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UMI ABell&Howdl Information Compaty 300 North Zed» Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600 Analytical Methods for Mixed Signal Processing Systems DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Hung-Chuan Pai, B.S.E.E., M.S.E.E. ***** The Ohio State University 1998 Dissertation Committee: Approved by Professor Steven Bibyk, Adviser Professor Mohammed Ismail Adviser / Professor Joanne DeGroat Department of Electrical Engineering UMI Number: 9822355 UMI Microform 9822355 Copyright 1998, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 (c) Copyright by Hung-Chuan Pai 1998 ABSTRACT With the emergence of computers, engineers found applications of powerfiil signal processing, signal transmission, as well as information storage methods using digital systems. When applying data to digital systems, the transfer of signals from analog to digital is the first step. Conventionally, this operation was dealt with using a variety of high precision components, such as flash converters. Other approaches, like DPCM and Delta Modulation, increase system accuracy by reducing the variation of the signal processed. However, these approaches are inefficient because precision in the quantizer and D /A converter is still required; they do not take advantage of modem VLSI technology. As VLSI technology progresses, very high speed clocking rates and instruction processing have become available and should now be applied to simplify traditional systems. In this dissertation, we apply oversampling and Sigma-Delta modulation (SAM) approaches to propose an implementation structure for a general purpose, programmable, and multipherless DSP chip. The preceding anti-aliasing filter will become less important as a result of oversampling. Diverse SA modulators, including one first order lowpass SAM, several second order cascade-structure lowpass SAM’s, one second order MASH-stracture lowpass SAM, and one second order bandpass SAM, will be discussed using additive quantization noise to model an one-bit quan­ tizer. A second order lowpass SA modulator is especially suitable for VLSI technology 11 because of its tolerance of component mismatch as well as nonideal circuit behavior. Therefore, a second order EAM structure will be used throughout the discussion of a complete SAM system. To maintain the simplicity of DAC linearity, an one-bit quantizer will be chosen. A wide input range SA modulator structure is proposed. This structure can extend the input range by at least threefold when compared with its competitive traditional SA modulators. Advanced (quasilinear) models for the one-bit quantizer with respect to a DC input and a sinusoidal input to a SA modulator are analyzed. Stability issues are discussed using this advanced model for second and higher order SA modulators. A highly important contribution of knowing the theoretical quan­ tization noise shape is to confidently design the required decimation stages/filters in lieu of trial and error approaches as well as overstrained conditions. Sinusoidal signals will be applied to explain and test the theoretical/realistic system because, by the Fourier analysis (Fourier Series), all signals can be approximately decomposed as the summation of sinusoidal components. The exploration of the linearized SAM model with respect to different sinusoidal magnitude inputs will be crucial for the advanced inspection and design of the optimized SAM system. Diverse decimation-stage design strategies are going to be discussed. The feasibility of a multiplierless SAM system is also of interest. Because of the reduction of multipliers, the proposed SAM system structure will not only be simplified but also possess high data throughput and ex­ cellent resolution. A few high performance and multiplierless decimation-stages are presented. m To my parents and my wife IV ACKNOWLEDGMENTS I wish to acknowledge my adviser, Dr. Steven Bibyk, for his direction, guidance, advice, and support throughout my research. I also wish to thank Dr. Mohammed Ismail and Dr. Joanne DeGroat for their guidance, dedication, and encouragement for my research. Many thanks go to Dr. George Majda for being in my committee and reading my dissertation. I extend heartfelt appreciation to my family, especially my parents and my wife, Yun-I Patricia Liu, for their encourgement and support. I am also indebted to my friends, Hung-Chih Chiang, Tsung-Yuan Chang, and John Fisher, for their valued discussion. Many thanks go to Micrys Inc. for providing assistance and support. VITA February 7, 1966 ...............................................Bom—Tainan, Taiwan, R.O.C. June 1989 ........................................................... B.S. Electrical Engineering, National Cheng-Kung University Tainan, Taiwan, R.O.C. 1989 - 1991 ....................................................... Military second lieutenant Taipei, Taiwan, R.O.C. 1991 - 1992 ....................................................... Research engineer Lieu Ming Company Tainan, Taiwan, R.O.C. 1992 - 1994 ....................................................... M.S. Electrical Engineering, The Ohio State University Columbus, Ohio, U.S.A. 1994 - present .................................................. Graduate Research Associate The Ohio State University Columbus, Ohio, U.S.A. VI PUBLICATIONS Research Publications Hung-Chuan Pai and Steven B. Bibyk “High Dynamic Range Design for SAM with Wide Input Ranges”. 1st Analog VLSI Workshop Proceedings, May, 1997. Hung-Chuan Pai and Steven B. Bibyk “High Dynamic Range Design for SAM with Wide Input Ranges”. Submitted to the Special Issue of the Intematinal Journal of Analog Integrated Circuits and Signal Froccesing, 1998. FIELDS OF STUDY Major Field: Electrical Engineering Studies in: Topic 1 Signal Processing Topic 2 System Circuit Design vu TABLE OF CONTENTS P age A bstract........................................................................................................................ ii Dedication........................................................................................................................ iv Acknowledgments ........................................................................................................ v V i t a .................................................................................................................................. vi List of Tables............................................................................................................... x List of Figures ............................................................................................................... xi Chapters: 1. Introduction ......................................................................................................... 1 2. Relationship of DPCM, AM, and EAM .......................................................... 7 2.1 Differential Pulse Code Modulation (DPCM) ................................... 7 2.2 Delta Modulation (A M )......................................................................... 8 2.3 Sigma-Delta (EA) M odulation ............................................................. 10 2.4 Example for Oversampling and First-Order EA Modulation .... 11 3. Modeling and Analyzing EAM ...................................................................... 15 3.1 Modeling EA Modulators ...................................................................... 15 3.2 Second Order Lowpass EA Modulators ................................................ 23 3.3 Second Order Bandpass EA Modulator................................................ 27 viu 4. Advanced Model for EAM and Noise Shaping .............................................. 30 4.1 The Advanced EAM Model as DC Input............................................. 32 4.2 The Advanced EAM Model as Sinusoidal Input................................ 38 4.3 Affect of Quantization Noise Signal Component Gain Gx in Stability 43 4.4 Affect of Quantization Noise

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