DESIGN, MODELING AND NOISE MEASUREMENT OF OSCILLATORS USING A LARGE SIGNAL NETWORK ANALYZER DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Inwon Suh, M.S.E.E. Graduate Program in Electrical and Computer Engineering The Ohio State University 2011 Dissertation Committee: Prof. Patrick Roblin, Adviser Prof. Steven B. Bibyk Prof. Roberto Rojas-Teran Prof. James Peck °c Copyright by Inwon Suh 2011 ABSTRACT Oscillators play a crucial role in wireless communication systems since they are used together with mixers for frequency translation. To design discrete oscillators in a more efficient way in terms of output power, a multi-harmonic real-time open-loop active load- pull technique was developed and used to find the optimal fundamental and harmonic load impedances. Multi-harmonic loaded load circuits were then designed and implemented to approach the optimal multi-harmonic load impedances and realize a stand-alone oscillator. Then, a new behavioral modeling technique based on power dependent Volterra series was developed to model negative-resistance oscillators. The derived behavioral model pre- dicts the harmonic load-pull behaviors and the output power characteristics of oscillators and assists with the oscillator design. The noise characteristic of oscillator is also of great importance in communication cir- cuits. A new generalized 1/f Kurokawa noise analysis applicable to both low and high Q oscillators is proposed for 1/f phase and amplitude noise. A theoretical correspon- dence between the new generalized Kurokawa theory and the impulse sensitivity function and the perturbation projection vector analyses is also derived. The proposed generalized Kurokawa theory is then applied to a Van Der Pol oscillator, a BJT Colpitts oscillator and a CMOS ring-oscillator, and a pHEMT oscillator and is verified to yield comparable results to those obtained from the matrix conversion method and the experimental result. ii Also, an 1/f additive phase noise analysis for the injection-locked oscillator is presented. An additive phase noise measurement system integrated with an LSNA is also developed to effectively acquire the model parameters needed. The validity of the analytic solution is finally verified to yield reasonable agreement to the experimental result. The additive phase noise measurement system integrated with a LSNA and a tunable monochromatic light source is further applied to characterize the additive phase noise per- formance of the both passivated and unpassivated AlGaN/GaN HEMT at 2 GHz under various operating conditions. Illumination with different photon energies, different drain voltages, and different load impedances are used to probe the dependence of the additive phase noise on the trap and 2DEG population. iii This is dedicated to my family. iv ACKNOWLEDGMENTS First of all, I would like to express my deep appreciation to my respected advisor Pro- fessor Patrick Roblin for his teaching and support. His outstanding insights and creative ideas have made various impossible researches possible whenever we have faced difficul- ties. Most of all, he has been an excellent role model for me as a researcher and even as a human being. All of the knowledge and experiences I have learned from him will inspire me for the rest of my life. I also would like to thank Professor Roberto Rojas and Professor Steven Bibyk for their valuable time and guidance throughout my graduate studies as excellent committee members. Without their supports and advices, it would not have been possible for me to complete my doctorate studies. It is also my great pleasure to thank visiting scholars: Professor Hyo Dal Park, Professor Young Gi Kim, and Dr. Dominique Chaillot. They always gave me fruitful advices and encouragements for my research whenever needed. I would also like to give my gratitude to Jeff Strahler and Christian Bean. They were great mentors during my internship at Andrew Wireless Solutions. I also would like to express my gratitude for all of the colleagues in our Non-Linear RF Lab. Especially, I thank Professor Seok Joo Doo who greatly helped me for doing many experiments in the lab. Also Dr. Sukkeun Myoung, Dr. Sunyoung Lee, Dr. Jongsoo Lee, and Dr. Xian Cui greatly helped me understanding many difficult concepts and ideas v related to the research as senior students. Also I spent many enjoyable days with Venkatesh Balasubramanian discussing various research areas. I also would like to thank Haedong Jang, Jiwoo Kim, and Youngseo Ko for providing great research discussions as well as their time for entertainments. Also Chie-Kai Yang, Xi Yang, Chunjoo Yang, Andres Zarate-de-Landa, and Dounia Baiya helped me a lot under- standing various different research areas. I also owe a lot of appreciation to my parents and brother in South Korea for their continuous encouragement and support. Without their love and support, it would not have been possible to complete this work. Finally I would like to express my deepest gratitude to my wife Junghoon Lee, son Jonathan Suh, and daughter Jenny Suh for their endless love and support during my grad- uate studies. Especially Junghoon has sacrificed so much time for me and it will never be forgettable. I love you and let’s enjoy this memorable time of our life. vi VITA January, 1979 . Born - Seoul, Republic of Korea August, 2005 . B. S. Electrical Engineering, Korea University, Seoul, Republic of Korea June, 2007 . .M. S. Electrical & Computer Engineering, The Ohio State University. June, 2007 - present . Ph. D. Student, Electrical and Computer Engineering, The Ohio State University. June 2007 - September 2007 . Graduate Research Associate, Electrical and Computer Engineering, The Ohio State University. September 2007 - June 2008 . Graduate Teaching Associate, Electrical and Computer Engineering, The Ohio State University. June 2008 - September 2008 . Intern, Andrew Wireless Solutions, Westerville, OH. September 2008 - March 2009 . .Graduate Teaching Associate, Electrical and Computer Engineering, The Ohio State University. March 2009 - September 2009 . .Graduate Research Associate, Electrical and Computer Engineering, The Ohio State University. September 2009 - June 2010 . Graduate Teaching Associate, Electrical and Computer Engineering, The Ohio State University. vii June 2010 - September 2010 . Graduate Research Associate, Electrical and Computer Engineering, The Ohio State University. September 2010 - present . Graduate Teaching Associate, Electrical and Computer Engineering, The Ohio State University. PUBLICATIONS Research Publications P. Roblin, Y. Ko, C. K. Yang, I. Suh, and S. J. Doo, “NVNA Techniques for Pulsed RF Measurements”. IEEE Microwave Magazine, vol. 12, no. 2, pp. 65-76, Apr. 2011. I. Suh, P. Roblin, S. J. Doo, X. Cui, J. Strahler, and R. G. Rojas, “A Measurement-Based Methodology to Design Harmonic Loaded Oscillators Using Real-Time Active Load-Pull”. IET Microwaves, Antennas and Propagation, vol. 5, no. 1, pp. 77-83, Jan. 2011. I. Suh, P. Roblin, Y. Ko, C. K. Yang, A. Malonis, A. Arehart, S. Ringel, C. Poblenz, Y. Pei, J. Speck, and U. Mishra, “Additive Phase Noise Measurements of AlGaN/GaN HEMTs Using an Large Signal Network Analyzer and a Tunable Monochromatic Light Source”. ARFTG 74th Conf., Broomfield/Boulder, CO, Dec. 2009. J. Mukherjee, Y. G. Kim, I. Suh, P. Roblin, W. R. Liou, Y. C. Lin and M. Shojaei Baghini, “Microstrip Equivalent Parasitic Modeling of RFIC Interconnects”. 50th Midwest Symp. on Circuits and Systems, Montreal, Canada, Aug. 2007. I. Suh, S. J. Doo, P. Roblin, X. Cui, Y. G. Kim, J. Strahler, M. V. Bossche, R. Rojas, and H. D. Park, “Negative input resistance and real-time active load-pull measurements of a 2.5GHz oscillator using a LSNA”. ARFTG 69th Conf., Honolulu, HI, June 2007. FIELDS OF STUDY Major Field: Electrical and Computer Engineering Studies in Microwave and Microelectronics: Prof. Patrick Roblin viii TABLE OF CONTENTS Page Abstract . ii Dedication . iv Acknowledgments . v Vita ........................................... vii List of Tables . xii List of Figures . xiii Chapters: 1. Introduction . 1 1.1 Measurement-based oscillator design . 1 1.2 Oscillator 1/f phase noise models . 4 1.2.1 1/f phase noise model for oscillator . 4 1.2.2 1/f phase noise model for injection-locked oscillator . 8 1.3 Additive phase noise measurement system . 9 1.4 Research outline and new contributions . 10 2. Measurement-based methodology to design harmonic loaded oscillators using real-time active load pull . 13 2.1 Description of the Measurement System . 15 2.1.1 Negative Resistance Oscillator Design . 15 2.1.2 Real-Time Active Load-Pull Measurement System . 16 2.2 Experimental Results . 18 2.2.1 Negative Input Resistance . 18 ix 2.2.2 Harmonic Tuning . 18 2.2.3 Device Line Measurement . 23 2.3 Stand Alone Oscillator . 26 2.3.1 Design of Harmonic Load Circuits . 26 2.3.2 Experimental Results . 26 2.4 Conclusion . 28 3. Behavioral modeling of oscillators using real-time active load pull . 30 3.1 Power-Dependent Volterra Series Modeling . 31 3.1.1 Volterra Algorithm . 31 3.1.2 Model Extraction . 33 3.2 Model Validation . 35 3.2.1 Error Evaluation . 38 3.3 Conclusion . 42 4. Model comparison for 1/f noise in oscillators with and without AM to PM noise conversion . 43 4.1 Kurokawa 1/f Noise Models for an Oscillator . 47 4.1.1 Derivation of Sa,1/f (∆ω) ..................... 53 4.1.2 Derivation of Sφ,1/f (∆ω) ..................... 55 4.1.3 Comparison of Kurokawa theory with ISF theory for 1/f noise . 57 4.1.4 Comparison of Kurokawa theory with PPV theory for 1/f noise . 59 4.2 Modified Van der Pol Oscillator . 62 4.2.1 Kurokawa Coefficients Extraction . 64 4.2.2 Amplitude and Frequency of Oscillation and Phase Noise . 67 4.2.3 PPV Analytic Solution . 68 4.3 Model Comparison for 1/f noise in Van der Pol Oscillator .