HARMONIC MATCHING NETWORK FOR AN...

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

Hongxu Zhu HARMONIC MATCHING NETWORK FOR AN AMPLIFIER

i

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.


ii


iii

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.


iv


v

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


vi

4 Uncertainty analysis ...................................................................................................................... 40

4.1 Efficiency uncertainty ............................................................................................................ 41

4.2 Tuner characterization uncertainty ......................................................................................... 43

5 Discussion ..................................................................................................................................... 45

6 Conclusions ................................................................................................................................... 47

References ............................................................................................................................................. 48


vii

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


viii

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


ix

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


x

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


1

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


2

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.


3

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.


4

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.


5

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.


6

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.


7

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.


8

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


9

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.


10

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].


11

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.


12

(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].


13

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


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.


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


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

]


16

Fig. 3.4. Magnitude plot of S11with tuner positions for 2nd


Fig. 3.5. Magnitude plot of S11with tuner positions for 3rd


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

]


17

Fig. 3.6. S11 and limitation circle in Smith Chart for 2nd


Fig. 3.7. S11 and limitation circle in Smith Chart for 3rd


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)


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.


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)


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


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.


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.


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


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


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


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


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)


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



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.


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


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


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.


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.


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



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.


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


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.


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


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


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


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. 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


38

Fig. 3.27 shows the output power level comparison with and without harmonic matching at the

fundamental frequency, 2nd


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


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.


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.


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)


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.


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.


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


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


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.


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.


48

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227.

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