHz.
Chapter 4: PA drain supply modulation is introduced as a method of achieving
high-efficiency performance for high-PAR signals. General requirements are outlined
for the PA and drain supply circuit components. An ET architecture is presented
which allows a tradeoff between system efficiency and linearity using the “signal split”.
Finally, a measurement-based system analysis method is developed which clearly shows
the impact of the signal split, and also component non-idealities, on system performance.
Original contributions in the area of general supply modulation include the following:
• [42] A conference paper and presentation describing a measurement-based ET
system analysis method used to illustrate the usefulness of the signal split to trade
system efficiency vs. linearity, and also to determine EM fidelity requirements.
• [23] A conference paper and poster concerning the tradeoff between efficiency and
linearity of an X-band digital polar transmitter under load pull conditions.
• [43] An intellectual property disclosure concerning a low-parasitic PA-EM interconnect.
• [44] An intellectual property disclosure describing measurement methods for PA
characterization data used to predict ET system performance.
Chapter 5: An automated testbed is developed to demonstrate proof of concepts
in Chapter 4. Commercial test and measurement equipment is employed for signal
generation and capture, and custom Matlab scripting is used to implement signal
processing. Linearization algorithms are investigated and applied, targeting specific
distortion mechanisms. The final system exhibits over 50% system PAE with a 40-W
PEP 7 dB PAR W-CDMA test signal with excellent linearity. Original contributions in
the area of envelope tracking and system integration include:
25
• [45] A conference presentation discussing integration of a signal split to optimize
PA efficiency with a polynomial-based digital pre-distortion algorithm.
• [46] An intellectual property disclosure concerning methods of Vdd -ṽin time alignment.
• [47] A conference presentation discussing the benefits of ET architecture in radar
applications.
• An invited follow-on article for a special issue of Microwave Theory and Techniques elaborating on the high-efficiency S-band PA design techniques and results
presented in [2], and also including integration of the prototype into the ET system.
• [48] A four-part invited course spanning the areas of active devices, PA theory,
high-efficiency PA design techniques, load pull methods, digital pre-distortion,
general supply modulation, and the envelope tracking architecture developed in
this thesis, including concepts, methods, and results.
Chapter 6: Performance of the ET system is compared to that of traditional
drive modulation, clearly demonstrating the benefits of the ET architecture described
in Chapter 5. The contributions of this thesis are summarized, followed by discussion
of future work and applications.
26
Chapter 2
High-Efficiency PA Theory
Contents
2.1
High-Power Microwave Transistors . . . . . . . . . . . . . . . . . . . .
28
2.2
Load Line and Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
2.3
Reduced Conduction Angle PAs . . . . . . . . . . . . . . . . . . . . . .
33
2.4
Harmonic-Tuned PAs . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
2.5
Switched-Mode PAs . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
2.6
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
This chapter provides background and theoretical basis for the design of power
amplifiers, and in particular the high-efficiency PA designs presented in Chapter 3. The
chapter begins with a brief discussion of high-power microwave transistors and basic
PA operation followed by three approaches for achieving high PA efficiency: reduced
conduction angle, harmonic-tuned, and switched-mode operation. The relevant classes
of operation in each theory are discussed along with the benefits and pitfalls of each.
The following is intended to provide theoretical context for Chapters 3-6. The interested reader is referred to the following comprehensive treatments for more information:
• Bahl [49], for a complete overview of theory, implementation, and practical issues
involved in many types of amplifier design running the gamut of frequency, power,
and technology.
• Krauss [1], for a long-standing and concise description of PA fundamental concepts.
• Schwierz [50], for an understanding of device technology, advantages, and limitations, including more recent advances in technology.
• Cripps [21], for an insightful, more advanced discussion of theory and design issues
for all types of PAs.
The complexities of high-power microwave transistors in high-efficiency operation are
not adequately reproduced by many nonlinear models or rigorous theoretical treatments,
leading to measurement-driven PA design methods described in Chapter 3. A deep
understanding of the theory and underlying transistor behavior is necessary to develop
and make appropriate use of such methods.
2.1
High-Power Microwave Transistors
Design of high-efficiency PAs begins with consideration of the active device, a simplified model of which is shown in Fig. 2.1. FETs are more common than BJTs in
high-power RF applications and are the only type of device considered throughout this
work. Furthermore, microwave devices are almost exclusively used in common-source
configuration.
The impedance presented to the current source at plane P1 in the model of Fig. 2.1 is
denoted Zds,1 . This is the impedance critical in PA design and analysis. Reference planes
P2 and P3 are also defined because their impedances can be more easily measured. The
parameters in this model can be extracted from small-signal S-parameters [51], provided
that S-parameters are measured inside the package reference plane. The total output
28
P1
vds +
+
ids
vgs Cgs
-
Rd
P2
package
package
gate
Cgd
P3
drain
Cds
Rs
source
Figure 2.1: First order model of a FET. Important output-side reference planes are
denoted P1, P2, and P3.
capacitance is calculated as:
Cout = Cds + Cgd ||Cgs
(2.1)
The FET is most simply described as a voltage-controlled current source. In the case
of enhancement-mode devices, such as the LDMOS transistor, a positive gate voltage
vgs is required to enhance the channel below the gate, allowing current to flow from
the drain terminal to source terminal. Depletion-mode devices, for example HEMTs1 ,
require negative voltage to deplete the channel thus preventing current flow. N-type
devices are dominant in microwave power amplifier applications. A cross-section for a
high-power LDMOS microwave transistor is shown in Fig. 2.2.
LDMOS devices for high-power microwave applications are slightly modified from
Gate
Source
n-
n+
p + sinker
Drain
SiO2
p body
n+
p - epi
p + substrate
Source
Figure 2.2: Cross section of a high-power LDMOS microwave transistor.
1
high electron mobility transistors
29
traditional MOS2 structures. A lightly doped drain region n− separates the drain terminal from gate and source terminals, increasing breakdown voltage [50]. The channel
is formed by a p-type region directly beneath the gate, and is considerably shorter than
the gate length. High-power LDMOS device technology is currently viable for class AB
applications up to 2.5 GHz and with power exceeding 100 W from a single transistor.
LDMOS technology is mature, inexpensive, and dominates the cell-phone base station
market as well as many other infrastructure applications in that frequency range [52].
It will be shown in this chapter and the next that LDMOS lacks the performance
necessary for high-efficiency operation at S-band, requiring the use of alternate technology. HEMTs built on wide-bandgap semiconductor materials will be discussed in the
next chapter along with high-efficiency design examples using Si3 LDMOS at UHF and
GaN HEMT at S-band.
2.2
Load Line and Bias
A general PA block diagram is shown in Fig. 2.3. Input and output terminals are always
50 Ω. DC bias is supplied to the gate and drain via bias tees, represented in the figure
by a DC blocking capacitor and an RF choke. Chokes are assumed to be ideal such
that currents Igg and Idd do not vary at the RF frequency. The same reference planes
are noted as in Fig. 2.1, but a simpler equivalent circuit represents the active device. In
most PA analysis Ron is neglected and Cds , Cgs , and Cgd are combined into Cout using
Eqn. 2.1.
Fig. 2.4 shows the DC operation of a FET, commonly referred to as IV curves. A
DC bias (Vdd and Idq , set by Vgg ) is applied to the device, referred to as the quiescent
bias point. Increasing vgs beyond a minimum value Vpinch causes linearly increased ids .
Above some maximum value of vgs the channel is saturated and ids cannot increase any
2
metal oxide semiconductor
3
silicon
30
Vdd
Vgg
P1
P2
ids
package
package
imedance
matching
50Ω
Input
Terminal
vds +
Ron Cout
-
P3
imedance
matching
Idd
Transistor Die
Igg
50Ω
Output
Terminal
Figure 2.3: PA block diagram showing bias, matching, and important reference planes.
further, converging to a value Imax . vds exceeding Vbreak causes drain-source breakdown.
Vk is called the knee voltage, below which maximum current Imax cannot be achieved.
The quiescent bias point is set by the voltages Vdd and Vgg , resulting in some quiescent current Idq . The RF input signal varies vgs around its DC value of Vgg , resulting
in subsequent variation in ids . Assuming a purely real load impedance at P1, called
RL , the current variation will result in linearly related drain-source voltage and current.
The ids vs. vds trajectory, or load line, has slope equal to the inverse of RL .
ids
Imax
load line slope = 1/R L
quiescent bias point
Idq
vgs
vgs=Vpinch
0
Vk
Vdd
Vbreak
vds
Figure 2.4: Idealized IV curves for a FET transistor showing a class A bias point and
load line.
31
Amplifier design using a small-signal conjugate match aims to extract maximum
gain from a device. In large-signal PA design the goal is to extract maximum power at
the expense of gain. The load impedance is designed to achieve maximum voltage and
current excursion on the same load line, resulting in maximum output power.
Class A bias requires that Idq is set to 50% Imax . Given a recommended value of Vdd
(typically about Vbreak /2.5 [50]), the load required to achieve Imax can be calculated:
RL =
(Vdd − Vk ) · 2
Imax
(2.2)
It is important to recall that this load resistance must be presented to the transconductance at P1, also called the virtual drain. All PA analysis and theory is based at
this reference plane. Simultaneous voltage across (vds ) and current through (ids ) the
virtual drain is the primary source of power dissipation in a PA. High-power devices
are constructed by placing many unit cell transistors in parallel. Based on Fig. 2.1 we
conclude that a higher-power version of the same transistor will have increased Cout ,
increased Imax , and thus reduced RL .
Drain efficiency of a theoretical PA can be calculated based on drain waveforms
shown in Fig. 2.5:
η=
2
Pout,fo
vds,fo · ids,fo
=
Pdd
Vds,DC · Ids,DC
(2.3)
vds/Vdd
1.5
Vdd
1
0.5
0
ids/Imax
Idq
pdiss
0
0.2� 0.4� 0.6� 0.8�
�
1.2� 1.4� 1.6� 1.8�
2�
Figure 2.5: Class A drain voltage and current waveforms.
32
For the case of the class A bias point, the consumed power is constant (Vdd · Idq ) over
√
√
the whole range of output power, and the maximum output power is Vdd / 2 · Idq / 2,
resulting in 50% efficiency at maximum output power. Efficiency degrades linearly with
reduced output power, to only 10% when output power is 7 dB less than maximum.
Another way to evaluate efficiency is by observing the amount of overlap in drain
voltage and current waveforms. Simultaneous voltage across and current through a
current source results in power generation or dissipation, depending upon the sign.
Note that in Fig. 2.5 the ids · vds product is always non-zero except for the instants
when voltage or current itself is zero. Instantaneous power dissipated is indicated by
the black line in Fig. 2.5.
The class A PA is linear to the degree that the transconductance is linear - that is,
a reduction in input power leads to a linearly proportional reduction in output power.
High-efficiency modes of operation use the transistor in saturation and cutoff, sacrificing
gain linearity for increased efficiency.
2.3
Reduced Conduction Angle PAs
High efficiency operation has traditionally been achieved through the use of reduced
conduction angle PAs. These modes of operation reduce quiescent current to less than
the class A 50% Imax , preventing conduction through the current source for some fraction of the RF period. When the transistor does not conduct it is said to be in “cutoff”.
The length of time (in radians) when the transistor is conducting current during each
RF cycle is called the conduction angle α.
2.3.1
Class AB, B, and C Operation
Allowing the transistor to enter cutoff leads to non-sinusoidal drain waveforms with
frequency content at harmonics of the fundamental frequency. Traditional reduced33
conduction angle classes of operation (AB, B, C) require that a short circuit is presented
to the current source at harmonic impedances [1]. A harmonic short circuit causes
harmonic voltage to be zero (leading to fundamental-frequency sinusoidal drain voltage
waveforms) while allowing the drain current waveform to contain harmonic energy.
The conduction angle (α) is defined as the portion of the RF cycle during which
current ids is allowed to flow, achieved by reducing the value of Idq relative to Imax .
Class AB bias requires α between 2π and π, class B bias requires α equal to π, and class
C bias requires α less than π. Class AB, B, and C drain waveforms are shown in Fig.
2.6.
Note (visually) that in all cases the amount of drain voltage-current overlap is significantly reduced from the class A waveforms of Fig. 2.5, leading to reduced dissipation
in the transistor current source. Input power requirements and resulting fundamental
frequency output power are also different in each case.
Efficiency of ideal reduced conduction angle modes can be calculated using Eqn. 2.3,
approximating the half-rectified sine wave drain current as a function of α. The DC
component of ids can be reduced to:
ids,DC =
1
·
2π
Z
α/2
−α/2
ids,DC =
Imax
· (cos θ − cos (α/2)) · dθ
1 − cos (α/2)
Imax 2 · sin (α/2) − α · cos (α/2)
·
2π
1 − cos (α/2)
(2.4)
(2.5)
The harmonic components of ids can be expressed as:
ids,fn =
1
·
π
Z
α/2
−α/2
Imax
· (cos θ − cos (α/2)) · cos nθdθ
1 − cos (α/2)
(2.6)
Of primary importance for power and efficiency calculations is the fundamental frequency component of ids , which can be simplified to:
ids,f0 =
Imax
α − sin α
·
2π 1 − cos (α/2)
(2.7)
In the case of class B operation the DC component of ids is Imax /π while the fundamental frequency component of ids is Imax /2. Output power is thus equal to the class
34
2
vds/Vdd
1.5
Vdd
1
ids/Imax
0.5
0
Idq
pdiss
0
0.2� 0.4� 0.6� 0.8�
�
1.2� 1.4� 1.6� 1.8�
2�
(a)
2
vds/Vdd
1.5
Vdd
1
ids/Imax
0.5
0
pdiss
Idq=0
0
0.2� 0.4� 0.6� 0.8�
�
1.2� 1.4� 1.6� 1.8�
2�
(b)
2
vds/Vdd
1.5
Vdd
1
ids/Imax
0.5
0
pdiss
Idq=0
0
0.2� 0.4� 0.6� 0.8�
�
1.2� 1.4� 1.6� 1.8�
2�
(c)
Figure 2.6: Class AB with α = 1.2π (a), class B with α = π (b), and class C with
α = 0.8π (c) drain voltage and current waveforms. Instantaneous dissipated power is
shown in black on all plots.
A case while DC power is reduced by a factor of π/2, resulting in an ideal class B efficiency of π/4, or 78.5%. This increase in efficiency, however, is not without cost. Twice
the gate voltage swing, an increase of in 6 dB input power, is required as compared to
class A, though the same maximum output power is achieved. Therefore ideal class B
operation has 6 dB less gain than class A at peak output power.
Fig. 2.7 shows efficiency and relative output power for changing conduction angle.
35
Notice that class C approaches 100% efficiency only as output power drops to zero.
The reduced conduction angle modes of operation lack linearity that was intrinsic to
the class A mode. Even so, the class AB PA is the most dominant design for high-power
communications applications today [49].
2.3.2
Overdriven PAs
Previous analysis assumes vgs is sufficient to achieve ids equal to Imax , but no more.
Input “overdrive” causes the transistor to operate in current saturation, the region above
which increased vgs no longer produces increased ids . Increased input drive results in
increased output power, but dissipated power remains nearly constant (ids -vds overlap
does not increase notably). Overdriven class B drain waveforms are shown in Fig. 2.8.
Even more significant harmonic content is introduced, and gain is reduced (input
power rises faster than output power). An analysis of overdriven class B is presented in
[53], demonstrating theoretical efficiency well above that of the unsaturated class B PA.
Cripps [21] describes an analysis similar to the result of Fig. 2.7 detailing the efficiency
1
95
0
85
−1
80
75
−2
70
−3
60
55
50
Class-C
0
π/2
Class-AB
π
3π/2
Conduction Angle [rad]
Class-A
65
Class-B
Drain Efficiency [%]
90
−4
−5
2π
Output Power Normalized to Class-A [dB]
100
Figure 2.7: Theoretical efficiency and output power for reduced conduction angle modes
of operation.
36
2
vds/Vdd
1.5
Vdd
1
ids/Imax
0.5
0
pdiss
Idq
0
0.2� 0.4� 0.6� 0.8�
�
1.2� 1.4� 1.6� 1.8�
2�
Figure 2.8: Overdriven class B drain voltage and current waveforms.
and power trends for reduced conduction PAs at varying levels of overdrive.
Many practical PA designs make use of overdrive. Performance is often specified
at the P1dB and P3dB operating points, indicating that the PA is overdriven to compress gain by 1 dB or 3 dB as compared to gain in linear operation. Compression and
saturation are frequently used interchangeably, but have very different meanings. Gain
compression describes power gain of the PA at a given input power level, while current
saturation refers to a condition in which the transistor cannot source more current.
Gain compression can be caused by many factors, one of which is current saturation.
2.3.3
Practical Issues
Theoretical analysis is a very useful tool in understanding and synthesizing PA behavior.
Throughout literature many complexities of high-power transistors and PA implementation are neglected or approximated to make such analysis analytically tractable. Design
of actual hardware, however, involves many non-ideal effects that are difficult to account
for in theory.
The requirement for harmonic impedance terminations is seldom enforced in modernday PA design [21]. Short circuit harmonic impedance terminations make analysis
simple by forcing fundamental frequency sinusoidal drain voltage waveforms, but are
difficult to realize depending upon device parameters, frequency of operation, and parasitic package effects (discussed in detail in Chapter 3). The next section will discuss
37
methods of increasing PA efficiency by presenting alternate impedances at harmonic
frequencies with the intention of shaping drain voltage and current waveforms to avoid
power dissipation.
The efficiency analysis supposes that the knee voltage Vk is very small compared
to the drain supply voltage. In reality, many high power transistors have significant
knee voltage on the order of 4 V to 7 V compared to drain supply voltage of 28 V or
32 V. Implementation of the PA described by theory requires an increase in drain supply
voltage to keep the load line above the knee voltage. An increase in DC supply voltage
reduces efficiency of the class AB PA to the following:
ηknee =
Vdd − Vk
Vdd
(2.8)
In this case the drain current waveform is no longer a rectified sine shape due to
reduced current when drain voltage is below Vk . The resulting “bifurcated” shape is
more difficult to analyze, as shown in Fig. 2.9. Reduced fundamental-frequency current
reduces output power.
Current waveform bifurcation due to the knee voltage can be an advantage in terms
of the harmonic-tuned PAs discussed in the next section. An approximate analysis of
load lines below knee voltage is presented in the literature (e.g. [49]).
An alternative way to look at loss due to knee region is in terms of Ron , the total
resistance encountered by ids . Ron includes drain and source resistance and also the
2
vds/Vdd
1.5
Vdd
1
ids/Imax
0.5
0
Idq=0
0
0.2� 0.4� 0.6� 0.8�
�
pdiss
1.2� 1.4� 1.6� 1.8�
2�
Figure 2.9: Class B drain voltage and current waveforms assuming realistic knee behavior.
38
effective resistance of the transconductance saturation effect [1]. This resistance leads
to a voltage drop with high current, and largely defines the slope of the IV curves below
Vknee . The impact of this loss on efficiency can be calculated as follows:
ηRon =
1
1 + ψ RRon
L
(2.9)
Different classes of amplifiers use varying values of ψ to account for different theoretical ids waveform shapes. For class B operation ψ = 2, while in class E operation
(discussed later in this chapter) ψ = 1.365. Also note that the efficiency reduction is
made worse when RL is small, as is the case with high-power transistors. [54] suggests
that ψ = 1.3652 can be considered a practical upper-bound on PA efficiency given finite on-resistance. Maximum possible efficiency due to on-resistance is a useful figure of
merit in comparing transistors for high-efficiency applications, independent of operating
mode.
Drive power requirements can become a significant factor in high-efficiency designs.
An additional 6 dB input power required for class B may result in unacceptably low
gain, despite the resulting efficiency enhancement. Output power reduction carries the
same concern: despite drain efficiency over 90% a class C PA may be unacceptable due
to a 5 dB output power reduction as compared to class A output power.
High power transistors are formed by the parallel combination of many unit cells
and therefore typically have small RL and large Cout . Recall from Fig. 2.1 that the
ideal load line RL must be presented at P1. Thus the impedance match at P2 must be
designed to include the effect of the output capacitance. Large values of Cout lead to
high-Q matching requirements and further reduced impedance at P2. Sub-ohm output
matching is not uncommon for a 100-W LDMOS transistors, resulting in very high
impedance transformation ratio and significant matching network losses. [49] includes
an analysis for distributed and lumped matching network losses given the quality factor
of the matching components.
39
Many transistors are packaged with internal matching components to achieve matching with lower loss and broader bandwidth [18], as shown in Fig. 2.10.
Matching networks can be easily formed by series bond wire inductance and shunt
chip capacitance. Internal input and output matching networks raise the impedance at
P2 over a desired bandwidth but limit the packaged transistor’s usefulness outside of
the intended band. Such internal networks also limit the PA designer’s ability to control
harmonic impedances required for high-efficiency modes of operation, discussed in the
next section.
Stability is difficult to analyze and predict in high-power large-signal operation.
As mentioned previously, small-signal S-parameter techniques cannot be used due to
the nonlinear operating point. In practice, stability is dealt with by (1) mismatching
the source to reduce gain, (2) adding a resistive input or output termination at the
frequency of oscillation, or (3) improving bias network design. Inadequate low-frequency
termination of bias networks is perhaps the most prevalent source of instability for highpower UHF to S-band PA designs.
Figure 2.10: A packaged 45-W LDMOS transistor with internal prematching. Active
device is the center die. Bond wire inductance is used with a shunt capacitor die on
either side of the active device to form internal input and output matching networks.
40
2.4
Harmonic-Tuned PAs
Recall that a short at P1 for all harmonic frequencies is required for ideal classes A,
AB, B, and C. This constraint forces vds to remain sinusoidal (no harmonic voltage can
be produced across a short) but allows harmonic components to exist in ids , changing
the shape of the drain current waveform to a half rectified sine wave. Power dissipation
in the current source is reduced and even eliminated by shaping vds and ids to avoid
overlap in time (e.g. class C) at the expense of fundamental frequency output power
and gain. In this section other drain voltage and current waveform shapes are discussed
which reduce power dissipation without the downfalls of class C.
2.4.1
Wave Shaping
The time harmonic nature of PA operation limits the designer’s ability to arbitrarily
change the shape of drain waveforms. The only means available is the addition of
harmonic energy to the fundamental voltage and current waveforms. We assume for
now that harmonic voltage and current energy is available, and can be either added or
eliminated by presenting appropriate harmonic impedance at the virtual drain.
Ability to shape current and voltage drain waveforms creates many possibilities for
high-efficiency operation. Harmonic impedances can be used to generate specific combinations of voltage and current wave shapes which avoid overlap but still result in high
output power at the fundamental frequency. Many well-known configurations [1] are
analyzed in literature, along with theoretical exploration [55] of other possible configurations, many of which are used less frequently for practical reasons. The harmonic
terminations in these cases are limited to “open” or “short”. If this condition is met
there cannot be both harmonic voltage and current at the load, effectively suppressing
harmonic output power.
Cripps [21] suggests that many supposed class AB designs actually have capacitive
41
harmonic terminations, in which the transistor’s own output capacitance approximates
nearly a short circuit. Theory for a new mode of operation is developed based on such
harmonic terminations and a reactive load impedance. The class J mode of operation
[56] has been used to achieve high efficiency (12 W with over 81% at 2.1 GHz) over a
broad bandwidth. Harmonic-tuned amplifier design in this work is limited to the more
traditional classes F and F−1 (class F-inverse).
2.4.2
Class-F and -F−1
The class F mode of operation was invented by Tyler [57]. An open circuit is presented
at odd harmonics while a short circuit is presented at even harmonics. The presence of
only odd-harmonic voltage is used to synthesize a square wave, and the even-harmonic
current causes current peaking as shown in Fig 2.11. Theory [58] and measurement
[59] have shown increased efficiency and output power under compressed operation for
a broad range of applications up to S-band [60].
In reality the ideal waveforms of Fig. 2.11 cannot be realized, as infinite harmonic
content and control would be required. An approximation of the square wave can be
achieved using only 3rd harmonic voltage content, where the resulting shape depends
upon the relative magnitude of the 3rd harmonic component, as shown in Fig. 2.12.
A maximally flat voltage waveform (e.g. vds,3fo /vds,fo = 1/9 for only 2nd and
3rd harmonic terminations) results in class F operation by definition. An analysis in
2
vds/Vdd
1.5
Vdd
1
ids/Imax
0.5
0
pdiss=0
Idq=0
0
0.2� 0.4� 0.6� 0.8�
�
1.2� 1.4� 1.6� 1.8�
2�
Figure 2.11: Ideal class F drain voltage and current waveforms.
42
1.5
cos(wot)
cos(wot) + 1/18 cos(3wot)
cos(wot) + 1/9 cos(3wot)
cos(wot) + 1/6 cos(3wot)
1
0.5
0
1/9 cos(3wot)
−0.5
−1
−1.5
0
1
2
3
4
Time [Rad]
5
6
7
Figure 2.12: Sine wave with addition of a 3rd harmonic component of various relative
amplitudes.
[61] explores the range of waveform shapes possible with varying relative harmonic
amplitudes, and provides expressions for resulting power and efficiency gains. As a
result of imperfect squaring, the optimum efficiency for the 3rd harmonic case is 88.4%,
with a 0.5 dB increase in output power as compared to class B. Class F waveforms
considering only 2nd and 3rd harmonic content are shown in Fig. 2.13.
As additional harmonics are considered (5th, 7th, etc) further theoretical efficiency
and power gains are observed [62]. Consideration of the 5th harmonic yields 94.8%
efficiency and a 0.82 dB increase in output power compared to class B.
2
vds/Vdd
1.5
1
Vdd
ids/Imax
Idq=0
0.2� 0.4� 0.6� 0.8�
pdiss
0.5
0
0
�
1.2� 1.4� 1.6� 1.8�
2�
Figure 2.13: Class F drain voltage and current waveforms assuming only 2nd and 3rd
harmonic termination.
43
Class F−1 [63] reverses the even and odd harmonic terminations to achieve current
squaring and voltage peaking. As compared to class F, higher vds peaks and lower ids
peaks are expected (relative to Vdd and Idd ). Higher peak voltage is undesirable, requiring careful attention to drain-source breakdown. However, lower current peaks cause
reduced degradation in efficiency with increasing Ron [64], and theoretical fundamental
load impedance is also higher. Expressions for fundamental load impedance of class F
and class F−1 and a comparison of efficiency degradation with Ron can be found in [59].
Higher fundamental load impedance results in lower transformation ratios and reduced
matching circuit losses. Further practical reasons making class F−1 desirable will be
discussed in the next section.
2.4.3
Practical Issues
Addition of even harmonics creates a result with larger amplitude than the original
fundamental waveform. In-phase addition of even voltage harmonic components can
result in larger-than-intended peak vds , nearing Vbreak . With short circuit harmonic
termination (as required for class AB), the peak vds should be no greater than 2Vdd , but
practical class AB amplifiers do not often enforce 2nd and 4th harmonic short circuit
terminations. As a result, drain supply voltage is commonly limited to Vbreak /2.5 [50].
The problem of voltage breakdown is even more pronounced for classes of high-efficiency
operation requiring open circuit terminations at even harmonics. A reduction of Vdd
prevents breakdown but also reduces output power, a common tradeoff in high-efficiency
design.
Matching circuits become impractical, sensitive, and lossy as the number of harmonics under consideration rises. Control of higher harmonic impedances is further
complicated by the nature of high-power microwave transistors. Large package parasitic effects and output capacitance must be absorbed into the matching network to
present the correct impedance at the intrinsic drain (plane P1).
44
The active device must be capable of producing harmonic content. Low gain at harmonics and high output capacitance limit the harmonic content available to be shaped
by harmonic impedance. For example, a high-performance 100-W LDMOS microwave
device performs well in class AB mode at 2 GHz but has inadequate performance at
4 GHz and 6 GHz for harmonic-tuned operation.
The efficiency enhancement benefit of harmonic tuning is only realized when the
PA operates in compression. Until the device operates in saturation or cutoff there can
be no harmonic energy generated. Furthermore, the amplitude of harmonic content
relative to that of the fundamental content is very difficult to predict and accurately
control. Variation of Idq , drive level, and fundamental load impedance will produce a
wide range of harmonic content.
The knee voltage effect is a source of significant harmonic content. Consider a
fundamental load and drive level which forces vds below the knee voltage in each RF
cycle. The typical half-sinusoid ids current waveform will be “bifurcated”, naturally
generating large amounts of 3rd harmonic drain current as shown in Fig. 2.9. This
behavior proves even more beneficial for current-squaring class F−1 , where a large 3rd
harmonic component can be difficult to achieve at high fundamental frequencies.
It is more difficult to present an open at plane P1 than it is to present a short.
A short at plane P2 is in parallel with the output capacitance and results in a short
at plane P1 regardless of the value of Cout . An open at plane P2 presents an open in
parallel with Cout (a capacitive termination) at plane P1. Presenting an open at P1
requires that Cout be accurately estimated and resonated with an inductance at plane
P2, resulting in an open termination at P1. This becomes a challenge as Cout becomes
larger resulting in a more sensitive high-Q resonance.
In the same vein, higher frequency harmonic open circuits are more difficult to
realize than lower frequency harmonic terminations. The same value of Cout incurs a
larger reactance with increasing frequency, dominating the impedance at plane P1 to an
45
ever larger degree and approximating a short. When terminating only two harmonics,
Class F−1 is more practically realizable than class F because it requires an open circuit
termination at the 2nd harmonic rather than the 3rd harmonic.
Throughout this section, and literature also, harmonics are said to be terminated
in an “open” or “short”. In reality a perfect open or short is impossible to achieve,
leading to the question: how low or high must an impedance be to produce the desired
waveform shaping effect? [62] addresses this question by analyzing 2nd and 3rd harmonic
termination impedances as a continuum, and with respect to the fundamental load
impedance. Reactances of 0.3RL and 3RL are stated as approximate transitions between
short, resistive, and open terminations for harmonic-tuned classes. [21] also notes that,
when considering 2nd and 3rd harmonic class F with a realistic knee voltage model,
the resistance of the 3rd harmonic short needs only to be “reasonably smaller” than
the fundamental load. In this work the criteria has been adopted that open and short
terminations have Rfn > 3RL and Rfn < 0.3RL .
2.5
Switched-Mode PAs
Switched modes of amplification are fundamentally different from those based on load
line theory and the harmonic-tuned modes described in the previous section. Instead of a
current source with linear transconductance the transistor is modeled as an ideal switch,
eliminating all notion of load lines and DC bias. Instead of the frequency-domain wave
shaping used in harmonic-tuned PAs, switched-mode theory shapes waves by directly
controlling time-domain voltage and current transients after a change in switch state.
The ideal switch is always in one of two states: completely on - a perfect short circuit,
or completely off - a perfect open, and can move between the two states instantaneously.
Switched-mode circuits are very popular in DC-DC conversion applications [65], but at
microwave frequencies it is difficult to identify transistors that can be approximated as
46
a switch. A number of criteria must be satisfied for the switched-mode assumption:
• The transistor must be biased at cutoff (class B) to prevent current from flowing
when the switch is off.
• Input drive level must be large to transition from cutoff to saturation (just as a
switch transitions from completely off to completely on) very quickly.
• The transistor must have gain at many harmonics of the fundamental to allow for
fast transitions between off and on states.
The simplest switching amplifier consists of an ideal switch connected to a load by
an ideal DC blocking capacitor and is fed with constant current through a DC choke
and driven at a 50% duty cycle. Such an amplifier is shown in Fig. 2.14 and produces
drain waveforms shown in Fig. 2.15.
Vdd
Idd
+
vsw
isw
-
RL
Figure 2.14: Schematic representation of a simple switching amplifier.
2
vsw/Vdd
1.5
Vdd
1
isw/Imax
0.5
0
pdiss=0
Idq=0
0
0.2� 0.4� 0.6� 0.8�
�
1.2� 1.4� 1.6� 1.8�
2�
Figure 2.15: Drain voltage and current waveforms for a simple switching amplifier.
47
The ideal simple switching amplifier avoids power dissipation in the switch, making
the DC-RF conversion 100% efficient. However, almost 20% of the RF energy delivered to the load is at harmonic frequencies. The maximum drain efficiency (defined in
Chapter 1 to include only power at the fundamental frequency) is just over 80%. This
example illustrates the need for a harmonic tuning network between the output of a
switched-mode amplifier and the load.
Other problems with the concept illustrated in 2.14 include the output capacitance
inherent in semiconductor devices. A realizable switching amplifier must include the
output capacitance shunting the switch. Other classes of switching amplifiers include D,
E, and S. Class D is frequently used in analog applications at much lower frequencies,
and requires two transistors driven in a complementary fashion [1]. Square voltage
and current switch waveforms result in ideally 100% efficiency and an output network
removes harmonics to restore sinusoidal load voltage and current. Common-source
configuration is preferred at UHF and higher RF frequencies to enhance stability, so
class D has found limited application in this frequency range.
Class S makes use of pulse width modulation to control the load voltage amplitude
[1]. As in class D, complementary transistor configuration is required along with switching frequencies many times higher than the fundamental frequency. These factors make
class S impractical for the carrier frequencies used in this work.
2.5.1
Class E
Like other switched modes, class E was invented for very low frequency applications [66].
Ideal class E performs 100% efficient conversion of DC to fundamental-frequency RF
energy, in exchange for reduced output power, gain, and high-frequency performance.
Mader et. al. [67] pioneered the use of the class E method at GHz frequencies. A block
diagram of the ideal class E PA is shown in Fig 2.16.
As compared to the simple switching PA of Fig. 2.14 the class E amplifier incor48
Vdd
Idd
+
vsw
isw
Ls
Cs
ic
RL
Ron Cout
iload
Figure 2.16: Schematic representation of an ideal class E amplifier.
porates a harmonic open circuit termination at the output capacitance. In Fig. 2.16 a
high-Q resonance formed by Cs and Ls presents an open to all harmonic frequencies but
is resonant at the switching frequency fs (also referred to in this section as the angular
switching rate ωs ). In contrast to other harmonic termination requirements discussed
previously, the class E harmonic open circuit must be placed at the load side of the
output capacitance, corresponding to plane P2 of Fig. 2.3.
Class E operation specifies a transient response that should occur between each RF
cycle. This response is synthesized by the matching network and output capacitance
Cout . The following assumptions must be satisfied to achieve class E operation:
(1) The choke which feeds drain current from the supply is ideal, and current Idd does
not vary during the RF cycle,
(2) All harmonics are terminated in an open circuit, resulting in sinusoidal load current, and
(3) The switch is ideal and operates with 50% duty cycle, which results in highest
output power [68].
This problem has been rigorously solved in many ways in the literature ([3] [4] [69]
49
[66]), and such analysis will not be repeated here. However, class E operation can be
qualitatively understood using the following:
• Beginning with condition 1, require that a constant current Idd flows into the
circuit from the DC supply. Current must go into the load, into the capacitor, or
through the switch.
• Next, condition 2 requires sinusoidal load current, so the load resistor can be
replaced by an AC current source of unknown phase and amplitude (iload = Idd +
a · cos(ωt + θ)).
• Since currents from the DC supply and from the load are known we see that
the switch-capacitor combination must source or absorb the difference such that
Isw + Ic = Idd − Iload .
• When the switch is closed, vsw is zero by condition 3, and the current flows entirely
through the switch (Isw = Idd − Iload , Ic = 0).
• When the switch is open, the same current flows entirely into (and out of) the
capacitor (Ic = Idd − Iload , Isw = 0), and vsw is the voltage developed across the
capacitor.
The following three boundary conditions are also required to eliminate power dissipation in the switch-capacitor combination:
(1) vcap = vsw = 0 while the switch is closed,
(2) vsw = 0 when the switch closes to avoid dissipating energy remaining in the
capacitor, and
(3) dvsw /dt = 0 when the switch closes to facilitate “soft switching” (the capacitor is
fully discharged). This requirement corresponds to ZVS4 in high-efficiency DC-DC
4
zero voltage switching
50
converters [65].
Based on these boundary conditions the unknown amplitude and phase of the AC
current source can be uniquely determined to be a = 1.862 and θ = −32.48◦ . The AC
current source can then be converted back to the form of a fundamental load impedance:
ZE =
0.28 j49◦
e
Cout · ωs
(2.10)
Expressions for switch voltage and current can now be written in piecewise fashion:
(0 ≤ ws t ≤ π) : vsw (t) =
Idd
(ws t + a(cos (ws t + θ) − cos θ))
ws t
(2.11)
(π ≤ ws t ≤ 2π) : vsw (t) = 0
(2.12)
(0 ≤ ws t ≤ π) : isw (t) = 0
(2.13)
(π ≤ ws t ≤ 2π) : isw (t) = Idd (1 − a sin (ws t + θ))
(2.14)
These equations describe the ideal class E waveforms shown in Fig. 2.17.
Though these waveforms are highly nonlinear and rich in harmonic content, the highQ filter network maintains purely fundamental output power at the load. Fundamental
output power delivered to the load is about 78% (-1.07 dB) of that which would be
delivered by the same device operating in class B [1].
4
vds/Vdd
3
2
1
0
0
Vdd
ids/Imax
pdiss=0
Idq=0
0.2� 0.4� 0.6� 0.8�
�
1.2� 1.4� 1.6� 1.8�
2�
Figure 2.17: Drain waveforms for an ideal class E amplifier.
51
2.5.2
Practical Issues
Stress on the microwave transistor is extreme for switched modes. In class E operation
the switch current peaks at 2.86×Idd , and the maximum switch voltage is 3.56×Vdd . A
device must be carefully selected to withstand this stress, and drain supply voltage may
need to be reduced to avoid drain-source voltage breakdown. Furthermore, microwave
devices commonly exhibit nonlinear output capacitance variation with drain voltage.
[3] determined that a certain nonlinear characteristic describing an HBT5 device would
increase peak switch voltage by 28%,
Recall that drain supply voltage for class AB is conservatively set to Vdd = Vbreak /2.5.
Ideal class E instead requires that Vdd = Vbreak /3.6, resulting in significant reduction
of output power capability for a given transistor. Practical designs do not experience
such high peaks due to a finite number of harmonic terminations, but some reduction
in drain voltage from class AB levels is typically required for reliable operation.
The ideal switch transitions between open and closed states instantaneously. A microwave transistor can only emulate a short transition time from cutoff to saturation
with a high level of overdrive (compare Fig. 2.6(b) with Fig. 2.8). Class E amplifiers
thus operate in heavy gain compression and have high input drive power requirements.
Additionally, the amplifier is completely nonlinear in the sense that reduced input power
does not linearly reduce output power. As input drive is reduced, the switch approximation begins to fail, and the amplifier no longer exhibits class E characteristics.
Output amplitude control of class E amplifiers has been performed through the use
of drain supply modulation (e.g. [20], [23]). Class E has a desirably linear relationship
between peak RF load voltage and drain supply voltage (as shown in [70]):
vload = ±Vdd (26 · fs Cout
p
RE · 50)
(2.15)
where RE is the real part of ZE as defined in Eqn. 2.10. This method and similar drain
5
heterojunction bipolar transistor
52
supply modulation methods are discussed in greater detail in Chapter 4.
A transistor must have a very small output capacitance relative to the fundamental
frequency to satisfy the switch approximation. A maximum class E frequency can be
defined based on Imax , Cout , and Vdd [3]:
fE,max '
Imax
56.5Cout Vdd
(2.16)
Above this frequency the capacitor of size Cout cannot completely discharge in one
RF period, and ideal class E operation is impossible. In these cases sub-optimal class
E has still been shown to provide significant efficiency enhancement [67]. Even so, this
relationship requires the use of transistor technology that is advanced, and typically
very expensive relative to the center frequency [5].
At UHF and microwave frequencies, lumped elements Ls and Cs of Fig. 2.16 are
not available. Instead transmission line networks are used to emulate the resonator’s
harmonic open circuit impedance (e.g. [71], [40]). As with harmonic-tuned PAs, these
networks can become lossy, sensitive, and large when controlling an increasing number
of harmonics. The effect class E loss mechanisms including finite harmonic termination
Q-factor and finite switch on- and off-resistance are considered in [72]. Termination of
a finite number of harmonics is analyzed in [62]. As with all practical PA topologies,
matching and bias circuitry also make a significant contribution to loss especially with
large impedance transformation ratios.
2.6
Summary
Following the general discussion of transistors and load line theory, three categories
of high-efficiency operation were discussed in this chapter: reduced conduction angle, harmonic-tuned, and switched mode. Though the philosophies are different, each
method has the goal of increasing efficiency by reducing power dissipation in the virtual
53
drain while preserving fundamental-frequency output power. Varying tradeoffs exist
among the methods:
• Reduced conduction angle modes are very commonly used, relatively easy to implement, and provide moderate efficiency. Linearity, gain, and output power can
be traded for efficiency by variation of the conduction angle.
• Harmonic-tuned modes require a better understanding of device packaging and
output capacitance, and precise control of harmonic impedances. The transistor
must have gain at harmonics and withstand high drain voltage and current peaks.
Dramatic increase in efficiency is possible for compressed operation, along with a
theoretical increase in output power over class B operation. Broadband harmonic
terminations are difficult to implement, typically resulting in a more narrowband
operational bandwidth than reduced conduction angle modes.
• Switched modes (specifically class E) operate fundamentally differently than the
previous two, and require a very high-performance device relative to that required
for class AB operation. The transistor must satisfy switch approximations, with
very high frequency performance and high voltage breakdown limits. Gain is
reduced due to high levels of compression, and theoretical output power is 1.1 dB
lower. Bandwidth is limited, as in the harmonic-tuned classes. The class E mode
of operation does, however, offer 100% theoretical efficiency.
In the next chapter transistor characterization and high-efficiency PA design methods are presented to deal with non-idealities of real-world active devices. Class E and
class F−1 designs with 110 W at UHF and 40 W at S-band with excellent results validate
the approach.
54
Chapter 3
High-Efficiency PA Design
Contents
3.1
Load Pull Characterization . . . . . . . . . . . . . . . . . . . . . . . .
57
3.2
UHF Class E Load Pull and PA Design . . . . . . . . . . . . . . . . .
70
3.3
S-Band Transistors and Packaging . . . . . . . . . . . . . . . . . . . .
78
3.4
S-Band Class F−1 Load Pull and PA Design . . . . . . . . . . . . . . .
84
3.5
Conclusion
97
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter 2 provided theoretical basis of PA operation, templates for PA design, and a
framework for understanding behavior. The theory is highly idealized to allow for mathematical tractability and intuitive understanding, and fails to account for many complex non-idealities of high-power transistors, especially when operated in high-efficiency
modes. Nonlinear models are widely used for many types of PA design, but most are
unreliable in the compressed regime required for high-efficiency operation. Relatively
new transistor technologies often lack nonlinear models. Load-pull transistor characterization [73] is used to map transistor performance under different impedance, bias, and
drive conditions. In this chapter, load-pull-based high-efficiency PA design methods are
discussed and example PA designs are demonstrated.
Load-pull is an empirically-based PA design method guided by theory and sup-
plemented by models. This chapter contributes extensions to standard load-pull to
facilitate measurements for harmonic-tuned and switched-mode operation. The method
is applied to high-efficiency characterization of high-performance transistors, and the
resulting data is used for numerous high-efficiency UHF PA designs (e.g. [5] [40] [38]
[39]). As a representative example, an LDMOS device is characterized to illustrate the
techniques for class E design at UHF, resulting in a demonstrated PA with 110 W output
power at 360 MHz with 83% drain efficiency and 16.0 dB gain [6].
High-performance GaN HEMT transistors developed over the last decade have enabled high-power, high-efficiency PA operation at S-band [74]. As fundamental frequency rises, package and transistor parasitic effects have increasing impact, adding
to the difficulty of harmonic impedance control. Transistor and FEM package analysis are used to evaluate devices and packaging technology for high-efficiency operation.
New methods are developed in this chapter to determine feasibility and realize design
of harmonic-tuned PAs. A swept harmonic load-pull technique was developed using
fundamental-frequency tuners to allow verification of transistor and package approximations. Feasibility analysis of two GaN transistors shows that only one is suitable for
harmonic-tuned operation at S-band, and also shows the benefit of reducing package
parasitics. Load-pull contours are presented illustrating the dramatic impact of varying
2nd harmonic termination. A 3rd harmonic termination is added to satisfy conditions
for class F−1 load-pull, resulting in an 8% efficiency improvement over the best-case
2nd harmonic termination. Load-pull measurements are verified by design and measurement of a 36-W class F−1 PA prototype at 2.14 GHz with 81% drain efficiency and
14.5 dB gain (78% PAE) in pulsed operation [2], among the best reported results with
this frequency, power level, and device technology.
56
3.1
Load Pull Characterization
Load-pull is a highly customizable measurement method for nonlinear devices requiring
a great deal of experience in both calibration and measurement to perform correctly.
This section describes highlights of the methods used in this work, but is by no means
a comprehensive discussion of the procedure and does not cover all intermediate steps
required to obtain the presented results. Focus Microwaves hosts a library [75] of useful
application notes, and [4] treats some underlying concepts.
The impedance and gain of active devices in small signal operation is commonly
measured using a VNA1 with 50Ω ports. Linearity allows mathematical post-processing
to predict the device’s behavior with non-50Ω ports. Large signal transistor behavior,
by contrast, changes nonlinearly with port impedance, requiring that measurements be
made with the appropriate port impedance. Load-pull involves measurement of active
devices under varying load impedances. Note that “source-pull” denotes variation of the
input impedance, and not variation of the impedance at the transistor’s source terminal.
Similarly, “source impedance” refers to input impedance.
Many types of active devices, ranging from low-noise-terahertz to high-power-megahertz,
can make use of load-pull techniques. Load-pull equipment is therefore far less standard than a VNA and is often highly specialized in terms of frequency, power level,
and parameter of interest (e.g. noise, power, efficiency). Fig. 3.1 shows photographs of
load-pull measurement benches at UHF and S-band along with a block diagram of a
general power transistor load-pull setup.
In the block diagram, a synthesizer drives a highly linear pre-amplifier whose output
power is measured using a coupler. The circulator ensures that pre-amplifier performance and the coupler’s coupling factor do not change with input impedance. Circulators are inherently narrow-band, so an attenuator of perhaps 3 dB is used to prevent
1
vector network analyzer
57
Figure 3.1: Photographs (top) of two load-pull benches and an end-to-end block diagram (bottom) for a power transistor load-pull configuration. Inset photograph is an
enlargement of the input prematch, output prematch, and device under test.
58
highly reflective out-of-band input impedance. In this case the input reflection coefficient will be at least 6 dB even if the circulator presents a short out-of-band. These
components make up the “input block”.
Mechanical tuners and prematch circuits achieve impedance transformation between
system impedance and desired DUT2 impedances. Both will be described in more detail
in the next section.
Output attenuators must be selected to avoid variation due to temperature under
high load. Instead of one 30-dB attenuator capable of 100 W input power, a cascade of
three attenuators might be preferable: a 150 W 6 dB attenuator, a 50 W 6 dB attenuator,
and a 25 W 20 dB attenuator. A spectrum analyzer is critical in detecting instability,
and output power is measured using a bandpass filter to eliminate harmonic energy
from the measurement. These components make up the “output block”.
3.1.1
Mechanical Tuners and Prematching Circuits
Mechanical tuners are commercially available from Focus Microwaves and Maury Microwave and exist to transform the 50Ω system impedance to a new input (or output)
impedance presented to the DUT. A schematic representation of a single-slug tuner is
shown in Fig. 3.2.
The tuners consist of a 50Ω coaxial air line and a metallic slug which can be repeatably moved along two axes: closer to or farther from the DUT (X) and closer to
Plane
P4
DUT
Slug
X
Y
50Ω Transmission Line
Output
Block
Figure 3.2: Single-slug mechanical load-pull tuner schematic.
2
device under test
59
or farther away from the center conductor (Y). As Y becomes small the slug becomes
increasingly capacitively coupled to the center conductor, transforming the impedance
as would a single-stub matching network. A small gap Y transforms the 50Ω system
impedance to a high reflection coefficient of variable phase. The phase is adjusted by
slug movement in the X direction. A predefined set of impedances which the tuner
can present is called a constellation. Note in the typical tuner constellation shown in
Fig. 3.3(a) that the constellation has a maximum reflection coefficient magnitude, which
defines minimum and maximum impedances.
In this work, load-pull is performed at UHF (360 MHz) and S-band (2.14 GHz) at
power levels up to 120 W. Recall from Chapter 2 that high-power transistors have small
load and source impedance values. Impedances on the order of 5Ω are poorly represented
on the tuner constellation of Fig. 3.3(a), and near the edge of the constellation where
power calibration uncertainty is large. A prematch circuit is used to implement a
fundamental impedance transformation from 50Ω to 5Ω, translating each impedance
in the constellation by the same ratio and resulting in the constellation of Fig. 3.3(b).
Fig. 3.3(c) shows the constellation at planes P2 on a Smith chart normalized 5Ω.
Traditional load-pull tuners described earlier precisely control fundamental frequency
50Ω Smith Chart
6
0
2
2
0
0
2.
0
0
6
0.
1.0
0 8
0 8
10
5Ω Smith Chart
6
0 8
1.0
50Ω Smith Chart
3
0
4
4
4
0
4
0
0
3.
(b)
0 0
0
-2
1.
0 8
0 8
0
6
2
6
-1 0
1.
0.8
-0
.6
-2
0
-3
-0
5
4
0
-5.
0
(a)
3 0
2 0
0
0 2
0
40
30
1
8
04
0
0
5
2 0
1 0
0
0 4
0 2
50
-4
-0
3.
0
4
0
-10.
5
0
2
-0.
4.
0 0
- 10 0
0
10.0
5.
2
0
5.0
10.0
2
-0
-0
4.
10 0
10.0
-0.
0
3.
0
5 0
2
5.0
0 2
0
4.
0.
4
0
3.
(c)
Figure 3.3: Fundamental (blue) and 2nd harmonic (red) impedance constellations at
plane P4 (a), P3 (b), and P2 (c). The constellation at P2 is plotted on a Smith chart
normalized to 5Ω.
60
impedances while harmonic impedances are allowed to vary arbitrarily as evidenced by
the 2nd harmonic constellation of Fig. 3.3(a). Elaborate active [76] and passive [77]
harmonic load-pull techniques are available but are less common and significantly more
expensive. Later in this work it is shown that varying harmonic impedance has a dramatic impact on performance of some transistors, making it important to fix harmonic
impedance conditions for repeatable results. In this chapter, harmonic quarter-wave
transmission-line stubs are added to prematch circuits, placing a short at a fixed distance from the DUT reference plane. The output prematch circuit at the right side of
Fig. 3.4 implements harmonic termination in this way, and the circuit at the left is used
to measure the impedance of the output prematch.
Any harmonic tuner impedance will combine in parallel with the prematch short,
resulting in a constant high-gamma harmonic impedance for the whole fundamental
frequency impedance constellation. The distance of the short from the DUT determines the phase of the high reflection coefficient termination at the harmonic frequency.
The prematch implemented to achieve the constellations of Fig. 3.3(c) terminates the
2nd harmonic (red) in a constant inductive high reflection coefficient impedance for all
fundamental frequency impedances.
Figure 3.4: Break-apart TRL impedance verification standard (left) and output prematch circuit (right) which incorporates a fundamental impedance transformation to
5Ω, 2nd and 3rd harmonic termination stubs, and a bias tee. The bias tee choke is
implemented by a quarter-wave transmission line terminated at the DC end by a capacitor resonant at the center frequency. Additional shunt bias tee capacitance for
low-frequency termination is not shown on this prematch.
61
Available gain increases as frequency decreases, requiring careful bias network design. Bias networks should present a low-impedance termination at low frequencies (10s
to 100s of MHz). This is most commonly achieved by placing the bias network close
to the DUT and placing a bank of shunt bypass capacitors on the DC side of the RF
choke. In this work the DC bias is supplied as close to the device as possible, through
the prematch circuit.
3.1.2
Calibration
Before load-pull measurement can take place a VNA is used to measure two-port Sparameters of the input block, output block, and prematch circuits. The S-parameters
of the tuners are also measured over a constellation of XY positions. The S-parameters
at each XY point are cascaded with input and output block and prematch circuit Sparameters resulting in a constellation of input and output impedances and corresponding input and output power calibration factors (procedure detailed in appendix of [4]).
The calibration factors take into account both resistive and reflection loss from the DUT
measurement plane to the input or output power meter. It is important to understand
that the uncertainty of this factor rises with increasing mismatch. Near the outside
edge of the calibrated constellation (high reflection coefficients) power measurements
have larger uncertainty [78].
When dealing with non-50Ω port impedances (e.g. output prematch circuits) it is
important to distinguish between types of loss. In a 50Ω system it can be said that
loss (in dB) is simply 10 log |S21 |2 . If, for example, the device is mismatched at the
input port to 40Ω instead of the desired 50Ω, the reflection loss will be included in that
calculation. However, if the device is designed to have a 40Ω input impedance we do
not wish to penalize the device for input mismatch loss. This is the case for load-pull
and PA matching networks, where the input prematch is designed to operate with a 5Ω
input port and a 50Ω output port. After 50Ω S-parameters are measured, insertion loss
62
effectively re-normalizes the data such that port 1 is conjugately matched:
IL = 10 log
|S21 |2
1 − |S11 |2
(3.1)
Output prematch S-parameters are measured from the DUT reference plane P3 to
the coaxial reference plane P4. This measurement is performed using standard coaxial
VNA calibration and a microstrip verification standard. The photograph of Fig. 3.4
shows such a standard placed to the left of the prematch circuit. The standard’s Sparameters are determined from three measurements using the TRL3 procedure described in [79]. Two verification standards are constructed along with an insertable line
of well-known impedance, as shown in Fig. 3.5.
The TRL standards and prematch circuits are soldered to modular copper blocks
and can be very repeatably connected to each other. The TRL procedure outlined in
[80] solves the S-parameters of TRL blocks A and C using S-parameter measurements of
A+C, A+B+C, a 1-port measurement of A alone, and a 1-port measurement of B alone.
After S-parameters of block A are known it can be connected to an output prematch
as shown in 3.4. The cascade of A with the output prematch is measured, and then
the known S-parameters of A are de-embedded. Only the S-parameters of the prematch
remain and are referred to planes P3 and P4 as desired.
Guidelines for design of TRL standards can be found in [80]. Fields across the
Figure 3.5: Input, line, and output line standards for a break-apart microstrip TRL
calibration kit.
3
thru reflect line
63
junction between blocks should be as continuous as possible (same substrate, same line
width, no discontinuities near the junction). In the case of harmonic prematch circuits
it is critical that the verification blocks be well-characterized over a bandwidth including
the highest harmonic frequency of interest.
Some load-pull methods use the input and output prematch as the verification standards as well. Prematch circuits with harmonic terminations have deep resonance at the
harmonic frequencies, resulting in a singularity in the TRL solution. Therefore separate
verification standards are required which do not have such resonances and can be solved
over the whole frequency range using the TRL method.
Small errors in S-parameter measurements of any load-pull component have two
impacts on load-pull accuracy. The first is obvious: a slightly different input or output impedance will be presented to the DUT than is expected from calibration data.
Secondly, an error in S-parameters impacts calculation of reflection loss, and thus the
calibration factor added to the output power measurement. At each impedance point
in the constellation the error will be different, resulting in a gradient of power measurement error over impedance. Best performance contours are skewed toward regions of
increasingly optimistic power measurement error and give a false impression of device
performance. A number of verification measurements can be performed to determine
calibration accuracy for each branch of the system. For example, Fig. 3.6 shows a measurement of gain contours when no DUT is present, and the source is tuned very near
50Ω. If the load-pull system is well-calibrated, a conjugate load impedance should result
in 0 dB gain, and gain should decrease uniformly with increasing reflection coefficient
magnitude due to mismatch loss:
M L = 10 log(1 − |Γ|2 )
(3.2)
The maximum gain and gain contours of Fig. 3.6 therefore indicate good calibration.
More time is often devoted to calibration of a load-pull system than to actual DUT
64
2.0
1.0
0.8
0.6
Figure 3.6: Gain contours spaced by 0.05 dB for a load-pull of a source tuner set to
Zsource =48.0-j0.2Ω. Maximum gain is -0.02 dB at Zload =47.9+j0.2Ω, and gain decreases
uniformly in all directions with increasing reflection coefficient magnitude, verifying that
the load-pull system is well-calibrated.
measurements. Extreme attention to detail is critical when high output power and efficiency are expected, as very slight power, voltage, and current measurement errors have
a large impact. Some degree of constant error in efficiency or output power is acceptable
for load-pull measurements, because transistor performance at one impedance relative
to another is correctly shown. Errors which vary significantly over the impedance constellation are not tolerable, as they indicate false trends. Drain efficiency and gain
measurements are used separately in this work to limit error sources and more clearly
expose error trends caused by incorrect S-parameter calibration data. Though PAE
provides a more comprehensive picture of performance, it combines input, output, and
bias power into one metric along with errors from each. Fig. 3.7 shows the impact on
calculated drain efficiency for an output power or current measurement error.
For example, 45.5 dBm output power with 36 V and 1.26 A supply voltage and current results in 78.2% drain efficiency, but a supply current measurement error of only
20 mA changes efficiency by as much as 1.2%. Similarly, a power measurement error of only 0.05 dB changes drain efficiency by as much as 0.9%. Sensitivity to these
errors increases as output power and efficiency rise, making clear the importance of
high-precision calibration.
65
1.35
Drain Current [A]
1.3
70% ηd
72%
74%
76%
1.25
78%
80%
82%
1.2
84%
86%
1.15
45.2
45.3
45.4
45.5
45.6
Output Power [dBm]
88%
45.7
90%
45.8
Figure 3.7: Drain efficiency for varying Idd and Pout with constant Vdd .
3.1.3
Power Measurement
In modulated or pulsed power applications high-power PA performance is often better
than in CW4 applications due to transistor self-heating effects. Pulsed-RF (or simply
“pulsed”) load-pull measurements are used in some of this work to emulate the pulsed
power application. The synthesizer is set to produce pulses of a certain duty cycle and
period and sends a trigger to start measurements at the beginning of each pulse. RF
power, RMS drain current, and RMS drain voltage are measured over the middle 80%
of the pulse to avoid startup transients and timing-related errors.
Measurement of drain current is complicated by the drain bias tee capacitance required for stable operation of high-power transistors. The drain bias circuit for pulsedRF measurement is shown in Fig. 3.8. Idd would ideally be measured directly using an
oscilloscope, but the addition of a current probe (and its parasitic inductance) would impact RF performance. Therefore the current measurement is made immediately before
the PA bias network. Recall that low-frequency bias network termination is impor4
continuous wave
66
DC
Supply
+
--
Wire
Inductance
Pulsed-RF Supply
Circuit
Is
Cp
Multi-pin
Header
Ip
RF Power
Amplifier
Idd
CPA
Current Probe
Figure 3.8: Drain bias circuit schematic for a pulsed-RF measurement.
tant for stable operation of high-power transistors, and is implemented by the capacitor
bank CP A . When the RF pulse starts and current is drawn into the RF transistor some
current will initially come from this capacitance CP A , thus the measured current Ip
does not equal Idd . This error is transient, and quickly becomes small provided the
capacitance CP A is sufficiently low. The portion of the pulse being measured should
not begin until this error is small. A multi-pin header is used to connect the pulsed-RF
supply circuit to the PA to minimize parasitic reactance between the two components.
On the DC supply side of the current measurement the DC supply and wire inductance
respond very slowly to a step change in current Ip . Therefore, to keep the voltage at the
PA from dipping, a large value of capacitance Cp is required, implemented as a bank of
capacitors of varying size to provide very low impedance over a broad frequency range.
The values and components used to implement CP A and Cp depend on PA stability
requirements, pulse width, and Idd during the pulse.
Pulsed RF power is measured with a spectrum analyzer set to zero span. The
instrument is connected to either the input or output power measurement ports by
means of an RF SPDT5 switch. The spectrum analyzer is not an acceptable instrument
for absolute power measurement, so the high degree of accuracy inherent in a CW power
sensor is transferred to the spectrum analyzer by means of a power offset calibration
factor. A zero-span spectrum analyzer measures CW power and pulsed power with the
5
single pole double throw
67
same relative accuracy.
Mechanical tuner power limits range from 10’s to 1000’s of watts and can be defined
at both peak and average power levels. High average power causes heating and expansion
of the center conductor leading to loss of precise calibration and protrusion of the center
pin in external connectors. Provided the pulse duration is smaller than the thermal time
constant of the center conductor, the average power of the waveform should be used to
ensure compliance with the the average power limitation. Duty cycle can be varied to
set average power as desired:
Pavg,dBm = Ppeak,dBm + 10 log DC
(3.3)
For example, 50 dBm peak power with a 5% duty cycle pulse results in 37 dBm average
power.
The manufacturer suggests a maximum average power of 30 W, limited by the tuner’s
APC-7 coaxial connectors, but does not provide any guidance about maximum peak
power [75]. We wish to use the tuners to characterize transistors up to 250 W peak, so
an analysis was performed to approximate the safe peak power level for a given tuner.
High peak power causes air breakdown between the center conductor and the slug in the
tuner, leading to damage of the slug and center conductor. The critical field between
the two surfaces is not well known due to variation in air humidity and a dielectric
coating on the slug. The minimum spacing between the two surfaces is 5 mil in the
Focus CCMT-1816 tuners used in this work [81]. Peak voltage along a transmission line
can be derived from basic transmission line expressions [82] as a function of mismatch
and peak power:
s
Vpeak =
2Zo P
(1 + |Γ|)
1 − |Γ|2
(3.4)
Thus the peak power limit of the tuner is dependant upon the VSWR6 produced
by the tuner. Fig. 3.9 was produced using the relationship between peak power, tuner
6
voltage standing wave ratio
68
VSWR, and critical field. Based on discussions with the manufacturer [81], it is reasonable to expect that the critical field should be higher than 35 kV/cm, so peak power
of 100 W can be safely used provided tuner reflection coefficient magnitude is less than
0.9. Fig. 3.9 therefore provides a conservative estimate of the peak power which can
be applied to a tuner given a maximum reflection coefficient magnitude. This analysis
proves to be a useful tool for high-power load-pull.
3.1.4
General Measurement Procedure
After calibration, the transistor is slowly brought to the quiescent bias point, watching
for potential oscillation. In some cases the load or source impedance must be adjusted,
or the bias network low-frequency termination improved, to avoid instabilities.
Realistic transistors are bilateral, so source and load-pull must be performed in an
Peak Power [W]
10
10
10
3
2
25kV/cm
30kV/cm
35kV/cm
40kV/cm
45kV/cm
1
0.6
0.65
0.7
0.75
0.8
0.85
0.9
Reflection Coefficient Magnitude
0.95
1
Figure 3.9: Peak power limit analysis for Focus CCMT-1816 load-pull tuners. The plot
shows power and impedance mismatch required to achieve the specified maximum electric field strength on a transmission line. This plot is used to determine the maximum
safe peak power level in the load-pull tuners. For the tuners used in this work the
maximum allowable field is assumed to be 35 kV/cm.
69
iterative fashion. First source-pull is performed using a small input signal to determine
input impedance for high gain. Load impedance during this source-pull should be set
to a reasonable value, typically the theoretical load line impedance.
High gain is a key ingredient in large-signal oscillation. During initial load-pulls it is
sometimes helpful to intentionally mismatch the input impedance away from maximum
gain. Gain will be reduced because power is reflected, or not effectively delivered, to
the transistor gate. Roughly the same output power and efficiency will be achieved
by supplying more incident power to make up for the power which was reflected. The
tradeoff between reduced gain and stability must be made when selecting final prototype
impedances as well. Fortunately, in many cases the input impedance has very little
impact on large signal output power and efficiency provided the same level of gain
compression is achieved.
Transistor performance measurements are be performed at each impedance in the a
constellation under one of many input power conditions including constant input power,
swept input power, and constant gain compression. In this work the constant gain
compression method is implemented for GaN HEMT devices by increasing input power
until a consistent value of gate current Igg is measured, indicating an approximately
constant level of device compression.
3.2
UHF Class E Load Pull and PA Design
An example of class E load-pull and subsequent PA prototype design procedure is presented in this section. The DUT is an LDMOS transistor (TriQuint PLD365F) intended
to produce about 100 W at 2 GHz and does not make use of internal input or output
matching networks. The same procedure was also used to characterize a collection of
lower-powered devices as well, including GaN on Si HEMT, GaN on SiC7 HEMT, SiC
7
silicon carbide
70
MESFET8 , and LDMOS [5] [83] [40]. The load-pull system was configured, calibrated,
and verified; and transistor load-pull data was collected over a four-day period using a
UHF load-pull system (shown in Fig. 3.1 at the top-right) located at dBm Engineering,
now TriQuint Semiconductor, in Boulder, CO.
3.2.1
Class E Load Pull
Output capacitance of the large LDMOS transistor is estimated to be 45 pF, leading to
a theoretical class E fundamental load impedance of 1.8+j2.1 at 360 MHz (Eqn. 2.10).
The device is specified for class AB operation at Vdd =28 V, so breakdown voltage is
estimated to be about 70 V. This class E implementation will make use of only 2nd
harmonic termination, avoiding the ideal class E 3.6 · Vdd peak drain-source voltage
[62]. Still, the drain supply voltage is de-rated for class E operation to 24 V, assuming
Vds,max ≤ 3Vdd for the one-harmonic case. Imax is not specified by the manufacturer
for this device, but load-line approximations and IV curve simulation of similar devices
indicate Imax >21 A. Maximum frequency for ideal class E operation (FE,max from
Eqn. 2.16) can be calculated for a 24 V drain voltage as 340 MHz, below the target
frequency of 360 MHz. Ideal class E performance is not expected in this case, but
instead a sub-optimal class E mode.
General prematch circuits were constructed to center the fundamental constellation
at 10Ω and fix the second harmonic at an open. The impact of device packaging and
bond wires is small and was assumed negligible at harmonic frequencies - that is, a
harmonic open at the prematch plane (P3) edge is assumed to represent an open at
the output capacitance (P2). Reference planes are shown in Fig. 2.3. The input and
output prematch circuits were fastened to break-apart aluminum blocks with nylon
screws and measured using TRL verification standards. A photograph of the load-pull
fixture is shown in Fig. 3.10. This characterization was performed with a CW input
8
metal semiconductor field effect transistor
71
Figure 3.10: Photograph of a break-apart load-pull fixture used for characterization of
the 100-W LDMOS device in class E mode.
signal, consistent with the target application. A very large heat sink was used during
the load-pull procedure because some load impedance regions produce highly inefficient
operation, resulting in a large amount of dissipated heat.
Small-signal source-pull measurement was performed with the output impedance
set near the ideal class E impedance, and results are shown in Fig. 3.11. Note that
contours do not close because the well-calibrated source constellation did not extend
to a high-enough reflection coefficient magnitude to achieve decreasing gain. We can,
however, reasonably predict that the 20 dB contour is the largest that would occur. The
j10
j5
j20
18
20
19
j2
19
18
2
5
10
20
Figure 3.11: Source-pull gain contours for an LDMOS transistor, black square at 2+j5Ω
is source impedance selected for final prototype design. Smith chart is normalized to
10Ω.
72
black square in Fig. 3.11 shows the input impedance (2+j5Ω) used in the final prototype
design. This impedance has a high ratio of reactance to resistance - a relatively high-Q
impedance. Low-loss matching networks insensitive to manufacturing errors are difficult
to design with very high-Q impedances.
Load-pull measurement was carried out with constant input power levels. Low
input power was applied for the first load-pull to map regions of high heat dissipation
or oscillation. Those regions were noted and avoided in subsequent load-pulls. A final
load-pull measurement is shown in Fig. 3.12. Note that output power (red) is shown
in watts. The green circle indicates the theoretical class E impedance, and the black
square shows the impedance used in the final prototype design. Again, contours do
not close due to limitations of the prematch circuit fundamental transformation. A
transformation centered at 5Ω would have provided a constellation that more completely
encompassed the region of interest, but a transformation centered at 2Ω would have put
the high-reactance optimal source impedance at the edge of the constellation.
j10
j5
58
8
75 4
67
84
j2
74
2
58
49
94
64
55
10
Figure 3.12: Load-pull power (red, in watts), and drain efficiency contours (blue) for the
LDMOS device in class E configuration. Theoretical class E impedance of 1.8+j2.1Ω
is shown with a green circle, prototype impedance of 1.8+j2.9Ω shown with a black
square. Smith chart is normalized to 10Ω.
73
3.2.2
Prototype Design
Low-impedance matching networks can incur significant loss and also frequently have
very narrow bandwidth [49]. Losses at the input have the effect of reducing PA gain,
and thus PAE, while output loss reduces ultimate output power and drain efficiency,
as shown in Fig. 3.13. For example, a 0.3 dB output matching loss (typical for these
applications) results in a 7% reduction in efficiency. If the transistor was originally
80% efficient the PA efficiency should be 74.4% (80% reduced by 7%). The impact of
loss clearly becomes less when initial efficiency is not as high. Thus, a large part of
high-efficiency PA design focuses on low-loss matching network design.
A broad-band low-loss coaxial unbalanced-unbalanced transformer (un-un) can achieve
matching from 50Ω PA terminals to 12.5Ω by connecting transmission lines in parallel
at the low-impedance end and in series at the high-impedance end [84], [85]. The same
structure can be used to achieve transformation from an unbalanced 50Ω port to two
90
70
60
25
50
Rel. Eff. Reduction (%)
Relative Efficiency Reduction (%)
80
40
30
20
10
0
0
1
2
3
20
15
10
5
00
0.2 0.4 0.6 0.8
Output Loss (dB)
4
5
6
Output Loss (dB)
7
8
1
9
10
Figure 3.13: Fractional drain efficiency reduction due to output loss. Y-axis indicates
the percentage by which the drain efficiency is reduced from the original value given
loss in an output matching network.
74
balanced 6.25Ω ports (called a bal-un, or balun). The constructed un-un transformer
and a schematic representation is shown in the photograph of Fig. 3.14.
Low-loss matching from the 12.5Ω output of the coaxial transformer to the desired
input and output impedances obtained using load-pull was achieved using both distributed and lumped elements. Another segment of coaxial line is used to implement a
quarter-wave open-circuit stub at the 2nd harmonic, placing a short on the transmission
line at some electrical distance away from the DUT. This method of harmonic termination is used throughout this work with increasing complexity as additional harmonics
are controlled and is described in [86]. One advantage of the coaxial stub is the ability
to move the position of the harmonic short nearer and further from the DUT, making slight adjustments to the phase of the 2nd harmonic termination at the DUT. The
complete prototype output matching circuit is shown in Fig. 3.14 with a block diagram.
Adjustment to the physical position of lumped elements and the 2nd harmonic stub
was required. The final output impedance trajectory is shown in Fig. 3.15 with the black
box indicating the impedance at the fundamental, the red circle showing the 2nd harmonic termination, and the green circle showing ideal class E fundamental impedance.
drain
bias
network
2fo
coaxial
stub
4:1 coaxial
transformer
50Ω
output
terminal
Figure 3.14: Low-loss output matching and bias network for the UHF class E LDMOS
PA prototype. Final fundamental impedance at plane P3 is 2.5+j3.2Ω with a 2nd harmonic open-circuit. A block diagram of the circuit (right) shows microstrip transmission
lines in blue and semi-rigid coax in red.
75
The matching circuit impedance trajectory was measured using the same procedure
used to measure load-pull prematch circuits.
3.2.3
Prototype Performance
Fig. 3.16 shows a photograph of the complete class E UHF PA prototype. Note that
the transistor package houses two identical devices, but this PA prototype makes use of
only one.
Input and output terminal connections are made with N-connectors. Both input and
output matching circuits use semi-rigid coaxial 4:1 impedance transformers to transform
the 50Ω terminal impedance to 12.5Ω. A combination of lumped and distributed matching techniques are used to achieve transformation from 12.5Ω to the desired DUT input
and output impedances. All capacitors are from the Advanced Technical Ceramics
ATC100B series, selected for high breakdown voltage and relatively low loss. The substrate is 30-mil-thick 2-oz copper-clad Rogers RO4350B, with r =3.5, selected primarily
for low loss, high power handling capability, and ease of manufacturing. The dielectric
constant and thickness allow microstrip lines over a reasonable range of Zo , important
j10
j20
j5
j2
2
5
10
20
Figure 3.15: Fundamental (black square) and 2nd harmonic (red circle) measured
impedance of the 110 W class E UHF prototype. Theoretical class E fundamental
impedance is 1.8+j2.1Ω for Cout = 45 pF at 360 MHz, is shown in green. The Smith
chart is normalized to 10Ω.
76
Figure 3.16: Photograph of the 110 W class E UHF PA prototype.
for low-impedance matching. Gate bias is supplied through a 100Ω resistive choke, and
drain bias is supplied through a custom inductor wound around a torroidal ferrite. The
2nd harmonic termination is implemented by an open-ended stub made of semi-rigid
coax which is λ/4 at the 2nd harmonic frequency. The prototype is mounted on the
same fixture blocks used for load-pull characterization, though in class E mode very
little heat is dissipated (less than 23 W at 110 W output power), making the large heat
sink unnecessary.
Final measurement results of the UHF class E PA prototype under CW operation
are presented in [6]. The prototype is biased at 24 V drain and with less than 50 mA
quiescent current. In ideal class E operation the transistor should be in complete cutoff
when the “switch” is not on. A more practical design allows some quiescent current to
allow the transistor to turn on and reach saturation more quickly. In the end, selection
of quiescent current is a tradeoff between power dissipation in the switch’s off-state and
power dissipation due to slow turn-on.
Standard power and frequency sweep measurements are shown in Fig. 3.17 and
Fig. 3.18. The class E UHF prototype measures 110 W output power with 16 dB gain
77
and 83% drain efficiency at 360 MHz. 80% drain efficiency is achieved over an 8%
bandwidth. This result compares well with other high-efficiency work at this frequency
and approximate power level, even when more expensive and exotic device technology
is used (e.g. [5] [87] [83]). Note from the power sweep that gain is quite nonlinear with
input power due to the low quiescent current. For low modulation bandwidth signals,
techniques have been used for many decades to restore linearity to non-linear power
amplifiers such as class E [19]. A similar supply modulation technique is discussed,
simulated, and implemented in Chapters 4 and 5.
3.3
S-Band Transistors and Packaging
The previous section described a method of load-pull characterization and class E PA
design in the UHF range, where transistors which meet the criteria for high-efficiency
operation are readily available, and packaging parasitics have little effect. In this section,
S-band transistors and packaging are considered. The target application is a harmonictuned PA with more than 30 W peak power and over 70% PAE in the 2.14 GHz downlink
W-CDMA cell phone band. Only recently has device technology advanced to make this
possible [74]. Packaging is found to be a critical consideration at this frequency.
3.3.1
GaN HEMT Transistor Technology
The Si LDMOS transistor technology described in Chapter 2, and used earlier in
this chapter for the UHF class E PA, lacks high-frequency performance required for
harmonic-tuned or switched-mode operation at S-band. Output capacitance for a 50 W
LDMOS device is on the order of 25 pF, and very closely approximates a short at harmonics of a 2.14 GHz fundamental frequency. The approximate short relieves the designer of explicitly enforcing harmonic terminations for high-power class AB PA designs
when output capacitance is high relative to the fundamental frequency.
78
100
ηd
25
PAE
20
Gain
90
80
70
60
15
50
40
Output Power
10
Efficiency [%]
Output power [dBW] and Gain [dB]
30
30
20
5
10
0
−15
−10
−5
Input Power [dBm]
0
0
Figure 3.17: Measured gain, output power, and efficiency over input power for the final
110 W class E UHF PA prototype using an LDMOS transistor.
100
90
25
Output Power
20
ηd
80
PAE
70
60
Gain
15
50
40
10
Efficiency [%]
Output power [dBW] and Gain [dB]
30
30
20
5
10
0
350
355
360
365 370 375
Frequency [MHz]
380
385
0
390
Figure 3.18: Measured gain, output power, and efficiency over frequency for the final
110 W class E UHF PA prototype using an LDMOS transistor.
79
GaN HEMT transistor technology has been made commercial in the last decade
with unprecedented power density per unit cell and holding the possibility of excellent
high-frequency performance [50]. A summary of Si and GaN semiconductor materials
is given by Table 3.1.
GaN outshines Si in every category except thermal conductivity. However, to date
GaN for HEMTs is grown on other substrates such as Si or SiC, meaning only a thin
layer of GaN is used and limits the impact of its thermal conductivity. Instead thermal
performance of GaN-based devices depends on the thermal conductivity of the substrate.
SiC has a thermal conductivity of 120 W/mK - a great potential advantage over devices
built using Si substrates - but is much more expensive.
PA design benefits from these enhancements in a number of tangible ways [88],
including the following:
• Output capacitance reduced as much as an order of magnitude compared with
LDMOS,
• Increased input and output impedance allowing lower-loss and broader-band matching circuits,
• Increased reliability under high temperature operation,
• Maximum operating frequency increased by more than a factor of 8 compared
with LDMOS, and
• Increased drain voltage breakdown limits.
Table 3.1: Material properties of Si and GaN.
Metric
Si
GaN
Bandgap Energy
Breakdown Field
Electron Low-Field Mobility
Electron Peak Velocity
Thermal Conductivity
1.12 eV
5.7e5 V/cm
710 cm2 /Vs
1e7 cm/s
1.3 W/mK
3.40 eV
38e5 V/cm
1200 cm2 /Vs
2.46e7 cm/s
1.2 W/mK
80
HEMT operation [50] is fundamentally different than that of MOSFETs9 described
in Chapter 2. The conduction channel is made a junction between two materials having different band gaps (called a heterojunction). In this way current is not slowed
by traveling through a channel doped with impurities (as in a MOSFET), but instead
travels using high-mobility electrons generated at the heterojunction in a thin layer
called the 2DEG10 . Instead of the MOSFET gate oxide, the HEMT has a Shottky gate
which allows forward current conduction under saturation. Also unlike MOSFETs, microwave HEMTs are almost exclusively depletion mode meaning that a negative voltage
is required to turn off the channel.
GaN HEMTs are not without downsides. The relatively immature technology carries
with it a large price tag, optimistically 4 times the cost per watt of comparable LDMOS;
as demand and volume increase the cost is expected to decrease. Reliability, performance
drift, and manufacturing issues are gradually being addressed [89], and a number of GaN
devices are commercially available from manufacturers such as TriQuint, Nitronex, Cree,
Sumitomo, and RF Micro Devices.
A type of memory effect behavior usually attributed to charge trapping [90] is particular to III-IV semiconductor devices. The behavior can be qualitatively described as
a reduction in quiescent current immediately following a high-power pulse. The quiescent current recovers gradually to its original value with a time constant ranging from
microseconds to minutes depending upon device design. This leads to time-varying quiescent current which depends on the history of the output power, and thus time-varying
PA gain.
9
10
metal oxide semiconductor field effect transistors
2D electron gas
81
3.3.2
Traditional High-Power Transistor Packaging
A traditional high-power microwave package available from Zentrix and other wellknown package manufacturers, and traditionally used for LDMOS PA designs, was
simulated using HFSS. A photograph and the CAD11 drawing used for simulation are
shown in Fig. 3.19. The goal of the simulation was to determine the fundamental and
harmonic impedance transformation from the microstrip circuit edge to the die “drain
manifold,” where bond wires contact the active device. Note that planes P3 and P2 in
the figure are located at the microstrip prematch edge and at the die drain manifold,
respectively, and include 16 gold bond wires of 1.25 mil diameter. The simulation results
are de-embedded to these reference planes. The microstrip transmission line connects to
the package lead, which is supported vertically by a dielectric “windowframe”. In many
cases this material is alumina (Al2 O3 ), with a relative dielectric constant of about 8.8.
The transistor sits on the flange, built of a material providing a good thermal match to
the transistor’s substrate. The transistor is attached to the flange with eutectic AuSn12
or similar solder.
The HFSS analysis shows that package parasitics between planes P3 and P2 are
quite significant at the 2nd harmonic of the intended 2.14 GHz center frequency. The
Figure 3.19: Photograph and HFSS simulation of the transformation between a transistor and microstrip circuit edge through bond wires and the RF705 package.
11
computer aided design
12
gold tin
82
transformation can be roughly approximated below 4.7 GHz as a shunt capacitance
of 1.8 pF at plane P2 and a shunt capacitance of 3.5 pF connected by an inductance
of 320 pH. A resonance occurs at 4.7 GHz, indicating the difficulty of 3rd harmonic
impedance control through the transformation. This package is unsuitable for harmonictuned applications at 2.14 GHz.
In the case of this package a much simpler analysis, based only on the width of a
required microstrip transmission line used to interface between the PA output circuit
and the transistor, yields the same result. Gupta et. al. [91] discusses a number of issues
which impact the maximum useful frequency for microstrip lines. The cutoff frequency
of the first higher-order mode can be approximated as the following:
fc = √
300
r (2W + 0.8h)
(3.5)
where W and h are specified in millimeters and fc is in GHz. Higher order radiating
modes can also be excited at transmission line discontinuities. Significance of radiating
modes can be determined using the radiating Q-factor of a λ/2 resonator, approximated
by the following:
Qrad
3r
= 2
8h
λo
2
2
Zo
120π
(3.6)
Radiation loss is of concern for transmission lines with a low radiating Q-factor of,
perhaps, less than 50. Radiating Q and cutoff frequency for a typical substrate (30-mil
Rogers 4350B) are shown in Fig. 3.20 for various microstrip line widths. Low values of
Qrad imply that energy is easily transferred to the radiating mode. For example, the
10Ω line on this substrate will radiate 10 times more effectively at 6 GHz compared to
2 GHz.
Though this package is widely used for LDMOS 2 GHz class AB applications, it
exhibits a very low value of radiating Q and cutoff frequency at 6 GHz for the 13.5 mm
microstrip line. This simple analysis indicates that this package likely is not suitable for
harmonic-tuned applications at 2.14 GHz. Special attention must be paid to packaging
83
500
10 Ω, W=13.5mm, f c =6.1GHz
20 Ω, W=6mm, f c=13.3GHz
35 Ω, W=3mm, f c=25.4GHz
50 Ω, W=1.7mm, f c =41.8GHz
450
Radiating Q Factor
400
350
300
250
200
150
100
50
0
2
3
4
5
6
Frequency [GHz]
7
8
Figure 3.20: Radiating Q-factor for microstrip transmission lines constructed on 30-milthick Rogers RO4350B substrate. Transmission line width W , characteristic impedance
Zo , and cutoff frequency fc for the next higher-order mode are shown in the legend.
when considering harmonic termination of high-power devices. Methods for quantifying
and mitigating package limitations are presented next.
3.4
S-Band Class F−1 Load Pull and PA Design
In this section a simple, low cost method for control and systematic variation of harmonic
impedances based on the block diagram of Fig. 3.21 is described. The source side of the
load-pull setup is identical to that described earlier, and only the load side is considered
here.
By convention, fundamental frequency impedance is referenced to plane P3 (as in
previous sections of this chapter) and harmonic frequency impedances are referenced to
plane P1 (as in Chapter 2). Fig. 3.22 shows the position of reference planes P2 and P3
from Fig. 3.21 for two packaging configurations.
Full-wave electromagnetic analysis of these configurations, presented in the next
84
P1
P2
P4
P3
Cout
Virtual
Drain
FEM
Transition
Analysis
Harmonic
Prematch
Circuit
Fundamental Power
LoadPull
Meas.
Tuner
Figure 3.21: Block diagram of the load-pull system including device and package parasitic effects. Transistor virtual drain (P1) is a critical reference plane for high-efficiency
operation. The package reference plane (P3) is most frequently used for load-pull and
PA design. FEM transition analysis is used to model only the output half of the transistor.
(a)
(b)
Figure 3.22: Photograph and FEM model for the transformation incurred for a microwave power transistor package (Zentrix RF701) (a), and chip/wire construction for a
typical 50 W GaN transistor (b). Both models include eight gold bond wires of 1.25-mil
diameter.
section, is used to calculate the impedance at the unmeasurable plane P1 based on
the measured impedance at P3. A swept harmonic load-pull method and accuracy
verification are described, followed by results from load-pull under varying harmonic
conditions.
85
3.4.1
Feasibility of Harmonic Termination
The ability to terminate harmonics at the virtual drain is determined by device and
package characteristics. In this section two 50 W GaN HEMTs are compared. Properties
of both GaN HEMTs are summarized in Table 3.2.
Most of the data in Table 3.2 is available from the manufacturer. RL,classAB is the
load line resistance at P1 for an ideal class AB design (as in Eqn. 2.2). ZL,classAB
is the impedance which must be presented at P2 to realize RL,classAB at P1. ηRon is
the upper-bound on possible efficiency due to on-resistance, as described in Chapter
2 (Eqn. 2.9). Where appropriate, the data in the table is based on a fundamental
frequency of 2.14 GHz.
Recall that an open-circuit harmonic termination at P1 requires an inductive harmonic termination at P2 to resonate Cout , resulting in a high impedance. In Chapter 2 it
was also determined that 3 · RL,fo is the minimum resistance which can be considered an
“open” termination. Therefore we can define the impedance with minimum resistance
at plane P2 required to present an “open” at P1 for the n-th harmonic frequency:
Znfo ,P 2 =
1/(j2πnfo Cout ) · 3 · RL,fo
1/(j2πnfo Cout ) − 3 · RL,fo
Table 3.2: Characteristics of two GaN HEMT transistors.
Metric
DUT1 [92]
DUT2 [93]
Max. Application Freq.
Gate Periphery
Pout,AB
Cout
Vk
Imax
Vdd,AB
RL,AB at P1
ZL,AB at P2
Ron
ηRon
Q2fo ,open
Q3fo ,open
18 GHz
10 mm
50 W
2.7 pF
5V
9A
35 V
6.7Ω
6.6+j0.8Ω
0.10Ω
97%
1.2
1.8
4 GHz
16 mm
50 W
7.4 pF
7V
9.8 A
32 V
5.1Ω
4.8+j1.2Ω
0.23Ω
92%
2.5
3.8
86
(3.7)
The difficulty of presenting an open harmonic termination at P1 can be quantified by
the Q-factor of this impedance, Qnfo ,open . Note that larger output capacitance increases
the harmonic open-circuit Q-factor, and that Q3fo ,open > Q2fo ,open , indicating that a
3rd harmonic open-circuit is more difficult to realize than a 2nd harmonic open-circuit.
Conversely, a harmonic short at P2 appears in shunt with the output capacitance. From
this perspective, it is easier to accurately present a short termination than an open
termination, especially at higher harmonics and when the output capacitance estimate
is poor.
DUT1 and DUT2 are characterized in the two package configurations shown in
Fig. 3.22. The first is a standard package used for medium-power (50 W) S-band applications [94] (shown in Fig. 3.22(a)). The second is a chip/wire construction in which
the die is eutectic-attached to a 15-mil-thick gold-plated CuMo13 pedestal, which is
soldered to an underlying copper block. The die is directly connected to the input and
output matching circuits (built with 30-mil Rogers 4350B) by eight 1.25-mil-diameter
gold wire bonds. Both configurations are simulated using Ansoft’s HFSS FEM software.
The ports are de-embedded to planes P1 and P3 of Fig. 3.21. The goal of the analysis
is to determine what impedance must be presented by the prematch circuit at P2 to
achieve a harmonic short or open at the virtual drain (P1).
A comparison between two devices in both packaged and chip/wire configurations is
shown in Fig. 3.23 and Fig. 3.24. The following conclusions can be drawn from these
plots:
• It is important to normalize harmonic impedances to the load line impedance.
When presenting an approximate open termination, a reactance of j5Ω is unimportant compared to a 50Ω load line, but unacceptably large compared to a 5Ω
load line. Plots are therefore normalized to the load line impedance.
13
copper molybdenum
87
10
0 8
6
0
0
0.
3
0
0
4
4
5 0
04
-1
-0 8
-
.6
.0
.0
0
10.0
0
.4
4
-0
- .
0
3fo = 6.42GHz
Zo = RL = 6.6Ω
Cout = 2.7pF
2
10 0
- 1 0. 0
02
0. 2
-
Plane P3
Plane P1, No Package
Plane P1, Package
Plane P1, Chip and Wire
(a)
Reflection Coefficient Phase at P1
450
Zo = RL = 6.6Ω
Cout = 2.7pF
Plane P1, No Package
Plane P1, Chip and Wire
Plane P1, Package
360
270
Solid: 2f0=4.28GHz
Dashed: 3f0=6.42GHz
180
90
0
-90
0
90
180
270
Reflection Coefficient Phase at P3
360
(b)
Figure 3.23: Impedance transformation from P3 to P1 for DUT1 for different package
configurations represented by different colors. The Smith chart (a) shows transformation of a constellation of high-reflection-coefficient 3rd harmonic impedances through
three package configurations. The rectangular plot (b) is a clear indicator of reflection coefficient phase sensitivity at P1 relative to phase at P3 in each configuration.
Sensitivity increases with Cout and package parasitics making harmonic termination at
P1 difficult. Red and green arcs and bands indicate regions of approximately short
and open harmonic termination as defined in Chapter 2. Plots are normalized to the
theoretical device load line impedance of 6.6Ω.
88
10
0 8
6
2
0
0
0.
3
0
4
4.
Plane P3
Plane P1, No Package
Plane P1, Package
Plane P1, Chip and Wire
50
10.0
10 0
40
02
0. 2
0
0
5 0
- 0. 0
0
.0
0
0
0. 8
.6
2
0
3.
4
-4
0.
3fo = 6.42GHz
Zo = RL = 5.1Ω
Cout = 7.4pF
- 5.
0 2
(a)
Reflection Coefficient Phase at P1
270
Zo = RL = 5.1Ω
Cout = 7.4pF
180
90
0
-90
Plane P1, No Package
Plane P1, Chip and Wire
Plane P1, Package
-180
-270
0
Solid: 2f0=4.28GHz
Dashed: 3f0=6.42GHz
90
180
270
Reflection Coefficient Phase at P3
360
(b)
Figure 3.24: Analysis of Fig. 3.23, repeated for DUT2. Plots are normalized to the
theoretical device load line impedance of 5.1Ω.
• Considering only the transformation of Cout (magenta), both devices have a reasonable range of phase angle at P3 which result in an approximate short or open
at P1 (indicated by red and green bands of the rectangular representations).
• Addition of the chip/wire transformation to Cout (blue) has a large impact for
DUT2 angle sensitivity at the 3rd harmonic. This corresponds to the significantly
89
smaller and more irregularly spaced constellation of Fig. 3.24(a). Also, the slope
of the dashed blue line in Fig. 3.24(b) is quite steep, indicating a narrower range
of angles at P3 which result in an approximate short or open at P1.
• The standard package with Cout (black) makes an approximate short or open
termination impossible at the 3rd, and difficult at the 2nd harmonic for DUT2.
Conclusions of the analysis have clear implications for load-pull methodology. Package parasitics and Cout can clearly restrict the ability to enforce harmonic terminations at the virtual drain. The harmonic terminations of DUT2 in the standard package are nearly fixed under traditional load-pull (fundamental frequency only) due to
large parasitic reactances at harmonic frequencies. In chip/wire configuration harmonic
impedance of DUT1 can be easily controlled at a 2.14 GHz fundamental frequency.
3.4.2
Swept Harmonic Load Pull Method
High-power fundamental-frequency load-pull is carried out with the addition of pulsed
power measurement and harmonic impedance tuning; the measurement setup is shown
in Fig. 3.25, corresponding to the block diagram of Fig. 3.21. The pulse duty cycle is
5% and the period is 1 msec.
In the block diagram of Fig. 3.21 the harmonic prematch circuit [5] performs the
following functions:
• Transforms the 50Ω fundamental constellation to 5Ω,
• Supplies DC bias near the device drain to avoid large signal oscillation,
• Constrains 2nd harmonic impedance to a single high reflection coefficient value
for the whole fundamental impedance constellation, and
• Increases the angle of the 2nd harmonic termination by decreasing the length of a
tuning stub, labeled “I” in Fig. 3.25, with only a small impact on the fundamental
90
Figure 3.25: Photograph of the load-pull equipment (top) corresponding to the block
diagram of Fig. 3.21: A-Agilent ESG4438C Synthesizer, B-Agilent PSA4440A VSA, CAgilent 4419B Power Meter, D-Tektronix DSO2023 Oscilloscope, E- Focus CCMT-1816
Mechanical Tuners, F-Custom Matlab instrument and tuner control software. Photograph of the load-pull fixture and detail of the harmonic tuning stub (bottom): G-Input
prematch transformer to 5 Ω and bias network, H-Output prematch transformer to 5 Ω
with bias network, I-Detail of 2nd harmonic tuning stub.
frequency impedance transformation. Note that the tuning stub exists to load the
transmission line connecting the device to the resonant stub (shown at the right
of the photograph), and reducing tuning stub length makes the electrical distance
between the two shorter.
The fundamental and 2nd harmonic constellations at reference planes P3, P2, and P1
are shown in Fig. 3.26. Note the great importance of considering even the low-parasitic
chip/wire transformation from P3 to P2.
91
10
0 8
6
0
0
0
2
0
0
0.
6
6
0.8
1.0
0 8
5Ω Smith Chart
.0
5Ω Smith Chart
5Ω Smith Chart
0.
4
3.
4.
0 2
0
0
0
8
6
0
0
-0
-1.0
0.8
0.
6
6
-2
3.
0
1.
4
(b)
10
0
(a)
-0
0
2.
.4
0 8
5.
4.
-0
3.
0
-2
2
10.0
0
5
4 0
2 0
.
1 0
0 0
0
5
3 0
2 0
0 4
4.
0
0 8
2
0
0
0 2
-5.
6
-0
-3
10.0
2
-0.
4
0 2
0
10.0
0
10 0
0
0
0
5 0
-5
0 2
4
4
10 0
0.
4
-0
0
10.0
10.0
2
-0.
3
0
5.0
0 2
0
5.0
4
4.
0
0
3.
(c)
Figure 3.26: Load-pull impedance constellation at reference planes P3 (a), P2 (b), and
P1 (c) for the fundamental (blue) and 2nd harmonic (red) frequencies.
Two-port S-parameters of the output prematch, mechanical tuner, and output attenuators are separately measured to allow de-embedding of resistive and reflection loss
at each fundamental impedance in the load-pull constellation. The input and output
prematch blocks are built as break-apart fixtures [5], allowing S-parameter measurement
using a microstrip TRL calibration kit.
Two identical prematch circuits are constructed, one for S-parameter measurement
(A) and one to remain permanently wire bonded to the device (B) thus eliminating
parasitic variations and limiting potential for damage to the device. Both circuits’ 2nd
harmonic stubs are tuned identically so that S-parameters from A can be de-embedded
from the load-pull measurements made using B. The accuracy of this method is verified
after tuning the 2nd harmonic termination by measuring small-signal gain contours as
shown in Fig. 3.27.
Varying harmonic termination should change large-signal transistor performance,
but small-signal gain at a given fundamental frequency impedance should remain constant.
Five of the contours are tightly grouped, indicating that the measured S-
parameters of A match the S-parameters of B, and power measurement error is acceptably small. The dashed-red curve shows an instance where the calibration check
failed, indicating that A measurements did not match that of B, and must be repeated.
92
40
50
30
20
10
08
06
04
02
Figure 3.27: Small-signal gain contours for six prematch harmonic terminations are
used for validating load-pull calibration. Disagreement of dashed red contour indicates
a calibration error. The Smith chart is normalized to 5Ω.
3.4.3
Load Pull and PA Prototype Results
Swept-harmonic load-pull procedure was performed for the GaN HEMTs (DUT1 and
DUT2) described earlier in this section. Consistent with the feasibility analysis, harmonic tuning did not have a notable impact on efficiency as compared to standard
class AB operation for DUT2 using standard microwave packaging. From this we can
surmise that the harmonic termination at P1 is dominated by the package and output
capacitance and could not be adequately varied by harmonic impedance variation at P3.
Some variation in drain efficiency with harmonic termination at P2 was noted for DUT2
in chip/wire configuration; maximum efficiency did not exceed the maximum efficiency
achieved using standard microwave packaging. As predicted by the analysis, DUT2 was
found to be unsuitable for harmonic-tuned operation at 2.14 GHz. The remainder of
this section presents details of the swept-harmonic load-pull and results for DUT1.
DUT1 was biased at 28 V drain supply with a class AB bias of 300 mA. High vds
peaks are possible in harmonic-tuned operation, as noted in the class E analysis of
Chapter 2. Drain voltage is reduced from the suggested class AB bias point by 20%
for the initial harmonic sweep to prevent such peaks from exceeding Vbreak . Sourcepull was first performed to optimize small-signal gain, followed by large-signal load-pull
measurements at the six 2nd harmonic reflection coefficient angles shown by colored dots
93
in Fig. 3.28, referenced to the virtual drain at P1. At each impedance point input power
was increased until gate current measured 20 mA, corresponding to an approximately
consistent level of gain compression. Fig. 3.28 shows power and drain efficiency achieved
at each harmonic termination. The figure also illustrates the required modification to
the prematch circuit to achieve each harmonic termination. The highest efficiency region
(77%) is achieved with 2nd harmonic nearest an open circuit (blue). In this case the 3rd
harmonic was not explicitly controlled, but was nearly fixed at a capacitive impedance.
Next we investigate the impact of 3rd harmonic control. Another output prematch
circuit was designed to terminate 2nd and 3rd harmonics in an open and short at P1,
respectively (the class F−1 condition). Fig. 3.29 compares results from this measurement
to the 2nd-harmonic-only measurement of Fig. 3.28. Intentional termination of the 3rd
harmonic with a short at P1 increases transistor drain efficiency by 8% without reducing
1.0
67.5%
46.2dBm
2.
0
0
6
0.8
output power.
73.5%
0
45.7dBm 3
0.
4
2fo resonant stub
0
4
74.5%
5. 0
46.2dBm
5Ω Smith Chart
10.0
-10.0
76.5%
46.3dBm
0
0
-2
-1.
-0.8
-0
.6
-3
.0
74.0%
46dBm
4
tuning stub
fo matching stub
.4
-0
10.0
5.0
4.
0
5mm
3mm
1mm
4mm
2mm
0mm
5 .0
0. 2
P3
2
-0 .
77.0%
46.2dBm
Figure 3.28: Fundamental frequency constant drain efficiency contours (referenced to
P3) shown in colors that correspond to six 2nd harmonic terminations (dots, referenced
to P1). Efficiency and maximum power of each contour is indicated next the corresponding harmonic termination dot of the same color. The Smith chart is normalized
to 5Ω.
94
1.0
0. 8
6
2.
0
0.
20
10
06
0. 2
04
08
4
02
4.
0
5. 0
10. 0
0
0.
0
.0
m
dB
45 Bm
d
46
3fo
3
%
7075%
%
0
8 %
75 %
85
70%
45dBm
m
46dB
2fo
2fo
- 10. 0
5Ω Smith Chart
0
.0
.0
3fo
-1.0
- 0. 8
-0
.6
-2
.0
.4
-3
-0
-4
2
- 5.
- 0.
Figure 3.29: Power (dashed) and drain efficiency (solid) load-pull contours with two
different harmonic environments (red and blue, referenced to P3). Both sets of 2nd (o)
and 3rd (x) harmonic terminations are shown referenced to plane P1. The Smith chart
is normalized to 5Ω.
A prototype PA was designed using results of the measurements in Fig. 3.29. A
fundamental load impedance of 10.2 + j6.2Ω was presented at plane P3 with 0.27 dB
insertion loss in the output matching circuit. 2nd and 3rd harmonic impedances approximate an open and short at plane P1 similar to those shown Fig. 3.29. Fig. 3.30
shows the measured and simulated output impedance of the final PA prototype.
A load-pull method is presented to systematically sweep harmonic termination and
is verified by the prototype PA performance, resulting in a high-efficiency class F−1 PA
prototype. A photograph of the prototype is shown in Fig. 3.31. The die is mounted on
a CuMo gold-plated pedestal using AuSn eutectic solder. The pedestal is soldered to the
copper block below, providing a low-resistance thermal path. SMA connectors are used
at the 50Ω PA input and output terminals. The matching circuit is made from 30-mil
1-oz copper-clad Rogers RO4350B substrate with r =3.5. The circuit is soldered to the
copper block below with a reflow process, ensuring ground plane continuity between
the SMA connectors, matching circuits, and die. Impedance matching at the input and
95
output is achieved with a combination of lumped and distributed techniques. Capacitors
are from the American Technical Ceramics (ATC) 600S or 100B series, depending upon
desired loss, resonance, and form factor characteristics. Harmonic terminations are
realized by transmission line stubs.
Input and output bias networks use a quarter-wave transmission line choke, where
one end is terminated in a narrow-band short formed by a resonant ATC 100B capacitor.
The gate bias tee connects to the DC supply using banana jacks, and the choke includes
a 10Ω resistor. In saturated operation this resistor passes gate current, developing a
voltage and varying Vgg at the transistor. Both bias networks include bypass capacitance
on the DC supply side of the RF choke. The PA drain supply is connected via a 100-mil
double-row Molex header to a pulse-power measurement board, containing a current
measurement loop and large bypass capacitors to prevent drain voltage sag during the
2.
0
0.
6
0. 8
1.0
pulse. The 100-mil header interface is also required for work in Chapter 5, where this
0.
3.
0
0
4
4.
5. 0
5Ω Smith Chart
0. 2
10.0
0
40
fo
30
20
10
08
06
0
02
3fo
04
10. 0
2fo
- 0. 0
2
0
.0
.0
-1.0
-0 8
-0
.6
-2
0
-3
.4
-4
-0
-5
- 0.
Figure 3.30: Simulated (blue) and measured (red) output impedance for the 36-W
class F−1 S-band prototype at plane P1. Simulated and measured fundamental load
impedances were 17.4+j1.0 Ω and 17.8+j2.4Ω, respectively. The Smith chart is normalized to 5Ω.
96
Figure 3.31: Photograph of the TGF2023-10 die (left, detail blurred). The complete
fabricated PA prototype is shown at the right.
PA is integrated with an envelope modulator in an envelope tracking system.
Output power of 36 W was measured with 14.5 dB gain and 81% drain efficiency, or
78% PAE at 2.14 GHz, consistent with load-pull characterization results. Further details
of PA performance are presented in Chapter 5, where this PA is used in an envelope
tracking system.
3.5
Conclusion
Important features of general load-pull configuration, calibration, and measurement
were discussed followed by two examples with varying output power, frequency, mode
of operation, device technology, and input stimulus. New load-pull techniques were introduced in both cases to enable and enhance measurement for high-efficiency operation.
Contributions described in this chapter include the following:
• Development of a harmonic load-pull characterization methodology used with variety of transistors at UHF [38] [39] [48]. The methodology is verified by design of
many high-efficiency class E UHF power amplifiers with up to 100 W and efficiencies up to 90% [40] [5] [41], and illustrated in this work using a class E LDMOS PA
at 360 MHz, resulting in greater than 83% drain efficiency, 110 W output power,
and 16.0 dB gain [6].
97
• Extension of the load-pull method including full-wave electromagnetic analysis of
microwave packages parasitics and alternative construction methods to determine
and enhance feasibility of effective harmonic terminations. These techniques are
illustrated in this work using a class F−1 PA at 2.14 GHz resulting in greater than
81% drain efficiency, 36 W output power, and 14.5 dB gain [2].
98
Chapter 4
Envelope Tracking Components
and Simulation
Contents
4.1
Supply Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2
Envelope Modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3
Power Amplifiers for Envelope Tracking . . . . . . . . . . . . . . . . . 113
4.4
Signal Split . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.5
System Analysis Tool
4.6
Conclusion
. . . . . . . . . . . . . . . . . . . . . . . . . . . 128
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Chapters 2 and 3 focused on improving efficiency of the PA in compressed operation at peak output power. This chapter applies supply modulation to achieve highefficiency compressed operation over a wide range of output power levels. A general
ET transmitter is developed (shown in Fig. 4.1) which utilizes both drive and drain
modulation, followed by a discussion of PA and envelope modulator hardware requirements and limitations. A block called the signal split is introduced to control the ratio
of drain modulation to drive modulation, and is used to trade PA efficiency and EM
requirements. A simulation method is developed for modeling the impact of component
Digital
~y[n]
α[n]
Signal
Split
~
β[n]
Envelope
Modulator
Analog
Vdd(t)
Idd(t)
re( v~in e jωt )
Up
Converter
Rdd(t)
PA
re( ~
vout e jωt )
RF
Figure 4.1: Simplified block diagram of the ET transmitter system. The PA is driven
with an input signal ṽin modulated with both amplitude and phase, and the envelope
modulator (EM) varies drain voltage Vdd . At low output power levels drain voltage
is reduced, causing PA gain compression and thus improving PA efficiency. Digital
algorithms pre-correct the PA input signal to account for variations in PA gain and
insertion phase, achieving system linearity from input ỹ to output ṽout .
non-idealities on system performance, starting from hardware measurement data. An
example analysis evaluates tradeoffs between ET system linearity, PA efficiency, and
EM requirements for a W-CDMA downlink transmitter.
4.1
Supply Modulation
High-efficiency PA theory and designs described in Chapters 2 and 3 provide significant
improvement in PA efficiency in compressed operation. Efficiency still drops quickly as
output power is reduced and the PA operates in an ever-more linear regime. Amplitudemodulated signals such as W-CDMA have probability distributions weighted far away
from maximum output power, resulting in inefficient operation at the average power
level. Fig. 4.2 shows PA performance over instantaneous output power along with the
PDF for a typical 8 dB PAR W-CDMA test signal. For example, the blue line with
square markers of Fig. 4.2 shows PAE for a class AB 120-W PA based on a GaN HEMT
transistor at 2.14 GHz. The PA has over 60% PAE near the maximum output power,
but efficiency falls quickly as power level decreases. The average power of the 8 dB PAR
W-CDMA signal is produced with less than 25% PAE.
100
Power Added Efficiency [%]
70
60
50
Vdd : 32V
Vdd : 28V
Vdd : 24V
Vdd : 20V
40
Vdd : 16V
30
Vdd : 8 V
20
Mantain high PAE over dynamic range
with drain voltage variation
Vdd : 12V
8dB PAR
WCDMA PDF
8dB PAR
10
0
20
25
30
35
40
Output Power [dBm]
45
50
Figure 4.2: Measured efficiency vs. output power for varying drain voltage for a
2.14 GHz class AB PA prototype. The PDF of an 8 dB PAR W-CDMA signal is shown
in the PDF bar plot.
The solid lines of Fig. 4.2 show PA performance at varying drain supply voltage
levels, indicating that the average power level of 42 dBm could be produced with 50%
PAE if voltage were reduced to only 12 V. Supply modulation techniques aim to continuously vary drain supply voltage, maintaining efficient saturated PA operation over
a wide range of output power levels as shown by the dashed red line in Fig. 4.2.
The first application of supply modulation was introduced by Kahn [19] in 1952 in
the form of EER, described earlier in this thesis. Kahn, along with many other authors
(e.g. [1] [95]), viewed supply modulation as a method for restoring amplitude linearity
to efficient, nonlinear PAs. By contrast, the ET technique used in this work begins
with a fundamentally linear PA. Supply modulation is applied to achieve efficient PA
operation at the expense of linearity. Digital techniques are developed and applied to
restore system linearity. Classical EER supply modulation also does not make use of
input power level modulation. The heavy drive required to achieve saturation at peak
output power causes distortion and wasted input power at low output power levels. For
high-PAR signals, and also when the signal is required to instantaneously achieve near
101
zero output power, some level of drive modulation is desirable [20].
Nomenclature in the literature is somewhat inconsistent and many authors choose
new names for similar concepts. The definition of envelope tracking used here is based
on several excellent and leading references ([96] [21] [28] [10] [97]): Drain voltage of a
fundamentally linear PA is varied to maintain saturation and to improve modulated PA
efficiency.
A great deal of work has been done in this area with varying modulation types,
output power levels, center frequencies, and device technologies. Each application poses
unique challenges to different parts of the system. For example, a low-power application
at X-band with narrowband modulation [23] will naturally involve smaller EM voltage
and current swings, easing that aspect of the EM design task. However, high-frequency
efficient PA design and integration into the system is a larger challenge than at lower
frequencies.
In this work the target application is a W-CDMA downlink transmitter with 10200 W peak output power at 2.14 GHz. The combination of power level, modulation
signal, frequency, and stringent linearity requirements create major challenges in all
three aspects of the ET system:
RF – High power relative to the center frequency requires new high-efficiency techniques
described in Chapters 2 and 3,
Analog and Power Electronics – High-PAR signal and high peak drain voltage and
current requirements demand new EM architectures and careful attention to the
EM-PA interface, and
Signal Processing – Linearity requirements force the use of new and more complex
correction algorithms and high signal bandwidth requires a high degree of timing
precision.
Transmitters with similar requirements have been investigated in the literature [29]
102
[30] [31] with excellent results. This thesis work takes a system-level approach to the
problem, contributing an ET framework and system simulation tool used to analyze
the impact of component performance on system performance. The signal split concept
proves useful for trading PA performance with EM linearity requirements, resulting in
new transmitter architectures.
Fig. 4.1 is a highly simplified block diagram of the system implemented in this
work. As in Chapter 1, variables beneath a tilde (e.g. ỹ[n]) indicate complex vectors.
Variables such as α[n] indicate discrete digital signals while v(t) indicates continuous
analog signals. A desired signal ỹ[n] is used to create digital drain voltage α[n] and
complex baseband β̃[n] components. Many combinations of α[n] and |β̃[n]| exist which
would produce the required output magnitude, each with a different impact on insertion
phase and PA efficiency. The signal split defines the combinations of α[n] and |β̃[n]|
which should be used to obtain a desired output power and can be designed to maximize
PA efficiency or EM efficiency. The PA insertion phase for each output power level is
known, and the signal split pre-corrects β̃[n] to maintain constant PA insertion phase.
A wide range of dynamic distortion mechanisms accompany the static distortion
(insertion gain and phase variation) incurred by varying the PA drain voltage. Digital
techniques will be introduced in Chapter 5 to identify and deal with dynamic issues.
4.2
Envelope Modulator
While design of the EM hardware is outside the scope of this work, some level of understanding is crucial for system integration. At the system level it is easy to optimize for
high PA efficiency without regard for the impact on EM efficiency or linearity requirements. As in PA design, linearity and efficiency are continually opposed in EM design.
It is clear from the simple block diagram of Fig. 4.1 that distortion in the EM will
impact system linearity to some degree. The simulation tool described in this chapter
103
is used to determine the level of EM distortion which can be tolerated in exchange for
EM efficiency. The ability to account for EM operation and design tradeoffs is critical
in achieving a high-performance ET system.
Design of the many EM prototypes used throughout this work was performed by
collaborators in the field of analog and power electronics - primarily Mr. Mark Norris, a
Ph.D. candidate at the time studying under Prof. Dragan Maksimović at the Colorado
Power Electronics Center (CoPEC). If there is only one point made in this chapter, it
should be that design of ET components cannot be done in isolation. Analog, RF, and
system engineers must effectively communicate the challenges, limitations, and tradeoffs
in their design tasks to achieve a high-performance system.
4.2.1
EM Requirements for Linearity
The EM is generally responsible for amplifying a voltage waveform, but more specifically:
• with a certain minimum and maximum output voltage level,
• with flat gain and insertion phase over a specified bandwidth,
• with given maximum short- and long-term slew rates, and
• while driving a time-varying load.
The first and second requirements are opposed due to the same problem facing highfrequency high-power RF devices: realizable high-power devices incur large capacitance,
limiting maximum speed. High-speed processes and off-the-shelf parts are limited in
voltage and power handling capability. For example, many components offer to 36 V
maximum supply rails and require several volts of headroom to maintain linearity, incurring a 30 V output dynamic range voltage. Architecture may allow a DC offset to
be applied to the output voltage range to allow higher peak voltages at the expense of
higher minimum voltage. The maximum and minimum drain voltages available to the
PA impact PA efficiency (shown later in this chapter).
104
Many analog applications intentionally make use of gain peaking to extend bandwidth, but in this case a flat EM gain is desired to maintain Vdd linearity (and thus
system linearity). In Chapter 5 flat EM gain and group delay are achieved using a linear
equalizer, allowing the hardware to retain the extended bandwidth associated with gain
peaking.
Bandwidth and frequency response are small-signal measurements, only valid for
purely linear operation. For example, inadequate bandwidth can be observed by increasing the frequency of a very low-amplitude input sine wave and watching the output
waveform decrease in amplitude as gain rolls off. Slew rate, conversely, is a measurement
of large-signal phenomena. As an example, a fast voltage ramp into a low-impedance
load may deplete the charge stored in EM decoupling capacitors, causing the EM supply
voltage rail to dip. The resulting output signal distortion is the result of inadequate slew
rate capability. A wide variety of complex transistor, component, and circuit problems
can be responsible for this type of behavior.
Bandwidth and dynamic performance requirements for an EM cannot be estimated
based on the bandwidth of the complex modulation. Some references generalize that
EM bandwidth should be 3x-5x the modulation bandwidth. Instead, the required EM
bandwidth is related to the bandwidth of the amplitude of the complex modulation.
GMSK1 modulation with 4 MHz double-sided complex modulation bandwidth has a
constant amplitude, with 0 KHz modulation bandwidth. In this case the EM must
have bandwidth equal to “0x” the complex modulation bandwidth (no EM is required),
showing the 3x-5x rule to be faulty. Conversely, consider the spectrum of the four-tone
signal shown in Fig. 4.3.
Though the in-phase and quadrature components are nicely band-limited to 4 MHz
(double-sided, just as the GMSK signal) note that the amplitude component has frequency components extending far beyond that bandwidth, so the degree of amplitude
1
Gaussian multiple shift keying
105
Power Spectral Density [dB/Hz]
0
Amplitude
In-Phase Component
-20
Quadrature Component
-40
-60
-80
-100
0
5
10
Frequency [MHz]
15
20
Figure 4.3: PSD of the in-phase, quadrature, and amplitude components of a four-tone
signal.
bandwidth expansion depends upon the structure of the modulation. Complex modulation signals with amplitude passing through zero will have sharp amplitude nulls in the
time-domain; amplitude quickly descends to zero before instantly changing direction
and increasing toward a peak. This feature can be observed in the time-domain plot
of W-CDMA amplitude shown in Fig. 1.6. The PSD of the in-phase, quadrature, and
amplitude components is shown in Fig. 4.4. More than 85% of the spectral power of the
W-CDMA amplitude signal is concentrated below 300 kHz, and the higher-frequency
portion of the signal has significant content beyond the in-phase or quadrature component bandwidth.
The signal split applies a nonlinear transformation to this waveform (described in
more detail later in this chapter), changing its time-domain characteristics and further
complicating the issue. The waveform bandwidth may be either expanded or condensed
depending upon the design of the signal split. Therefore, the required EM bandwidth
and dynamic performance is not straightforward to predict, since the input signal depends on both system configuration and modulation signal characteristics.
106
0
Amplitude
In−Phase Component
Quadrature Component
Power Spectral Density [dB]
−10
−20
−30
−40
−50
−60
−70
−80
−90
−100
0
2
4
6
8
10 12 14
Frequency [MHz]
16
18
20
Figure 4.4: PSD of the in-phase, quadrature, and amplitude components of a W-CDMA
downlink signal.
The load driven by the EM (Rdd = Vdd /Idd ) at the PA drain supply terminals is
referred to as the drain resistance, shown in Fig. 4.1. Carefully note that this is not
directly related to the PA load line or any RF impedance and is constant over the RF
cycle by virtue of the RF choke. Rdd varies with PA output power and efficiency as
follows:
Rdd =
V 2 ηd
Vdd
= dd
Idd
Pout
(4.1)
Later in this chapter it will be shown that the variation is dependent upon design of
the signal split.
Consider an op-amp driving a load which steps from 3Ω to 100Ω with a constant
voltage. A small EM output impedance of 1Ω will cause an insignificant voltage division
with a 100Ω load, but will cause a significant voltage error with the 3Ω load. Negative feedback will effectively lower the output impedance, but is subject to frequency
response. Output impedance control is found to have a large impact for high-power
applications where Rdd can easily swing between 3Ω and 100Ω for a reasonably efficient
100 W PA. Therefore output impedance of the EM is kept low over a wide frequency
107
range to limit Vdd error at the PA drain due to voltage division between EM output
impedance and PA load impedance.
The gain and delay of the EM are impacted by more complex mechanisms than can
be discussed in this work. Practical designs optimized for efficiency exhibit changing
behavior with frequency, slew rate, varying DC signal amplitude, varying AC signal
amplitude, DC load, and load variation. Variation in small-signal frequency response
(100 mV peak-peak) at 10 V DC is shown in Fig. 4.5 for three different DC loads. High
gain peaking at 40-50 MHz is used to extend the useful bandwidth and will be flattened
with a digital equalizer in Chapter 5. The equalizer can attenuate the frequency response (to flatten the gain peaking which occurs between 20 MHz to 65 MHz) but has
limited capability for amplifying high-frequency components (as would be necessary
above 65 MHz). After equalization the EM characterized in Fig. 4.5 has about 65 MHz
bandwidth where gain is 31 dBV. The variation with load means that the same linear
equalizer will not provide a good correction under all load conditions.
Gain [dBV]
50
40
30
20
Delay [nsec]
15
10
50Ω
10Ω
5Ω
5
0
10
20
40
30
Frequency [MHz]
50
60 70
Figure 4.5: Measured small-signal frequency response for an EM prototype under varying DC loads. Excitation signal is a frequency chirp of 100 mV with a 10 V DC component.
108
The problem of frequency response variation with load is only one example of the
difficulty of completely specifying EM fidelity requirements. Some level of frequency
response variation under light load will likely provide an acceptably linear ET system. However, the quantitative amount of acceptable variation is system- and signaldependent, and also depends on the other non-idealities simultaneously involved.
EM bandwidth, slew rate, and output impedance required to reproduce the Vdd
signal “accurately enough” to achieve system linearity is a function of the input signal,
the PA behavior, and the signal split. Reduced EM dynamic requirements lead to
improved EM efficiency, but also force a signal split resulting in lower PA efficiency.
The system simulation method presented in this chapter quantifies these relationships.
4.2.2
EM Architecture for Efficiency
ET system efficiency is the ratio of all power consumed to average output power delivered. Therefore EM efficiency must be high to minimize the impact on system efficiency.
Purely linear amplifiers are inherently inefficient and unsuitable for the EM design. The
SMPS2 class of DC-DC converters [65] share much of the same theory as the switching
amplifiers described in Chapter 2 and have high efficiency but low bandwidth and linearity. For example, [22] used an EM comprised of an SMPS with 4.33 MHz switching
frequency and a 1.3 MHz output filter. The transmitter met spectral requirements of
the 270.8 kHz-bandwidth EDGE downlink signal. Similar bandwidth-frequency ratios
for the W-CDMA system in this work would call for SMPS switching frequencies higher
than are practically realizable. The class S EM architecture suggested by Raab et. al.
[95] can be thought of as a pulse-width modulated amplifier with a very high switching
frequency. This technique showed excellent performance in an EER system for using
two-tone modulation signals of up to 150 kHz bandwidth. The W-CDMA signal has RF
bandwidth more than 30 times larger, making the class S design similarly unsuitable
2
switched-mode power supply
109
for use in this work.
Many EM designs in literature utilize a combination of linear and SMPS blocks to
produce high- and low-frequency components. Band separation [98] divides the desired
signal into the two components in the digital realm, while other techniques utilize analog
control of either the SMPS or linear blocks based on performance of the other component. A simplified circuit diagram of the EM used in this work is shown in Fig. 4.6, and
is based on the configuration described in [28].
The linear amplifier provides current to the load through a small sense resistance.
The SMPS controller opens and closes the switch Q1 , ramping inductor current up
and down in an effort to minimize current which must be supplied by the linear amplifier. The SMPS responds slowly with bandwidth on the order of 300 kHz, and the
linear amplifier has very high bandwidth up to perhaps 80 MHz. The simulated waveforms shown in Fig. 4.7 illustrate the SMPS and linear amplifier current contribution
when driving the W-CDMA envelope voltage into a constant resistive load. The SMPS
produces the contents of the signal within its useful bandwidth (shown in red) very ef-
VEM
SMPS
control
Q1
ISMPS
Vdd,in
~
vin
Ilinear
Vdd
Idd
~v
out
Figure 4.6: Block diagram of an EM architecture using a SMPS supplemented by a
linear amplifier.
110
Normalized Amplitude
2.5
2
300kHz SMPS Bandwidth
1.5
1
0.5
0
−0.5
−1
−1.5
0
1
2
3
4
Time [usec]
5
6
5
6
(a)
Normalized Amplitude
2.5
900kHz SMPS Bandwidth
2
1.5
1
0.5
0
−0.5
−1
−1.5
0
1
2
3
4
Time [usec]
(b)
Normalized Amplitude
2.5
2
1.5MHz SMPS Bandwidth
1.5
1
0.5
0
−0.5
−1
−1.5
0
W-CDMA Envelope
SMPS Contribution
Linear Amplifier Contribution
1
2
3
4
5
Time [usec]
6
(c)
Figure 4.7: Ideal W-CDMA envelope and simulation of SMPS and linear amplifier
components considering three different SMPS bandwidths. Vertical scale is normalized
to the RMS value of the ideal W-CDMA envelope.
111
ficiently, while the linear amplifier contribution (shown in blue) provides the difference
between the SMPS output and the desired output. As the SMPS bandwidth increases
less low-efficiency linear amplifier correction (blue) is required to achieve the desired
output waveform. However, high-bandwith SMPS design also results in reduced SMPS
efficiency; optimal design of a SMPS-linear EM requires careful investigation of these
tradeoffs in order.
Depending upon implementation, SMPS efficient may be more than 90% while the
linear amplifier is only 30% efficient. Thus, high-frequency content is produced much
less efficiently than is low-frequency content. Fortunately, about 85% of the W-CDMA
envelope energy is concentrated below 300 kHz as shown in Fig. 4.4, and can be reproduced by the efficient SMPS.
If the SMPS sources less of the required dynamic current peak linear amplifier current
requirements are increased. Higher peak current requires a more capable linear amplifier
design. The larger linear amplifier will dissipate more quiescent current, degrading EM
efficiency. In the same way, increased EM linearity can be gained at the expense of a
more powerful, inefficient, linear amplifier design. These decisions are made at design
time, and cannot be easily scaled or modified during operation. The goal of ET system
simulation tool is to determine at design time what type and amount of EM nonlinearity
can be allowed at the system level in exchange for additional EM efficiency.
4.2.3
EM-PA Interface
Impedance between the EM output and PA drain cause distortion in the output voltage waveform with varying current, similar to the effect of non-zero op-amp output
impedance. In early experiments the EM and PA were connected with a BNC cable,
which was later found to be the source of significant Vdd distortion. Resistance and
inductance of a cable connecting the two incurs a significant system linearity penalty,
so a double-row 100-mil-pitch header is used to connect the PA and EM [43] to minimize
112
interconnect impedance. The pulsed-power measurement circuit board is connected to
the PA using such a connector in Fig. 3.31. Additionally, the EM feedback loop sense
point was placed on the PA side of the interconnect so that the closed loop gain of the
linear amplifier rejects some Vdd distortion caused by the interconnect impedance.
A traditional PA bias tee includes significant bypass capacitance which provides a
low-frequency termination, enhancing PA stability. The EM cannot be made to efficiently drive a large capacitance at a high speed, so the bias tee capacitance must be
eliminated. Fortunately, the EM provides a low output impedance over a range of low
frequencies, emulating the low-impedance low-frequency termination of a traditional
PA bias network. PA bias networks for ET application is discussed further in the next
section.
In the linearized system, even insertion of a current probe to measure instantaneous
current results in a decrease of ACP1 from -52 dBc to -43 dBc, indicating a significant
change in instantaneous drain voltage, though average RF output power remains constant. Inability to measure drain current without impacting system linearity makes it
difficult to gauge EM efficiency under real ET conditions and emphasizes the importance
of a low-impedance interconnect.
4.3
Power Amplifiers for Envelope Tracking
Chapters 2 and 3 described theory and design of PAs for CW and pulsed applications.
Like most PA designs, these applications have fixed drain supply voltage, constant
quiescent current, and some static thermal load. ET operation changes many of these
assumptions and requires a new PA design method for optimal ET efficiency. It is
impossible to predict how an RF transistor will perform in an ET system based upon
characterization in standard conditions. An RF transistor datasheet performance and
suggested application circuit is optimized for a specific modulation or pulsed mode of
113
operation, almost certainly not the ET mode of operation.
The next chapter will compare a standard drive-modulated PA to the same PA
operated in ET mode, showing that power dissipated in the transistor drops from 19.8 W
to only 2.7 W. The transistor thermal load is only 13.6% of that which the transistor was
designed for, leading to improved RF performance. Reduced thermal load requirements
also opens possibilities for the design of ET-application-specific microwave transistors,
which could be optimized for higher power, efficiency, or breakdown voltage in the
absence of a heavy class AB-type thermal load.
4.3.1
ET PA Theory and Design
Drain supply modulation modifies the load line of a class AB PA as shown in Fig. 4.8.
When Vdd is maximum at 32 V the transistor operates in cutoff for a significant fraction
of the RF period, providing the class AB boost in peak efficiency. As Vdd is reduced the
output power is reduced, along with the required drive level. Recall that the theoretical
load line depends upon Vdd , and thus can only be optimized at one point in the Vdd
range. Some efficiency at the infrequent high-Vdd levels may be sacrificed for an efficiency
i ds
I max
v gs
I dq
Vk
Vdd= 8V
16V 24V
32V
v gs=Vpinch
v ds
Vbreak
Figure 4.8: Load lines notionally corresponding to varying drain voltage and input drive
levels of Fig. 4.2.
114
enhancement at the more frequent low-Vdd levels. As an approximation, [29] suggests
that the PA be designed for maximum efficiency at the RMS voltage of the expected
Vdd waveform. More generally, the design should achieve the efficiency vs. drain voltage
profile which most reduces PA power dissipation given signal statistics.
The knee voltage of many high-power devices is significant compared to nominal
drain supply voltage as shown in Table 3.2 and becomes a major factor in ET mode.
As Vdd is reduced very little output power can be produced without running into the
knee voltage region, corresponding to low gain or even attenuation at low drain voltage.
From a PAE standpoint it does not, therefore, make sense to use Vdd values lower than,
or even near to the knee voltage to produce low output power.
Full control of the amplitude through drain voltage is used in the EER technique, but
does not provide any benefit for signals with high linearity requirements and significant
low-power output power distribution. Instead, amplification of small signals is done
with the minimum, or “troughing,” drain supply voltage. The PA must be designed
with a load line that preserves a significant small-signal gain at low Vdd .
The issue is more complex when considering harmonic-tuned and switched-mode PA
design. Output capacitance is of critical importance in correct harmonic termination
and varies with drain supply voltage [54]. Fortunately for the class E case, ZE remains
constant over drain voltage, though class E operation is only realized while the device is
saturated (operating like a switch). Switched-mode class E lacks the small-signal gain
required for this application and is not considered in this ET application.
As in Chapter 3, load-pull characterization was used to facilitate PA design. The
Nitronex NPT25100 transistor is a GaN on Si HEMT transistor designed to produce
125 W at 3 dB gain compression between 2.1 GHz and 2.7 GHz. The device has internal
input prematching only, output capacitance of about 17 pF, and is designed for operation
up to 32 V drain supply in class AB operation. The harmonic termination feasibility
analysis described in Chapter 3 was performed to determine that the packaged device is
115
not a good candidate for harmonic-tuned PA design. The part was evaluated for class
AB operation at many drain voltages under pulsed conditions, resulting in the load-pull
contours of Fig. 4.9.
In ET configuration only one load impedance must be selected which is a good
compromise of performance over all drain voltage levels. The gain at the troughing
drain voltage is important, so a 12 V gain contour is shown in green. Between minimum
and maximum Vdd , compressed drain efficiency determines PA efficiency because the
ET drive power will be controlled at each point to achieve compressed operation. Drain
efficiency was measured with input power sufficient to achieve a consistent level of
gain compression (as described in Chapter 3), resulting in blue, magenta, maroon, and
red contours at 12 V, 24 V, 32 V, and 40 V, respectively. Finally, output power at the
maximum output voltage will determine the ET system peak envelope power capability,
and is shown in black contours.
Based on this data, a matching circuit was designed to achieve a fundamental load
impedance of 1.7+j1.5, resulting in near-maximum output power at 40 V, peak efficiency
ηd (40V)
j2Ω
67%
j1Ω
67%
15dB
67%
ηd (32V)
Pout (40V)
50.5dBm
51.5dBm
52.5dBm
ηd (24V)
67%
12dB
Sm
a
Ga ll Sig
in ( na
12V l
)
-j1Ω
j5Ω
5Ω
ηd (12V)
5Ω Smith Chart
Figure 4.9: Summary of measured load-pull data for designing a PA for ET operation,
shown for the Nitronex NPT25100 GaN HEMT at plane P3.
116
near 24 V, and greater than 13 dB small-signal gain at 12 V. This design varies from
the traditional PA designed for peak power, peak efficiency, or maximum gain at a
single drain voltage. The resulting class AB prototype in Fig. 4.10 was constructed
and measured under pulsed conditions resulting in the PAE vs. output power plot of
Fig. 4.2.
4.3.2
ET PA Bias Network
PA designs for ET application require non-standard bias network design [43]. Many
PA bias tees implement the RF choke as a large-valued inductor, providing a high
impedance over a relatively broad bandwidth. However, such an inductor has significant
impedance at the envelope bandwidth, adding a voltage drop proportional to current
slope. PAs for ET application therefore must use a narrowband RF choke. Such a
choke is implemented in this work as a quarter-wave transmission line shorted at the
drain supply side by a capacitor resonant at the fundamental frequency (as shown in
Fig. 4.10). At the transistor drain the quarter-wave transmission line appears to be an
Figure 4.10: Photograph of the 100 W class AB PA prototype designed for ET applications using the Nitronex NPT25100 GaN HEMT, shown here connected to the
pulse-power measurement board in place of an EM.
117
open at the fundamental frequency and odd harmonics thereof, but presents negligible
impedance at the envelope bandwidth.
A traditional bias tee also makes use of a bank of large shunt capacitors on the
drain supply side to present low impedance at the envelope bandwidth, enhancing lowfrequency stability. In an ET application the EM would be forced to drive the bias tee
capacitance in parallel with the RF transistor, leading to high capacitor power losses,
low EM efficiency, and dramatically reduced EM bandwidth. In the ET application
the capacitance is removed. Recall that the EM output impedance is ideally low over a
bandwidth much larger than the envelope bandwidth, and thus presents a low impedance
to the RF transistor at low frequencies just as the bank of capacitors had previously.
The stabilizing effect has been observed when a PA for ET applications (lacking bias
network bypass capacitance) exhibits low-frequency oscillation when connected to a
standard DC drain supply, but is stable when connected to an EM drain supply.
The PA of Fig. 4.10 is designed for ET operation but being measured in pulsed RF
power mode using a constant DC supply. Note the quarter-wave line and fundamentalfrequency-resonant capacitor at the drain supply side of the line. Without the EM
present, additional shunt capacitance is used for stability and to keep the drain voltage
from sagging or ringing when a current pulse is drawn. In ET mode the pulsed-RF
measurement circuit is replaced with an EM prototype, and all capacitors are removed
from the drain bias network except for the fundamental-frequency-resonant capacitor.
4.3.3
ET PA Characterization
In an ET transmitter the PA acts as a nonlinear combiner of ṽin and Vdd , and the
output signal ṽout is a strong function of both inputs. The gain, insertion phase, and
drain current of the PA must be characterized over Vdd and |ṽin | rather than just the
traditional constant-Vdd input power sweeps. Some methods of characterization are
discussed in literature (e.g. [99], [45]), resulting in plots such as the ones shown in
118
Fig. 4.11 and Fig. 4.12. PA behavior is completely described for every combination of
|ṽin | and Vdd . For example, if an an instant in time the |ṽin | and Vdd are 15 V and 25 V
respectively the PA insertion gain and phase will be 14 dB and 110 degrees while PA
efficiency and drain current will be 58% and 4.2 A.
The impact of a ṽin or Vdd error on ṽout can now be determined. In ET simulations
this data set will be used as a static 2-d look-up table (LUT) model for PA behavior.
This static measurement method reflects PA behavior under pulsed operating conditions faster than the thermal time constant of the device. As the pulse becomes longer
heat builds up in the device, raising junction temperature and reducing output power,
gain, and efficiency. In this measurement the pulse was set to be short enough that
no degradation in transistor performance could be observed over the pulse duration.
Therefore dynamics due to thermal loading, charge storage, and other PA memory effects [100] are isolated from static behavior, leading to a memoryless PA model. In this
way ET system dynamics can be analyzed separately from PA dynamics. Chapter 5
will address sources and mitigation of dynamic distortion.
As noted in the introduction to this section, the measurement conditions are critical
to correctly evaluate PA performance. The thermal conditions for pulsed-RF (constantVdd ) operation are meant to approximate conditions of ET operation. However, in ET
operation quiescent current is continually varying with drain supply voltage, resulting
in a different (likely lower) thermal load. This characterization data will, therefore, not
predict absolute PA performance in ET mode, but will prove a useful tool in determining
trends and evaluating sensitivity to distortion in the Vdd and ṽin paths.
A second characterization method was also employed to pulse both the RF input
power and the DC drain supply voltage. By reducing Vdd between RF pulses (called
pulsed-RF/DC measurement) the measurement conditions are brought closer to those
of a real ET system. This method requires equipment capable of providing large voltage
and current pulses; an EM is the ideal drain supply pulse generator. Output impedance
119
PA Insertion Gain [dB] and Phase [deg]
30
14dB
15dB
120°
12dB
Vdd [V]
25
110°
20
9dB
100°
15
5dB
90°
10
5
10
15
~
|vin | [V]
20
25
Figure 4.11: Gain and insertion phase for the NPT25100-based PA prototype measured
over a matrix of input and drain voltage measured in pulsed-RF mode biased with
600 mA quiescent current.
PA PAE [%] and Drain Current [A]
30
5%
40%
[V]
5A
60%
25
20
V
dd
6A
55%
3.5A
15
10
0.5A
5
40%
2A
10
15
~
|vi n| [V]
20
25
Figure 4.12: Drain current and PAE for the NPT25100-based PA prototype measured
over a matrix of input and drain voltage measured in pulsed-RF mode biased with
600 mA quiescent current.
120
of the EM must be very low to maintain output voltage in the presence of large drain
current when the RF pulse begins (slightly after the Vdd pulse begins). Measurements of
this type were collected for the prototype presented in Chapter 5, used in simulations,
and are compared to system efficiency measurements in that chapter as well.
Fig. 4.13 shows simulated contours of transistor PAE over a range of output power
levels for varying drain voltages. Simulation was performed using the Angelov largesignal nonlinear model available from Nitronex for the NPT25100 GaN HEMT. The top
plot includes self-heating effects and the bottom plot ignores heating effects.
In this model self-heating applies a thermal load as though the device were in steady
state (CW) operation. When self-heating is turned off the nonlinear model operates as
though the device is at room temperature. Pulsed-RF operation is close to zero self
heating performance, but still incurs the thermal load of quiescent bias current. PulsedRF/DC is even closer to the zero self heating case, as the quiescent current is eliminated
between pulses. Pulses close together will still cause a temperature rise, but not so
significant as the pulsed-RF or CW operation modes. The ET mode of operation falls
between pulsed-RF and pulsed-RF/DC operation, as some reduced quiescent current
(due to reduced drain voltage) is present even when output power is low.
Note the significant performance change in simulation due to thermal effects. When
self-heating is considered the device is output-power-limited at 100 W, but in the absence
of the thermal load an additional 2.6 dB, or 180%, more output power is possible from
the same device, along with an appreciable increase in low-voltage gain and efficiency.
Clearly, the mode of operation (CW, pulsed, or ET) will have a dramatic impact on PA
performance. Very different performance should be expected from the same transistor
operated in class AB CW, drive modulated, Doherty, and ET configurations.
121
Vdd [V]
35
60
30
50
25
40
20
30
15
20
10
10
5
20
40
60
80
|v~out| [V]
100
120
0
PAE [%]
(a)
60
Vdd [V]
35
30
50
25
40
20
30
15
20
10
10
5
20
40
60
80
|v~out| [V]
100
120
0
PAE [%]
(b)
Figure 4.13: Comparison of simulated output power and efficiency over drain voltage
with (a) and without (b) self-heating effects for a PA using the NPT25100 GaN HEMT
transistor.
4.4
Signal Split
The ET transmitter can be optimized for PA efficiency using the signal split to vary
Vdd to operate the transistor along the dashed line in Fig. 4.2 with 50% efficiency at
the average output power level. However, the PA is not the only component in an
122
ET transmitter, and highest PA efficiency does not necessarily translate to highest
transmitter efficiency. It is clear from previous discussions of EM architecture that
increased EM dynamic requirements translate to lower EM efficiency. It will be shown
that the improving PA efficiency leads to increased EM dynamic requirements. Thus a
tradeoff exists between EM efficiency and PA efficiency.
Classical EER systems sets Vdd equal to the signal envelope amplitude, sacrificing
system linearity, EM efficiency, and PA gain at the lower envelope power levels. In
Fig. 4.14 the colored gradient shows measured PA efficiency for all |ṽout | levels at every
possible Vdd for the 100-W class AB PA prototype of Fig. 4.10. Note that as |ṽout |
increases a minimum level of Vdd is required, below which |ṽout | cannot be achieved.
Three Vdd trajectories, denoted T1, T2, and T3, achieve different modulated PA
efficiencies as summarized in Table 4.1. These trajectories describe the Vdd value that
should be applied when the desired output signal ṽout has a given magnitude. The
60
25
50
20
40
Vdd [V]
30
15
Vtrough = 12V
Vtrough = 10V
Vtrough = 8V
30
10
T1
T2
T3
5
0
20
10
0
10
20
30
40
50 60 70
|v~out |[V]
80
90 100 PAE [%]
Figure 4.14: Measured PAE for the 120-W class AB PA prototype shown in colored
contours over a range of output voltage levels for a range of drain voltage levels. Three
possible Vdd trajectories are shown.
123
Table 4.1: Expected average PA efficiency for three signal split trajectories.
Signal
Split
PA
PAE
T1
T2
T3
50.6 %
47.5 %
43.4 %
minimum, or “troughing,” voltage for a trajectory is called Vtrough . Each trajectory
presents a different tradeoff between PA efficiency and EM dynamic requirements. For
example, T1 has a lower troughing voltage and a sharper inflection point, presenting a
challenge to the EM which must produce higher bandwidth voltage waveforms over a
wider voltage dynamic range. In exchange for the more difficult EM requirement the
PA operates in a high-efficiency region over a larger dynamic range, increasing average
PA efficiency. By contrast, T3 requires less EM dynamic capability (a more efficient
EM design is possible) at the expense of high-efficiency PA operation at reduced output
power levels.
Fig. 4.15 shows estimated PA insertion gain and phase variation for each trajectory
based on measured PA characterization data. These curves are digitally implemented
by the signal split as a transfer function ỹ → β̃ to produce a pre-corrected ṽin which
restores system linearity. This transformation is analogous to the memoryless predistortion used in [29]. Fig. 4.15 also shows the change in PA drain resistance (EM
load resistance) for each trajectory. T1 is associated with the largest first derivative of
the drain resistance, and thus the most difficult dynamic load regulation challenge to
the EM. Stated another way, T1 requires low EM output impedance over the broadest
bandwidth.
Each trajectory defines a different time domain Vdd and ṽin waveform for a given
W-CDMA signal, placing new requirements on the RF up-conversion chain and EM.
Changing bandwidth, slew rate, voltage range, and average load requirements will have
124
~
|v~i n | [V], < vi n [deg], Rd d [Ω]
30
T1
T2
T3
<v~in
25
20
|v~in |
15
10
5
0
Rdd
0
20
40
60
|v~out | [V]
80
100
Figure 4.15: Projected ṽin and Rdd trajectories based on measured PA data for three
signal split Vdd trajectories.
an impact on maximum possible EM design efficiency, which may entirely negate the
increase in PA efficiency. Based on the relationships of Fig. 4.15, Vdd , |ṽin |, and Rdd
waveforms can be projected given an ideal W-CDMA signal. The resulting time-domain
waveforms are shown in Fig. 4.16. Note how quickly the load changes from only 5Ω to
45Ω in Fig. 4.16(c) and how variation in the signal split can change the shape of Vdd ,
|ṽin |, and Rdd waveforms, impacting frequency content and amplitude distribution of
each.
Error in the EM output waveform Vdd will cause variation in the PA output ṽout
which has not been pre-compensated by the signal split, resulting in ET system distortion. The plot of Fig. 4.17 shows contours for the ratio of %4|ṽout |: %4Vdd , or
Vdd → ṽout sensitivity. The red region indicates that a 1% Vdd error corresponds to a
1% |ṽout | error.
An interesting observation can be made from the sensitivity plot of Fig. 4.17 with
regard to bias line memory effects in traditional PAs [100]. A common cause of memory effects in traditional drive-modulated power amplifiers is inadequate drain supply
125
35
T1
T2
T3
30
Vdd [V]
25
20
15
T3
10
T1
5
0
0
0.5
1
1.5
2
2.5
3
Time [usec]
3.5
4
4.5
5
(a)
25
T1
T2
T3
20
|v~in| [V]
15
10
T1
5
T3
0
0
0.5
1
1.5
2
2.5
3
Time [usec]
3.5
4
4.5
5
4
4.5
5
(b)
50
T1
T2
45
40
T3
Rdd [Ω]
35
30
25
20
15
T3
10
5
0
T1
0
0.5
1
1.5
2
2.5
3
Time [usec]
3.5
(c)
Figure 4.16: Projected Vdd , |ṽin |, and Rdd time domain waveforms resulting from the
three signal split trajectories of Fig. 4.14 based on measured PA data.
126
1
30
0.9
0.8
25
0.7
Vdd [V]
20
0.6
0.5
15
0.4
10
0.3
0.2
5
0
0.1
0
20
40
60
|vout| [V]
80
100
0
Figure 4.17: Contours calculated from PA characterization data indicating sensitivity
of ṽout to Vdd error. Sensitivity metric is the ratio %4|ṽout |: %4Vdd .
capacitance, resulting in a drain voltage sag when a current spike is demanded by the
PA. Fig. 4.17 demonstrates that, especially at high output power levels, deviation from
nominal drain voltage will bring a significant deviation in the output signal. Variation of output waveform due to supply voltage variation is a problem known to analog
electronics as poor supply rejection ratio.
The signal split (and PA behavior) determine EM design requirements including
small-signal bandwidth, large-signal slew rate, voltage range, load regulation, and efficiency. These requirements impact the following:
• ET system efficiency is defined as ηET = ηEM × ηP A , demanding high EM efficiency;
• High ηP A requires large voltage and current swings, reducing ηEM ;
• Inadequate bandwidth, slew rate, or load regulation will translate through the PA
into ṽout distortion and degrade system linearity.
Increasing bandwidth and slew rate requirements forces the high-bandwidth linear am127
plifier to produce a larger portion of the output power, reducing EM efficiency. EM
efficiency/linearity compromises cannot be easily quantified, as a change in architecture
or technology is often required rather than the adjustment of a load line or quiescent
current. The system analysis tool thus proves very useful in optimizing a simulated
EM design to achieve maximum efficiency while not significantly degrading transmitter
linearity.
4.5
System Analysis Tool
A method has been developed to quantify the impact of component non-idealities
and inter-dependency on the overall ET transmitter linearity (ỹ → z̃) and efficiency
(ηET = ηEM × ηP A ). The method is also useful for design, simulation, and optimization of algorithms by emulating ideal or non-ideal hardware. The method is applied to
evaluation of PA efficiency vs. EM requirements for an ET transmitter.
Each of the components in the previous section has been implemented in a Matlab
simulation environment using the simplified block diagram of Fig. 4.1. A standard WCDMA downlink signal is generated at a 20x oversampling rate, and de-crested to 8 dB
PAR (ỹ[n]), followed by the signal split which produces α[n] and β̃[n] according to one
of the trajectories shown in Fig. 4.4. EM and up-converter models translate α[n] and
β̃[n] into Vdd (t), and ṽin (t). The PA is modeled using the 2-d LUT formed by the data of
Fig. 4.11 and Fig. 4.12. A variety of non-idealities are synthesized to distort Vdd (t) and
ṽin (t). A few examples include DAC quantization, up-converter phase imbalance, EM
group delay, and ADC path frequency response. The impact of component non-ideality
on system efficiency, linearity, and the performance of other components can thus be
easily observed.
A generic EM was modeled using the cascade of a low-pass filter and a slew-rate
limiter (two key limitations in EM design directly opposing ET efficiency). Fig. 4.18
128
shows the impact of a 6-MHz Bessel low pass response on an ideal Vdd waveform.
The ideal Vdd waveform of Fig. 4.19 has been processed with a 100 V/µsec slew rate
limiting algorithm followed by a 12-MHz Bessel response. Applying the slew rate before
a band limiting filter removes non-physical high-frequency artifacts of the mathematical
slew-limiting process. The ideal and impaired slew rate is shown in the bottom of
Fig. 4.19.
The filters used in the two previous examples have significant group delay (as does
real EM hardware), but impaired waveforms have been shifted in time to match with
the original waveform with smallest RMS error.
The ideal Vdd (t) signal component was distorted by this EM model for a variety
of different EM bandwidth and EM slew rate impairments and then recombined with
the ṽin (t) signal using the PA model. The ṽout (t) signal linearity was then evaluated
using EVM and ACP. As expected from [35] ACP was found to be the limiting metric.
Fig. 4.20 shows degradation in ET system linearity due exclusively to two specific cases
of EM impairment.
As mentioned in the previous section, increased PA efficiency can be achieved with
an aggressive signal split at the expense of increased EM requirements. The method
described above was used to quantify the EM bandwidth and slew rate performance
required to achieve ET system linearity of -45 dBc ACP and -65 dBc ACP (at which
point the EM has a nearly negligible system linearity impact) with the three signal split
trajectories shown in Fig. 4.14. The simulation noise floor for these simulations due to
quantization, interpolation, and numerical accuracy was less than -69 dBc ACP.
Fig. 4.21 summarizes the resulting EM requirements for each signal split trajectory,
drawing a clear connection between EM component behavior and ET system performance. From a system design perspective we see that signal splits weighted toward
high PA efficiency clearly require higher EM bandwidth, slew rate, and voltage dynamic range (all of which lead to reduced EM efficiency). Summarized in Table 4.2,
129
18
17
Original
Impaired
16
Vdd [V]
15
14
13
12
11
10
0
0.2
0.4
0.6
0.8
Time [µsec]
1
1.2
1.4
Figure 4.18: Ideal and EM-impaired drain voltage waveform for a W-CDMA signal
using signal split trajectory T2 assuming a 6-MHz EM bandwidth limit impairment.
Vdd [V]
30
20
15
10
Slew Rate [V/µsec]
Ideal
Impaired
25
0
0.5
1
1.5
Time [µsec]
2
200
2.5
3
Ideal
Impaired
100
0
−100
−200
0
0.5
1
1.5
Time [µsec]
2
2.5
3
Figure 4.19: Ideal and EM-impaired drain voltage waveform for a W-CDMA signal
using signal split trajectory T2 assuming a 100-V/µsec slew limit impairment.
130
0
18MHz
Bandwidth
Limit
6MHz
Bandwidth
Limit
−30
150V/usec
Slew Rate
Limit
−40
ACP: -65dBc
100V/usec
Slew Rate
Limit
ACP: -45dBc
Power Spectral Density [dBc]
−10
−20
−50
−60
−70
−80
−20
−10
Simulation Noise Floor
0
10
Frequency [MHz]
20
Figure 4.20: Simulated ET system output PSD for a W-CDMA waveform using trajectory T2 from Fig. 4.14 given two non-ideal EM models. Degradation in ACP is due
only to EM non-ideality. The simulation noise floor shown in gray.
EM Maximum Slew Rate [V/usec]
200
ACP=−65dBc
T1
150
ACP=−45dBc
T2
T3
T1
100
T2
T3
50
5
10
15
20
EM Small Signal Bandwidth [MHz]
Figure 4.21: EM bandwidth and slew rate required to meet -45dBc (3GPP minimum
spec) and -65dBc adjacent channel power considering only distortion from the Vdd path
for each of the signal split trajectories shown in Fig. 4.4 are shown.
131
these results give the EM and system designers a starting point for designs and insight
into system-level tradeoffs.
Another useful analysis includes the effects of resistance and inductance in the path
between the EM and PA, which result in current-dependent distortion of the Vdd signal.
Fig. 4.22 and Fig. 4.23 shows the impact of series DC resistance and inductance on ET
system linearity. These simulations were performed using a lower oversampling ratio
and different interpolation technique, resulting in a -54 dBm ACP1 simulation noise
floor.
EM prototypes with frequency-dependent output impedance can be modeled in the
same way. After finite bandwidth and slew rate, output impedance was found in this
work to be the next most dominant source of EM-path distortion. Defining EM linearity
requirements is a much more difficult task than for other analog circuit designs. It
becomes apparent that some types of distortion at some output voltage levels are more
tolerable than others. The ET system analysis method is useful for translating actual
component behavior into system performance.
4.6
Conclusion
General supply modulation was discussed with an emphasis on ET techniques, in which
a fundamentally linear amplifier is used. Requirements, architecture, and typical nonidealities of EM hardware were discussed to provide context for ET system discussion.
New PA design goals were outlined, emphasizing the importance of gain, efficiency, and
Table 4.2: Simulated ET system PA performance and EM requirements.
Signal
Split
PA
PAE
Min./Mean/Max.
Vdd
Min. EM
Bandwidth
Min. EM
Slew Rate
T1
T2
T3
50.6 %
47.5 %
43.4 %
8.0 V / 11.0 V / 31.5 V
10.0 V / 12.3 V / 31.5 V
12.0 V / 14.0 V / 31.5 V
20 MHz
18 MHz
15 MHz
150 V/usec
130 V/usec
110 V/usec
132
ACP1 [dBc]
−40
−45
−50
−55
0
0.1
0.2
0.3
0.4
0.5
EM Interface Resistance [Ω]
0.6
0.7
Figure 4.22: Degradation in ET system ACP1 due to EM-PA interface resistance.
ACP1 [dBc]
−48
−50
−52
−54
−56
0
5
10
15
20
EM Output Inductance [nH]
25
30
Figure 4.23: Degradation in ET system ACP1 due to EM-PA interface inductance.
output power at different points in the Vdd range. Other changes to conventional PA
design include bias network design and special attention to the interface between the PA
and drain supply. The signal split was introduced as a method of trading PA efficiency
and EM requirements and illustrated using an ET system simulation method.
Many other types of analysis are possible using the presented simulation technique.
The bandwidth, slew rate, and output impedance EM models can be replaced with a
more complex mathematical model, a circuit simulation, or even EM prototype measurements. This simulation method has been used extensively by EM design collaborators
with circuit-level Cadence models to validate linearity.
Another use for the simulation method is diagnosis of system distortion in hardware.
Once assembled all components of the ET system contribute unique distortion mecha133
nisms that are mixed together, making it difficult to determine which component is at
fault. The simulation can be driven by measured data from the ET test bench to determine the impact of EM distortion with a perfect PA. The ability to observe the impact
of only one type of distortion (EM, PA, up-converter, driver, etc.) provides insight into
system-level problems. Similarly, a suspected EM distortion mechanism can be added
to the simulation and correlation drawn between the simulated and measured results.
The simulation method has been used as a diagnostic tool in achieving the measured
ET system results in Chapter 5.
Contributions described in this chapter include the following:
• A systematic framework for drive/drain modulated ET transmitters making use
of a “signal split” to trade component performance, resulting in optimal system
efficiency given linearity constraints [45].
• Identification of important design issues and requirements for EM prototypes including bandwidth, slew rate, output impedance, and PA-EM interconnect design
[43].
• Adaptation of traditional PA design techniques discussed in Chapter 3 to PA
design for ET applications. The load-pull procedure is modified to help select a
load impedance achieving gain, efficiency, and power at appropriate points in the
drain voltage range, and the drain bias network is modified to allow fast variation
of drain supply voltage and current [48].
• Pulsed-RF and pulsed-RF/DC characterization methods to emulate PA performance in ET mode over the range of input power and drain voltage, resulting in
data ultimately used for system simulation and signal split configuration [44].
• ET system simulation using custom-designed Matlab software to observe the
impact of component non-idealities on system performance [42]. This method is
134
used by our collaborators in EM prototype design, in hardware integration as a
diagnostic tool, and in the next chapter to design and evaluate signal processing
algorithms.
135
136
Chapter 5
Envelope Tracking System
Integration
Contents
5.1
System Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.2
System Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.3
Final Proof of Concept ET System . . . . . . . . . . . . . . . . . . . . 159
5.4
Conclusion
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
This chapter describes the integration of the EM and PA hardware into an ET
testbed. In addition to the idealized static interaction of an EM and PA described in
Chapter 4, realization of an ET system in hardware requires attention to the following
details:
• calibration of EM output DC voltage level,
• equalization of EM frequency response,
• delay adjustment of ṽin with respect to Vdd at the PA to ensure time alignment,
• adaptation of PA static nonlinear transfer function x̃ → β̃, implemented as a
complex gain LUT1 , and
• correction of PA and system dynamic nonlinear characteristics using polynomialbased digital pre-distortion.
These issues were identified and solutions formulated over the course of a 2-year
integration effort in parallel with EM and PA prototype design. Initial, intermediate,
and final results are presented at the end of this chapter after discussing several key integration and testbed issues. Signal processing techniques are discussed with illustrative
examples taken from various stages of system development. The final proof-of-concept
ET system PAE was 50.6% with greater than 7 dB ACP margin with a W-CDMA 7 dB
PAR test signal at 40 W PEP, and incorporated an optimized PA, and an EM designed
using the static simulation method of Chapter 4.
5.1
System Block Diagram
The ET proof-of-concept system was assembled from commercial test and measurement
equipment and integrated with custom Matlab-based software. This state-of-the-art
testbed was designed to be flexible enough to accommodate a wide range of ET research,
far exceeding the requirements for an implemented ET system. A great deal of time
was dedicated to designing the testbed, which subsequently allowed PA and EM prototype integration, linearization algorithm development, research to identify distortion
mechanisms, and the final proof-of-concept demonstration.
Fig. 5.1 shows a block diagram of the ET proof-of-concept system including signal
(top) and hardware (bottom) block diagrams. Signal processing algorithms are developed and implemented using Matlab. The hardware in the bottom of the block diagram
emulates ideal transmitter up- and down-conversion, A/D, and D/A functionality. Each
piece of equipment was selected specifically for this application, incorporating special1
look-up table
138
ized features required for desired ET testbed functionality (e.g. high-precision waveform
generator time alignment, wide-bandwidth IQ demoduator/digitizer). All testbed hardware functionality is automated using Matlab-based instrument control. The complex
nature of this powerful system makes manual operation difficult, highly error- prone,
and easily leads to damaged equipment or hardware prototypes. The system operates
in batch mode (not real time): a single frame of data is run as a continuous loop until
the capture can be completed, data is analyzed, system parameters are updated, and a
new frame of data is loaded.
5.1.1
Signal Flow
Signal flow through the block diagram proceeds as follows:
• Standard W-CDMA test signals are generated, circularly filtered, de-crested, and
scaled to the desired output power level, resulting in the complex sampled baseband signal ỹ. If the system were perfect, ỹ would be equal to transmitter output
ṽout .
• A polynomial-based DPD algorithm is used to pre-correct dynamic transmitter
distortion (e.g. PA memory effects), resulting in the new, pre-corrected, input
signal x̃. The expansion function weighting vector k̃ describes the DPD behavior
and is adapted to signal type and transmitter distortion signature.
• Desired drain voltage Vdd is represented in the digital domain by α. α is a nonlinear
function of either the original signal ỹ (configuration B) or the pre-distorted signal
x̃ (configuration A). The transfer function is set by the signal split Vdd trajectory
as described in Chapter 4.
• Gain, offset, and linear frequency response corrections account for non-idealities in
the Vdd path. These are applied to α, resulting in the corrected signal α0 required
to obtain calibrated EM output voltage, such that Vdd = α.
139
140
MATLAB
Instrument Communication
y~
y~
Adapt DPD
Coefficients
~
k
Digital
Pre-Distortion
~z
x~
Cfg. A
y~
Signal Split
~
β’
Trigger
Generator
α’
Vdd,awg
Waveform
Generator
v~in,awg
Memory
Clock
Waveform
Generator
IQ
Modulator
Figure 5.1: Block diagram of the ET transmitter system.
RF
Preamplifier
Vdd,in
RF Switch
re( v~in e jωt )
Envelope
Preamplifier
~
g’PA
Adapt LUT
PA
~ ~
|x|→β
~
g’
Signal Split
~
z
~
~
{|y| or |x|}→α
Test and Measurement Equipment, Prototype Hardware
MATLAB Digital Signal Processing
Scale to
Desired PEP
Crest Factor
Reduction
Oversample,
Circular
RRC Filter
WCDMA TM1
Chip Generator
Configuration B
y~
PA
g~PA
~
z
~
β’
Vector
Signal
Analyzer
10MHz
Ref. B
10MHz
Ref. A
in
~v
out
~v
Idd
Vdd
Vdd,in
Oscilloscope
~v Path
out
out
~
vin Path
α’ Vdd Path
~
z=v~out(t-τout)
~v
Capture Time
Alignment
Vdd Path
Equalizer
RF Switch
y~
~
β[n-τEM]
Attenuator
re( ~
vout e jωt )
Adapt Delay
Adjustment
τEM
Delay
Adjustment
Gain/Offset
Correction
Reference Path
Vdd
EM
~
β
α
MATLAB
Instrument Communication
• The signal split in the ṽin path transforms x̃ into β̃, accounting for variations in
the complex PA gain g̃P A , which varies as a function of Vdd and ṽin . β̃ is calculated
as x̃/g̃P A .
• Delay is added to β̃ to account for group delay mismatch between the Vdd and ṽin
paths, resulting in β̃ 0 . The optimal value of delay τEM is determined by iteration
and has sub-sample precision.
• Closely synchronized waveform generators are fed α0 and β̃ 0 , producing analog
voltages Vdd,awg and ṽin,awg . An up-converter modulates ṽin,awg onto an RF carrier. Preamplifiers in both Vdd and ṽin paths bring signals to the expected voltage
and power levels.
• Signal components Vdd and <(ṽin ejωt ) are recombined in the PA to produce the
modulated RF output <(ṽout ejωt ).
• A digitizing oscilloscope captures Vdd,in and Vdd . Idd can be captured to evaluate
performance of EM and PA components individually, but requires use of a current
sense loop which degrades system linearity due to Vdd distortion.
• A VSA2 is used to demodulate and digitize either PA input (ṽin ) or output (ṽout )
signals, selectable using mechanical RF switches.
• All captured signals are sub-sample time aligned to a digital reference signal using
correlation techniques. z̃ is the digital capture of ṽout and used in adaptation
of DPD, signal split, and delay adjustment algorithms. Captured Vdd and Vdd,in
waveforms are used in calibrating the Vdd path gain, offset, and equalizer.
2
vector signal analyzer
141
5.1.2
Peripheral Hardware
In the testbed system commercial TM3 equipment is used to emulate typical transmitter functionality. Power required for these components is not considered when stating
system efficiency (consistent with literature). High-performance TM equipment is employed to control non-ideal effects like quantization, finite sample rate, IQ imbalance,
and distortion, thus limiting the possible sources of distortion. Especially in early stages
of development, there is enough non-ideality inherent in the system without these additional concerns. Non-ideal system effects can be added artificially in the testbed to
evaluate absolute component performance requirements for an embedded implementation.
Signal Generation
In the final testbed system two RS4 AFQ 100B AWGs5 were selected for Vdd and ṽin
path signal generation at up to 300 MSps. The maximum rate far exceeds the typical
sample rates (between 30.72 MSps and 69.12 MSps) used for the single-carrier W-CDMA
work. A specialized synchronization feature was employed to lock the memory clocks
and achieve very precise triggering between the two generators. An RS SMBV100A
signal generator was selected to upconvert the IQ modulation to RF. A highly linear
RF preamplifier with more than 50 W PEP and gain around 55 dB was used in the ṽin
path. Clearly not the choice for an embedded system, these components were selected to
avoid non-ET-related distortion mechanisms. A variable-gain three-stage EM preamplifier was designed using the LM6703 operational amplifier with more than 1.2 GHz
gain-bandwidth product preserve bandwidth. The EM preamplifier also achieves level
shifting to accommodate EM prototypes requiring a bipolar input signal.
3
test and measurement
4
Rohde and Schwarz
5
arbitrary waveform generators
142
In addition to the typical transmitter D/A and upconversion paths, ET architecture
requires an additional D/A channel for the Vdd path. Synchronization between the two
paths must be very repeatable; requirements depend on the signal bandwidth. In the
next section the linearity impact of uncompensated delay between the Vdd and ṽin paths
is shown to be dramatic. This analysis shows that for single-carrier W-CDMA, time
alignment between the two paths should be adjusted with resolution on the order of
500 psec. Thus the drift or jitter in time alignment between the two paths must be
some fraction of that resolution, near 250 psec.
The ṽin path incorporates two mechanical RF switches, allowing ṽin to be routed
to either the PA input or to the VSA. The “reference path” is useful for evaluating
ṽin path linearity and for input power measurement. Care must be taken to avoid
biasing the PA when the switches are in the “reference path” position, as some PA
prototypes are unstable without 50Ω terminations at input and output terminals. The
power attenuator network following the PA has attenuation approximately equal to the
peak PA gain, such that PEP is the same at the VSA for the the PA and reference
paths. Excessive attenuation leads to reduced SNR6 in VSA waveform measurements.
Signal Capture
The RS FSQ was selected with an option for 120 MHz digitizing bandwidth and 14 bits
dynamic range, again exceeding the typical sample rates used for single-carrier work.
SNR was improved by applying frame averaging, in which one long consecutive capture
consists of many repeated loops of the same signal. Digitally captured samples of each
loop will be perfectly time aligned with respect to each other provided one full loop is
comprised of an integer number of samples, allowing for highly precise averaging not
possible with multiple triggered capture events. A deep capture memory and fast data
transfer is therefore an essential VSA feature.
6
signal to noise ratio
143
Especially in early system iterations (before linearization correction) the bandwidth
of ṽout is much larger than that of ṽin , resulting in high Nyquist sampling rates. However, ṽout data acquisition sample rate can be varied depending upon where it is to
be used. Signal split adaptation can be performed with undersampled data, and some
DPD algorithms also allow adaptation using ṽout captured at the Nyquist rate for the
ṽin signal rather than the ṽout signal [101]. Reduced sample rate allows capture of data
over a longer time span, and therefore additional averaging, and is also makes an embedded system more tractable. A digitizing oscilloscope was used to capture signals
associated with the EM. Frame averaging was used in this case as well, and was even
more important given the 8-bit resolution of almost all digitizing oscilloscopes.
Time Reference
A 10-MHz reference signal is commonly used to frequency lock multiple pieces of TM
equipment, forcing all to agree on a common definition of time. In the testbed it is critical that equipment generating and capturing a signal share this definition. Otherwise,
the generator may stretch a 10 msec signal over 10.01 msec though the VSA captures for
only 10.00 msec, missing a portion of the signal. The digitizing oscilloscopes used here
have the ability to supply a 10-MHz reference but cannot lock to an external reference.
The oscilloscope reference is distributed to generators, upconverter, and VSA while the
oscilloscope is used to capture waveforms. The VSA’s more stable 10-MHz reference is
substituted when the VSA is used to capture waveforms.
5.2
System Linearization
This section discusses distortion mechanisms in each part of the transmitter. Signal
processing techniques are selected and adapted to linearize each in the most direct way
and in the correct sequence.
144
5.2.1
Distortion Mechanism Investigation
System distortion is investigated using two methods: (1) experiments on the testbed
making use of test signals designed to emphasize specific distortion sources; and (2)
experiments in the controlled environment of the ET system simulation tool described
in Chapter 4.
For example, the following experiment was used in early work to identify a time
alignment problem: a triangle-shaped amplitude waveform was filtered to remove highbandwidth peaks and used in the Vdd and ṽin paths. When the two waveforms are
misaligned, the Vdd waveform will either lead or lag the ṽin waveform, leading to a
different combination of Vdd and |ṽin | for rising and falling edges of the waveform, and
thus different PA gain. Fig. 5.2 shows this effect for a segment of a W-CDMA waveform
rather than a triangle, but the result is the same.
The use of a filtered triangle waveform reduced the impact of high-bandwidth EM
distortion of a W-CDMA signal that was present due to the EM prototype in use at
the time of this experiment. However, when a signal split is applied with a troughing voltage, Vdd is constant for a portion of the triangle. The varying gain effect of
time misalignment cannot be observed for that portion of the waveform, making the
~ [V]
|v~out| [V] and |y|
100
80
Vtrough < Vdd < Vdd,max
60
~
|y|
~
|vout| with
path delay error
80
60
A
40
40
20
0
100
20
Vdd = Vtrough
0
0.4
0.8
B
1.2
Time [usec]
1.4
1.6
0
1.0
1.2
Time [usec]
1.3
Figure 5.2: Simulated |ỹ| and |ṽout | with a small Vdd -path delay error (left), and close-up
showing how error can be positive or negative for the same expected amplitude in the
presence of Vdd path delay error (right).
145
time alignment algorithm described in [24], and later in this section, unsuitable for ET
applications with large troughing voltage. The diagnostic waveform led to a deeper
understanding of the time delay distortion and also sheds light on a possible solution.
The fact that PA gain varies for rising and falling edges at high amplitude levels (above
Vtrough ) can be used to determine if path time alignment should be advanced or delayed.
In another case the ET system simulation tool was used to determine the source of
system distortion on the testbed. Both the Vdd and ṽin paths exhibited some level of
distortion. The testbed and ET simulation tool were configured to operate identically,
and the Vdd waveform was captured from the testbed. After applying the measured Vdd
waveform in the simulation (assuming an ideal ṽin waveform) similar degradation in the
simulated linearity was noted, pointing to the EM distortion as the dominant source of
the problem. Further ET simulations with bandwidth-limited EM models showed that
simulated and measured Vdd matched, indicating that the measured waveform distortion
was primarily caused by limited EM bandwidth. In this case the ET system analysis tool
proved quite useful in attributing system-level distortion to a component-level problem.
The above examples illustrate only two specific cases of distortion mechanism investigation. Many such experiments were performed in gaining the insight needed to
develop the linearization methods described in the rest of this section.
5.2.2
EM Gain, Offset, and Equalization
The Vdd path includes several analog components, each requiring some level of DC gain
and offset calibration. Correction for the whole path is determined by measuring a
very slow ramp from minimum to maximum drain voltage without Vdd gain and offset
correction. The relationship between measured Vdd and α is linearly fit resulting in gain
and offset calibration factors. These values are not expected to change dramatically
over time, temperature, or operating condition. In the lab environment this calibration
is performed only once for each new EM prototype.
146
Measurement of the frequency response is achieved by driving the Vdd path with a
logarithmic chirp ranging from 1 MHz to 110 MHz. Non-ideal response of the path causes
variation in gain and delay of the EM output signal, as captured by the oscilloscope.
The captured data is first multiplied by the original chirp signal and then multiplied by
the original chirp shifted by 90 degrees and low-pass filtered, yielding an in-phase and
quadrature component of gain at each instant in time.
In this measurement the chirp signal is actually “modulated” by the frequency response of the Vdd path. The modulated chirp signal is down-converted by a “mixer,”
implemented with multiplication by in-phase and quadrature versions of the original
chirp (the carrier signal) followed by a low-pass filter. Frequency variation in time is
combined with amplitude and phase variation in time to yield the frequency response.
The measured response of the Vdd path for a 100 mVpp chirp at 10 Vdc is shown in
Fig. 5.3.
Frequency response in the Vdd path is measured and corrected using an FIR filter
with the inverse response. In some testbed revisions the filter was implemented as a
Gain [dBV]
46
44
Pre-Equalization
42
Post-Equalization
40
38
Relative Delay [nsec]
36
2
0
−2
−4
10
20
30
40
Frequency [MHz]
50
60 70
Figure 5.3: Vdd path frequency response before and after equalization. The linear frequency equalizer makes up a portion of the transfer function α → α0 .
147
feature of the commercial TM signal generator. The corrected response is shown in
Fig. 5.3. The issue of EM frequency response variation with load, power level, and
voltage was mentioned in Chapter 4; this method is used to evaluate EM prototype
hardware at the component level under small- and large-signal excitation, over a range
of DC signal levels and under varying load conditions.
This measurement and correction is only valid for linear frequency response. The
addition of nonlinear distortion results in an invalid measurement and errors in correction frequency response. Note also that the frequency response of the oscilloscope
will cause errors in the correction, but the error is assumed to be insignificant in this
application.
Gain and offset correction are the first step in ET system calibration, followed by
Vdd path linear frequency equalization. As noted in the introduction to this section,
Vdd path error will be corrected to some degree (although with larger computational
complexity) by the system DPD algorithm. Therefore we wish to make the Vdd path as
linear as possible before applying other linearization techniques.
5.2.3
Signal Split
Vdd Signal Path
The Vdd path signal split is selected as a system design parameter, as discussed in Chapter 4, and is not adapted. Configurations A and B shown in the block diagram of Fig. 5.1
allow the Vdd signal to be derived from the desired signal ỹ or the post-DPD signal x̃.
The post-DPD signal x̃ contains broadband anti-distortion components, requiring additional EM bandwidth, while in configuration B the Vdd path input signal properties
remain constant throughout system linearization. Configuration B was preferred for the
final proof-of-concept system. Note that ṽin path signal split adaptation is performed
before DPD adaptation, so for the remainder of this discussion, x̃ = ỹ.
148
ṽin Signal Path
Variation of Vdd causes a change in PA gain and insertion phase (ṽin → ṽout , also called
complex gain g̃P A ). To achieve linear transmitter gain g̃ (ỹ → ṽout ) an adjustment must
therefore be made to each sample of ṽin to account for g̃P A . ỹ is scaled to the desired
output power level, so the ideal PA input signal accounting for Vdd variation is calculated
by β̃ = ỹ/g̃P A . The signal split implements β̃ = ỹ/g̃P0 A where g̃P0 A is the current estimate
of g̃P A . Unfortunately g̃P A is a nonlinear function of the input signal statistics, which are
determined by g̃P0 A . Therefore g̃P0 A must be determined iteratively. When the solution
is accurate, the transmitter gain g̃ becomes unity: ṽout = ỹ ÷ g̃P0 A × gP A = ỹ × g̃.
In a perfectly static (non-time-variant) system, g̃P A should always be the same for
a given level |ỹ|. Therefore the same value of g̃P A can be applied to all values of |ỹ|.
This procedure can be thought of as LUT implementation of static (or memoryless)
predistortion [29]. However, dynamic effects do still exist in the system, as shown by
the plot of complex transmitter gain in Fig. 5.4. Note from the plot that gain drops
with reduced output power level due to the application of reduced Vdd .
The objective of the ṽin path signal split adaptation is therefore to correct for the
average complex gain at each level ỹ. After adaptation the black transfer function
of Fig. 5.4 will still be thick (indicating dynamics have not been corrected), but the
average value of gain and insertion phase at each level ỹ should be unity and zero,
respectively. Dynamic effects will be corrected using other techniques (time alignment,
DPD) in subsequent steps.
Initially the LUT implements a single value of linear gain g̃ for all values of ỹ
and no variation of insertion phase (g̃P0 A = 1∠0◦ for all values of |x̃|). Thus, for this
first iteration the PA gain g̃P A is equal to the measured transmitter gain g̃ as shown
in Fig. 5.4. Signal split adaptation takes place by linear adjustment of the PA gain
estimate: g̃P0 A,next = g̃P0 A,prev /g̃. If the PA had a linear gain characteristic over the
149
Figure 5.4: Measured instantaneous transmitter gain and insertion phase (g̃) after the
first iteration, and the extracted trend used to adapt the estimate of PA gain (g̃P0 A )
used in the second iteration.
whole Vdd and ṽin range only one adaptation would be necessary to set g̃P0 A equal to
g̃P A . However, the PA compression characteristic indicates that as input power rises
gain decreases, making the increase still inadequate to achieve desired output power.
Additionally, PA insertion phase also changes with |ṽin |, requiring further adaptation
to achieve flat insertion phase.
PA gain is highest at PEP and decreases with reduced Vdd , so the initial gain is
set equal to PEP gain. PA gain at low power (and low Vdd ) will be inadequate for
initial iterations, resulting in insufficient output power at those levels, but this practice
avoids applying of too much power resulting in excessive output power or excessive
compression.
Fig. 5.5 shows the adaptation history of the transfer function |ỹ| → β̃, defined by
the inverse of the complex gain estimate g̃P0 A . Note that the last two iterations come
to approximately the same solution, indicating acceptable convergence. The signal split
150
0.04
Adaptation
1
2
3
4
5
6
|β| (|v~in|) [V]
0.03
~
0.02
cted
e
Exp
0.01
0
0
20
40
0
20
40
n
Gai
EP
at P
60
~ [V]
|y|
80
100
60
80
100
~
∆‚β (∆‚v~in) [deg]
15
10
5
0
-5
-10
-15
~ [V]
|y|
Figure 5.5: Adapted |ỹ| → β̃ transfer function after each of six signal split iterations.
aims to eliminate the average PA static nonlinear characteristics. This is a challenge
in the presence of strong dynamic distortion (shown by the thickness of the transfer
function of Fig. 5.4). The dominant source of such dynamic distortion is path time
misalignment between the Vdd and ṽin paths. On the testbed signal split adaptations
are performed until no further improvement can be made due to interference from
dynamic effects. Delay adjustment (described next) is performed next to eliminate the
highest-order source of dynamic distortion, followed by further iterations of signal split
adaptation.
5.2.4
Delay Adjustment
The importance of correct time alignment between Vdd and ṽin paths has been discussed
earlier in this chapter. Delay in the Vdd path is contributed primarily by the EM, and
is between 5 nsec and 15 nsec for the EM prototype hardware used in this work. Some
151
small group delay is also naturally present in the ṽin path, but an adjustment is always
required to synchronize Vdd and ṽin signals at the PA. The absolute amount of differential
delay between a modulated RF and an analog signal cannot be directly measured, so
the correct value is inferred by observing system performance metrics while delay is
varied.
The problem is illustrated in Fig. 5.2 by output from an ET simulation, in which both
PA and EM are ideal and the only source of distortion is a small time alignment error
(Vdd path is slightly advanced with respect to the ṽin path). Recall that Vdd = Vtrough
for low values of |ṽout |, in this case 34 V. Since Vdd does not vary in the low range, delay
mismatch has no effect, but above this value the time-advanced Vdd creates an advance
in |ṽout |. In the close-up (right) note the impact on PA gain error (ṽout /ỹ) at points A
and B. At both points |ỹ|=70 V, but, due to the path alignment error, |ṽout | is lower or
higher than expected, resulting in gain error which changes in time. This type of gain
error is also called dynamic distortion, and contributes directly to the thickness of the
PA transfer function of Fig. 5.4.
Various metrics and methods have been proposed to directly compute the correct
value of delay which must be added to the ṽin path [24]. The method assumes that
the magnitude of ṽout is dominated by the Vdd path and the phase of ṽout is dominated
by the ṽin path. Correlation of |ṽout | with |ỹ| yields an optimal magnitude-component
delay, and correlation of ∠ṽout with ∠ỹ yields an optimal phase-component delay. The
difference between the two delays indicates the error in path time alignment. This
method proves inadequate for the ET system presented in this work, resulting in delay
estimates which degrade final system linearity compared to blind optimization of delay
values. In this ET system it cannot be assumed that the magnitude of ṽout is dominated
by the Vdd path, due to the Vdd troughing region. Therefore the delay value obtained
from correlation of |ṽout | with |ỹ| reflects the best compromise between low- and highvalued ṽout delay.
152
A delay adjustment method was discussed earlier in this section which is based on
PA gain variation for rising and falling edges. That method is still under investigation,
so a less elegant, brute force method is used to obtain the results presented in this
work. Dominant distortion mechanisms mask the impact of corrections to less dramatic
distortion mechanisms. Static nonlinear distortion typically dominates initially, so signal
split adaptations are first performed to achieve coarse system linearity. Path delay
adjustment is then swept through a reasonable range, searching for a minimum in ACP,
as shown in Fig. 5.6.
The delay sweep must be performed after sufficient signal split adaptation, otherwise
the ACP minimum will be very shallow and difficult to identify due to more-dominant
nonlinear distortion. The trend can be fit to a spline and the minimum-delay value
estimated using measurements at only 3-4 delay points, reducing algorithm run-time.
Finally, it is critical that delay adjustment be performed before DPD correction. If
path delay error is present DPD algorithms can provide some correction, though with
significantly more computational overhead.
−40
Channel Power [dBc]
−41
−42
−43
ACP5−
−44
ACP5+
−45
−46
ACP10−
−47
ACP10+
−48
0
2
4
6
8
Relative Delay [nsec]
10
12
Figure 5.6: ET system ACP given varying τEM value.
153
5.2.5
Digital Pre-Distortion
The area of digital pre-distortion encompasses a wide variety of techniques [11], all with
the same goal: to create a digital “inverse” of the PA distortion such that the cascade of
DPD and PA is linear. Fig. 5.7 illustrates this concept by cascading an expanding-gain
DPD
PA
Output [V]
DPD with a compressing-gain PA resulting in a linear overall system.
Input [V]
Figure 5.7: Digital pre-distortion conceptual block diagram and transfer functions.
It turns out that an adaptive static DPD has already been implemented earlier
in this section to account for PA gain variation with Vdd . However, the LUT-based
adaptation and correction used in the ṽin path signal split is limited to correction of
static nonlinearity. The linear equalizer used in the Vdd path is another type of predistortion, in that case limited to linear time invariant distortion. In this work DPD
refers to polynomial-based techniques which can correct dynamic linear and nonlinear
distortion.
Polynomial-based predistorters use a set of weighted expansion functions to synthesize the inverse of the PA transfer function as shown in Fig. 5.8. Expansion functions
are computed based on the desired signal ỹ, weighted, and summed to produce DPD
output x̃. Some representative expansion functions are shown in the figure which account for static nonlinearity (y p [n]), linear frequency response (y[n − m]), and dynamic
nonlinearity. The complete set of these expansion functions is called the Volterra series
[102], and it can describe a general nonlinear time-variant system. Due to complexity,
Volterra series are practical for modeling only weakly nonlinear systems with memory. Transmitter DPD requires careful down-selection of expansion functions to limit
154
~y
Expansion Weighting
Matrix Y
Vector k
~
~
k1
y[n]
~
~
y2[n]
k2
~
~y3[n]
k3
...
~
~y[n-1]
k4
~
~
k5
y[n-2]
~
~
y[n-3]
k6
...
~
~y2[n-1]
k7
~
~
~y[n]·y[n-1]
k8
+
~
k
~
x
PA
~
z
~ ~
k = Z-1·x~
Figure 5.8: General polynomial predistorter with indirect learning.
computational complexity.
PA modeling is concerned with determination of the PA transformation x̃ → z̃. The
DPD transfer function would ideally invert the PA response: ỹ → x̃ = z̃ → x̃. The
indirect learning method [103] is used in this work and shown in the block diagram of
Fig. 5.8. In this method the expansion matrix Z̃ is formed from the PA input and a
weighting vector k̃ calculated to satisfy the relationship Z̃ k̃ = x̃. This combination of
expansion functions and weights is now set to emulate the inverse PA transfer function
z̃ → x̃, and is next implemented in the forward path, applying the same transformation
on ỹ resulting in x̃, the predistorted input signal.
A primary challenge in design and application of DPD algorithms is selection of an
appropriate expansion function set. A small set will be unable to reproduce complex PA
behavior, and a large set becomes computationally intractable. Addition of expansion
functions which do not correctly represent the distortion also dilutes DPD correction
power. The MP7 [104] and DDR8 [105] are two expansion sets used in literature. Both
were investigated in this work, but the final proof-of-concept made use of the DDR
7
memory polynomial
8
dynamic deviation reduction
155
predistorter. The real-valued form of the DDR is shown below.
x[n] =
P
X
kp,0 (0, ..., 0)y p [n]+
p=1
P
X
p=1



p
M
M
r
X
X
X
Y

y p−r [n]
···
kp,r (0, ..., 0, i1 , ..., ir )
y[n − ij ]
r=1
i1 =1
ir =ir−1
(5.1)
j=1
The DDR leaves three degrees of flexibility: P , M , and R. Nonlinear order P determines
the maximum nonlinear order for expansion functions; only odd orders are included.
Memory depth M limits the number of historical expansion functions included in the
model. Long-term memory effects (or dynamic distortion) require high values of M .
This parameter is also dependent upon the selected capture and signal generator sample
rates. High dynamic order R adds terms to bring the polynomial closer to the original
Volterra series, while R = 0 is full reduction to a memoryless power series polynomial.
In this work the useful range for P, M, and R was 3-7, 2-5, and 1-2. Increase in value
of any parameter causes an increase in computational complexity. If model parameters
are set for higher nonlinear order, memory depth, or dynamic order than is present in
the system, the DPD can become overfit. Rather than describing system behavior it
begins to describe the particular dataset.
Expansion functions are defined by the following expression for a first-order dynamic
(R = 1) DDR predistorter, shown in the low-pass equivalent:
P −1
x̃[n] =
M
2 X
X
k̃2h+1,1 (i)|ỹ[n]|2h ỹ[n − i]+
h=0 i=0
P −1
2
M
XX
k̃2h+1,2 (i)|ỹ[n]|2(h−1) ỹ 2 [n]ỹ ∗ [n − i]
(5.2)
h=1 i=1
The decomposed piecewise Volterra series [106] is an extension to the DDR theory that
is especially useful to ET applications. In this work the PA is operated in two fundamentally different modes - linear or saturated - depending upon if the drain voltage is
at or above Vtrough . These modes exhibit different types of dynamic distortion. Rather
than fitting one pre-distorter to both regions this method applies threshold vector de156
composition, splitting the original signal into two components as shown in Fig. 5.9.
A predistorter can be designed for each region with its own expansion functions and
weighting vector. The components are then re-combined to form the full predistorted
signal. Baseband signals are complex, and special attention is required to maintain
phase continuity during signal decomposition and recombination. This method was
applied in the final proof-of-concept system.
DPD is adapted and applied only after all other linearizing corrections have been
made. Using the system simulation tool of Chapter 4 it was determined that an MP
DPD is capable of compensating for a significant delay adjustment error, but requires
additional expansion functions and thus increases computational complexity. As a result
DPD should be disabled before adapting delay adjustment or signal split, and then readapted afterward.
Commercially available DPD implements feedback to continually adapt the weighting vector, responding to changing transmitter operating conditions. Such a DPD solution could integrate the ṽin signal split LUT capability along with the polynomial-based
dynamic correction.
Original Signal
Region 2
Component
Vbreak
Region 1
Component
Time
Figure 5.9: Threshold decomposition of an amplitude-only signal into two components.
157
5.2.6
Circular Signal Generation and Time Alignment
A single frame (10 msec) of W-CDMA chips are generated, oversampled, and filtered
with a root-raised-cosine filter. In the batch-mode system the same frame is continually
repeated, and the capture will likely not begin precisely at the first sample. Therefore
circular convolution is used when filtering so there is no discontinuity between the
amplitude and phase of the last and first samples. A CFR algorithm is applied to
reduce waveform PAR to the desired level (7 dB throughout this chapter) as described
in Chapter 1. In industry and literature PAR is commonly reduced to values ranging
from 6.5 dB to 8 dB depending upon the acceptable level of CFR-induced distortion and
the capability of the CFR algorithm in use. The resulting waveform is the complex
baseband vector ỹ, representing the desired system output.
Note that waveforms captured from the hardware (ṽout , ṽin , Vdd , Idd , and Vin ) are
time aligned with a digital waveform before analysis or use in adaptation. The alignment must have sub-sample precision, which is achieved using Whittaker-Shannon interpolation. This process requires that waveforms be circular, band limited, and Nyquist
sampled and is implemented by circularly convolving the waveform with a shifted sinc
function. In practice, measured waveforms can contain aliasing due to sub-Nyquist sampling. This method continues to provide good results in these cases as well, provided
that the aliased energy is not significant compared to the in-band energy.
5.2.7
Order of Adaptions
Gain, offset, linear equalization, delay adjustment, LUT adaptation, and DPD are all
used to linearize different aspects of the ET system. Each block is carefully placed
in the signal flow and performed in a specific sequence to correct a specific distortion
mechanism. Some techniques can correct multiple mechanisms, linearizing them in an
inefficient way or transforming distortion into a more complex problem.
158
For example, DPD adaptation must be performed last because it has the ability
to correct the simple problem of path time misalignment in a very complex way. The
DPD effectively implements an FIR9 filter to shift the ṽin signal with respect to the
Vdd signal. Several weights for each tap of the filter must be adaptively determined,
and several expansion functions must be calculated for each sample. This use of DPD
increases complexity and reduces its effectiveness for other types of distortion. Instead,
adjustment of a single number - the path time delay adjustment - can be used to fix
this distortion, allowing the DPD to be simplified and to better adapt to the remaining
distortion it was intended to correct.
As another illustration consider a non-ideal, but linear frequency response in the Vdd
path. Normal Vdd variation causes variation in PA gain and insertion phase which are
pre-corrected by the signal split. Frequency-dependent amplitude distortion of Vdd will
cause un-corrected variation in PA gain and insertion phase. Recall from Fig. 4.17 of
Chapter 4 that Vdd distortion causes a different amount of ṽout distortion depending upon
|ṽin | (or rather, depending on the level of gain compression). Therefore, a simple linear
frequency response in the EM path causes ṽout distortion which varies with both Vdd
frequency content and ṽin amplitude. This nonlinear, frequency dependent (dynamic)
distortion can be corrected with a relatively simple linear equalizer (a FIR filter) in the
Vdd path or with a significantly more complex DPD algorithm. Therefore it is important
to make simple corrections in the Vdd path before applying more global techniques with
increased complexity and corrective power.
5.3
Final Proof of Concept ET System
The testbed described above has been used to investigate many EM and PA prototypes
as well as linearization techniques over the course of this work. Results spanning output
9
finite impulse response
159
power level, PAR, linearity, PA technology, and signal type have been measured and
used in development. The measurements presented in this section make use of the
latest design iterations, and represent state-of-the-art ET performance for a 7 dB PAR
W-CDMA signal with 40 W PEP at 2.14 GHz. Final system efficiency is greater than
50% with at least 7 dB ACP linearity margin.
5.3.1
PA and EM Prototype Hardware
The class F−1 PA of Chapter 3 was designed with ET operation in mind. The load
impedance was selected for peak efficiency at 28 V, around 15 dB small signal gain near
the troughing voltage, and 50 W PEP at 36 V using the load-pull contours shown in
Fig. 5.10.
The latest EM prototype available at the time of this testing was designed to operate
between 8 V and 33 V, so maximum system voltage was limited to 32 V and maximum
output power limited to 40 W. Additionally, the EM prototype was designed to provide
400 W peak power to the PA though a maximum around only 50 W was required for this
j10Ω
ain at Vdd=12V
Small Signal G<15dB
>15dB
ηd at Vdd=28V
81%
ηd at Vdd=36V j25Ω
81%
ηd at Vdd=20V
81%
Pout at Vdd=36V
47.0dBm
10Ω
15Ω
47.2dBm
dBm
47.4
5Ω
j15Ω
25Ω
j5Ω
Figure 5.10: Measured load-pull contours for the TGF2023-10 GaN HEMT with class
F−1 harmonic terminations. Efficiency is shown at 20 V, 28 V, and 36 V, small signal
gain is shown at 12 V, and output power is shown at 36 V to facilitate PA design for an
ET application. The black square indicates the load design impedance of 10+j6Ω.
160
test. Design of an EM optimized for the lower power level would reduce EM quiescent
currents and improve EM efficiency. The photograph of Fig. 5.11 shows the final PA
and proprietary EM prototype hardware.
5.3.2
Linearization
The EM prototype gain, phase, and frequency response were first calibrated as discussed earlier in this chapter. Next the PA was characterized under pulsed-RF/DC
conditions using the measurement technique described in Chapter 3. Three Vdd signal
split trajectories were selected for system measurement. PA efficiency and the signal
split trajectories are shown in Fig. 5.12. Trajectories T1, T2, and T3 result in theoretical PAEP A of 75.4%, 71.1%, and 67.1%, respectively for the W-CDMA test signal with
40 W PEP and 7 dB PAR.
Initial adaptation of the ṽin path signal split was successful for trajectories T2 and
T3, but failed for trajectory T1. Notice how T1 comes very close to the edge in Fig. 5.12,
requiring the absolute maximum amount of output power possible at each drain voltage
level. Each successive adaptation of the signal split demanded higher levels of input
power as shown in Fig. 5.5, but the demand was not decreased with each iteration. The
Figure 5.11: Photograph of the final PA prototype connected to the proprietary EM
hardware designed by colleagues in analog and power electronics.
161
Vdd [V]
Vdd=32V
30
70
25
60
20
50
T1
T2
T3
15
T3
|v~in| [V]
10
40
30
T1
T1
5
20
0
T3
0
10
20
30
40
|v~out| [V]
50
60
10
PAEPA
Figure 5.12: Three Vdd trajectories (black) and ṽin trajectories (blue) expected based
on PA characterization data. PAEP A (colored contours) is measured under the pulsedRF/DC condition.
maximum safe input power limit was reached before the ṽin signal split converged. No
system results are available for this test case, but it serves to illustrate the problem of
an overly-aggressive Vdd signal split trajectory.
Delay adjustment was performed, followed by additional signal split adaptations to
minimize static nonlinearity. The DDR predistortion method with threshold decomposition was then used to correct dynamic nonlinearity. Region 1 was defined from 0 V
≤ |ṽin | < 14 V and used a predistorter with parameters P , M , and R set to 5, 4, and
2, respectively. Region 2 was defined from 14 V ≤ |ṽin | < 65 V and used a predistorter
with parameters P , M , and R set to 7, 3, and 1, respectively. The threshold and DPD
parameters were set by manual optimization, but in a real system these parameters will
not change with operating condition or test signal.
Fig. 5.13 shows ET system output PSD at the various stages of linearization with
trajectory T2. Linearized adjacent and alternate channel power levels were lower than
-55 dBc and -57 dBc. Comparison with the -45 dBc and -50 dBc specifications shows a
162
0
Initial
Power Spectral Density [dB]
−10
−20
Initial Signal Split,
Time Alignment
Two-Level
DDR DPD
−30
−40
Final
Signal Split
−50
−60
−70
Reference
2.13
2.14
Frequency [GHz]
2.15
Figure 5.13: ET system output PSD at various stages of linearity correction.
linearity margin of 10 dB for ACP1 and 7 dB for ACP2. Additive EVM was less than
1%. Final linearity performance was not notably different for trajectory T3.
5.3.3
Power and Efficiency Measurements
It was noted in Chapter 3 that high efficiency is difficult to measure precisely due to
uncertainty in RF power and current measurements. The problem is exacerbated here
by output power modulation and the difficulty of measuring Idd . The most precise,
complete, and trustworthy measurements are those of average power at the system level
(including loss in both the PA and EM). For these measurements a wideband RF power
meter was used to measure RF input and output average power, and RMS voltage and
current meters measured power into the EM. Measured average gain was 13.7 dB with
8.47 W output power. System ηd was 52.8%, resulting in a system PAE of 50.6%.
Separate EM and PA efficiency calculation requires measurement of power flowing
between the two components. A heavy-gauge current loop was added between the
163
EM and PA, and the Idd waveform was measured with a 120 MHz-bandwidth current
probe. Making no other changes, the adjacent channel power rose from -55.7 dBc to
-48.3 dBc, indicating a significant degradation in system linearity performance. Under
this condition ηd,P A was 75.9% and PAEP A was 72.3%, and ηEM was 69.1%. Based
on these component efficiency measurements system ηd (calculated ηEM × ηP A ) should
be 52.4%, and system PAE (calculated ηEM ×PAEP A ) should be 50.0%. Given the
extremely close agreement between system efficiency directly measured and calculated
from component efficiency we assume that the component efficiency measurements are
usefully accurate, despite the degradation in system linearity.
As a final comparison the PA was operated with a constant drain voltage supply set
to 32 V. This was the maximum voltage used in the ET case and is near the minimum
required to obtain 40 W PEP. DPD was applied to achieve comparable linearity to the
previously described ET result with the same W-CDMA test signal. While average gain
was higher (nearly 18 dB), PA drain efficiency fell from 72.3% to 30.0%.
A comparison of simulated and measured efficiency for three ET test cases and
the constant-Vdd case is shown in Table 5.1. Note that PA efficiency is consistently
higher in ET mode than was projected by simulation, even though the simulation is
based on measured data. This is due to the change in operating conditions from the
pulsed-RF/DC measurement to ET operation. Reduced quiescent current and dramatically reduced heating produces a change in operating conditions and total efficiency.
Simulated efficiency under constant-Vdd operation is higher than measurement because
Table 5.1: Simulated and measured ηd,P A for ET and constant-Vdd operation.
Trajectory
Simulated ηd,P A
Measured ηd,P A
T1
T2
T3
Vdd =32V
75.4 %
71.1 %
67.1 %
37.2 %
–
75.9 %
71.3 %
30.0 %
164
thermal loading is dramatically higher in constant-Vdd operation than in pulsed-RF/DC
operation.
5.4
Conclusion
A state-of-the-art testbed has been designed for ET research capable of synthesizing the
signal processing, generation, and capture portions of an ET transmitter. The testbed
far exceeds the requirements of an implemented transmitter, limiting possible sources
of distortion to the ET components and providing flexibility in the research direction.
System distortion mechanisms were identified and a system of of linearization techniques
were applied targeting each mechanism, along with a method to most efficiently adapt
the corrections.
The testbed and linearization algorithms were developed in parallel with PA and
EM prototypes over the course of approximately two years. Many useful discoveries
were only possible by integration of hardware, making the early EM and PA prototypes
valuable learning tools despite their inefficiency. Hardware and system configurations
can be grouped into one of four configurations:
Initial Proof-of-Concept A 45-W PEP LDMOS class AB PA operated primarily in
the linear region was driven by an EM prototype comprised only of a linear stage.
Neither EM or PA was optimized for efficiency, but the combination was used to
facilitate system level investigation and understand design requirements for future
prototypes. Useful results include a signal processing method to divide Vdd and ṽin
signals [45] and identification of component integration issues [43]. The system was
operated in block diagram configuration A.
PA/EM Revision The higher-power 120-W PEP GaN HEMT overdriven class AB
PA described in Chapter 4 was driven by an EM prototype incorporating a SMPS
for improved efficiency. Further improvements at the system level include path time
165
alignment methods [46] and PA characterization methods [44] enabling the system
analysis method of Chapter 3 [42].
System/EM Revision The same 120-W PEP GaN HEMT PA was driven by a new
EM prototype with significantly more dynamic capability. A signal split algorithm
to adapt the |x̃| → β̃ transfer function was also incorporated [42].
Final Proof-of-Concept The 40-W PEP GaN HEMT class F−1 PA described in
Chapter 3 provided a significant increase in PA efficiency. An advanced EM prototype was designed by collaborators with design guidance from the static ET
simulation tool presented in Chapter 4 [42]. A DDR DPD algorithm with amplitude decomposition was used in place of the previous memory polynomial method,
and block diagram configuration B was found to provide more system-level linearity
correction.
Table 5.2 summarizes results obtained at each stage of development, spaced by
roughly six months. The final proof-of-concept configuration achieves excellent efficiency
and significant system and PA efficiency improvement. A comparison between drive
modulation and this ET configuration is presented in the next chapter.
The primary contributions of this chapter are the following:
• A state-of-the-art automated ET testbed was developed using specialized commercial test and measurement equipment. Signal processing and hardware control is
achieved through the use of custom Matlab-based software. The testbed exceeds
requirements for an implemented ET system, an essential feature for ET research
which also provides a great deal of flexibility.
• ET system distortion mechanisms are identified and quantified with hardware experiments using diagnostic waveforms. Linearization methods are developed targeting each distortion mechanism including Vdd DC calibration and path equaliza166
tion, signal split adaptation, path delay adjustment, and polynomial-based DPD.
A procedure is also outlined to achieve system linearization in the most computationally efficient manner.
• Several iterations of PA and EM design and integration produce prototypes and
linearization techniques incorporated into a final proof-of-concept demonstration.
The ET proof-of-concept transmitter meets 3GPP W-CDMA linearity specifications with more than 7 dB ACP margin and 50.6% system PAE at 2.14 GHz with
7 dB PAR W-CDMA modulation at 40 W PEP.
167
Parameter
System Performance
Test Signal PAR
Pout,avg
Pout,peak
Gain
Additive EVM
ACP5
ACP10
System ηd
System PAE
EM Performance
Design Type
Component ηd
PA Performance
Design Type
Transistor
Component ηd
Component PAE
Linear Amp
34.6 %
10.0 dB PAR
2.0 W
20.6 W
10.2 dB
<1 %
-52.0 dB
-56.0 dB
9.9 %
8.9 %
Initial PoC
Overdriven Class AB
NPT25100 GaN
54.5 %
52.0 %
Lin+SMPS rev1
61.2 %
8.0 dB PAR
17.0 W
121.9 W
13.4 dB
<1 %
-46.7 dB
-55.7 dB
33.2 %
31.6 %
PA/EM Revision
Overdriven Class AB
NPT25100 GaN
55.3 %
52.6 %
Lin+SMPS rev2
60.8 %
7.0 dB PAR
26.5 W
151.2 W
12.9 dB
<1 %
-50.5 dB
-59.5 dB
33.3 %
31.6 %
System/EM Revision
Class F−1
TGF2023-10 GaN
75.9 %
72.3 %
EM rev3
69.1 %
7.0 dB PAR
8.5 W
40.0 W
13.7 dB
<1 %
-55.7 dB
-57.8 dB
52.8 %
50.6 %
Final PoC
Table 5.2: Summary of four milestone ET transmitter measurement results.
Backed-off Class AB
AGR21045 LDMOS
28.6 %
25.7 %
168
Chapter 6
Conclusion
Contents
6.1
6.1
Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.2
Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.3
Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
Thesis Summary
The goal throughout this work has been to reduce power dissipation in high-power microwave transmitters for high-PAR signals while maintaining a high degree of linearity.
Chapter 1 described statistics of a representative high-PAR signal (single-carrier WCDMA downlink), in which the average power level is 6 dB to 10 dB higher than the
infrequently-occurring peak power level. PA efficiency naturally degrades with reduced
output power level, resulting in low average PA efficiency for high-PAR signals.
This research combines three different approaches in different frequency and signal
regimes to achieve high efficiency and linearity for high-PAR signals: (1) high-efficiency
PAs at the RF carrier frequency; (2) supply modulation at the envelope bandwidth
frequency; and (3) linearization and signal processing in the digital domain.
1) High-Efficiency PA Design - In a high-efficiency PA transistor dissipation is
reduced by shaping drain voltage and current waveforms using harmonic energy. This
RF design technique dramatically increases PA efficiency in compressed operation, but
efficiency still degrades with output power back-off. Theory of high-efficiency design was
discussed in Chapter 2. Chapter 3 developed practical design techniques demonstrated
with example prototypes at UHF and S-band.
2) Supply Modulation - Analog electronics are required to precisely vary the PA
drain supply voltage for compressed operation at reduced output power levels. The
ET system presented here maintains a specific relationship between drain voltage and
input power to achieve high PA efficiency over a wide range of output power levels.
Chapter 4 described requirements and interaction of the two components and introduced
a measurement-based system simulation method for system analysis, design validation,
and diagnostics.
3) Linearization - Adaptive signal processing techniques at baseband include linear
equalization, static look-up-table predistortion, path delay adjustment, and polynomialbased dynamic predistortion. Design, choice of technique for specific distortion mechanisms, and adaptation algorithms for each signal processing block is discussed in this
chapter.
Fig. 6.1 illustrates these concepts with projections of traditional and ET operation
based on measured data from the class F−1 design used in the final proof-of-concept
demonstration described in Chapter 5.
PA drain efficiency over 70% is shown over an 8 dB output power range, provided
drain supply voltage is varied between 12 V and 32 V. This combination of high-power,
high-frequency, high-efficiency performance is made possible by using the theory and
techniques described in Chapters 2 and 3. In conventional operation drain voltage
remains fixed with output power level and efficiency quickly degrades, as shown by the
blue “32 V Drive Modulation” curve. The signal PDF in the middle plot reveals that the
170
80
ηd,PA
60
32V Drive Modulation
Envelope Tracking
28V, 24V, 20V, 16V, 12V
40
20
20
25
30
35
Output Power [dBm]
40
45
20
25
30
35
Output Power [dBm]
40
45
20
25
30
35
Output Power [dBm]
40
45
Pdiss Distribution
Pout Distribution
0
Figure 6.1: Measured drain efficiency vs. output power for the class F−1 GaN HEMT
PA at 2.14 GHz described in Chapter 5. Measurements are made with varying drain
supply voltages under pulsed-DC/RF condition (top). Projected efficiency in ET mode
is shown by the red efficiency vs. output power curve. Output power distribution for
the 40 W PEP, 7 dB PAR W-CDMA test signal (middle). Distribution of PA power
dissipated in the RF transistor for 32-V drive modulated and ET modes (bottom).
bulk of the output distribution is produced with low efficiency, leading to high power
dissipation as shown by the blue area in the bottom plot. ET operation maintains
high efficiency over a much larger output power range, dramatically reducing the power
171
dissipated in the RF transistor.
Table 6.1 compares power measurements for the class F−1 PA prototype under drive
modulation and ET configurations with 7 dB PAR W-CDMA modulation, both exceeding W-CDMA linearity requirements with significant margin. Envelope tracking results
offer a significant improvement over equivalent drive modulated PA performance, bringing transmitter drain efficiency from 30.0% to 52.6%. System power consumption drops
from 28.3 W to only 16.2 W. Operating from a fixed power supply, the ET solution
provides 74.7% longer operation than the drive modulated solution. The ET solution
consumes 42.8% less power than the drive modulated solution, cutting energy cost and
emissions.
Fig. 6.2 compares power dissipation in ET and drive modulation conditions. Cooling
requirements are greatly reduced in the ET transmitter. In addition to dissipating less
total power, the ET transmitter divides power dissipation into two blocks. The EM
dissipates 5.0 W and the PA dissipates 2.7 W in ET mode, as compared to the singlepoint thermal load of 19.8 W at the RF transistor in drive-modulated mode.
PA efficiency is dramatically increased in ET mode as well, bringing ηd,P A from only
30.0 % to 75.9 %. Power dissipated in the RF transistor thus falls from 19.8 W to only
Table 6.1: Transmitter power budget in traditional and ET configurations using a highefficiency class-F−1 PA.
Average RF Output Power
Peak RF Output Power
Transmitter Drain Efficiency
Transmitter Supply Power
Transmitter Dissipated Power
Drive Modulation
Envelope Tracking
8.5 W
40.0 W
30.0%
28.3 W
19.8 W
8.5 W
40.0 W
52.5%
16.2 W
7.7 W
–
–
–
69.1%
16.2 W
5.0 W
30.0%
28.3 W
19.8 W
75.9%
11.2 W
2.7 W
EM Efficiency
EM Input Power
EM Dissipated Power
PA Drain Efficiency
PA Drain Supply Power
PA Dissipated Power
172
EM Dissipation
5.0W, 25.3%
PA Dissipation
2.7W, 13.6%
PA Dissipation
19.8W, 100%
Envelope Tracking
Drive Modulation
Total Dissipation
7.7W, 38.9%
Figure 6.2: Transmitter power dissipation in drive modulated and ET configurations
using the final proof-of-concept class F−1 PA prototype with 7 dB PAR W-CDMA modulation.
2.7 W in ET mode, dramatically reducing thermal loading. Reduced die temperature
leads to higher RF performance and improved reliability. Lifting the requirement that
an RF transistor operate under a high thermal load allows new degrees of flexibility in
device design, potentially leading to higher performance transistors in the future.
6.2
Contributions
All the theory and techniques described in this thesis target high-efficiency linear transmitter design and can be grouped into three areas of contribution: (1) high-efficiency PA
design techniques and prototypes; (2) ET architecture and system simulation; and (3)
ET system integration and proof-of-concept hardware demonstration. A list of publications, presentations, courses, and disclosures is presented in Chapter 1. Contributions
are listed at the end of Chapters 3, 4, and 5, and also summarized here:
1) High-Efficiency PA Design Techniques and Prototypes
• High-efficiency PA design relies heavily upon empirical design techniques due to
complex and non-ideal behavior of high-power microwave devices as described in
Chapter 2. A new load-pull technique is developed which makes use of harmonic
pre-match circuits to enforce harmonic impedance terminations necessary for highefficiency operation. This innovation allows harmonic impedance control without
173
the use of expensive and not commonly available mechanical harmonic tuners.
The method is demonstrated for the case of a switched-mode class E LDMOS
design at 360 MHz producing 110 W with 83% drain efficiency and 16.0 dB gain.
• Package and device parasitic effects play an increasing role as power and frequency
of operation rise. A method is developed to determine feasibility of different modes
of high-efficiency operation given these impediments, requiring full-wave analysis
of packaging technology and extraction of device parasitics. A demonstration of
the method results in a 36-W GaN HEMT class F−1 design example at 2.14 GHz
achieving 81% drain efficiency with 14.5 dB gain, a literature-leading result to the
best of the author’s knowledge.
2) ET Architecture and System Simulation
• High PA efficiency can be maintained over a range of output power levels using
supply modulation. An ET architecture is presented making use of both drain
and drive amplitude modulation in a ratio defined by a “signal split”. The signal
split is designed at the system level to emphasize EM linearity or PA efficiency in
an effort to optimize overall transmitter efficiency and linearity.
• New methods for PA design considering ET applications are described. A collection of load-pull contours are measured at varying drain voltage, at different levels
of compression, and showing different performance metrics. Load impedance must
be a compromise of performance in several categories: low-drain-voltage smallsignal gain; high efficiency at a specific drain voltage (typically the RMS value
of the Vdd waveform); and peak power at maximum EM voltage. The drain bias
network is also re-designed to allow modulation supply voltage and current at the
envelope bandwidth.
• A method of PA characterization is developed and used to build an ET system
174
simulation. A number of simulation analyses are used to: 1) demonstrate how
the signal split connects EM dynamic performance, PA efficiency, and system
linearity; 2) show the impact of EM output impedance on system linearity; and
3) investigate the power of DPD to correct path delay adjustment and Vdd path
distortion. In the process of system integration the simulation also proved useful
as a diagnostic tool for identifying causes of system distortion.
3) ET System Integration and Proof-of-Concept
• A flexible ET testbed is constructed using commercial TM equipment and Matlab
signal processing. The successful final implementation was the result of four increasingly better EM prototypes and PA prototypes and their integration. The
EM prototypes were designed by analog and power electronics colleagues based
on knowledge gained through the work described in Chapters 4 and 5. The ET
system simulation tool was instrumental in providing specifications and validating
EM performance in the ET system. It should be noted that one of the biggest
challenges in this work is successful integration of analog, digital, and RF components. For example, integration of the PA and the EM requires design of a new
type of bias network in which the EM provides the low-frequency low-impedance
termination, replacing the bypass capacitance traditionally required for PA stability. Additionally, the inductance of the RF choke and interconnect must be
minimized, in contrast to the usually desired large inductance of an ideal RF
choke. This leads to new insights into PA stability in an ET system.
• ET distortion mechanisms were identified through the use of the ET simulation
tool and in hardware through the use of diagnostic experiments using test waveforms designed to isolate specific behaviors. For example, the problem of EM
output impedance peaking was only identified through the use of the ET simulation tool, leading to new EM design guidelines. The various distortion mecha175
nisms that were identified and corrected for with signal processing include linear
EM frequency response, path time delay, static PA nonlinearity due to Vdd and
|ṽin | operating conditions, and PA dynamic distortion including self-heating and
charge trapping effects. This investigation led to a new understanding of how ET
distortion mechanisms are distributed among different ET components, as well
as in the time, frequency, and amplitude domains. This, in turn, led to targeted
linearization approaches which result in a simpler, more computationally efficient,
and better final performance system.
• A 40-W class F−1 PA is designed for ET application at 2.14 GHz using the harmonic load-pull techniques described earlier and paired with an advanced EM
prototype developed by collaborators. System linearization techniques provide
greater than 7 dB ACP linearity margin with a 7 dB PAR W-CDMA test signal at
40 W PEP (8.5 W average power), and system PAE over 50%. This performance
is among the highest reported in literature at this power level, frequency, and
modulation type.
6.3
Future Directions
The broad scope of this work leaves open questions in the areas of high-efficiency PA
design, analog and power electronics, signal processing techniques, and system integration. Additionally, the concepts presented in this work can be used in applications
besides the W-CDMA base station, bringing new requirements and challenges. The
flexibility of the ET simulation method and hardware testbed will allow us in the future
to investigate applications well outside the scope of the high-power S-band W-CDMA
downlink base-station transmitter. Several of the most interesting avenues for future
investigation are described below.
Harmonic-Terminated Module Design - Chapter 3 described chip/wire con176
struction used to eliminate package parasitics, allowing the microstrip harmonic termination network to be placed closer to the transistor. Alternately, the harmonic resonators could be implemented inside a microwave package in the form of an IPD1 , or
with chip capacitors and bond-wire inductors. The result is a packaged module with
internal harmonic termination networks, simplifying external matching network design.
Module-level terminations can be placed electrically closer to to the transistor, potentially lowering the Q-factor of the harmonic match. Modules can also be built with
tight dimensional tolerance, allowing precise repeatability for sensitive high-Q terminations. This work would begin with investigation of the types of resonant structures
which can practically be constructed in a module, e.g. coaxial resonators, MOS capacitors, followed by full-wave EM simulations verified by component measurements.
This requires industrial-type resources and to the best of the author’s knowledge some
transistor manufacturers (e.g. Freescale, Sumitomo) have started pursuing this path.
RF Transistors Optimized for ET Operation - Chapter 6 noted dramatically
reduced power dissipation in the RF transistor when operating in ET mode (from 19.8 W
under drive modulation to only 2.7 W). In Chapter 5 it was noted that transistor performance was improved in ET mode, even as compared to low-duty-cycle pulsed operation.
It is clear that operation in ET mode is quite different from other traditional modes,
and it follows that some requirements of traditional modes no longer apply (e.g. no
need to withstand a large thermal load). Potential exists for microwave devices to be
optimized for the ET mode of operation, giving up the ability to operate in CW or
pulsed modes for further increased ET mode efficiency.
Integrated DPD Solution for ET - Due to the highly proprietary nature of
DPD chipsets, it is not known whether or not a given commercially-implemented DPD
solution would be suitable for ET applications. Ideally, an integrated DPD solution
would implement both an adaptive static LUT (signal split adaptation), an adaptive
1
integrated passive device
177
polynomial-based memory correction, and path delay adjustment. An ET-specific DPD
should also compute the drain voltage signal based on the desired Vdd path signal split
trajectory and apply Vdd path equalization.
Combination Doherty-ET Architecture - Doherty operation was discussed in
Chapter 1 as an alternative method for efficient amplification of high-PAR signals.
Benefit could be realized from merging the two concepts. Consider a typical Doherty
design with an EM controlling drain voltage of the carrier amplifier. In the simplest case
the carrier PA is supplied maximum drain voltage while the peaking PA is operating,
and ET operation takes over when the peaking amplifier turns off. The carrier amplifier
would continue to operate in compression until the minimum drain voltage was reached,
extending the high-efficiency output power range below the 6 dB range typical of Doherty
operation. This basic idea is already under investigation [107], and a wide variety of
more complex control schemes can also be considered.
Mobile Applications - Mobile high-power high-PAR transmitters, such as those in
UAVs2 , operate from a fixed power supply and are sensitive to mass and size. ET offers
the possibility of reducing battery size or extending battery life. Additionally, less heat
dissipation spread over a larger area can lead to smaller and lighter thermal management
solutions. New cellular standards make use of OFDM and SC-FDMA3 modulation [108],
as well as MIMO4 transmit diversity to improve performance of the uplink. These
improvements increase signal PAR, making the ET architecture described in this thesis
an attractive alternative to traditional drive modulation. The low power and small form
factor of the handset application adds a number of ET implementation challenges not yet
addressed in this thesis, such as: 1) miniaturization of the EM switching components,
requiring a higher switching frequency to reduce the size of magnetics; 2) simplification
2
unmanned arial vehicles
3
single-carrier frequency division multiple access
4
multiple input multiple output
178
of the signal processing algorithms to keep DSP5 power consumption low; and 3) design
of harmonic-tuned low-power MMIC6 PAs for ET applications.
Radar Transmitters - The most common radar transmit modulation is the constantamplitude, phase-modulated pulse. The high power levels required demanded pulsed
operation and an efficient class C amplifier strictly from a heat management perspective.
Because the class C amplifier is so inherently nonlinear, and to keep efficiency high, no
amplitude modulation is incorporated. Unfortunately, these constant-amplitude waveforms often produce large spectral skirts, interfering with frequency-adjacent applications. Availability of a highly-efficient transmitter for high-PAR waveforms opens a
new degree of freedom for radar waveform designers: amplitude modulation. Recent
work [47] has shown that radar performance and spectral benefits can be realized even
using the simplest amplitude-modulated radar waveforms. Furthermore, the amplitude
modulation of these waveforms is likely to have far less dynamic content than the communications applications considered here, easing the EM design challenge and improving
system efficiency.
5
digital signal processing
6
monolithic microwave integrated circuit
179
180
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