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A Multi-Port Measurement System for Large-Signal Characterization of MicrowaveDevices

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UNIVERSITY OF CALGARY
A Multi-Port Measurement System for Large-Signal Characterization of Microwave
Devices
by
Walid Saber Abdel Aleam Ibrahim El-Deeb
A THESIS
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
CALGARY, ALBERTA
APRIL, 2011
© Walid Saber Abdel Aleam Ibrahim El-Deeb 2011
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Abstract
The accurate design of microwave and radio frequency (RF) systems has to
successfully pass a complex protocol of four main steps: characterization, modeling,
simulating and prototyping. The key consideration in successful RF design is the accurate
characterization of the RF and microwave components employed in the design. The
tremendous progress in wireless communication systems requires system components to
work in the nonlinear region, in order to achieve high performance. In order to build an
accurate nonlinear model that perfectly describes the behaviour of the RF component,
several kinds of measurements and instrumentations are required. Most of the existing
measurement systems were designed for a specific kind of measurement; and,
unfortunately, they are not able to extract all the parameters required to build an accurate
nonlinear model for the RF components.
This work presents a multi-port measurement system that incorporates the scope
and vector network analyzer capabilities for time-domain and frequency-domain
measurements, respectively. The system has also the capability to work with varying load
impedances for coaxial or on-waver terminals of the device under test (DUT). The
proposed calibration algorithms for on-wafer power de-embedding and waveform
measurements enhance the system capability for extracting the required figures of merit
to build an accurate nonlinear model for the DUT. The proposed power de-embedding
calibration algorithm enables the system to calculate the absolute power at the on-wafer
DUT terminals without the need for absolute power calibration. The waveform
calibration algorithm eliminates the need for a multi-harmonic generator and the golden
standard for accurate waveform measurements.
ii
The measurements provided in this thesis validate the robustness and accuracy of
the proposed system and calibration algorithms through a comparison with the
measurements obtained using commercial instruments for the same measurement
environments.
iii
Acknowledgements
All praise is due to ALLAH the Almighty and the Glorious for his guidance and support
through all my life.
I wish to express my deep thanks and gratitude to Prof. Fadhel M. Ghannouchi for
his valuable assistance, support and encouragement during the period of my study, which
made the completion of this work possible. I am grateful to Dr. Ghannouchi for giving
me the honorable opportunity to work under his wise supervision in the iRadio lab,
University of Calgary, Canada.
I would like to thank the Egyptian Government for funding and supporting this
work by honoring me a postgraduate scholarship.
My deep thanks to Dr. Souheil Bensmida and Dr. Noureddine Boulejfen for their
active support and guidance during this work.
I would like to pay my deep love, respect and appreciation to my dear parents,
brother, and sisters for their encouragement and prayers during my whole life.
I am deeply grateful to my dear wife Amira and beautiful daughters Sarah and
Salma for the great help, prayers and warm atmosphere they provide me during my life.
I would like to thank my colleagues and friends, especially Mohamed Boraey, for
their practical support, sincere advices and warm friendship.
At last I would like to pay my deep respect to all those who stood beside me and
gave me a hand, suggestion, or even a good wish to complete this work and make it see
the light.
iv
Dedication
To…...
My dear respected parents;
Precious wife, Amira;
Sweet daughters, Sarah and Salma;
Dear brother, Dr. Usama, and lovely sisters, Wesam and Amira.
v
Table of Contents
Abstract ............................................................................................................................... ii Acknowledgements ............................................................................................................ iv Dedication ............................................................................................................................v Table of Contents ............................................................................................................... vi List of Tables ..................................................................................................................... ix List of Figures and Illustrations ...........................................................................................x List of Symbols ................................................................................................................ xiv List of Abbreviations .........................................................................................................xv List of Publications that Have Resulted from the Research Project ................................ xvi CHAPTER ONE: INTRODUCTION ..................................................................................1 1.1 Motivation ..................................................................................................................1 1.2 Problem Definition ....................................................................................................2 1.3 Objective ....................................................................................................................4 1.4 Thesis Outline ............................................................................................................4 CHAPTER TWO: OVERVIEW OF MEASUREMENT SYSTEMS FOR THE
CHARACTERIZATION OF RF DEVICES ..............................................................7 2.1 Introduction ................................................................................................................7 2.2 S-Parameter Measurement Systems – Overview .......................................................8 2.2.1 Vector network analyzer..................................................................................10 2.2.2 S-parameter measurements for N-port devices ...............................................11 2.3 Power De-Embedding Techniques and Apparatus – Overview ..............................13 2.3.1 Power de-embedding measurement system using VNA .................................13 2.3.2 Power de-embedding measurement system using six-port reflectometer .......15 2.4 Waveform Measurement Systems – Overview .......................................................17 2.4.1 Waveform measurement systems using sampling oscilloscope ......................18 2.4.2 Waveform measurement systems using VNA .................................................21 2.4.3 Waveform measurement systems using microwave transition analyzer .........23 2.4.4 Waveform measurement systems using six-port reflectometer.......................26 2.5 Summary ..................................................................................................................27 CHAPTER THREE: THE PROPOSED MULTI-PORT MEASUREMENT SYSTEM ...28 3.1 Introduction ..............................................................................................................28 3.2 The Measurement System Architecture ...................................................................29 3.3 The Microwave Transition Analyzer .......................................................................34 3.3.1 The MTA data acquisition process ..................................................................35 3.3.2 The MTA sampling process ............................................................................36 3.4 System Calibration ...................................................................................................38 3.5 System Verification .................................................................................................46 3.5.1 Two-port measurement verifications ...............................................................46 3.5.2 Multi-port measurement verifications .............................................................48 3.6 Summary ..................................................................................................................53 vi
CHAPTER FOUR: COMPLEX DISTORTION MEASUREMENTS OF THE
NONLINEAR MICROWAVE SYSTEMS ..............................................................54 4.1 Introduction ..............................................................................................................54 4.2 Two-Port Measurements ..........................................................................................55 4.2.1 Characterization of a single-input single-output (SISO) PA without
crosstalk ...........................................................................................................56 4.2.2 Characterization of a dual branch PA with crosstalk ......................................59 4.3 Multi-Port Measurements ........................................................................................62 4.3.1 Characterization of a single-input dual-output (SIDO) PA without
crosstalk ...........................................................................................................62 4.3.2 Characterization of a single-input dual-output (SIDO) PA with crosstalk......64 4.4 Summary ..................................................................................................................68 CHAPTER FIVE: PROPOSED DE-EMBEDDING TECHNIQUE FOR ON-WAFER
POWER FLOW MEASUREMENTS.......................................................................69 5.1 Introduction ..............................................................................................................69 5.2 General Calibration Procedure.................................................................................70 5.2.1 The power flow calibration method ................................................................70 5.2.2 On-wafer reflection coefficient measurements ...............................................75 5.3 Measurement Results ...............................................................................................78 5.3.1 Reflection and power de-embedding measurements for 50 Ω passive
devices..............................................................................................................78 5.3.2 Reflection and power de-embedding measurements for non 50 Ω passive
devices..............................................................................................................83 5.3.3 Power de-embedding measurements for active devices ..................................84 5.4 Summary ..................................................................................................................86 CHAPTER SIX: PROPOSED CALIBRATION ALGORITHMS FOR WAVEFORM
MEASUREMENTS ..................................................................................................87 6.1 Introduction ..............................................................................................................87 6.2 Relative Phase Calibration Algorithm for Waveform Measurements .....................90 6.3 Relative Waveform Measurement Results ..............................................................96 6.3.1 Two-port waveform monitoring ......................................................................96 6.3.2 Multi-port waveform monitoring ....................................................................99 6.4 Absolute Phase Calibration Algorithm for Waveform Measurements ..................102 6.5 Measurement Validation ........................................................................................106 6.5.1 Time-domain validation ................................................................................107 6.5.2 Frequency-domain validation ........................................................................110 6.6 Waveform Engineering ..........................................................................................112 6.7 Summary ................................................................................................................115 CHAPTER SEVEN: CONCLUSION AND FUTURE WORK ......................................117 7.1 Multi-Port Measurement System Development ....................................................117 7.2 Proposed Calibration Algorithms ..........................................................................117 7.2.1 Power de-embedding calibration algorithm ..................................................118 7.2.2 Waveform calibration algorithm with relative phase measurements ............118 vii
7.2.3 Enhanced waveform calibration algorithm with absolute phase
measurements .................................................................................................119 7.3 System Capabilities and Measurement Validations...............................................119 7.3.1 S-parameter measurements ............................................................................120 7.3.2 AM-AM and AM-PM conversion measurements .........................................120 7.3.3 Impedance and absolute power measurements..............................................121 7.3.4 Waveform measurements ..............................................................................121 7.4 Recommendations for the Future Work.................................................................122 7.5 Summary of Contributions.....................................................................................123 REFERENCES ................................................................................................................125 APPENDIX A: DATASHEETS ......................................................................................142 A.1 Datasheet of Agilent P940xA/C Solid State PIN Diode Switches .......................142 A.2 Datasheet of MAC C4238-20 Bi-Directional Couplers ........................................153 A.3 Datasheet of ANAREN 41620 Power Divider .....................................................154 A.4 Datasheet of CMOS 82C55A Programmable Peripheral Interface ......................157 A.5 Datasheet of ZFL-2500 Medium-Power Amplifier ..............................................163 A.6 Datasheet of ZHL-24W Medium-Power Amplifier ..............................................165 A.7 Datasheet of NPTB00004 Gallium Nitride RF Power Transistor ........................167 viii
List of Tables
Table 3-1: Specifications of the instruments and components employed in the multiport measurement setup ............................................................................................ 33 Table 3-2: Measured S-parameters for 3dB attenuator at 4 GHz frequency and 0 dBm
input power ............................................................................................................... 47 Table 3-3: Measured S-parameters for 6dB attenuator at 4 GHz frequency and 0 dBm
input power ............................................................................................................... 47 Table 5-1: The first error box parameters and verification at 4 GHz and 0 dBm [91] ..... 80 Table 5-2: The reflection measurement results of unknown loads at 4 GHz frequency
and 0 dBm input power [91] ..................................................................................... 80 Table 5-3: Power de-embedding results at the end of the coaxial plane at 4 GHz
frequency and 0 dBm input power [91] .................................................................... 80 Table 5-4: The second error box parameters and verification for a 50 Ω system at 4
GHz frequency and 0 dBm input power [91]............................................................ 81 Table 5-5: The reflection measurement results of unknown loads for a 50 Ω system at
4 GHz frequency and 0 dBm input power [91]......................................................... 82 Table 5-6: Power de-embedding results at the end of the on-wafer plane for a 50 Ω
system at 4 GHz frequency and 0 dBm input power [91]......................................... 82 Table 5-7: The second error box parameters and verification for a non 50 Ω system at
4 GHz frequency and 0 dBm input power [91]......................................................... 83 Table 5-8: The reflection measurement results of unknown loads for a non 50 Ω
system at 4 GHz frequency and 0 dBm input power [91]......................................... 83 Table 5-9: Power de-embedding results at the end of the on-wafer plane for a non 50
Ω system at 4 GHz frequency and 0 dBm input power [91]..................................... 84 Table 5-10: Power spectrum measurements for ZFL-2500 PA at 0.5 GHz
fundamental and three harmonics for different input power levels [91]................... 85 Table 6-1: Output reflection coefficient measurements of the power amplifier at
1GHz fundamental frequency and 4 harmonics ...................................................... 113 ix
List of Figures and Illustrations
Figure 2-1: S-parameters representation of the two-port network ...................................... 9 Figure 2-2: Functional block scheme of two-port VNA ................................................... 11 Figure 2-3: Power de-embedding measurement system built around VNA, developed
by Ferrero and Pisani [10]......................................................................................... 14 Figure 2-4: Large-signal measurement system based around a double six-port
reflectometer, developed by Bergoff et al. [12] ........................................................ 16 Figure 2-5: Two-port waveform measurement system built around a sampling scope,
developed by Sipila et al. [19] .................................................................................. 19 Figure 2-6: Two-port waveform measurement system built around VNA, developed
by Lott [32] ............................................................................................................... 22 Figure 2-7: Waveform measurement system built around MTA, developed by
Williams and Tasker [37].......................................................................................... 25 Figure 2-8: Waveform measurement system based on six-port reflectometer,
developed by Ghannouchi et al. [41] ........................................................................ 27 Figure 3-1: Block diagram of the developed measurement system .................................. 31 Figure 3-2: Photo of the real multi-port measurement system ......................................... 32 Figure 3-3: HP70820A microwave transition analyzer .................................................... 34 Figure 3-4: Simplified block diagram of microwave transition analyzer [52] ................. 35 Figure 3-5: RF to IF time-domain down-conversion process within MTA using
harmonic repetitive sampling technique ................................................................... 37 Figure 3-6: Block diagram of the N-port calibration procedure ....................................... 38 Figure 3-7: Signal flow graph for the error box between port 1 of the MTA and port 1
of the DUT ................................................................................................................ 39 Figure 3-8: Flowchart of the calibration algorithm for the multi-port measurement
setup .......................................................................................................................... 45 Figure 3-9: Return losses at ports 1 and 3 of the 3 dB power divider (VNA vs.
developed setup) [71] ................................................................................................ 49 Figure 3-10: Return loss at port 2 of the 3 dB power divider (VNA vs. developed
setup) [71] ................................................................................................................. 49 x
Figure 3-11: Transmission coefficients between ports 1 and 2 for the 3 dB power
divider (VNA vs. developed setup) [71] ................................................................... 50 Figure 3-12: Transmission coefficients between ports 1 and 3 for the 3 dB power
divider (VNA vs. developed setup) [71] ................................................................... 50 Figure 3-13: Isolation between ports 2 and 3 for the 3 dB power divider (VNA vs.
developed setup) [71] ................................................................................................ 51 Figure 3-14: Transmission coefficients between ports 1 and 2 for the 3 dB power
divider at Pin=0 dBm and Pin=10 dBm [71] ............................................................ 52 Figure 3-15: Transmission coefficients between ports 1 and 3 for the 3 dB power
divider at Pin=0 dBm and Pin=10 dBm [71] ............................................................ 53 Figure 4-1: Measured direct conversion AM-AM for the ZFL-2500 amplifier using
the developed measurement system at 1 GHz [88] ................................................... 56 Figure 4-2: Measured direct conversion AM-PM for the ZFL-2500 amplifier using
the developed measurement system at 1 GHz [88] ................................................... 57 Figure 4-3: AM-AM of harmonics for the ZFL-2500 PA using the developed
measurement system at 0.5 GHz [88] ....................................................................... 58 Figure 4-4: AM-PM of harmonics for the ZFL-2500 PA using the developed
measurement system at 0.5 GHz [88] ....................................................................... 59 Figure 4-5: Balanced PA using FLL351ME GaAs FETs from Fujitsu with crosstalk at
the output .................................................................................................................. 60 Figure 4-6: Efficiency of the balanced PA with different output coupling effects [88] ... 61 Figure 4-7: AM-AM and AM-PM of the two amplifiers without output coupling [88]... 63 Figure 4-9: AM-AM and AM-PM of the amplifiers with 20 dB output coupling [88] .... 64 Figure 4-10: Gain and efficiency of the amplifiers with 20 dB output coupling [88] ...... 65 Figure 4-11: AM-AM and AM-PM of the amplifiers with 10 dB output coupling [88] .. 65 Figure 4-12: Gain and efficiency of the amplifiers with 10 dB output coupling [88] ...... 66 Figure 4-13: AM-AM and AM-PM of the amplifiers with 6 dB output coupling [88] .... 66 Figure 4-14: Gain and efficiency of the amplifiers with 6 dB output coupling [88] ........ 67 Figure 5-1: On-wafer absolute power calibration procedure [91] .................................... 71 xi
Figure 5-2: Signal flow graph for error boxes between port1 of the MTA and port1 of
the DUT .................................................................................................................... 72 Figure 5-3: The overall error box between port 1 of the MTA and port 1 of the DUT .... 76 Figure 6-1: Simplified block diagram of the developed multi-port measurement
system [95] ................................................................................................................ 90 Figure 6-2: Error model for a multi-port DUT connected between port 1 and port k of
the multi-port measurement system .......................................................................... 91 Figure 6-3: Waveform comparison between the scope and the measurement setup for
ZFL-2500 PA at -10 dBm input power [97] ............................................................. 97 Figure 6-4: Waveform comparison between the scope and the measurement setup for
ZFL-2500 PA at -15 dBm input power [97] ............................................................. 98 Figure 6-5: Output waveforms of ZFL-2500 PA for several input powers using the
measurement setup [97] ............................................................................................ 98 Figure 6-6: Balanced PA using FLL351ME GaAs FETs from Fujitsu .......................... 100 Figure 6-7: Voltage and current waveforms at port 1 of the balanced PA [98].............. 100 Figure 6-8: Voltage and current waveforms at port 2 of the balanced PA [98].............. 101 Figure 6-9: Voltage and current waveforms at port 3 of the balanced PA [98].............. 101 Figure 6-10: Error model for the thru standard connected between port 1 and port k of
the measurement system ......................................................................................... 103 Figure 6-11: Error model for the coaxial line connected between port 1 and CH1 of
the MHR to measure bcoax ....................................................................................... 105 Figure 6-12: Output waveforms of the ZHL-42W PA at -9 dBm input power .............. 108 Figure 6-13: Output waveforms of the ZHL-42W PA at -6 dBm input power .............. 108 Figure 6-14: Output waveforms of the ZHL-42W PA at -3 dBm input power [95]....... 109 Figure 6-15: Comparison of the voltage waveforms at the output port of the ZHL42W PA at 0 dBm input power while employing the relative and the enhanced
calibration algorithm in the developed measurement system ................................. 110 Figure 6-16: Spectrum of the output waveforms of the ZHL-42W PA at 0 dBm input
power....................................................................................................................... 111 Figure 6-17: Waveform measurements for different output loads at 20 dBm input
power for an NPTB00004 GaN HEMT transistor [95]........................................... 114 xii
Figure 6-18: Comparison between the measurements of the scope and the developed
system for the waveform of case 3.......................................................................... 115 Figure 7-1: Integration of the proposed multi-port measurement system with the
passive load-pull setup to build a wide-range waveform measurement system ..... 123 xiii
List of Symbols
Symbols
Definition
α k(n )
Wave normalization factor
Time Delay
Phase of the nth harmonic
Reflection Coefficient
Measured Reflection Coefficient
Ohm
Measure incident Wave
Measured reflected Wave
S-parameters of the error box
Error Box
Frequency of the fundamental
Sampling Frequency
Current at port k of the DUT for n frequencies
Power calibration constant at coaxial plane
Power calibration constant at on-wafer plane
Number of harmonics
Power de-embedded at the ON-wafer plane
Absolute power reading of the power meter
Output Power
Sampled power reading at the MTA
Measured S-parameters of the thru connected between port 1 and port k
Sampling Period
Fundamental Signal Period
Time-domain voltage waveform at port k of the DUT
∆T
φn
Γ
ΓM
Ω
am
bm
eij
Ei
f
Fs
I k(n )
k′A
kA
Nh
PA
PPWM
Pout
PSA
S mT 1k
Ts
Tsignal
vk(n )
V0 k
(n )
k
V
Direct current component of the voltage waveform at port k of the DUT
Voltage at port k of the DUT for n frequencies
xiv
List of Abbreviations
Abbreviations
Definition
AM-AM
AM-PM
ADC
Balun
CMOS
dB
dBm
DC
DSP
DUT
FET
FFT
GaAs
GaN
Gbps
GPIB
HEMT
Hz
IF
IFFT
LPF
MHG
MHR
MTA
OSL
OSLT
PA
PAE
PC
PPI
RF
SIDO
SIMO
SRD
SISO
SOLT
S-parameters
TRL
VNA
VSWR
Amplitude Modulation to Amplitude Modulation
Amplitude Modulation to Phase Modulation
Analog-to-Digital Converter
Balanced-to-Unbalanced
Complementary Metal Oxide Semiconductor
Decibel
Decibel per Milliwatt
Direct Current
Digital Signal Processing
Device Under Test
Field-Effect Transistor
Fast Fourier Transformation
Gallium Arsenide
Gallium Nitride
Giga Bit Per Second
General Purpose Interface Bus
High Electron Mobility Transistor
Hertz
Intermediate Frequency
Inverse Fast Fourier Transformation
Low-Pass Filter
Multi-Harmonic Generator
Multi-Harmonic Receiver
Microwave Transition Analyzer
Open-Short-Load
Open-Short-Load-Thru
Power Amplifier
Power-Added Efficiency
Personal Computer
Programmable Peripheral Interface
Radio Frequency
Single-Input Dual-Output
Single-Input Multi-Output
Step Recovery Diode
Single-Input Single-Output
Short-Open-Load-Thru
Scattering Parameters
Thru-Reflect-Line
Vector Network Analyzer
Voltage Standing Wave Ratio
xv
List of Publications that Have Resulted from the Research Project
Journal Papers
1.
W. S. El-Deeb, S. Bensmida, N. Boulejfen, and F. M. Ghannouchi, "An
Impedance and Power Flow Measurement System Suitable for On-Wafer
Microwave Device Large-Signal Characterization," International Journal of
RF and Microwave Computer-Aided Engineering, vol. 20, pp. 306-312, 2010.
2.
W. S. El-Deeb, N. Boulejfen, and F. M. Ghannouchi, "A Multi-Port
Measurement System for Complex Distortion Measurements of Nonlinear
Microwave Systems," IEEE Transactions on Instrumentation and Measurement,
vol. 59, pp. 1406-1413, 2010.
3.
W. S. El-Deeb, M. S. Hashmi, S. Bensmida, N. Boulejfen, and F. M. Ghannouchi,
"Thru-Less Calibration Algorithm and Measurement System for On-Wafer
Large-Signal Characterization of Microwave Devices," IET Microwaves,
Antennas & propagation, vol. 4, pp. 1773-1781, 2010.
4.
W. S. El-Deeb, M. S. Hashmi, N. Boulejfen, and F. M. Ghannouchi, "SmallSignal, Complex Distortion and Waveform Measurement System for MultiPort Microwave Devices," IEEE Instrumentation & Measurement Magazine,
Accepted, Mar. 2011.
5.
W. S. El-Deeb, M. S. Hashmi, N. Boulejfen and F. Ghannouchi, "Systematic
Calibration of Nonlinear Two-Port Network Analyzer for Measurement and
Engineering of Absolute Nonlinear Waveforms," IOP Measurement Science
and Technology, Submitted, Feb. 2011.
Conference Papers
6.
W. S. El-Deeb, S. Bensmida, and F. M. Ghannouchi, "A De-Embedding
Technique for On-Wafer Simultaneous Impedance and Power Flow
Measurements," in IEEE Instrumentation and Measurement Technology
Conference, I2MTC 2008, Victoria, BC, Canada, 2008, pp. 58-61.
7.
W. S. El-Deeb, N. Boulejfen, and F. M. Ghannouchi, "An Automated MultiPort Measurement System for Linear and Non-Linear Characterization of
N-Port Microwave Devices," in IEEE Instrumentation and Measurement
Technology Conference, I2MTC 2009, Singapore, Singapore, 2009, pp. 12151219.
xvi
8.
W. S. El-Deeb, M. S. Hashmi, N. Boulejfen, and F. M. Ghannouchi, "Dynamic
Distortion Characterization of Multi-Port RF PAs Using MTA-Based MultiPort Measurement Setup," in Workshop on Integrated Nonlinear Microwave
and Millimetre-Wave Circuits, INMMiC 2010, Goteborg, Sweden, 2010, pp. 152155.
9.
W. S. El-Deeb, M. S. Hashmi, N. Boulejfen, and F. M. Ghannouchi, " TimeDomain Waveform Measurement System for the Characterization of MIMO
RF Power Amplifiers," in The 12th Annual IEEE Wireless and Microwave
Technology Conference, WAMICON 2011, Florida, USA, 2011, Accepted.
Conference Abstracts
10. W. S. El-Deeb, M. S. Hashmi, N. Boulejfen, and F. M. Ghannouchi, "Relative
Waveform Measurement Technique for the Characterization of Multi-Port
Microwave Devices," in IEEE Antennas and Propagation Society International
Symposium, APS-URSI 2010, Toronto, Canada, 2010.
11. W. S. El-Deeb, N. Boulejfen, and F. M. Ghannouchi, "A Measurement Setup
for AM-AM and AM-PM Characterization of MIMO RF Power Amplifiers,"
in IEEE Antennas and Propagation Society International Symposium, APS-URSI
2010, Toronto, Canada, 2010.
xvii
1
Chapter One: Introduction
1.1 Motivation
The microwave power amplifier is the key subsystem of any wireless communications
transceiver. It converts simple direct current (DC) power into complex radio waves that
travel through space to enable wireless communication [1]. The bottle neck in the design
of a high-efficiency radio frequency power amplifier (PA) is the transistor used to build
the amplifier itself. The power transistors often do not behave the way the designer
expects. It is the responsibility of the power amplifier designers to make sure that they
can integrate the power transistor into a well-behaved power amplifier that obeys the
strict regulations and meets the standard requirement mainly in terms of spectrum mask
etc. [2].
The first step in power amplifier design is the selection of a proper transistor
model. This model should perfectly describe the behaviour of the transistor under a wide
range of excitation signals and operating points.
The radio frequency (RF) power amplifier designers start the design process by
implementing the selected transistor model to a commercially available simulator to
predict the performance of the power amplifier before building the prototype [3]. Using
the simulator, the designers can tune the design parameters to optimize the performance
of the amplifier to meet the desired criteria. The accuracy of the simulators is determined
mainly by the accuracy of the large-signal nonlinear model. If the transistor model is
accurate, the prototype will meet the desired specifications, although some tuning may be
2
necessary for the stabilization and matching circuits. However, if the transistor model is
not accurate enough, this will lead to the failure of the design process.
In order to have a good transistor model, several kinds of small-signal and largesignal characterizations have to be performed on the transistor that is going to be used in
the design of the power amplifier. These characterizations require many different
measurements for the transistor under test, such as scattering parameters (S-parameter),
power sweep, amplitude modulation to amplitude modulation (AM-AM) conversion,
amplitude modulation to phase modulation (AM-PM) conversion, gain, power-added
efficiency (PAE) and time-domain waveform measurements [4].
1.2 Problem Definition
From studying the literature of the previously developed measurement systems over the
past few decades, as described in Chapter Two, it is obvious that many good
measurement systems and effective calibration algorithms have been developed for largesignal characterization of microwave devices. However, the limitations of these systems
can be summarized in the following points:
•
Most of the existing measurement systems have been designed to perform a
specific kind of measurement, like S-parameters, power sweep or waveform
measurement. Unfortunately, none of them is able to perform all the
measurements required for the large-signal characterization of the device under
test (DUT) with fast, generic and accurate calibration procedure [5-41].
3
•
Some of the existing measurement systems are employed to work in 50 Ω
environments only, and they are not suitable for non 50 Ω environments [12, 1518, 32].
•
Some of the existing measurement systems can perform two-port measurements
only, and they do not have the capability to characterize the N-port devices [14,
19, 20, 28, 32].
•
Some of the measurement systems rely on the use of a multi-harmonic generator
(MHG) for accurate phase calibration purposes. The MHG needs a special type of
calibration and, therefore, adds complexity to the measurement system and the
calibration process [19, 20, 32, 35-37, 41].
•
The calibration processes of many waveform measurement systems are mainly
dependent on the use of the so-called ‘golden diode’ or ‘golden standard’
approach, in order to achieve the desired accuracy [32, 33, 38, 40, 41]. The golden
standard is an ingenious phase reference method used to align the harmonic phase.
This golden standard is difficult to design and is limited to the design frequency
range.
•
Some of the calibration algorithms applied for these measurement systems are
very complicated and time-consuming [18, 20, 33, 38, 40].
These limitations in commercially available measurement systems make the
characterization of the microwave device difficult, time-consuming, expensive and
sometimes inaccurate.
4
1.3 Objective
The main objective of this work is the development of an automated multi-port
measurement system that is suitable for frequency- and time-domain characterization of
N-port linear and nonlinear microwave devices. This measurement system should be
capable of extracting most of the required linear and nonlinear figures of merit to provide
a model that can accurately describe the behaviour of the microwave device in 50 Ω or
non 50 Ω impedance environments.
To overcome the problem of inaccuracy and time consumption, the proposed
calibration algorithms should be generic, accurate and suitable for different kinds of
measurements. The proposed measurement system should also be simple, precise,
relatively inexpensive, and have a user friendly interface to facilitate the calibration and
the measurement procedures.
1.4 Thesis Outline
The thesis presents the development of a multi-port measurement system and the
calibration algorithms for time- and frequency-domain characterization of N-Port
microwave devices. The thesis is organized in seven chapters as follows:
•
Chapter One states the problem definition, motivation behind the research and
the main goal of the work.
•
Chapter Two highlights the existing measurement systems developed for linear
and nonlinear characterization of RF and microwave devices. The chapter
5
describes the advantages, disadvantages and limitations of the available
measurement systems.
•
Chapter Three describes the development of the proposed multi-port
measurement system and the function and specifications of each of its elements.
The calibration algorithm for multi-port measurements is described, and some
linear measurements are introduced to validate the accuracy and the functionality
of the developed system.
•
Chapter Four shows the ability of the developed multi-port measurement system
to measure the AM-AM and AM-PM conversions with and without the output
coupling effect. The measurements prove that the system is capable of measuring
the complex distortion for single-input single-output (SISO) and single-input
multi-output (SIMO) power amplifiers in a one-step measurement connection that
increases the accuracy and the credibility of the measurement results.
•
Chapter Five presents an absolute power and impedance de-embedding
technique that can be applied for 50 Ω and non 50 Ω impedance environments to
perform on-wafer passive source- and load-pull measurements.
•
Chapter Six describes two proposed calibration algorithms for multi-port
waveform measurements. The first calibration algorithm is based on relative
phase measurements of the error box parameters between the DUT plane and the
measuring plane. The second waveform calibration algorithm is proposed to
correct the phase problem in the relative phase measurements by directly
measuring the magnitude and phase of the error box parameters.
6
•
Chapter Seven concludes with the measurement capabilities of the developed
system along with the calibration algorithms and provides recommendations for
the future work.
7
Chapter Two: Overview of Measurement Systems for the Characterization of RF
Devices
2.1 Introduction
The design of RF systems requires several kinds of linear and nonlinear measurements.
For passive elements, which can be assumed to be linear, the extraction of the scattering
matrix can be considered enough for identifying the behaviour of the element [42].
However, this is not the case for active elements that have nonlinear behaviour and are
usually driven in the mild or deep nonlinear region. These nonlinearities play a major role
in the overall behaviour of the active device with the input signal, as they generate
spectral components, harmonics or intermediation products that are not present in the
excitations.
The characterization of active devices, therefore, requires different kinds of
measurements that take into consideration the effect of devices’ nonlinearities, in order to
acquire an accurate model for microwave devices. An accurate model will lead to good
simulation results and, therefore, an accurate overall system design. To build a good
device model, several figures of merit have to be extracted from the DUT, which in turn
requires different instruments and measurement systems.
This chapter highlights the available measurement systems that have been
developed for the characterization of RF and microwave devices. It also describes the
advantages, disadvantages and limitations of these measurement systems. The discussion
8
on the limitations and drawbacks of the existing systems clearly identifies the direction of
the current research.
2.2 S-Parameter Measurement Systems – Overview
In systems that work in high frequencies, the usual short circuit and open circuit analysis
techniques, such as h-parameters and z-parameters, are difficult to use. This is due to the
fact that one cannot guarantee that the short and open circuits will behave in the same
manners as in low frequencies. A short circuit at high frequencies can depend on the
inductive behaviour of the wire; therefore, it will not be a pure short. An open circuit, on
the other hand, has a capacitive behaviour at high frequencies, which lowers the
impedance to a small value. S-parameters are the tool that is used to solve this problem.
S-parameters are used to model high-frequency networks. Unlike the usual
network analyses, where the parameters are expressed as the relationships between
voltages and currents, the S-parameters are expressed as relationships between traveling
waves. S-parameters are the reflection and transmission coefficients between the incident
and reflected waves [43]. They completely describe the behaviour of a device under
linear conditions at the microwave frequency range.
9
Figure 2-1: S-parameters representation of the two-port network
The S-parameters of the two-port network shown in Figure 2-1 can be expressed
as a function of the incident waves (a1 and a2) and the reflected waves (b1 and b2) using
the following equations [44]:
b1 = S11a1 + S12 a2
(2-1)
b2 = S 21a1 + S 22 a2
(2-2)
where S12, and S21 are called the transmission ratios, while S11 and S22 are called the
reflection coefficients for ports 1 and 2, respectively.
By measuring these S-parameters, a clear idea about the DUT can be obtained by
extracting the commonly used parameters, such as gain, stability, reflection coefficients
and input/output impedances. S-parameter measurements are mainly dependent on the
accurate measurements of the incident and reflected waves, as can be noticed from
10
equations (2-1) and (2-2). Several measurement systems have been developed for Sparameters measurement, as described in the following section.
2.2.1 Vector network analyzer
The vector network analyzer (VNA) is a fundamental test-set instrument for all
microwave laboratories. It can measure the magnitude and phase of a microwave signal
with respect to a reference. Direct measurements of magnitude and phase for microwave
devices are carried out on a replica of the incoming signal and down-converted to
intermediate frequency (IF) [42].
The VNA basically consists of a high-frequency generator (RF synthesizer), an Sparameter test-set that acquires the input and the reflected power at the DUT at both
ports, a receiver to down-convert and detect the signals, and a processor and display unit
(mainframe) for calculating and reviewing the results, as shown in Figure 2-2.
The VNA completely characterizes the DUT by measuring the respective signal
magnitude ratios and phase differences. In fact, the VNA in commercial realizations
comes with S-parameter test-set options that include the power splitters, switches and
couplers necessary to route signals to and from the DUT and the appropriate receivers.
The VNA is usable only in the case when the device is stimulated by one
frequency at a time and when the response is linear. The VNA measurement ignores the
distortion effects in the device and, hence, is not optimized to characterize the device in
the nonlinear mode of operation [45].
11
Read-Out Unit
Processing Unit
b0 a0
RF
a3 b3
LO
a1
b1
DUT
b2
a2
Figure 2-2: Functional block scheme of two-port VNA
2.2.2 S-parameter measurements for N-port devices
With the increasing proliferation of multi-port devices at both RF and microwave
frequencies, it is sometimes essential to measure the n × n complex scattering matrix of
an N-port device. This kind of measurement can be performed with a multi-port VNA or
a two-port VNA with or without a special test-set [5].
12
The multi-port VNA is very expensive and not available for many research labs.
In the case of using a two-port VNA without a special test-set for the characterization of
an N-port device, C N2 successive two-port measurement series have to be carried out to
obtain the full S-parameters matrix of the N-port device. During these measurements, N –
2 matched loads have to be used to terminate the ports of the device that are not
connected to the network analyzer [6]. As the number of ports of the DUT increase, the
process becomes more complicated, time-consuming and inaccurate, since there are many
measurement steps that have to be performed to get the full S-parameters matrix of the
DUT. Furthermore, the imperfection of the terminators that are used during the
measurement process to terminate the unconnected ports of the DUT adds uncertainty to
the obtained results.
Some methods have been developed to acquire the scattering matrix of an N-port
network from measurements using a reduced-port VNA by applying certain mathematical
formulations [7].
Some companies have tried to overcome this problem by developing a special
multi-port test-set that can be connected to the two-port VNA to provide S-parameter
measurements for the N-port devices [8]. The basic function of the test-set in multi-port
measurements is to provide multiplexing from the two-port VNA to the N-port DUT.
This approach is less expensive, to some extent, than a custom N-port VNA; and, in some
cases, particularly as N increases, may be the only option available. While the
measurements are similar to the conventional VNA approaches, there are architectural,
calibration and performance differences that should be carefully analyzed.
13
2.3 Power De-Embedding Techniques and Apparatus – Overview
Absolute power measurements at the ports of microwave devices are extremely critical
for the optimal design and characterization of power amplifiers (PAs). An absolute power
calibration requires, in most cases, the connection of a power meter at the reference
plane, which is possible if the reference plane is coaxial. The problem becomes very
difficult in the case of on-wafer characterization of nonlinear devices, such as transistors.
Several de-embedding techniques have been used to extract the error box parameters
introduced by the test fixture used for the characterization of on-wafer devices [9-18].
2.3.1 Power de-embedding measurement system using VNA
In 1987, Hecht [9] developed a measurement system for large-signal characterization of
microwave devices with coaxial connectors. The system was built around the VNA as a
measuring instrument for measuring both the large-signal reflection coefficients and the
power at the coaxial terminals of the DUT.
In this system, the RF signal is fed to the measurement system from a high-power
microwave generator. The level of the input power to the DUT is controlled using a
variable attenuator with the help of a computer that controls the RF generator. The load
impedance is controlled manually with a passive tuner at the output. Using Hecht’s
measurement system, the absolute power at the coaxial terminals of the DUT can be
measured using the VNA after being calibrated with microwave power meter.
In order to apply this technique to on-wafer measurements, a power meter with
on-wafer sensors has to be connected to the non-coaxial terminals of the DUT for
14
calibration purposes. Otherwise, a de-embedding calibration algorithm has to be carried
out on the measurement system to compensate for the effect of the on-wafer probes of the
VNA [10].
In 1993, Ferrero and Pisani [10] updated the measurement system that was
initially developed by Hecht, in order to be suitable for on-waver device
characterizations. The modified measurement system is based on adding coaxial
directional couplers and RF coplanar wafer probes before the DUT terminals, as shown in
Figure 2-3. The dual directional couplers are used to sample the incident and reflected
power traveling at the input and the output of the DUT and sent them to be measured by
the automatic VNA.
HP8510 Vector Network Analyzer
HP8511A Four Channel Converter
a0
RF
b0
b3
a1
b1
0
1
DUT
b2
a2
2
3
in
a3
L
4
5
Figure 2-3: Power de-embedding measurement system built around VNA, developed
by Ferrero and Pisani [10]
15
The calibration process starts the calculations of the input error box by connecting
the coplanar open, short and matched load (OSL) standards to on-wafer input port 2. The
on-wafer input and output ports are connected together using the on-wafer thru standard.
Finally, the overall error box, which contains the input and output error boxes, is
calculated by connecting other coaxial OSL calibration standards at coaxial output port 5.
These two error boxes allow for the de-embedding of power at the on-wafer plane using
the power meter measurement at the output coaxial plane. The power calibration process
can be performed by connecting a coaxial power meter to port 5 during the calibration
process. This coaxial power meter provides an absolute power reference value for the
whole system up to the on-wafer probe tips.
Roth et al. [11] also utilized the same calibration technique, but extended it to
three measurement ports.
2.3.2 Power de-embedding measurement system using six-port reflectometer
Berghoff et al. [12] used a different principle to measure absolute power in the reference
plane by using a double six-port network analyzer and a thru-reflect-line (TRL)
calibration technique. He used two TRL calibrations, one in a coaxial plane and one onwafer, to de-embed the transmission characteristics of the elements forming the
connection between the two calibration planes, as shown in Figure 2-4.
The proposed calibration process can be described in two steps. The first step is
carried out by performing the full calibration process at the end of the coaxial plane
shown in Figure 2-4, using coaxial TRL calibration standards and a power meter. After
16
this calibration step, the three error parameters and calibration constant are obtained for
the first reference plane.
When the on-wafer probe station is connected to the double six-port
reflectometer, it adds another error box, which represents the transformation from the
coaxial plane to the coplanar plane. Hence, another on-wafer TRL calibration step has to
be performed at the on-wafer plane to calculate the error parameters of the second error
box. The absolute power constant of the second error box can be derived from the
corresponding constant in the first calibration plane with the help of de-embedding the
transmission characteristics.
Figure 2-4: Large-signal measurement system based around a double six-port
reflectometer, developed by Bergoff et al. [12]
17
All of the above methods for power de-embedding measurements have been
proposed to sample the incident and reflected waves, in order to measure the impedances
and the absolute power flow at the DUT terminals. The sampling of these waves is
performed via a bi-directional coupler inserted between the DUT and the impedance
control module. Therefore, an active impedance control system is required to compensate
for the losses introduced by the bi-directional coupler. This results in increased cost and
complexity of the measurement system.
2.4 Waveform Measurement Systems – Overview
Time-domain waveform measurements [46] for the design and optimization of
microwave power amplifiers are establishing themselves as an effective design approach
for a number of reasons [47]. Waveform-based transistor device optimization is an
alternative approach to the traditional device characterization method [48]. The shape of
the waveform at the transistor ports aids the amplifier designers in determining the
appropriate impedance and, in turn, the matching circuits. The ability to visualize
waveforms helps in the determination of optimal performance from the device.
Furthermore, waveform measurement systems are important tools in the design of rapidly
emerging high-efficiency power amplifiers, such as class F and class F-1 [49, 50].
Different approaches have been developed for waveform measurements. The first
approach employs the sampling scope, as a waveform measurement tool, which is
suitable for measurements at RF frequencies [19-31]. The second approach is built
around the VNA as an RF measuring instrument, by extending its measurement
18
capability from small-signal S-parameter measurement, which is suitable for measuring
the magnitude and phase of the incident and reflected waves [32, 33]. The third approach
makes use of the microwave transition analyzer (MTA), as a harmonic complex receiver
from DC to 40 GHz, for reconstructing the waveform at the DUT terminal based on the
information of the magnitude and the phase of the fundamental and harmonic frequencies
[34-40]. The fourth approach is built around the six-port reflectometer [41], as a
homodyne VNA, which is calibrated in magnitude and phase by means of a reference
multi-harmonic generator.
2.4.1 Waveform measurement systems using sampling oscilloscope
The operation of the sampling oscilloscope for waveform measurement is based on the
definition of sampling, which is the process of converting a portion of an input signal into
a number of discrete electrical values for the purpose of storage, processing and display.
The magnitude of each sampled point is equal to the amplitude of the input signal at the
instant in time that the signal is sampled. Sampling is like taking snapshots. Each sample
or snapshot corresponds to a specific point in time on the waveform. These snapshots can
then be arranged in the appropriate order in time so as to reconstruct the input signal.
According to the Nyquist sampling theorem, the sampling frequency should be at
least twice the highest frequency contained in the signal. With RF signals, the sampling
technique is different. The RF signal is sampled only once every period. This means that
each sampling point represents the value of the RF signal, which is slightly moved on the
RF waveform in time compared to its previous point. As a result, the sampling points
19
create a time-stretched replica of the RF signal, which represents the IF down-converted
signal for the RF input one. In order to reconstruct the RF waveform for the IF signal, it
is necessary to sample the RF signal over a large amount of periods.
In 1988, Sipila et al. [19] developed a measurement system suitable for waveform
measurements of two-port microwave devices. The system is based on measuring the
time-domain voltage and current waveforms using a high-speed sampling oscilloscope.
The RF signal is fed to the DUT through a power divider, linear power amplifier,
harmonic filter and a step attenuator, as shown in Figure 2-5. All these devices are
necessary to provide sufficient power to drive the DUT into the nonlinear region, in order
to have distorted voltage and current waveforms at the device terminals. The system is
able to measure only two traveling waves, which are called the reflected input wave (b1)
and the transmitted output wave (b2). The reflected and transmitted waves are measured
using a fast sampling scope through the input and output coupling networks, respectively.
Figure 2-5: Two-port waveform measurement system built around a sampling
scope, developed by Sipila et al. [19]
20
The calibration algorithm is based on measuring the S-parameters of the input and
the output coupling networks at the fundamental and harmonic frequencies of the
operating frequency. The corrected waveforms at the DUT terminals can be obtained by
converting the measured time-domain waves into the frequency domain and then
compensate for the effect of the input and output coupling networks using their measured
S-parameters. The system is suitable for a frequency range of DC to 2 GHz. It has a
strong likelihood of introducing significant errors above this frequency.
Kompa et al. [20] developed a measurement system for waveform measurements
based on the VNA and sampling scope to provide higher accuracy compared to the
system proposed by Sipila. This accuracy can be achieved by measuring the phase and
magnitude relationship of the fundamental waves using the high accuracy of the VNA.
On the other hand, the signal amplitude and waveforms are measured using a twochannel sampling scope.
The calibration algorithm of the system is based on performing a one-path twoport calibration procedure using the OSL calibration standards. This calibration process
evaluates the reflected and transmitted waveforms after correcting for the source and load
mismatch, tracking and directivity errors. The absolute power at the reference plane is
measured with a power meter when the short standard is connected to the test port of the
test-set. The error correction algorithm transforms the measurement data into frequencydomain wave quantities at the coaxial reference planes of the DUT.
21
2.4.2 Waveform measurement systems using VNA
The main purpose of the VNA is to measure the S-parameters of the DUT by measuring
the ratios between the incident and reflected waves at the DUT terminals.
In order to incorporate the VNA in waveform measurements, two modifications
have to be carried out on the measurement system. First, the system should be able to
measure the ratios of the incident and reflected waves for the harmonic frequencies.
Second, the system has to be accurately calibrated for phase measurements. The first
modification can be achieved by inserting a signal source multi-harmonic generator,
which provides a signal with the same spectrum as the waveform to be measured. The
second modification can be performed by connecting an additional waveform standard
between the VNA ports during the calibration process. This waveform standard, termed
the golden standard, is used for the phase calibration process by producing a well
specified waveform.
With the help of the VNA, Lott [32] succeeded in increasing the accuracy of the
measurements compared to the previous systems, by simultaneously measuring the
magnitude and phase of the harmonic frequencies generated from a two-port microwave
device. The system, shown in Figure 2-6 , is built around the VNA as a frequencydomain measuring instrument and the phase-locked signal generator as an RF source.
The raw measurement results are obtained in the frequency-domain from the
VNA. The time-domain waveforms can be reconstructed using inverse fast Fourier
transformation (IFFT) after applying the suitable calibration algorithm for measurement
corrections.
22
The calibration process consists of two main parts: one for phase correction and
the second for absolute power calibration. A Schottky diode is used as a reference device
for phase calibration at the harmonic frequencies. The idea behind using a step recovery
diode (SRD) is to provide a device that has a much faster switching time than the DUT.
Computer
LPF
Atten
AMP
Ref
CH1
RF
Power
Meter
Ref.
Diode
a1
b1
DUT
Vector Network
Analyzer
CH2
LPF
b2
a2
Figure 2-6: Two-port waveform measurement system built around VNA, developed
by Lott [32]
The power calibration in this measurement system is carried out with a power
meter connected to the bi-directional coupler, shown in Figure 2-6, when the DUT is
disconnected.
Although the measurement system developed by Lott improved the accuracy of
the waveform measurements, it did not offer waveform engineering capability, because
23
the DUT is connected to a 50 Ω impedance, instead of actual source and load
impedances.
In 1998, Barataund et al. [33] proposed a time-domain waveform measurement
system based on the combination of a harmonic source and load-pull setup with a
modified VNA. Conventional VNAs can only measure the complex power wave ratios at
their ports for each frequency component of the operating frequency range. To overcome
this limitation, the test-set of the applied VNA was modified to provide the capability of
absolute phase measurement to the system.
The calibration process of the developed system is complicated, since there are
many error parameters that must be calculated to reconstruct the waveforms at the DUT
ports. The process starts by performing a TRL calibration at ports 1 and 2 of the modified
VNA, and then a complete OSL is applied at the RF inputs. The power meter is also
connected to the RF inputs for the purpose of magnitude calibration. The phase
calibration is performed using an absolute phase harmonic generator built with an SRD
and microwave power amplifier.
Despite the fact that the VNA used in the system is modified for phase capability
measurements, the harmonic measurement is slow; and, it is difficult to achieve an
accurate phase measurement, due to the complicated calibration procedure.
2.4.3 Waveform measurement systems using microwave transition analyzer
In early 1990s, the microwave transition analyzer (MTA) appeared as a fundamental and
harmonic receiver from DC to 40 GHz. The MTA principle of operation is similar to the
24
sampling oscilloscope, but with a built-in trigger on the IF frequencies. The incoming RF
signals are mixed down to the IF frequencies, and the IF signals are then digitized by an
analog-to-digital converter (ADC). The MTA has several advantages compared to the
sampling oscilloscope. It offers time- and frequency-domain measurements, so it can also
be used as a VNA. It is also much faster than the traditional sampling scope, due to its
high sampling rate of approximately 20 MHz.
Raay and Kompa [35] developed a waveform measurement system built around
the MTA as a receiver instead of using a VNA or a high-speed scope. The system has the
ability to measure the four incident and reflected waves using a multiplexing technique.
The calibration process is carried out in two steps. The first calibration step is done at the
coaxial plane, like the calibration of the conventional one-path two-port network
analyzer. The second calibration step is performed to evaluate the S-parameters of the
wafer probe heads.
Demmler et al. [36] developed a measurement system based on the MTA, which
is similar to the one described above [35], but with much higher input power levels.
The measurement system developed by Williams and Tasker [37] is also built
around the MTA with the capability of source- and load-pull measurements and with
fundamental frequencies of 800 MHz to 2 GHz. The system has the ability to measure the
four wave components with a multiplexing operation, by connecting two RF switches
between the dual couplers and the MTA channels, as shown in Figure 2-7. The system
incorporates the load-pull capability, which makes the system useful for waveform
engineering.
25
The calibration process consists of conventional on-wafer two-port error
calibration using on-wafer short-open-load-thru (SOLT) standards. In addition to Sparameter calibration, it is necessary to perform a power calibration at a defined reference
plane. The system is useful for two-port large-signal characterization, but suffers from a
slow load-pull operation and a complicated calibration algorithm.
Figure 2-7: Waveform measurement system built around MTA, developed by
Williams and Tasker [37]
26
2.4.4 Waveform measurement systems using six-port reflectometer
In principle, the six-port reflectometer consists of linear circuits, with dividers and
combiners interconnected in such a way that four or “N” different vectorial additions of a
reference signal and the signal to be measured are obtained. The six-port technique is a
method of network analysis. It is well established that the six-port technique can be used
for reflection coefficient measurements [41]. This kind of reflection measurement can be
performed by connecting the signal generator at the input port and the DUT to the output
port, while the other four ports are connected to power detection sensors. According to
the six-port theory of operation [51], the reflection coefficient of the DUT is directly
related to the power at each of the four auxiliary ports.
Ghannouchi et al. [41] reported a new application for the six-port reflectometer. They
built a large-signal measurement system using the six-port reflectometer as homodyne
VNA for waveform measurements, as shown in
Figure 2-8. The system employs an active load-pull setup to control the source
and load impedances at the fundamental and harmonic frequencies.
A reference multi-harmonic generator based on the SRD is used for wave
calibration in magnitude and phase to measure the waveform at the input and output
terminals of the DUT. The system gives accurate results for the waveform measurements,
but this accuracy depends mainly on the design of a good multi-harmonic generator,
which is not always easy and fast to achieve.
27
SP3
Load Impedance
Tune System
SP2
b2
DUT
Multi-Harmonic
Generator
a2
a1 b1
Atten
SP1
Figure 2-8: Waveform measurement system based on six-port reflectometer, developed
by Ghannouchi et al. [41]
2.5 Summary
This chapter presented an overview of the measurement systems developed for largesignal characterization of RF and microwave devices. The chapter highlighted the
advantages and limitations of the different measurement systems for S-parameters, power
de-embedding and waveform measurements.
Some of these measurement systems are limited to two-port measurements, and
others are not suitable for non 50 Ω impedances. Also, the existing systems do not have
the capability of extracting most of the required parameters to build a nonlinear model of
the DUT.
These limitations directed this research work to focus on the development of a
multi-port measurement system that is suitable for different kinds of linear and nonlinear
characterizations.
28
Chapter Three: The Proposed Multi-Port Measurement System
3.1 Introduction
As described in the previous chapter, many measurement systems have been developed
for the characterization of microwave devices. Some of these systems were designed for a
certain application; therefore, they are not suitable for linear and nonlinear
characterization of the DUT. Other systems have limitations regarding the number of
measuring ports, the simplicity of the calibration algorithm, and the accuracy of the
measurements.
The goal of this work is the development of a multi-port measurement system
suitable for linear and nonlinear characterization of microwave devices and capable of
working in the 50 Ω and non 50 Ω environments with coaxial or on-wafer connectors. To
achieve this goal, an accurate, fast and simple multi-functional calibration algorithm is
employed along with the proposed measurement system.
In this chapter, the development of the proposed multi-port measurement system
is presented with a description for the function and the specifications of each of its
elements. The calibration algorithm for the multi-port measurements is described, and
some linear measurements are introduced to validate the accuracy of the developed
system.
29
3.2 The Measurement System Architecture
The multi-port measurement system developed for N-port microwave device
characterization consists of the HP70820A microwave transition analyzer as a multiharmonic complex receiver from DC to 40 GHz, an RF generator, three RF four-way
absorptive switches (SW2, SW3 and SW4), one RF two-way absorptive switch (SW1),
one power divider, four directional couplers (C1, C2, C3 and C4) and four bias tees
(DC1, DC2, DC3 and DC4). The block diagram and the real photo of the developed
measurement system are shown in Figure 3-1and Figure 3-2, respectively.
The RF signal coming from the Agilent E4433B generator is divided into two
parts using ANAREN 41620 power divider. The first part is routed to the DUT via the
source switching matrix represented by the Agilent P9404C switch, SW4. The RF signal
is sent to ports 1, 2, 3, and 4 of the DUT according to the position of SW4. The second
part of the RF signal is directed to CH2 of the MTA as a reference signal.
The incident and reflected waves at ports 1, 2, 3 and 4 of the DUT are sampled
with the help of the MAC C4238-20 bi-directional couplers, C1, C2, C3 and C4. Then the
sampled incident and reflected waves are routed one at a time to channel CH1 of the
MTA to be measured through the receiver switches matrix, which consists of SW1, SW2
and SW3.
The control of the source and receiver switching matrices is performed using the
parallel port of a personal computer (PC) via a special control circuit based on a
complementary metal oxide semiconductor (CMOS) programmable peripheral interface
(PPI 82C55A, INTEL) designed for that purpose.
30
The control word, which consists of 8 data bits, is sent to the PPI chip via the
parallel port of the PC. The PPI chip generates 3 words with 8 bits each in order to
control the four RF switches. The control word indicates the position of each switch in
order to send one wave at a time to be measured as the ratio between channel 1 and
channel 2 at the MTA plane.
The MTA, the RF source and the multi-meter are automated using the PC via a
general purpose interface bus (GPIB). The data is sent from the PC to the RF source to
set the required input power and to sweep the frequency range of the required
measurements. The measured DC components and waves are collected from the multimeter and the MTA, respectively and sent back to the PC for data processing.
The whole measurement process is controlled using a user friendly interface
program developed using visual C++ developer. This program allows the user to setup all
the parameters of the measurement environment and also to capture the measured data for
data processing.
Table 3-1 shows the specifications of the instruments and components used in the
measurement setup. The detailed specifications and datasheets for each component are
given in Appendix A.
31
Source Switching N/W
RF Generator
RF Path
RFin
DC Path
GPIB Path
PD
4 SW4
3 2
1
Parallel Port
Switching
Control Circuit
GPIB
1
SW2
2
3
C1
4
RFout
GPIB
GPIB Multimeter
DC 1
SW1
C2
MTA
DC 2
1
CH2
CH1
2
SW3 3
4
Receiver Switching N/W
C3
DC 3
C4
DC 4
Port 4
Port 3
Port 2
GPIB
Figure 3-1: Block diagram of the developed measurement system
Port 1
32
Figure 3-2: Photo of the real multi-port measurement system
33
Table 3-1: Specifications of the instruments and components employed in the multiport measurement setup
Instrument /
Model number
Specifications
Component
Freq. Range
MTA
HP 70820A
( DC – 40 GHz)
Freq. Range
RF generator
Agilent E4433B
(250 KHz – 4 GHz)
Isolation (-80 dB),
2-way switch
Agilent P9402C
Freq. Range
(100 MHz – 8 GHz)
Isolation (-80 dB),
4-way switches
Agilent P9404C
Freq. Range
(100 MHz – 8 GHz)
Coupling Factor (20 dB)
Bi-directional couplers
MAC C4238-20
Freq. Range
(1GHz – 8 GHz)
Isolation (-25 dB)
Power divider
ANAREN 41620
Freq. Range
(0.5 GHz – 3 GHz)
34
3.3 The Microwave Transition Analyzer
The HP 70820A microwave transition analyzer, shown in Figure 3-3, is a two-channel
sampler-based instrument with an RF bandwidth covering the range from DC to 40 GHz.
The instrument is called a transition analyzer because of its ability to measure very fast
magnitude and phase transitions under pulsed-RF conditions. The main advantage of
employing the MTA in the developed measurement system is that it incorporates the
scope capability for time-domain measurement and the commercial VNA capability for
frequency-domain measurements since it has the ability to make time-domain
measurements for the RF and microwave components.
Figure 3-3: HP70820A microwave transition analyzer
35
3.3.1 The MTA data acquisition process
The block diagram shown in Figure 3-4 illustrates that the MTA has two identical signal
processing channels that have the ability to sample and digitize the input signals over the
bandwidth from DC to 40 GHz [52]. The input signals to the MTA channels are sampled
by a microwave sampler with sampling frequency (Fs) between 10 MHz and 20 MHz.
The sampling rate depends on the signal frequency and the type of measurements to be
performed. The outputs of the sampler are fed into the DC-to-10 MHz IF sections, which
consist of a switchable low-pass filter (LPF) and an IF step-gain amplifier. The DC
components of the measured signals are separated before the microwave sampler and
summed into the IF signal separately. The outputs of the IF section are sampled at the
same sampling rate of the input signal and then converted to digital signals using analogto-digital converters (ADCs). The microwave samplers and ADCs are operated at the
same frequency. The maximum sampling frequency is 20 million samples per second.
Figure 3-4: Simplified block diagram of microwave transition analyzer [52]
36
The digital signals at the outputs of the ADCs are fed into buffer memories, which
hold the samples until the trigger point is determined. The data is sent to the digital signal
processing (DSP) unit after the determination of the trigger point and the acquiring of all
necessary data.
The time-domain data that was sent to the DSP unit is converted to the frequencydomain data using fast Fourier transformation (FFT). The IF corrections are applied to
the frequency-domain data, in order to compensate for the non-ideal operation of the
analog signal processing path. After correcting the frequency-domain data, the signal is
reconverted to the time-domain by performing inverse fast Fourier transformation (IFFT).
3.3.2 The MTA sampling process
The MTA is in principle a sampling oscilloscope with a built-in trigger on IF frequencies.
The built-in trigger eliminates the need for an external trigger and in turn simplifies the
building of the measurement system. The MTA acquire the data in the time domain using
a harmonic repetitive sampling technique. This sampling technique is mainly dependent
on down-converting the RF to IF signal as shown in Figure 3-5.
The IF signal is obtained by sampling the RF signal once every Nth RF periods.
The sampling period (Ts) is calculated as a function of the fundamental signal period
(Tsignal) ,the number of trace points (N) and the time delay (∆T) as indicated in equations
(3-1) and (3-2) [53].
Voltage (V)
37
Figure 3-5: RF to IF time-domain down-conversion process within MTA using
harmonic repetitive sampling technique
TS =
1
= ( N × TSignal ) + ΔT
FS
ΔT =
Time Span
Number of Trace Points
(3-1)
(3-2)
The sampling rate is set such that an integer number of the signal period plus a
small time increment occurs between successive sampling points. This means that each
sampling point represents the value of the RF signal, which is slightly moved on the RF
waveform in time compared to its previous point. As a result, the sampling points create a
time-stretched replica of the RF signal as shown in Figure 3-5. The maximum sampling
frequency is approximately 20 MHz (50 ns/point) [53].
The value of ∆T determines the resolution of the down-converted signal.
Decreasing the value of ∆T reduces the time step with which the sampling point moves
over the waveform and, hence, increases the resolution of the resulting IF signal.
38
3.4 System Calibration
In the developed measurement system, the measurements are performed at the MTA as
ratios between channel 1 as a measuring channel for the incident and reflected waves and
channel 2 as a reference. These raw measurements have to be de-embedded to get the
real measurements at the DUT terminals. At the beginning, the system can be verified for
linear measurements by calibrating it using either thru-reflect-line (TRL) calibration
algorithm [54-62] or open-short-load-thru (OSLT) calibration algorithm [51, 63-70].
The calibration algorithm used for the system verification step is based on making
full calibration for port 1 using the OSL standards and then making two-port calibration
by connecting a thru standard between port 1 and the remaining ports of the multi-port
measurement system [64].
The multi-port measurement system shown in Figure 3-1 can be described as a
measuring two-channel receiver, which is the MTA, a switching test-set network and the
N-port DUT.
Figure 3-6: Block diagram of the N-port calibration procedure
39
The switching network is modeled by the error boxes between the MTA and the
DUT planes, as shown in Figure 3-6. In order to get the actual S-parameters of the DUT,
the error box parameters, which are frequency dependent, should be identified and used
together with the measured raw S-parameters at the MTA plane. The error box (EK)
represents the transformation from each port of the DUT to the measuring channels of the
MTA and can be described using the following equation [64]:
⎡ e k e12k ⎤
E K = ⎢ 11k
k ⎥
⎣e21 e22 ⎦
(3-3)
where k = 1, 2, 3, ………, N and N is the number of ports of the DUT.
The first error box, E1, between the MTA measuring plane and port 1 of the
developed multi-port measurement system can be described in terms of S-parameters as
shown in Figure 3-7.
e121
e111
e122
e121
Γ1dut
Γ1m
Figure 3-7: Signal flow graph for the error box between port 1 of the MTA and port
1 of the DUT
40
The measured S-parameters can be defined in terms of the measured incident and
reflected waves, am and bm , respectively, using equation (3-4).
bm = S m × am
(3-4)
The measured incident and reflected waves at the MTA plane can be defined as
follows:
⎡ a1m ⎤
⎢a ⎥
am = ⎢ 2 m ⎥
⎢ ⎥
⎢ ⎥
⎣ anm ⎦
(3-5)
⎡ b1m ⎤
⎢b ⎥
bm = ⎢ 2 m ⎥
⎢ ⎥
⎢ ⎥
⎣bnm ⎦
(3-6).
In order to measure the raw S-parameters of the N-port DUT, the RF generator
signal is routed to port 1 of the measurement system and then the incident and reflected
waves are measured at all ports of the DUT. Similar procedure is repeated while routing
the RF generator signal to the remaining ports of the measurement system. At the end of
these measurement steps, the incident and reflected waves ( am and bm ) of the DUT are
used in equations (3-4) for the calculation of the raw S-parameters of the DUT. The
41
calibration procedure to de-embed the raw S-parameters can be described in the
following steps.
Step 1:
In order to de-embed the S-parameters of the DUT, the error matrix, Ei, for each port has
to be calculated and applied to the raw S-parameters of the DUT. This calibration can be
performed in two steps. The first step is performed by making the OSL calibration for
port 1. Figure 3-7 shows the signal flow graph of the error box between port 1 of the
DUT and the MTA measuring port.
In this case, the reflection coefficient at port 1 of the DUT ( Γ1dut ) can be described
as a function of the measured reflection coefficient at the MTA plane ( Γ1m ) using the first
error box parameters, as shown in equation (3-7):
1
Γ1m = e11
+
1
1
Γ1dut − Δe1Γ1dut + e11
e121e12
=
1 − e122 Γ1dut
− e122 Γ1dut + 1
(3-7)
where:
(
1 1
1
Δe1 = e11
e22 − e121e12
)
(3-8)
By connecting the OSL at port 1 and applying equation (3-7), a system of three
linear equations can be established in a matrix form, as shown in equation (3-9):
42
⎡ ΓMopen ⎤ ⎡1 Γopen × ΓMopen
⎢Γ
⎥ ⎢
⎢ Mshort ⎥ = ⎢1 Γshort × ΓMshort
⎢⎣ ΓMload ⎥⎦ ⎢⎣1 Γload × ΓMload
1
⎤
− Γopen ⎤ ⎡ e11
⎢ 2 ⎥
⎥
− Γshort ⎥ × ⎢ e22 ⎥
− Γload ⎥⎦ ⎢⎣Δe1 ⎥⎦
(3-9)
where Γopen , Γshort and Γload are the actual and known reflection coefficients of the OSL
standards; and, ΓMopen , ΓMshort and ΓMload are the measured reflection coefficients of the
OSL standards using the MTA.
The parameters of the first error box can be calculated using the following
equation:
1
⎤ ⎡1 Γopen × ΓMopen
⎡ e11
⎢ 2 ⎥ ⎢
⎢ e22 ⎥ = ⎢1 Γshort × ΓMshort
⎢Δe1 ⎥ ⎢⎣1 Γload × ΓMload
⎣ ⎦
−1
− Γopen ⎤
⎡ ΓMopen ⎤
⎥
− Γshort ⎥ × ⎢⎢ΓMshort ⎥⎥
⎢⎣ ΓMload ⎥⎦
− Γload ⎥⎦
(3-10)
Step 2:
The second step of the calibration procedure is performed by connecting the thru standard
between port 1 and the remaining (N-1) ports of the measurement system in order to
evaluate the coefficients of the error boxes between these ports and the MTA plane.
These error coefficients are calculated by using the measured raw S-parameters when the
thru standards are connected between port 1 and port k using equations (3-11), (3-12), (313) and (3-14).
1k
1
S mT 11
− e11
e =
1k
1
t11 + e122 ( S mT 11
− e11
)
k
22
(3-11)
43
1 1
t11 = e11
e22 − Δe1
T 1k
e11k = S mkk
−
t kk e122
k
1 − e122 e22
t kk = e e = S
k k
12 21
(3-12)
T 1k
mk 1
S
T 1k
m1k
(3-13)
(1 − e
−
)
1 k 2
22 22
e
t11
(3-14)
where k is the port number and S mT 1k is the measured S-parameters of the thru standard
connected between port 1 and port k.
The term t kj characterizes the path between port k and port j using equations (315), (3-16) and (3-17) for j=2, 3, ... , N-1, where N is the number of ports. Step 2 is
repeated until k=N to determine the error coefficients of A and Γ22 described in equations
(3-19) and (3-20).
(
)
(3-15)
(
)
(3-16)
k
t1k = S mT11kk 1 − e122e22
T 1k
1 k
tk1 = S mk
1 1 − e22 e22
tkj =
tk 1t1 j
t11
(3-17)
Step 3:
After calculating all the error coefficients between the N ports of the DUT and the MTA
plane, the last step is the de-embedding of the S-parameters of the DUT using these error
44
box coefficients and the raw S-parameters of the DUT. The de-embedding process can be
described using the following relations [64]:
S = A × ( I + Γ22 × A) −1
(3-18)
where:
(
1
⎡ S m11 − e11
⎢
t11
⎢
⎢ S m 21
A=⎢
t 21
⎢
⎢
⎢ S mN 1
⎢⎣
t N1
)
(S
m 22
1
− e11
S m1N
t1N
Sm2 N
t2 N
)
t 22
(S
mNN
− e11N
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦
(3-19)
)
t NN
2
3
Γ22 = diag (e122 , e22
… , e22N )
, e22
(3-20)
⎡1
⎢0
I =⎢
⎢
⎢
⎣0
(3-21)
0
1
0⎤
0⎥⎥
⎥
⎥
1⎦
Step 4:
All of the above calibration steps have to be performed for all frequencies of interests,
and in most cases for the harmonics of the fundamental frequency.
The flow chart shown in Figure 3-8 describes the steps of the applied calibration
algorithm. The function (g) in the flowchart relates the measured reflection coefficients
of the OSL standards to their known values as described in equation (3-9), while the
function (h) relates the measured S-parameters of the thru to the known values as
described in step 2 of the calibration algorithm.
45
Figure 3-8: Flowchart of the calibration algorithm for the multi-port measurement
setup
46
This calibration algorithm has the advantage of calculating the error box
parameters of each port k with reference to port 1 with only thru connection between
them. It also takes into consideration the crosstalk between ports, which leads to accurate
results compared to other calibration algorithms.
3.5 System Verification
After developing the measurement system, it is very important to verify its stability and
repeatability. It is also crucial to make sure that the algorithm used for calibration is
giving good results. Therefore, measurements of S-parameters for several components
and devices have been conducted to ensure the system stability, robustness, and the
accuracy of the calibration algorithm.
3.5.1 Two-port measurement verifications
The S-parameters of 3 dB and 6 dB attenuators have been measured using the developed
measurement system and then compared to the measurements obtained using a
commercial VNA at 4 GHz frequency with 0 dBm input power as described in Table 3-2
and Table 3-3, respectively.
An excellent agreement between the results of Agilent N5230A VNA and the
proposed measurement setup based on HP 70820A MTA has been achieved.
A
maximum phase shift of 0.4 degree between the VNA and the MTA-based system has
been obtained for S12 and S21.
47
Table 3-2: Measured S-parameters for 3dB attenuator at 4 GHz frequency and 0
dBm input power
VNA Results
Meas. Setup
S-parameters
Magnitude
Phase
Magnitude
Phase
S11
-34.53 dB
-65.1°
-35.53 dB
-165.1°
S12
-3.01 dB
-28.18°
-2.98 dB
-27.88°
S21
-3.11 dB
-27.87°
-3.06 dB
-27.65°
S22
-32.23 dB
23.42°
-32.11 dB
-118.6°
Table 3-3: Measured S-parameters for 6dB attenuator at 4 GHz frequency and 0
dBm input power
VNA Results
Meas. Setup
S-parameters
Magnitude
Phase
Magnitude
Phase
S11
-35.23 dB
73.64°
-35.1 dB
5.29°
S12
-5.92 dB
-30.05°
-5.84dB
-29.64°
S21
-6.03 dB
-29.94°
-5.95 dB
-29.98°
S22
-31.68 dB
-146.9°
-31.49 dB
83.34°
The phases of S11 and S22 for 50Ω are not relevant information because the
reflection coefficients at the input and output ports are very small for both 3 dB and 6 dB
attenuators.
48
3.5.2 Multi-port measurement verifications
In order to validate the system capability for multi-port device characterization, a
commercial 3 dB power divider, ANAREN 41620 with isolation 15 dB, VSWR 1.6, input
and output insertion loss 0.75 dB maximum, amplitude balance 0.4 dB, and phase
balance 88° has been measured using the developed measurement system and the results
have been compared to those obtained using a commercial VNA.
The measurement process started by calibrating the system for three-port
measurements over the frequency range of 0.5 to 3 GHz with 0 dBm input power. The Sparameters of the 3 dB power divider have been obtained in one measurement step using
the developed multi-port measurement system, while they have been obtained with
successive two-port measurements steps using a two-port commercial VNA.
Good agreement between the proposed measurement setup and the commercial
VNA has been obtained [71]. Figure 3-9 shows the return losses measurements at ports 1
and 3 of the 3 dB power divider. Figure 3-10 shows the return loss measurements at port
2 of the 3 dB power divider. The transmission coefficients between the input port (port
1) and the two output ports (port 2 and port 3) are shown in Figure 3-11 and Figure 3-12,
respectively. The isolation between ports 2 and 3 is shown in Figure 3-13.
49
-10
-15
Magnitude (dB)
-20
-25
-30
S11 VNA
S33 VNA
S11 Developed Setup
S33 Developed Setup
-35
-40
0
0.5
1
1.5
2
2.5
3
Frequency (GHz)
Figure 3-9: Return losses at ports 1 and 3 of the 3 dB power divider (VNA vs.
developed setup) [71]
-10
Developed Setup
VNA (P2,P3 connected)
VNA (P2,P1 connected)
-12
Magnitude S22 (dB)
-14
-16
-18
-20
-22
-24
-26
-28
-30
0
0.5
1
1.5
2
2.5
3
Frequency (GHz)
Figure 3-10: Return loss at port 2 of the 3 dB power divider (VNA vs. developed
setup) [71]
50
-2
Magnitude (dB)
-2.5
-3
-3.5
S12 Developed Setup
S21 Developed Setup
S12 VNA
S21 VNA
-4
-4.5
0
0.5
1
1.5
2
2.5
3
Frequency (GHz)
Figure 3-11: Transmission coefficients between ports 1 and 2 for the 3 dB power
divider (VNA vs. developed setup) [71]
-2
Magnitude (dB)
-2.5
-3
-3.5
-4
-4.5
S13 Developed Setup
S31 Developed Setup
S13 VNA
S31 VNA
0
0.5
1
1.5
2
2.5
3
Frequency (GHz)
Figure 3-12: Transmission coefficients between ports 1 and 3 for the 3 dB power
divider (VNA vs. developed setup) [71]
51
-10
-15
Magnitude (dB)
-20
-25
-30
-35
-40
S23 Developed Setup
S23 VNA
S32 Developed Setup
S32 VNA
-45
-50
0
0.5
1
1.5
2
2.5
3
Frequency (GHz)
Figure 3-13: Isolation between ports 2 and 3 for the 3 dB power divider (VNA vs.
developed setup) [71]
Figure 3-14 and Figure 3-15 show the ability of the system to give accurate results
with input power variation without the need for recalibration. The system was first
calibrated at 0 dBm input power, and the first set of measurements was performed. After
that, the system was driven with a 10 dBm input power, and another set of measurements
for the same 3 dB power divider was taken. As shown in Figure 3-14 and Figure 3-15,
there is good agreement between the two sets of measurements.
52
-2
S12 (Pin=0 dBm)
S21 (Pin=0 dBm)
S12 (Pin=10 dBm)
S21 (Pin=10 dBm)
Magnitude (dB)
-2.5
-3
-3.5
-4
-4.5
0
0.5
1
1.5
2
2.5
3
Frequency (GHz)
Figure 3-14: Transmission coefficients between ports 1 and 2 for the 3 dB power
divider at Pin=0 dBm and Pin=10 dBm [71]
The reason for this is due to the fact that the proposed measurement system is
built to measure the ratio between the waves at port 1 and port 2 of the MTA where port
2 is considered as reference. Actually, the reference signal at port 2 of MTA is part of the
driving RF signal connected to the MTA via the power divider, so when the input RF
signal is changed the reference signal is also changed and the ratio between port 1 and
port 2 of the MTA is kept constant for different input power levels.
53
-2
S13 (Pin=0 dBm)
S31 (Pin=0 dBm)
S13 (Pin=10 dBm)
S31 (Pin=10 dBm)
Magnitude (dB)
-2.5
-3
-3.5
-4
-4.5
0
0.5
1
1.5
2
2.5
3
Frequency (GHz)
Figure 3-15: Transmission coefficients between ports 1 and 3 for the 3 dB power
divider at Pin=0 dBm and Pin=10 dBm [71]
3.6 Summary
This chapter presented the architecture of the developed multi-port measurement system
with a description of the MTA function as a multi-harmonic receiver from DC to 40 GHz.
The chapter shows the advantage of employing the MTA in the developed measurement
system as a general-purpose, multi-domain tool that can be used to link the new timedomain measurements with the traditional frequency-domain techniques, particularly in
the areas of pulsed-RF and nonlinear device characterization.
The system has been validated with some linear measurements for two-port and
multi-port passive devices and the measurements were compared with a commercial
VNA to show the robustness and the accuracy of the developed system.
54
Chapter Four: Complex Distortion Measurements of the Nonlinear Microwave
Systems
4.1 Introduction
The nonlinearity of RF power amplifiers is one of the major concerns in the design of
modern radio communication systems. The key point in the design of such
communication systems is to achieve highly linear power amplification with
simultaneous high conversion efficiency.
To improve the power amplifier efficiency without compromising its linearity,
power amplifier linearization is essential. In order to perform the different linearization
techniques, a precise behaviour model that represents the nonlinearity of high-power
amplifiers, is necessary. This model can be obtained by making large-signal
characterization of the power amplifier to extract the most important figures of merit such
as AM-AM, AM-PM, output power, gain, and power-added efficiency.
The power amplifier figures of merit are highly affected by the variations of the
output load impedance [72]. The effect of output load impedance variation on the
performance of power amplifier is called the load-pull effect. Load-pull measurements
are widely used in radio frequency power amplifier design and characterization because
they allow the direct measurement of the device under test at actual operating conditions.
By varying the source and load impedances for given biasing conditions, the performance
of the transistor can be optimized to meet the desired performance, in terms of output
power, linearity and/or power-added efficiency of the transistor [73].
55
A lot of research work has been done for the AM-AM and AM-PM
characterization of power amplifiers [73-88]. Usually, AM-AM and AM-PM
characteristics are extracted with a VNA [73-75]. Other techniques have been proposed
for the same purpose using six-port reflectometers [76, 77] or power detectors and
oscilloscopes [78]. These measurement systems have been designed to characterize the
two-port DUT using load-pull measurements at either the fundamental frequency or at the
fundamental frequency and a number of harmonics.
As described in Chapter Three, the system has been calibrated and verified for the
linear two-port and multi-port measurements. This chapter describes how the developed
multi-port measurement system is suitable for the large-signal characterization of the
multi-port power amplifiers at the fundamental frequency and its harmonics in a one-step
measurement connection, which increases the accuracy and the credibility of the
measured results.
4.2 Two-Port Measurements
In this section, the developed system is verified for two-port nonlinear characterization
with and without output loading effect. The measurement process starts by calibrating the
system for two-port measurements at 1 GHz frequency using the calibration algorithm
described in Chapter Three.
56
4.2.1 Characterization of a single-input single-output (SISO) PA without crosstalk
This section describes the characterization of two-port devices without crosstalk at the
output. A commercial two-port power amplifier ZFL-2500, was tested and characterized
using the developed measurement system and the results have been compared to the
specifications given in the datasheet of the DUT [89]. The characteristics of ZFL-2500
are: operating frequency range = 0.5-2.5 GHz, gain = 31 dB, voltage standing wave ratio
= 2.5 and maximum output power @ 1dB compression = 15 dBm.
Figure 4-1 and Figure 4-2 show the AM-AM and AM-PM characteristics of the
ZFL-2500 amplifier at 1 GHz, respectively. The two figures accurately match the
specifications of the amplifier given in the datasheet.
Figure 4-1: Measured direct conversion AM-AM for the ZFL-2500 amplifier using
the developed measurement system at 1 GHz [88]
57
Figure 4-2: Measured direct conversion AM-PM for the ZFL-2500 amplifier using
the developed measurement system at 1 GHz [88]
The system provides the capability of measuring the AM-AM and AM-PM direct
conversions for the harmonics as well as the fundamental frequency. In this case the
system was calibrated at 0.5 GHz fundamental frequency and three harmonics. A
complex harmonics characterization for the same amplifier is shown in Figure 4-3 and
Figure 4-4. These two figures show the behaviour of the 2nd, 3rd and 4th harmonics in
different regions of the PA operation at 0.5 GHz input signal.
In Figure 4-4, it is worth noticing that the phase distortion of the harmonics
occurred in the transition region, and there was almost no distortion when the amplifier
was driven beyond saturation: this contradicts the results for the fundamental frequency
[88]. Such harmonic distortion measurements cannot be obtained using spectrum or
58
conventional network analyzers, since the conventional network analyzer does not have
the ability to measure the magnitude and phase of the harmonics. Also, the spectrum
analyzer can measure the magnitude of the harmonics only and does not have the ability
to measure the phase of the spectrum at the same time.
Figure 4-3: AM-AM of harmonics for the ZFL-2500 PA using the developed
measurement system at 0.5 GHz [88]
59
Figure 4-4: AM-PM of harmonics for the ZFL-2500 PA using the developed
measurement system at 0.5 GHz [88]
4.2.2 Characterization of a dual branch PA with crosstalk
To show the crosstalk effect on the efficiency of the PA, a balanced PA designed at 1
GHz, as shown in Figure 4-5, was characterized using the developed measurement
system.
The balanced PA consisted of two amplifier branches, based on the FLL351ME
high-power gallium arsenide (GaAs) field-effect transistor (FET) from Fujitsu, with input
and output matching circuits. The matching circuit at the input was designed by
conventional circuit techniques to obtain maximum power gain and low input return loss
and to improve device stability. The output matching circuit was designed to achieve
maximum output power at the fundamental frequency and a perfect reflection for the
60
second and third harmonics. Two balanced-to-unbalanced transformers (baluns) were
also designed at 1 GHz. The first balun was used to distribute out of phase the input
signal to the two inputs of the amplifier. The second balun was used to combine the two
outputs of the amplifier into a single output so that the two-branch PA can be operated as
a push-pull amplifier or class-D RF amplifier, as shown in Figure 4-5. The ZHL-42W PA
driver was used to provide the balanced amplifier with a suitable input power for the
measurements.
Figure 4-5: Balanced PA using FLL351ME GaAs FETs from Fujitsu with crosstalk
at the output
To emulate the cross coupling between branches, which may take place in real
systems and in particular for integrated designs, two bi-directional couplers with a certain
coupling factor have been connected to the outputs of the PA. The coupling ports of the
couplers are then connected together with a segment of coaxial line, as indicated in
Figure 4-5, to provide a crosstalk path between the two amplifier branches. Three
61
different sets of measurements were performed using bi-directional couplers with 6 dB,
10 dB and 20 dB coupling factors.
Figure 4-6 shows the efficiency of the balanced PA at different crosstalk levels
using 20 dB, 10 dB, and 6 dB bi-directional couplers to provide crosstalk between the
two output branches of the balanced PA.
Compared to the efficiency of the PA without the crosstalk effect, it is obvious
that the efficiency decreased as the coupling effect between the two branches of the PA
increased. This is because of the variation of the output impedance seen by the PA due to
the variation of the output coupling between the two branches [88]. This impedance
variation results in output power variation, which affects the overall efficiency of the
balanced PA.
Figure 4-6: Efficiency of the balanced PA with different output coupling effects [88]
62
4.3 Multi-Port Measurements
The proposed system was previously tested with multi-port passive components and the
measurement of the S-parameters showed good agreement with the ones obtained with a
commercial VNA, as described in Chapter Three.
In this section, the system is used to characterize multi-port nonlinear devices to
prove the ability of the system to assess the impact of crosstalk between the two branches
of the PA on the performance of a single-input dual-output power amplifier [87]. In this
case, the output balun shown in Figure 4-5 was removed, and the crosstalk between the
two branches of the balanced PA was emulated by adding two bi-directional couplers at
the outputs of the two amplifier branches (Amp1 and Amp2), as in the previous case of
SISO two branch PA with crosstalk.
4.3.1 Characterization of a single-input dual-output (SIDO) PA without crosstalk
In this case, the characterization of the SIDO PA was performed without adding cross
coupling between the two branches of the balanced PA, in order to be able to compare the
characteristics of the PA without crosstalk with those after adding the crosstalk effect.
Figure 4-7 and Figure 4-8 show the AM-AM and AM-PM conversions and the
gain and efficiency of Amp1 and Amp2, without a coupling effect at the output. Both
Amp1 and Amp2 reached saturation at an input power of 25 dBm with maximum output
power of 32 dBm. In this case, the maximum gain is 8 dB, the drain efficiency was
around 45%, and the phase shift between the outputs of both amplifiers was about 180°,
as anticipated.
63
Figure 4-7: AM-AM and AM-PM of the two amplifiers without output coupling [88]
Figure 4-8: Gain and efficiency of the two amplifiers without output coupling [88]
64
4.3.2 Characterization of a single-input dual-output (SIDO) PA with crosstalk
In order to show the ability of the proposed multi-port measurement system to track the
crosstalk effect, the same characteristics of the two amplifier branches are measured with
20 dB, 10 dB and 6 dB bi-directional couplers connected at the output of the two
branches to provide crosstalk between the output ports of the PA, as shown in Figure 4-9,
Figure 4-10, Figure 4-11, Figure 4-12, Figure 4-13, and Figure 4-14.
Figure 4-9: AM-AM and AM-PM of the amplifiers with 20 dB output coupling [88]
65
Figure 4-10: Gain and efficiency of the amplifiers with 20 dB output coupling [88]
Figure 4-11: AM-AM and AM-PM of the amplifiers with 10 dB output coupling [88]
66
Figure 4-12: Gain and efficiency of the amplifiers with 10 dB output coupling [88]
Figure 4-13: AM-AM and AM-PM of the amplifiers with 6 dB output coupling [88]
67
Figure 4-14: Gain and efficiency of the amplifiers with 6 dB output coupling [88]
Reading the curves in Figure 4-9, Figure 4-10, Figure 4-11, Figure 4-12, Figure
4-13, and Figure 4-14 and comparing them with the curves in Figure 4-7 and Figure 4-8,
it is obvious that the crosstalk between the two branches of the balanced PA negatively
affects the gain and the efficiency of the PA. The gain and efficiency started to decrease
when the cross coupling between the two branches started to increase, until the PA lost
about 3dB in gain and about 10% in efficiency with a 6 dB cross coupling between the
two branches of the PA.
The output power variation for the two PA branches resulted from the changing of
the output impedances seen by the two amplifiers, due to the coupling effect between
them [88]. The phase of the output signals was shifted up and down, depending on the
68
phase characteristics of the bi-directional couplers used to emulate the coupling effect,
but the phase difference between the two outputs was almost 180° in all cases.
4.4 Summary
In this chapter, the capability of the developed measurement system to extract the most
important figures of merit for the two-port and multi-port PAs has been demonstrated.
The measurements described in this chapter show that the system can measure the
AM-AM and AM-PM conversions for the fundamental and harmonic frequencies for
nonlinear microwave devices on a single step measurement without any need for
reconnection or change in the calibration technique or the measurement setup.
As described in the measurement results, the system can accurately quantify the
impact of the crosstalk on the performance of the multi-port nonlinear microwave
systems in terms of power efficiency and signal distortion.
69
Chapter Five: Proposed De-Embedding Technique for On-Wafer Power Flow
Measurements
5.1 Introduction
The complete active power characterization of the on-wafer microwave devices under
large-signal behaviour requires extraction of several parameters at the device terminals,
such as input impedance, load impedance and absolute power measurements. The
absolute power calibration requires direct connection of the power meter sensor at the
reference plane, which is possible if the reference plane is coaxial. For the on-wafer
absolute power calibration, the connection of the coaxial power sensor is impractical;
therefore, there is a need for a de-embedding algorithm to calculate the absolute power at
the on-wafer device terminals.
As described in Chapter Two, several power de-embedding calibration algorithms
have been proposed [9-18].
In this chapter, an absolute power and impedance de-embedding technique that
can be applied for 50 Ω and non 50 Ω impedance environments to perform on-wafer
passive source- and load-pull measurements is proposed.
The proposed calibration algorithm has certain advantages over other reported
methods:
•
Using the proposed technique, not only on-wafer power de-embedding can be
done, but also impedance measurement can be performed for 50 Ω and non 50
Ω terminated devices.
70
•
The proposed calibration algorithm is relatively simple to use in practical
applications because it is based only on reflection coefficient measurements
using the OSL standards. In case that the OSL technique is not suitable, the
TRL technique can be used and the errors box parameters can be related
directly to the parameters obtained by the TRL algorithms [90].
The proposed calibration algorithm can be applied to any two-port or multi-port
network analyzer. The measurements discussed in this chapter were obtained by applying
the proposed calibration algorithm to the developed multi-port measurement system.
5.2 General Calibration Procedure
The proposed calibration algorithm for power flow and impedance measurements is
based on reflection measurements using two sets of the OSL standards. The first set is
coaxial OSL standards, which are connected at the end of the coaxial plane, to determine
the error parameters between the measuring plane and the coaxial plane. The second set
is on-wafer OSL standards, which are connected at the on-wafer plane, to determine the
error parameters from the end of the coaxial plane to the end of the on-wafer plane.
5.2.1 The power flow calibration method
The absolute power measurement of a non-coaxial DUT is difficult as it is not possible to
connect the DUT to a coaxial power meter sensor. In this case, the device has to be
mounted on a test fixture with coaxial connectors, in order to be able to measure the
71
power at these coaxial connectors, and then find a way to de-embed this power at the
DUT terminations.
ΓA′ PA′
Γ1m
ΓA PA
PB ΓB
PB′ ΓB′
Γ2m
Figure 5-1: On-wafer absolute power calibration procedure [91]
With this test fixture, two error boxes (A'1 and A1) have to be determined to deembed the power at the DUT plane as shown in Figure 5-1. The first error box (A'1)
represents the transformation from the MTA receiver plane to the coaxial plane. The
second error box (A1) models the transformation from the coaxial plane to the on-wafer
plane [91].
For simplicity, only one port is considered in the analytical description of the
calibration procedure as shown in Figure 5-2, since the same equations are valid for the
second port.
The signal flow graph in Figure 5-2 shows that the first and second error boxes
can be described using S-parameters, eij′ and eij , respectively.
72
Coaxial Plane
Coaxial Plane
A'1
A1
e'21
e21
e'11
MTA
Non-Coaxial Plane
e'22
e11
e'12
e22
DUT
e12
A
1m
A
Figure 5-2: Signal flow graph for error boxes between port1 of the MTA and port1
of the DUT
Solving the signal flow graph shown in Figure 5-2, the reflection coefficient at the
coaxial plane ( Γ' A ) and the non-coaxial plane ( ΓA ) can be calculated as follows [91]:
Γ1m =
(e12′ e21′ − e11′ e22′ )ΓA′ + e11′ = A′ΓA′ + B′
(− e22′ )ΓA′ + 1
C ′ΓA′ + 1
(5-1)
ΓA′ =
(e12e21 − e11e22 )ΓA + e11 =
(− e22 )ΓA + 1
(5-2)
AΓA + B
CΓA + 1
where eij′ and eij are the entries of the scattering matrices [A′1] and [A1], respectively.
Also, parameters A′, B′, C′ and A, B, C are the three complex constants modeling the
matrices [A′1] and [A1], respectively. These parameters can be calculated by connecting
three known standards (OSL) successively at the coaxial and non-coaxial planes of
73
Figure 5-2. The three complex parameters, A′, B′ and C′, can be expressed using the
following three equations [91]:
B' = Γload
C' =
(5-3)
Γ'short (Γopen − Γload ) + Γ'open (Γload − Γshort )
Γ'short Γ'open (Γshort − Γopen )
A' = ΓopenC '+
(Γopen − Γload )
Γ'open
(5-4)
(5-5)
The power flow at the coaxial plane (P'A) is related to the error matrix [A′1], the
reflection coefficient at coaxial plane ( Γ' A ), the sampled power reading at the MTA plane
(PSA), and the power calibration constant (k′A) as follows [91]:
PA′ =
k ′A PSA
1 2
a1′ =
2
2
1 + C ' ΓA′
(5-6)
The unknown power flow calibration factor (k′A) can be obtained via a power
calibration procedure by connecting a coaxial power meter to the coaxial port at the
output of the first error box network and its value can be obtained using the following
equation:
74
PPWM
(
)
(
k ′ P 1 − ΓA′
1 2
2
= a1′ 1 − ΓA′ = A SA
2
2
1 + C ' ΓA′
2
)
(5-7)
where PSA is the sampled power reading at the MTA plane and PPWM is the absolute
power reading of a reference power meter connected at the coaxial plane.
The power calibration factor (k′A) can be calculated using the following equation:
k ′A =
PPWM 1 + C ' ΓA′
2
2
PSA (1 − ΓA′ )
(5-8)
Similarly, the power flow at the non-coaxial plane (PA) can be calculated as a
function of the sampled power (PSA) and the power calibration constant (kA) as follows:
PA =
1
k A PSA
2
a1dut =
2
2
1 + C ′′ΓA
(5-9)
Since the reference plane at the output of the second error box is a non-coaxial
port, no power calibration can be performed as described above for the first error box. It
can be demonstrated using equation (5-9) that the second power calibration parameter
(kA) given by equation (5-10) is related to the parameters (A, B, C, and C′) of the error
boxes (A1and A′1), the power calibration parameter (k′A) and the reflection coefficient at
the non-coaxial plane ( ΓA ) as follows [91]:
75
kA =
A − BC k ′A
1 + C ′ΓA
2
(5-10).
The power calibration factor (k′A) was previously determined by an absolute
power calibration at the coaxial plane. The A, B and C parameters are determined by a
calibration procedure similar to that used to determine A′, B′ and C′. The parameter, C′′,
in equation (5-9) is the entire value of the overall matrix containing the two error boxes
(A′1 and A1), and it can be calculated using the following relation:
C ′′ =
C ′A + C
C ′B + 1
(5-11)
Using equation (5-9), it is obvious that the power flow at the non-coaxial plane
can be calculated using the value of the sampled power reading and the calculated values
of the power calibration constant without any need to perform extra power calibration at
the non-coaxial plane.
5.2.2 On-wafer reflection coefficient measurements
Using the proposed calibration algorithm described in the previous section, it is also
possible to perform reflection coefficient measurements for on-wafer DUT. The two error
boxes shown in Figure 5-2 can be combined as one error box with eij′′ error matrix as
shown in Figure 5-3.
76
′′
e11
′′
e21
′′
e12
Γ1m
′′
e 22
Γdut
Figure 5-3: The overall error box between port 1 of the MTA and port 1 of the DUT
In this case, the incident and reflected waves at the MTA (a1m and b1m) and the DUT
planes (a1dut and b1dut) can be written as a function of the error box eij′′ as follows:
⎛ e′′ ⎞
⎛ e′′ e′′ − e′′ e′′ ⎞
a1dut = ⎜⎜ 12 21 11 22 ⎟⎟a1m + ⎜⎜ 22 ⎟⎟b1m
′′ ⎠
′′
e12
⎠
⎝ e12
⎝
(5-12)
⎛ − e′′ ⎞
⎛ 1 ⎞
b1dut = ⎜⎜ 11 ⎟⎟a1m + ⎜⎜ ⎟⎟b1m
′′ ⎠
′′ ⎠
⎝ e12
⎝ e12
(5-13).
′′ , one can define the
By multiplying equations (5-12) and (5-13) by α = 1 e21
normalized waves (a'1dut and b'1dut) at the DUT plane related to the measured waves (a1m
and b1m) at the MTA plane in terms of the error box parameters (A'', B'' and C''), that
model the two error boxes A'1 and A1 shown in Figure 5-2, as follows :
77
⎛ e′′ e′′ − e′′ e′′ ⎞
⎛ e′′ ⎞
B′′C ′′ ⎞
⎛
⎛ − C ′′ ⎞
a1′dut = ⎜⎜ 12 21 11 22 ⎟⎟a1m + ⎜⎜ 22 ⎟⎟b1m = ⎜1 −
⎟a1m + ⎜
⎟b1m
′′ e12
′′
′′ e12
′′ ⎠
e21
⎝ A′′ − B′′C ′′ ⎠
⎝ A′′ − B′′C ′′ ⎠
⎝
⎠
⎝ e21
(5-14)
⎛ − e′′ ⎞
⎛ 1 ⎞
1
⎞
⎛ − B′′ ⎞
⎛
⎟⎟b1m = ⎜
b1′dut = ⎜⎜ 11 ⎟⎟a1m + ⎜⎜
⎟a1m + ⎜
⎟b1m
′′ ⎠
′′ e12
′′ ⎠
⎝ A′′ − B′′C ′′ ⎠
⎝ A′′ − B′′C ′′ ⎠
⎝ e′21′ e12
⎝ e21
(5-15)
where a1′dut and b1′dut are the normalized versions of a1dut and b1dut respectively.
The complex error parameters, A' ' , B' ' and C ' ' , in equations (5-16) and (5-17)
can be defined using the following equations:
′′ e′21′ − e11
′′ e22
′′
A′′ = e12
(5-16)
′′
B′′ = e22
(5-17)
′′
C ′′ = −e11
(5-18)
These complex error parameters ( A' ' and B' ' ) for the overall error box can be
calculated based on the error parameters of the first and the second error boxes calculated
in the previous power de-embedding calibration steps using the following equations:
A′′ =
A′A + B′C
C ′B + 1
(5-19)
B′′ =
BA′ + B′
C ′B + 1
(5-20).
The same method can be applied to calculate the incident and reflected waves of
the DUT at port 2 using the following equations:
78
⎛
⎛ − C2′′ ⎞
B2′′C2′′ ⎞
⎟⎟a2 m + ⎜⎜
⎟⎟b2 m
a′2 dut = ⎜⎜1 −
⎝ A2′′ − B2′′C2′′ ⎠
⎝ A2′′ − B2′′C2′′ ⎠
(5-21)
⎛ − B2′′ ⎞
⎛
⎞
1
⎟⎟a2 m + ⎜⎜
⎟⎟b2 m
b2′ dut = ⎜⎜
⎝ A2′′ − B2′′C2′′ ⎠
⎝ A2′′ − B2′′C2′′ ⎠
(5-22)
where A'', B'' and C'' are the error box parameters that model the two error boxes, B'2 and
B2, shown in Figure 5-1.
Once the incident and reflected waves at the DUT plane have been determined
using equations (5-19), (5-20), (5-21), and (5-22), the reflection coefficients at the noncoaxial plane of the DUT can be calculated using equations (5-23) and (5-24).
′ 1 ) a′
S11dut = (b1′dut adut
2 dut
=0
S 22dut = (b2′ dut a2′ dut ) a′
1 dut =0
(5-23)
(5-24)
5.3 Measurement Results
This section describes the reflection coefficients and power measurements after applying
the proposed calibration algorithm described in the previous section on the developed
multi-port measurement system. The measurements have been performed for active and
passive microwave devices in 50 Ω and non 50 Ω environments.
5.3.1 Reflection and power de-embedding measurements for 50 Ω passive devices
The measurement process starts by calibrating the developed measurement system for the
two-port measurements using the proposed power de-embedding calibration algorithm in
79
section 5.2.1. Then, reflection measurements for several components and devices have
been conducted to ensure the system stability, robustness and the accuracy of the
calibration algorithm.
As described in section 5.2.1, to de-embed the power at the terminations of the
DUT, in a configuration similar to that presented in Figure 5-2, the two error boxes have
to be calculated first. In this setup, the first error box represents the transformation from
the MTA to the end of the coaxial cables. The following measurements for first and
second error boxes verification were performed for the 50 Ω system at 4 GHz frequency
with 0 dBm input power.
Table 5-1 gives the values of the first error box parameters and the reflection
coefficient of the three calibration OSL standards. These measurements were performed
with a commercial vector network analyzer and the proposed system at 4 GHz.
Table 5-2 shows the measurements in terms of the reflection coefficients of a 3dB
attenuator and a passive tuner, performed with the VNA and the developed system.
Table 5-3 shows the results of the power de-embedding at the end of the coaxial
plane.
The good agreement between the reflection measurements obtained using the
proposed system and a commercial VNA shows the efficiency and robustness of the
proposed calibration algorithm. Also, the absolute power de-embedding gives good
results compared to the power meter measurements [91].
80
Table 5-1: The first error box parameters and verification at 4 GHz and 0 dBm [91]
First Error Box
VNA Results
Meas. Setup
A′
0.328-j0.049
Open
1∠-52
Open
0.99∠- 52
B′
0.005 +j0.046
Short
1 ∠132
Short
0.98∠ 131.9
C′
-0.320-j0.207
Load
0.001∠-106
Load
0.001∠- 44
Table 5-2: The reflection measurement results of unknown loads at 4 GHz
frequency and 0 dBm input power [91]
Load
VNA Results
Meas. Setup
3dB (open-ended)
0.52∠-13.8
0.53∠-12.7
3dB (50 Ω-ended)
0.03∠-38.8
0.03∠-34.6
Impedance Tuner
0.30∠-81.5
0.31∠-81.7
Table 5-3: Power de-embedding results at the end of the coaxial plane at 4 GHz
frequency and 0 dBm input power [91]
Parameter
Value
Pin
0 dBm
K′ A
0.0059
Pcalculated
-9.21 dBm
Pmeasured
-9.20 dBm
Error
0.01 dB
81
The second error box represents the transformation from the coaxial cable to the
on-wafer terminal of the DUT. In order to verify the proposed absolute power flow
calibration technique at a non-coaxial plane, the second error box is simulated by a
coaxial 3dB attenuator. A coaxial sensor of a power meter can be connected to the end of
the second error box, and the verification of the de-embedded power can be easily
performed. Moreover, in order to show that the model of the second error box is valid for
non 50 Ω coaxial-non-coaxial transitions, an intentionally mismatched tuner was used in
place of the 3dB attenuator as the second error box as will be described section 5.3.2.
Table 5-4 includes the values of the second error box parameters (3dB attenuator)
and the three calibration standards measurement verifications. The measurements of
unknown loads connected to the end of the second error box are summarized in Table
5-5.
Table 5-4: The second error box parameters and verification for a 50 Ω system at 4
GHz frequency and 0 dBm input power [91]
Second Error Box
VNA Results
Meas. Setup
A
0.492+ j0.014
Open
1∠-52
Open
0.99∠ -52.3
B
0.024 - j0.016
Short
1∠132
Short
0.98∠131.4
C
-0.012+j0.032
Load
0.001∠-106
Load
0.004∠ 7.1
82
Table 5-5: The reflection measurement results of unknown loads for a 50 Ω system
at 4 GHz frequency and 0 dBm input power [91]
Load
VNA Results
Meas. Setup
3dB (open-ended)
0.52∠-13.8
0.5∠-13
3dB (50 Ω-ended)
0.03∠-38.8
0.02∠-41.3
Impedance Tuner
0.3∠-81.5
0.32∠ -81.1
Table 5-6: Power de-embedding results at the end of the on-wafer plane for a 50 Ω
system at 4 GHz frequency and 0 dBm input power [91]
Parameter
Value
Pin
0 dBm
KA
0.003
Pcalculated
-12.21 dBm
Pmeasured
-12.17 dBm
Error
0.04dB
In Table 5-6, the results of power de-embedding for a 50 Ω system (3dB
attenuator) are given. The power at the non-coaxial plane was calculated using equation
(5-9), which is a function of the power at the coaxial plane and the second error box
parameters without any power measurement at the non-coaxial plane.
83
5.3.2 Reflection and power de-embedding measurements for non 50 Ω passive devices
The same measurement procedure is also used for a non 50 Ω system using the
impedance tuner (with Γ = 0.3∠-81.18) as the second error box. Table 5-7, Table 5-8 and
Table 5-9 indicate that, the proposed technique for power de-embedding at the noncoaxial plane gives good results for a non 50 Ω system.
Table 5-7: The second error box parameters and verification for a non 50 Ω system
at 4 GHz frequency and 0 dBm input power [91]
2nd Error Box
VNA Results
Meas. Setup
A
-0.563-j0.758
Open
1∠-52
Open
0.98∠-53
B
0.040-j0.296
Short
1∠132
Short
0.99∠133
C
0.240-j0.177
Load
0.001∠-106
Load
0.004∠52
Table 5-8: The reflection measurement results of unknown loads for a non 50 Ω
system at 4 GHz frequency and 0 dBm input power [91]
Load
VNA Results
Meas. Setup
3dB (open-ended)
0.52∠-13.8
0.51∠-13
3dB (50 Ω-ended)
0.03∠-38.8
0.02∠-39.3
84
Table 5-9 shows the measurements for several tuner states to ensure that the
power calibration procedure is valid in a variable impedance environment. Therefore, the
developed measurement setup with the proposed calibration algorithm are suitable for
source- and load-pull characterization using passive tuners situated as close as possible to
the DUT plane.
Table 5-9: Power de-embedding results at the end of the on-wafer plane for a non 50
Ω system at 4 GHz frequency and 0 dBm input power [91]
Value
Γ = 0.1
Γ = 0.3
Γ = 0.5
Γ = 0.7
∠-45.13
∠-81.18
∠-131.02
∠140.74
Pin (dBm)
0
0
0
0
KA
0.0108
0.0061
0.0084
0.005
Pcalculated (dBm)
-6.35
-9.13
-6.72
-9.08
Pmeasured (dBm)
-6.53
-9.04
-6.82
-9.16
Error (dB)
0.17
0.096
0.1
0.08
Parameter
5.3.3 Power de-embedding measurements for active devices
The proposed power de-embedding technique can be easily extended to large-signal
measurements of active devices. This can be carried out by calibrating the system for
impedance and power flow measurements at the fundamental frequency and its
85
harmonics. In this case, the errors box and the power normalization factors can be
obtained for each frequency.
In this setup, a medium power amplifier, ZFL-2500, was tested and characterized
using the proposed measurement system for the fundamental and harmonics power
measurements. The device was driven at different input power levels to show that the
system is capable of de-embedding the power at the output of the amplifier in its linear
and nonlinear regions at the fundamental frequency and its harmonic.
The same power measurements were performed with a commercial spectrum
analyzer, Agilent E4405B, and the measurements were compared to the one obtained
using the proposed setup. Good agreement is obtained between both sets of
measurements as shown in Table 5-10 [91].
Table 5-10:
Power spectrum measurements for ZFL-2500 PA at 0.5 GHz
fundamental and three harmonics for different input power levels [91]
Input
Output power (dBm)
Output power (dBm)
Power
Measurement setup
Spectrum analyzer
(dBm)
@fο
@2fο
@3fο
@4fο
@fο
@2fο
@3fο
@4fο
-15
-3.53
-18.69
-28.5
-33
-3.62
-19.31
-29.14
-33.54
-12.5
-1.37
-15.39
-24.77
-30.73
-1.46
-16.67
-24
-30.86
-10
-0.42
-14.56
-19.64
-28.92
-0.58
-14.48
-19.9
-29.48
-7.5
0.25
-9.48
-19.94
-27.9
0.13
-9.6
-20.42
-28.5
86
5.4 Summary
This chapter presents the proposed reflection-based thru-less calibration algorithm for
simultaneously calculating the impedances and the absolute power flow at the DUT plane
with coaxial or non-coaxial terminations. The proposed calibration algorithm can be
applied for any two-port or multi-port vector network analyzer.
The calibration algorithm depends on calculating three complex error parameters
for each error box between the DUT terminal and the measuring plane of the multiharmonic receiver. This method requires two sets of the OSL calibration standards, one
coaxial and one coplanar. An absolute power calibration performed at the coaxial
reference planes using a reference power meter is also required for power measurement
purposes at the coplanar reference planes of the microwave probes.
The measurements discussed in this chapter have been obtained by applying the
proposed calibration technique on the developed multi-port measurement system
described in Chapter Two. The measurements demonstrate the ability of the calibration
algorithm and the measurement system to de-embed the power at the coaxial or noncoaxial terminals of the DUT for the 50 Ω and non 50 Ω environments. The developed
measurement system is also capable of performing large-signal frequency-domain
characterization of nonlinear transistors. The performance of the proposed system is
compared to that of the commercial ones, and the results prove the robustness of the
proposed calibration procedure and the measurement system [91].
87
Chapter Six: Proposed Calibration Algorithms for Waveform Measurements
6.1 Introduction
The thrust towards achieving the optimal performances from the microwave devices
forces them to operate in the nonlinear mode of operation. Power amplifier is one of the
most critical components in the microwave transmitters and is the major source of power
consumption as well as the signal distorter block. Therefore, the challenge for the PA
design is in the trade-off between efficiency and linearity. There are different techniques
for the PA design and optimization [48, 92-94]. In these techniques, the designers of the
RF PAs used to build their design approaches on figures of merit that can be measured in
the frequency-domain, such as bias dependent S-parameters, output power spectrum,
AM-AM and AM-PM direct conversion measurements.
In the last decades, the time-domain waveform measurement technique becomes
one of the most important tools for the design and optimization of RF PAs [46]. In fact,
the classification of the RF PAs according to their modes of operation is mainly based on
the voltage and current waveforms at the device terminals [46]. This makes the waveform
based design approach the emerging solution as the accurately measured voltage and
current waveforms at the device ports comprise the magnitudes and phase of all spectral
components generated by the nonlinear operation of microwave devices.
The measured waveforms can be analyzed in various ways to determine the
design parameters. These waveforms can be converted to the frequency domain and then
the spectral components can be plotted as a function of the input power, thereby
88
generating the same information familiar to traditional performance plots associated with
device characterization, for instance Pin/Pout, efficiency, etc. In the time domain, the
current and voltage can be plotted against each other, relating the familiar I-V plots of the
devices, such as the transfer characteristics, which are often captured by the DC curve
tracers. The measured waveforms also provide the complete visibility of the impedance
environments as a simple calculation of the V/I ratio present at the device port over the
entire spectra. Thus, it can be clearly concluded that the waveform measurement at the
device ports provides the complete information of the device behaviour.
As described in Chapter Two, different approaches have been developed for the
waveform measurements. The first approach is based on the sampling scope as a timedomain measuring instrument [19-26]. The second approach employs the VNA after
modifying it with certain test-set to be suitable for measuring the magnitude and phase of
the incident and reflected waves [32-34]. The third technique is built around the MTA as
a multi-harmonic receiver with time-domain measuring capability for microwave devices
from DC to 40 GHz [27-30, 35-38, 40]. The fourth technique is employing the six-port
reflectometer as a homodyne vector network analyzer [41].
The earlier reported nonlinear waveform measurement systems are capable of
measuring the absolute amplitudes and phases, but the majority of them rely on a certain
type of nonlinear golden standard [32, 33, 38, 40, 41], like step recovery diode, in
achieving the desired accuracy in phase calibration and measurements. Some
measurement systems rely on active device based standard phase reference generator [19,
20, 32, 35-37, 41].
89
Problems in achieving the desired accuracy using the existing measurement and
calibration strategies have resulted in reluctance, on the part of industry, to widely adopt
used waveform measurement techniques in designing nonlinear power amplifiers.
The majority of problems arise due to the non-generic calibration approach
adopted in the capture and correction of waveforms at the ports of microwave devices.
For example, the calibration approaches adopted in [14, 18-20, 28, 32, 33, 38, 40] are
either limited to two ports [14, 19, 20, 28, 32] or are very time-consuming [18, 20, 33, 38,
40], due to the number of steps involved.
The calibration algorithm for multi-port waveform measurement reported in this
work eliminates the need for the phase reference generator in the calibration process and
thus achieves inherent accuracy and reliability. The developed algorithm is simpler and
requires less computation steps and thus significantly expedites the measurement and
calibration time. Furthermore, the calibration algorithm does not rely on the use of a
multi-harmonic generator to achieve accurate waveform measurements. Additionally, this
work reports the use of the calibration algorithm on a multi-harmonic phase-locked
receiver, MHR, in the development of a reliable multi-port waveform measurement
system. Overall, this work provides an enhanced waveform measurement system and
calibration algorithm for the characterization, measurement, and modeling of microwave
devices.
In this chapter, the calibration algorithm proposed in Chapter Five will be
extended to multi-port relative waveform measurements. Then, the proposed calibration
90
algorithm for absolute waveform measurements will be discussed along with
measurement validations.
6.2 Relative Phase Calibration Algorithm for Waveform Measurements
The simplified block diagram for the developed multi-port measurement system is
presented in Figure 6-1.
Multi-Port Test-Set
Power
Divider
RF Generator
10 MHz
CH2
CH1
AParallel
Porta
AGPIBA
Multi
Harmonic
Receiver
Receiver Switching Matrix
Source Switching Matrix
Port N Port N-1
Port 2 Port 1
N-Port DUT
Computer
Figure 6-1: Simplified block diagram of the developed multi-port measurement
system [95]
91
The error model for the multi-port DUT connected between port 1 and port k of
the multi-port measurement system is presented in Figure 6-2 based on the entire Sparameters of each error box.
As described in Chapter Five, the power de-embedding calibration algorithm is
based on reflection measurements for the OSL calibration standards connected to each
k
k k
, e01
e10 and e11k ,
port of the measurement system to calculate the error parameters, e00
between the DUT and the MHR measuring plane for each port. Knowing these error
parameters for each error box, the incident and reflected traveling waves at the DUT
terminals (akdut and bkdut) can be calculated in terms of the measured incident and
reflected waves at the MHR plane (akm and bkm) by solving the signal flow graph shown
in Figure 6-2 for (n) number of frequencies as described in equations (6-1) and (6-2).
1
e10
1
e00
e10k
1
e11
k
e00
e11k
k
e01
e101
Figure 6-2: Error model for a multi-port DUT connected between port 1 and port k
of the multi-port measurement system
92
⎛ e k ( n ) e k ( n ) − e k ( n ) e k ( n ) ⎞ ( n ) ⎛ e11k ( n ) ⎞ ( n )
( n)
= ⎜⎜ 01 10 k ( n ) 00 11 ⎟⎟akm
+ ⎜⎜ k ( n ) ⎟⎟bkm
akdut
e01
⎝
⎠
⎝ e01 ⎠
(6-1)
⎛ − ek ( n) ⎞ ( n) ⎛ 1 ⎞ ( n)
(n)
⎟a + ⎜⎜ k ( n ) ⎟⎟bkm
= ⎜⎜ k 00
bkdut
( n ) ⎟ km
⎝ e01 ⎠
⎝ e01 ⎠
(6-2)
The above equations could not provide the required relation between the traveling
k
waves at the measuring plane and those at the DUT plane as the error parameters, e01
, in
the above equations is presented separately, while the calibration algorithm has calculated
k k
the error parameter, e01
e10 , as one term. Equations (6-1) and (6-2) can be modified by
multiplying them with the scaling factor α k( n ) = 1 e10k ( n ) to define the normalized waves
(n )
(n )
′(n ) and bkdut
′(n ) ) at the DUT plane, related to the measured waves ( akm
( akdut
and bkm
) at the
MTA plane, for fundamental and (n) number of harmonics as follows :
k (n) k ( n)
k (n) k (n)
⎛ e01
e10 − e00
e11 ⎞ ( n ) ⎛ e11k ( n ) ⎞ ( n )
( n)
′
⎜
⎟⎟akm + ⎜⎜ k ( n ) k ( n ) ⎟⎟bkm
akdut = ⎜
k (n) k ( n)
e
e
01
10
⎝
⎠
⎝ e01 e10 ⎠
(6-3)
⎛ − ek (n) ⎞ (n) ⎛
⎞ (n)
1
′( n ) = ⎜⎜ k ( n )00k ( n ) ⎟⎟akm
+ ⎜⎜ k ( n ) k ( n ) ⎟⎟bkm
bkdut
⎝ e01 e10 ⎠
⎝ e01 e10 ⎠
(6-4)
Equations (6-3) and (6-4) can be expressed in terms of the three complex error
parameters ( Ak(n ) , Bk(n ) , and Ck(n ) ) of the power calibration algorithm represented in
Chapter Five using equations (6-5) and (6-6).
93
⎞ ( n)
⎛
B ( n) C ( n ) ⎞ ( n) ⎛
− C ( n)
′(n) = ⎜⎜1 − (n) k (kn) ( n) ⎟⎟akm
akdut
+ ⎜⎜ ( n) k( n) (n) ⎟⎟bkm
⎝ Ak − Bk Ck ⎠
⎝ Ak − Bk Ck ⎠
(6-5)
⎞ ( n)
⎛
⎞ (n) ⎛
− Bk( n )
1
⎟b
′( n ) = ⎜⎜ ( n )
⎟a + ⎜⎜ ( n )
bkdut
( n ) ( n ) ⎟ km
( n ) ( n ) ⎟ km
⎝ Ak − Bk Ck ⎠
⎝ Ak − Bk Ck ⎠
(6-6)
where:
k (n) k (n)
k (n) k (n)
Ak( n ) = e01
e10 − e00
e11
(6-7)
k (n)
Bk( n ) = e00
(6-8)
Ck( n ) = −e11k ( n )
(6-9)
The normalized voltage and current, V' and I', at each port of the DUT can be
calculated and related to the absolute voltage and current, V and I, at each port of the
DUT plane for (n) frequencies using the following equations:
′( n ) + bkdut
′( n ) ) = α k( n )Vk( n )
Vk′( n ) = 2 Z 0 (akdut
(6-10)
′( n ) − bkdut
′( n ) ) = α k( n ) I k( n )
I k′( n ) = 2 Z 0 (akdut
(6-11)
where Z0 is the reference impedance of the measurement system.
The next step in the calibration process is the absolute power calibration at the
DUT plane in order to calculate the scaling factor ( α k( n ) ), which will be used to determine
the absolute voltage and current at the DUT plane. This can be performed using the
94
power calibration technique described in [91] for calculating the absolute power at the
DUT plane as follows:
(n)
Pkdut
=
β
(n)
k
=
(n)
1 (n) 2
β k( n ) × PkMTA
akdut =
k (n)
(n)
2
1 + (−e00
)Γkdut
( n)
( n)
k (n)
PPWM
1 + (−e00
)Γkdut
(6-12)
2
2
(6-13)
(n) ⎛
(n) 2 ⎞
PMTA
⎜1 − Γkdut
⎟
⎝
⎠
(n)
PkNORM
=
1 (n) 2
′
akdut
2
(6-14)
(n )
is the absolute power at the DUT plane,
where β k(n ) is the power calibration factor, Pkdut
(n )
(n )
PkNORM
is the normalized power at the DUT plane, PPWM
is the absolute reading of the
(n)
is the sampled power reading at the
power meter connected at the DUT plane, and PkMTA
MTA plane for each port of the DUT at the fundamental frequency and the harmonics.
The relation between the normalized and the absolute power at the DUT plane
described in equation (6-15) can be used to calculate the normalization power factor α k( n )
as illustrated in equation (6-16).
(α ) P
(n) 2
k
( n)
kdut
( )
1
( n) 2
( n)
= α k( n ) × akdut
= PkNORM
= α k( n )
2
2
( n)
β k( n ) × PkMTA
k (n)
(n)
1 + (−e00
)Γkdut
2
(6-15)
95
α
(n)
k
=
( n)
PkNORM
=
(n)
Pkdut
(n)
( n)
k (n)
PkNORM
× 1 + (−e00
)Γkdut
( n)
β × PkMTA
(6-16)
Once the normalized incident and reflected waves at the DUT terminals are
calculated using equations (6-5) and (6-6) and the normalization factor α k(n ) is calculated
using equation (6-16), the voltage and the current for the fundamental frequency and the
harmonics at the DUT terminals can be calculated using the well-known equations (6-17)
and (6-18).
(
)
(6-17)
(
)
(6-18)
Vk( n ) = 2Z 0 ak( n ) + bk( n )
I k( n ) = 2 Z 0 ak( n ) − bk( n )
where n represents the harmonic order, k is the port number, and Z0 is the characteristic
impedance of the measurement system.
The harmonic components, ak( n ) and bk( n ) , are measured by the MTA and their
phases are referenced to the phase of the fundamental component. Knowing the
fundamental and harmonic components of the voltage at the DUT plane, the voltage timedomain waveform can be reconstructed using the following relation:
n
vk( n ) (t ) = V0 k + ∑ Vk( n ) cos(2πnft − ϕ n )
n =1
(6-19)
96
where V0k is the direct current component, Vk( n ) is the magnitude of the fundamental
frequency and harmonics, n is the number of harmonics, f is the frequency of the
fundamental, and φn is the phase of the nth harmonic.
6.3 Relative Waveform Measurement Results
The previous calibration algorithm has been applied to the developed measurement
system for waveform measurements of the two-port and multi-port microwave active
devices as will be described in the following sections.
6.3.1 Two-port waveform monitoring
In this setup, a medium power amplifier, ZFL-2500 [89], was tested and characterized in
terms of input and output time-domain voltage waveforms, with the developed system
and calibration algorithm. The same characterization was performed with a commercial
high-speed digital oscilloscope, Tektronics TDS 794D [96], and compared to the
measurements obtained using the developed system in order to verify the voltage timedomain waveforms. The proposed measurement system was calibrated at the fundamental
frequency of 500 MHz and four harmonics were taken into account to construct the
voltage waveform, since the bandwidth of the digital oscilloscope was 2 GHz. The device
was driven at different input power levels to determine the ability of the system to
recover the signal in the linear and nonlinear regions of the amplifier.
Figure 6-3 and Figure 6-4 show the comparison between the reconstructed
waveform and the waveform seen by the TDS 794D oscilloscope for two different input
97
power levels. The overall view of the measured waveforms in Figure 6-3 and Figure 6-4
indicates that the proposed measurement system is able to reconstruct and characterize
the waveform directly at the non-coaxial terminals of the transistor for both linear and
nonlinear modes of operation.
0.3
0.2
Voltage
0.1
0
-0.1
-0.2
Scope
Setup
-0.3
2
4
Time
6
8
x 10
-9
Figure 6-3: Waveform comparison between the scope and the measurement setup
for ZFL-2500 PA at -10 dBm input power [97]
Some deviations have been observed in the waveform obtained by the developed
system at high input power, as shown in Figure 6-3, due to the phase ambiguity in the
k k
error parameter, e01
e10 , calculated using relative waveform calibration algorithm. The
effect of this phase ambiguity is neglected when the device is working in its linear mode,
as observed in Figure 6-4.
98
0.2
Voltage
0.1
0
-0.1
-0.2
Scope
Setup
2
4
Time
6
8
x 10
-9
Figure 6-4: Waveform comparison between the scope and the measurement setup
for ZFL-2500 PA at -15 dBm input power [97]
0.3
0.2
Voltage
0.1
0
-0.1
-0.2
pin= -12.5 dBm
pin= -10 dBm
pin= -7.5 dBm
pin= -5 dBm
-0.3
-0.4
1
2
3
4
5
Time
6
7
8
x 10
-9
Figure 6-5: Output waveforms of ZFL-2500 PA for several input powers using the
measurement setup [97]
99
Figure 6-5 shows the reconstructed output waveform of the amplifier for several
input powers. It is clear that the distortion of the output signal seemed to become
significant as the input power of the DUT increased. This demonstrates that the proposed
system is able to sense the nonlinearities generated by an active device.
6.3.2 Multi-port waveform monitoring
In this section the system is used to characterize multi-port nonlinear devices to prove the
ability of the system to monitor the waveform at the inputs and outputs of a multi-port
DUT.
A four port balanced power amplifier designed at 1 GHz in the iRadio lab, shown
in Figure 6-6, was used for relative waveform measurements validation of the proposed
calibration technique and measurement system. The balanced amplifier consists of two
amplifier branches using FLL351ME high-power GaAs FETs from Fujitsu with input and
output matching circuits. An input balun was also designed at 1 GHz to distribute the
input signal to the two inputs of the amplifier.
The input and output waveforms of the amplifier shown in Figure 6-7, Figure 6-8,
and Figure 6-9 have been monitored by sending 1 GHz for the input of the amplifier,
which was connected to port 1 of the developed measurement system at different input
power levels. The two outputs of the amplifier have been connected to port 2 and 3. The
measurement system was calibrated for 1 GHz fundamental signal and 3 harmonics.
100
Figure 6-6: Balanced PA using FLL351ME GaAs FETs from Fujitsu
1.5
0.03
1
0.02
0.5
0.01
0
0
‐0.5
‐0.01
‐1
‐0.02
‐1.5
V1@Pin=-5dBm
V1@Pin=-10dBm
V1@Pin=-15dBm
I1@Pin=-5dBm
I1@Pin=-10dBm
I1@Pin=-15dBm
Current (A)
Voltage (V)
‐0.03
‐2
‐0.04
0
0.5
1
1.5
2
2.5
Time (nSec)
Figure 6-7: Voltage and current waveforms at port 1 of the balanced PA [98]
101
5
0.1
4
0.08
3
0.06
0.04
1
0.02
0
0
‐1
‐0.02
‐2
Current (A)
Voltage (V)
2
‐0.04
‐3
‐0.06
‐4
‐5
V2@Pin=-5dBm
V2@Pin=-10dBm
V2@Pin=-15dBm
I2@Pin=-5dBm
I2@Pin=-10dBm
I2@Pin=-15dBm
‐0.08
‐6
‐0.1
0
0.5
1
1.5
2
2.5
Time (nSec)
Figure 6-8: Voltage and current waveforms at port 2 of the balanced PA [98]
5
0.1
4
0.08
3
0.06
2
Voltage (V)
0.02
0
0
‐1
‐0.02
‐2
Current (A)
0.04
1
‐0.04
‐3
‐0.06
‐4
‐5
V3@Pin=-5dBm
V3@Pin=-10dBm
V3@Pin=-15dBm
I3@Pin=-5dBm
I3@Pin=-10dBm
I3@Pin=-15dBm
‐0.08
‐6
‐0.1
0
0.5
1
1.5
2
2.5
Time (nSec)
Figure 6-9: Voltage and current waveforms at port 3 of the balanced PA [98]
102
It is evident that the developed system can be used to monitor the voltage and
current waveforms at the DUT ports and thus enables the new paradigm of multi-port PA
design, characterization and measurements.
6.4 Absolute Phase Calibration Algorithm for Waveform Measurements
The relative phase calibration algorithm described in section 6.2 works well for the linear
mode of operation as shown in Figure 6-4. However, it does not give accurate waveform
measurements when the device switches to the nonlinear mode of operation as shown in
k k
Figure 6-3. This is due to the relative phase measurements of the error parameter, e01
e10 ,
for each error box between the DUT terminals and the measuring plane of the MTA.
The proposed calibration algorithm for multi-port waveform measurements with
absolute phase measurement is based on the multi-port calibration algorithm for Sparameters measurement described in section 3.4 as a first step for calculating the error
k k
k
box parameters, e00
, e11k and e01
e10 .
The second step is to use the power de-embedding technique described in section
′( n ) and
6.2 to calculate the scaling factor ( α k( n ) ) in order to find the normalized waves ( akdut
(n)
(n)
′( n ) ) at the DUT plane as a function of the measured waves ( akm
bkdut
and bkm
) at the MTA
plane using equations (6-3) and (6-4). After the second step, the voltage and current
waveforms can be reconstructed at the DUT plane with the absolute magnitude and a
relative phase using equations (6-17) and (6-18). The power de-embedding technique
described in section 6.2 gives a clear idea about the absolute magnitude of the waveforms
103
at the DUT plane, but these waveforms still suffer from lack of phase information due to
k k
the error term e01
e10 .
In order to overcome the problem of phase ambiguity, it is evident that the
k
complex values of e10k and e01
need to be obtained for the determination of the absolute
incident and reflected waves at the DUT ports. Two extra calibration steps based on the
use of a known coaxial line and thru standard will be performed to calculate the absolute
k
values of the error parameters, e01
and e10k .
The third step is performed when the thru standard is connected between ports 1
and k in the multi-port calibration technique for S-parameters measurement described in
1 k
section 3.4. In this case, two possible values of e10
e10 can be calculated using (6-20) and
(6-21) by solving the signal flow graph shown in Figure 6-10, assuming the thru is
reciprocal (S12=S21) [99].
SkT11mk
1
e10
1
e00
1
e11
e101
S11T1mk
e10k
T1k
Skkm
1k
S1Tkm
k
e00
e11k
k
e01
Figure 6-10: Error model for the thru standard connected between port 1 and port
k of the measurement system
104
1( n ) k ( n ) 2
1( n ) 1( n )
k (n)
)=0
S kT11mk ( n ) (e10
e10 ) − S1Tkm1k ( n ) (e01
e10 )(e10k ( n ) e01
(6-20)
1( n ) 1( n )
k (n) k ( n)
S1Tkm1k ( n ) (e01
e10 )(e01
e10 )
=±
T 1k ( n )
S k 1m
(6-21)
1( n ) k ( n )
10
10
e
e
Knowing the length of the thru standard, the appropriate solution for the
1 k
transmission tracking between ports 1 and k ( e10
e10 ) can be selected using the inequality
represented in (6-22).
⎡ e −γl ⎤
Re ⎢
⎥>0
⎣ S k1 ⎦
(6-22)
where γ is the propagation constant, l is the length of the thru standard, and Sk1 is the
corrected S-parameter of the thru standard connected between ports 1 and k.
The fourth step is performed to measure the absolute value of the traveling wave,
(n )
( bcoax
) at the measuring plane of the MTA. A coaxial line, with known S-parameters, is
(n )
used to measure the value of bcoax
by connecting it between port 1 of the DUT and the
CH1 of the MHR as shown in Figure 6-11.
The bcoax and a1m waves are measured simultaneously at CH1 as ratios relative to
1
the reference signal at CH2. Once the measured ratio bcoax a1m is known, the value of e10
can be calculated by solving the signal flow graph given in Figure 6-11 such that:
(
)(
) (
1( n ) ( n )
(n)
( n)
1( n ) ( n )
(n)
(n)
⎛ b ( n ) ⎞⎛ 1 − e11
S11coax 1 − ΓMHR
S 22
1( n )
coax − e11 ΓMHR S 21coax S12 coax
⎜
⎟
e10
= ⎜⎜ coax
( n)
( n ) ⎟⎜
S 21
coax
⎝ a1m ⎠⎝
) ⎞⎟
⎟
⎠
(6-23)
105
(n )
, at the input of the MHR is always given in the
The reflection coefficient, ΓMHR
specification of the instrument or it can be measured using other calibrated instrument.
(n )
tends to zero when the system has a 50 Ω impedance.
Generally, ΓMHR
s21coax
1
e10
1
e00
1
e11
1
e01
s11coax
s22coax
s12coax
Figure 6-11: Error model for the coaxial line connected between port 1 and CH1 of
the MHR to measure bcoax
1
, the absolute values of the other
After calculating the magnitude and phase of e10
error parameters can be calculated using equations (6-24), (6-25) and (6-26).
1( n )
e01
=
1( n ) 1( n )
e01
e10
t11( n )
=
1( n )
1( n )
e10
e10
(6-24)
e10k ( n ) =
1( n ) k ( n )
e10
e10
1( n )
e10
(6-25)
k (n)
e01
=
k (n)
e10k ( n ) e01
tkk( n )
=
e10k ( n )
e10k ( n )
(6-26)
106
k
k
, e11k , e01
and e10k , for each error box
After calculating the error parameters, e00
between the DUT terminals and the measuring plane, the incident and reflected waves at
ports 1 and k of the DUT, shown in Figure 6-10, can be de-embedded using (6-27), (628), (6-29), and (6-30), respectively.
1( n )
1( n )
1( n )
1( n )
⎞ (n)
⎞ ( n ) ⎛ e11
⎛ e1( n ) × e10
− e00
× e11
n)
⎟b
⎟
⎜
a1(dut
a
+
= ⎜⎜ 01
1m
1( n )
1( n ) ⎟ 1m
⎟
⎜
e01
⎠
⎝ e01 ⎠
⎝
(6-27)
⎛ 1 ⎞
⎛ − e1( n ) ⎞
n)
b1(dut
= ⎜⎜ 1(00n ) ⎟⎟a1(mn ) + ⎜⎜ 1 ⎟⎟b1(mn )
⎝ e01 ⎠
⎝ e01 ⎠
(6-28)
k (n)
k (n)
⎞ (n)
⎛ e k ( n ) × e10k ( n ) − e00
× e11k ( n ) ⎞ ( n ) ⎛ e00
(n)
⎟b
⎟
⎜
akdut
a
+
= ⎜⎜ 01
km
k ( n ) ⎟ km
k ( n)
⎟
⎜
e10
⎠
⎝ e10 ⎠
⎝
(6-29)
⎛ − e k (n) ⎞ ( n) ⎛ 1 ⎞ ( n)
(n)
bkdut
+ ⎜⎜ k ( n ) ⎟⎟bkm
= ⎜⎜ k11( n ) ⎟⎟akm
⎝ e10 ⎠
⎝ e10 ⎠
(6-30)
After calculating the incident and reflected waves at each port of the DUT, the
voltage, current and waveforms at these ports can be calculated using equations (6-17),
(6-18), and (6-19), respectively.
6.5 Measurement Validation
The calibration algorithm and the measurement system have been verified for a two-port
system using a medium high-power Mini-Circuits ZHL-42W power amplifier [100],
which was driven at 0.5 GHz with a 17 V DC bias. To demonstrate the functionality of
the developed waveform measurement system, the device was driven at different input
107
power levels, so that the measurement could be carried out and verified in the linear and
nonlinear regions of the power amplifier operation.
6.5.1 Time-domain validation
The system was calibrated at a fundamental frequency of 0.5 GHz, while considering up
to four harmonics, in order to measure the voltage waveform at the DUT ports using the
proposed calibration algorithm described in Section 6.4.
The vector of the measured and corrected waveforms using the developed
measurement system was compared to that obtained using a commercial 4 Gbps digital
oscilloscope, Tektronix TDS 794D [96], for the validation of the voltage time-domain
waveforms at the DUT ports.
The measurement was carried out by connecting the ZHL-42W power amplifier
between ports 1 and 2 of the measurement system. The power amplifier was then tested
under the same bias conditions and for the same driving power using the oscilloscope.
The measured waveforms, using the developed system and the commercial scope, show a
good agreement, as evident from the results in Figure 6-12, Figure 6-13, and Figure 6-14.
This is true for both linear, as well as nonlinear, operating regions of the power amplifier.
It can be concluded that the developed measurement system and its calibration algorithm
can be relied on during the characterization, optimization and measurement of the
transistor devices and power amplifiers.
108
Figure 6-12: Output waveforms of the ZHL-42W PA at -9 dBm input power
Figure 6-13: Output waveforms of the ZHL-42W PA at -6 dBm input power
109
Figure 6-14: Output waveforms of the ZHL-42W PA at -3 dBm input power [95]
k
and e10k , in the
The significance of the enhanced phase calibration of terms, e01
overall waveform measurement can be understood by the results shown in Figure 6-15.
The plot in Figure 6-15 compares the voltage waveform measurements for the amplifier
obtained using the scope and those of the developed calibration procedures, reported in
sections 6.2 and 6.4, at 0 dBm input power.
It is clear that the calibration procedure, which measures the absolute phase as
reported in section 6.4, replicates the measurement from the commercial scope. The
calibration algorithm reported in section 6.2, which measures relative phase values, gives
results that are substantially off target. This anomaly in the measurement can be
k k
attributed to the phase ambiguity while calculating the complex error parameter, e01
e10 ,
using the relative calibration algorithm in section 6.2.
110
Figure 6-15: Comparison of the voltage waveforms at the output port of the ZHL42W PA at 0 dBm input power while employing the relative and the enhanced
calibration algorithm in the developed measurement system
6.5.2 Frequency-domain validation
To validate the accuracy of the measured data and to increase confidence in the
developed calibration procedure and the measurement system, it is important to compare
the spectrum components of the output waveform to see how accurately the reconstructed
waveform can match the measured one using the commercial scope.
111
Figure 6-16: Spectrum of the output waveforms of the ZHL-42W PA at 0 dBm input
power
For this purpose, the measured output waveform of the power amplifier at an
input power of 0 dBm, using the scope and the developed measurement system, have
been converted to the frequency domain, using the fast Fourier transform applied to 512
points for each signal. The comparison between the spectral components of the two
signals is shown in Figure 6-16.
It can be observed from Figure 6-16 that the frequency components of the two
signals are fairly well matched. This indicates that the proposed waveform calibration
algorithm and the measurement system are working properly. Thus, it can be concluded
that the developed measurement system can be trusted, as both the time- and frequency-
112
domain results show good agreement with those obtained from a standard commercial
oscilloscope.
6.6 Waveform Engineering
It is a standard practice to characterize a linear microwave device in a 50 Ω impedance
environment. This kind of measurement is essential in understanding the behaviour of the
microwave devices in the linear mode of operation. However, it does not provide enough
information on the nonlinear mode of operation of the microwave devices. Therefore, to
obtain the optimal performance from the microwave devices, the experiments are carried
out in a non 50 Ω impedance environment. The non 50 Ω impedance environment is
achieved by deploying load tuners or load-pull systems [101-105]. The combination of
the waveform measurement and load-pull systems is called a waveform engineering
system.
To demonstrate the waveform engineering capability of the developed
measurement system, a gallium nitride (GaN), 28 V, 4 W high electron mobility
transistor (HEMT) NPTB00004 [106], was measured in a non 50 Ω impedance
environment. The transistor was mounted on a Focus test fixture. A coaxial harmonic
tuner, Maury Microwave Corporation 2612C2, was connected at the output port of the
transistor to provide a variable output impedance environment. The transistor was biased
at Vgs = -1.4 V and Vds = -28 V through the bias tees connected to the drain and gate of
the transistor.
113
Table 6-1: Output reflection coefficient measurements of the power amplifier at
1GHz fundamental frequency and 4 harmonics
Output Reflection Coefficient
Case
Case 1
Case 2
Case 3
@fο
@2fο
@3fο
@4fο
@5fο
0.63
0.788
0.347
0.234
0.736
∠41.9°
∠110.8°
∠-61.1°
∠92.4°
∠-0.4°
0.26
0.78
0.58
0.196
0.75
∠-15.5°
∠110.3°
∠-28.5°
∠78.8°
∠-1.5°
0.786
0.805
0.33
0.207
0.21
∠-0.4°
∠-3.4°
∠11.52°
∠98.9°
∠12.8°
The output current and voltage waveforms, measured at three different output
impedances, are shown in Figure 6-17. The output impedances for these cases have been
measured for a fundamental frequency of 1 GHz and four harmonics at an input power of
20 dBm, as indicated in Table 6-1.
It is evident from Figure 6-17 that the system is able to measure the voltage and
current waveforms for different load impedances. The transistor gives a quasi distortionfree voltage and current waveforms at its optimum load impedance presented by threestub tuner corresponding to reflection coefficients of case 1 as shown in Figure 6-17. The
distortions started to appear in the waveforms when the tuner reflection was varied to a
114
non-optimal value. Additionally, the transistor also began to lose its gain and behaves in a
nonlinear manner.
Figure 6-17: Waveform measurements for different output loads at 20 dBm input
power for an NPTB00004 GaN HEMT transistor [95]
Once again, in order to verify the measured output waveform in a non 50 Ω
environment, the measured waveform of case 3 was compared to the same measurements
using a commercial 18 Gbps high-speed scope, Hewlett Packard 54750A [107].
115
Figure 6-18: Comparison between the measurements of the scope and the developed
system for the waveform of case 3
The comparison of the results in Figure 6-18 shows good agreement. Thus, it can
be concluded that the developed measurement system can be trusted during its
deployment in microwave device optimization, characterization and measurements.
6.7 Summary
This
chapter
presented
two
calibration
techniques
for
multi-port
waveform
measurements. The first technique is an extension to the power de-embedding calibration
technique represented in section 5.2 named relative phase calibration algorithm as
described in section 6.2. It relies on calculating the error parameters of the error boxes
between the DUT terminals and the measuring plane using reflection calibration
116
standards and power calibration process reported in [91]. This calibration process results
k
and e10k as a one complex error
in the calculation of the complex error terms e01
parameter, e10k e10k . The measurements presented in section 6.3 shows that this calibration
process gives good results when the DUT is working in the linear mode of operation, but
some discrepancies started to appear when the DUT moves to the nonlinear mode of
operation [97]. These discrepancies are due to the phase ambiguity in the calculated error
parameters, e10k e10k .
The second part of the chapter proposed another multi-port calibration algorithm
for waveform measurements to avoid the phase ambiguity problem appeared in the
previous calibration algorithm. This calibration process is based on measuring the
k
absolute phase of the error parameter, e01
, by directly connecting a coaxial line with
known S-parameters between port 1 of the measurement system and the measuring
channel of the MHR as described in section 6.4.
The measurements presented in section 6.5 show that the proposed calibration
algorithm for absolute phase measurement gives accurate results compared to the
waveforms obtained using a high-speed sampling scope. The measurements also
demonstrate that the proposed calibration algorithm provides good results for waveform
engineering when measuring the output waveforms of the DUT at different load
impedances as presented in section 6.6.
117
Chapter Seven: Conclusion and Future Work
7.1 Multi-Port Measurement System Development
A multi-port measurement system suitable for time- and frequency-domain large-signal
characterization has been developed. The system is built around the microwave transition
analyzer (MTA) as a multi-harmonic receiver from DC to 40 GHz, which provides the
system with the scope capability for time-domain measurements and the vector network
analyzer (VNA) capabilities for frequency-domain measurements.
Moreover, the system and the proposed calibration algorithms are suitable to work
with any multi-harmonic receiver or sampling scope other than the MTA for measuring
the sampled traveling waves.
7.2 Proposed Calibration Algorithms
As a preliminary step for evaluating the system accuracy and functionality, the system
has been calibrated for multi-port S-parameter measurements using the open-short-loadthru (OSLT) multi-port calibration algorithm reported in [64]. The system shows good
agreement for multi-port S-parameter measurements compared to the results obtained
using a commercial VNA [71].
118
7.2.1 Power de-embedding calibration algorithm
•
In Chapter Five, a reflection based and thru-less calibration method is presented
to simultaneously calculate the impedances and the absolute power flow at the
coaxial or non-coaxial terminals of the DUT [13, 91].
•
The main advantage of this technique is that, no second power calibration is
needed at the tips of the coplanar probes. Such power calibration is almost
impossible to perform, because there is no accurate coplanar power sensor that
can be connected to the tip of the probes to calculate the power calibration factors.
7.2.2 Waveform calibration algorithm with relative phase measurements
•
In Chapter Six, the power de-embedding calibration algorithm [91] has also been
extended for waveform characterization with relative phase measurements for the
error parameters of the error boxes between the DUT plane and the measuring
plane [97].
•
The waveform measurement validations show the ability of the system and the
calibration algorithm to monitor the waveforms at the DUT plane for two-port and
multi-port active devices [98].
•
The calibration algorithm shows good results when the device is working in the
linear mode of operation, but there are some discrepancies when the device moves
to the nonlinear mode of operation [97].
119
•
The slight discrepancies between the waveforms obtained using the calibration
algorithm and the scope are mainly due to the phase ambiguity in the calculation
k k
of the error parameter, e01
e10 .
7.2.3 Enhanced waveform calibration algorithm with absolute phase measurements
•
An
enhanced
multi-port
calibration
algorithm
for
absolute
waveform
measurements is proposed to overcome the phase ambiguity that appears with the
proposed relative waveform measurements [95].
•
The proposed calibration algorithm utilizes a standard signal frequency generator
and does not rely on the use of a multi-harmonic generator to calculate the error
box parameters at the fundamental and harmonic frequencies. The algorithm is
also applicable to any multi-harmonic phase-locked receiver based measurement
system.
•
The developed calibration strategy discards the use of the golden standard and,
thus, significantly improves the existing calibration techniques reported earlier
[32, 33, 38, 40, 41].
7.3 System Capabilities and Measurement Validations
The main advantage of the developed measurement system and the proposed calibration
algorithm is the ability to perform different kinds of measurements for an N-port active or
120
passive DUT with coaxial or non-coaxial terminals in 50 Ω and non 50 Ω measurement
environments.
7.3.1 S-parameter measurements
•
As described in Chapter Three, the measurements prove the system capability of
characterizing the N-port device with only one set of measurements without the
need for C N2 successive two-port measurements, which have to be carried out to
obtain the full S-parameter matrix of the N-port device using a commercial twoport VNA [6].
•
The system is also able to give accurate results under different input power levels
without the need for recalibration [71].
7.3.2 AM-AM and AM-PM conversion measurements
•
The system has the capability of measuring the AM-AM and AM-PM conversions
for the fundamental and harmonic frequencies of nonlinear N-port microwave
devices [87]. These kinds of measurements cannot be performed with traditional
methods using the VNA.
•
The measurements provided in Chapter Four show that the system has the
capability of measuring the effects of crosstalk on the overall performance of the
N-port DUT, in terms of AM-AM and AM-PM conversions, gain and power
efficiency [88]. This measurement capability of the system helps in the design of
121
power amplifiers during the behavioural modeling, linearization and impairment
compensation phases.
7.3.3 Impedance and absolute power measurements
•
By applying the absolute power calibration algorithm described in Chapter Five,
the system is capable of measuring the impedance and absolute power at the noncoaxial terminals of the DUT.
•
The proposed calibration algorithm has been applied to the developed multi-port
system, and measurement verifications have been applied for the 50 Ω and non 50
Ω terminated passive and active devices. The measurement results show very
good agreement with those obtained using commercial instruments [91].
7.3.4 Waveform measurements
•
It has been systematically proven that the developed calibration procedures and
measurement system provide accurate results compared to the results obtained
using a commercial high-speed scope. The measurements carried out by this setup
can, therefore, be trusted when deployed in the application of microwave
characterization. The significance of the determination of the phase of the error
k
parameters, e01
and e10k , has been also demonstrated through the measurement
results [95].
122
•
Finally, it has been demonstrated that the measurement system is capable of
performing waveform engineering measurements. The comparison of waveforms
obtained in 50 Ω and non 50 Ω impedance environments using the developed
system and standard commercial high-speed scopes shows good agreement. This
enhances confidence in the measurement data obtained from the developed
measurement system [95].
7.4 Recommendations for the Future Work
The measurements described in this work prove that the multi-port measurement system
and the proposed calibration algorithms are working properly for the characterization of
N-port linear and nonlinear microwave devices. The recommendations for future work
can be summarized in the following points.
•
Utilization of the proposed system and the calibration algorithms with a passive
load-pull setup, as shown in Figure 7-1, to build a wide-range waveform
measurement setup that has the ability to characterize RF and microwave devices
using the waveform engineering technique.
•
Integration of the software of the proposed measurement system with the opensource software of the Focus load-pull setup to provide a fully automated
waveform engineering system.
•
Use of the proposed waveform measurement system in the design of switchingmode power amplifiers by monitoring the output waveform with the variation of
the output impedance.
123
Figure 7-1: Integration of the proposed multi-port measurement system with the
passive load-pull setup to build a wide-range waveform measurement system
7.5 Summary of Contributions
•
A multi-port measurement system has been developed and verified for the smalland large-signal characterization of N-port microwave devices [71]. The
developed measurement system shows the capability of measuring the effect of
the crosstalk for dual branch amplifiers on the overall performance of the DUT in
terms of power efficiency and signal distortion [88].
•
An on-wafer calibration algorithm for absolute power de-embedding has been
proposed and verified using the developed measurement system [13, 91].
•
Two waveform calibration algorithms for relative and absolute waveform
measurements have been proposed and verified using the developed system. The
124
waveform reconstruction is based on the measurements of incident and reflected
waves for the fundamental frequency and a number of harmonics at the DUT
ports [95, 97, 98].
The contributions presented in this work have been published in four journal
papers [88, 91, 95, 97] and six international conferences [13, 71, 87, 98, 108, 109]. The
linear and nonlinear measurements of the system and the calibration algorithms show
good agreement with that obtained using commercial instruments.
125
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Appendix A: Datasheets
A.1 Datasheet of Agilent P940xA/C Solid State PIN Diode Switches
143
144
145
146
147
148
149
150
151
152
153
A.2 Datasheet of MAC C4238-20 Bi-Directional Couplers
154
A.3 Datasheet of ANAREN 41620 Power Divider
155
156
157
A.4 Datasheet of CMOS 82C55A Programmable Peripheral Interface
158
159
160
161
162
163
A.5 Datasheet of ZFL-2500 Medium-Power Amplifier
164
165
A.6 Datasheet of ZHL-24W Medium-Power Amplifier
166
167
A.7 Datasheet of NPTB00004 Gallium Nitride RF Power Transistor
168
169
170
171
172
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