harmonic matching network for an...
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FACULTY OF ENGINEERING AND SUSTAINABLE DEVELOPMENT .
HARMONIC MATCHING NETWORK FOR AN
AMPLIFIER
Hongxu Zhu
September 2012
Master’s Thesis in Electronics
Master’s Program in Electronics/Telecommunications
Examiner: Prof. Daniel Rönnow
Supervisor: Efrain Zenteno
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Acknowledgements
I would like to express my deepest gratitude to my supervisor Mr. Efrain Zenteno, for giving me a lot
of help and wise advices during the whole process of this thesis. I really appreciate his excellent
support during many difficulties in this thesis project.
I would love to equally express my gratitude to my examiner Prof. Daniel Rönnow, for his valuable
commands to improve this thesis project.
I am also very grateful to Dr. Per Landin, who several times gave me suggestions and discussed some
problems with me. I also wish to thank other Ph.D. students in the electronics department at University
of Gävle for the helpful discussions.
I would like to also thank my friends in Sweden and in China for supporting me during the tough time.
Gratitude goes to all my teachers in the electronics department at University of Gävle, for helping me
during my master study.
Finally, to my dear father and mother, I really appreciate their love, trust, and wonderful support in my
life.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
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Abstract
Nowadays, ‘green’ communication is of great importance to save electric energy. In communication
systems, power amplifiers (PAs) play an important role and consume large amount of power. As a
consequence, the enhancement of amplifier efficiency is significantly important for saving energy.
This thesis describes a method to enhance the amplifier efficiency. The goal for this thesis is to find
the matching impedances of harmonics for optimum efficiency performance of an amplifier. The idea
is to control and change the load impedances at 2nd
and 3rd
harmonics for maximum efficiency
performance of an amplifier at fundamental frequency and finally to build a matching network
according to the matching impedances at harmonics.
The load pull technique is applied in this thesis to control the impedances with automatically
controlled tuners. In this way, different impedances correspond to specific tuner positions. Then for
different tuner positions, the corresponding load impedances of the harmonics are determined, the
input, output as well as DC power of the amplifier are measured, and the corresponding efficiency is
computed. Therefore, after appropriate efficiency sweep for specific tuner positions, the matching
impedances with maximum efficiency performance can be found.
The efficiency of the amplifier with harmonic matching (the method implemented in this thesis) can
be improved 2.13 percent which proves the feasibility of the method investigated in this thesis.
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Table of Contents
Acknowledgements .................................................................................................................................. i
Abstract .................................................................................................................................................. iii
Table of Contents .................................................................................................................................... v
List of Figures ....................................................................................................................................... vii
List of Tables .......................................................................................................................................... ix
List of Abbreviations ............................................................................................................................... x
1 Introduction ..................................................................................................................................... 1
1.1 Problem statement .................................................................................................................... 1
1.2 Background .............................................................................................................................. 1
1.3 Goal .......................................................................................................................................... 2
1.4 Thesis outline ........................................................................................................................... 2
2 Theory ............................................................................................................................................. 3
2.1 Load pull technique .................................................................................................................. 3
2.1.1 Harmonic impedance tuning ............................................................................................. 3
2.2 Tuner Operation ....................................................................................................................... 4
2.3 Device characterization ............................................................................................................ 5
2.4 The amplifier behavior ............................................................................................................. 7
2.4.1 Linear region and non-linear region ................................................................................. 7
2.4.2 Non-linear behavior .......................................................................................................... 8
2.4.3 Power added efficiency (PAE) ....................................................................................... 10
3 Process and results......................................................................................................................... 13
3.1 Process and results of tuner characterization ......................................................................... 13
3.2 Triplexer parameters .............................................................................................................. 18
3.3 Efficiency measurement ......................................................................................................... 20
3.4 Maximum efficiency search method ...................................................................................... 23
3.5 Matching network manufacture ............................................................................................. 30
3.6 Efficiency enhancement comparison of different techniques ................................................ 38
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4 Uncertainty analysis ...................................................................................................................... 40
4.1 Efficiency uncertainty ............................................................................................................ 41
4.2 Tuner characterization uncertainty ......................................................................................... 43
5 Discussion ..................................................................................................................................... 45
6 Conclusions ................................................................................................................................... 47
References ............................................................................................................................................. 48
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List of Figures
Fig. 2.1. Phase control of tuner impedance. ............................................................................................ 4
Fig. 2.2. Magnitude control of tuner impedance. .................................................................................... 5
Fig. 2.3. Basic idea of tuner characterization. ......................................................................................... 6
Fig. 2.4. Linear region and non-linear region of an amplifier[17]. ......................................................... 7
Fig. 2.5. Fundamental signal and the harmonics [18]. ............................................................................ 8
Fig. 2.6. Typical output spectrum of the 3rd
and 5th order of two-tone intermodulation products [18]. .. 9
Fig. 2.7. 3-order intercept point (IP3) [17]. ........................................................................................... 10
Fig. 2.8. Efficiency measurement setup. ............................................................................................... 11
Fig. 3.1. Setup of tuner characterization................................................................................................ 13
Fig. 3.2. Phase plot of S11with tuner positions for 2nd
harmonic (4.28 GHz). ..................................... 15
Fig. 3.3. Phase plot of S11with tuner positions for 3rd
harmonic (6.42 GHz). ...................................... 15
Fig. 3.4. Magnitude plot of S11with tuner positions for 2nd
harmonic (4.28 GHz)............................... 16
Fig. 3.5. Magnitude plot of S11with tuner positions for 3rd
harmonic (6.42 GHz). .............................. 16
Fig. 3.6. S11 and limitation circle in Smith Chart for 2nd
harmonic (4.28 GHz). ................................. 17
Fig. 3.7. S11 and limitation circle in Smith Chart for 3rd
harmonic (6.42 GHz). .................................. 17
Fig. 3.8. Triplexer. ................................................................................................................................. 18
Fig. 3.9. Triplexer parameters. .............................................................................................................. 19
Fig. 3.10. Setup for measuring amplifier efficiency. ............................................................................. 20
Fig. 3.11. Comparison of ideal output power and measured output power of the amplifier vs. input
power. ............................................................................................................................................ 22
Fig. 3.12. Efficiency of the amplifier vs. input power. ......................................................................... 23
Fig. 3.13. Well-distributed S11 of whole Smith Chart (2nd
harmonic, 4.28 GHz, 72 points). .............. 24
Fig. 3.14. Well-distributed S11 of whole Smith Chart (3rd
harmonic, 6.42 GHz, 72 points). ............... 25
Fig. 3.15. Points (S11) with best enhanced efficiency in Smith Chart for whole Smith Chart efficiency
sweep ............................................................................................................................................. 26
Fig. 3.16. Specific area with high efficiency in Smith Chart ................................................................ 26
Fig. 3.17. Matching Points (S11) with maximum efficiency in Smith Chart for specific area efficiency
sweep ............................................................................................................................................. 27
Fig. 3.18. Comparison of efficiency and enhanced efficiency with harmonic matching impedances of
the amplifier vs. input power. ........................................................................................................ 28
Fig. 3.19. Efficiency enhancement of the amplifier with harmonic matching impedances vs. input
power. ............................................................................................................................................ 29
Fig. 3.20. Simulated circuit for 2nd
harmonic matching network (left) and simulated result of S11 at 2nd
harmonic frequency: 4.28 GHz (right) .......................................................................................... 30
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Fig. 3.21. Simulated circuit for 3rd
harmonic matching network (left) and simulated result of S11 at 3rd
harmonic frequency: 6.42 GHz (right) .......................................................................................... 31
Fig. 3.22. Manufactured matching network for 2nd
harmonic: 4.28 GHz (left) and 3rd
harmonic: 6.42
GHz (right) .................................................................................................................................... 31
Fig. 3.23. Setup for measuring the amplifier efficiency with matching network. ................................. 33
Fig. 3.24. Amplifier efficiency with manufactured matching network vs. input power. ...................... 34
Fig. 3.25. Comparison of amplifier efficiency and enhanced efficiency vs. input power. .................... 35
Fig. 3.26. Comparison of efficiency enhancement with matching impedances and with manufactured
matching network vs. input power. ............................................................................................... 36
Fig. 3.27. Comparison of output power level with and without harmonic matching vs. specific
frequency. ...................................................................................................................................... 37
Fig. 3.28. IP3 comparison with and without harmonic matching. ......................................................... 38
Fig. 4.1. Uncertainty region of the tuner characterization for 2nd
harmonic: 4.28 GHz (blue circle) and
3rd
harmonic: 6.42 GHz (green circle). .......................................................................................... 44
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List of Tables
Table 1.1. Thesis outline. ........................................................................................................................ 2
Table 3.1. Devices used for the whole process. .................................................................................... 13
Table 3.2. Functions of devices in Fig.3.10. ......................................................................................... 21
Table 3.3. Measured cable loss, triplexer loss, coupler factor and attenuation. .................................... 21
Table 3.4. Points with best enhanced efficiency for whole Smith Chart efficiency sweep. .................. 25
Table 3.5. Points with maximum efficiency for specific area efficiency sweep. .................................. 27
Table 3.6. Parameters of manufactured matching network and matching impedances for harmonics. 32
Table 3.7. S11-parameters shift between manufactured network and matching impedances for
harmonics. ..................................................................................................................................... 32
Table 3.8. Comparison of output power level with and without harmonic matching. .......................... 37
Table 3.9. Comparison of different efficiency enhancement techniques. ............................................. 39
Table 4.1. Correspondence of the uncertainty sections and the devices used in Fig.3.10. .................... 41
Table 4.2. Measured results of the devices and the computed variances. ............................................. 42
Table 4.3. Uncertainty of the power meter. ........................................................................................... 42
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List of Abbreviations
ADS : Advanced Design Software
DC : Direct Current
DUT : Device Under Test
DPD : Digital Predistortion
DLA : Dynamic Load Adaptation
EER : Envelope Elimination and Restoration
ET : Envelope Tracking
HEPAs : High Efficiency Power Amplifiers
IM : Intermodulation
IMD : Intermodulation Distortion
IP3 : 3rd
-order Intercept Point
LINC : Linear Amplification using Nonlinear Components
PA : Power Amplifier
PAs : Power Amplifiers
PAE : Power Added Efficiency
PC : Personal Computer
RF : Radio Frequency
VSWR : Voltage Standing Wave Ratio
VNA : Vector Network Analyzer
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1 Introduction
For high efficiency requirements, the amplifiers operate in the compression region with non-linear
behavior. For improving the power added efficiency (PAE) of an amplifier, the matching impedances
at harmonic frequencies (the harmonic matching) were determined in order to design the matching
network of an amplifier in this work.
The load pull technique is used to control and determine the impedance in order to find the matching
impedance for providing optimum efficiency performance [1, 2]. The way the load pull technique
works is to change the impedance using a tuner. The tuners should firstly be characterized at the 2nd
and 3rd
harmonic frequencies in order to make sure the correspondence of tuner positions, impedances
and S11-parameters in the Smith Chart are realized. As a consequence, the load impedances at 2nd
and
3rd
harmonics are controlled by the corresponding tuners’ positions. For specific tuners’ positions, the
efficiency is determined correspondingly, which means that an efficiency sweep is taken. After
sweeping the efficiency of well-distributed points (S11-parameters) which cover the whole Smith
Chart, the specific area in the Smith Chart with high efficiency performance is found, and then the
harmonic matching points (S11-parameters) with maximum efficiency are determined within this
specific area by further efficiency sweep. Thus, the harmonic matching impedances are determined
due to the strong relation of S11-parameter and load impedance.
The harmonic matching is the key part of this thesis project. Once the harmonic matching impedances
are determined, the matching network with maximum efficiency performance can be built accordingly.
1.1 Problem statement
Power amplifiers are used widely in communications. In order to minimize the operating cost and save
electric energy, high power efficiency of an amplifier is required [3]. To achieve high efficiency, the
amplifier is operated in a non-linear region [4]. As a consequence, harmonics appear and consume
some power causing a waste of energy. Thus, to enhance the amplifier efficiency, matching
impedances at harmonics should be determined to minimize the power delivered to the harmonics.
1.2 Background
In communication system, power amplifiers (PAs) play an important role and have large power
consumption. Thus, the improvement of power added efficiency (PAE) of an amplifier becomes more
and more important. With PAE increased, the battery life can be extended and the operating cost can
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
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be decreased [3]. High efficiency requires the amplifier to operate in large signal mode which pushes
the amplifier into compression region [4]. In compression region, amplifiers have non-linear behaviors
such as harmonics and intermodulation distortion (IMD). In this thesis project, the input signal
includes one single frequency, thus ideally there are no intermodulation products, and only the
harmonics should be the problem to be solved to enhance the efficiency. So the harmonic matching
impedances should be determined in order to decrease the influence of harmonics.
The most popular way to determine the matching impedance is the load pull technique which can
control the impedance using an automated tuner [1].
1.3 Goal
The goal for this thesis is to find the matching impedances of harmonics for optimum efficiency
performance of an amplifier.
1.4 Thesis outline
The structure of this thesis can be summarized as the Table 1.1 below.
Table 1.1. Thesis outline.
Section Contents
Introduction The background, aim as well as the major work of this thesis.
Theory Load-pull technique, tuner operation and characterization, amplifier behavior and so on.
Process and results Process of the measurement, analysis and comparison of the measured results.
Uncertainty analysis Measurement uncertainty determination and analysis.
Discussion The results, the chosen method, the strengths and weakness of the thesis as well as future work.
Conclusions The summary of the outcomes of this thesis and suggestion.
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2 Theory
2.1 Load pull technique
Load pull technique is a way to control the load impedance seen by the device under test (DUT) and to
measure the performance of a DUT in the mean time [5]. For the requirement of impedance control, an
automated tuner is a suitable choice for the load pull technique [6]. The automated tuner can control
the impedance with high accuracy and repeatability [7]. Moreover, automated tuners are easily
controlled by a PC (personal computer) through a tuner controller, which gives convenient data
acquisition. The idea of load pull technique with a tuner is to change the load impedance as desired.
For different tuner positions (positions of two stepper motors inside the tuner), the incident and
reflected wave are different which lead to different S-parameters. Since the S11-parameter is strongly
related to load impedance, for one specific S11-parameter, there is unique impedance corresponding to
this S11-parameter [8]. Then through appropriate measurements, from the corresponding tuner
positions, desired impedances and S11-parameters can be realized. Thus, the load impedance can be
controlled by the corresponding tuner positions. Nowadays, the load pull technique becomes
particularly important to optimize the power amplifier efficiency [8].
In this thesis, the harmonic load pull which can control the load impedances at the harmonics is used.
Harmonic load pull can influence the power, PAE (power added efficiency), and gain of an amplifier
[9].
2.1.1 Harmonic impedance tuning
PAs (power amplifiers) operate at a fundamental frequency. However, the PAE of an amplifier can be
significantly influenced by the load impedances at harmonic frequencies [9]. HEPAs (high efficiency
power amplifiers) require harmonic matching according to the significant influence of harmonic
terminations [10]. For this requirement, harmonic impedance tuning is needed in order to find
harmonic matching impedances which can provide optimum efficiency performance of an amplifier at
fundamental frequency.
Typically the 2nd
and 3rd
harmonics are of great concern and should be tuned independently [11]. In
this thesis, the harmonic tuning is made at 2nd
and 3rd
harmonic frequencies respectively. The goal for
harmonic impedance tuning is to determine the matching impedances at the harmonics to optimize the
amplifier efficiency. Once the matching impedances are determined, the matching network can be
designed for the maximum efficiency performance accordingly.
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2.2 Tuner Operation
Nowadays, automated tuners are often applied in load pull systems to achieve accurate, fast and
repeatable measurements [7]. The function of a tuner is to control and change the impedance.
Generally, the tuner impedance is a complex number, and it can be controlled through the controlling
of phase and magnitude of the impedance.
In order to control the phase and magnitude of the tuner impedance, the internal slug of a tuner should
be controlled appropriately. There are two precision stepper motors inside a tuner to drive the internal
slug along a straight section of a waveguide horizontally and vertically. As shown in Fig. 2.1, one of
the stepper motors controls the horizontal position of the slug which is the distance from the slug to
the load. In this way, the phase of the impedance is mainly controlled and determined. As shown in
Fig. 2.2, the other stepper motor controls the vertical position of the slug which is the distance from
the slug to the center of waveguide. In this way, the magnitude of the impedance is mainly controlled
[7, 9, 12].
Fig. 2.1. Phase control of tuner impedance.
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Fig. 2.2. Magnitude control of tuner impedance.
The advantage of automated tuners is that the tuner impedance can be controlled and determined with
high accuracy and repeatability [7, 13].
2.3 Device characterization
The harmonic load pull technique is important for optimizing efficiency performance of an amplifier
[1, 2, 9]. The key device for the harmonic load pull measurement system in this thesis is the automated
tuners. Precise tuner characterization is of great importance for making accurate and repeatable load
pull measurements, it is because even small inaccuracy in S11-parameters of the tuner can lead to
large errors for the measurements [7, 14].
The goal of tuner characterization is to make accurate correspondence of tuner positions, impedances
and S11-parameters in the Smith Chart in order to make sure the measurement can be highly
repeatable. That is to say, after tuner characterization, for a given tuner position, the corresponding
impedance is known as well as the relevant S11-parameter in Smith Chart. The basic idea of tuner
characterization is shown in Fig. 2.3 below.
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Impedances
S11-parameters in
Smith Chart
Tuner positions
(m1,m2)
corresponding to
corresp
ondin
g to
corr
espondin
g to
Fig. 2.3. Basic idea of tuner characterization.
It should be noticed that before tuner characterization, the VNA (vector network analyzer) should be
well calibrated. Because well calibrated VNA is of great concern to make sure the reliability of the
data provided by the load pull measurement [15, 16].
The procedure of tuner characterization is to use a VNA (vector network analyzer) to measure the
S11-parameter for each chosen tuner position. In the mean time, plot the S11-parameters at 2nd
and 3rd
harmonic frequencies in Smith Chart. This procedure is repeated for thousands of random tuner
positions in order to make the correspondence of tuner positions, impedances and S11-parameters in
Smith Chart. Then measured S11-parameters and the corresponding tuner positions are stored in arrays
for use during the following measurement. As a consequence, the load impedances at harmonics can
be varied by changing the corresponding tuner positions. Once the tuner positions are set according to
the results of tuner characterization, the corresponding impedances and S11-parameters in Smith Chart
are known.
Typically the 2nd
and 3rd
harmonics are crucial for the amplifier efficiency [11]. Consequently, in order
to control and determine the matching impedances of harmonics for providing maximum efficiency
performance of an amplifier, the tuners are characterized at the 2nd
and 3rd
harmonic frequencies.
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2.4 The amplifier behavior
2.4.1 Linear region and non-linear region
P
Burn out
(dBm)
P (dBm)out
Linea
r re
gion
Noise floor 1 dB compression point
Non-linear region
1 dB
Ideal amplifier
in
Real amplifier
Fig. 2.4. Linear region and non-linear region of an amplifier[17].
When the input power level of an amplifier is under a certain range, the output of the amplifier will be
dominated by the noise as shown in Fig. 2.4. In this case, the amplifier output power level is called
noise floor [17]. Along with the increment of input power level of the amplifier, the output is not noise
anymore. Under such condition, the amplifier starts to work in the linear region. In the linear region,
the output power is proportional to the input power and the proportion is the gain of the amplifier [17].
With the increase of the input power at the upper boundary of the linear region, the output starts to
saturate. Then the relation of the output and input power of an amplifier is no longer linear. The onset
of the non-linear region is often determined by the 1 dB compression point which means the output
power is 1 dB lower than the ideal output power given by the linear region relationship. When the
input power is too high above the 1 dB compression point, the amplifier might burn and be destroyed
[17]. In this thesis, for the requirements of both high efficiency performance and amplifier protection,
the amplifier should operate around the 3 dB compression point.
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2.4.2 Non-linear behavior
In non-linear region, the non-linear behaviors such as the harmonics and intermodulation distortion
exist.
Due to the nonlinearity of an amplifier, signals at integer multiples of the input frequency are
generated, these signals are the harmonics [18]. Assume the fundamental frequency is f, then the
signal at frequency 2f which caused by the nonlinearity is the 2nd
harmonic, similarly, the generated
signal at frequency 3f is the 3rd
harmonic. Typically 2nd
and 3rd
harmonics are crucial for amplifier
efficiency [11].
Power
f 2f 3f 4f 5f Frequency
Fig. 2.5. Fundamental signal and the harmonics [18].
In Fig. 2.5, the signal at fundamental frequency and four harmonics are shown. The power levels of
the harmonics are dependent of the fundamental signal power level [18]. With the increment of
fundamental signal power, the power levels of harmonics will also increase. For high efficiency
requirement, the fundamental signal power should be high enough to drive the amplifier into non-
linear region, but not burn the amplifier, thus the amplifier should operate around the 3 dB
compression point in order to fulfill the high efficiency requirement as well as the amplifier protection.
Notice that the higher the order of the harmonics, the lower the power level will be. Compare to the
fundamental power level, the 4th and 5
th harmonics typically can be ignored.
Besides the harmonics, the intermodulation distortion which also caused by the nonlinearity is
important as well [18]. When the input signal includes more than one frequency, mixing products are
created, thus intermodulation distortion (IMD) is generated [18]. The IMD will cause the interference
in adjacent channels of the system and influence the whole system. Take the input signal that
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composed of two frequencies for example, the IMD products will not only at the harmonic frequencies
but also at the combined frequencies of the two input frequencies and harmonic frequencies [19]. As
shown in Fig. 2.6, the 3rd
order of the two-tone intermodulation products will be near the original input
signals and influence the signals [19]. This effect can be called as 3rd
order intermodulation distortion.
Power
3*f1-2*f2 2*f1-f2 f1 f2 2*f2-f1 Frequency3*f2-2*f1
IM5
IM3
IM3
IM5
Fig. 2.6. Typical output spectrum of the 3rd
and 5th
order of two-tone intermodulation products [18].
The relationship of the frequencies of the intermodulation products and the original input signal
frequencies ( and ) can be determined as follows [18].
(2.1)
where = intermodulation product’s frequency
m, n = positive integers
m + n = the order of the intermodulation products
But for this thesis project, the input signal only includes a single frequency, thus ideally there is no
two-tone intermodulation products, only the harmonics should be considered in this thesis.
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P (dBm)
P (dBm)out
in
Lin
ear re
spon
se (sl
ope=
1)C
ubic
res
ponse
(sl
ope=
3)
Compression
Intercept point
Fig. 2.7. 3-order intercept point (IP3) [17].
Fig. 2.7 shows the ideal output power level versus the input power level for both the 1-order product
and the 3-order product. In this thesis, the input signal only includes one frequency, thus the 1-order
product and the 3-order product represent the fundamental signal and 3rd
harmonic separately. The
output power of the fundamental signal is proportional to the input power, so the line with a slope of 1
represents the response of the fundamental signal. However, the output power of the 3rd
harmonic
increases with a rate of cubic times of the input power, so the line with a slope of 3 represents the
response of the 3rd
harmonic. With high input power, the output power of both fundamental signal and
3rd
harmonic will be compressed. And the dotted lines describe the ideal responses for the fundamental
signal and 3rd
harmonic, with the increase of the input power, the output power of fundamental signal
will equal to that of the 3rd
harmonic, this intercept point is called as the 3-order intercept point (IP3)
[17]. Typically, the IP3 is above the onset of compression as shown in Fig. 2.7 [17].
2.4.3 Power added efficiency (PAE)
The PA (power amplifier) is a major consumer in communications. With high efficiency of an
amplifier, the overall cost of a communication system can be reduced [19].
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PAE (power added efficiency) represents the ratio of the RF output power minus RF input power
versus the total required DC power [19]. The power added efficiency of an amplifier can be defined by
equation 2.2 [20].
(2.2)
where power added efficiency
G = power gain of an amplifier
Pin = RF input power of an amplifier
Pout = RF output power of an amplifier
PDC = DC power of an amplifier
coupler
Power meter 1
AMP
Power supply
PC
Pin,measure
Pin
sig
nal
genera
tor
1 triplexer
2
3
4
30dB attenuator
Tuner 1
Tuner 2
Pout,measurePower meter 2
Tuner controller
f 0
3f 0
2f 0
Pout
PD
C
Fig. 2.8. Efficiency measurement setup.
In this thesis, the efficiency will be measured by the setup shown in Fig. 2.8 above. This setup can be
used to measure the amplifier efficiency both without harmonic tuning and with harmonic tuning.
Notice that when measuring the amplifier efficiency without tuning, both of the two tuners should be
set to the positions at which the corresponding load impedances at 2nd
and 3rd
harmonics are 50 ohms.
That is because the 50 ohms load impedances at harmonics can be seen as no tuning. And under this
condition, the determined efficiency is the amplifier efficiency without any enhancement. With this
certain setup in Fig. 2.8, PAE (power added efficiency) of the amplifier be computed using formula
2.2 together with equations 2.3 to 2.5.
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(2.3)
(2.4)
, (2.5)
where Pin, measure = measured input power of the amplifier
Pout, measure = measured output power of the amplifier at fundamental frequency
C1 = the coupler factor
B1 = the input cable loss
L1 = the output cable loss + triplexer loss + attenuation
= losses of the path from Pout, measure to Pout
The amplifier actually operates at the fundamental frequency, and efficiency at fundamental frequency
is of great importance and interest, even during the harmonic tuning process. So the output power of
the amplifier is always measured at the fundamental frequency.
In this thesis, a class-A amplifier is chosen. Class-A amplifier is a kind of amplifiers that always turn
on during the whole cycle of the input RF waveform and can operate with high linearity [21].
Typically, among all the amplifier modes, class-A has the best linearity performance. However, the
power efficiency is very poor. Mathematically, the maximum theoretical efficiency of class-A
amplifier is 50% which can not be reached in practice [19].
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3 Process and results
Table 3.1. Devices used for the whole process.
Device Model Function
Signal generator Agilent E4432B Generate input signal for the amplifier.
VNA
(vector network
analyzer )
Agilent Technologies N5242A Measure S-parameters that correspond to specific
tuners’ positions.
Power supply Agilent 6673A Provide bias power to the amplifier and sense DC
power of the amplifier.
Tuner Maury Microwave MT982E Control load impedance.
Tuner controller ATS tuner controller Control motor positions of tuners.
Power meter Anritsu ML2438A Measure the input power.
Power meter hp E4418A Measure the output power.
Table 3.1 above describes the devices used in the experimental setup in Fig. 2.8. The experimental
process can be divided into three major parts which were i) tuner characterization, ii) amplifier
efficiency measurement, and iii) maximum efficiency search. In addition these three major parts, other
parts like triplexer parameters measurement and matching network manufacture were presented as
well.
3.1 Process and results of tuner characterization
The function of tuners used in this project was to control and change load impedances at 2nd
and 3rd
harmonics. For achieving appropriate controlling, tuner characterization should be made to build the
correspondence of tuner positions, impedances and S11-parameters in Smith Chart for both 2nd
and 3rd
harmonics. For the requirement of accurate and repeatable measurement, tuner characterization was
crucially important.
1 triplexer
2
3
4
f 0
3f 0
2f 0
Load
Tuner 1
Tuner 2
VNAS11(f ,2f ,3f )0 0 0
Fig. 3.1. Setup of tuner characterization.
The setup of tuner characterization was shown in Fig. 3.1. When doing tuner characterization, the
triplexer should be connected all the time. It was because the signal sent by the VNA (vector network
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
14
analyzer) included the products at the fundamental frequency and harmonic frequencies. Thus, the
triplexer should be used here to separate the signals at fundamental, 2nd
and 3rd
harmonic frequencies
to make sure load impedances at 2nd
and 3rd
harmonics can be tuned respectively. As shown in Fig. 3.1,
tuner 1 was used to control load impedance at 3rd
harmonic, and tuner 2 was to control load impedance
at 2nd
harmonic.
For the process of tuner characterization, S11-parameters of the signal were considered. That was
because the S11-parameters were related to the impedances uniquely and each point of the S11-
parameters in the Smith Chart was given for certain impedance at specific frequency. During the
procedure of tuner characterization, the S11-parameters were measured and recorded for thousands of
tuner positions for both tuners. After measuring S11-parameters for different tuners’ positions at the
input port of triplexer for whole frequency bandwidth, the S11-parameters at 2nd
and 3rd
harmonic
frequencies can be collected. As a consequence, the tuner positions and S11-parameters at specific
harmonic frequencies were corresponded with each other. This relationship was clear to see after
plotting the S11-parameters at 2nd
and 3rd
harmonics respectively. Once the correspondence of tuner
positions, impedances and S11-parameters in Smith Chart was built, the tuner characterization was
finished.
Generally, the idea of tuner characterization was to make the correspondence of tuner positions,
certain impedances and S11-parameters in the Smith Chart. Ideally, after tuner characterization, the
S11-parameters that corresponded to certain impedances and specific tuner positions would cover the
whole area of Smith Chart. However, in reality, the S11-parameters plotted in Smith Chart according
to tuner characterization result can not cover the whole area of the Smith Chart, although a major part
of Smith Chart. That was because the triplexer loss and cable loss along with the difference of tuner
operation frequency and harmonic frequencies in this project gave a limitation circle in Smith Chart.
The S11-paramters plotted according to tuner characterization result would be within this limitation
circle in Smith Chart.
After tuner characterization, the load impedance can be controlled by tuner positions (positions of two
stepper motors inside the tuner). The phase and magnitude plot of S11-parameters with tuner positions,
and also S11-parameters along with limitation circle in the Smith Chart are presented in following. In
Fig. 3.2 to Fig. 3.5, M1 and M2 represent the positions of stepper motor one and stepper motor two,
respectively. And stepper motor one was used to drive the slug inside a tuner horizontally, stepper
motor two was used to drive the slug inside a tuner vertically.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
15
Fig. 3.2. Phase plot of S11with tuner positions for 2nd
harmonic (4.28 GHz).
Fig. 3.3. Phase plot of S11with tuner positions for 3rd
harmonic (6.42 GHz).
Fig. 3.2 and Fig. 3.3 above show the phase plot of S11-parameters with tuner positions for both the 2nd
and 3rd
harmonics. The whole phase range can cover from -200 degrees to +180 degrees. This
indicates that a careful selection of the tuner positions can reach any point (S11-parameter) in a
VSWR (voltage standing wave ratio) circle in the Smith Chart.
00.5
11.5
22.5x 10
4 0
1000
2000
3000
4000
5000
-200
-100
0
100
200
M2
M1
an
g(S
11
) [d
eg
ree
]
0 0.5 1 1.5 2 2.5
x 104
0
5000
-200
-150
-100
-50
0
50
100
150
200
M2
M1
an
g(S
11
) [d
eg
ree
]
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
16
Fig. 3.4. Magnitude plot of S11with tuner positions for 2nd
harmonic (4.28 GHz).
Fig. 3.5. Magnitude plot of S11with tuner positions for 3rd
harmonic (6.42 GHz).
Fig. 3.4 and Fig. 3.5 above show the magnitude plot of S11-parameters with tuner positions for both
2nd
and 3rd
harmonics. The maximum magnitudes of the S11-parameters for the 2nd
harmonic and 3rd
harmonic were -7 dB and -5.2 dB respectively. This indicates that through a careful selection of the
tuner positions, the points (S11-parameters) of 2nd
and 3rd
harmonics can reach as far as -7 dB and -5.2
dB of a VSWR (voltage standing wave ratio) circle in the Smith Chart respectively.
0 0.5 1 1.5 2 2.5
x 104
02000
40006000
-60
-50
-40
-30
-20
-10
0
M2M1
|S1
1|
[dB
]
0 0.5 1 1.5 2 2.5
x 104
0
5000-45
-40
-35
-30
-25
-20
-15
-10
-5
0
M2M1
|S1
1|
[dB
]
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
17
Fig. 3.6. S11 and limitation circle in Smith Chart for 2nd
harmonic (4.28 GHz).
Fig. 3.7. S11 and limitation circle in Smith Chart for 3rd
harmonic (6.42 GHz).
After characterizing thousands of random tuner positions for both the tuners for 2nd
and 3rd
harmonics,
the correspondence of tuner positions, impedances at harmonics and S11-parameters in Smith Chart
was built. Fig. 3.6 and Fig. 3.7 show the S11-parameters in the Smith Chart according to the results of
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
5.0
10
20
30
40
50
0.1
0.1
0.2
0.2
0.2
0.2
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.6
0.6
0.6
0.6
0.7
0.7
0.8
0.8
0.8
0.8
0.9
0.9
1.0
1.0
1.0
1.0
1.2
1.2
1.4
1.4
1.6
1.6
1.8
1.8
2.0
2.0
3.0
3.0
4.0
4.0
5.0
5.0
10
10
20
20
30
30
40
40
50
50
0.0
00.0
10.0
20.0
30.0
4
0.05
0.06
0.07
0.080.09
0.100.11 0.12 0.13 0.14
0.150.16
0.17
0.18
0.19
0.20
0.2
10.2
20.2
30.2
40
.25
0.2
60.2
70.2
80.2
9
0.30
0.31
0.32
0.330.34
0.350.360.370.380.39
0.400.41
0.42
0.43
0.44
0.45
0.4
60.4
70.4
80.4
9
measured S11 at 2nd harmonic
frequency (green)
the limitation circle of -7dB (yellow)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
5.0
10
20
30
40
50
0.1
0.1
0.2
0.2
0.2
0.2
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.6
0.6
0.6
0.6
0.7
0.7
0.8
0.8
0.8
0.8
0.9
0.9
1.0
1.0
1.0
1.0
1.2
1.2
1.4
1.4
1.6
1.6
1.8
1.8
2.0
2.0
3.0
3.0
4.0
4.0
5.0
5.0
10
10
20
20
30
30
40
40
50
50
0.0
00.0
10.0
20.0
30.0
4
0.05
0.06
0.07
0.080.09
0.100.11 0.12 0.13 0.14
0.150.16
0.17
0.18
0.19
0.20
0.2
10.2
20.2
30.2
40
.25
0.2
60.2
70.2
80.2
9
0.30
0.31
0.32
0.330.34
0.350.360.370.380.39
0.400.41
0.42
0.43
0.44
0.45
0.4
60.4
70.4
80.4
9
measured S11 at 3rd harmonic
frequency (red)
the limitation circle of -5.2dB (yellow)
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
18
tuner characterization for both 2nd
and 3rd
harmonics. But unfortunately, the points (S11-parameters)
shown in Fig. 3.6 and Fig. 3.7 can not cover the entire Smith Chart, the limitation of coverage was -7
dB for the 2nd
harmonic and -5.2 dB for the 3rd
harmonic.
There were two reasons leading to this limitation. One reason was the tuner limitation itself. The
operation frequency of tuners in the lab was 1.8-2.8 GHz/4.9-6.0 GHz. However, the frequencies of
2nd
and 3rd
harmonics were 4.28 GHz and 6.42 GHz respectively which meant that the tuners did not
work in their specified operation frequency band for the entire process. The other reason was the
triplexer and cable losses. During the process of tuner characterization, the triplexer and cables were
connected all the time. Thus, except for the limitation caused by the tuners themselves, the triplexer
loss and cable loss also gave a limitation of the coverage in the Smith Chart.
As a consequence, no matter how to change the tuners’ positions, the corresponding S11-parameters at
2nd
or 3rd
harmonic frequencies can not reach the boundary of the Smith Chart.
From Fig. 3.6 and Fig. 3.7, it was clear to see the yellow circles in both of the two figures represented
the limitation caused by tuners themselves, triplexer loss as well as cable loss. The S11-parameters
plotted in the Smith Chart could not go beyond the limitation circle as shown in Fig. 3.6 and Fig. 3.7
above.
3.2 Triplexer parameters
1 triplexer
2
3
4
f 0
3f 0
2f 0
(f +2f +3f )0 0 0
Fig. 3.8. Triplexer.
The function of a triplexer used here was to separate the signals at fundamental frequency, 2nd
harmonic frequency and 3rd
harmonic frequency so that the impedances at 2nd
and 3rd
harmonics can be
tuned respectively.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
19
As shown in Fig. 3.8 above, signals at different frequencies would pass though different paths of the
triplexer. The paths for signal at fundamental, 2nd
harmonic and 3rd
harmonic frequencies were S21,
S41 and S31 respectively. Thus, the measured values of S21, S41 and S31 represented the path losses
for the corresponding paths.
Fig. 3.9. Triplexer parameters.
The measured results of the triplexer parameters are shown in Fig. 3.9 above. At the fundamental
frequency, S21 was -0.45 dB, S41 was -108 dB and S31 was -69 dB. Due to the high losses for paths
S41 and S31, actually the signal at fundamental frequency can only pass through path S21 but not path
S41 or path S31. Similarly, the signal at 2nd
harmonic can only pass through path S41. The signal at
the 3rd
harmonic can only pass through path S31. As a result, the signals at fundamental, 2nd
harmonic
and 3rd
harmonic frequencies can be separated from each other.
The reason for the triplexer to separate the signal paths according to frequencies was that the triplexer
had a low pass filter for fundamental frequency, a band pass filter for 2nd
harmonic frequency and a
high pass filter for 3rd
harmonic frequency [22].
2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7-120
-100
-80
-60
-40
-20
0
Frequency [GHz]
Pa
th lo
ss
[d
B]
S21(path loss for the signal at fundamental frequency)
S31(path loss for the signal at 3rd harmonic frequency)
S41(path loss for the signal at 2nd harmonic frequency)
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
20
Moreover, from the measured triplexer parameters shown in Fig. 3.9, the bandwidth for the
fundamental is 100 MHz. Similarly, the bandwidths for the 2nd
and 3rd
harmonics are 200 MHz and
300 MHz respectively. Thus, the bandwidth of the method investigated in this thesis is limited to 100
MHz.
3.3 Efficiency measurement
The goal of the measurements was to determine the ‘testing point’ around the 3 dB compression point
and the amplifier efficiency for different input power. The setup and process of the measurements are
presented in the following.
coupler
Power meter 1
AMP
Power supply
PC
Pin,measure
Pin
sig
nal
genera
tor
1 triplexer
2
3
4
30dB attenuator
Tuner 1
Tuner 2
Pout,measurePower meter 2
Tuner controller
f 0
3f 0
2f 0
PoutP
DC
Fig. 3.10. Setup for measuring amplifier efficiency.
In order to make sure that the future comparison of amplifier efficiency and enhanced amplifier
efficiency are under the same condition and reduce the difference caused by different setups, the setup
for measuring the efficiency and enhanced efficiency of an amplifier should be the same as shown in
Fig. 3.10 above.
Notice that when using the setup in Fig. 3.10 to measure the amplifier efficiency, tuners should be set
to the positions which correspond to 50 ohms load impedance for both 2nd
and 3rd
harmonics. Then the
tuners can be seen as 50 ohms load which meant no tuning was made. Thus the measured efficiency
was the amplifier efficiency without enhancement.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
21
Before measuring the efficiency, the power meters were well calibrated, the tuners were initiated, and
the path losses were measured as well. Referring to Fig. 3.10, the idea of this setup was to measure the
input and output power as well as DC power of the amplifier at the same time with different
generating power of the signal generator in order to determine the amplifier efficiency for different
input RF power. Notice that the generated RF input power should be checked by the power meter all
the time in order to decrease the error caused by the signal generator itself. The functions of the
devices in Fig. 3.10 are described in Table 3.2 below.
Table 3.2. Functions of devices in Fig.3.10.
Device Function
Signal Generator Generate input signal for the amplifier.
Coupler Split the input signal and help the power meter to check input power.
Power Supply Supply biasing power to the amplifier and sense DC power of the amplifier.
Triplexer Separate the signals at fundamental, 2nd
and 3rd harmonic frequencies.
Attenuator Protect the power meter that used to measure output power.
Tuners
(used for the efficiency
measurement without tuning)
Used as 50 ohms loads.
Tuners
(used for the efficiency
measurement with tuning)
Used to change and control load impedances at harmonics in order to determine the
matching impedances at harmonics.
Tuner controller Control the motors’ positions inside the tuners in order to control the impedances the
tuners represent for.
Power meter 1 Measure a branch of input power of the amplifier in order to determine the total input
power.
Power meter 2 Measure the output power of the amplifier.
PC (personal computer) Control the devices used for the efficiency measurement and collect the measured data
in the mean time.
The measured cable loss, triplexer loss for fundamental signal path, coupler factor and attenuation in
the setup in Fig. 3.10 are shown in Table 3.3 below.
Table 3.3. Measured cable loss, triplexer loss, coupler factor and attenuation.
Section Measured value (dB)
Input cable loss -0.24
Output cable loss -1.4
Triplexer loss for fundamental signal path -0.45
Coupler factor -20.2
Attenuation -30.2
With the measured results and path losses shown in Table 3.3, the PAE (power added efficiency) of
the amplifier was determined by the equations 2.2 to 2.5 in theory part. And the measurement results
are as follows.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
22
Fig. 3.11. Comparison of ideal output power and measured output power of the amplifier vs. input power.
Referring to Fig. 3.11, the comparison of ideal output power and measured output power of the
amplifier is presented. With the increase of input power, the output power starts to saturate which
indicates that the amplifier was driven into the non-linear region. Moreover, when input power was 3.8
dBm, the measured output power was 3.3 dB lower than the ideal value, thus the amplifier operated
around 3 dB compression point. Around the 3 dB compression point, the requirements for both high
harmonic power level and amplifier protection were fulfilled. Thus the amplifier efficiency
performance around this point is of great concern. The method implemented in this thesis (harmonic
matching) was expected to be more effective around this point in non-linear area.
In the following, the point with 3.8 dBm input power is called ‘testing point’. Measurements presented
in this thesis are always referring to this point.
-20 -15 -10 -5 0 510
15
20
25
30
35
40
Pin [dBm]
Po
ut
[dB
m]
measured output power
ideal output power
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
23
Fig. 3.12. Efficiency of the amplifier vs. input power.
As shown in Fig. 3.12, at the ‘testing point’, the amplifier efficiency was 24.94%. It was clear to see
the efficiency increased with the increase of input power and became stable in non-linear region.
3.4 Maximum efficiency search method
The aim of the measurement in this section was to see how the amplifier efficiency could be improved
with harmonic tuning and find the harmonic matching impedances with maximum efficiency
performance of the amplifier. The setup to measure and search the enhanced amplifier efficiency with
harmonic tuning was the same as the setup in Fig. 3.10.
During the process of searching maximum efficiency, the input power of the amplifier was always set
to 3.8 dBm which was the ‘testing point’. However, due to the influence of environment and devices
themselves, the input power had some variations during the measurement, thus the input power should
be also measured during the entire process.
In order to compute the amplifier efficiency and see how the efficiency changed with the tuner
positions, the input and output power along with DC power of the amplifier were measured with every
specific tuner positions. The harmonic matching impedances can be determined by searching the
points (S11-parameters) in Smith Chart with maximum efficiency. The steps of searching the points
-20 -15 -10 -5 0 50
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Pin [dBm]
Eff
icie
nc
y
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
24
(S11-parameters) in the Smith Chart with maximum efficiency can be divided into two parts which
were efficiency sweep for the whole Smith Chart and efficiency sweep for specific areas in Smith
Chart. Once the points (S11-parameters) in the Smith Chart with maximum efficiency were found, the
harmonic matching impedances with maximum efficiency can be determined according to the strong
relation of S11-parameter and impedance.
The efficiency sweep meant that for every chosen point (S11-parameter) in the Smith Chart, the
specific efficiency was determined correspondingly. The aim of the efficiency sweep for the whole
Smith Chart was to find the specific area in the Smith Chart with high efficiency performance. The
whole area here was not every single point (S11-parameter) in Smith Chart, but the well-distributed
points (S11-parameters) that can cover the maximum part of Smith Chart according to tuner
characterization results. As shown in Fig. 3.13 and Fig. 3.14, 72 well-distributed points (S11-
parameters) were chosen to cover the whole area of Smith Chart for both 2nd
harmonic and 3rd
harmonic, and the efficiency sweep was taken for these points. Then points (S11-parameters) with best
enhanced efficiency for the whole Smith Chart were found and the specific area with high efficiency
performance can be determined as well.
Fig. 3.13. Well-distributed S11 of whole Smith Chart (2nd
harmonic, 4.28 GHz, 72 points).
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
5.0
10
20
30
40
50
0.1
0.1
0.2
0.2
0.2
0.2
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.6
0.6
0.6
0.6
0.7
0.7
0.8
0.8
0.8
0.8
0.9
0.9
1.0
1.0
1.0
1.0
1.2
1.2
1.4
1.4
1.6
1.6
1.8
1.8
2.0
2.0
3.0
3.0
4.0
4.0
5.0
5.0
10
10
20
20
30
30
40
40
50
50
0.0
00.0
10.0
20.0
30.0
4
0.05
0.06
0.07
0.080.09
0.100.11 0.12 0.13 0.14
0.150.16
0.17
0.18
0.19
0.20
0.2
10.2
20.2
30.2
40.2
50.2
60.2
70.2
80.2
9
0.30
0.31
0.32
0.330.34
0.350.360.370.380.39
0.400.41
0.42
0.43
0.44
0.45
0.4
60.4
70.4
80.4
9
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
25
Fig. 3.14. Well-distributed S11 of whole Smith Chart (3rd
harmonic, 6.42 GHz, 72 points).
In Fig. 3.13 and Fig. 3.14 above, the well-distributed S11-parameters that can cover the whole Smith
Chart the tuner characterization results can achieve were plotted for both 2nd
and 3rd
harmonics. For
both tuner 1 for 3rd
harmonic and tuner 2 for 2nd
harmonic, 72 different tuner positions that correspond
to 72 specific impedances and 72 well-distributed S11-parameters were chosen to cover the whole
Smith Chart. There were 5184 combinations of the two tuners’ positions. For each combination, the
efficiency sweep was taken, the points (S11-parameters) with best enhanced efficiency were
determined as well.
Table 3.4. Points with best enhanced efficiency for whole Smith Chart efficiency sweep.
Point S11-parameter Phase (degree) Magnitude (dB) The corresponding
amplifier efficiency at
fundamental frequency
The point with best
enhanced efficiency
for 2nd harmonic
-0.0004 + 0.4339i 90.0 -7.2
26.53%
The point with best
enhanced efficiency
for 3rd harmonic
0.4206 + 0.2411i
29.8
-6.2
As shown in Table 3.4 above, the best enhanced efficiency for the whole Smith Chart efficiency sweep
was 26.53%. The improvement was 1.59% compared with the amplifier efficiency. The points (S11-
parameters) with this best enhanced efficiency were plotted in Fig. 3.15 below.
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
5.0
10
20
30
40
50
0.1
0.1
0.2
0.2
0.2
0.2
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.6
0.6
0.6
0.6
0.7
0.7
0.8
0.8
0.8
0.8
0.9
0.9
1.0
1.0
1.0
1.0
1.2
1.2
1.4
1.4
1.6
1.6
1.8
1.8
2.0
2.0
3.0
3.0
4.0
4.0
5.0
5.0
10
10
20
20
30
30
40
40
50
50
0.0
00.0
10.0
20.0
30.0
4
0.05
0.06
0.07
0.080.09
0.100.11 0.12 0.13 0.14
0.150.16
0.17
0.18
0.19
0.20
0.2
10.2
20.2
30.2
40.2
50.2
60.2
70.2
80.2
9
0.30
0.31
0.32
0.330.34
0.350.360.370.380.39
0.400.41
0.42
0.43
0.44
0.45
0.4
60.4
70.4
80.4
9
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
26
Fig. 3.15. Points (S11) with best enhanced efficiency in Smith Chart for whole Smith Chart efficiency sweep
(Green for 2nd
harmonic: 4.28GHz, red for 3rd
harmonic: 6.42 GHz).
According to the points (S11-parameters) with best enhanced efficiency for the whole Smith Chart
efficiency sweep for both 2nd
and 3rd
harmonics shown in Fig. 3.15, the specific area with high
efficiency can be determined. This specific area with high efficiency was determined as the region
covering the entire blind area (the missing points in Fig. 3.13 and Fig. 3.14) around the points shown
in Fig. 3.15. This specific area with high efficiency for 2nd
and 3rd
harmonics was shown in Fig. 3.16
below.
Fig. 3.16. Specific area with high efficiency in Smith Chart
(green for 2nd
harmonic: 4.28 GHz, red for 3rd
harmonic: 6.42 GHz).
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
5.0
10
20
30
40
50
0.1
0.1
0.2
0.2
0.2
0.2
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.6
0.6
0.6
0.6
0.7
0.7
0.8
0.8
0.8
0.8
0.9
0.9
1.0
1.0
1.0
1.0
1.2
1.2
1.4
1.4
1.6
1.6
1.8
1.8
2.0
2.0
3.0
3.0
4.0
4.0
5.0
5.0
10
10
20
20
30
30
40
40
50
500.0
00.0
10.0
20.0
30.0
4
0.05
0.06
0.07
0.080.09
0.100.11 0.12 0.13 0.14
0.150.16
0.17
0.18
0.19
0.20
0.2
10.2
20.2
30.2
40.2
50.2
60.2
70.2
80.2
9
0.30
0.31
0.32
0.330.34
0.350.360.370.380.39
0.400.41
0.42
0.43
0.44
0.45
0.4
60.4
70.4
80.4
9
The point (S11) with best enhanced efficiency for
the whole Smith Chart efficiency sweep at 2nd
harmonic frequency
The point (S11) with best enhanced efficiency for
the whole Smith Chart efficiency sweep at 3rd
harmonic frequency
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
5.0
10
20
30
40
50
0.1
0.1
0.2
0.2
0.2
0.2
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.6
0.6
0.6
0.6
0.7
0.7
0.8
0.8
0.8
0.8
0.9
0.9
1.0
1.0
1.0
1.0
1.2
1.2
1.4
1.4
1.6
1.6
1.8
1.8
2.0
2.0
3.0
3.0
4.0
4.0
5.0
5.0
10
10
20
20
30
30
40
40
50
50
0.0
00.0
10.0
20.0
30.
04
0.05
0.06
0.07
0.080.09
0.100.11 0.12 0.13 0.14
0.150.16
0.17
0.18
0.19
0.20
0.2
10.2
20.2
30.2
40
.25
0.2
60.2
70.2
80.29
0.30
0.31
0.32
0.330.34
0.350.360.370.380.39
0.400.41
0.42
0.43
0.44
0.45
0.4
60.4
70.4
80.4
9
area with high efficiency
for 2nd harmonic (green)
area with high efficiency
for 3rd harmonic (red)
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
27
As shown in Fig. 3.16 above, the green part was the specific area for 2nd
harmonic and red part was for
3rd
harmonic. This specific area was determined based on the efficiency sweep for the whole Smith
Chart. The points (S11-parameters) shown in Fig. 3.16 were all around the points with best enhanced
efficiency for the whole Smith Chart efficiency sweep.
In order to find the matching points (S11-parameters) with maximum efficiency, the further efficiency
sweep for the specific area was taken. This further efficiency sweep meant that for every combination
of the points (S11-parameters) in this specific area for 2nd
and 3rd
harmonics, the efficiency was
determined accordingly. After taking the further efficiency sweep for the points in Fig. 3.16, the
harmonic matching points (S11-parameters) with maximum efficiency were found as shown in Table
3.5 and Fig. 3.17 below.
Table 3.5. Points with maximum efficiency for specific area efficiency sweep.
Point S11-parameter Phase (degree) Magnitude (dB) The corresponding
amplifier efficiency at
fundamental frequency
The point with
maximum efficiency
for 2nd harmonic
0.1088 + 0.4176i 75.4 -7.3
27.07%
The point with
maximum efficiency
for 3rd harmonic
0.3247 + 0.3703i 48.7
-6.2
Fig. 3.17. Matching Points (S11) with maximum efficiency in Smith Chart for specific area efficiency sweep
(Green for 2nd
harmonic:4.28 GHz, red for3rd
harmonic:6.42 GHz).
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
5.0
10
20
30
40
50
0.1
0.1
0.2
0.2
0.2
0.2
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.6
0.6
0.6
0.6
0.7
0.7
0.8
0.8
0.8
0.8
0.9
0.9
1.0
1.0
1.0
1.0
1.2
1.2
1.4
1.4
1.6
1.6
1.8
1.8
2.0
2.0
3.0
3.0
4.0
4.0
5.0
5.0
10
10
20
20
30
30
40
40
50
50
0.0
00.0
10.0
20.0
30.0
4
0.05
0.06
0.07
0.080.09
0.100.11 0.12 0.13 0.14
0.150.16
0.17
0.18
0.19
0.20
0.2
10.2
20.2
30.2
40.2
50.2
60.2
70.2
80.2
9
0.30
0.31
0.32
0.330.34
0.350.360.370.380.39
0.400.41
0.42
0.43
0.44
0.45
0.4
60.4
70.4
80.4
9
Matching point (S11) with maximum
efficiency for the 3rd harmonic.
Matching point (S11) with maximum
efficiency for the 2nd harmonic.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
28
The maximum efficiency for the specific area efficiency sweep was 27.07%. As shown in Table 3.5
and Fig. 3.17 above, at the two matching points (S11-parameters), the amplifier efficiency was
improved to 27.07%. The improvement was 2.13% compared with the amplifier efficiency 24.94%.
This efficiency enhancement proved the usefulness of method implemented in this thesis.
Of course, after finding the matching points (S11-parameters) in the specific area in Smith Chart, a
new specific area which was around the matching points shown in Fig. 3.17 can be determined, a new
efficiency sweep can be taken in order to find the matching points in new specific area with even
higher efficiency. However, after taking efficiency sweep for the new specific area, the maximum
efficiency was lower than 27.07%. Thus, the points shown in Fig. 3.17 were the matching points for
this whole thesis measurement. The corresponding impedances of these two points were the harmonic
matching impedances.
The comparison of amplifier efficiency and enhanced amplifier efficiency as well as the efficiency
improvement are discussed in the following.
Fig. 3.18. Comparison of efficiency and enhanced efficiency with harmonic matching impedances of the
amplifier vs. input power.
As shown in Fig. 3.18, the comparison of efficiency and enhanced efficiency with harmonic matching
impedances of the amplifier is presented. At the ‘testing point’, the amplifier efficiency was 24.94%,
-20 -15 -10 -5 0 50
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Pin [dBm]
Eff
icie
nc
y
amplifier efficiency
enhanced amplifier efficiency with harmonic matching impedances
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
29
and the enhanced efficiency was 27.07%. The efficiency was improved effectively with harmonic
matching impedances. In the non-linear region, enhanced efficiency around the ‘testing point’ was
around 27% and it was stable. However, in the linear region i.e. Pin 0 dBm, the efficiency was
almost not improved, because the harmonic power level in this region was too low and even lower
than the noise floor. Then the harmonic matching would almost not improve the efficiency in this
region. In the non-linear region, the matching impedances of harmonics can improve the efficiency
performance effectively because of high harmonic power level in this region.
Fig. 3.19. Efficiency enhancement of the amplifier with harmonic matching impedances vs. input power.
In Fig. 3.19, the efficiency enhancement of the amplifier with harmonic matching impedances is
presented. It was clear to see in the linear region of the amplifier i.e. Pin 0 dBm, the efficiency
enhancement was from -0.036% to 0.39%, this indicated that the efficiency was not improved
effectively in this region and even decreased at some points. However, around the ‘testing point’ in the
non-linear region, the efficiency enhancement was around 2% to 2.3%. The reason for the harmonic
matching impedances can only improve the amplifier efficiency in non-linear region effectively was
that the harmonic power level was high in non-linear region and too low to be ignored in linear region.
-20 -15 -10 -5 0 5-0.005
0
0.005
0.01
0.015
0.02
0.025
Pin [dBm]
Eff
icie
nc
y e
nh
an
ce
me
nt
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
30
3.5 Matching network manufacture
After finding the matching impedances of 2nd
and 3rd
harmonics, the matching network can be built
and simulated through ADS (Advanced Design Software) according to the S11-parameters of
matching impedances shown in Table 3.5. The matching network is manufactured in microstrip
technology. The simulated circuits and the simulated results are presented in the following.
Fig. 3.20. Simulated circuit for 2nd
harmonic matching network (left) and simulated result of S11 at 2nd
harmonic
frequency: 4.28 GHz (right)
In Fig. 3.20, the simulated circuit for the 2nd
harmonic matching network and the simulated results are
shown. L2nd and d2nd above represent the open-circuit stub length and distance from the load to the
stub respectively, and W is the width of the microtrip line. Note that the simulated S11-parameter
equals to the value of S11-parameter in Table 3.5. Thus, the 2nd
harmonic matching network can be
manufactured accordingly.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
31
Fig. 3.21. Simulated circuit for 3rd
harmonic matching network (left) and simulated result of S11 at 3rd
harmonic
frequency: 6.42 GHz (right)
In Fig. 3.21, the simulated circuit for the 3rd
harmonic matching network and the simulated results are
shown. L3rd and d3rd above represent the open-circuit stub length and distance from the load to the
stub respectively. W is the width of the microtrip line. The simulated S11-parameter in Fig. 3.21
equals to the value of S11-parameter in Table 3.5. Thus, the 3rd
harmonic matching network can be
manufactured according to this circuit.
Fig. 3.22. Manufactured matching network for 2nd
harmonic: 4.28 GHz (left) and 3rd
harmonic: 6.42 GHz (right)
In Fig. 3.22, the manufactured harmonic matching networks are presented. The left one is the 2nd
harmonic matching network. The right one is the 3rd
harmonic matching network. Ideally, the S11-
parameters of manufactured matching network should be exactly the same as that of the matching
impedances. However, during the process of manufacture, the impedances of manufactured network
had some shift, the corresponding S11-paramters shifted as well. As a consequence, the efficiency
enhancement changed.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
32
Table 3.6. Parameters of manufactured matching network and matching impedances for harmonics.
Section
S11-parameter Phase of S11
(degree)
Magnitude of S11
(dB)
The corresponding
amplifier efficiency at
fundamental frequency
The matching impedance
for 2nd
harmonic
0.1088 + 0.4176i 75.4 -7.3
27.07%
The matching impedance
for 3rd harmonic
0.3247 + 0.3703i 48.7
-6.2
The manufactured
network for 2nd
harmonic
0.0877+0.4125i 78 -7.5
26.77%
The manufactured
network for 3rd
harmonic
0.2782+0.3561i 52 -6.9
Referring to Table 3.6 above, it was easy to see the S11-parameters of the manufactured matching
network were not exactly the same as that of the matching impedances. This S11-parameter shift
indicated the impedance shift during the manufacture. Due to the impedance shift between the
matching impedances and manufactured network, the efficiency with manufactured network was 0.3%
lower than the efficiency with matching impedances.
Table 3.7. S11-parameters shift between manufactured network and matching impedances for harmonics.
Section
The phase shift (degree) The magnitude shift (dB)
The S11 shift between the manufactured network and
the matching impedance for 2nd harmonic
2.6 -0.2
The S11 shift between the manufactured network and
the matching impedance for 3rd harmonic
3.3 -0.7
Table 3.7 showed the phase and magnitude shift of S11-parameters between manufactured network
and matching impedances. Since S11-parameters were strongly related to impedances, the shift of
S11-parameters would lead to the shift of impedances. Due to the impedance deviation, efficiency
with manufactured matching network was not as high as efficiency with matching impedances.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
33
coupler
Power meter 1
AMP
Power supply
PC
Pin,measure
Pin
sign
al
genera
tor
1 triplexer
2
3
4
30dB attenuator
matching network for 3rd harmonic
matching network for 2nd harmonic
Pout,measurePower meter 2
f 0
3f 0
2f 0
Pout
PD
C
Fig. 3.23. Setup for measuring the amplifier efficiency with matching network.
Referring to Fig. 3.23, the manufactured matching network of both 2nd
and 3rd
harmonics was
connected in order to achieve the optimum efficiency performance. The measured efficiency of the
amplifier with matching network and some comparisons are discussed below.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
34
Fig. 3.24. Amplifier efficiency with manufactured matching network vs. input power.
As shown in Fig. 3.24, after connecting the manufactured matching network, the efficiency was
enhanced to 26.77% at the ‘testing point’, and the enhancement was 1.83 %, not as much as the
enhancement with matching impedances. The reason for the lower efficiency enhancement was the
impedance shift during the process of manufacture.
-20 -15 -10 -5 0 50
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Pin [dBm]
Eff
icie
nc
y
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
35
Fig. 3.25. Comparison of amplifier efficiency and enhanced efficiency vs. input power.
Fig. 3.25 shows the comparison of amplifier efficiency and the enhanced efficiency with manufactured
matching network as well as with matching impedances. In the linear region, the amplifier efficiency
was almost not enhanced either with manufactured matching network or with matching impedances. In
the non-linear region, the efficiency started to be improved both with manufactured matching network
and matching impedances. That was because in the non-linear region, the harmonics were not covered
by the noise floor anymore and started to increase quickly. Then with high harmonic power level in
this region, the harmonic matching would enhance the efficiency effectively. At the ‘testing point’, the
amplifier efficiency was 24.94%, the enhanced efficiency was 26.77% with manufactured matching
network and it was 27.07% with matching impedances. The efficiency enhancement with
manufactured matching network was lower than that with matching impedances due to the impedance
shift during the manufacture process. The impedances of manufactured network were not exactly the
same as the matching impedances, as a consequence, the efficiency was not enhanced that much.
-20 -15 -10 -5 0 50
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Pin [dBm]
Eff
icie
nc
y
amplifier efficiency
enhanced amplifier efficiency with manufactured matching network
enhanced amplifier efficiency with harmonic matching impedances
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
36
Fig. 3.26. Comparison of efficiency enhancement with matching impedances and with manufactured matching
network vs. input power.
Fig. 3.26 shows the efficiency enhancement with harmonic matching impedances and with
manufactured matching network. In the linear region, the efficiency was not improved effectively
either with matching impedances or with manufactured matching network. In the non-linear region,
the efficiency enhancement was higher than that in linear region and grew with the increase of the
input power. That was because with the increase of the input power, the harmonic power level would
increase as well, and then the harmonic matching would improve the efficiency more. However, the
efficiency enhancement can not increase without any limitation due to the limit of the input power for
not burning the amplifier and the limit of harmonics’ increments. At the ‘testing point’, the efficiency
enhancement was 2.13% with harmonic matching impedances and 1.83% with manufactured network.
The reason of the lower efficiency enhancement with manufactured network was the impedance shift
during the manufacture process.
The major factor of the impedance shift was the limitation of manufacturing accuracy. The
manufacturing accuracy of the dimension was not enough for the requirements in this thesis. As a
consequence, the manufactured matching network had some impedance shift and the efficiency
enhancement was not as high as possible.
-20 -15 -10 -5 0 5-0.005
0
0.005
0.01
0.015
0.02
0.025
Pin [dBm]
Eff
icie
nc
y e
nh
an
ce
me
nt
efficiency enhancement with harmonic matching impedances
efficiency enhancement with manufactured matching network
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
37
The comparison of harmonic power level with and without harmonic matching as well as the
comparison of IP3 (3rd
-order intercept point) with and without harmonic matching are presented
below.
Table 3.8. Comparison of output power level with and without harmonic matching.
Frequency Output power level (dBm) Output power level (mW)
Without matching With matching Without matching With matching
Fundamental (2.14 GHZ) 33.276 33.5753 2126 2277
2nd harmonic (4.28 GHz) 10.5 6.1 11.22 4.07
3rd harmonic (6.42 GHz) 0.16 -5.29 1.04 0.296
Table 3.8 shows the comparison of output power level with and without harmonic matching at
fundamental frequency, 2nd
harmonic frequency and 3rd
harmonic frequency. This measurement was
made at the ‘testing’ point and the output power is presented both in dBm and in mW. Note that with
harmonic matching, the fundamental output power level increased, the 2nd
and 3rd
harmonic output
power level decreased compared with the value without matching. This indicates that the harmonic
matching network reduces the power that delivered to the harmonics and also helps to increase the
power delivered to the fundamental signal in the mean time. Moreover, it was clear to see that in linear
number (mW), regardless if with or without harmonic matching, the fundamental output power level
was hundreds times of the 2nd
harmonic power level and thousands times of the 3rd
harmonic power
level. This indicates that compared to the fundamental power, the harmonics’ power levels of this
class-A amplifier are small.
Fig. 3.27. Comparison of output power level with and without harmonic matching vs. specific frequency.
2.14 2.14 2.14 2.1432.8
33
33.2
33.4
33.6
Fundamental Frequency [GHz]
without matching
with matching
4.28 4.28 4.28 4.280
5
10
15
2nd Harmonic Frequency [GHz]
without matching
with matching
6.42 6.42 6.42 6.42-10
-5
0
5
3rd Harmonic Frequency [GHz]
Ou
tpu
t P
ow
er
Level [d
Bm
]
without matching
with matching
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
38
Fig. 3.27 shows the output power level comparison with and without harmonic matching at the
fundamental frequency, 2nd
harmonic frequency and 3rd
harmonic frequency separately. This
comparison was made at the ‘testing’ point. With harmonic matching, the fundamental output power
increased, the 2nd
and 3rd
harmonic power levels decreased. This means the harmonic matching
network decreases the output power at the harmonics and helps to increase the fundamental output
power.
Fig. 3.28. IP3 comparison with and without harmonic matching.
Fig. 3.28 shows the comparison of IP3 with and without harmonic matching. The blue line describes
the ideal response of the fundamental signal, and the red line and green line describe the ideal
responses of the 3rd
harmonic without and with matching respectively. Thus, the crossing point of the
blue line and red line is the IP3 without matching. The crossing point of the blue line and green line is
the IP3 with matching. Note that, the green line was lower than the red line, which indicates that with
matching, the harmonic output power level deceases. Hence, the input power of IP3 with matching
was higher than that of IP3 without matching.
3.6 Efficiency enhancement comparison of different techniques
Besides the method investigated in this thesis, there are also some other efficiency enhancement
techniques such as DPD (Digital Predistortion), Doherty, DLA (Dynamic Load Adaptation), ET
(Envelope Tracking), EER (Envelope Elimination and Restoration), LINC (Linear Amplification using
-10 -5 0 5 10 15 20 25 30 35-60
-40
-20
0
20
40
60
80
100
Pin [dBm]
Po
ut
[dB
m]
ideal fundamental response
ideal 3rd harmonic response without matching
ideal 3rd harmonic response with matching
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
39
Nonlinear Components) and so on. And with different techniques that implemented in different types
of amplifiers, the efficiency enhancements are various.
Table 3.9. Comparison of different efficiency enhancement techniques.
Efficiency enhancement
techniques
Amplifier type Efficiency
enhancement (%)
Reference
Harmonic matching
(this thesis project)
class-A 2.13 -
Harmonic matching Inverse class-F 5 [23]
DPD - 10-20 [24], [25]
Doherty class-AB and class-C 6.8 [26]
Doherty GaN 10 [27]
Doherty class-E 17 [28]
DLA class-AB 5.1 [29]
ET class-E 4-5 [30]
EER class-F 4 [31]
LINC class-E 33 [32]
Table 3.9 shows the comparison of different efficiency enhancement techniques. It was clear to see in
this thesis project, the efficiency was enhanced by 2.13% with harmonic matching for a class-A
amplifier. Compared with the efficiency enhancements with other techniques that implemented in
different kinds of amplifiers, the efficiency enhancement of this thesis is lower. That is because the
efficiency enhancement mainly depends on the implemented technique as well as the amplifier type.
In this thesis project, a class-A amplifier was used, and due to its low harmonic power level as shown
in Table 3.8 as well as the limitation of the tuner characterization discussed in section 3.1, the
efficiency was lower compared with other techniques and other amplifiers. For example, in the
literature, the efficiency enhancement of an inverse class-F amplifier with harmonic matching was 5%
[23].
In addition, the techniques shown in Table 3.9 work on different levels. The DPD works on the
software and the main idea is to modify the input signal. Except for DPD, other techniques shown in
Table 3.9 work on the hardware, for example, the Doherty and LINC require redesigning the amplifier,
ET and EER require modifying the bias circuit of the transistor. Further, it is expected that the
combination of the harmonic matching and DPD might improve the efficiency.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
40
4 Uncertainty analysis
The measurement uncertainty can be defined as the difference of measured value of the parameter and
the true value it should be [33].
The uncertainties in measured variables will influence the uncertainty of whole measurement result.
The uncertainty can be determined by the Taylor’s Series uncertainty propagation [33].
Assume R=f (X, Y, Z…), where X, Y, Z…are independent measured variables, R are all the
measurement results which needed to be determined by the measured variables X, Y, Z and so on. In
this thesis, R is the measured efficiency, and X, Y, Z are corresponding to the DC power, input and
output power which determine the measured efficiency. Then the uncertainty of the measured results
can be computed by equation 4.1 [33].
(4.1)
where uncertainty of measurement result
uncertainty of measured parameter X
uncertainty of measured parameter Y
uncertainty of measured parameter Z
influence of the uncertainty of X on the whole measurement uncertainty
influence of the uncertainty of Y on the whole measurement uncertainty
influence of the uncertainty of Z on the whole measurement uncertainty
The uncertainty above is the standard uncertainty. The uncertainty discussed in the following is on
the assumption that the environment and the temperature are always the same. It is also assumed that
the different variables are independent.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
41
4.1 Efficiency uncertainty
The efficiency uncertainty can be determined as follows.
(4.2)
(4.3)
where eff = PAE (power added efficiency) of an amplifier
uncertainty of amplifier efficiency
uncertainty of power gain
uncertainty of output power
uncertainty of DC power
power gain of an amplifier
output power of an amplifier
DC power of an amplifier
The uncertainty sections of formula 4.3 above are related to the devices for the whole measurement,
the correspondence of these uncertainty sections and related devices is in Table 4.1 below.
Table 4.1. Correspondence of the uncertainty sections and the devices used in Fig.3.10.
Uncertainty section The related devices for the measurement
Power meter for the input, power meter for the output, input cable, output cable, triplexer,
attenuator, and coupler.
Power meter for the output, output cable, triplexer, attenuator.
DC power supply.
The variances of uncertainty sections in Table 4.1 can be determined as following.
(4.4)
(4.5)
(4.6)
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
42
where variance of power gain
variance of output power
variance of measured DC power
variance of power meter for the input
variance of power meter for the output
variance of input cable loss
variance of the output cable loss
variance of the triplexer loss
variance of the measured coupler factor
variance of the measured attenuation
The different parts in equations 4.4 to 4.6 were determined from the variance of different
measurements taken on different days. The measured results and the calculated variances are shown in
Table 4.2 below. The variances in Table 4.2 were all determined in linear number.
Table 4.2. Measured results of the devices and the computed variances.
Section
First day
5 days later
20 days later
Variance
(in linear number)
Input cable loss -0.23 (dB) -0.24 (dB) -0.22 (dB) 4.7691*10^(-6)
Output cable loss -1.38 (dB) -1.4 (dB) -1.43 (dB) 1.7576*10^(-5)
Triplexer loss -0.49 (dB) -0.46 (dB) -0.45 (dB) 1.8494*10^(-5)
Coupler factor -20.17 (dB) -20.16 (dB) -20.2 (dB) 2.1136*10^(-9)
Attenuation -30.12 (dB) -30.18 (dB) -30.16 (dB) 4.6213*10^(-11)
DC power 8.5155 (V) 8.3796 (V) 8.5087 (V) 0.0059
The uncertainty of the power meter can be found in the data sheet. The power meters used for this
project and their uncertainties are shown in Table 4.3 below.
Table 4.3. Uncertainty of the power meter.
Section Model number Standard Uncertainty
Power meter for the input Anritsu ML2438A 0.012
Power meter for the output hp E4418A 0.024
From Table 4.3 above, the uncertainty of power meter for the input is 0.012, which means is
equal to 0.012. The uncertainty of power meter for the output is 0.024, thus is 0.024.
Thus, with the measured results discussed above and the equations 4.3 to 4.6, the efficiency
uncertainty is determined as follows.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
43
Thus, the standard uncertainty ( ) of the efficiency is determined as below.
From the results above, when determining the efficiency, the standard uncertainty is 0.0039. It means
that the measured amplifier efficiency is actually 0.2494 0.0039, and the efficiency with harmonic
matching impedance is 0.2707 0.0039. Similarly, the measured efficiency with manufactured
matching is actually 0.2677 0.0039. This standard uncertainty always gives 0.0039 deviation on
the efficiency determination.
4.2 Tuner characterization uncertainty
Precise tuner characterization is extremely important for making accurate and repeatable load pull
measurements, thus the uncertainty of tuner characterization should be taken serious consideration.
It should be noticed that the measurements contain two types of errors: systematic and random errors.
The systematic error gives a constant bias of the measured S-parameter and can be compensated with a
well calibrated VNA. The random error can not be compensated, and it is mainly caused by the noise
in the instruments.
Tuner characterization uncertainty can be expressed as an uncertainty circle which is determined by
measuring the S11-parameter that corresponds to the same tuner positions several times on different
days. From the repeated measurements, the differences of the measured S11-parameters can be
computed and the maximum magnitude value of the difference is the diameter of the uncertainty
region. From the measured result and computation, in Smith Chart, the radius of the uncertainty region
for 2nd
harmonic is 0.0098 and 0.0179 for 3rd
harmonic. The uncertainty regions of tuner
characterization are shown in Fig. 4.1 for both 2nd
and 3rd
harmonics as follows.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
44
Fig. 4.1. Uncertainty region of the tuner characterization for 2nd
harmonic: 4.28 GHz (blue circle) and 3
rd
harmonic: 6.42 GHz (green circle).
In Fig. 4.1 above, the purple point is the matching point (S11-parameter) for 2nd
harmonic, the red one
is the matching point (S11-parameter) for 3rd
harmonic, the blue circle and green circle represent for
the uncertainty region for 2nd
and 3rd
harmonics respectively. It is easy to see that the uncertainty
region for 2nd
harmonic concentrates to almost one point, thus the impedance for 2nd
harmonic can be
controlled with high repeatability. However, for 3rd
harmonic, the uncertainty region it is not that
concentrated. As a consequence, the repeatability of impedance control for 3rd
harmonic is not as high
as 2nd
harmonic.
One reason of the low repeatability of 3rd
harmonic impedance control is that the tuner is more
sensitive at high frequency. The higher the frequency is, the faster the phase and amplitude will
change, the harder the accurate impedance control will be. Then the uncertainty region of 3rd
harmonic
is bigger than that of 2nd
harmonic. The other reason is that the power level of 3rd
harmonic is lower
compared to the fundamental and 2nd
harmonic power level, and it is near to the noise floor. Thus the
signal at 3rd
harmonic is influenced badly by the noise, and the repeatability of the 3rd
harmonic
impedance control is influenced as well.
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
5.0
10
20
30
40
50
0.1
0.1
0.2
0.2
0.2
0.2
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.6
0.6
0.6
0.6
0.7
0.7
0.8
0.8
0.8
0.8
0.9
0.9
1.0
1.0
1.0
1.0
1.2
1.2
1.4
1.4
1.6
1.6
1.8
1.8
2.0
2.0
3.0
3.0
4.0
4.0
5.0
5.0
10
10
20
20
30
30
40
40
50
50
0.0
00.0
10.0
20.0
30.0
4
0.05
0.06
0.07
0.080.09
0.100.11 0.12 0.13 0.14
0.150.16
0.17
0.18
0.190.20
0.2
10.2
20.2
30.2
40
.25
0.2
60.2
70.2
80.2
9
0.30
0.31
0.32
0.330.34
0.350.360.370.380.39
0.400.41
0.42
0.43
0.44
0.45
0.4
60.4
70.4
80.4
9
Matching point (red) and uncertainty
region (green) for 3rd harmonic
Matching point (purple) and uncertainty
region (blue) for 2nd harmonic
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
5.0
10
20
30
40
50
0.1
0.10.2
0.2
0.2
0.2
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.6
0.6
0.6
0.6
0.7
0.7
0.8
0.8
0.8
0.8
0.9
0.9
1.0
1.0
1.0
1.0
1.2
1.2
1.4
1.4
1.6
1.6
1.8
1.8
2.0
2.0
3.0
3.0
4.0
4.0
5.0
5.0
10
10
20
20
30
30
40
40
50
50
0.0
00.0
1
0.0
2
0.0
3
0.0
4
0.0
5
0.06
0.07
0.08
0.09
0.10
0.11
0.12 0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
0
0.2
1
0.2
2
0.2
3
0.2
40
.25
0.2
6
0.2
7
0.2
8
0.2
9
0.3
0
0.31
0.32
0.33
0.34
0.35
0.36
0.370.38
0.39
0.40
0.41
0.42
0.43
0.44
0.4
5
0.4
6
0.4
7
0.4
8
0.4
9
Matching point (red) and uncertainty
region (green) for 3rd harmonic
Matching point (purple) and uncertainty
region (blue) for 2nd harmonic
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
45
5 Discussion
This thesis work implemented a method to improve amplifier efficiency. According to the purpose of
efficiency enhancement, the method of harmonic matching was chosen, the matching impedances of
the 2nd
and 3rd
harmonics were determined. Load pull measurement is a key part to realize the
impedance control. It should be noticed that precise tuner characterization is crucial for making
accurate and repeatable load pull measurements. In this thesis work, the load impedances at harmonics
can be controlled and determined precisely by automated tuners and tuner controller, the harmonic
matching impedances were determined with high accuracy.
The strengths of this thesis work can be discussed as follows. Firstly, referring to Fig. 3.18, the
enhanced efficiency is clear to see, this proves the availability of the implemented method. And the
goal of this thesis has been achieved according to the measured results shown in Fig.3.18 and Fig.3.19.
Secondly, with the setup shown in Fig. 3.10, it is easy to control the tuners and collect the measured
data by PC, which makes it simple and fast to take the efficiency sweep as well as to determine the
harmonic matching impedances. Thirdly, the matching network is manufactured in microstrip
technology, and it is easy to be applied into industry.
The weakness of this thesis can be discussed as follows. Firstly, referring to Fig. 3.6 and Fig. 3.7, for
both 2nd
and 3rd
harmonics, no matter how to change the tuners’ positions, the corresponded S11-
parameters can not reach the boundary of Smith Chart but limited in the center part of the Smith Chart
due to the tuner characterization limitation. Moreover, because of this limitation, the points (S11-
parameters) picked for the whole Smith Chart efficiency sweep can not actually cover the entire Smith
Chart as shown in Fig. 3.13 and Fig. 3.14. Then the load impedance control, efficiency enhancement
as well as the final matching network determination is limited. Because if the S11-parameters
according to tuner characterization results could cover the entire part of Smith Chart, there would be a
high chance that the amplifier efficiency can be improved even more. Secondly, as shown in Fig. 3.18,
the method chosen for this thesis basically can only improve the efficiency performance effectively in
non-liner region. That is because the method of this project is harmonic matching, which makes it
effective when harmonics appear. In linear region, harmonics are negligible and covered by the noise,
and in non-linear region, harmonics appear with high power level. Thirdly, the harmonic matching can
improve the amplifier efficiency but not as much as that compared with the inverse class-F amplifier
(Table 3.9). Because the amplifier chosen for this project is a class-A amplifier, and among all the
amplifier modes, class-A amplifier has high linearity but low harmonic power level (Table 3.8).
However, the method implemented in this thesis is harmonic matching which means the higher the
harmonic power level, the more effective the method will be, and the higher the efficiency
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
46
enhancement will be. Due to the low harmonic power level of class-A amplifier, the matching
impedances of harmonics can not improve the amplifier efficiency as much as that of inverse class-F
amplifier. Last but not least, as shown in Fig. 3.25 and Fig. 3.26, the efficiency enhancement with
manufactured matching network is lower than that with harmonic matching impedances due to the
impedance shift during manufacturing process. The major reason causing the impedance shift is the
limitation of manufacturing accuracy.
Besides the method investigated in this thesis, there are other techniques for improving amplifier
efficiency (Table 3.9). The results obtained by using these techniques are dependent on the amplifier
type and their principles of operation.
The stability in an amplifier depends on the impedance at the fundamental frequency [34]. However,
the working principle of harmonic tuning is to change only the harmonic impedances and not affecting
the fundamental. Thus, it is expected that the stability of an amplifier will not be compromised by
using this technique.
In the future, some related projects can also be performed. For example, in practice, the two-tone
intermodulation always exists. So instead of using an input signal at only one frequency, the signal
includes two frequencies can be applied. Then except for the harmonics, the two-tone intermodulation
should also be considered and solved. It is hard to separate the intermodulation products’ frequencies
from the fundamental frequency for now, so the requirement of impedance control is hard to meet for
the harmonics and intermodulation products at the same time. But with the progress of technology
development, this kind of problems might be solved in the future and the related project can be
performed.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
47
6 Conclusions
The harmonic matching was implemented as a method in this thesis work to enhance the amplifier
efficiency. According to the high efficiency requirement, the amplifier was operated in the non-linear
region, thus harmonics caused by the non-linearity were the major problem that influenced amplifier
efficiency performance. So the determination of harmonic matching impedances is the key part to
enhance amplifier efficiency. With load impedance control and efficiency sweep, the harmonic
matching impedances with maximum efficiency were determined and the matching network was
manufactured as well.
From the measurement results, the goal of this thesis has already been achieved. The efficiency was
enhanced around 2%, which can be considered low compared with recent studies [23]. The reasons for
this result are the limitation of tuner characterization joined with a low harmonic power level of the
amplifier (Table 3.8). According to the method chosen for this thesis, the higher the harmonic power
level, the higher the efficiency enhancement will be. Then with other amplifier modes which have
high harmonic power level, the efficiency enhancements are expected to be higher than the results
shown in this thesis.
For any measurement system, the accuracy is extremely important. And high accuracy is always
desired. However, no matter how high quality of the equipments and components, the measurement
uncertainty always exists. As analyzed in section 4.1, the uncertainties of components in the
measurement setup leaded to the uncertainty of efficiency determination. Moreover, it should be
noticed that precise tuner characterization is crucially important for the whole repeatable and accurate
measurement. From section 4.2, the accuracy of tuner characterization was high enough to make
repeatable measurement although the accuracy of 3rd
harmonic tuner characterization was lower than
that of 2nd
harmonic.
The manufacturing accuracy is still need to be improved. Due to the low accuracy of manufacturing,
the impedance shifted, which leaded to lower efficiency enhancement with manufactured network than
that with harmonic matching impedances.
To summarize, the method implemented in this thesis is simple and effective and easy to apply into
industry. Moreover, in the daily life, a huge amount of electrical power is consumed every day, it is
crucially important to save the energy, and the efficiency enhancement is an effective way to do that.
Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER
48
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