Analysis & Design of Non-Linear Amplifiers for Efficient Microwave Transmitters by Michael Dean Roberg B.S., Bucknell University, 2003 M.S., University of Pennsylvania, 2006 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Electrical, Computer, and Energy Engineering 2012 Roberg, Michael Dean (Ph.D., Electrical Engineering) Analysis & Design of Non-Linear Amplifiers for Efficient Microwave Transmitters Thesis directed by Professor Zoya Popović This thesis addresses analysis and design of high efficiency microwave power amplifiers and rectifiers. The focus of this body of work is to optimize narrow band power amplifiers for maximization of Power-Added-Efficiency (PAE) and rectifiers for maximization of RF-DC power conversion efficiency. A power amplifier performs DC-RF conversion while a rectifier performs RF-DC conversion, therefore a strong analogy exists between the two. Design with non-linear devices suffers from lack of accurate models characterizing large signal behavior, therefore measurement based techniques are often adopted in order to create high per- formance designs. The theoretical analysis presented in this thesis provides the microwave circuit designer intuition concerning performance expectations of design options rather than a recipe for creating a successful design. The complexity of non-linear device physics results in behavior which is often limited to qualitative description, complicating accurate model development. The presented theoretical analysis is applied to load-pull based design of S-Band and X-Band power amplifiers and S-Band power rectifiers. The measured circuits exhibit high efficiency consistent with the analysis. An implementation of a high efficiency pulsed S-band AM radar transmitter is presented along with measured results. An extension of the presented analysis is investigated in the form of a harmonic injection amplifier, which conceptually allows realization of a high power, high efficiency broadband amplifier. In summary, this thesis details 1) the load-pull measurement based design technique applied to microwave power amplifiers and rectifiers, 2) a theoretical analysis technique characterizing the performance limitations of harmonically terminated power amplifiers which may be applied to power rectifiers as well, 3) the design and measurement of several successful high efficiency power amplifiers and rectifiers and 4) interesting implementations of the presented theory in a system context. iii Dedication I dedicate this thesis to my family which includes my parents Craig & Deb Roberg, my sister Becky Mashburn, my brother-in-law Justin Mashburn and my two pugs Alice & Stella. Thank you all for the support and for keeping my perspective on life grounded! Personal Acknowledgments First and foremost I would like to thank former research group member John Hoversten for teaching me the foundations on which the research I performed was based. His hard work and attention to detail are things which I attempted to carry forward in the lab since his graduation. I would also like to thank Jon Chisum, Erez Falkenstein and Rob Scheeler for keeping the mood in the lab light and not letting things get too serious. It’s always important to have a little bit of fun at work in my opinion. I would like to thank Asmita Dani and Jennifer Imperial for helping me solidify my knowledge of many concepts relative to amplifiers through helping them with their projects. To the other group members I have had the pleasure of working with, including Frank Trang, Scott Schafer, Andrew Zai, Ignacio Ramos, Xavi Palomer, Ceśar Sańchez-Peŕez, David Sardin, Evan Cullens, Nicola Kinzie, Brad Lindseth, Dan Kuester, Leonardo Ranzani, Negar Ehsan, Mike Elsbury, Milos Janković and Luke Sankey, I thank you for the many helpful discussions and good times in the lab. v Professional Acknowledgments My adviser Dr. Zoya Popović deserves special recognition for deciding to admit and fund me as a student with no practical microwave engineering experience. I am indebted to her for giving me the opportunity to learn about microwave engineering and apply my background to the research and solution of many problems within microwave engineering. I would also like to thank the other University of Colorado professors from whom I’ve learned so much, including Dr. Dejan Filipović, Dr. Edward Kuester, Dr. Dragan Maksimović, Dr. Shannon Hughes and Dr. Albin Gasiewski. I would like to extend my thanks to Dr. José Garcia from the University of Cantabria in Spain for interesting me in high efficiency rectifier design. For providing detailed reviews of my papers, I am grateful to Dr. Srdjan Pajić, Dr. Quianli Mu and Dr. Fred Raab. Iextendmanythankstomyfundingagencies,includingTexasInstruments(formerlyNational Semiconductor), the Air Force Research Lab, MIT Lincoln Labs and the Defense Advanced Research Projects Agency. I am additionally indebted to TriQuint Semiconductor, especially Bill McCalpin and Dr. Charles Campbell,for their help during my stay at the University of Colorado. I look forward to working with both of them as an employee of TriQuint in the near future. Finally, I would like to thank my undergraduate advisor, Dr. David Kelley, for developing my interest in electromagnetics and microwave systems in the first place. Without that initial inspiration, who knows what I would be doing today. vi Contents 1 Introduction 1 1.1 Basic Efficiency Concepts 2 1.2 Research Problems & Chapter Overview 5 1.2.1 Chapter 2 Overview 5 1.2.2 Chapter 3 Overview 6 1.2.3 Chapter 4 Overview 7 1.2.4 Chapter 5 Overview 7 1.2.5 Chapter 6 Overview 7 2 Load Pull Based Power Amplifier Design 9 2.1 Introduction 10 2.2 Load Pull Measurement Theory 11 2.3 Load Pull Measurement Network Design 13 2.4 Tuner Characterization & Calibration 18 2.5 Load Pull With Fixed Class-F−1 Harmonic Terminations 26 2.5.1 Prototype PA & Measured Performance 28 2.6 X-Band MMIC Load Pull 31 2.6.1 Calibration Procedure 32 2.6.2 Relevant GaN on SiC Design Parameters and Limitations 35 2.6.3 Test Structures 36 2.6.4 MMIC Measurements 48 2.6.5 Acknowledgements 54 vii 2.7 Conclusion 54 3 Harmonically Terminated Power Amplifier Analysis 56 3.1 Introduction 57 3.2 Harmonically Terminated PA Analysis Approach 59 3.3 Efficiency Optimization Procedure 64 3.3.1 Evaluating the Global Minimum of a Function From Its Fourier Series Representation 66 3.4 Real Fundamental Load Impedance 71 3.4.1 Second-Harmonic Only PA 71 3.4.2 Second & Third Harmonic PA 78 3.5 Complex Fundamental Load Impedance 82 3.5.1 Contour Discontinuity 86 3.6 Extension to Practical PA with Parasitic Output Network 87 3.7 Alternate Normalization Conditions 91 3.8 Qualitative Experimental Validation 93 3.9 Conclusion 96 4 Supply Modulated Radar Transmitter Analysis & Design 97 4.1 Introduction 98 4.2 Radar System Performance Metric Analysis 99 4.2.1 Transmitted Spectrum 101 4.2.2 Received Radar Filter Output 104 4.2.3 Transmit Power Reduction & Receive Filter Mismatch Loss 111 4.2.4 Range Resolution & Time Side-lobe Level 112 4.3 Efficient and Linear Amplification of Spectrally Confined Pulsed AM Radar Signals 117 4.3.1 Pulsed Radar Transmitter Architecture 117 viii 4.3.2 Static Digital Pre-Distortion Concept 119 4.3.3 Experimental Setup and Measurements 121 4.4 Conclusion 123 5 High Efficiency Microwave Power Rectifier Analysis & De- sign 125 5.1 Introduction 126 5.2 Relationship to Power Amplifiers 127 5.3 Power Rectifier Analysis 128 5.3.1 Class-C Power Rectifier 129 5.3.2 Class-F Power Rectifier 136 5.3.3 Class-F−1 Power Rectifier 144 5.4 Conclusion 152 6 Harmonic Injection Power Amplifier 153 6.1 Introduction 153 6.2 Electrical Impedance Synthesis 155 6.3 Second Harmonic Injection Drain Waveforms 160 6.4 Third Harmonic Injection Drain Waveforms 167 6.5 Practical Implementation Issues & Limitations 175 6.6 Injection Circuit Analysis 176 6.7 Conclusion 183 7 Summary and Future Work 185 7.1 Summary & Contributions 185 7.2 Some Directions for Future Work 189 Bibliography 193 ix List of Tables 2.1 Harmonic power at PA output 28 2.2 SiC Substrate Parameters 35 2.3 Output Impedance vs. Frequency 52 3.1 Polynomial Coefficients for Waveform Containing up to Second Harmonic Terms 69 3.2 Example Fourier Coefficients 69 3.3 Example Roots and Critical Points 70 3.4 Harmonically Terminated Amplifier Parameters 79 x