Asmita Dani (Ph.D. 2013),
Efficiency and Linearity Enhancement of
M i c rowav e G a N P ow e r A m p l i f i e r s u s i n g
Harmonic Injection
by
A s m i ta R a j i v Da n i
B.S., University of Mumbai, India, 2008
M.S., University of Colorado, 2010
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, Computer and Energy Engineering
2013
This thesis entitled:
Efficiency and Linearity Enhancement of Microwave GaN Power Amplifiers using Harmonic Injection
written by Asmita Rajiv Dani
has been approved for the Department of Electrical, Computer and Energy Engineering
Zoya Popović
Dragan Maksimović
Date
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.
Dani, Asmita Rajiv (Ph.D., Electrical Engineering)
Efficiency and Linearity Enhancement of Microwave GaN Power Amplifiers using Harmonic Injection
Thesis directed by Professor Zoya Popović
This thesis addresses an architecture for enhancing efficiency and linearity of GaN power amplifiers
using external second harmonic injection at the output. This transmitter architecture has potential uses
in communication and radar systems which have stringent requirements of low DC power dissipation and
minimum out of band interference. An idealized theoretical analysis based on expansions of the nonlinear
transfer function of a PA predicts the measured improvements in linearity and efficiency.
The experimental demostration is performed with both hybrid and integrated harmonically-injected PA
using discrete GaN 6 W transistors in class-AB mode with 55% PAE at a fundamental frequency of 2.45 GHz.
Harmonic injection at the output is shown to enhance the efficiency of the PA to 89%. For a slightly reduced
efficiency of 78%, the linearity can be improved and > 15 dB reduction of third and fifth order intermodulation
distortion tones is measured in compression.
Integration of a dynamic supply of the harmonically-injected PA is also investigated in order to achieve
high efficiency and linearity for signals with Peak-to-Average ratios (PARs) of 6 dB and higher. Experimental
results demonstrate a 70-80% efficient HI-PA for an output power variation of 6 dB. Reduction in third order
nonlinear products and AM-PM distortion shows improved linearity of the PA over the entire range of power
levels.
Finally, the concept is extended to an X-band GaN MMIC to demonstrate integration and efficiency
enhancement at 10 GHz with a 4 W, 47% efficient class-AB PA, with an expected final efficiency of over 60%
with harmonic injection.
iii
D e d i c at i o n
To my family
P e r s o n a l Ac k n ow l e d g m e n t s
I would like to thank my parents who have taught me to be independent, strong willed and encouraged me
to pursue higher studies. I want to thank my entire family for being so supportive and loving. Next, I would
like to thank my husband, Gokul for being there for me always and supporting me throughout my graduate
school career. I am blessed to have you in my life. I would like to thank my best friend, Urvi for helping me
adapt to the culture in a different country and also getting me through the tough times. I want to thank
my college friends for giving me fun moments in my undergraduate studies and helping me in my studies
in India. I would like to acknowledge my teacher, Mrs. Tulsi Rao for teaching me mathematical analysis
of problems and showing me how to answer questions with details and accuracy. Finally, I would like to
thank Prof. Vakil for exposing me to the magical world of electronics and keeping me interested in design
and analysis of communication systems.
v
P ro f e s s i o n a l
Ac k n ow l e d g m e n t s
I extend my deepest regards and thanks to Professor Zoya Popović for having encouraged me, shown faith
in me and tapping my interests in the field of RF/Microwave circuit design. I am extremely lucky to have
worked with you and I will always apply the professionalism you have taught me in my career. I would also
like to thank the U.S. Airforce for funding this project and TriQuint Semiconductor for providing access to
their GaAs and GaN MMIC foundary. A special thanks to Dr. Charles Campbell for providing teaching us
design tricks and providing knowledgable feedback on the MMIC design. I want to thank Dr. Michael Roberg
for teaching me practical microwave circuit design and power amplifier basics. I would specially like to thank
Dr. Erez Falkenstein, Dr. Rob Scheeler, Dr. Jonathan Chisum, Dr. Frank Trang, and Michael Litchfield for
making me feel so welcome in the lab and helping me get through my research with useful discussions and
inputs. I would like to acknowledge Dr. Tibault Reveyrand and Dr. Jose Angel Garcia for giving useful ideas
and input on the project and help me take measurements. I would also like to thank Dr. Luke Sankey for
teaching me how to design MMIC circuits. I would like to extend a special thanks to Lavanya P., for being a
good friend and being there for me. Finally, I would like to thank all the past and present group members for
being great friends and providing inputs and discussions related to the thesis and other projects in the lab.
vi
Contents
1
1 I n t ro d u c t i o n
2
1.1
Overview
1.2
GaN Microwave Devices
1.3
PA classes of operation
4
7
10
1.3.1
Standard PA classes of operation
1.3.2
Harmonically-tuned and Switched Mode PAs
1.4
PA Trade-off Characteristics
1.5
Transmitter architectures
12
13
14
2 T h e o r e t i c a l B a s i s f o r PA s w i t h H a r m o n i c I n j e c t i o n
2.1
Concept of Harmonic Injection PA (HI-PA)
2.2
Theoretical Analysis
2.3
2.2.1
Waveform Analysis
25
2.2.2
Efficiency Analysis
27
Linearity
2.3.1
2.4
25
32
Waveform shaping
Conclusion
33
39
3 P ro o f - O f - P r i n c i p l e S - B a n d H I - PA
41
41
3.1
Introduction
3.2
3-Port output Injection Network
3.3
Linearity Measurements
42
47
vii
21
20
3.4
Conclusion
49
50
4 H y b r i d H I - PA i n t e g r at e d D e s i g n a n d T e s t
51
4.1
Hybrid HI-PA Integrated Design
4.2
Measurements
4.3
Maximum Efficiency Characteristic
54
58
4.3.1
Fundamental Output Power
4.3.2
Drain Efficiency (ηD ) Characterization
4.3.3
Drain current
4.3.4
Linearity Measurements and Characterization
4.4
Input Power Sweep
4.5
Conclusion
60
60
62
68
69
71
5 L i n e a r i z at i o n o f H I - PA s
5.1
56
74
Variable tone spacing
76
5.1.1
1 MHz tone spacing
5.1.2
10 MHz tone spacing
77
5.1.3
20 MHz tone spacing
77
79
5.2
Input power sweep
5.3
Harmonic Balance Simulations
5.4
Conclusion
82
86
6 S u p p ly M o d u l at i o n I n t e g r at i o n w i t h H a r m o n i c a l ly - I n j e c t e d PA
89
6.1
Introduction
6.2
Theory
6.3
Nonlinear Simulations
6.4
90
90
6.3.1
Approach I: Constant Input Drive
91
6.3.2
Approach II: Variable Input Drive
94
Measurements
97
viii
88
6.4.1
Approach I
6.4.2
Approach II
6.5
Discussion 105
6.6
Conclusion 106
98
99
7 C o n t r i b u t i o n s a n d F u t u r e Wo r k
7.1
Introduction 109
7.2
X-Band MMIC Design 109
7.3
Measurements 112
7.4
Future Work 116
7.5
Contributions 118
108
Bibliography
122
ix
L i s t o f Ta b l e s
4
1.1
Comparison of GaAs and GaN properties
1.2
Several manufacturers of high performance GaN devices for commercial and military
applications.
8
10
1.3
Basic PA modes of operation.
1.4
Transmitter Architectures
6.1
Measured parameters of supply modulated HI-PA.
16
x
99
List of Figures
1.1
Nonlinear distortion characterisitc of a power amplifier showing the original signal (blue)
2
and the spectral regrowth (red) caused due to distortion in the PA.
3
1.2
DC power consumption in various stages of a radio base station transmitter.
1.3
Comparion of various solid state technologies in terms of maximum frequency of operation
and breakdown voltages [1].
5
8
1.4
Block diagram of a general power amplifier [2].
1.5
IV-curves for a 6 W GaN on SiC HEMT by TriQuint Semiconductor, TGF2023-01 showing
a class-A bias point condition and load line.
9
10
1.6
Pictorial representation of current conduction angle, α in a transistor.
1.7
Current conduction angle for class-A and AB modes of operation for the PA.
1.8
Theoretical efficiency and output power for reduced conduction angle modes of PA w.r.t
class-A PA efficiency and output power [2].
11
12
13
1.9
Current peaking and voltage squaring in class-F mode of a power amplifier.
1.10
Efficiency, gain and output power characteristics of a power amplifier.
1.11
General block diagram of a PA architecture in transmitters to achieve high efficiency for
high Peak-to-average ratios.
14
15
1.12
General block diagram for a envelope tracking transmitter system [3].
1.13
General block diagram for an outphasing transmitter system [3].
18
1.14
General block diagram for a Doherty PA transmitter system [3].
18
xi
17
2.1
Block diagram of a harmonic-injection power amplifier (HI-PA) with 2nd harmonic injection
at the output. A three-port network at the output allows isolation between waves at f0
and 2f0 between ports 2 and 3, while allowing low loss at f0 between ports 1 and 2. The
phase of the injected harmonic is critical to obtaining high efficiency.
21
22
2.2
Variation in PAE and drain efficiency with change in second harmonic path length [4].
2.3
TWT output spectrum for a two-tone 15 dBm/tone input signal with harmonic injection
showing a 21.3 dB reduction in upper IMD3 levels [5].
2.4
23
Two-tone response of 880 MHz amplifier without (a) and with (b) injection of difference
frequency showing IM D3 and IM D5 improvement of 20 and 30 dB respectively [6].
2.5
Harmonic injection class-J PA results for a constant magnitude and phase offset between
the input and injected signals [7].
2.6
24
24
(a) Block diagram of a harmonic-injection power amplifier (HI-PA) with 2nd harmonic
injection at the output. A three-port network at the output allows isolation between waves
at f0 and 2f0 between ports 2 and 3, while allowing low loss at f0 between ports 1 and
2. The phase of the injected harmonic is critical to obtaining high efficiency. (b) Ideal S
parameters for the three port injection network.
2.7
25
Optimal drain current and voltage waveforms for second harmonic injection amplifier,
normalized to 1 W output power.
26
28
2.8
Contour plot for ηtotal as a function of a2 and injector circuit efficiency ηinj .
2.9
Optimal solution for Fourier coefficient a2 and second harmonic delivered power relative
to fundamental frequency output power versus second harmonic injector circuit efficiency
ηinj .
28
29
2.10
Total efficiency ηtotal versus injector circuit efficiency ηinj .
2.11
Power reduction and normalized supply voltage relative to class-A vDD,A versus injector
efficiency ηinj .
2.12
31
Typical transfer function and its derivatives for different gate bias voltages in FET power
amplifier. The corresponding classes of operatiion are shown on top of the figure [8].
xii
32
34
2.13
Effect of second order nonlinearity on sinusoidal waveform.
2.14
Square wave representation with the first four terms in the Fourier series.
2.15
Effect of third order nonlinearity on sinusoidal waveform with negative gm3 values.
35
2.16
Effect of third order nonlinearity on sinusoidal waveform with positive gm3 values.
36
2.17
Measured voltage levels of odd order intermodulation distortion products for a two-tone
signal with f1 = 2.45 GHz and 1 MHz tone spacing.
2.18
38
Effect on odd order distortion products (IMD3,5,...) due to mixing of fundamental, second
and third order products.
2.19
35
38
Cancellation in intermods due to mixing products formed from second harmonic injection
with opposite phase. Here, r1 represents the IMD products from amplifier nonlinearity,
r2 represents the IMD products created by mixing of fundamental and injected second
harmonic signal. The resultant red phasor shows reduced amplitude resulting in reduction
in overall distortion.
3.1
39
Measured S parameters for the three port injection network designed on Rogers 4350B
substrate with a photograph of the circuit shown in the inset.Port 1 represents the drain
of the fundamental PA, port 2 is the output of the PA and port 3 represents the injection
port.
3.2
42
Block diagram for the experimental validation of a harmonically-injected PA concept using
two pre-built broadband Cree PAs.
3.3
43
Comparison of measured (a) drain efficiency, (b) Pout (f0 ) and (c) gain for the HI-PA to
the PA with no harmonic injection at VDD = 22V, 28V and VGG = -1.6V (class AB).
Dashed green line indicates input power at which the PA becomes nonlinear.
3.4
Efficiency and output power of HI-PA over a range of gate bias levels for VDD = 22, 28 V
and Pin = 30 dBm.
3.5
46
47
Measured ratio of injected 2nd harmonic power, Pinj (2f0 ), to output power at the fundamental, Pout (f0 ), for various bias points as a function of input power at the fundamental.
xiii
47
3.6
Comparison of power levels for single tone and 3rd order IMD products for HI-PA and
class-AB PA without harmonic injection.
4.1
48
General block diagram of the designed amplifier with DUT representing the TriQuint 6 W
GaN discrete die with reference planes, output capacitance, cds and bond wire transitions
from die to copper on the input and output matching networks.
4.2
51
Measured input and output impedances, Z11 = 49 − 11.6jΩ and Z22 = 9.6 + 11.6jΩ for
the passive 2-port input matching network.
52
53
4.3
Measured Z11 for the output network at f0 = 2.45 GHz and 2f0 = 4.9 GHz.
4.4
Measured loss in the output network low pass(blue) and high pass(pink) filter paths.
4.5
Hybrid harmonic injection power amplifier (HI-PA) with a 6W TriQuint TGF2023-01
53
die. The output network integrates the harmonic injection three port network with Ropt
at f0 matched to 65Ω and Ropt at 2f0 matched to 71 Ω. The input network does an
impedance transformation from 50 Ω to 10 Ω in order to achieve high gain and Pout at the
fundamental.
4.6
54
Measured drain efficiency, Pout at f0 and 3f0 and gain for the class-AB PA shown in
Fig.4.5 without injection.
4.7
55
Block diagram of the HI-PA measurement setup. The input signal is split and frequency
doubled to create the injected harmonic, Pinj (2f0 ). A voltage controlled phase shifter and
variable gain amplifier are used to control the amplitude and phase of Pinj (2f0 ).
4.8
Comparison of measured (a) ηD , (b) Pout (f0 ) and (c) gain for discrete die protoype of
HI-PA optimized for maximum efficiency.
4.9
58
Contour plots of measured fundamental output power, Pout (f0 ) at (a) input power, Pin =
10 dBm, (b) Pin = 16 dBm.
4.11
57
Drain efficiency, Pout (f0 ), Pout (3f0 ) for different Vdd bias voltages with the ratio Pinj (2f0 )/Pout (f0 )
= 0.1 and Pin (f0 ) = 16.2 dBm.
4.10
55
59
Contour plots for measured drain efficiency, ηD at (a) input power, Pin = 10 dBm, (b)
Pin = 16 dBm.
61
xiv
4.12
Contour plots for measured drain current, Idd at (a) input power, Pin = 10 dBm, (b) Pin
= 16 dBm.
4.13
62
Contour plots for power measured at second harmonic, Pout (2f0 ) at (a) input power, Pin
64
= 10 dBm, (b) Pin = 16 dBm.
4.14
Contour plots for power measured at third harmonic, Pout (3f0 ) at (a) input power, Pin =
10 dBm, (b) Pin = 16 dBm.
4.15
65
Total drain efficiency (b) and output power at second harmonic (a) as functions of the
amplitude of the injected harmonic signal for various input drive levels. The phase of the
injected signal is set to the optimal value for these measurements.
4.16
66
Minimum Pout (2f0 ) and Pout (3f0 ) measured at virtual drain of the HI-PA for Pin (f0 )
= 16.2 dBm. The minimum for Pout (2f0 ) is obtained with Pinj (2f0 ) = -17.8 dBc w.r.t.
Pout (f0 ), whereas minimum for Pout (3f0 ) is obtained for Pinj (2f0 ) = -8.9 dBc.
4.17
A comparison of drain efficiency and gain for HI and PA with no injection as a function
of Pin (f0 ).
4.18
67
68
Comparison of Pout (f0 ) and Pout (3f0 ) as a function of Pin (f0 ) for HI and PA with no
injection. The graph also shows the amplitude of Pinj (2f0 ) as function of Pin (f0 ) in order
to achieve high efficiency and linearity performance for the HI-PA.
5.1
Block diagram of measurement setup for two tone test on the harmonic injection power
amplifier.
5.2
72
Measured power level of IM D3L (2f1 -f2 ) as a function of the amplitude and phase of the
injected second harmonic tone 2f1 .
5.3
73
Measured power level of IM D5L (3f1 -2f2 ) as a function of the amplitude and phase of
74
the injected second harmonic tone 2f1 .
5.4
69
Measured power levels for IM D3L and IM D5L with harmonic injection at 2f1 and Pin
= 16 dBm. The minima for IM D3L and IM D5L are obtained for Pinj (2f1 ) = -11.5 dBc
and -9.5 dBc, respectively.
74
xv
5.5
Measured intermodulation distortion products in the upper and lower half of the spectrum
for two tone signals with 1 MHz tone spacing
5.6
Measured intermodulation distortion products in the upper and lower half of the spectrum
for two tone signals with 10 MHz tone spacing
5.7
78
Measured intermodulation distortion products in the upper and lower half of the spectrum
for two tone signals with 20 MHz tone spacing
5.8
76
79
Comparison of power at IM D3L (2f1 -f2 ), IM D5L (3f1 -2f2 ) for HI-PA and PA without
harmonic injection as a function of input drive level. The graph also shows the power
injected at the second harmonic tone (2f1 ) to achieve lowest IM D3L .
5.9
80
Comparison of power at IM D3L (2f1 -f2 ), IM D5L (3f1 -2f2 ) for HI-PA and PA without
harmonic injection as a function of input drive level. The graph also shows the power
injected at the second harmonic tone (2f1 ) to achieve lowest IM D3L .
5.10
80
Harmonic balance simulations in ADS for harmonic injection at both the harmonic tone
signals for the designed HI-PA with TriQuint 6 W GaN discrete die transistor having Pout
= 36.28 dBm. A single harmonic balance source is used with two ports for fundamental
and injected harmonic tone signals.
5.11
83
(a) Minimum IM D3 (red) and IM D5 (blue) contours for a class-AB without harmonic
injection at the fundamental tones f1 and f2 with tone seperation of 1 MHz and total Pin
= 16 dBm. (b) Spectral plot of the intermodulation distortion products for class-AB PA
with load impedance, Zopt = 14 + 12j Ω.
5.12
84
(a) Minimum IM D3 (red) and IM D5 (blue) contours for HI-PA with optimal injection
signal phase and amplitude for a fundamental tone seperation of 1 MHz and total Pin =
16 dBm. (b) Spectral plot of the intermodulation distortion products for HI=PA with load
impedance, Zopt = 68.707+29.466j Ω.
5.13
85
Spectral plot of the intermodulation distortion products for HI-PA at Zopt = 68.707+29.466j
Ω with tone spacing of (a) 10 MHz and (b) 20 MHz.
xvi
85
6.1
Block diagram of simulation setup in ADS for varying drain supply and injected second
harmonic power in a class-AB PA with constant input drive power. The 3-port network at
the output is a diplexer as shown in [7, 9].
6.2
91
Simulated variation in (a) drain efficiency, ηD (%), (B) Pout (f0 ), in dBm, and (c) ratio
Pinj (2f0 )/Pout (f0 ), in dBc, w.r.t. change in drain voltage and Pinj (2f0 ).
6.3
92
Variation in IMD3 with change in supply voltage and injected harmonic power. The input
power is kept constant at 16 dBm. The contours show constant IMD3 levels for both
sidebands and with a 1 MHz tone spacing.
6.4
Gain characteristic of a class-AB PA with increase in input drive levels and suppy voltage
from 10 to 28 V.
6.5
94
AM-PM characteristic of a class-AB PA with increase in input drive levels and suppy
voltage from 10 to 28 V.
6.6
93
94
Quadratic approximation for supply voltage variation as a function of variation in the
input drive level for constant gain and AM-PM characteristics.
6.7
Variation in fundamental output power and gain with constant AM-PM distortion maintained in a PA with supply and input drive variation.
6.8
95
95
Block diagram of simulation setup in ADS for varying drain supply and fundamental
input drive level in a class-AB PA. A constant ratio is maintained between Pinj (2f0 ) and
Pout (f0 ).
6.9
96
Simulated results for drain efficiency, ηD with simultaneous variation in fundamental input
drive and drain supply voltage. The ratio, Pout (f0 )/Pinj (2f0 ) = 0.1 for each input drive.
97
6.10
Simulated results for Pout (3f0 ) with simultaneous variation in fundamental input drive
and drain supply voltage. The ratio, Pinj (2f0 )/Pout (f0 ) = 0.1 for each input drive.
xvii
97
6.11
Variation in measured drain efficiency w.r.t. the drain voltage, VDD and injected second
harmonic power, Pinj (2f0 ). The amplifier has G = 19 dB at Pin = 16 dBm for a bias of
VDD = 28 V and IDQ = 130 mA. The gain varies between 13 and 19 dB over the entire
range of values.
6.12
98
Measured Pout (f0 ) (dBm), ηD (%) and Pout (3f0 ) (dBc) for a harmonically injected PA
with variable supply and input drive level. The ratio of Pout (f0 )/Pinj (2f0 ) = 10.5 dB for
each of the input drive levels. 100
6.13
Measured variation in the fundamental output power, Pout (f0 ) as a function of the input
drive level and supply voltage for a harmonically-injected PA with optimal amplitude and
phase of the second harmonic. 101
6.14
Measured variation in gain as a function of input power, Pin and supply voltage, VDD for
the harmonically-injected PA with supply variation. 101
6.15
(a) Measured PAE contours as a function of the input drive level, Pin and supply voltage,
VDD , (b) Measured drain efficiency as a function of the output power and drain voltage
showing constant high efficiency of 75% for a PAR of 6 dB. 102
6.16
(a) dynamic AM-PM distortion for HI-PA with variation in input drive level and supply
voltage. (b) Measured improvement in the AM-PM distortion of a harmonically-injected
PA over a non harmonically-injected PA. 103
6.17
Simulated error in output voltage, Vout with 1 V error in drain bias voltage for various
injected harmonic power levels (approach I). 104
6.18
Measured static load presented by the PA to the supply as a function of the output
power. 105
6.19
Measured dynamic AM-PM distortion for a class-AB GaN 6 W PA without harmonic
injection. The plot shows the AM-PM distortion for various drain voltages as a function
of the input drive level, Pin . 106
7.1
Simulated IV curves for the 12x100 µ periphery TriQuint GaN device. The bias point
selected is shown in the figure with Idq = 152 mA. 109
xviii
7.2
(a) Impedances for the ideal and non-ideal simulated input matching network with port
1 matched to 50 Ω (blue) and port 2 matched to Zin (green - ideal, red- non-ideal). (b)
Simulated S parameters for non-ideal input matching network. 111
7.3
Simulated load-pull contours in order to obtain maximum output power, Pout at 10 GHz. 112
7.4
Simulated loss in the through and injection paths of the 3-port output diplexer network. 112
7.5
Ideal harmonic balance simulations showing variations in (a) fundamental output power,
Pout (f0 ) (b) second harmonic output power, Pout (2f0 ) (c) third harmonic output power,
Pout (3f0 ), and output drain current, Idd , for the design HI-PA with phase of the injected
harmonic swept from 0 to 360◦ and amplitude from -20 to -8 dBc w.r.t. fundamental
output power. 113
7.6
Final MMIC layout of the designed HI-PA (bottom) and 20 GHz driver PA (top). 114
7.7
Comparison of the simulated (10 GHz) and measured (10.6 GHz) X-band class-A PA
without harmonic injection in terms of drain efficiency,ηD , fundamental output power,
Pout and gain at Vdd = 20 V and Idq = 130 mA. 114
7.8
Class-AB PA performance in X-band without harmonic injection. 115
7.9
Measured response for the 20 GHz driver PA in terms of PAE (green), Pout (blue) and
gain (red). 115
7.10
Measured and projected total efficiency, ηtotal of HI-PA as a function of fundamental input
drive, Pin (f0 ) at 10 GHz (red) and 10.6 GHz (blue) with Pout (f0 ) = 3.5 W. 116
7.11
Block diagram describing measurement setup HI-PA with standard communication signal
modulation schemes. An upconverter is used to create the injection signal along with a
voltage controlled phase shifter to change the relative phase of the injected signal w.r.t.
the fundamental signal. 117
xix
7.12
(a) Fixturing for 10 GHz MMIC provided by TriQuint Semiconductor. Alumina lines with
bond pads wire-bonded to the RF and DC pads on chip which is mounted on a copper
molly substrate. (b) Measurement setup with launcher fixtures to measure the MMIC chip
in 50 Ω environment. 117
7.13
MMIC design for 10 GHz HIPA integrated with 20 GHz Driver PA using an integration in
the output diplexer network (B). A pre-driver at 20 GHz designed for high gain in the
injection path (A). 118
xx
Chapter 1
I n t ro d u c t i o n
Happiness is not something ready made. It comes from your own actions.
—Dalai Lama
Do not go where the path may lead,
go instead where there is no path and leave a trail.
—Ralph Waldo Emerson
Contents
1.1
Overview
2
1.2
GaN Microwave Devices
1.3
PA classes of operation
4
7
1.3.1
Standard PA classes of operation
1.3.2
Harmonically-tuned and Switched Mode PAs
1.4
PA Trade-off Characteristics
1.5
Transmitter architectures
13
14
10
12
1.1
Ov e rv i e w
Power amplifiers used in modern RF/microwave transmitters are required to have extremely low levels of
distortion in order to transmit complex, broadband and high number of channels with acceptable levels of
intermodulation and spectral regrowth. Also, high efficiency is an important criterion since transmitters used
for communication and radar applications usually consume a large fraction of the available power in the
transmitter. The power amplifier is located directly behind the antenna and is often operated in a saturated
regime in order to be more efficient as shown in Fig.1.1. This results in nonlinearity and signal distortion at
the output of the transmitter.
Figure 1.1: Nonlinear distortion characterisitc of a power amplifier showing the original signal (blue) and the
spectral regrowth (red) caused due to distortion in the PA.
A large portion of current research in high-power amplification of signals with carriers in the microwave
range focuses on improving efficiency and linearity. There are many power amplifier (PA) topologies that
achieve high efficiency by driving the active device into a nonlinear region and shaping voltage and current
waveforms across the device via proper selection of the output loading network at harmonic frequencies. These
techniques, such as class-F and F−1 PA topologies, rely on the nonlinear active device for harmonic current or
voltage generation and have been heavily researched, eg. in [10, 11, 12, 13]. Modern communication systems
utilize amplitude and phase modulation schemes with high peak-to-average ratios (PARs) and bandwidths.
The primary challenge of a transmitter design is to achieve high efficiency and maintain linearity over the
entire range of power levels and bandwidth [14, 15]. Some of the solutions which address this requirement
include outphasing (LINC), Doherty PA with DPD and envelope tracking PA with DPD [16, 17]. In this thesis,
an architecture in which power at one or more harmonics of the operating frequency is supplied externally to
either the input, output, or both input and output of the active device, referred to as harmonically-injected
2
Figure 1.2: DC power consumption in various stages of a radio base station transmitter.
PAs or HI-PAs is studied as a possible solution.
Why is power amplifier design so critical in transmitters? According to a study performed by Energy
Efficient Radio Access Network Technologies, Alcatel-Lucent in 2009, the PA including feeder network consumes
almost 50-80% of DC power in a transmitter as shown in Fig.1.2. In 2009, the total number of cell phone users
were estimated to be around 3 billion across the globe which required almost 4 million Radio base stations
(RBS). Each RBS consumes 1 KW of power along with network contol consuming 1 KW and servers consuming
10 kW of DC power. Therefore, it is of the highest prority to reduce the DC power consumption in order to
have energy efficient use of cell phones and base stations. In satellite transmitters, tens of watts of microwave
power is required. As mentioned in [18], during eclipses, the satellite gets powered by onboard batteries which
loose lifetime due to unecessary waste of power in power amplifiers. Various device technologies have been
researched and are being used to design PAs for transmitters which include GaAs, LDMOS, CMOS, BiCMOS,
GaN, InP, etc. However, these solid state technologies have their limitations which do not yield an optimal
performance required in terms of PAs. Out of these solid state technologies, the most common ones used
in the wireless and cellular frequency bands (700-2.45 GHz) are LDMOS, GaAs and CMOS technologies.
GaAs and CMOS have a severe ouput power density limitation with GaAs transistors providing a maximum
of 1-2 W. These devices also have a frequency limitation with lower cut-off frequencies, ft which results in
lower gain at high frequencies and hence limits the usage of the devices for high efficiency and output power.
Also, technologies like GaAs and LDMOS require better thermal power management since these devices have
detrimental self-heating effects [19, 20, 21].
3
Table 1.1: Comparison of GaAs and GaN properties
Property
Bandgap Energy
Permittivity
Operating voltage
Current Density
Breakdown Field
Thermal Conductivity
1.2
GaAs
1.4 eV
13.1
5-24 V
0.5A/mm
0.4x106 V/cm
47 W/m.K
GaN
3.4 eV
9.6
20-60 V
1-2A/mm
5x106 V/cm
150 W/m.k
G a N M i c rowav e D e v i c e s
In recent years, GaN has become a prime material for research in order to build powerful devices which can
deliver high performance in terms of power, efficiency and linearity. GaN has several advantages over other
solid state technologies in use today such as LDMOS, GaAs, CMOS, etc. Gallium Nitride or GaN wafer
technology is not as developed and therefore the devices made from GaN are based on a Silicon or Silicon
Carbide substrate (SiC) which provides high thermal conductivity on the order of 490 W/m.K. A comaprison
of GaAs with GaN devices is shown in table 6.1. Since GaN devices have a much higher bandgap energy
which is 2 eV higher than that of GaAs, more energy is required for conduction which results in GaN handling
higher voltages and hence having high Psat values compared to GaAs. Also as reported in [22], one of the
potential advantagess of using wide bandgap devices is to have higher junction temperatures and thinner
drifting regions which can result in lower on state resistance.
The superior performance of GaN in terms of current density, thermal conductivity and wide bandgap gives
it a superior advantage over the use of GaAs devices for high power microwave power amplifier applications.
Another advantage of GaN is its high cutoff frequency, ft which results in high gain at frequencies well
above the ones which devices like GaAs and LDMOS can handle. Fig.1.3 shows a comparison of various solid
state technologies as a function of frequency and power. It is seen that although devices made from Indium
Phosphide, InP can work up in the 100s of GHz range, however, the power density is lower as compared to
GaN devices.
Most of the GaN devices use the High electron mobility transistor (HEMT) technology for current research.
One of the first works reported in [23] for GaN HEMTs at X band showed devices fabricated on two inch Si
4
Figure 1.3: Comparion of various solid state technologies in terms of maximum frequency of operation and
breakdown voltages [1].
substrate with CW power densities of 3.9 and 6.2 W/mm. These devices were tested at three different drain
bias levels of 20, 35 and 40 V with a Idq of 200mA/mm. The measured PAEs for the two power densities were
reported to be 52 and 36% respectively. A reliability study in [23] showed that low cost, large area MMICs
on Si could be realized for GaN devices at X band. However, since SiC is a better thermal conductor and
provides a good lattice match for AlGaN/GaN heterojunction, GaN on SiC devices are more popular. A
comparison between various substrates for GaN devices has been reported in [22] where the electron and
hole mobility along with critical breakdown field, thermal conductivity and coefficent of thermal expansion is
studied for various substrate materials such as Si, SiC, Diamond and Sapphire. Of these substrates, diamond
has been found to be the best in terms on thermal conductivity and lattice constant. However, the material
and fabrication techonology is much less mature as compared to SiC and GaN. Also, it would be extremely
expensive process to produce GaN on diamond for commercial applications. A clear comparison in [24]
between GaN and GaAs HEMTs shows that GaN HEMTs have a power density in W/mm which is 23 times
more than GaAs HEMTs along with a breakdown voltage which is five times higher than GaAs devices.
Even though GaN on SiC devices have exhibited superior performance in terms on power density, cut-off
frequency limits, etc., these devices have limitations in terms of output power density at microwave frequencies
and performance degradation with temperature as shown in [25, 26]. In [27], thermal characterization of
high performance millimeter-wave GaN on SiC devices is presented where changes in output power, pinch-off
voltage , knee voltage and saturated drain current is measured. The drain current drops by almost 44%
5
with a temperature variation from -25 to 125 ◦C and the on-resistance changes by 2-3 Ω/mm over the entire
temperature range. A time dependent model to examine current power and temperature in pulsed and CW
mode is shown in citeWu2007. In[28, 29, 30], thermal analysis of GaN FETs is shown with critical voltage
levels due to electronic degradation. In this paper, the drain current dispersion effects are investigated in
AlGaN/GaN HEMTs by measuring pulsed and small signal variations. The gate and drain current lags
are related to the traps formed in the heterojunction as explained in [31] where the DC, small signal and
microwave output power characteristics in AlGaN/GaN HEMTs are studied.
In [31], a maximum drain current of > 1 A/mm and gate-drain breakdown voltage of > 80 V is achieved
for devices with gate lengths of 0.4 µm, ft of 30 GHz and fmax of 70 GHz. It is reported that at high drain
voltages, the electrons injected into the GaN buffer layer get trapped resulting in depletion of the 2-D electron
gas layer at the heterojunction and a reduction in drain current. It is shown that reduction of these trapping
effects result in a CW power density of 3.3 W/mm and pulsed power density of 6.7 W/mm at 3.8 GHz. These
trapping effects cause self heating which can be detrimental to the reliability of GaN devices as shown in [32].
A time dependent model to examine current power and temperature under pulsed operation for GaN devices
is studied in [33]. The self-heating of GaN devices is studied which shows that as the SiC substrate thickness
is increased along with the GaN buffer layer thickness, the thermal resistance also increases. A comparison in
the reduction of transconductance for both SiC and sapphire substrates shows that the transconductance, gm
reduces by nearly 100mS/mm due to heating in both the substrates.
Variations in the chemical composition of the heterojunctions have also been investigated. For example,
In [34], performances of AlInN/GaN heterojunction transistors exhibited 10 W/mm power density with 60%
associated PAE at 3.5 GHz, 6.6 W/mm power density with 39% PAE at 10.34 GHz and 4.2 W/mm power
density with 43% PAE at 18 GHz. In order to operate these devices at higher frequencies and have greater ft ,
the gate lengths for the devices can be scaled and reduces in order to achieve optimal performance at higher
frequencies. In [35], the author mentions that in order to achieve high gain and efficiency at Ka band and
above, the gate lengths should be scaled well below 0.2 µm. In [35], the short channel effects on gate lengths
less than 0.05 µm are presented. A comparison of various wafers with different thicknesses ranging from 207
to 240 A◦ and gate length of 0.32 µm in terms of the ft and fmax is shown in this paper. The aspect ratio of
6
gate length, Lg to substrate thickness t is a crucial factor in deciding the output resistance and heating effects
with exponential increase in these parameters with increase in the ratio. It is concluded that the breakdown
voltage and output resistance benefit from high aspect ratio greater than 15. In [24], performance capabilities
for AlGaN/GaN HEMTs and HBTs at mm-waves is shown. Studies cited in [24] show that a 20% increase in
cut-off frequency, ft will result in a 20% improvement in transconductance, gm . Also, higher values of gm can
be achievable with thin AlGaN barrier layer and low contact resistance.
In recent years, there has been lot of successful work published for GaN power amplifiers at microwave
frequencies with high efficiency and output power and several companies which manufacture commercial
GaN devices today are listed in Table 1.2. A C-band GaN based high power amplifier was shown to have
achieved a CW power of 208 W with 12 dB of small signal gain and 34% efficiency at 5 GHz in [36]. C band
PAs with over140 W of output power using 0.8 µm GaN HEMTs and X band PA with 100 W of output power
using 0.25 µm GaN devices has been reported in [37, 38]. A wideband amplifier working in the S-band from
1.9-4.3 GHz with PAE ranging from 50% - 62% is demonstrated with output power of 10 W over the entire
bandwidth. Also, it is shown that the linearity specifications related to the ACPR of the PA in the entire
band ranges from -44 to -42 dBc for a 11.2 dB peak to average ratio and PAE ranging from 25-27% for this
ACPR. GaN PAs designed for frequencies > 70 GHz have been demonstrated in [39, 40] where the devices
are developed at HRL laboratories. The gate peripheries for these devices range from 150 to 1200 µm. The
PAE at 90 GHz ranges from 13-20% with output power ranging from 1.5 W to 2 W. In [41], X-band MMICs
PAs using TriQuint GaN on SiC 0.25 µm process are presented with PAEs ranging from 45-69% with output
powers ranging from 2.5-13 W and upto 20 dB of large signal gain.
Several companies which manufacture GaN devices today are listed in Table 1.2.
1.3
PA c l a s s e s o f o p e r at i o n
A general block diagram of a power amplifier is shown in Fig.1.4. The gate and drain bias voltages are denoted
as Vgg and Vdd respectively. The drain current is denoted as Idd where as the quiescent drain bias current
is denoted as Idq . There are three reference planes shown at the output of the transistor. Reference plane
P1 is known as the virtual drain of the amplifier. Output impedance matching results in a real impedance,
7
Table 1.2: Several manufacturers of high performance GaN devices for commercial and military applications.
M anuf racturer
TriQuint Semiconductor
Cree
Nitronex
RFMD
Device
Discrete devices (GaN on SiC) with cutoff at 32 GHz
Packaged devices upto 6 GHz
Packaged devices (GaN on Si)
Discrete and packaged devices (GaN on SiC) upto
10 GHz
High performance GaN devices for Military applications
GaN hybrid and wideband amplifiers upto 3 GHz
GaN Power transistors upto 3 GHz
L to C band packaged GaN devices with highest PAE
of 50%
GaN power transistors upto 6 GHz with 50% PAE
and 11 dB gain in C band.
Northrup Grumman, BAE systems, Raytheon, etc
RFHIC
Fujitsu
Mitsubishi Electric
United Monolithic Semiconductors (UMS)
Ropt at this reference plane. Plane P2 represents the reference plane after the output nonlinear capacitance.
Impedance matching at this reference plane results in complex impedance Zopt and is capacitve. Reference
plane P3 denotes a packaged transistor which includes the package parasitics. The fundamental input and
output powers are denoted as Pin and Pout with the total DC power dissipated, PDC = Vdd · Idd .
Figure 1.4: Block diagram of a general power amplifier [2].
The knee voltage, Vknee is the minimum voltage required for the device to operate in the linear region.
This voltage limits the lower values for an RF signal with sinusoidal waveforms and is a cause of distortion.
8
Fig.1.5 shows a typical plot of IV curves for a GaN on SiC device with thermal heating effects. The red curve
shows a trace of DC load line which represents the response of the device to DC and RF input signals.
1200
VGG
IDQ (mA)
1000
800
600
V
,I
DQ
DQ
400
200
0
0
Vknee10
20
VDD (V)
30
40
Figure 1.5: IV-curves for a 6 W GaN on SiC HEMT by TriQuint Semiconductor, TGF2023-01 showing a
class-A bias point condition and load line.
Two definitions of efficiency for a normal mode of operation for a power amplifier are used in the work
presented. These can be defined as the following:
• The drain efficiency, ηD is defined as:
ηD =
Pout (f0 )
PDC
(1.1)
• The power added efficiency or PAE takes into account the gain of the amplifier:
P AE =
Pout (f0 ) − Pin (f0 )
PDC
P AE = (1 −
1
)ηD
G
(1.2)
(1.3)
Note that the RF and DC power levels used in the calculation of efficiencies are in Watts. A power amplifier
is designed to operate in a specific class of operation depending on the bias voltage and current waveform
shaping at the virtual drain of the PA which is the reference plane at the current source within the transistor
and does not take into account the nonlinear output capacitance. In order to design a power amplifier with a
9
specific class of operation, the transistor has to be terminated with the optimal load impedance, Zload as
shown in [42]. The real part of this load impedance, Rload has to be presented at the reference plane P1 as
shown in Fig.1.4.
There are four basic power amplifier classes of operation defined as class A, AB, B and C. These classes of
operation can be distinguished based on the gate bias turn on voltage and the DC quiescent current for the
device. The DC load line for each of the classes of operations varies resulting in different current waveforms.
The efficiency and maximum output power is also a function of class of operation for the PA. A PA is designed
to operate at a certain input drive level in order to achieve one of the basic classes of operation. These modes
of a PA can be distinguished by the current conduction angle α. which is defined as the time for which the
current conducts in the postive cycle and is shown in Figure 1.6.
Figure 1.6: Pictorial representation of current conduction angle, α in a transistor.
1.3.1
S ta n da r d PA c l a s s e s o f o p e r at i o n
A summary of the standard PA classes of operation normalized to maximum current Imax and drain voltage
Vdd is presented in Table.1.3.
Table 1.3: Basic PA modes of operation.
M ode
A
AB
B
C
Vdq
0.5
0-0.5
0
<0
Idq
0.5
0-0.5
0
0
α
2π
π − 2π
π
0-π
M ax.η
50%
50-78.5%
78.5%
100%
When a PA is operating in class-A mode of operation, the Q point defined by drain voltage (Vdq ) and
quiescent drain current (Idq ) is picked at the center of the DC load-line where the DC quiescent current, Idq
10
and DC voltage, Vdq to be set to 50% of the Imax and Vdd values respectively. This allows the current to have
maximum swing for a complete ac cycle of 360◦ . The load, RL can now be defined as follows [2, 43]:
RL =
(Vmax − Vknee )
Imax
(1.4)
The theoretical analysis of reduced conduction angle modes of operation assume that all the harmonics
are presented with short circuit at the virtual drain or reference plane P1 of the transistor. In class-B mode of
operation, the bias point is at cut-off i.e.minimum quiescent drain current. This results in only the positive half
of the ac current cycle to conduct and the resultant conduction angle for the current is 180◦ . The maximum
theoretical efficiency for a class-B mode of operation is 78.5%.
Class-AB can be defined as class of operation with gate bias between class-A and class-B mode. The
conduction angle is therefore greater than π but less than 2π as shown in Fig.1.7. The theoretical maximum
efficiency for a class-AB mode of operation is 65% with the maximum output power 1 dB more than that for
a class-A mode of operation.
Figure 1.7: Current conduction angle for class-A and AB modes of operation for the PA.
In Class-C mode of operation, the transistor is biased below the cut-off region resulting in the current
conduction angle to be less than 180◦ . Therefore, theoretically, this class of operation is designed to achiveve
a 100% efficiency since there is no overlap between the current and voltage ac waveforms resulting in zero DC
power dissipation. However, this class of operation is not practical, since the output power of the device now
reduces significantly. A comparison of the efficiency and fundamental output power normalized to class-A
mode of operation for the lower conduction angle classes (AB,B and C) is shown in Fig.1.8 from [2].
11
1
95
0
85
1
80
75
2
70
3
60
55
50
Class-C
0
/2
Class-AB
3 /2
Conduction Angle [rad]
Class-A
65
Class-B
Drain Efficiency [%]
90
2
4
Output Power Normalized to Class-A [dB]
100
5
Figure 1.8: Theoretical efficiency and output power for reduced conduction angle modes of PA w.r.t class-A
PA efficiency and output power [2].
1.3.2
H a r m o n i c a l ly - t u n e d a n d S w i t c h e d M o d e PA s
In switched-mode PAs, wave shaping is done by directly controlling the time-domain voltage and current
transients after a change in the switching state. The completely on state is a perfect short circuit and the off
state is a perfect open. In order to achieve swtiched-mode of operation , the transistor should be biased at
cut-off (class B) to prevent the current from flowing in the off state. Also, the input drive level must be large
enough to transition from cut-off to saturation very quickly. The ideal switching PA avoids power dissipation
in the switch resulting in a 100% efficient PA. However, this class of operation is nonlinear since almost 20%
of the output power is in the harmonics of the fundamental frequency [2]. Some of the common classes of
switched-mode PAs are class-D, E and S.
In harmonically-tuned PAs, such as class F and F−1 , waveform shaping is done at the virtual drain of
the amplifier by terminating the harmonics in a specific manner as shown in [44, 45, 46]. This results in
reduced DC power dissipation by squaring either voltage (F) or current (F−1 ) and resulting in high efficiency
PAs. Fig.1.9 shows waveform squaring by addition of third harmonic content to the fundamental sinusoidal
waveforms which results in voltage squaring and current peaking for class-F and vice-versa for class F−1
mode.
As explained in [44], in class F mode of operation, the even order harmonics are short circuited and the
odd order harmonics are open circuited at the virtual drain of the PA with a class-B bias condition. This
12
Figure 1.9: Current peaking and voltage squaring in class-F mode of a power amplifier.
results in current peaking and voltage squaring waveforms as shown in Fig.1.9. In class F−1 , the odd order
harmonics are short circuited where as the even order harmonics are open circuited resulting in current
squaring and voltage peaking. However, in practice, it is not possible to achieve ideal square waveforms for
either voltage or current because this will require infinite number of odd harmonics to be terminated. If
only the second and third harmonic is terminated for F/F−1 mode of operation, the maximum theoretical
efficiency is 88.4% with a 0.5 dB increase in the output power as compared to class-B PA. If the terminations
are increased to fifth harmonic, this efficiency increases to 94.8% with 0.82 dB increase in the output power.
However, in order to drive a PA in class-F/F−1 , the PA needs to compressed beyong 1 dB compression so
that it produces significant harmonic content which can then be used to shape the waveforms. Therefore,
this mode of operation, even if highly efficient, is nonlinear by itself. The maximum theoretical efficiency for
class-F mode of operation with addition of third and fifth harmonic is 94.8% with output power comparable
to class-A mode.
1.4
PA T r a d e - o f f C h a r ac t e r i s t i c s
As shown in Fig.1.10, a PA design always involves trade-off between efficiency and linearity. If the PA is
designed to be highly efficient, then PA needs to generate harmonics which makes it very nonlinear. If the
input vs. output power characteristic of the PA is observed in Fig.1.10, the PA has maximum drain efficiency,
13
ηD and PAE at the 1 dB compression point where the output power of the PA is maximum and the PA is
higly nonlinear. Therefore, the output spectrum is distorted due to spectral regrowth and intermodulation
products. This is a significant issue with PA design in industry today since distortion causes band interference.
In order to minimize this distortion, the PA is backed-off in input power. However, at this point, the PA looses
efficiency significantly. Therefore, design of PA for communication and radar systems involves a trade-off
between high efficiency and linearity.
Figure 1.10: Efficiency, gain and output power characteristics of a power amplifier.
Also, modern communication signals have Peak-to-average ratios of > 6 dB which requires the PA to not
only be efficient at a signal drive level but to be consistently efficient and linear for a variation in input power.
This problem can be addressed by designing complex transmitter architectures such as envelope tracking,
Doherty PA design, etc.
1.5
T r a n s m i t t e r a rc h i t e c t u r e s
The stringent requirements in the transmitter designs for handset and base stations require complex PA
architecures to be implemented as explained in [3]. A brief summary of these PA architectures is presented in
Table1.4 with a general block diagram shown in Fig.1.11. The general transmitter architectures consists of
four blocks representing an input signal division between the main PA and secondary PA with a final block
14
for combining the signals from the two PAs at the output.
3
PA2
I/P
1
4
INPUT
SIGNAL
DIVISION
SIGNAL
COMBINING
O/P
2
PA1
MAIN
Figure 1.11: General block diagram of a PA architecture in transmitters to achieve high efficiency for high
Peak-to-average ratios.
15
Table 1.4: Transmitter Architectures
Block
1
16
DohertyP A
Digital, hybrid
LIN C
Digital phase split
2
Class AB RFPA at f0
Class-E high efficiency at
f0 , highly saturated
3
Peaking amplifier, class-C
at f0
Identical to 2
4
Doherty combiner
Isolated/Chireix combiner
Load-pull,
impedance
transformation from 2Z0
(low power state) to Z0
(high power state)
Load-pull with conjucate
impedances
Efficiency enhancement method
EER
Digital baseband, both
magnitude and phase
(polar)
high efficiency class of
RFPA at f0 , optimized
over Vdd
High efficiency, high slewrate PA at envelope bandwidth
Active, low-inductance
bias line in RFPA
Supply modulation
HI − P A
Baseband and RF upconversion
Class A/AB linear RFPA
at f0
Linear PA at 2f0 with gain
> 15 dB and PAE > 40%
3-port diplexer network
2nd harmonic active load
pull
The Kahn envelope elimination and restoration (EER) technique uses a highly efficient but nonlinear
RF PA and a highy efficient envelope amplifier in order to achieve high efficiency PA architecture for high
peak to average ratios. The block diagram of this technique is shown in Fig.1.12. As explained in [3, 47], the
EER approach is based on the fact that a narrow band signal can be produced by simultaneous amplitude
and phase modulations and the transmitters based on Kahn technique provide high efficiency for wide range
of signals and power levels. In this technique, the two most important parameters affecting linearity of the
system are the envelope bandwidth and the alignment of envelope and phase modulators. The envelope
tracking technique is similar to Kahn EER method, except that the supply voltage is changed dynamically.
Figure 1.12: General block diagram for a envelope tracking transmitter system [3].
In the outphasing or LINC technique invented by Chireix, the transmitter produces an amplitude-modulated
signal by combining the outputs of two PAs which are driven by signals with different phases [48, 49]. The
phase modulation causes the instantaneous vector sum of the two output signals to follow the desired signal
amplitude. Fig.1.13 shows a basic block diagram of the system architecture.
In the Doherty PA design technique explained in [50, 51], two PAs are combined with equal power through
quarter-wavelength lines or networks. The main PA is biased in class B mode, while the second PA also
known as the peaking amplifier is biased in class-C. Only the first PA is active when the signal amplitude is
half or less than the peak amplitude. The PA architecture is operated in three different modes with low power,
medium power and peak power. In the low power regions, the peaking PA is off. As the signal amplitude
increases, the peaking PA starts becoming active. The additional current sent to the load of the peaking
PA now causes load modulation at the first PA while maintaining the system efficiency at a constant level.
17
Figure 1.13: General block diagram for an outphasing transmitter system [3].
Fig.1.14, shows a block diagram and the resultant efficiency curve due to Doherty PA design.
Figure 1.14: General block diagram for a Doherty PA transmitter system [3].
All the above mentioned architectures are complex and require more than one PA in order to operate
efficiently for signals with high peak-to-average ratios. The design for these architectures requires challenging
design steps to be taken in terms of efficiency of individual PAs, isolation and maintaining constant load for
the PAs. In order to provide linearization, digital pre-distortion is required in all the architectures as shown in
[52, 53, 54, 55]. Some of the other linearization techniques involves feedback where a portion of the RF-output
signal from the amplifier is fed back to the RF input signal and substracted from it without detection. In this
technique, the delays involved should be small in order to have system stability and loss of gain is also an issue.
Another technique to achieve linearization involves the feedforward technique where the input signal is split
into two paths, with one going to the main PA and other going to a delay element. The output signal from
the main PA then consists of both desired and distorted signal. This signal is then combined with the delayed
18
input part of the signal to eliminate the error signal. Analog pre-distortion technique as explained in [56], can
also be used to achieve linearization. Some of the recent work has been concentrated towards integration of
supply modulation with other transmitter architectures to achieve high efficiency for >6 dB Peak-to-Average
ratio signals. It is shown in [57] that a Doherty PA topology integrated with supply modulation results in
PAE ranging from 51 - 70% with 8 dB back-off in input power level.
However, all these techniques require large system considerations and design challenges so as to integrate
linearization techniques and achieve high efficiency for high Peak-to-Average Ratio signals. Some of the newer
techniques being researched involve active load modulation which can help achieve high efficiency as well as
reduce the intermodulation distortion to a certain level so that linearization as baseband does not provide
high complexity and design challenges for a PA designer. This thesis talks about one of the active load
modulation techniques known as second harmonic injection at the output of a PA where a external second
harmonic signal with optimal phase and amplitude is injected into the drain of a PA with a diplexer network.
However, even in this approach, the efficiency of the injector circuit can play a crucial role and result in
design challenges at the desired input drive level. In the work presented, results from integration of harmonic
injection PA architecture with supply variation are also analyzed and presented in Ch.6.
19
Chapter 2
T h e o r e t i c a l B a s i s f o r PA s
with Harmonic Injection
Progress is impossible without change, and those who cannot change their minds cannot change anything.
—George Bernard Shaw
Contents
2.1
Concept of Harmonic Injection PA (HI-PA)
2.2
Theoretical Analysis
2.3
2.2.1
Waveform Analysis
25
2.2.2
Efficiency Analysis
27
Linearity
2.3.1
2.4
25
32
Waveform shaping
Conclusion
39
33
21
2.1
C o n c e p t o f H a r m o n i c I n j e c t i o n PA ( H I - PA )
The concept of harmonic injection refers to architectures in which power at one or more harmonics of the
operating frequency is supplied externally to either the input, output or both of an active device. A general
block diagram describing the concept for harmonic injection at the output of a PA is shown in Fig.2.1.
This concept incorporates the use of the fundamental frequency input signal to create the harmonics using
frequency doublers which are then injected into the output of the PA at an optimal amplitude and phase. The
amplitude and phase of these harmonics can be adjusted using phase shifters and attenuators. The concept of
injection at the second harmonic is shown in theory and experiment in this work.
Figure 2.1: Block diagram of a harmonic-injection power amplifier (HI-PA) with 2nd harmonic injection at
the output. A three-port network at the output allows isolation between waves at f0 and 2f0 between ports 2
and 3, while allowing low loss at f0 between ports 1 and 2. The phase of the injected harmonic is critical to
obtaining high efficiency.
Harmonic injection has been performed at the second harmonic at both input and output of an amplifier
in order to achieve high efficiency or linearity criteria for the designed PA. In 1992, a patent was issued for a
harmonic injection amplifier in which the harmonic signal created using a frequency multiplier is injected into
the transistor output [58]. Analysis of efficiency improvement of tube PAs using harmonic injection into both
the grid (input) and plate (output) has been presented in [59, 60, 61]. A harmonic injection scheme referred
to as a harmonic reaction amplifier was presented in [4]. In this PA architecture, PAE of 75% is achieved
for a 3-W GaAs PA at 1.7 GHz. The architecture uses two similar PAs in parallel which utilize the second
harmonic produced by each of the PAs to enhance the efficiency. Signal rejection filters for fundamental and
21
second harmonic are integrated in the output network to provide isolation between the PAs. Fig.2.2 shows
the variation in PAE and draine efficiency with 2nd harmonic path length variation.
Figure 2.2: Variation in PAE and drain efficiency with change in second harmonic path length [4].
Harmonic injection technique has also been used at the input of a PA for enhancement of linearity in
the PA. [62] showed theoretical analysis for linearization of power amplifiers based on second harmonic
injection and base-band frequency injection at the input of the PA. In this method, the second-order frequency
components generated by the predistortion circuits are provided at the input of the PA in order to generate
mixing products for IM D3 cancellation. However, the practical limitations shown are subject to the gain
and phase error associated with RF and baseband circuitry. Demonstration of reduction in third order
intermodulation distortion products or IMD3, by over 24 dB for the upper sideband using a two tone signal
with 5 MHz spacing is shown in [5] with harmonic injection at the input of a TWT amplifier. Fig.2.3 shows
the measured results for a two-tone test on TWT with harmonic injection showing a 21.3 dB reduction in
upper IMD3 levels.
In [63], a design concept of the PA’s load impedance and bias network with second harmonic injection is
22
single-harmonic injection experimental setup.
ns that were made with the TWT deactivated.
behavior in TWTs. Other investigators [4],
d harmonic injection behavior in multitone
injected signal amplitude and phase sensially studied in detail. Furthermore, Sauseng
7 dB, while we have found
Figure 2.3: TWT output spectrum for a two-tone 15 dBm/tone input signal with harmonic injection showing
a 21.3 dB reduction in upper IMD3 levels [5].
shown using volterra-series analysis. The design presented here shows a final stage PA with drain efficiency of
53% and output power of 21 dBm. It is shown in [6] that the second harmonic injection at the input reduced
the IMD3 levels by 43 dB at 835 MHz resulting in a linear power amplifier. Also, it was shown that injection
at the difference frequency can also result in high linearity with a 20 dB improvement in IM D3 and 30 dB
improvement in IM D5 as shown in Fig.2.4. Second harmonic injection using feedback from output to the
input of a PA resulting in 16 dB reduction of IMD3 levels has also been demostrated in [64].
More recently, An experiment demonstrating 15.2% efficiency improvement of a 2 GHz GaN PA using second
harmonic injection at the input is reported in [65]. More recently, a concept for efficiency improvement via
injection of harmonics into the output of a narrowband and broadband class-B/J amplifier was demonstrated
[7, 66]. Fig.2.5 shows the measured efficiency for a class-B/J PA with second harmonic injection at the output.
A novel scheme of efficiency improvement of a class-E amplifier using input harmonic injection via a feedback
loop was shown in [67]. Also, a class-E VHF PA at 3.5 MHz with a secondary class-E 7 MHz PA injector is
23
(a)
(b)
Figure 2.4: Two-tone response of 880 MHz amplifier without (a) and with (b) injection of difference frequency
showing IM D3 and IM D5 improvement of 20 and 30 dB respectively [6].
presented in [68].
Figure 2.5: Harmonic injection class-J PA results for a constant magnitude and phase offset between the
input and injected signals [7].
As shown in [69, 70, 6, 5, 71], second harmonic injected at the input of a power amplifier results in
null points in the intermodulation distortion products or IMDs resulting in linear PAs. However, harmonic
injection at the output of the PA, as shown in [9, 7] results in a highly efficient power amplifier with total
drain efficiencies ranging from 70-80% in compression. Harmonic injection at the output of the PA also results
in direct impedance synthesis at the harmonics resulting in lower distortion content. This results in higher
linearity as well. In the next section, a theoretical explanation for the concept of second harmonic injection at
the output of the PA is derived using fourier waveforms expansion [43].
24
VDD
iD
f0
f0
1 Linear 2
3-port
3
2f0
Z(2f0)
Min
f0
Mout
ZL
2f0
(a)
(b)
Figure 2.6: (a) Block diagram of a harmonic-injection power amplifier (HI-PA) with 2nd harmonic injection
at the output. A three-port network at the output allows isolation between waves at f0 and 2f0 between
ports 2 and 3, while allowing low loss at f0 between ports 1 and 2. The phase of the injected harmonic is
critical to obtaining high efficiency. (b) Ideal S parameters for the three port injection network.
2.2
T h e o r e t i c a l A n a ly s i s
The theoretical analysis of the efficiency for a harmonically injected PA (HI-PA) shown in Fig.2.6 is developed
based on Fourier expansions of the voltage and current waveforms at the current source of the transistor,
detailed in [7, 72]. First, expressions are derived for injected voltage which optimizes efficiency, followed by
the analysis of total dissipated power and a discussion of linearity. This analysis, though ideal, reveals the
main purpose of the HI-PA and is summarized here for completeness from[43]. Following an overview of
efficiency and power, a theoretical development of linearity for the HI-PA using taylor series expansion of the
PA nonlinear characteristics is shown.
2.2.1
Wav e f o r m A n a ly s i s
In the discussion of the efficiency and power for an HI-PA shown in M. Roberg’s thesis [43] and similar
discussions in [73], the normalized drain voltage and current waveforms at the virtual drain of a linear FET
PA are considered:
v̄D (θ) = V̄DD +
īD (θ) = I¯DD −
√
√
2 sin θ
(2.1)
2 sin θ
(2.2)
where θ = 2πf0 t , and the bar indicates a normalized quantity. For instance, when V̄DD = I¯DD =
√
2, the
normalized class-A output power is 1W and the waveforms result in 50% efficiency. If the drain waveforms
25
can be shaped by harmonic content in a manner such that the overlap of the voltage and current is minimized
for a given fundamental frequency output power, then drain efficiency will be maximized.
Consider the addition of only the second harmonic term in (2.1) and (2.2). In order to maintain waveform
symmetry, only co-sinusoidal components are added. Such a condition will result in the voltage waveform of
the same shape but 180◦ out of phase with the current waveform. The waveforms following addition of a
second harmonic term become:
v̄D (θ) = V̄DD +
īD (θ) = I¯DD −
√
√
2 sin θ + a2 cos(2θ)
(2.3)
2 sin θ + a2 cos(2θ)
(2.4)
as shown in Fig.2.7, showing minimal overlap of the voltage and current waveforms.
3
vD(θ)
iD(θ)
Normalized v, i
2.5
2
1.5
1
0.5
0
0
45
90
135 180 225 270 315 360
θ
Figure 2.7: Optimal drain current and voltage waveforms for second harmonic injection amplifier, normalized
to 1 W output power.
From (2.3) and (2.4), it can be concluded that the impedance at 2f0 is the negative of that at f0 . Effectively,
this requires that power is delivered to the transistor at the second harmonic. An optimal value of a2 that
maximizes the efficiency can be found by analyzing the critical points of the drain current and voltage
waveforms. The resultant optimal values of a2 are then calculated to be:
√
a2 > + 2/4,
v̄D (θcritical,v ) is a minimum
(2.5)
√
a2 < − 2/4,
v̄D (θcritical,v ) is a maximum
(2.6)
26
2.2.2
E f f i c i e n c y A n a ly s i s
The normalized total DC power consumed by the amplifier is expressed as
a2
a2
2
+ 2
P̄DC = V̄DD I¯DD + 2 = V̄DD
2ηinj
2ηinj
(2.7)
where ηinj is the efficiency of the injector circuit. Note that due to the symmetry of the current and voltage
waveforms, V̄DD = I¯DD , the optimal DC supply voltage is that which results in a drain voltage waveform
with minimum of zero. Therefore, from (2.3),
√
V̄DD = − 2 sin θmin,v − a2 cos(2θmin,v )
(2.8)
The total DC power may now be expanded to the form
P̄DC =
1 + 4a22
4a2
2
+
a22
,
2ηinj
a2 ≤
and
P̄DC
√
− 2
4
√
− 2
a2 >
4
√
a2
= ( 2 + a2 )2 + 2 ,
2ηinj
(2.9)
(2.10)
Since we use a normalization that sets the fundamental output power to 1 W, the total efficiency is calculated
as the inverse of the normalized DC power.
ηtotal (a2 , ηinj ) =
1
P̄DC
(2.11)
Fig.2.8 shows the total efficiency plotted as a function of both injector efficiency, (ηinj ) and normalized
magnitude of 2nd harmonic (a2 ).
The value of a2 is optimized by setting the partial derivative of PDC w.r.t. the Fourier coefficient a2 to
zero and solving for a2 :
a2 = − q
√
− 2
a2 ≤
4
1
,
1
8(2 + ηinj
)
√
√
2 2
− 2
a2 = −
a2 >
1 ,
4
2 + ηinj
4
(2.12)
(2.13)
1
These values minimize PDC . Given ηinj = 1, the optimal Fourier coefficient reduces to − √
. A plot of a2
4
24
which corresponds to the amplitude of the required injected 2nd harmonic versus ηinj is shown in Fig.2.9.
As one would expect, the magnitude of the Fourier coefficient decreases as the injector efficiency decreases.
27
1
0.
1
0.15
0.15
00.05
.00.1
30.53.2050.1.25 8.9898e−008
0.8
0.25
0.4
0.45
0.5
5
0.5 .45
0.5 300.35
.
0.05
.4
0
0.02.250 8.9898e−008
0.1
0.15
a2
4
0.
0.6
−0.2
−0.4
−0.6
−0.8
0.25
0.25
0.3
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0
0.7 .75
0.60.65
0.50.55
0.4
0.45
0. 0 0
25 .3 .35
2
0.2
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.55
0.65
0.7
0.75
0.8
0.
85
0.8
0.7 0.75
0.
0.6 65
0.55
0.5
0.45
0.4
0.65
0.
0.1
−1
0
0.2
0.3
0.35
0.4
0.2
0
0.2
0.2
0.6
0.4
ηinj
0.85
0.8
0.75
0.7
0.65
0.6
0.5
0.6
0.8
1
Figure 2.8: Contour plot for ηtotal as a function of a2 and injector circuit efficiency ηinj .
Another interesting parameter to investigate is the ratio of the delivered fundamental output power to the
a2 required delivered second harmonic injected power, 20 log10 √
, also shown in Fig.2.9. The PA efficiency is
2
0
−8
−12
a2
−0.2
−14
−0.3
−16
−0.4
Power Ratio (dB)
−10
−0.1
−18
−0.5
0
0.2
0.4
η
0.6
0.8
−20
1
inj
Figure 2.9: Optimal solution for Fourier coefficient a2 and second harmonic delivered power relative to
fundamental frequency output power versus second harmonic injector circuit efficiency ηinj .
determined by inserting a2 into (2.9) and (2.10):
P̄DC =
2+
2
q
1
2(2 + ηinj
) +2
q
,
1
8 2(2 + ηinj
)
28
√
− 2
a2 ≤
4
(2.14)
and
1
P̄DC =
ηinj
ηtotal
q
8
ηinj
+ 16
+q
2
8
ηinj
1
+ ,
+ 16 2
q
1
)
8 2(2 + ηinj
=
,
2
q
1
2 + 2(2 + ηinj
) +2
and
s
ηtotal = ηinj
8
ηinj
!
+ 16 − 4 ,
√
− 2
a2 >
4
(2.15)
√
− 2
4
(2.16)
√
− 2
a2 >
4
(2.17)
a2 ≤
A plot of the total efficiency versus injector circuit efficiency, ηinj is shown in Fig.2.10 for optimized solution
at a2 and a plot for the total efficiency, ηtotal as a function of ηinj and a2 is shown in Fig.2.8. The maximum
value is 89.9%, and it rolls off reasonably slowly with decreasing injector efficiency. This is intuitive because
the power required from the injector is significantly lower than the fundamental output power of the amplifier,
as shown in Fig.2.9. As expected, when the amplifier efficiency reaches 50%, the injector circuit is turned off.
In this case the amplifier degenerates to the canonical class-A mode.
0.9
ηtotal
0.8
0.7
ηinj =
Pinj (2f0 )
Pinj,DC
0.6
0.5
0
0.2
0.4
ηinj
0.6
0.8
1
Figure 2.10: Total efficiency ηtotal versus injector circuit efficiency ηinj .
As previously mentioned, the load presented to at the second harmonic is the negative of that presented
at the fundamental, so the load resistance normalized to the class-A fundamental load is −1. To find the
output power of the PA normalized to class-A output power, normalization conditions corresponding to peak
voltage and current constraints are enforced. V̄DD and I¯DD are now found, enabling determination of the
maximum instantaneous normalized voltage V̄max and current I¯max , and the output power normalized to the
29
class-A amplifier output power is determined. The normalized DC voltage is expressed as
V̄DD = −
V̄DD =
√
− 2
4
√
− 2
a2 >
4
1 + 4a22
,
4a2
√
a2 ≤
2 + a2 ,
(2.18)
(2.19)
Note that due to the symmetry of the current and voltage waveforms, V̄DD = I¯DD , the maximum normalized
voltage is calculated as
V̄max = −
√
1 + 8a22 − 4 2a2
,
4a2
and
V̄max
√
= 2 2,
a2 ≤
√
− 2
4
√
− 2
a2 >
4
(2.20)
(2.21)
The output power normalized to class-A is then given by
pLA (f0 ) = pLA (f0 ) =
8
√
2 ,
1+8a22 −4 2a2
4a2
8
√
= 1,
(2 2)2
√
− 2
a2 ≤
4
(2.22)
√
− 2
4
(2.23)
a2 >
Fig.2.11 depicts the fundamental frequency output power reduction relative to a class-A amplifier versus the
injector efficiency. This was calculated by computing a2 as a function of ηinj , then computing the output
power from a2 and determining the ratio relative to 1 W. When ηinj = 1, the output power is only reduced
by only 0.13 dB relative to the class-A amplifier.
Also, it is of practical interest to find the supply voltage and current normalized to class-A:
V̄DD
vDD,A = √
2
(2.24)
Fig.2.11 shows the normalized supply voltage which is approximately 0.7107 for ηinj = 1.
A similar analysis can be performed for third harmonic injection at the output, since symmetric square
waveforms can be achieved using odd harmonics only. In the case of third harmonic injection, the impedance
at the third harmonic is positive rather than negative, so the ideal waveforms can be realized with a passive
set of output terminations. The analysis shows, however, that the total efficiency given by (2.16)-(2.17) is
around 65% for injector efficiencies above 40% and does not reach the high efficiencies of the second harmonic
30
0.02
1
0.95
−0.02
0.9
−0.04
−0.06
0.85
−0.08
vDD,A
Power Reduction (dB)
0
0.8
−0.1
0.75
−0.12
−0.14
0
0.2
0.4
ηinj
0.6
0.8
0.7
1
Figure 2.11: Power reduction and normalized supply voltage relative to class-A vDD,A versus injector efficiency
ηinj .
injection case. The complete theoretical analysis for third harmonic injection at the output can be found in
[43].
Since doing second harmonic injection at the output of the amplifier requires additional power at second
harmonic to be generated, the efficiency calculation cannot be done by just taking into account, the fundamental
output power and DC power dissipated in the main PA. Now the DC power dissipated in the injection
circuit is critical and needs to be considered for overall efficiency of the harmonically-injected PA. This drain
efficiency can be described as follows:
ηD =
Pout (f0 )
Pinj (2f0 )
PDCinj =
PDCf0 + PDCinj
ηinj
(2.25)
where PDCf0 is the DC power dissipated in the fundamental PA and PDCinj is the DC power dissipated in
the injection circuit. Since, the injector circuit not only consists of driver amplifiers, but also other components
such as phase shifters, variable attenuators and mixers, the DC power dissipated in the injector circuit is
defined as function of the injection circuit efficiency, ηinj and the total RF power delivered at second harmonic,
Pinj (2f0 ).
31
2.3
Linearity
Transistors exhibit nonlinearities due to various factors such as input and output device capacitance, transconductance and drain-source resistance resulting in nonlinear transfer function which can be described in terms
of input gate voltage, vgs and drain current, id as follows:
gm =
∂id
∂vgs
(2.26)
where gm is the transconductance of the amplifier. As shown in Fig.2.12, this transconductance varies as
a function of gate bias for each of the harmonics produced by the PA in a specific manner. The fundamental
frequency transconductance, gm1 , increases as the PA gate voltage increases from pinch-off voltage. However,
the third harmonic transconductance, gm3 has negative values in the class-A/AB region where as it is positive
when the PA is biased at pinched-off. The interaction of harmonics in the PA with different transconductance
Transfer function & its derivatives
values with the fundamental frequency results in waveform shaping and power compression.
0.02
C
B
AB
A
0.01
0
2 iDS[vGS]
2 G1
G2
G3
0.01
0.02
0.5
1
1.5
2
VGS,bias [V]
2.5
3
Figure 2.12: Typical transfer function and its derivatives for different gate bias voltages in FET power
amplifier. The corresponding classes of operatiion are shown on top of the figure [8].
The general transfer function for a PA output system in terms of input and output voltage can be defined
with the power series as follows:
32
vout
= k1 vin + k2 vin 2 + k3 vin 3 + ...
1
3
2
3
=
k2 A + k1 A + k3 A cos ωo t +
2
4
1
1
k2 A2 cos 2ωo t + k3 A3 cos 3ωo t
2
4
(2.27)
where vin = A cos ω0 t. k represents the general transfer function for the entire PA system.
As seen in (2.27), the second order nonlinearity causes an additional DC component and a signal at
twice the fundamental frequency to appear in the output voltage. For a two tone signal, the second order
nonlinearity can be easily filtered out and does not cause any in-band distortion of the signal. However, the
third order nonlinearity results in in-band distortion products. The gain of the fundamental component under
nonlinear operation can be expressed in terms of the fundamental gain and the third order gain and amplitude
and the derivation is given in [74]. The analysis in [74] also shows that the amplitude of the second harmonic
output signal is inversely proportional to the magnitude of the transfer characteristic of the amplifier at the
third harmonic, which is referred to in section IV. A good discussion on extracting linearity information
from a CW-fed amplifier by measuring the third harmonic output content is presented in [75]. Based on this
theory, in this paper, a CW signal is used for harmonic injection analysis as the device enters saturation. In
particular, we measure 2nd and 3rd harmonic as a function of the injected power and phase in order to assess
the linearity.
2.3.1
Wav e f o r m s h a p i n g
An amplifier’s simplest form on nonlinearity can be described by adding the second term to the transfer
characteristic as shown in Eq.2.27. When the PA starts compressing, the amplitude of the second harmonic
increases as the square of the fundamental power. Therefore, the transconductance, gm2 also increases. From
Fig.2.12, this transfer function is remains positive when the PA is operating in class-A/AB mode. Now
consider a sinusoidal input fundamental signal to the PA with the fundamental transconductance value, gm1
= 10. If only the second order nonlinearity is considered, then for various values of gm2 , the output current
waveform will distort as shown in Fig.2.13.
33
15
gm2 = 0
1
1.5
2
2.5
Amplitude
10
5
0
−5
−10
0
1
2
3
4
5
Time (mS)
6
7
8
Figure 2.13: Effect of second order nonlinearity on sinusoidal waveform.
It is seen that as the value of gm2 increases, the sinusoidal signal becomes more asymmetric resembling
half wave sinusoidal waveforms similar to class-B waveforms for a PA. This results in an additional DC
component and the second harmonic due to the second order nonlinearity as shown in (2.27) and Fig.2.13.
Therefore, the optimal amplitude required for the injected second harmonic depends on the input drive level
and the power of the second harmonic produced by the PA itself.
In order to analyze third order nonlinearity, first lets consider the Fourier series approximation of a square
wave which can be represented as follows:
x(t) =
4
1
1
(sin(2πf t) + sin(6πf t) + sin(10πf t) + ......)
π
3
5
(2.28)
where x(t) represents the square wave. The Fourier series representation of square wave is shown in
Fig.2.14.
It is seen that ideal square wave results from infinite number of terms in the Fourier series expansion.
However, with limited number of terms, the Fourier series representation of a square wave is non-ideal and
results in flat waveforms with ripples. In a PA, odd order nonlinearities, such as 3rd , 5th ,... result in squaring
of the fundamental sinusoidal signal resulting in power compression.
Now, if only addition of the third order nonlinearity of a PA with the transconductance, gm3 is considered,
then depending on the polarity of gm3 , the power of the fundamental signal can either increase or decrease.
34
1.5
x=sin(θ)
y=x+ (1/3)sin(3θ)
z=y+(1/5)sin(5θ)
w=z+(1/7)sin(7θ)
1
Amplitude
0.5
0
−0.5
−1
−1.5
0
1
2
Time (ms)
3
4
Figure 2.14: Square wave representation with the first four terms in the Fourier series.
From Fig.2.12, the values of gm3 for classA/AB conditions have negative sign. This results in waveform
squaring and power compression in a PA as shown in Fig.2.15.
10
Amplitude
5
0
gm3= 0
−0.5
−1.5
−2.5
−3.5
−5
−10
0
1
2
3
4
5
Time (ms)
6
7
8
Figure 2.15: Effect of third order nonlinearity on sinusoidal waveform with negative gm3 values.
If the absolute values of gm3 are positive, then the sinusoidal waveform for various gm3 values results in
waveform peaking and increase in power level as shown in Fig.2.16.
It is known from Fig.2.12 that the values for gm3 are negative for class-AB or deep class-A mode of
operation. Therefore, in order to avoid squaring of fundamental waveforms resulting in reduced output power
35
15
g
10
5
Amplitude
m3
=0
0.5
1.5
2.5
3.5
0
−5
−10
−15
0
1
2
3
4
5
Time (ms)
6
7
8
Figure 2.16: Effect of third order nonlinearity on sinusoidal waveform with positive gm3 values.
and shaping the waveforms such that the resultant response is similar to the one shown in Fig.2.16, the
values og gm3 should be positive. From the theory presented in section 6.2, it is known that the injected
second harmonic signal needs to be 180◦ out of phase w.r.t. the fundamental voltage and current waveforms.
Therefore, when harmonic injection is performed on the PA, the mixing of the injected second harmonic and
fundamental signal results in a third harmonic with opposite phase w.r.t. the third harmonic produced by the
PA. This results in minimizing of the third harmonic and improving the linear performance of the PA.
Even though CW signal evaluation can give a general idea about the linearity of the PA, two-tone
tests provide a better approximation of spectral regrowth and Adjacent channel power ratio (ACPR) with
intermodulation distortion products or IM D products. First, the general behavior of PA with two-tones is
analyzed w.r.t various gate bias levels. It is shown in [8, 76, 77] that the intermodulation distortion products
characterisitcs vary as the gate voltage is swept from cut-off region to active region for transistors. The odd
order distortion products are of relevance as they result in in-band distortion which is not easy to filter out.
The third and fifth order distortion products (IMD3 and IMD5) are the most relevant parameters discussed
in this work.
The intermodulation distortion products in an amplifier exhibit a behavior with sweet spots depending on
the gate bias and input drive level. These sweet spots largely termed as large signal IMD sweet spots occur
when the small signal IMD is in phase with the fundamental component. This behavior is associated with the
36
power expansion series as shown in [78].
Consider the simplified transfer function for a power amplifier based on Taylor series expansion with the
output current id as a function of the input gate voltage, vgs only. The power series can be written as:
id = gm1 .vgs + gm2 · vgs 2 + gm3 · vgs 3 gmk =
δ k id
, k = 1, 2, 3...
δ k vgs
(2.29)
Assuming a two tone input signal with amplitude A1 , the input gate voltage can be written as:
vgs = A1 · (cos(ω1 t) + cos(ω2 t))
(2.30)
By substituting (2.30) in (2.29), the fundmental and third order IMD components of id are:
9
if und = [gm1 A1 + gm3 A1 3 ] · cos(ω1 t)
4
(2.31)
3
iimd3 = [ · gm3 A1 3 ] · cos(2ω1 t − ω2 t)
4
(2.32)
Since the transconductance is strongly dependent on the gate bias and the current depends on the
transconductance, gmk which can take positive or negative values depending on the bias, it follows that for a
particular vgs , gm3 = 0. This results in nulling of IMD3 products resulting in the sweet spot condition.
As seen from Fig.2.12, in class-A bias, the initial value of gm3 is negative, so no sweet spots are expected
for this class of operation. But for reduced conduction angle modes, the values of gm3 in small signal are
positive, resulting in sign change at large signal power levels. Hence, a zero crossing takes place and there
exists sweet spots. This condition described here is for the third order distortion product only. However, if
we look at higher odd order nonlinearities, such as gm5,7,9... , the resultant sweet spots will not follow the
behavior for different classes of operation as the IMD3 products. Fig.2.17 shows the odd order distortion
products calculated for a TriQuint 6 W GaN on SiC device in class-A mode.
When harmonic injection is performed on a PA at the output, the injected signal now mixes with the
fundamental frequency and other harmonic frequencies, the PA produces by itself. As shown in [43], active
impedance synthesis at second harmonic at the drain of the PA requires the PA also to produce harmonic
37
Figure 2.17: Measured voltage levels of odd order intermodulation distortion products for a two-tone signal
with f1 = 2.45 GHz and 1 MHz tone spacing.
content. Hence, the impedance synthesis at 2f0 now affects the other harmonic frequencies causing mixing
products with different amplitude and phase. Fig.2.18 shows impact of second order products on the third
and fifth order intermodulation distortion products.
Figure 2.18: Effect on odd order distortion products (IMD3,5,...) due to mixing of fundamental, second and
third order products.
From Fig.2.8, the second harmonic injection signal is 180◦ out of phase with the fundamental signal in
38
order to achieve high efficiency. Mixing of the second harmonic with other intermodulation products such as
IMD3,5,.... also results in harmonic components with opposite phase as shown in Fig.2.19. This results in
cancellation of the distortion products as an optimal phase and amplitude of the injected second harmonic.
Figure 2.19: Cancellation in intermods due to mixing products formed from second harmonic injection with
opposite phase. Here, r1 represents the IMD products from amplifier nonlinearity, r2 represents the IMD
products created by mixing of fundamental and injected second harmonic signal. The resultant red phasor
shows reduced amplitude resulting in reduction in overall distortion.
However, as shown in Fig.2.17, if the third and fifth order intermods are not increasing simultaneously
with sweet spot conditions exhisting for either of the intermods at specific input drive levels, then reduction
in both 3rd and 5th order intermods can be challenging. When the PA is operating in class-A mode, the sweet
spot condition exhists only for fifth and higher order distortion products. Therefore, when the input power is
swept, points in the input power sweep where sweet spots exhist for higher order intermods should be avoided
in order to achieve simultaneous reduction in all odd order intermodulation products. Note that IMD7,9,...
etc do not affect the perfomance of the PA as strongly as the third and fifth order distortion products due to
extremely low power levels.
2.4
Conclusion
The theoretical foundations for harmonically-injected PAs presented in this thesis are derived for a highly
idealized transistor model. Nevertheless, the fourier analysis predicts a maximum theoretical efficiency of
89.9% with a 0.13 dB reduction in output power and is able to predict trends in the optimal injected power
39
and phase for the second harmonic. The theory also predicts the required efficiency of the injector circuit of >
40% in order to achieve significant overall improvement in efficiency. The power series expansion of transistor
nonlinear characteristic gives insight into the linearity behavior of a harmonically-injected PA in terms of the
even and odd harmonic content produced at the output of the PA.
40
Chapter 3
P ro o f - O f - P r i n c i p l e S - B a n d
H I - PA
Excellence is not a skill. It is an attitude.
—Ralph Waldo Emerson
Contents
3.1
3.1
Introduction
41
3.2
3-Port output Injection Network
3.3
Linearity Measurements
3.4
Conclusion
42
47
49
I n t ro d u c t i o n
In this chapter, a proof-of-concept harmonic injection PA or HI-PA is presented using a hybrid proto-type
class-AB PA provided by Cree. The packaged device, CGH40006P has a maximum output power of 40 dBm
or 10 W in class-A mode and 6 W in class-B mode. The 50 Ω PA is designed by Cree to operate from DC to
6 GHz. This PA is used to demostrate the harmonic injection concept at f0 = 2.45 GHz with second harmonic,
2f0 at 4.9 GHz. To this end, a three port injection network is designed in a 50Ω environment which allows
the second harmonic to be injected into the output port of the PA. Initial experimental results demonstrate
improvements in both efficiency and linearity.
3.2
3 - P o rt o u t p u t I n j e c t i o n N e t wo r k
As shown in [43], a three-port output network satisfying the following conditions is required when injecting
only the second harmonic at the output of the PA.
This network acts like a diplexer which is a combination of a high pass filter and a low pass filter in
parallel. Such a three-port network is implemented in microstrip on a Rogers 4350B 30-mil thick substrate
with relative dielectric constant, r of 3.66 and loss tangent, tanδ of 0.0031, similar to the work reported in
[7] at 900MHz and in [66] from 0.6-2.4 GHz. Fig.3.1 shows the relevant measured S-parameters extending
beyond the second harmonic of the 2.45 GHz fundamental.
0
S parameters (dB)
10
20
30
S11
S21
40
S31
S33
50
2.5
3
3.5
4
Frequency (GHz)
4.5
5
Figure 3.1: Measured S parameters for the three port injection network designed on Rogers 4350B substrate
with a photograph of the circuit shown in the inset.Port 1 represents the drain of the fundamental PA, port 2
is the output of the PA and port 3 represents the injection port.
It is seen in Fig.3.1 that port 1 is matched for both the fundamental, f0 = 2.45 GHz and second harmonic,
2f0 , 4.9 GHz with |S11 < -40 dB for both the frequencies. The plot also shows that the through path from
42
port 1 to port 2 for the fundamental frequency provides a very low loss where as the second harmonic is
well isolated in this path since |S21|(2f0 ) < -25 dB. Therefore, the second harmonic will not leak into the
fundamental low pass network resulting in negligible interference between fundamental output signal and
injected second harmonic signal. Also, it is seen that port 3 is well isolated for f0 with |S31|(f0 ) < -25 dB
where as the second harmonic has extremely low loss in this path.
Once this network is designed, the concept of second harmonic injection is now validated by connecting
the Cree CGH40006P-TB amplifier to the injection network at the output. As shown in [79], the PA has a flat
gain of approximately 12 dB from 2.5 to 5 GHz at a drain voltage, VDD = 28 V and quiescent drain current,
IDQ = 100 mA. The PA drain effiency is, ηD = 60% in class-B configuration at 2 GHz. The PA compresses at
an input drive level of 32 dBm with a maximum output power, Pout ' 9 W at 2.45 GHz.
The harmonically-injected PA or HI-PA setup for f0 = 2.45 GHz, 2f0 = 4.9 GHz utilizes two Cree GaN
pHEMTs (CGH40006P) in broadband (DC-6 GHz) class-AB test-boards provided by the manufacturer. As
shown in Fig.3.2, one of the PAs is used as the fundamental PA and the other PA is used as a driver in the
second harmonic injection path. A single sweeper is used to generate the fundamental frequency signal at
2.45 GHz.
Figure 3.2: Block diagram for the experimental validation of a harmonically-injected PA concept using two
pre-built broadband Cree PAs.
A 3 dB splitter,is used to divide the signal between the main PA and the second harmonic path. A
low-efficiency commercial frequency doubler (Mini Circuits ZX90-2-36-S) is used to create the 2f0 CW signal
43
with a manual phase shifter and attenuator to adjust the phase and power level of the injected second harmonic
signal in order to achieve active impedance synthesis at 2f0 at the drain of the amplifier. As shown in [43], the
injected signal is required to have an optimal amplitude and phase w.r.t the output of the main PA. In order
to achieve the desired power level, two driver stages are used in the second harmonic injection path. The
three port injection network designed is used to inject the second harmonic into the output of the main PA.
Due to the low dynamic range of the frequency doubler, the input power to the main PA is limited and
swept from Pin = 27 dBm to 34 dBm (linear to saturation region). A signle sweeper is used in order to
preserve the relative phase in the two paths between measurements.
The drain supply is varied and measurements are performed at VDD = 22, 25 and 28 V. The gate variation
is also performed with VGG = -1.6, -1.8 and -2 V. Since the harmonically-injected PA involves an external
second harmonic signal being used to shape the fundamental voltage and current waveforms, the efficiency
calculation of the entire PA system cannot just take into account the fundamental output signal and the DC
power dissipated by the main PA only. In order to achieve the correct efficiency, the DC power dissipated in
the second harmonic injection path needs to be taken into account. The harmonic injection circuit not only
consists of amplifier, but also mixers with conversion loss and phase shifters. Hence, a better way to calcuate
the DC power dissipated in the harmonic injection path is to take into account the amount of RF power
being injected into the main PA at the second harmonic and the efficiency of the second harmonic injection
circuit. The drain efficiency of HI-PA is therefore calculated as follows:
ηD =
where Pinj,DC =
Pout (f0 )
PDC + Pinj,DC
(3.1)
Pinj (2f0 )
.
ηinj
This efficiency calculation takes into account the 2f0 injected power and the DC power dissipated by the
2f0 generating amplifier.
Fig.3.3 compares the measured efficiency, output power and gain for the PA with and without harmonic
injection. It is seen that the HI-PA saturates at a higher input power (32 dBm) as compared to the class-A
PA (27 dBm), resulting in higher linearity. The gain of the HI PA is lower by about 1 dB as compared to the
fundamental PA in the linear region, but remains higher in saturation.The drain efficiency is calculated at
44
the output terminal of the test board which is designed for a 50Ω system. Measured results show that higher
efficiency can be achieved for a constant output power with HI PA by changing the operating bias point. For
instance, the drain efficiency of the PA with no injection improves from 58% to 75% for an output power of
40 dBm by changing the drain bias from 28 V to 22 V for the HI-PA case.
The measurements in Fig.3.3 show the performance of the HI-PA in class-AB mode where a total drain
efficiency improvement of 17% with the same output power as achieved for a class-AB PA without harmonic
injection. In order to achieve higher efficiencies, the PA bias can be further reduces for the PA to operate in a
class-B mode. In this case as shown in [7, 66], the output power of the fundamental signal is reduced by more
than 1 dB and the PA is not as linear as in class-AB mode. Fig.3.4 shows a comparison of the efficiencies and
output powers obtained for the HI-PA in various bias conditions.
As seen in Fig.3.4, the maximum output power is achieved at a gate bias of VGG = -1.45 V and maximum
drain efficiency is achieved with a gate bias of VGG = -2.5 V. This just re-instates the behavior of nonlinear
PAs where maximum output power is achieved in class-A mode and maximum efficiency is achieved when PA
is operated close to cut-off.
As seen in the results shown above, external second harmonic injection to a PA works well to achieve
high efficiency. But the question arises as to how much of the injected power is actually required in order to
achieve the required performance from the PA? Is it possible to achieve 100% efficient PA if we keep injecting
power into the PA? Note that in these measurements, the PA is not optimized for linear behavior. It is seen
in simulations,that if the injected power to the PA increases, the efficiency of the PA also increases. However,
the PA starts to become nonlinear after a certain power level of injected harmonic, since there is more than
required harmonic content being produced due to mixing of the fundamental frequency and the injected second
harmonic. Also, as the injected power is increased, the efficiency of the injection circuit also contributes to the
total efficiency. Therefore, high total efficiency can only be achieved for an optimal level of injected harmonic
power and phase. In this experiment, since we are using a pre-built PA, the loss in the output network of the
PA is unknown at both fundamental and second harmonic frequencies. Therefore, measurements cannot be
calibrated at the virtual drain of the amplifier. The calibration is, therefore performed at the 50Ω input and
output ports of the PA. Fig.3.5 shows the magnitude of the injected power required in order to achieve the
45
90
Drain efficiency %
80
70
60
50
40
30
22
24
26
28
30
Pin (dBm)
32
34
32
34
32
34
(a)
42
41
Pout (dBm)
40
39
38
37
36
22
24
26
28
30
Pin (dBm)
(b)
20
Gain (dB)
15
10
VD = 22V, no HI
VD = 28V, no HI
5
VD = 22V, HI
VD = 28V, HI
0
22
24
26
28
30
Pin (dBm)
(c)
Figure 3.3: Comparison of measured (a) drain efficiency, (b) Pout (f0 ) and (c) gain for the HI-PA to the PA
with no harmonic injection at VDD = 22V, 28V and VGG = -1.6V (class AB). Dashed green line indicates
input power at which the PA becomes nonlinear.
46
70
38.3
65
38.2
60
38.1
ηD %
38.4
Pout (dBm)
75
55
38
50
37.9
45
HI, 22V
37.8
40
no HI, 28V
37.7
35
−2.5
−2.25
−2
−1.75 −1.5
VGG (volts)
−1.25
37.6
−1
Figure 3.4: Efficiency and output power of HI-PA over a range of gate bias levels for VDD = 22, 28 V and Pin
= 30 dBm.
high efficiency in Fig.3.3.
−3.5
35
−4
34
inj
−5
P (2f )/P
0
−5.5
32
(f )
−6
31
out 0
Pinj(2f0) (dBm)
−4.5
33
−6.5
30
VG = −1.6V, VD = 28V
−7
VG = −2V, VD = 22V
29
22
24
26
28
30
Pin (dBm)
32
−7.5
34
Figure 3.5: Measured ratio of injected 2nd harmonic power, Pinj (2f0 ), to output power at the fundamental,
Pout (f0 ), for various bias points as a function of input power at the fundamental.
3.3
Linearity Measurements
In order to understand the nature of linearity for a harmonically-injected PA, a two-tone linearity test is
performed at bias points: VDD = 22 and 28V and VGG = -1.8V. The two tones are kept 5 MHz apart with
47
40
30
−43.2dB
−18.34dB
dBm
20
10
0
f1(HI)
−10
2f1−f2(HI)
2f1−f2(no−HI)
−20
2f2−f1(HI)
−30
22
24
26
Pin (dBm)
28
30
Figure 3.6: Comparison of power levels for single tone and 3rd order IMD products for HI-PA and class-AB
PA without harmonic injection.
f1 =2.45 GHz and f2 = 2.455 GHz with the 3rd order intermodulation distortion products or IMD3 generated
at 2f1 -f2 = 2.445 GHz and 2f2 -f1 = 2.46 GHz. In order to perform second harmonic injection for a PA with
two-tones, both harmonic tones, 2f1 and 2f2 need to be injected at the output of the PA simultaneously.
However, due to test setup limitations, the experiment is performed with harmonic injection at 2f1 (Fig.3.6),
2f2 , orf1 +f2 only, each requiring a different phase adjustment in order to achieve the optimal performance
from the harmonically-injected PA (HI-PA). The measured results in Fig.3.6 show that the HIPA (red line)
saturates at a higher input power than the PA with no HI (blue line). At lower input powers, the third order
distortion product, IMD3L/H (3rd order intermodulation distortion) level is 30 dB lower for the HI-PA and
remains 10 dB lower after the PA saturates. In Fig.3.6, only the 2f1 frequency is injected, resulting in a
decrease in the 2f1 -f2 IM DL while the 2f2 -f1 IM DH is unchanged. Symmetrically, when 2f2 is injected,
the 2f2 -f1 reduces. Both IMD products will be equally reduced for a signal injected at (f1 +f2 ). However, the
amount of reduction in this case is almost 10 dB lower than the case where either one of the two harmonic
tones is injected at the output of the PA.
48
3.4
Conclusion
In summary, this chapter demonstrates efficiency and linearity improvements for a commercial broadband
class A/AB PA with second harmonic injection at the output.
A 50 Ω diplexer network was designed with low loss in order to achieve second harmonic injection at the
output of the PA. Because the harmonic content at the output is not generated by the device non-linearities,
the HI PA has improved linearity compared to harmonically-terminated efficient PAs. A resultant 17%
efficiency improvement with similar output power as compared to a class-AB PA is achieved for the HI-PA.
Gain measurements show shift in the 1 dB compression point to a higher input drive level.
Two tone tests for the HI-PA result in > 30 dB improvement in IM D3 levels in the linear region and >
10 dB improvement in saturation over a class-A/AB PA for a 5 MHz tone spacing with f0 = 2.45 GHz. The
harmonic injection at one of the two harmonic tone signals results in reduction of upper or lower sidebands
which are directly related to the injected harmonic frequency. The measurements and analysis for the HI-PA
in a 50 Ω environment with a commercial class-AB PA are reported in [72].
49
Chapter 4
H y b r i d H I - PA i n t e g r at e d
Design and Test
Accomplishments will prove to be a journey, not a destination.
—Dwight D. Eisenhower.
Contents
4.1
Hybrid HI-PA Integrated Design
4.2
Measurements
4.3
Maximum Efficiency Characteristic
51
54
56
4.3.1
Fundamental Output Power
4.3.2
Drain Efficiency (ηD ) Characterization
4.3.3
Drain current
4.3.4
Linearity Measurements and Characterization
4.4
Input Power Sweep
4.5
Conclusion
69
58
60
60
68
62
4.1
H y b r i d H I - PA I n t e g r at e d D e s i g n
As mentioned in Ch.3, a commerically built amplifier is difficult to characterize in terms of losses in both the
through and the injection path at the output. In order to better understand the relationship between the
fundamental and second harmonic injected powers, a hybrid power amplifier is designed with the three port
injection network integrated within the output matching network of the PA along with the bias tee. The PA
is designed using a 6 W GaN on SiC discrete die provided by TriQuint Semiconductor. The design of the PA
is based on load-line analysis at drain voltage Vdd = 28 V, with break apart TRL fixturing as explained in
[2, 80]. The measurements are calibrated at plane P1 behind the output capacitance of the device, cds shown
in Fig.4.1 which is also the virtual drain of the transistor. De-embedding to the virtual drain of the device id
done by calculating the output capacitance of the device from the datasheet [81] and an EM model solution
for gold bond wires simulated in Ansys HFSS.
P1
D
U
T
INPUT
MATCH
Zin
Rout
P2
Bondwire
Transition
P3
OUTPUT
MATCH
Cds
Zout
Figure 4.1: General block diagram of the designed amplifier with DUT representing the TriQuint 6 W GaN
discrete die with reference planes, output capacitance, cds and bond wire transitions from die to copper on
the input and output matching networks.
Based on the S parameters of the device, the input matching network of the PA is designed to have
maximum small-signal gain at the fundamental frequency, f0 = 2.45 GHz by doing conjugate matching
at the input. The input matching network is designed to transform from 50 Ω to an input impedance,
Zin = 10 + j ∗ 12 Ω. The second and third harmonics are shorted at the input of the PA although harmonic
terminations at the input do not affect the performance of the PA in small signal regime. The input matching
network consists of an input port which is 50 Ω, a bias tee network to prevent the DC bias signal leaking
into the input port, and impedance transformation from 50 Ω to Zin = 10 + j ∗ 12 Ω. The design of the input
51
matching network is done by considering a two-port passive network with port 1 terminated in 50 Ω and
∗
port 2 terminated in Zin
. Hence, the Z22 is matched to the Zin impedance value and the Z11 is matched to
50 Ω. The input block is measured seperately using a break apart TRL calibration method. Fig.4.2 shows the
measured S-parameters of the input network. An advantage in using break apart TRL calibration is that
precise adjustments can be made to the circuit in order to achieve the exact impedances desired. This is due
Swp Max
8000MHz
2 .0
0.6
0 .8
1.0
to small variations in the measured vs. simulated results due to milling tool tolerances.
0.
3 .0
4. 0
5. 0
4
2450 MHz
r 9.63102 Ohm
x 11.6585 Ohm
0.2
10.0
4.0
5.0
3.0
2.0
1.0
0.8
0.6
0.4
2450 MHz
r 49.0432 Ohm
x -11.6933 Ohm
- 0. 2
-10.0
0
0.2
10.0
- 4.
0
-5.0
-3
.0
.4
-1.0
input_block_10ohms_prematch_6W
Schematic 1
- 0. 8
-0 .
6
.0
-2
-0
Swp Min
2000MHz
Figure 4.2: Measured input and output impedances, Z11 = 49 − 11.6jΩ and Z22 = 9.6 + 11.6jΩ for the passive
2-port input matching network.
The output network design for the PA is based on class-A bias design in [42] where the optimal impedance,
Ropt is calculated from Eq.1.4 as 65Ω at the fundamental frequency, f0 = 2.45 GHz. As shown in [43], in order
to design a harmonicallly-injected PA with high efficiency, the impedance presented at P1 for the second
harmonic, Zout (2f0 ), should be equal to the fundamental output impedance, Zout (f0 ). In order to achieve
the optimal performance of the PA with harmonic injection, the impedance at the 2nd harmonic was also
matched close to Ropt at the fundamental frequency. The three port injection network which is a 3-port
passive network is integrated into the output matching network with reference design from [7, 66]. Although,
in this design, the matching at both fundamental and second harmonic is done in a non-50 Ω environment.
The output network is designed such that the three port injection network allows the impedances required
to be presented at the virtual drain of the PA to be matched from a 50 Ω port in both the through and
injection paths. The three port network can be seen as a low pass and a high pass filter connected in parallel
52
1.0
0 .8
2 .0
0.6
Swp Max
8000MHz
output_inj_02242012
0.
3 .0
4
output_thru_01252012
4. 0
5. 0
10.0
4.0
5.0
3.0
2.0
1.0
0.8
0.6
0.4
0
0.2
0.2
4900 MHz 10.0
r 79.7319 Ohm
x -21.128 Ohm
2450 MHz
r 66.567 Ohm
x -10.453 Ohm
-10.0
- 0. 2
- 4.
0
-5.0
-3
.0
.4
-1.0
- 0. 8
-0 .
6
.0
-2
-0
Swp Min
2000MHz
Figure 4.3: Measured Z11 for the output network at f0 = 2.45 GHz and 2f0 = 4.9 GHz.
with each other allowing the fundamental signal to pass through the low pass network to the output port
while rejecting the second harmonic signal. Similarly, the high pass filter path allows the second harmonic to
be injected into the drain of the PA while rejecting the fundamental signal coming from the output of the
amplifier. Both paths have an isolation of > 30 dB between them. The measured loss for the output network
in both the through and injection paths is shown in Fig.4.4. The loss in the through network is about 0.5 dB
as compared to a 0.9 dB loss in the injection path. However, since the measurements are calibrated to the
virtual drain of the device, these losses are calibrated out for measurements.
0
Loss (dB)
-20
-40
-60
DB(|S(2,1)|)
output_thru_01252012
DB(|S(2,1)|)
output_inj_01252012
-80
2000
3000
4000
5000
6000
Frequency (MHz)
7000
8000
Figure 4.4: Measured loss in the output network low pass(blue) and high pass(pink) filter paths.
53
The design is based on the one presented in [7], although addtional stubs are used to do impedance
transformation from Ropt to 50 Ω at both the output and injection ports. Bias tee is integrated with the
output matching network providing high isolation between RF and DC paths. Measured S parameters of
the output network are shown in Fig.4.3. This measurement is performed using break apart TRL method as
explained in [43]. Due to fabrication tolerances, the fundamental f0 impedance at the virtual drain of the
device was found to be matched to 66 Ω and the 2f0 impedance to 79 Ω.
Figure 4.5: Hybrid harmonic injection power amplifier (HI-PA) with a 6W TriQuint TGF2023-01 die. The
output network integrates the harmonic injection three port network with Ropt at f0 matched to 65Ω and
Ropt at 2f0 matched to 71 Ω. The input network does an impedance transformation from 50 Ω to 10 Ω in
order to achieve high gain and Pout at the fundamental.
The class-AB PA is designed to have a 58% drain efficiency with an output power of 37 dBm without
any harmonic injection at a drain bias voltage of Vdd = 28V and Idq = 130 mA. Fig.4.6 shows the measured
drain efficiency ηD , output power at fundamental (Pout (f0 )) and third harmonic (Pout (3f0 )), and the gain as
a function of fundamental input drive power (Pin (f0 )).
4.2
Measurements
The block diagram shown in Fig.4.7 shows the modified measurement setup from Ch.3. A portion of the
fundamental input is frequency doubled to create the second harmonic (2f0 ) for injection. A voltage controlled
phase shifter and variable gain amplifier are used to control the amplitude Pinj (2f0 ) and phase at 2f0 .
All the measurements are de-embedded to the virtual drain of the transistor (reference plane P1 in Fig.4.1
54
60
30
50
20
40
D
η %
10
30
Pout(f0)
P
out
(dBm), Gain(dB)
40
Gain
0
20
Pout(3f0)
Drain Eff
−10
2
4
6
8P (f 10
12
) (dBm)
in 0
14
10
16
Figure 4.6: Measured drain efficiency, Pout at f0 and 3f0 and gain for the class-AB PA shown in Fig.4.5
without injection.
RF source
-10dB
coupled
f0
3dB power
split
x2
VGA
2f0
Driver
2f0
phase
shifter
VDD
HI-PA
iD
f0
Min
f0
1 Linear 2
3-port
3
2f0
f0
Mout
ZL
Figure 4.7: Block diagram of the HI-PA measurement setup. The input signal is split and frequency doubled
to create the injected harmonic, Pinj (2f0 ). A voltage controlled phase shifter and variable gain amplifier are
used to control the amplitude and phase of Pinj (2f0 ).
by calibrating the loss in the output network and taking into account the intrinsic device parasitics i.e. output
capacitance of the device. A bondwire model in HFSS was simulated to consider the inductance loss in the
bondwire transition for the hybrid PA design.
55
4.3
M a x i m u m E f f i c i e n c y C h a r ac t e r i s t i c
The HI-PA using a TriQuint 6W GaN discrete HEMT in a class-AB PA achieves a high total drain efficiency
of 89% with external second harmonic injection at the output at a bias voltage of Vdd = 22 V. This efficiency
is very close to the theoretical efficiency of 89.9% from Fig.2.8, though one would expect it to be lower,
since the theory derived in Ch.2 for a device with ideal IV curves with no harmonic content and zero knee
voltage. Note that in both the theoretical and experimental efficiency calculations here, the injection circuit
efficiency is assumed to be 100%. But in practice, the PA always generates some harmonic content even at
lower input power levels. The gain of the amplifier is reduced by 1 dB as compared to the amplifier without
any harmonic injection. Fig.4.8 shows a comparison of the measured performance for the HI-PA and PA
without harmonic injection. These measurements are optimized for high efficiency and hence the amplifier
is nonlinear at P1dB . It is seen that a better performance is achieved with the discrete device as compared
to the results presented in Fig.3.3 for the packaged device, as expected. As seen in the theoretical analysis
presented for harmonically-injected PAs in [43], harmonic injection implies a shift in the bias voltage in order
to get the optimum performance from the amplifier.
Fig.4.9 shows the performance of the HI-PA at different drain bias voltages for a fundamental input drive
(Pin (f0 )) of 16.2 dBm which is the 1 dB compression point for the class-AB GaN PA. This HI-PA is then
optimized in order to achieve higher linearity.
As explained in section 2.3, for a CW amplifier, the values of Pout (3f0 ) can give an estimate on the
linearity performance of the PA. It is seen from Fig.4.9 that at Vdd = 24 V, the drain efficiency of the HI-PA
is improved by over 20% as compared to the class-AB PA with no injection and the output power at the third
harmonic(Pout (3f0 )) is lowered by 30 dB for an input drive level of 16.2 dBm. At this bias point, conditions
for high linearity and high drain efficiency are obtained with a nominal fundamental output power (Pout (f0 ))
reduction of 0.26 dB over the PA without any injection. Note that when harmonic injection is performed, it
results in higher fundamental output power due to reduction in other harmonic content.
In order to keep the output power constant and reduce the DC power dissipation, the drain supply voltage
can be reduced to a certain extent, as shown in Fig.4.9. The supply voltage reduction is only advantageous
up to a device-dependent lower value when the output power starts decreasing. As seen in Fig.4.9, Pout (f0 )
56
100
ηD (%)
80
60
40
20
0
0
5
10
15
Pin(f0) (dBm)
20
(a)
40
Pout (dBm)
35
30
VD = 24V
VD = 28V
25
20
0
5
10
Pin(f0) (dBm)
15
20
10
15
Pin(f0) (dBm)
20
(b)
23
Gain (dB)
22
21
20
19
0
5
(c)
Figure 4.8: Comparison of measured (a) ηD , (b) Pout (f0 ) and (c) gain for discrete die protoype of HI-PA
optimized for maximum efficiency.
57
40
88
Pout(f0)
84
Pout(3f0)
82
80
30
20
10
78
0
76
74
16
Power (dBm)
Drain Efficiency %
86
18
20
22 (V) 24
VDD
26
−10
28
Figure 4.9: Drain efficiency, Pout (f0 ), Pout (3f0 ) for different Vdd bias voltages with the ratio Pinj (2f0 )/Pout (f0 )
= 0.1 and Pin (f0 ) = 16.2 dBm.
ranges from 32-38 dBm when the drain voltage is changed from 16 - 28 V. But, the output power remains
almost at a constant value of 38 dBm at Vdd = 24 V to 28 V. Therefore, to achieve higher efficiency, lower
voltage is selected. All the measurements presented in the next section are at a supply voltage Vdd = 24 V.
When the input power is swept on the fundamental PA, the required amplitude and phase of the injected
second harmonic in order to achieve the optimal performance from the HI-PA at each power level varies. This
is because the power levels of the harmonic content produced by the PA increases as the PA compresses. This
charateristic of PA is explaned clearly in literature including [42, 74, 73]. A comparison of the fundamental
output power, Pout (f0 ), drain efficiency, ηD , second and third harmonic output power, Pout (2f0 ), Pout (3f0 )
and drain current, Idd is shown next.
4.3.1
F u n da m e n ta l O u t p u t P ow e r
Since a PA uses a nonlinear device and saturates with increasing input power, this results in squaring of
the waveform and distortion at the output. The output power then reduces due to gain compression. But
for a PA with harmonic injection, the output power can degrade severly or increase to the benefit of higher
efficiency depending on the amplitude and phase of the injected signal. Theoretically, when the injected
signal is 180◦ out of phase with the fundamental signal, the ideal conditions for harmonic injection exist.
At this point, the output power is also higher than that for a non harmonically-injected PA. Fig.4.10 show
58
34.25
270
5
33.7 4
3
34.5
34.75
34.5
225
180
5
33.
34.25
34.75
34.75
35
35.2
35
5 5.5
3
35
90
35
45
35
0
−30
35
34.75
34.5
35
5
34.2 34
34.75
−25
−20
−15
Pinj(2f0) (dBc)
5
.7
35
135
.25
35
Phase shift at 2f0(deg)
5
.7
34
34
315
34
.5
360
35.25
35
34.75
34.5
34.25
34
33.75
33.5
−10
(a)
360
34.5
Phase shift at 2f0 (deg)
35
36
315
35.5
270
36
36
36.5
225
37
36.5
180
37.5
37
135
90
37
37
45
36.5
36
35.5
36.5
0
−20
−15
−10
Pinj(2f0) (dBc)
35.5
36
.5
6
3
37
5
37.
38
38
37.5
37
36.5
365.5
3
35
34.5
34
−5
(b)
Figure 4.10: Contour plots of measured fundamental output power, Pout (f0 ) at (a) input power, Pin = 10 dBm,
(b) Pin = 16 dBm.
59
the output power as a function of the injected signal amplitude and phase for different fundamental input
drive levels. It is seen that as the input drive level increases, the optimal point for high output power shifts
towards higher injection power level. The reason being that as the fundamental input power increases, the
PA starts producing more harmonic content. In order to compensate for the internally produced harmonics
and increase the fundamental output power, the required injected power also needs to increase. Also. since
the PA degrades in phase with increasing input power, the optimal phase required to achieve high effciency
and linearity also shifts with input drive level.
4.3.2
D r a i n E f f i c i e n c y (ηD ) C h a r ac t e r i z at i o n
The drain efficiency for the HI-PA is calculated from (2.25) which is a function of the DC power dissipated in
the main HI-PA and the DC power which is dissipated in the injection circuit. The drain efficiency for an
HI-PA takes into account the amount of second harmonic power injected into the virtual drain of the device
(Pinj (2f0 )) assuming ηinj = 1. Contour plots of variation in drain efficiency w.r.t. amplitude and phase of
the injected signal is shown in Fig.4.11. It is seen that at a maximum amplitude of -5 dBc w.r.t. fundamental
output power, the drain efficiency achieved in compression is 89%. However, at this point, the harmonic
content in the PA also increases as will be shown in the next section resulting in nonlinear PA. Therefore, a
trade-off between efficiency and linearity is required. It is seen that the total drain efficiency varies on the
order of 10% for every 45◦ phase shift and 15-20 dB amplitude shift of the injected harmonic. However, the
power reduces by > 1 dB for this range of values as seen in Fig.4.10.
4.3.3
Drain current
The optimal point for the amplitude and phase of the injected signal remains almost the same in terms of
minimum drain current and maximum efficiency. This point varies by 20◦ in phase of the injected signal for
maximum efficiency and minimum drain current. The current variation on the order of 10 mA for every 40◦
change in the phase and 2 dB change in the amplitude of the injected signal is shown in Fig.4.12. Also, it is
seen that the minimum points obtained for drain current at input drive levels in linear and saturation region
differ by almost 10 dB in amplitude.
60
50
35
45
315
40
270
50
225
45
50
45
50
180
55
60
50
55
135
65
55
90
60
Phase shift at 2f0(deg)
40
360
60
55
50
45
40
55
45
55
50
55
0
−30
−25
−20
−15
Pinj(2f0) (dBc)
−10
(a)
360
40
60
50
Phase shift at 2f0 (deg)
315
50
270
50
225
60
70
60
180
60
70
135
80
90
70
45
0
60
70
60
50
70
60
−20
−15
−10
Pinj(2f0) (dBc)
80
700
60
5
40
30
−5
(b)
Figure 4.11: Contour plots for measured drain efficiency, ηD at (a) input power, Pin = 10 dBm, (b) Pin =
16 dBm.
61
0.23
270
225
0.24
4
0.2
5
25
0.2
180
6
0.25
0.25
0.23
0.24
135
4
0.24
0
−30
0.23
−25
0.21
0.2
0.23 2
0.2
1
2
.
0
0.
2
0.21
0.22
0.2
90
45
0.2
0.
0.24
0.25
Phase shift at 2f0(deg)
315
0.2
6
23
0.
360
2
0.2
9
0.1
0.189
0.1
0.21
0.2
2
0.2
0.2.324
0
−20
−15
P (2f ) (dBc)
inj
−10
0
(a)
360
Phase shift at 2f0 (deg)
315
32
0.3
0.
270
1
0.3
225
0.32
180
0.31
0.31
135
90
0.3
45
0
0.27
0.29
0.28
0.29
−20
0.29
0.3
−15
−10
P (2f ) (dBc)
inj
0.28
0.26
0.25
0.22
0.2
0.24 3
0.25
0.26
0.27
0.28
0.219
0.3
0.3
−5
0
(b)
Figure 4.12: Contour plots for measured drain current, Idd at (a) input power, Pin = 10 dBm, (b) Pin =
16 dBm.
4.3.4
L i n e a r i t y M e a s u r e m e n t s a n d C h a r ac t e r i z at i o n
As shown in Ch.2, linear behavior of an amplifier can be recognized with CW measurements by monitoring
the even and odd order harmonic content in the PA. The third order nonlinearity creates the third harmonic
at the output of the PA which can give an estimate on the linear performance of the PA. The analysis in
[74] also shows that the amplitude of the second harmonic output signal is inversely proportional to the
magnitude of the transfer characteristic of the amplifier at the third harmonic, which is given as:
62
3
GN L = 20log(k1 + k3 A2 )
4
(4.1)
wherer k1 and k3 are the transfer functions at fundamental and third harmonic frequencies for a PA
system and A is the amplitude of the fudamental input sinusoidal signal.
A good discussion on extracting linearity information from a CW-fed amplifier by measuring the third
harmonic output content is presented in [75]. Based on this theory, here, a CW signal is used for harmonic
injection analysis as the device enters saturation. In particular, we measure 2nd and 3rd harmonic as a
function of the injected power and phase in order to assess the linearity characteristics of a PA. By performing
second harmonic injection at the output, mixing between injected 2f0 signal and fundamental output f0
signal results in third harmonic mixing product, 3f0 . At the optimal phase and amplitude of the injected
second harmonic, this mixing product will have a phase opposite to the third harmonic produced by the PA
resulting in cancellation and higher linearity. Also, there will be an efficiency vs linearity trade-off since, from
Fig.4.13, the level of second harmonic in the output signal is still significant. However, as shown in Fig.4.14,
the efficiency degrades by 8-9% for the PA driven at 1 dB compression while maintaining extremely low levels
of third order harmonic distortion.
From Fig.4.13 and 4.14, the optimal amplitude and phase of the injected signal also varies in order to
achieve a null in either the 2nd or 3rd harmonic. At 1 dB compression, the maximum amplitude and optimal
relative phase of the injected signal in order to achieve a null in the third harmonic is 10 dBc w.r.t. fundamental
output power and 80 ◦ , whereas it is 20 dBc and 110 ◦ for minimum second harmonic. This optimal phase for
the injected signal also varies with input drive level since the power of the harmonics produced by the PA
itself also increases with increasing input power. This can be directly related to the amplitude and phase
modulation (AM-PM) distortion in the PA.
With increasing input drive levels, the harmonic content in the PA also increases by a factor of two for
the second harmonic and a factor of three for the third harmonic. Also, the amplitude and phase modulation
distortion, also known as AM-AM and AM-PM distortion results from increasing harmonic content in the
main signal causing amplitude compression and phase deviation. Therefore, with increasing input drive levels,
the optimal amplitude and phase of the injected signal required to reduce the 2nd or 3rd harmonics will
63
25
360
30
270
25
225
25
20
180
20
15
90
15
105 5
20
10
25
30
10
15
135
0
Phase shift at 2f0(deg)
315
15
20
25
45
20
0
−30
−25
−20
−15
Pinj(2f0) (dBc)
−10
(a)
360
30
25
270
30
225
25
25
180
135
20
15
10
20
15
90
45
25
Phase shift at 2f0(deg)
315
10
25
30
20
30
15
20
15
0
−25
20
50
25
−20
−15
Pinj(2f0) (dBc)
−10
(b)
Figure 4.13: Contour plots for power measured at second harmonic, Pout (2f0 ) at (a) input power, Pin =
10 dBm, (b) Pin = 16 dBm.
64
360
15
15
20
270
225
20
180
20
135
15
15
90
10
15
45
5
0
10
15
15
0
−30
10
−25
−20
−15
P (2f ) (dBc)
inj
50
1
15
20
Phase shift at 2f0(deg)
315
−10
0
(a)
360
Phase shift at 2f0(deg)
315
20
270
25
20
225
180
20
135
20
20
90
45
0
−25
15
10
5
05
10
15
10
15
20
15
−20
−15
Pinj(2f0) (dBc)
15
20
−10
(b)
Figure 4.14: Contour plots for power measured at third harmonic, Pout (3f0 ) at (a) input power, Pin = 10 dBm,
(b) Pin = 16 dBm.
65
change. Fig.4.15 shows the minima obtained in the second harmonic as well as the PA efficiency for different
input drive levels from small signal to compression. At small signal, the PA efficiency and 2nd harmonic
produced by the PA are not affected by second harmonic injection. This is because in small signal regime, the
PA itself does not produce any significant harmonic components. Therefore, active impedance synthesis is not
achievable at these input drive levels. However, as the input power increases, the amount of injected power
required to achieve maximum efficiency and minimum harmonic content also increases.
−25
2dBm
3dBm
5dBm
7dBm
10dBm
13dBm
15dBm
16.2dBm
16.8dBm
Harmonics 2f0 dBc w/o offset
−30
−35
−40
−45
−50
−55
−60
−65
0
5
10
15
20
25
30
POUT(f0) − PINJ(2f0) dB
35
40
45
(a)
90
2dBm
3dBm
5dBm
7dBm
10dBm
13dBm
15dBm
16.2dBm
16.8dBm
80
70
ηD %
60
50
40
30
20
10
0
5
10
15
20
25
30
POUT(f0) − PINJ(2f0) dB
35
40
45
(b)
Figure 4.15: Total drain efficiency (b) and output power at second harmonic (a) as functions of the amplitude
of the injected harmonic signal for various input drive levels. The phase of the injected signal is set to the
optimal value for these measurements.
66
It is of interest to discuss some limitations on linearity and efficiency that are practically achievable. We
have shown that the third harmonic, which directly affects IMD performance [75], is minimized for a specific
phase and amplitude of the injected second harmonic. However, the injected signal also affects the nonlinear
content in the waveform produced by the transistor, which can be evaluated by measuring the level of the
second harmonic at the output. The amount of injected second harmonic power that results in a minimum of
harmonic content in the output is shown in Fig.4.16. Note that the 2nd and 3rd harmonic have minima for
different injected power levels of the second harmonic. The amplitude of Pinj (2f0 ) needed to lower Pout (2f0 )
is approximately 10 dB less than that needed to lower Pout (3f0 ). Also, the phase shift for Pinj (2f0 ) injection
differs by 50◦ . As seen from Fig.4.11, the drain efficiency drops by approximately 10% between these two
points in amplitude and phase.
Power (dBm)
30
20
10
Pout(3f0)
0
Pout(2f0)
−10
−200 −150 −100 −50
0
50
100 150 200
Phase shift Pinj(2f0) (dBm)
Figure 4.16: Minimum Pout (2f0 ) and Pout (3f0 ) measured at virtual drain of the HI-PA for Pin (f0 ) = 16.2 dBm.
The minimum for Pout (2f0 ) is obtained with Pinj (2f0 ) = -17.8 dBc w.r.t. Pout (f0 ), whereas minimum for
Pout (3f0 ) is obtained for Pinj (2f0 ) = -8.9 dBc.
Fig.4.11 & 4.14 show that for Pinj (2f0 ) = -9 dBc and a phase shift of 80◦ , high drain efficiency of 79%
is achieved using (2.25) along with extremely low values of Pout (3f0 ). Note that this efficiency takes into
account the power of the injected signal. However, the effciency of the injector circuit is not included in this
proof-of-concept experiment in which the HI-PA is not fully integrated. The value of Pout (f0 ) obtained at
this point is approximately 37 dBm, only 0.2 dB lower than the fundamental output power obtained with no
injection (Fig.4.6).
The measurements show that if Pinj (2f0 ) is not at the optimum phase and amplitude, the performance of
67
the amplifier can severely degrade. When the second harmonic voltage is out of phase relative to the optimal
value, the amplitude of Pout (3f0 ) increases making the amplifier extremely nonlinear. The efficiency reduces
from 80% to 40% while the output power drops more than 3 dB. If Pinj (2f0 ) is higher than the optimum
value (in this case, ≥ -9 dBc), then even at the optimum phase of the injected harmonic, the HI-PA is highly
nonlinear. This is due to undesired additional second harmonic content in the output voltage and current
waveforms generated by the strongly driven.
4.4
I n p u t P ow e r S w e e p
A sweep is performed at Pin (f0 ) in order to achieve the optimal performance of the HI-PA at various input
drive levels. Since an amplifier undergoes AM-AM and AM-PM distortion, the optimal phase and amplitude
of the injected second harmonic changes for different input drive levels. Fig.4.17 shows a comparison of the
gain and drain efficiency obtained for HI-PA and PA without harmonic injection as a function of Pin (f0 ).
The efficiency obtained at each input drive level is for an optimal value of amplitude and phase which are
also dependent on Pin (f0 ). The overall gain of the HI-PA is reduced by 1 dB and the 1-dB compression point
of the HI-PA is shifted to a higher Pin (f0 ) of 15.7 dBm implying improved linearity. The drain efficiency
improvement ranges from 8% to 20% as the input drive level increases.
80
23
70
22.5
50
D
η %
22
Gain (dB)
60
21.5
40
ηD HI
ηD no HI
30
20
Gain HI
Gain no HI
8
10
12
P (f ) dBm
14
21
P1dB
16
20.5
in 0
Figure 4.17: A comparison of drain efficiency and gain for HI and PA with no injection as a function of
Pin (f0 ).
68
The comparison of Pout (f0 ) and Pout (3f0 ) for the HI-PA and PA with no injection is shown in Fig.4.18
along with Pinj (2f0 ) as a function of Pin (f0 ).
40
Power (dBm)
30
20
Pout(f0) HI
P
10
(f ) no HI
out 0
P3f0 HI
P3f no HI
0
0
Pinj(2f0)
−10
−20
6
8
10
12
14
Pin(f0) (dBm)
16
18
Figure 4.18: Comparison of Pout (f0 ) and Pout (3f0 ) as a function of Pin (f0 ) for HI and PA with no injection.
The graph also shows the amplitude of Pinj (2f0 ) as function of Pin (f0 ) in order to achieve high efficiency
and linearity performance for the HI-PA.
The nominal class-A operation of the PA without harmonic injection with a 50% drain efficiency is achieved
at Pin (f0 ) = 13 dBm. Fig.4.18 shows that at this input drive level, the amplitude of Pinj (2f0 ) required in
order to achieve an optimum performance in terms of efficiency and linearity for the HI-PA is -10 dBc. This
result matches with the theoretical analysis presented in Fig.2.9 where for a 100% injector efficiency, the ratio
of Pinj (2f0 ) to Pout (f0 ) is 0.1 for a class-A bias point.
It is seen that a total improvement of 8% to 20% is observed in the overall drain efficiency of HI-PA as
compared to that of the class-AB PA without injection when the input power increases. Both the simulations
and the measurements show that as the injected power is increased to the fundamental PA, the drain efficiency
keeps increasing. However, after a certain level of injected signal, the PA again becomes extremely nonlinear
due to additional harmonic content as shown in Fig.4.14.
4.5
Conclusion
In this chapter, a hybrid HI-PA is designed using a discrete GaN HEMT die with the diplexer integrated in
the output matching network in a non-50 Ω environment at f0 = 2.45 GHz. The PA is designed for class-AB
69
mode of operation with large signal gain of 23 dB and Pout = 5 W. Optimization in efficiency and linearity
is performed with second harmonic injection at the output of the PA. Variation in PA parameters such as
Pout at fundamental and harmonics along with drain efficiency, ηD , gain and drain current, Idd w.r.t. the
amplitude and phase of the injected second harmonic are analyzed.
Measurements show maximum total efficiency improvement of 30% over class-AB PA with maximum ηD
= 89% for the HI-PA. The power required at the injected harmonic to achieve this efficiency is -5.5 dBc. The
PA performance is sensitive to the phase of the injected second harmonic with efficiencies reduced more than
5% for every 20◦ change in the relative phase of the injected second harmonic. The drain current is reduced
by more than 100 mA at the optimal amplitude and phase of the injected second harmonic along with only a
0.26 dB reduction in output power as compared to the class-AB PA without harmonic injection.
Linearity analysis is performed in terms of second and third harmonic content for the HI-PA. Optimization
for minimum third harmonic content results in total efficiency improvement of 20% for a CW signal with max
ηD = 78% and third harmonic reduction of 15 dB in compression with the injected harmonic power 10 dBc
w.r.t. fundamental output power. The design, analysis and comprehensive characterization of this integrated
HI-PA demonstrating high efficiency and linearity is reported in [9].
70
Chapter 5
L i n e a r i z at i o n o f H I - PA s
Our future discoveries must be looked for in the sixth place of decimals.
—A. A. Michelson, in Light Waves and Their Uses, 1903.
Contents
5.1
Variable tone spacing
74
5.1.1
1 MHz tone spacing
5.1.2
10 MHz tone spacing
77
5.1.3
20 MHz tone spacing
77
5.2
Input power sweep
5.3
Harmonic Balance Simulations
5.4
Conclusion
76
79
82
86
In this chapter, two-tone measurements are used to quantify linearity in terms of third and fifth order
distortion products. Measurements with optimization for the amplitude and phase of the injected second
harmonic in order to achieve lowest third and fifth order intermodulation products in both lower and upper
sidebands (IM D3L/H , IM D5L/H ) are performed. As shown in Ch.2, a harmonically-injected PA (HI-PA)
can be linearized by injection of second harmonic tones at the output resulting in mixing products which
cancel the ones produces by the PA itself. It was also shown in Ch.4 that the third order nonlinearities reduce
and the 1 dB gain compression point shifts to a higher input drive level resulting in linear behavior of the PA.
However, the third order nonlinearities for a CW signal only provide an estimate of the PA’s linear behavior.
In order to understand the actual signal distortion, two-tone measurements give a comprehensive analysis for
linearity behavior of a PA. In this measurement analysis , harmonic injection is performed with two tones
having bandwidths of 1, 5, and 10 MHz with the fundamental tone, f1 = 2.45 GHz. Due to setup limitations,
the harmonic injection is performed at one of the two harmonic tone frequencies, 2f1 or 2f2 . A basic block
diagram of the measurement setup is shown in Fig.5.1. One of the two tones is split using a 3 dB power
splitter, where one half of the tone is input to the PA and the other half is frequency doubled to create the
second harmonic injection tone. This signal is then adjusted in amplitude and phase with a variable gain
amplifier and a voltage controlled phase shifter.
f1
f2
-10dB
coupled
3dB power
split
f1
2f1
x2
VGA
Driver
2f1
phase
shifter
VDD
HI-PA
power
combiner
iD
f1+f2
f1+f2
65
Min
1
Three port
HI network
2f1
2
f1+f2
Mout
50
3
Z(2f1)
ZL
Figure 5.1: Block diagram of measurement setup for two tone test on the harmonic injection power amplifier.
External harmonic injection of 2f1 affects the performance of the third-order intermodulation distortion
product, IM D3L at 2f1 -f2 and IM D5L at 3f1 -2f2 due to active impedance synthesis at the second harmonic
tone frequency. It is important to note that the reduction in IM D5L results from mixing of IM D3L and
distortion products caused due to second order nonlinearities as explained in Ch.2. Also, the injection at one
of the two harmonic tone frequencies only affects either the lower or upper IMD products while the other side
remains unaffected.
72
The measurement analysis is performed for various amplitude and phase values of the injected harmonic.
The active impedance synthesis at the virtual drain of the PA results in an optimal impedance point for
the odd-order intermodulation products to have minimum power levels with a simultaneous increase in the
efficiency. Fig.5.2 shows the optimal amplitude and phase for injected second harmonic tone (2f1 ) in order to
achieve low IM D3L power levels for a fundamental input drive of Pin = 16 dBm. It is seen that the minimum
IM D3L is sensitive to both the amplitude and phase of the injected second harmonic with the IM D3 power
levels varying by a margin of 10 dBm with a 5 dB increase in the injected signal amplitude. Also, since the
variable phase shifter has a range from 0 to 450◦ , the optimal point with minimum IMD3 repeats itself at
5
0
−5
10
15
5 −1
0
15
15
300
20
10
375
20
225
20
150
25
20
20
20
75
0
15
10
15
15
−25
−20
−15
Pinj(2f1) (dBc)
0
Phase shift at 2f1 (deg)
450
15
phase shifts of approximately 40 and 400◦ .
15
10 5
1105
5
20
−10
Figure 5.2: Measured power level of IM D3L (2f1 -f2 ) as a function of the amplitude and phase of the injected
second harmonic tone 2f1 .
Similarly, a minimum for IM D5L is also a function of Pinj (2f1 ) as shown in Fig.5.3. However, it is seen
that the amplitude and phase shift required at the injected second harmonic to achieve lowest IM D5 products
differ by 2 dBm and 10◦ respectively as compared to the values for lowest IMD3 products as shown in Fig.
5.4. It is an expected result since IM D3 and IM D5 products produced by the PA itself differ in amplitude
and phase w.r.t. each other when an input power sweep is performed on the PA.
73
360
0
phase shift at 2f0 (deg)
0
5
5
315
5
270
5
10
225
10
180
15
10
135
10
10
90
5
5
45
5
0
5
−25
0
−5 −10
−5
0
0
5
5
10
−20
−15
Pinj(2f0) (dBm)
−10
Figure 5.3: Measured power level of IM D5L (3f1 -2f2 ) as a function of the amplitude and phase of the injected
second harmonic tone 2f1 .
25
20
Power (dBm)
15
10
5
0
−5
IMD5L
IMD3L
−10
−15
−200 −150 −100 −50
0
50 100
Phase shift at 2f1 (deg)
150
200
Figure 5.4: Measured power levels for IM D3L and IM D5L with harmonic injection at 2f1 and Pin = 16 dBm.
The minima for IM D3L and IM D5L are obtained for Pinj (2f1 ) = -11.5 dBc and -9.5 dBc, respectively.
5.1
Va r i a b l e t o n e s pac i n g
Next, the performance of the HI-PA with tone spacings of 1, 10 and 20 MHz is studied with linearization
using second harmonic tones. The PA is operated at two input drive levels in linear and saturated states.
The measurements are presented for Pin = 10 and 16 dBm with the amplitude of the second harmonic
maintained at -10 dBc w.r.t. the fundamental output power and an optimal phase shift between the injected
and fundamental output frequency tones.
A comparison of the minimas obtained for odd order IMDs ranging from third to ninth order is shown
74
in Fig.5.5 - 5.7. Here, the measurements show the behavior of IMD products as a function of the change
in phase for the injected second harmonic tone at the optimal amplitude which is 10 dBc w.r.t. the output
power. Also, two different input drive levels are shown with Pin = 10 and 16 dBm. As seen from Fig.2.17,
the fifth and higher order intermods have sweet spots or minima for the class-AB PA without injection at
some specific input drive levels. For example, the fifth order intermodulation products have a minimum at an
input drive level of Pin = 11 dBm or Pout = 33 dBm. Therefore, when harmonic injection is performed at
that particular input drive level, from Ch.2, these intermodulation products will no longer have minimas and
will increase in power levels. As shown in Fig.5.5a, the minimum obtained for the third order intermodulation
product is not coincident with that obtained for the fifth and higher intermodulation products. Therefore, in
order to have simultaneous reduction in all the odd order distortion products with harmonic injection, the
PA should be driven at input power levels where the odd-order intermods are an increasing function of the
input power and do not contain any sweet-spots which can result in asymmetry.
Also, as the PA is driven with two-tones with larger signal bandwidths, low-frequency memory effects
[82] start becoming critical which results in asymmetry of the lower and higher sidebands for the signal. The
PA is no longer symmetrical and the spectral regrowth can be lower or higher than that of the other side of
the spectrum. When harmonic injection is performed on such a PA, the simultaneous reduction in both the
upper and lower sidebands also becomes difficult and the spectral asymmetry is maintained. Nevertheless,
the power levels of the intermodulation products reduces as compared to that of a class-AB PA.
As the input power level to the PA is increased from linear (Pin = 10 dBm) to saturation (Pin = 16 dBm),
the amount of harmonic content and phase of the harmonics also changes. This results in amplitude and phase
modulation (AM-AM and AM-PM) distortion. Therefore, with harmonic injection, the amount of phase shift
required to achieve minima in the IMD products at these two power levels also differ. However, one should
expect the phase shift required to produce nulls in the upper and lower IMD products at a single power level
to be the same. But, even in this case, as shown in Fig.5.5, the phase differs by 10 to 20◦ . This is due to
injection of two different frequencies in order to achieve nulls in both upper and lower spectral components.
75
Power (dBm)
0
−10
20
IMDL3
IMDL5
10
IMDL7
Power (dBm)
10
IMD 9
L
−20
0
−10
−30
−20
−40
−200−150−100 −50 0 50 100 150 200
Phase shift at 2f1 (deg)
−30
−200−150−100 −50 0 50 100 150 200
Phase shift at 2f1 (deg)
(a) IM DL , 1 MHz tone spacing, Pin = 10 dBm
(b) IM DL , 1 MHz tone spacing, Pin = 16 dBm
Power (dBm)
0
−10
IMDH3
20
IMDH5
IMDH7
10
IMDH9
Power (dBm)
10
−20
0
−30
−10
−40
−200 −150 −100 −50 0 50 100 150 200
Phase shift at 2f2 (deg)
−20
−200−150−100 −50 0 50 100 150 200
Phase shift at 2f (deg)
(c) IM DH , 1 MHz tone spacing, Pin = 10 dBm
(d) IM DH , 1 MHz tone spacing, Pin = 16 dBm
2
Figure 5.5: Measured intermodulation distortion products in the upper and lower half of the spectrum for
two tone signals with 1 MHz tone spacing
5.1.1
1 M H z t o n e s pac i n g
Fig.5.5 shows the variation in the power levels obtained for odd-order intermodulation products with the
phase shift at the injected second harmonic in both upper and lower halves of the spectrum. The figure
compares the results for two different input drive levels with PA in linear region, i.e., Pin = 10 dBm and in
saturation with Pin = 16 dBm. Fig.5.5a - 5.5c show that at an input drive level of 10 dBm, the third order
intermodulation products IM D3L/H achieve minimum points with the phase shift at the injected harmonic
tones differing by 60◦ . Also, since the PA already exhibits a sweet spot condition for the fifth order intermods
at this input drive level, the minima obtained in the fifth order intermods differ from the minimum point
achieved in IM D3 by almost 180◦ in the phase shift required at the injected harmonic tone frequencies. The
76
higher order intermods such as IM D7, 9... achieve null points with phase shifts close to minimum IM D5
levels. This is due to IM D5 harmonics affecting the power levels of higher order terms.
Refering to Fig.5.5, when the input drive level is increased to 16 dBm, the sweet spot condition for fifth
order intermods no longer exhists. Hence, the minima obtained in IM D3 and IM D5 differs by only 50◦ in
terms of phase shift at the injected harmonic tones. However, the higher order intermods such as IM D7, 9...
exhibit sweet spot conditions at this input drive level. Therefore, the phase shift required to achieve a minimum
in these intermods differs by 180◦ from the phase shift required to achieve nulls at IMD3 products. Also, it
is seen that the optimal phase shift at 2f1 and 2f2 only differs by 10◦ for minimum IMD3 and 5 products.
Therefore, a symmetric reduction can be obtained in the odd order intermodulation products with harmonic
injection at both 2f1 amd 2f2 simultaneously.
5.1.2
1 0 M H z t o n e s pac i n g
Comparison of power levels achieved for odd order intermods at two different input drive levels for a tone
spacing of 10 MHz is shown in Fig.5.6. In Fig.5.6a - 5.6c, it is seen that the low frequency memory effects in
the PA are starting to affect the symmetry of the signal. The IM D3 products in upper and lower halves of
the spectrum achieve minimum power levels at phase shifts which differ by 50◦ for the two injected harmonic
tones. Again, the IM D5 products achieve nulls with phase shifts differing by 180◦ from minimum IM D3
points for input drive level of 10 dBm. For Pin = 16 dBm, it is seen that the phase shifts to obtain nulls in
IM D3 and 5 differ by 50◦ where as there is asymmetry between the upper and lower IM D7, 9 minimum
power level points. This asymmetry is partly due to the low frequency memory effects and also as the tone
spacing of the fundamental frequency increases, the spacing between the harmonic tones now doubles. This
results in a different optimal phase shift for minimizing upper and lower parts of the spectrum.
5.1.3
2 0 M H z t o n e s pac i n g
Tone spacing of the input two tone signal when increased to 20 MHz results in asymmetrical behavior of the
PA as seen in Fig.5.7. When harmonic injection is performed at the two harmonic tone frequencies, the phase
shifts required to achieve minimum power levels at IM D3 differ by 100◦ in phase shifts for injected harmonics
77
20
−10
10
Power (dBm)
Power (dBm)
0
−20
−30
0
−10
−40
−20
−200−150−100 −50 0 50 100 150 200
Phase shift at 2f1 (deg)
(a) IM DL , 10 MHz tone spacing, Pin = 10 dBm
(b) IM DL , 1 MHz tone spacing, Pin = 16 dBm
0
20
−10
10
Power (dBm)
Power (dBm)
−50
−200−150−100 −50 0 50 100 150 200
Phase shift at 2f1 (deg)
−20
−30
0
−10
−40
−20
−200−150−100 −50 0 50 100 150 200
Phase shift at 2f (deg)
−50
−200−150−100 −50 0 50 100 150 200
Phase shift at 2f2 (deg)
2
(c) IM DH , 10 MHz tone spacing, Pin = 10 dBm
(d) IM DH , 10 MHz tone spacing, Pin = 16 dBm
Figure 5.6: Measured intermodulation distortion products in the upper and lower half of the spectrum for
two tone signals with 10 MHz tone spacing
for the upper and lower spectrum. Also, for input drive level of 10 dBm, a minimum point is obtained for
IM D5L whereas IM D5H does not have a null point when the phase of the injected second harmonic is
varied from 0 to 360◦ . Also, it is seen that the minimum power levels obtained for IM D3, 5, ... for both upper
and lower spectrum differ by 10 dBm for input drive level of 16 dBm. Therefore, as the tone spacing increases,
the harmonically injected tone spacing doubles and the PA now becomes asymmetrical due to memory effects
and variable phase shifts at the two injected frequency tones. It can be concluded that this technique will
hence work for narrowband signals with bandwidths upto 10 MHz.
78
20
−10
10
−20
0
Power (dBm)
Power (dBm)
0
−30
−40
−10
−20
−30
−60
−200−150−100 −50 0 50 100 150 200
Phase shift at 2f1 (deg)
−40
−200−150−100 −50 0 50 100 150 200
Phase shift at 2f1 (deg)
(a) IM DL , 20 MHz tone spacing, Pin = 10 dBm
(b) IM DL , 20 MHz tone spacing, Pin = 16 dBm
0
20
−20
0
Power (dBm)
Power (dBm)
−50
−40
−60
−20
−40
−60
−80
−100
−200−150−100 −50 0 50 100 150 200
Phase shift at 2f2 (deg)
−80
−200−150−100 −50 0 50 100 150 200
Phase shift at 2f2 (deg)
(c) IM DH , 20 MHz tone spacing, Pin = 10 dBm
(d) IM DH , 20 MHz tone spacing, Pin = 16 dBm
Figure 5.7: Measured intermodulation distortion products in the upper and lower half of the spectrum for
two tone signals with 20 MHz tone spacing
5.2
I n p u t p ow e r s w e e p
Optimization can be performed in order to achieve lowest third order or fifth order distortion products with
input power sweep. The optimal injected 2nd harmonic power which results in minimum IM D3L is shown
in Fig.5.8 as a function of the input drive level. It is seen that the reduction in IM D3L using external
second harmonic injection is greater than 15 dB for different input drive levels, whereas IM D3H at 2f2 -f1
and IM D5H at 3f2 -2f1 remain unaffected. The total drain efficiency of the PA which takes into account the
amount of injected second harmonic as explained in [72] is improved from 53% for the two-tone class-A mode
to 58% using harmonic injection at one tone. The total output power is seen to reduce by 0.5 dB along with
1 dB lower gain as compared to the class-A PA. The maximum efficiency improvement is seen to be 8% but
79
this results in a trade-off between high efficiency and linearity.
32
24
Power (dBm)
16
IMD5 HI
IMD5 no HI
IMD3 no HI
Pinj(2f1)
15dB
IMD3 HI
8
0
−8
23dB
−16
−24
−32
6
8
10
12
14
Pin (dBm)
16
18
Figure 5.8: Comparison of power at IM D3L (2f1 -f2 ), IM D5L (3f1 -2f2 ) for HI-PA and PA without harmonic
injection as a function of input drive level. The graph also shows the power injected at the second harmonic
tone (2f1 ) to achieve lowest IM D3L .
Similarly, Fig.5.9 shows the power levels for IMD3 and 5 with second harmonic injection optimized for
lowest fifth order distortion.
40
Power (dBm)
20
IMD3 HI
IMD5 Hi
Pinj
IMD3
IMD5
0
−20
−40
5
10
Pin (dBm)
15
20
Figure 5.9: Comparison of power at IM D3L (2f1 -f2 ), IM D5L (3f1 -2f2 ) for HI-PA and PA without harmonic
injection as a function of input drive level. The graph also shows the power injected at the second harmonic
tone (2f1 ) to achieve lowest IM D3L .
It is seen that the reduction in IM D3L using external second harmonic injection is greater than 15 dB for
different input drive levels, whereas IM D3H at 2f2 -f1 and IM D5H at 3f2 -2f1 remain unaffected. Fig.5.8
shows the reduction in power levels for IM D3L and IM D5L achieved for different fundamental input drive
80
levels along with the amount of injected 2f1 power.
For practical communication signals, the harmonic injection path needs to be modified in order to inject
an exactly doubled spectrum of the signal. As seen in the two-tone measurements, injection at one harmonic
tone only affects the distortion products which are a function of that harmonic tone frequency. Since, a
modulated signal in general is a multi-tone signal, it will require a injected signal with twice the modulation
bandwidth and RF carrier. This can be accomplished by baseband signal up-conversion.
The results show that a PA with harmonic injection in the output can be both efficient and linear. In the
demonstrated results, we start with a class-AB PA, which is not perfectly linear. In fact, the theory shown in
Ch.2 assumes that some second harmonic content is generated by the active device. If the transistor fails to
generate second harmonic power and presents an impedance other than that of the fundamental frequency
output termination, the necessary negative impedance cannot be synthesized using harmonic injection. In
this case, harmonic injection at both the input and output of the transistor would be required.
For a modulated input signal, the third order nonlinearities have to be minimized since they create in-band
distortion which is extremely difficult to filter. The third order distortion products are a function of the
amplitude of second harmonic produced by the amplifier itself. Hence, a point in the amplitude and phase
of the injected signal needs to be chosen to optimize linearity by a trade-off between the second and third
harmonic content.
The main practical limitation on efficiency is the implementation of an efficient injector circuit. Fig.2.10
also shows that in order to achieve a significant improvement of > 20% in the total drain efficiency, the
injection circuit efficiency should be more than 40% efficient along with the injection signal power 10 dB
below the fundamental output power when the PA is operating at 1 dB compression point. But, this injection
circuit efficiency does not contribute much to the total drain efficiency, if the PA is not operated close to
saturation. It is seen that at lower input drive levels, the injected power required also reduces. Therefore, the
injection circuit efficiency will now not play a significant role. This can be seen from Eq.6.1 where the DC
power dissipated in the injected circuit is defined as a ratio of the injected RF power at the second harmonic
and the injection circuit efficiency.
As seen in Fig.2.10, for an input drive level of 10 dB, the drain efficiency is improved from 35% for a
81
class-AB PA without harmonic injection to 48% for a PA with injection. But, the injection circuit efficiency
does not affect the total efficiency and a flat response for total efficiency is achieved if the injection circuit
efficiency is atleast 20%. As the PA compresses, the amount of power required for the second harmonic
increases resulting in a higher impact of the injection circuit efficiency on the total drain efficiency of the PA.
This might present a challenge for very high power PAs, but is otherwise not a difficult constraint. In
the prototype characterization presented in this paper, a passive doubler was used to produce the harmonic.
This is not only inefficient, but not practical for amplifying a real signal, in which case significant distortion
would be introduced. The linearity tests (Fig.3.6) show that a clean doubled frequency spectrum needs to
be injected. Therefore, for signal amplification, a different approach is needed than was done for the CW
tests in this paper. A topic of current research is integration of an up-converter in the injection circuit with a
synchronized second baseband input. For very broadband signals, the phase control that achieves linearity
might prove to be challenging. An interesting extension of the concept to a broadband HI-PA will require a
three port injection network design with good harmonic isolation and low fundamental frequency loss over a
broad frequency range.
5.3
H a r m o n i c B a l a n c e S i m u l at i o n s
All the measurements presented above result from harmonic injection at one of the two second harmonic
tones at the output of the PA. It is shown that each harmonic tone only affects the intermodulation products
which are directly related to the injected tone. Therefore, simultaneous injection of both the harmonic tones
should result in equal reduction of intermods on both sides of the spectrum. This idea has been validated
using harmonic balance simulations in Advanced System Design (ADS) where a nonlinear model for the
TriQuint TGF2023-01 discrete GaN on SiC die is used along with the designed input and output matching
networks presented in Ch.4. A basic block diagram of the simulation setup is shown in Fig.5.10. Instead
of terminating the output network in a 50Ω load, a fundamental tuner is utilized to perform load-pull at
fundamental and intermodulation tones.
The harmonic balance simulation is setup to sweep the injected signal amplitude and phase along with
load-pull at the fundamental tones to achieve maximum efficiency and minimum 3rd and 5th order IMD
82
`
Port 1
f1 = RF + fs/2
f2 = RF - fs/2
P1 = P-3
P2 = P-3
Designed
HI-PA
f1 + f2
Load
Tuner
= 0 to 0.7
Zopt
Optimal
phase offset
Port 2
2f1 = 2*(RF + fs/2)
2f2 = 2*(RF - fs/2)
Pinj1 = Pinj-3
Pinj2 = Pinj-3
2f1 + 2f2
P = 16 dBm, Pinj = 26.5 dBm
fs = 1, 10 or 20\,MHz
RF = 2.450.5 GHz
Figure 5.10: Harmonic balance simulations in ADS for harmonic injection at both the harmonic tone signals
for the designed HI-PA with TriQuint 6 W GaN discrete die transistor having Pout = 36.28 dBm. A single
harmonic balance source is used with two ports for fundamental and injected harmonic tone signals.
products. First, the load-pull is performed on the PA with no harmonic injection and the results are then
compared to a PA with harmonic injection at both 2f1 and 2f2 . The results are analyzed for tone seperations
of 1, 10 and 20 MHz and an input drive level of Pin = 16 dBm which is the 1 dB compression point for the PA.
From Ch.1, it is known that waveform shaping is possible if short and open circuit impedances are presented
at the even and/or odd harmonics at the virtual drain of the PA. Therefore, if load-pull to achieve maximum
efficiency is performed on a PA without any harmonic terminations at the output, the optimum impedance
points for the harmonics lie on the edge of the smith chart as shown in Fig.5.11a. Now, if we consider a
two-tone signal at the input of the PA with a tone-spacing of 1 MHz and f1 = 2.45 GHz, then load-pull for
minimum 3rd and 5th order IMD products results in optimal impedance points at the fundamental tones
also to be on the edge of the smith chart. This is because the IMD products are resultant of the even and
odd-order nonlinearities from the PA [82].
Load-pull for maximum efficiency with two-tone input signal results in optimal impedance, Zopt point for
the fundmental tones to be close to 50Ω whereas for Zopt for maximum linearity results in an impedance
point to be on the edges of the smith chart. Therefore, trade-off is required between maximum efficiency and
maximum linearity impedance points at the fundamental tone frequencies. However, selecting Zopt = 14 +
12j Ω such that it lies in between minimum IM D3 point (Zopt = 1.8+32j Ω) and maximum P AE point (Zopt
= 50.35-32j Ω) can result in almost 40% degradation in the PAE from 60% to 20% and a 4 dB reduction in
83
fundamental output power. Also, the harmonic balance simulations show that the minimum power levels
obtained for IM D3 and IM D5 are -20.4 dBc and -33.95 dBc respectively for the optimum impedance points.
Hence, this trade-off is not an efficient way to design the PA since there is severe degradation in the PAE and
-16.08
IMD5
IMD3
-30.06
the intermodulation products are not minimized by a huge margin as shown in Fig.5.11.
(a)
(b)
Figure 5.11: (a) Minimum IM D3 (red) and IM D5 (blue) contours for a class-AB without harmonic injection
at the fundamental tones f1 and f2 with tone seperation of 1 MHz and total Pin = 16 dBm. (b) Spectral plot
of the intermodulation distortion products for class-AB PA with load impedance, Zopt = 14 + 12j Ω.
Next, the trade-off between efficiency and linearity in terms of Zopt is studied for a class-AB PA with
harmonic injection at both the harmonic tones i.e. 2f1 and 2f2 . Equal power is maintained in the fundamental
tones and the injected tones which is 3 dB less than the total power in both the frequency bands. Harmonic
injection is performed with total injected power to be 9.5 dBc w.r.t. fundamental power and an optimal phase
set for the injected tones. A single phase shifter is used to set the optimal phase at both the harmonic tones
in the load-pull setup. Since second harmonic tone injection results in active impedance synthesis at the tone
frequency, this affects the impedances at the IM D products as well. Also, phase reversal of 180◦ results in
cancellation of IM D products as explained in section .2.3.1 and hence, the Γopt for maximum linearity now
moves along the smith chart in phase and magnitude.
It is seen that the Zopt for minimum IM D5 moves from the edges of the smith chart towards the center
with a value of 89.856+j42 Ω shown in Fig.5.12 whereas Zopt for minimum IM D3 moves from to 12+j19.6 Ω.
The maximum efficiency point remains the same as that for class-AB PA without injection. Therefore, if an
impedance is chosen in order to achieve resonably high efficiency and linearity, then at Zopt = 68.707+29.466j
84
-22 dBc
-43.58 dBc
(a)
(b)
Figure 5.12: (a) Minimum IM D3 (red) and IM D5 (blue) contours for HI-PA with optimal injection signal
phase and amplitude for a fundamental tone seperation of 1 MHz and total Pin = 16 dBm. (b) Spectral plot
of the intermodulation distortion products for HI=PA with load impedance, Zopt = 68.707+29.466j Ω.
Ω, the values for IM D3 and IM D5 reduce by 5 dB and 10 dB respectively as compared to IM D power levels
shown in Fig.5.11b and the efficiency drops by 15% relative to the maximum efficiency point for Zopt . Also,
there is a 0.8 dB drop in the fundamental output power as compared to 4 dB reduction in output power for
class-AB PA without harmonic injection. Therefore, a non-expensive trade-off between efficiency and linearity
is achievable with improved performance for the HI-PA compared to the class-AB PA without harmonic
injection.
(a)
(b)
Figure 5.13: Spectral plot of the intermodulation distortion products for HI-PA at Zopt = 68.707+29.466j Ω
with tone spacing of (a) 10 MHz and (b) 20 MHz.
Similar analysis is performed for HI-PA with tone spacing of 10 and 20 MHz where it is seen that as
the tone spacing increases, the PA becomes asymmetric and the spectral components in both upper and
85
lower spectrum do not reduce equally. From Fig.5.13, as the tone spacing increases to 20 MHz, the upper and
lower IM D spectral components do not reduce symmetrically. However, the power levels for these distortion
products are still lower than a class-AB PA without harmonic injection. Therefore, this technique can result in
high symmetrical linearity with considerable efficiencies for narrowband signals of bandwidths upto 10 MHz.
5.4
Conclusion
In summary, this chapter focuses on a study of linearity of harmonically-injected PAs. The behavior of odd
order distortion products for fundamental two-tone signal with tone spacing from 1 to 20 MHz is studied in
harmonically-injected PA. Harmonic injection is performed at one of the two harmonic tones at the output of
the designed hybrid HI-PA resulting in reduction of distortion products which are directly related to the
injected harmonic tone frequency.
Variations in both IM D3 and IM D5 w.r.t. amplitude and phase of the injected harmonic are presented
where it is shown that the third and fifth order distortion products are reduced by more than 20 dB in linear
region of the PA and 10 dB in saturation with a maximum efficiency improvement of 9%. This result matches
with the results presented in Ch.4 where the reduction in third order nonlinearities for a CW signal are
presented with harmonic injection resulting in a higher linearity for the PA.
It is shown that the phase required for both the harmonic tones to reduce the upper and lower sideband
IM D3 products differs by 20◦ for tone spacings of 1 to 10 MHz. Also, as the tone spacing increases to 20 MHz,
the PA asymmetry from low frequency memory effects results in variation of minimum power levels in the
sidebands.
The analysis presented shows that simultaneous reduction in third and fifth order products can be achieved
with harmonic injection at both harmonic tones if there are no sweet-spots present in the distortion products
for the class-AB PA. The phase shift required in the injected harmonics to achieve maximum reduction in
IM D3 and IM D5 products differs by 50◦ for tone spacings of 1-10 MHz.
Finally, harmonic balance simulations of variation in the optimum load for maximum linearity is presented
showing that the trade-off required between efficiency and linearity for harmonically-injected PAs is less
costly as compared to class-AB PAs with 15% reduction in total efficiency and 5 dB reduction in IM D3
86
for the harmonically-injected PA at a load selected to achieve the trade-off. The linearity investigation and
measurement results that show reduction in IM D products for the HI-PA are presented in [83, 84].
87
Chapter 6
S u p p ly M o d u l at i o n
I n t e g r at i o n w i t h
H a r m o n i c a l ly - I n j e c t e d PA
The whole of science is nothing more than a refinement of everyday thinking.
—Albert Einstein
Machines are beneficial to the degree that they eliminate the need for labor, harmful to the degree that they
eliminate the need for skill.
—W.H. Auden
Contents
6.1
Introduction
89
6.2
Theory
6.3
Nonlinear Simulations
90
90
6.3.1
Approach I: Constant Input Drive
91
6.3.2
Approach II: Variable Input Drive
94
6.4
6.1
Measurements
97
6.4.1
Approach I
6.4.2
Approach II
6.5
Discussion
105
6.6
Conclusion
106
98
99
I n t ro d u c t i o n
Modern communication systems utilize amplitude and phase modulation schemes with high peak-to-average
ratios (PARs) and bandwidths. The primary challenge of a transmitter design is to achieve high efficiency
and maintain linearity over the entire range of power levels and bandwidth [14, 15]. For example, Some of the
solutions which address this requirement include outphasing (LINC), Doherty PA with DPD and envelope
tracking PA with DPD [16, 17].
As shown in this thesis, second harmonic injected at the output of a power amplifier results in reduction
of intermodulation distortion products or IMDs and high efficiency resulting in efficient and linear PAs.
In this chapter, the integration of supply modulation with second harmonic injection at the output of the
PA is investigated in order to achieve highly efficient and linear power amplifiers for peak-to-average ratios
(PARs) of > 7 dB. As shown in Ch.4 and 5,interaction of second harmonic with fundamental signal can result
in mixing products with odd order behavior. In order to shape the fundamental waveform to obtain high
efficiency, the injected signal has an optimal amplitude and phase w.r.t the fundamental signal. In addition,
the mixing products at the optimal phase cancel out resulting in high linearity. Therefore, in order to achieve
a linear and efficient PA for high PARs, the harmonically injected PA (HI-PA) is supply modulated in two
different ways.
In the first approach, the input drive level is kept constant, the supply is varied simulatenously along
with the amplitude of the injected second harmonic signal while maintaining the phase of the injected
second harmonic to a constant optimal value. Nonlinear simulations performed in Advanced Systems Design
(ADS) with a Modelithics nonlinear model of the TriQuint 6 W GaN on SiC device are shown along with
89
measurements validated with a proof-of-concept PA at a fundamental frequency of 2.45 GHz.
In the second approach, the input drive level is varied linearly with the supply and the ratio of the injected
second harmonic power to the fundamental output power is maintained constant at 0.1. The phase of the
injected second harmonic is set to an optimal value and the power varies linearly with input drive level and
supply. Nonlinear simulations show that for a 6 dB PAR , a high drain efficiency of 80% is achieved along with
a minimum point in the third order harmonic content, resulting in efficient and linear PA. The simulations
are validated with measured results along with AM-AM and AM-PM measurements on the proof-of-concept
PA at 2.45 GHz. Measured and simulated results show a high efficiency of 65% for a PAR of ≤ 7 dB along
with 6 deg/dB reduction in the AM-PM distortion resulting in a highly efficient and linear PA for high
Peak-to-Average ratio signals.
Finally, the requirements for an efficient supply modulator are discussed for both the approaches and a
comparison is presented for supply modulator design for PAs with and without harmonic injection.
6.2
T h e o ry
6.3
N o n l i n e a r S i m u l at i o n s
In order to achieve a highly efficient and linear PA for high PARs, two approaches are presented in order
to achieve high efficiency and linearity for ≤ 7 dB PARs using harmonic injection integrated with parital
supply modulation at 2.45 GHz. In the first approach, the fundamental input drive level is kept constant
with a simultaneous variation in the supply and the injected second harmonic power, Pinj (2f0 ), where as in
the second approach, the input drive level is varied and a constant ratio is maintained between the output
power at the fundamental, Pout (f0 ) and Pinj (2f0 ). In both approaches, there is a trade-off between the
injection circuit efficiency and linearity. The harmonic balance simulations are performed in Agilent Advanced
System Design (ADS) with a Modelithics non-linear model for the TriQuint 6-W GaN on SiC discrete device
(TGF2023-01). A bias point in class-AB mode with IDQ = 130 mA at VDD = 28 V is chosen.
90
6.3.1
A p p roac h I : C o n s ta n t I n p u t D r i v e
In this method, the simultaneous variation of the injected signal and drain supply achieves high efficiency for
a 7 dB variation in output power with a constant input drive level as shown in Fig.6.1.
VDD
Variable
supply
HI-PA
iD
RF source
f0
f0
1
2
Min
2f0
f0
Mout
3
Z(2f0)
ZL
2f0 Injection
Variable amplitude
---0
Figure 6.1: Block diagram of simulation setup in ADS for varying drain supply and injected second harmonic
power in a class-AB PA with constant input drive power. The 3-port network at the output is a diplexer as
shown in [7, 9].
First, an optimal phase for the 2f0 signal resulting in high efficiency and low third order harmonic content
is chosen by simulating the HI-PA in class-AB bias at a constant fundamental input drive level of Pin =
16 dBm (P1dB ) and G = 21.5 dB. This phase is then set to the optimal value and the drain bias is varied from
10-35 V along with the injected second harmonic power level from -35 dBc to -10 dBc. The drain efficiency
(ηD ) for the HI-PA is calculated from Eq.2.25
ηD =
Pout (f0 )
PDC,f0 + Pinj (2f0 )
(6.1)
In Fig.6.2, dashed line B shows that a 7 dB PAR can be achieved with constant high ηD = 68% by varying
VDD from 10-25 V and Pinj (2f0 ) from 13-26 dBm. In HI-PA without supply variation, the horizontal line A is
followed by applying a constant drain bias and fixed Pinj (2f0 ) in order to achieve high efficiency with only
a minimal 0.5 dB variation in the fundamental output power. As seen from Fig.6.2, the required Pinj (2f0 )
91
A
62
60
20 0
6
62
66
64
10
0
5
68
68
66
64
66
64
62
62 4
6
70
58
58
60
58
25
60
56
56
58
56
68
Drain Voltage (V)
54
54
30
15
54
52
52
74 76
70 72
10
15
Pinj(2f0) (dBm)
72
35
20
25
(a)
35
39
Drain Voltage (V)
30 38
25
20
15
38
38
37
37
36
36
35
35
35
34
33
32
34
33
32
34
33
32
31
10
0
5
30
37
B
36
31
31
10
15
Pinj(2f0) (dBm)
20
25
(b)
−25
−20
−15
−30
30
10
0
5
10
15
20
Pinj(2f0) (dBm)
−1
−1
5
−2
0
−2
5
0
−3
15
B
−15
20
−20
−25
−30
−35
25
0
Drain Voltage (V)
−35
35
25
(c)
92
Figure 6.2: Simulated variation in (a) drain efficiency, ηD (%), (B) Pout (f0 ), in dBm, and (c) ratio
Pinj (2f0 )/Pout (f0 ), in dBc, w.r.t. change in drain voltage and Pinj (2f0 ).
reduces at lower Pout (f0 ) in order to maintain constant high efficiency. Therefore, at lower power levels, the
injection circuit efficiency is less critical whereas at higher power levels, (close to P1dB ), the injection circuit
needs to be ≥ 40% efficient in order to maintain high amplifier efficiency [9].
35
−2
IMD3L/H
B
10
10
15
20
Pinj(2f1/2f2) dBm
4
0 2 −2
−2 −2
−2
6
−28
8
−1
−1
6
15
−18
6
20
−20
25
−1
Drain Voltage (V)
−16
0
−18
30
25
Figure 6.3: Variation in IMD3 with change in supply voltage and injected harmonic power. The input power
is kept constant at 16 dBm. The contours show constant IMD3 levels for both sidebands and with a 1 MHz
tone spacing.
As shown in [9, 71], high linearity can be achieved by maintaining an optimal power ratio, Pinj (2f0 )/Pout (f0 )
and phase of the injected signal. Here, this concept is further extended to integrate supply modulation with
HI-PA. First, a study is performed with nonlinear simulations with a tone spacing of 1 MHz. Fig.6.3 shows
that injection at both 2f1 and 2f2 with a fixed optimal phase results in a 5-12 dB reduction in both upper
and lower IMD3 as compared to a PA without harmonic injection. It is also seen that for lower range of Pout ,
the ratio of Pinj /Pout is higher than 0.1 in order to achieve high linearity and efficiency. The design of the
injection circuit can get challenging, since the efficiency of the injection circuit will now contribute more
to the overall efficiency even at lower output power levels. Referring to the dashed line B in Fig.6.2, which
describes the lookup table (LUT) in Fig.6.1, the simulated IMD3 curves show a 5 dB reduction at each power
level. Thus, by proper control of both Pinj (2f0 ) and VDD , both linearity and efficiency can be improved over
a range of output power levels.
93
6.3.2
A p p roac h I I : Va r i a b l e I n p u t D r i v e
In a power amplifier, reduction in the supply voltage results in the 1 dB compression point shift to lower input
drive levels as shown in Fig.6.4. Also, with increasing input drive levels and supply voltage, the amplitude
and phase modulation distortion, AM-PM can be maintained constant from Fig.6.5.
Figure 6.4: Gain characteristic of a class-AB PA with increase in input drive levels and suppy voltage from 10
to 28 V.
Figure 6.5: AM-PM characteristic of a class-AB PA with increase in input drive levels and suppy voltage
from 10 to 28 V.
Therefore, in order to maintain constant gain or constant AM-PM distortion characteristic for high PARs,
the supply voltage can be varied as a quadratic function of the input drive level shown in Fig.??. The constant
94
gain curve results in a 2◦ variation in the AM-PM distortion. However, if the AM-PM distortion is maintained
constant, For. example, -21◦ , then the output power can be varied from 26 to 34 dBm with a 2 dB variation
in the gain as seen in Fig.6.7. Also, if the constant AM-PM curve for variation in supply and input power
is chosen, then the ratio between the injected 2nd harmonic power and the fundamental output power will
remain constant over the high PAR.
Figure 6.6: Quadratic approximation for supply voltage variation as a function of variation in the input drive
level for constant gain and AM-PM characteristics.
Figure 6.7: Variation in fundamental output power and gain with constant AM-PM distortion maintained in
a PA with supply and input drive variation.
95
In the second approach, the fundamental input drive level is varied and a constant ratio of Pinj (2f0 )/Pout (f0 )
= 10.5 dB is maintained for each of the drive level along with a fixed optimal phase for the injected 2nd
harmonic as shown in Fig.6.8. This ratio gives the optimal value of the injected second harmonic power
required to achieve high efficiency and linearity. The drain supply is then varied from 10-35 V for each of
the input drive level. As seen in Fig.6.9, high efficiency of 75% is achieved for an output power variation of
Supply and f0
drive level control/LUT
VDD
Variable
supply
GND
f0
RF source
f0
1
2
Min
2f0
f0
Mout
3
ZL
2f0 Injection
amplitude = Pin + X dB
---0
Figure 6.8: Block diagram of simulation setup in ADS for varying drain supply and fundamental input drive
level in a class-AB PA. A constant ratio is maintained between Pinj (2f0 ) and Pout (f0 ).
7 dB when the supply is varied from 12-26 V and input power from 10-18 dBm. Also, since the input drive is
varying, a constant gain of 20 dB is maintained over the 7 dB PAR resulting in high PAE as well.
In terms of linearity, the third order nonlinear product i.e. the output power at 3rd harmonic, (Pout (3f0 )),
shows reduction at the peak efficiency points as shown in Fig.6.10. It is well known that lower third harmonic
implies lower third order distortion products (IMD3) levels [75]. Hence, this approach results in high efficiency
and linearity for all the output power levels. However, since the ratio between the instantaneous output power
and injected power is now constant, the injection circuit efficiency is critical even at lower input drive levels.
Two tone simulations show that IMD3 follows the same trend with ≤ -30 dBc reduction for a 7 dB variation
in Pout (f0 ) and a constant gain of 19 dB.
96
80
D
η (%)
60
V = 10V
DD
12V
14V
16V
20V
22V
24V
26V
40
20
0
24
26
28
30 32 34
P (f ) (dBm)
36
38
40
out 0
Figure 6.9: Simulated results for drain efficiency, ηD with simultaneous variation in fundamental input drive
and drain supply voltage. The ratio, Pout (f0 )/Pinj (2f0 ) = 0.1 for each input drive.
10
Pout(3f0) (dBc)
0
10
VDD = 10V
12V
14V
16V
20V
22V
24V
26V
20
30
40
24
26
28
30 32 34
Pout(f0) (dBm)
36
38
40
Figure 6.10: Simulated results for Pout (3f0 ) with simultaneous variation in fundamental input drive and drain
supply voltage. The ratio, Pinj (2f0 )/Pout (f0 ) = 0.1 for each input drive.
6.4
Measurements
The measurements are peformed on a harmonically-injected PA (HI-PA) proto-type designed using a 6 W
discrete GaN on SiC die from TriQuint Semiconductor. The PA is designed at a fundamental frequency of f0
= 2.45 GHz with a class-AB design at Idq = 130mA and Vdd = 28 V. The output matching network of the
PA incorporates a diplexer circuit in a non-50 Ω environment in order to inject the second harmonic into the
97
drain of the PA without affecting the fundamental output signal path. Detailed description of the PA design
can be found in [9, 7, 66]. The PA has a small signal gain of 23 dB in class-AB mode with a drain efficiency,
ηD = 55% at 1 dB compression. Note that all the measurements presented are calibrated at the output port
of the designed amplifier.
6.4.1
A p p roac h I
l The measurement setup consists of the HI-PA in a hybrid configuration with a TriQuint TGF2023-01 6-W
discrete GaN die integrated with the input and output networks on a Rogers 4350B 30-mil substrate. The
measurements include a total loss of 2 dB in the input and output networks of the PA. In order to validate
approach I, the drain supply voltage and Pinj (2f0 ) are varied simultaneously with VDD ranging from 12-32 V
and Pinj (2f0 ) from -25 to -10 dBc with a fixed optimal phase for the injected second harmonic. Fig.6.11 shows
58
60
58
62
60
28
62
26
68
64
66
24
70
68
70
22
74
78
74
5
10
15
20
Pinj(2f0) (dBm)
80
82
16
76
78
72
18
72
76
20
64
66
78
30
Drain Voltage (V)
56
56
80
32
25
Figure 6.11: Variation in measured drain efficiency w.r.t. the drain voltage, VDD and injected second harmonic
power, Pinj (2f0 ). The amplifier has G = 19 dB at Pin = 16 dBm for a bias of VDD = 28 V and IDQ = 130 mA.
The gain varies between 13 and 19 dB over the entire range of values.
measured drain efficiency curves for the HI-PA with supply modulation as a function of VDD and Pinj (2f0 ),
which compare well with the simulations in Fig.6.2. A 6 dB variation in Pout (f0 ) is achieved with a high ηD
= 66%. As seen from Fig.6.11, the injected power required to achieve high efficiency for lower output power
levels reduces. Hence, the injection efficiency for a transmitter at these power levels is not very important
98
and will not affect the total system efficiency. However, the gain varies by almost 6 dB over the entire range
and a constant 10 dB reduction is seen in the third harmonic output power as compared to a class-AB PA
with no harmonic injection.
Table 6.1: Measured parameters of supply modulated HI-PA.
VDD (V )
12-18
12-21.25
12-23.25
17-26.75
21.75-30.5
Pinj (dBm)
16.6-26.28
12.4-26.28
12.4-26.28
8.82-26.28
8.82-26.28
Pout (dBm)
30.9-34
30.7-35
30.65-36.5
33.2-36.27
34.8-37
ηD
72%
68%
66%
62%
58%
Rdd (Ω)
86.38-107.2
83.3-107.4
81.9-108
86-110
91.3-114
The measurements shown assume the injection efficiency to be 100% since the test bench setup consists of
instrumentation equipment. Table 6.1 shows the measured parameters for the harmonic injection PA with
supply modulation using approach I.
6.4.2
A p p roac h I I
In order to maintain linearity and constant gain over a high PAR, approach II explained in section 6.3.2
is validated, where the fundamental input drive is varied along with the drain supply of the harmonically
injected PA. The ratio,
Pout (f0 )
Pinj (2f0 )
is kept constant at a value of 10 dB for every input drive level. As shown in
Fig.6.12, a constant gain of 17 dB is maintained for a 6 dB variation in the output power along with a -32 dBc
reduction in the third order nonlinear harmonic content. The drain efficiency of the PA varies from 73% to
67% over a 6 dB change in the output power.
Note that in this case, the optimal phase of the injected harmonic is not varied with increasing drain voltage
and input drive level. Next, the dynamic AM-PM distortion is measured as explained in [85]. Fig.6.13 shows
the variation in output power as a function of input drive level and drain voltage for a harmonically-injected
PA. It is seen that for a PA without supply variation, trajectory T1 can be followed where there is a 7 dB
variation in output power with constant supply voltage of 28 V and variation in input drive level. However,
in this case, high efficiency is only achieved at higher power levels as shown in Fig.6.15. If trajectory T2 is
followed with harmonic injection, then a 10 dB variation in the output power is achieved with supply variation
from 14 to 26 V and input power varied by 8 to 16 dB. Fig.6.15 shows that we can achieve high efficiency
99
Pout(f0) (dBm), Pout(3f0) (dBc)
74
30
73
20
72
10
71
ηD (%)
40
Pout(f0)
0
70
Pout(3f0)
−10
69
−20
68
−30
67
−40
14
16
18
20 (V) 22
VDD
24
66
26
Figure 6.12: Measured Pout (f0 ) (dBm), ηD (%) and Pout (3f0 ) (dBc) for a harmonically injected PA with
variable supply and input drive level. The ratio of Pout (f0 )/Pinj (2f0 ) = 10.5 dB for each of the input drive
levels.
ranging from 60 to 78% for a 10 dB variation in output power. Measured results shown in Fig.6.15 match
closely with the simulated results shown in Fig.6.9 where we can see a constant high efficiency of 80% for a
6 dB variation in output power with drain voltage ranging from 16 to 26 V. As seen in Fig.6.14, if trajectory
T2 is followed for supply modulation, the PA gain varies by 3 dB with gain of 19 dB for lower output power
levels and 22 dB for higher power levels. Hence, as the peak of the signal increases in instantaneous power,
the gain of the PA also increases.
It is clear that high efficiency can be achieved for a PAR of > 7 dB through the integration of supply
modulation and harmonic injection. Approach II also is validated to acheive high linearity by measuring
dynamic AM-PM data from the experimental setup as explained above. Measured AM-PM distortion for the
class-AB PA with and without harmonic injection shows that as the supply voltage to the PA increases, the
AM-PM distortion reduces by a maximum of 6 deg/dB for a harmonically-injected PA as compared to a PA
without injection. Fig.6.16 shows the measured AM-PM distortion for the harmonically injected PA and the
improvement in AM-PM over non harmonically-injected PA.
Measurements show that the AM-PM distortion is greatly reduced by a maximum of 6 deg/dB with
harmonic injection hence resulting in a linear and efficient PA.
100
37
36
35
33
34
32
31
30
37
T1
31
32
T2
34
33
31
36
35
32
28
30
VDD (V)
29
32
30
28
26
24
22
20
18
16
14
12
10
26
25
24
23
27
29
30
28
27
6
8
33
32
31
29
10
12
Pin (dBm)
14
24
23
T1
24
22
23
24
23
23
T2
21
22
19
18
172216 13 14 15
32
30
28
26
24
22
20
18
16
14
12
10
24
VDD (V)
l
Figure 6.13: Measured variation in the fundamental output power, Pout (f0 ) as a function of the input drive
level and supply voltage for a harmonically-injected PA with optimal amplitude and phase of the second
harmonic.
19
21
20
21
20
18
17
19
18
16
17
6
8
10
12
Pin (dBm)
14
16
Figure 6.14: Measured variation in gain as a function of input power, Pin and supply voltage, VDD for the
harmonically-injected PA with supply variation.
The two main challenges in supply modulation integration are CPAE efficiency and the fact that the PA
is a dynamic load to the supply [15]. The integration of supply variation with harmonic injection will require
an efficient supply modulator where the total system efficiency can be calculated as follows:
ηtotal = ηSM ·
Pout (f0 )
PDC,f0 + PDC,2f0
101
(6.2)
0.6
6
0.6
0.5
0.5
0.6
0.6
0.
7
0.5
0.7
0.4
0.
T1
0.8
T2
0.6
0.4
VDD (V)
0.5
0.7
32
30
28 0.3
26
24
0.4
22
20
4
18
0.
160.4
0.5
14
12
10
6
8
0.7
0.5
10
12
Pin (dBm)
14
16
(a)
90
80
η D (%)
70
VDD = 10V
12V
14V
16V
18V
20V
22V
24V
26V
28V
60
50
40
30
20
22
24
26
28
30
32
Pout (dBm)
34
36
38
(b)
Figure 6.15: (a) Measured PAE contours as a function of the input drive level, Pin and supply voltage, VDD ,
(b) Measured drain efficiency as a function of the output power and drain voltage showing constant high
efficiency of 75% for a PAR of 6 dB.
where, PDC,2f0 = Pinj (2f0 )/ηinj and ηSM is the supply modulator efficiency. In order to design an efficient
supply modulator, the PA supply sensitivity is shown in Fig.6.17, defined as
ζ(%) =
∆Vout
Vout
∆VDD
VDD
· 100
(6.3)
In approach I, for lower values of Pinj (2f0 ) and VDD , the resultant error in output voltage into a 50 Ω load
102
10
8
AM/PM (deg/dB)
T1
12 V
14 V
16 V
18 V
20 V
22 V
24 V
26 V
28 V
9
7
6
5
4
3
T2
2
1
0
5
6
7
8
9 10 11 12 13 14 15 16
Pin (dBm)
(a)
7
VDD = 14V
16V
18V
20V
22V
24V
26V
∆ AM/PM (deg/dB)
6
5
4
3
2
1
0
5
6
7
8
9 10 11 12 13 14 15
Pin (dBm)
(b)
Figure 6.16: (a) dynamic AM-PM distortion for HI-PA with variation in input drive level and supply
voltage. (b) Measured improvement in the AM-PM distortion of a harmonically-injected PA over a non
harmonically-injected PA.
is as high as 95% and reduces to ≤ 40% for higher values of these parameters. Line B shows that the PA
supply sensitivity for a 6 dB PAR drops from 95% to 60% as the output power increases to its peak value.
The PA presents a dynamic load to the supply which can be defined as Rdd = VDD /IDD . For a harmonically
injected PA, this load also has a dependency on the injected power at the second harmonic. Hence the value
103
100
90
ζ (%)
80
70
B
60
Pinj(2f0) = 0 dBm
40
10 dBm
15 dBm
20 dBm
25 dBm
30
5
10
50
15
20
Vout (V)
25
30
Figure 6.17: Simulated error in output voltage, Vout with 1 V error in drain bias voltage for various injected
harmonic power levels (approach I).
of RDD can be calculated as follows:
Rdd =
VDD
V2
= DD
IDD
PDC,f0
(6.4)
Now, from (6.1), substituting for PDC,f0 , the value of Rdd can be computed:
Rdd =
2
· ηD
VDD
Pout (f0 ) − ηD · Pinj (2f0 )
(6.5)
In approach I, varying the drain supply with harmonic injection at a fixed input power results in a
maximum 30% increase in the load presented by the PA to the supply modulator for a 6 dB variation in the
output power as shown in the table 6.1.
Simulated results show that in approach II, the PA load defined in (6.5) remains almost constant at a
value of 105Ω and varies by a small value of 2% when the drain bias is varied from 14-26 V and a constant
gain is maintained over a 6 dB PAR with high efficiency. This small variation in Rdd means that the supply
modulator design in this case is much less stringent than for a pure envelope tracking transmitter [15].
Measured static load variation is shown in Fig.6.18 where it is seen that if trajectory T2 is followed, then
a 9% variation in the total load is seen from 110Ω to 120Ω. The trade-off involved in this approach is the
efficiency of the injection circuit which now plays a critical role at lower power levels as well. Hence, the
injection circuit would need to be designed for ≥ 40% efficiency over the entire 6-7 dB range of power levels.
104
13
12 0
01
10
150
14
0
22340
212200
0
2
1900
18 0
0
T1
110
0 0
0 13 12
14
90
0
110
10
170160
24
10
0
T2
2
19000
180
17
15
0
0 160
VDD (V)
32
30
28
26
24
22
20
18
16
14
12
10
26
28 30 32
Pout (dBm)
34
36
Figure 6.18: Measured static load presented by the PA to the supply as a function of the output power.
6.5
Discussion
A measure of linearity is AM-PM distortion in an amplifier because modern communication systems utilize
phase based modulation schemes. These include but are not limited to various PSK standards for satellite
communication links, WLAN, Bluetooth, Zigbee and RFID standard ISO14443. The ubiquity of phase
modulation and the varying characteristics of phase distortion among different SSPA technologies and
topologies make AM-PM distortion an important consideration in power amplifier design. If the input signal
to the PA is assumed to the following:
x(t) = X(t).cos[2π.f t + φ(t)]
(6.6)
The output of the PA exhibits nonlinear behavior both in amplitude and phase. Therefore, the output
signal can be written as follows:
y(t) = G[X(t)].cos2π.f t + φ(t) + Φ[X(t)]
(6.7)
where G[X(t)] and Φ[X(t)] represent the nonlinearites introduced in the amplitude and phase behavior
of the PA. In order to understand the trade-off between efficiency and linearity for a harmonically-injected
105
PA with supply variation, dynamic AM-PM measurements are taken on the HI-PA with a constant ratio
between the injected signal and output power of 10 dB and a fixed optimal phase for the injected harmonic
for each input power and drain voltage sweep. The theoretical analysis of the dynamic AM-PM measurements
is shown in [86, 85]. First, consider the AM-PM characteristics for a class-AB PA without harmonic injection
as a function of drain bias and input drive level. In fig.6.19, the measured AM-AM and AM-PM data for this
PA shows that the slope of the amplitude and phase distortion remains almost the same for drain voltages
ranging from 10 to 32 V for the GaN PA. Although, as the drain voltage to the PA is increased, the PA
compresses at higher input drive level. The AM-PM plot also shows that the nonlinear characteristic of the
PA is preserved with variation in supply with the exception of degradation at a higher input power level.
For example, in fig.6.19, a phase distortion of 4 deg/dB is obtained for drain voltages ranging from 12 to
32 V, but the input drive level at which this distortion is achieved increases with increase in the drain voltage.
Therefore, for a PA with supply modulation, if the supply voltage varies linearly with the input drive level,
then the compression and distortion characteristics of the PA remain the same.
10
VDD = 12V
16V
20V
24V
28V
32V
AM−PM (deg/dB)
8
6
4
2
0
5
6
7
8
9 10 11 12 13 14 15
Pin (dBm)
Figure 6.19: Measured dynamic AM-PM distortion for a class-AB GaN 6 W PA without harmonic injection.
The plot shows the AM-PM distortion for various drain voltages as a function of the input drive level, Pin .
6.6
Conclusion
In summary, to the best of the author’s knowledge, this is the first demonstration of a supply-modulated
harmonic injection PA. We have demonstrated a 2.45 GHz GaN 6-W PA with ηD = 67-73% over a 6 dB PAR.
106
The gain remains constant and linearity is improved significantly. shows first time, the integration of supply
variation with a harmonically-injected PA. Two different methods are presented to achieve high efficiency and
linearity for high Peak-to-Average ratios of > 6 dB.
In the first method, harmonic balance simulations are presented with variation in supply and injected
signal amplitude while keeping the input drive and relative phase of the injected harmonic at a constant
optimal value. The simulated and measured results show constant total efficiency of 66% for a 6 dB variation
in output power. The supply voltage and injected signal amplitude are varied linearly to achieve variation in
output power. In the second method, the supply is varied with the input drive level by maintaining a constant
ratio between the injected signal and the input drive level. The phase of the injected signal is again fixed to
an optimal value. The simulated and measured results show total efficiencies of 70-80% for a 7 dB variation in
outpput power. Measurements also show the reduction in third order nonlinearity i.e. Pout (3f0 ) by > 15 dB.
AM-PM measurements also show reduction in phase distortion in the PA resulting higher linearity.
The analysis presented shows that the second method yields better trade-off characteristics between
efficiency and linearity for the HI-PA, and is reported in [87].
107
Chapter 7
Contributions and Future
Wo r k
The whole of science is nothing more than a refinement of everyday thinking.
—Albert Einstein
Machines are beneficial to the degree that they eliminate the need for labor, harmful to the degree that they
eliminate the need for skill.
—W.H. Auden
Contents
7.1
Introduction
109
7.2
X-Band MMIC Design
7.3
Measurements
7.4
Future Work
7.5
Contributions
112
116
118
109
7.1
I n t ro d u c t i o n
This last chapter describes some directions for future work including preliminary results on a X-band MMIC
harmonically-injected PA designed in the TriQuint high frequency GaN process. The motivation for the design
is to demonstrate experimentally frequency scaling as well as high efficiency which includes the injection
circuit efficiency. In addition, a proposed architecture for a complete communication transmitter using HI-PA
is discussed. Finally, the contributions of this thesis are summarized.
7.2
X-Band MMIC Design
The design for the 10-GHz harmonically injected PA (HI-PA) in the TriQuint 0.15 µm GaN process is done
in AWR Microwave office with the nonlinear model, design and layout rules guide provided by TriQuint
Semiconductor for a GaN 12×100 µm gate periphery device. The first step in the design is to perform load-pull
simulations on the device with the specific bias point in class-AB mode in order to design the input and
output matching networks for the PA. Since, the aim here is to design a class-A PA which can then be made
more efficient using harmonic injection, the bias point is chosen from the DC load line as shown in Fig.7.1.
1000
Idc (mA)
800
600
400
200
0
0
VG = -3V
IDQ = 152mA
5
10
15
20
Vdd (V)
25
30
35
Figure 7.1: Simulated IV curves for the 12x100 µ periphery TriQuint GaN device. The bias point selected is
shown in the figure with Idq = 152 mA.
Once the bias point is selected with Vdd = 20 V, ideal load pull simulations result in the optimal output
109
impedance (Zout ) of the transistor for a class-A/AB mode of PA. A source pull is performed on the PA in
order to achieve maximum small signal gain for the device at 10 GHz. This impedance is found to be Zin =
3.0+5.1j Ω.
The input matching network is designed as a passive two-port network so that the gate of the device can
be matched to Zin along with low insertion loss and RF to DC isolation. Since the input network does not
require components to handle large current densities, a spiral inductor is used as an RF choke along with
resistance in series for stability. First, the input network is designed in AWR using ideal components in order
to achieve the desired Zin at port 2 of the two port input network. Once the desired impedance and |S21 | is
achieved with the ideal design, it is modified using on chip components using the 0.25µm process kit library
in AXIEM EM simulator. A comparison of the impedance match achieved with both ideal and non-ideal
MMIC components for the input matching network is shown in Fig.7.2 where port 1 of the input matching
network is matched at 50 Ω and port 2 is matching to Zin resulting in total insertion loss through the network
of 0.5 dB. Also, the DC and bypass blocking capacitors provide a RF-DC isolation of > 30 dB at 10 GHz.
Load-pull on the output is performed with the designed input matching network as shown in Fig.7.3 where
the load-pull results in Pout = 35.9 dBm at an impedance of Zout = 11+13j Ω. The output network design
is divided in two parts with one low pass filter and one high pass filter network in parallel connected to a
common node at the drain of the transistor. This network then represents a diplexer network design similar to
the one shown in [7]. The filter networks are considered at passive two port networks with one port matched
to Zout and the other port matched to 50 Ω. Since the line lengths calculated for these networks are too long
for the chip size, a combination of microstrip and capacitors is used to design the output diplexer network.
The simulated losses in both the low and high pass network is shown in Fig.7.4. In order to make this
network compact, the DC blocking and bypass capacitors are integrated within line lengths along with a
meandered section of wide microstrip line used as an RF choke which can handle the output current.
The simulated class-AB PA design results in 36.4 dBm output power at compression and 47% drain
efficiency with a small signal gain of 15 dBm. The layouts for the designed networks are then integrated with
that of the device in order to design the final chip layout as shown in Fig.7.6. The ideal design when tested
with harmonic injection results in characteristics similar to the hybrid HI-PA presented in Ch.4. It is seen
110
0.8
1.0
S(2,2)
input_match_MMI C
S(1,1)
input_match_MMI C
S(2,2)
input_match_mmic
2.0
0.6
S(2,2)
input_em
Swp Max
22GHz
0.
4
4.0
5.0
10 GHz
r 49.8432 Ohm
x 0.347281 Ohm
10.0
10.0
3.0
4.0
5.0
2.0
1.0
0.8
0.6
0.4
0
0.2
0.2
10 GHz
r 4.5249 Ohm
x
.
0 2 6.58386 Ohm
-10.0
-4.
0
-5.0
-3
.0
-
3.0
10 GHz
r 3.03386 Ohm
x 5.12955 Ohm
.0
-2
-1.0
-0.8
-0.
6
.4
-0
Swp Min
0GHz
(a)
0
S par ameter s (dB)
10 GHz
-0.5137 dB
-20
10 GHz
-20.23 dB
-40
-60
-80
8
10
12
14
16
Fr equency (GHz)
18
20
22
(b)
Figure 7.2: (a) Impedances for the ideal and non-ideal simulated input matching network with port 1 matched
to 50 Ω (blue) and port 2 matched to Zin (green - ideal, red- non-ideal). (b) Simulated S parameters for
non-ideal input matching network.
that when the injected signal amplitude is maintained at 10 dBc w.r.t. fundamental output power at 1 dB
compression, the output power at f0 and 3f0 have peak and minimum points with a 0-360◦ relative phase
shift at the injected second harmonic. The current also drops by > 100 mA as shown in Fig.7.5. This results
in an efficiency improvement of > 20% with peak drain efficiency of 70% with > 4 W of output power.
The final layout of the designed chip is shown in Fig.7.6 where the main PA is the harmonically-injected
PA at 10 GHz and the PA on the top left corner is a 20 GHz driver PA with ηD > 60% designed by Michael
Coffey for this part of the project.
111
+j1.0
+j0.5
32
22
+j5.0
34
+j0.2
24
23
33
34
+j2.0
2 27 26 25
29 8
31 30
21
31
27
26
25
−j0.2
30
21
−j0.5
5.0
2.0
32
28
29
28
27
2
25 6
29
33
1.0
0.5
0.2
35
0.0
∞
−j5.0
24
23
22
−j2.0
−j1.0
Figure 7.3: Simulated load-pull contours in order to obtain maximum output power, Pout at 10 GHz.
50
|Eqn(il_inj_1)|
3_port_loss_output
L oss (dB)
40
30
20
10
20 GHz
0.5949
10 GHz
0.6445
0
8
10
12
14
16
Fr equency (GHz)
18
20
22
Figure 7.4: Simulated loss in the through and injection paths of the 3-port output diplexer network.
7.3
Measurements
The two PAs in Fig.7.6 are measured separately using fixtures which interface the MMIC to coaxial connectors
as presented in [41]. The 10-GHz PA is measured without harmonic injection at a bias point of Vdd = 20 V
and Idq = 70 mA and the 20 GHz driver PA at a bias point of Vdd = 15 V and Idq = 20 mA. The 10-GHz
HI-PA is then tested with 2nd harmonic injection by optimizing the amplitude and phase of the injected 2f0
signal.
112
25
38
20
Power at 2f0 (dBm)
Power at f0 (dBm)
37
36
35
15
10
5
0
−5
33
−300 −275 −250 −225 −200 −175 −150 −125 −100
Phase shift at 2f0 (deg)
−10
−300 −275 −250 −225 −200 −175 −150 −125 −100
Phase shift at 2f0 (deg)
(a)
(b)
500
10
450
(mA)
20
Pinj = 20dBm
0
−10
DD
22 dBm
24 dBm
26 dBm
28 dBm
30 dBm
32 dBm
400
I
Power at 3f0 (dBm)
34
350
−20
−300 −275 −250 −225 −200 −175 −150 −125 −100
Phase shift at 2f0 (deg)
300
−300−275−250−225−200−175−150−125−100
Phase shift at 2f0 (deg)
(c)
(d)
Figure 7.5: Ideal harmonic balance simulations showing variations in (a) fundamental output power, Pout (f0 )
(b) second harmonic output power, Pout (2f0 ) (c) third harmonic output power, Pout (3f0 ), and output drain
current, Idd , for the design HI-PA with phase of the injected harmonic swept from 0 to 360◦ and amplitude
from -20 to -8 dBc w.r.t. fundamental output power.
f0 c l a s s - A B PA w i t h o u t h a r m o n i c i n j e c t i o n
In class-AB, the PA achieves a maximum efficiency of 48.5% at f0 = 10.6 GHz. A maximum Pout of 4 W or
36 dBm is achieved with a small-signal gain of 14 dBm. A comparison of the simulated vs. measured results
for the f0 PA are shown in Fig.7.7. It is seen that measurement and simulation match closely in terms of
gain and efficiency even though the frequency is shifted by 600 MHz. A frequency sweep of the f0 PA shows
efficiency and output power in the X-band range as seen in Fig.7.8.
113
Figure 7.6: Final MMIC layout of the designed HI-PA (bottom) and 20 GHz driver PA (top).
50
40
Meas
Sim
35
30
Pout (dBm)
ηD (%), Gain (dB)
40
30
25
20
20
10
0
0
15
5
10
15
20
Pin (dBm)
25
10
30
Figure 7.7: Comparison of the simulated (10 GHz) and measured (10.6 GHz) X-band class-A PA without
harmonic injection in terms of drain efficiency,ηD , fundamental output power, Pout and gain at Vdd = 20 V
and Idq = 130 mA.
Second-harmonic Amplifier
The 2f0 PA is designed for 20 GHz and measured with class-AB bias with a maximum Pout = 28.3 dBm and
PAE = 59% with a gain of 8 dB as shown in Fig.7.9. It is determined that the maximum power required at 2f0
for optimal second harmonic injection is approximately 27 dBm. Therefore, as seen from Fig.7.9, the injection
PA is > 50% efficient at this power level. The high efficiency of the 20-GHz PA reduces the degradation of
overall efficiency due to other microwave component losses in the injection path.
114
48
0.5
46
0.48
44
Idd (mA)
ηD (%)
0.46
42
0.44
40
0.42
38
0.4
36
34
9.9
10
0.38
10.1 10.2 10.3 10.4 10.5 10.6
Frequency (GHz)
Figure 7.8: Class-AB PA performance in X-band without harmonic injection.
70
P
(2f )
out
25
0
60
Gain
50
20
40
15
30
10
5
6
PAE (%)
Pout(2f0) (dBm), Gain (dB)
30
20
8
10
12 14 16 18
Pin(2f0) (dBm)
20
10
22
Figure 7.9: Measured response for the 20 GHz driver PA in terms of PAE (green), Pout (blue) and gain (red).
Harmonic Injection Test
The HI-PA when tested at 10 and 10.6 GHz with 2nd harmonic injection at an input drive level of 23 dBm
(close to P1dB ) results in a 15-point efficiency improvement along with a 60 mA reduction in the total drain
current. At 1 dB compression, the maximum Pout (f0 ) = 35.79 dBm with the drain current reduced from
0.39 A to 0.33 A at 10.6 GHz. The injected 2f0 power needed to achieve this 60 mA reduction in current is
approximately 26.2 dBm. Due to the high process ft [?], similar 2f0 driver PA efficiencies shown in Fig.7.9
can be obtained at 21.2 GHz. Therefore, at 10.6 GHz, an increase in the total efficiency from 48% to 70% can
be achieved by taking into account the 2f0 driver PA efficiency at the required 2f0 injection power as shown
in Fig.7.10.
115
70
(%)
60
η total HI PA
η D no i
50
40
30
20
10
0
12
16
20
P
i (f ) (dBm)
24
28
Figure 7.10: Measured and projected total efficiency, ηtotal of HI-PA as a function of fundamental input drive,
Pin (f0 ) at 10 GHz (red) and 10.6 GHz (blue) with Pout (f0 ) = 3.5 W.
7.4
F u t u r e Wo r k
Some of the on-going work in the field on harmonically-injected PAs can be applied to communication
system by analyzing the HI-PA with basic modulation schemes such as QPSK, 16-QAM, etc. The block
diagram shown in Fig.7.11 shows the basic set-up required to analyze the HI-PA with a commuication signal
modulation scheme. A linear and atleast 40% efficient injection PA is required in the injection path in order to
provide a low distortion injection signal to the main PA. An up-converter (Eg. Hittite HMC819LC5) can be
utilized in order to up-convert the input signal for injection. This upconverter has a high side-band rejection
of -35 dBc resulting in linear signal and a conversion gain of 15 dBm. Base-band processing can be performed
to create a base-band signal which has twice the bandwidth of the fundamental base-band signal. In this
technique, the basic parameters to measure for the PA in terms of linearity are the Adjacent channel power
ratio or ACPR and error vector magnitude or EVM.
The designed X-band MMIC PA can be measured with the 20 GHz driver PA integrated in hybrid and
on-chip environment. Since the maximum output power of the 10 GHz PA is close to 4 W, the maximum
power required at 20 GHz would be close to 27 dBm. The designed 20 GHz driver PA has a gain of 8 dB and a
resultant efficiency of 60% at compression. The 10 GHz PA and the 20 GHz PA can be connected in a hybrid
manner with fixturing provided by TriQuint Semiconductor shown in Fig.7.12 in order to measure the HI-PA.
Analog voltage controlled phase shifter (Eg. Hittite HMC933LP4E) and RF sweeper can be used to control
116
Figure 7.11: Block diagram describing measurement setup HI-PA with standard communication signal
modulation schemes. An upconverter is used to create the injection signal along with a voltage controlled
phase shifter to change the relative phase of the injected signal w.r.t. the fundamental signal.
the amplitude and phase of the injected harmonic signal.
(a)
(b)
Figure 7.12: (a) Fixturing for 10 GHz MMIC provided by TriQuint Semiconductor. Alumina lines with
bond pads wire-bonded to the RF and DC pads on chip which is mounted on a copper molly substrate. (b)
Measurement setup with launcher fixtures to measure the MMIC chip in 50 Ω environment.
The HI-PA can be measured in an integrated environment with the 20 GHz driver PA as designed and
shown in Fig.7.13. A pre-driver is also designed at 20 GHz with a smaller gate periphery of 4x75 µ to provide
high gain in the injection signal path. Hence, the phase shifter and amplitude control can be done in small117
signal regime which will allow the injection path to be more efficient. Since there is no coupler in the injection
path of the diplexer network for power calibration, the characterization of the pre-driver and driver PAs needs
to be performed first in order to understand the required input power level to achieve the maximum output
power required from the driver PA. Once the 20 GHz PA characterization is done, the integrated HI-PA can
be measured with an estimate of the injected signal amplitude.
Figure 7.13: MMIC design for 10 GHz HIPA integrated with 20 GHz Driver PA using an integration in the
output diplexer network (B). A pre-driver at 20 GHz designed for high gain in the injection path (A).
Some of the other work related to HI-PAs can be done in expanding the signal bandwidth and design of
diplexer network for broad-band applications. Harmonic injection at higher even order harmonics can also be
investigated to enhance efficiency and linearity in a PA. As seen in Ch.2, lot of work has been done to enhance
linearity by injection at the input. Therefore, harmonic injection can be investigated with simultaneous
injection at both input and output of the PA.
7.5
Contributions
Ch.2 presents theoretical analysis of achieving high efficiency and linearity for harmonically injected PAs
with second harmonic at the output. Waveform shaping with addition of even and odd harmonics is analyzed
along with intermodulation distortion (IM D) behavior for various classes of PA. Theoretical reasoning for
asymmetrical reduction of IM D products is given with power series analysis for a PA in terms of drain
current, id and transconductance, gm .
In Ch.3, the theoretical concept of harmonic injection at the output of a class-A/AB PA is validated with
118
experimental results using commercial broadband amplifiers from Cree. The PA is measured in S-band at f0 2.45 GHz with a diplexer network built for 50 Ω environment. Efficiency improvements of 15% are shown over
the class-AB PA with ηD improving from 58% to 75%. Two-tone measurements also demonstrate linearity of
the PA with >20 dB reduction in IM D3 products with harmonic injection at one of the two harmonic tones.
The measurements are results are presented in [72].
In Ch.4, an integrated hybrid HI-PA is designed with the diplexer network integrated with output matching
in a non-50 Ω environment. The PA is designed for class-AB mode of operation with large signal gain of
23 dB and Pout = 5 W. Characterization with 2nd harmonic injection at the output of the PA is performed
for optimization in linearity and efficiency. Variation in PA parameters such as Pout at fundamental and
harmonics along with ηD , gain and Drain current, Idd w.r.t. the amplitude and phase of the injected second
harmonic is presented in [9].
• Efficiency enhancement shows maximum total efficiency improvement of 30% over class-AB PA with
maximum ηD = 89% for the HI-PA. The power required at the injected harmonic to achieve this
efficiency is -5.5 dBc.
• Linearity analysis is performed in terms of second and third harmonic content for the HI-PA. Optimization
for minimum third harmonic content results in total efficiency improvement of 20% for a CW signal
with max ηD = 78% and third harmonic reduction by > 15 dB in compression with the injected
harmonic power 10 dBc w.r.t. fundamental output power. The total output power reduces by 0.26 dB
w.r.t. class-AB PA.
In Ch.5, the behavior of odd order distortion products for fundamental two-tone signal is studied in
harmonically-injected PA. Harmonic injection is performed at one of the two harmonic tones at the output of
the designed hybrid HI-PA resulting in reduction of distortion products which are directly related to the
injected harmonic tone frequency. It is shown that a corelation between CW and two-tone measurements can
be done based on third order nonlinearity of the PA. Linearization of PA using harmonic injection at the
output is presented in [83].
• Variation in both IM D3 and IM D5 w.r.t. amplitude and phase of the injected harmonic is presented.
119
This result is similar to the one presented for third harmonic at the output of the PA for CW tones in
Ch.4. The third and fifth order distortion products are reduced by > 20 dB in linear region of the PA
and > 10 dB in saturation.
• Reduction of distortion products is studied for harmonically injected PAs with tone spacings from
1-20 MHz. It is shown that the phase required for both the harmonic tones to reduce the upper and
lower sideband IM D3 products differs by 20circ for tone spacings of 1 to 10 MHz.
• The analysis presented shows that simultaneous reduction in third and fifth order products can be
achieved with harmonic injection at both harmonic tones if there are no sweet-spots present in the
distortion products for the class-AB PA. The phase shift required in the injected harmonics to achieve
maximum reduction in IM D3 and IM D5 products differs by 50circ for tone spacings of 1-10 MHz.
• Finally, harmonic balance simulations of variation in the optimum load for maximum linearity is
presented showing that the trade-off required between efficiency and linearity for harmonically-injected
PAs is less costly as compared to class-AB PAs with 15% reduction in total efficiency and 5 dB reduction
in IM D3 for the harmonically-injected PA at a load selected to achieve the trade-off.
Ch.6 shows first time, the integration of supply variation with a harmonically-injected PA. Two different
methods are presented to achieve high efficiency and linearity for high Peak-to-Average ratios of > 6 dB.
• In the first method, harmonic balance simulations are presented with variation in supply and injected
signal amplitude while keeping the input drive and relative phase of the injected harmonic at a constant
optimal value. The simulated and measured results show constant total efficiency of 66% for a 6 dB
variation in output power. The supply voltage and injected signal amplitude are varied linearly to
achieve variation in output power.
• In the second method, the supply is varied with the input drive level by maintaining a constant ratio
between the injected signal and the input drive level. The phase of the injected signal is again fixed to an
optimal value. The simulated and measured results show total efficiencies of 70-80% for a 7 dB variation
in outpput power. Measurements also show the reduction in third order nonlinearity i.e. Pout (3f0 ) by
> 15 dB. AM-PM measurements also show reduction in phase distortion in the PA resulting higher
120
linearity. The analysis of harmonically-injected PA with supply modulation is presented in [87] and a
journal paper describing these results in detail is in preparation [88].
Finally, an X-Band MMIC is designed for an integrated HI-PA at 10 GHz with a 20 GHz driver PA in
order to achieve 4 W of output power with > 65% efficiency at 10 GHz. The class-AB PA designed is 47%
efficient at 10.6 GHz with a small-signal gain of 14 dB.
121
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