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

код для вставкиСкачатьUNIVERSITY 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 Library and Archives Canada Bibliothèque et Archives Canada Published Heritage Branch Direction du Patrimoine de l'édition 395 Wellington Street Ottawa ON K1A 0N4 Canada 395, rue Wellington Ottawa ON K1A 0N4 Canada Your file Votre référence ISBN: 978-0-494-75276-0 Our file Notre référence ISBN: NOTICE: 978-0-494-75276-0 AVIS: The author has granted a nonexclusive license allowing Library and Archives Canada to reproduce, publish, archive, preserve, conserve, communicate to the public by telecommunication or on the Internet, loan, distrbute and sell theses worldwide, for commercial or noncommercial purposes, in microform, paper, electronic and/or any other formats. L'auteur a accordé une licence non exclusive permettant à la Bibliothèque et Archives Canada de reproduire, publier, archiver, sauvegarder, conserver, transmettre au public par télécommunication ou par l'Internet, prêter, distribuer et vendre des thèses partout dans le monde, à des fins commerciales ou autres, sur support microforme, papier, électronique et/ou autres formats. The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. L'auteur conserve la propriété du droit d'auteur et des droits moraux qui protege cette thèse. Ni la thèse ni des extraits substantiels de celle-ci ne doivent être imprimés ou autrement reproduits sans son autorisation. In compliance with the Canadian Privacy Act some supporting forms may have been removed from this thesis. Conformément à la loi canadienne sur la protection de la vie privée, quelques formulaires secondaires ont été enlevés de cette thèse. While these forms may be included in the document page count, their removal does not represent any loss of content from the thesis. Bien que ces formulaires aient inclus dans la pagination, il n'y aura aucun contenu manquant. 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 References [1] F. De Groote, J. P. Teyssier, O. Jardel, T. Gasseling, and J. Verspecht, "Introduction to measurements for power transistor characterization," IEEE Microwave Magazine, vol. 9, pp. 70-85, 2008. [2] S. Cripps, RF Power Amplifiers for Wireless Communications, 2nd ed. Norwood MA: Artech House, 2006. [3] K. S. Kundert and A. Sangiovanni-Vincentelli, "Simulation of nonlinear circuits in the frequency domain," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 5, pp. 521-535, 1986. [4] V. Teppati, A. Ferrero, V. Camarchia, A. Neri, and M. Pirola, "Microwave measurements - Part III: Advanced non-linear measurements," IEEE Instrumentation & Measurement Magazine, vol. 11, pp. 17-22, 2008. [5] I. Rolfes and B. Schiek, "Multiport method for the measurement of the scattering parameters of N-ports," Microwave Theory and Techniques, IEEE Transactions on, vol. 53, pp. 1990-1996, 2005. [6] J. C. Tippet and R. A. Speciale, "A rigorous technique for measuring the scattering matrix of a multiport device with a 2-port network analyzer," IEEE Transactions on Microwave Theory and Techniques, vol. MTT-30, pp. 661-666, 1982. [7] L. Hsin-Chia and C. Tah-Hsiung, "Multiport scattering matrix measurement using a reduced-port network analyzer," IEEE Transactions on Microwave Theory and Techniques, vol. 51, pp. 1525-1533, 2003. 126 [8] Technical-Datasheet, "S-Parameter Measurements with Multiport Balance VNA," in Anritsu, 2004. [9] I. Hecht, "Improved error-correction technique for large-signal load-pull measurements," IEEE Transactions on Microwave Theory and Techniques, vol. MTT-35, pp. 1060-1062, 1987. [10] A. Ferrero and U. Pisani, "An improved calibration technique for on-wafer largesignal transistor characterization," IEEE Transactions on Instrumentation and Measurement, vol. 42, pp. 360-364, 1993. [11] B. Roth, D. Kother, M. Coady, and T. Sporkmann, "A combined on-wafer measurement stand for linear and nonlinear microwave measurements," in 24th European Microwave Conference, Swanley, UK, 1994, pp. 962-967. [12] G. Berghoff, E. Bergeault, B. Huyart, and L. Jallet, "On-wafer calibration of a double six-port reflectometer including constants for absolute power measurements," IEEE Transactions on Instrumentation and Measurement, vol. 46, pp. 1111-1114, 1997. [13] 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, Victoria, BC, Canada, 2008, pp. 58-61. [14] R. Hajji, F. Beanregard, and F. M. Ghannouchi, "Multitone power and intermodulation load-pull characterization of microwave transistors suitable for linear SSPA's design," IEEE Transactions on Microwave Theory and Techniques, vol. 45, pp. 1093-1099, 1997. 127 [15] S. Bousnina, C. Falt, P. Mandeville, A. B. Kouki, and F. M. Ghannouchi, "An accurate on-wafer deembedding technique with application to HBT devices characterization," Microwave Theory and Techniques, IEEE Transactions on, vol. 50, pp. 420-424, 2002. [16] R. Groves, W. Jing, L. Wagner, and A. Wan, "Quantitative analysis of errors in on-wafer s-parameter de-embedding techniques for high frequency device modeling," in BiCMOS Circuits and Technology Meeting Piscataway, NJ, USA, 2006, pp. 1-4. [17] C. Ming-Hsiang, H. Guo-Wei, C. Chia-Sung, and C. Kun-Ming, "Unified parasitic de-embedding methodology of on-wafer multi-port device characterization," in IEEE MTT-S International Microwave Symposium, Piscatway, NJ, USA, 2005, pp. 1-4. [18] C. Ming-Hsiang, H. Guo-Wei, C. Kun-Ming, and P. An-Sam, "A novel cascadebased de-embedding method for on-wafer microwave characterization and automatic measurement," in IEEE MTT-S International Microwave Symposium Digest Piscataway, NJ, USA, 2004, pp. 1237-1240. [19] M. Sipila, K. Lehtinen, and V. Porra, "High-frequency periodic time-domain waveform measurement system," IEEE Transactions on Microwave Theory and Techniques, vol. 36, pp. 1397-1405, 1988. [20] G. Kompa and F. van Raay, "Error-corrected large-signal waveform measurement system combining network analyzer and sampling oscilloscope capabilities," IEEE Transactions on Microwave Theory and Techniques, vol. 38, pp. 358-365, 1990. 128 [21] J. Verspecht, "Broadband sampling oscilloscope characterization with the Noseto-Nose calibration procedure: a theoretical and practical analysis," IEEE Transactions on Instrumentation and Measurement, vol. 44, pp. 991-997, 1995. [22] G. Vandersteen, Y. Rolain, and J. Schoukens, "An identification technique for data acquisition characterization in the presence of nonlinear distortions and time base distortions," IEEE Transactions on Instrumentation and Measurement, vol. 50, pp. 1355-1363, 2001. [23] T. S. Clement, P. D. Hale, D. F. Williams, C. M. Wang, A. Dienstfrey, and D. A. Keenan, "Calibration of sampling oscilloscopes with high-speed photodiodes," IEEE Transactions on Microwave Theory and Techniques, vol. 54, pp. 3173- 3181, 2006. [24] K. A. Remley, P. D. Hale, and D. F. Williams, Magnitude and phase calibrations for RF, microwave, and high-speed digital signal measurements, 3rd ed. Piscataway, NJ: IEEE Press, 2007. [25] P. D. Hale, C. M. Wang, D. F. Williams, K. A. Remley, and J. D. Wepman, "Compensation of random and systematic timing errors in sampling oscilloscopes," IEEE Transactions on Instrumentation and Measurement, vol. 55, pp. 2146-2154, 2006. [26] D. Williams, P. Hale, and K. A. Remley, "The sampling oscilloscope as a microwave instrument," IEEE Microwave Magazine, vol. 8, pp. 59-68, 2007. [27] T. Van den Broeck and J. Verspecht, "Calibrated vectorial nonlinear-network analyzers," in IEEE MTT-S International Microwave Symposium Digest, San Diego, CA, USA, 1994, pp. 1069-1072. 129 [28] C. J. Clark, G. Chrisikos, M. S. Muha, A. A. Moulthrop, and C. P. Silva, "Timedomain envelope measurement technique with application to wideband power amplifier modeling," IEEE Transaction on Microwave Theory Technique, vol. 46, pp. 2531-2540, 1998. [29] J. Benedikt, R. Gaddi, P. J. Tasker, M. Goss, and M. Zadeh, "High power time domain measurement system with active harmonic load-pull for high efficiency base station amplifier design," in IEEE MTT-S International Microwave Symposium Digest, Piscataway, NJ, USA, 2000, pp. 1459-1462. [30] D. J. Williams, J. Leckey, and P. J. Tasker, "Envelope domain analysis of measured time domain voltage and current waveforms provide for improved understanding of factors effecting linearity," in IEEE MTT-S International Microwave Symposium Digest, Philadelphia, PA, United states, 2003, pp. 1411- 1414. [31] F. Macraigne, T. Reveyrand, C. Maziere, D. Barataud, J. M. Nebus, R. Quere, and A. Mallet, "A fully calibrated four channels time domain RF envelope measurement system for the envelope characterization of nonlinear devices in a load-pull environment," in European Microwave Conference, UK, UK, 2006, pp. 1-4. [32] U. Lott, "Measurement of magnitude and phase of harmonics generated in nonlinear microwave two-ports," IEEE Transactions on Microwave Theory and Techniques, vol. 37, pp. 1506-1511, 1989. [33] D. Barataud, C. Arnaud, B. Thibaud, M. Campovecchio, J. M. Nebus, and J. P. Villotte, "Measurements of time-domain voltage/current waveforms at RF and 130 microwave frequencies based on the use of a vector network analyzer for the characterization of nonlinear devices-application to high-efficiency power amplifiers and frequency-multipliers optimization," IEEE Transactions on Instrumentation and Measurement, vol. 47, pp. 1259-1264, 1998. [34] J. A. Jargon, D. C. DeGroot, and D. F. Vecchia, "Repeatability study of commercial harmonic phase standards measured by a nonlinear vector network analyzer," in 62nd ARFTG Microwave Measurements Conference, Piscataway, NJ, USA, 2003, pp. 243-258. [35] F. van Raay and G. Kompa, "A new on-wafer large-signal waveform measurement system with 40 GHz harmonic bandwidth," in IEEE MTT-S International Microwave Symposium Digest New York, NY, USA, 1992, pp. 1435-1438. [36] M. Demmler, P. J. Tasker, and M. Schlechtweg, "A vector corrected high power on-wafer measurement system with a frequency range for the higher harmonics up to 40 GHz," in 24th European Microwave Conference, Swanley, UK, 1994, pp. 1367-1372. [37] D. J. Williams and P. J. Tasker, "An automated active source and load pull measurement system," in 6th IEEE High Frequency Postgraduate Colloquium, Piscataway, NJ, USA, 2001, pp. 7-12. [38] C. J. Wei, Y. A. Tkachenko, and D. Bartle, "Waveform measurement technique and its applications to optimum loading studies on power FETs," in 2nd International Conference on Microwave and Millimeter Wave Technology Proceedings, ICMMT Piscataway, NJ, USA, 2000, pp. 666-669. 131 [39] C. J. Wei, P. DiCarlo, Y. A. Tkachenko, R. McMorrow, and D. Bartle, "Analysis and experimental waveform study on inverse class class-F mode of microwave power FETs," in IEEE MTT-S International Microwave Symposium Digest, Boston, MA, USA, 2000, pp. 525-528. [40] J. Verspecht, P. Debie, A. Barel, and L. Martens, "Accurate on wafer measurement of phase and amplitude of the spectral components of incident and scattered voltage waves at the signal ports of a nonlinear microwave device," in IEEE MTT-S International Microwave Symposium Digest, New York, NY, USA, 1995, pp. 1029-1032. [41] S. Bensmida, P. Poire, R. Negra, F. M. Ghannouchi, and G. Brassard, "New timedomain voltage and current waveform measurement setup for power amplifier characterization and optimization," IEEE Transactions on Microwave Theory and Techniques, vol. 56, pp. 224-231, 2008. [42] M. Pirola, V. Teppati, and V. Camarchia, "Microwave measurements Part I: Linear Measurements," IEEE Instrumentation & Measurement Magazine, vol. 10, pp. 14-19, 2007. [43] R. Ludwig and G. Bogdanov, RF Circuit Design - Theory and Applications, 2nd ed. New Jersey, USA: Prentice Hall, 2008. [44] K. Change, RF and Microwave Wireless Systems. New York: Jhon Wiley & Sons, 2000. [45] V. Camarchia, V. Teppati, S. Corbellini, and M. Pirola, "Microwave measurements. Part II. Non-linear measurements," IEEE Instrumentation & Measurement Magazine, vol. 10, pp. 34-39, 2007. 132 [46] P. J. Tasker, "Practical waveform engineering," IEEE Microwave Magazine, vol. 10, pp. 49-60, 2009. [47] M. V. Bossche, F. Verbeyst, and J. Verspecht, "The Three Musketeers of Large Signal RF and Microwave Design-Measurement, Modeling and CAE," in ARFTG Conference Digest-Spring, 53rd, 1999, pp. 1-8. [48] F. M. Ghannouchi, R. Larose, and R. G. Bosisio, "A new multiharmonic loading method for large-signal microwave and millimeter-wave transistor characterization," IEEE Transactions on Microwave Theory and Techniques, vol. 39, pp. 986-992, 1991. [49] J. D. Rhodes, "Output universality in maximum efficiency linear power amplifiers," International Journal of Circuit Theory and Applications, vol. 31, pp. 385-405, 2003. [50] F. H. Raab, "Class-F power amplifiers with maximally flat waveforms," IEEE Transactions on Microwave Theory and Techniques, vol. 45, pp. 2007-2012, 1997. [51] N. Boulejfen, A. B. Kouki, S. Khouaja, and F. M. Ghannouchi, "A homodyne multi-port network analyzer for S parameter measurements of microwave N-port circuits/systems," in IEEE Asia-Pacific Conference on Circuits and Systems, Piscataway, NJ, USA, 1998, pp. 687-689. [52] D. J. Ballo and J. A. Wendler, "The microwave transition analyzer: a new instrument architecture for component and signal analysis," Hewlett-Packard Journal, vol. 43, pp. 48-62, 1992. 133 [53] Product-Note70820-3, "HP 70820A Microwave Transition Analyzer: Picosecond Delta-Time Accuracy," in Hewlett-Packard Journal, USA, 1991. [54] T. Buber, A. Rodriguez, A. Jenkins, J. Mahon, C. Liss, J. P. Lanteri, N. Kinayman, R. Wohlert, I. Gresham, A. Khalil, J. Bennett, and L. P. Dunleavy, "Multimode TRL and LRL calibrated measurements of differential devices," in 64th ARFTG Microwave Measurements Conference, Piscataway, NJ, USA, 2004, pp. 157-166. [55] G. F. Engen and C. A. Hoer, "THRU-REFLECT-LINE : AN IMPROVED TECHNIQUE FOR CALIBRATING THE DUAL SIX-PORT AUTOMATIC NETWORK ANALYZER," IEEE Transactions on Microwave Theory and Techniques, vol. MTT-27, pp. 987-993, 1979. [56] D. Hollmann, G. Baumann, and R. Hierl, "Applying full two-port capabilities to a standard MM-wave system for TRL calibration," Microwave Journal, vol. 34, pp. 103-105, 1991. [57] L. Lin and W. Ke, "Multiport through-resistor (TR) numerical calibration," IEEE Microwave and Wireless Components Letters, vol. 15, pp. 883-885, 2005. [58] F. J. Lopez-Gonzalez, E. Marquez-Segura, P. Otero, and C. Camacho-Penalosa, "Robust statistical multi-line TRL calibration approach for microwave device characterization," in IEEE Mediterranean Electrotechnical Conference, Piscataway, NJ, USA, 2006, pp. 187-190. [59] D. F. Williams, C. M. Wang, and U. Arz, "An optimal multiline TRL calibration algorithm," in IEEE MTT-S International Microwave Symposium Digest Piscataway, NJ, USA, 2003, pp. 1819-1822. 134 [60] C. Woodin and M. Goff, "Verification of MMIC on-wafer microstrip TRL calibration," in IEEE MTT-S International Microwave Symposium Digest, New York, NY, USA, 1990, pp. 1029-1032. [61] D. Rubin, "De-embedding MM-wave MICs with TRL," Microwave Journal, vol. 33, pp. 141-142, 1990. [62] D. Kostevc, J. Mlakar, and L. Trontelj, "Calibration TRL for automatic network analyzer with 12 parameters error model," in Mediterranean Electrotechnical Conference, MELECON '85, New York, NY, USA, 1985, pp. 23-26. [63] P. S. Blockley and J. G. Rathmell, "Towards generic calibration," in 65th Spring ARFTG Conference Digest, Piscataway, NJ, USA, 2005, pp. 1-4. [64] A. Ferrero, U. Pisani, and K. J. Kerwin, "A new implementation of a multiport automatic network analyzer," IEEE Transactions on Microwave Theory and Techniques, vol. 40, pp. 2078-2085, 1992. [65] H. Heuermann, "GSOLT: the calibration procedure for all multi-port vector network analyzers," in IEEE MTT-S International Microwave Symposium Digest, Piscataway, NJ, USA, 2003, pp. 1815-1818. [66] A. Ferrero and F. Sanpietro, "A simplified algorithm for leaky network analyzer calibration," IEEE Microwave and Guided Wave Letters, vol. 5, pp. 119-121, 1995. [67] A. Ferrero, F. Sanpietro, and U. Pisani, "Multiport vector network analyzer calibration: A general formulation," IEEE Transactions on Microwave Theory and Techniques, vol. 42, pp. 2455-2461, 1994. 135 [68] A. Ferrero, V. Teppati, M. Garelli, and A. Neri, "A novel calibration algorithm for a special class of multiport vector network analyzers," IEEE Transactions on Microwave Theory and Techniques, vol. 56, pp. 693-698, 2008. [69] J. Martens, "Multiport SOLR calibrations: performance and an analysis of some standards dependencies," in 62nd ARFTG Microwave Measurements Conference, Piscataway, NJ, USA, 2003, pp. 205-213. [70] V. Teppati and A. Ferrero, "On-wafer calibration algorithm for partially leaky multiport vector network analyzers," IEEE Transactions on Microwave Theory and Techniques, vol. 53, pp. 3665-3671, 2005. [71] 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. 1215-1219. [72] A. Raghavan, N. Srirattana, and J. Laskar, Modeling and design techniques for RF power amplifiers: Wiley-IEEE, 2008. [73] F. Deshours, E. Bergeault, F. Blache, J. P. Villotte, and B. Villeforceix, "Experimental comparison of load-pull measurement systems for nonlinear power transistor characterization," IEEE Transactions on Instrumentation and Measurement, vol. 46, pp. 1251-5, 1997. [74] J. Liu, L. P. Dunleavy, and H. Arslan, "Large-signal behavioral modeling of nonlinear amplifiers based on load-pull AM-AM and AM-PM measurements," IEEE Transactions on Microwave Theory and Techniques, vol. 54, pp. 3191- 3195, 2006. 136 [75] G. Simpson, J. Horn, D. Gunyan, and D. E. Root, "Load-pull + NVNA = enhanced X-parameters for PA designs with high mismatch and technologyindependent large-signal device models," in ARFTG Microwave Measurement Symposium, 2008 72nd, 2008, pp. 88-91. [76] F. M. Ghannouchi, Z. Guoxiang, and F. Beauregard, "Simultaneous AMAM/AM-PM distortion measurements of microwave transistors using active loadpull and six-port techniques," IEEE Transactions on Microwave Theory and Techniques, vol. 43, pp. 1584-1589, 1995. [77] S. Bensmida, F. M. Ghannouchi, and E. Bergeault, "An original setup for power amplifier AM-AM and AM-PM Characterization," in IEEE Instrumentation and Measurement Technology Conference, I2MTC2008, Victoria, BC, Canada, 2008, pp. 54-57. [78] G. I. Abib, S. Bensmida, E. Bergeault, and B. Huyart, "A source-pull/load-pull measurement system including power amplifier linearization using simple instantaneous memoryless polynomial base-band predistortion," in 36th European Microwave Conference, 2006, pp. 252-254. [79] F. M. Ghannouchi, H. Wakana, and M. Tanaka, "New unequal three-tone signal method for AM-AM and AM-PM distortion measurements suitable for characterization of satellite communication transmitters/transponders," IEEE Transactions on Microwave Theory and Techniques, vol. 48, pp. 1404-1407, 2000. [80] E. G. Jeckeln, F. Beauregard, M. A. Sawan, and F. M. Ghannouchi, "Adaptive baseband/RF predistorter for power amplifiers through instantaneous AM-AM 137 and AM-PM characterization using digital receivers," in IEEE MTT-S International Microwave Symposium Digest, Boston, MA, USA, 2000, pp. 489- 492. [81] P. M. Asbeck, H. Kobayashi, M. Iwamoto, G. Hanington, S. Nam, and L. E. Larson, "Augmented behavioral characterization for modeling the nonlinear response of power amplifiers," in IEEE MTT-S International Microwave Symposium Digest, Seattle, WA, United states, 2002, pp. 135-138. [82] S. Boumaiza and F. M. Ghannouchi, "Realistic power-amplifiers characterization with application to baseband digital predistortion for 3G base stations," vol. 50, pp. 3016-3021, 2002. [83] C. J. Clark, C. P. Silva, A. A. Moulthrop, and M. S. Muha, "Power-amplifier characterization using a two-tone measurement technique," IEEE Transactions on Microwave Theory and Techniques, vol. 50, pp. 1590-1602, 2002. [84] P. Arno, F. Launay, J. M. Fournier, and J. C. Grasset, "A simple RF power amplifier characterization using AM-AM, AM-PM measurements based on CDMA signal statistics," in European Microwave Conference, London, United kingdom, 2004, pp. 693-696. [85] S. Boumaiza and F. M. Ghannouchi, "Dynamic nonlinear distortion characterization of wireless radio transmitters," in IEEE International Symposium on Electron Devices for Microwave and Optoelectronic Applications, Berg-en- Dal, Kruger National Park, South africa, 2004, pp. 92-95. [86] A. Zine, G. Maury, F. Ndagijimana, and C. Arnaud, "An RF power amplifier modelled with a simple fifth order polynomial extracted from basic 138 characterizations," in 5th ARFTG Microwave Measurements Conference Digest Long Beach, CA, United states, 2005, pp. 135-141. [87] W. S. El-Deeb, M. S. Hashmi, N. Boulejfen, and F. M. Ghannouchi, "Dynamic distortion characterization of multiport RF PAs using MTA-based multiport measurement setup," in Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits, INMMiC 2010, Goteborg, Sweden, 2010, pp. 152-155. [88] W. S. El-Deeb, N. Boulejfen, and F. M. Ghannouchi, "A Multiport Measurement System for Complex Distortion Measurements of Nonlinear Microwave Systems," IEEE Transactions on Instrumentation and Measurement, vol. 59, pp. 1406-1413, 2010. [89] Mini-Circuits, "ZFL-2500+ (Mini-Circuits) - Broadband AMPL / SMA / RoHS, Amplifiers," http://www.minicircuits.com/pdfs/ZFL-2500+.pdf. [90] Agilent-Technology, "Agilent Network Analysis Applying the 8510 TRL Calibration for Non- Coaxial Measurements," in Product Note 8510-8A. [91] 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. [92] F. De Groote, O. Jardel, J. Verspecht, D. Barataud, J.-P. Teyssier, and R. Quere, "Time Domain Harmonic Load-pull of an AlGaN/GaN HEMT," in 66th ARFTG Conference Proceedings, Washington, USA, 2005. [93] J. Verspecht, F. Verbeyst, and M. Vanden Bossche, "Network analysis beyond Sparameters: Characterizing and modeling component behaviour under modulated 139 large-signal operating conditions," in 30th European Microwave Conference, London, UK, 2000, pp. 373-376. [94] K. Kotzebue, T. S. Tan, and D. McQuate, "An 18 to 26.5 GHz Waveguide LoadPull System Using Active-Load Tuning," in IEEE MTT-S International Microwave Symposium Digest, 1987, pp. 453-456. [95] W. S. El-Deeb, M. S. Hashmi, N. Boulejfen, and F. M. Ghannouchi, "SmallSignal, Complex Distortion and Waveform Measurement System for Multi-Port Microwave Devices," IEEE Instrumentation & Measurement Magazine, 2011, Accepted. [96] Tektronix, "Tektronix TDS794D User’s Manual," http://www2.tek.com/cmswpt/psdetails.lotr?ct=PS&cs=psu&ci=13446&lc=EN. [97] 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 LargeSignal Characterization of Microwave Devices," IET Microwaves, Antennas & propagation, vol. 4, pp. 1773-1781, 2010. [98] 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. [99] A. Ferrero and U. Pisani, "Two-port network analyzer calibration using an unknown `thru'," IEEE Microwave and Guided Wave Letters, vol. 2, pp. 505-507, 1992. 140 [100] Mini-Circuits, "Coaxial medium high power amplifier, ZHL-24W, from 10 to 4200 MHz," http://www.datasheetarchive.com/ZHL-42W-datasheet.html. [101] Y. Takayama, "A New Load-Pull Characterization Method for Microwave Power Transistors," in IEEE-MTT-S International Microwave Symposium, 1976, pp. 218-220. [102] R. B. Stancliff and D. B. Poulin, "Harmonic Load-Pull," in IEEE MTT-S International Microwave Symposium Digest, 1979, pp. 185-187. [103] L. Di-Luan and F. M. Ghannouchi, "Multitone characterization and design of FET resistive mixers based on combined active source-pull/load-pull techniques," IEEE Transactions on Microwave Theory and Techniques, vol. 46, pp. 1201- 1208, 1998. [104] M. S. Hashmi, A. L. Clarke, S. P. Woodington, J. Lees, J. Benedikt, and P. J. Tasker, "Electronic multi-harmonic load-pull system for experimentally driven power amplifier design optimization," in IEEE MTT-S International Microwave Symposium Digest Piscataway, NJ, USA, 2009, pp. 1549-1552. [105] M. S. Hashmi, A. L. Clarke, S. P. Woodington, J. Lees, J. Benedikt, and P. J. Tasker, "An Accurate Calibrate-Able Multiharmonic Active Load-Pull System Based on the Envelope Load-Pull Concept," IEEE Transactions on Microwave Theory and Techniques, vol. 58, pp. 656-664, 2010. [106] Datasheet, "Gallium Nitride 28V, 5W RF Power Transistor, NPTB00004 ": http://www.nitronex.com/pdfs/NPTB00004.pdf. [107] Hewlett-Packard, "HP 54750A High-Bandwidth Digitizing Oscilloscope," http://www.airlink.dk/Dokumenter/HP54750A.pdf. 141 [108] W. S. El-Deeb, M. S. Hashmi, N. Boulejfen, and F. M. Ghannouchi, "Relative Waveform Measurement Technique for the Characterization of Multiport Microwave Devices," in IEEE Antennas and Propagation Society International Symposium, APSURSI, Toronto, Canada, 2010. [109] 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, APSURSI, Toronto, Canada, 2010. 142 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

1/--страниц