Practical Computer Analysis of Switch Mode Power Supplies Copyright 2005 by Taylor & Francis Group, LLC Practical Computer Analysis of Switch Mode Power Supplies JOHNNY C. BENNETT Boca Raton London New York Singapore A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa plc. Copyright 2005 by Taylor & Francis Group, LLC DK1137_Discl.fm Page 1 Tuesday, July 5, 2005 2:29 PM Published in 2005 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2005 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-10: 0-8247-5387-9 (Hardcover) International Standard Book Number-13: 978-0-8247-5387-0 (Hardcover) Library of Congress Card Number 2005050581 This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. 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Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Bennett, Johnny C. Practical computer analysis of switch mode power supplies / Johnny C. Bennett. p. cm. Includes bibliographical references and index. ISBN 0-8247-5387-9 1. Switching power supplies--Computer simulation. I. Title. TK7881.15.B46 2005 621.31'7--dc22 2005050581 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com Taylor & Francis Group and the CRC Press Web site at is the Academic Division of T&F Informa plc. http://www.crcpress.com Copyright 2005 by Taylor & Francis Group, LLC DK1137_C000.fm Page v Monday, June 20, 2005 2:18 PM Preface For many years prior to the 1970s, engineers designed and built switch mode power supplies (SMPSs) using methods based largely on intuitive and exper- imentally derived techniques. In general, these power supplies were able to achieve their primary goal of high-efficiency power conversion; unfortu- nately, due to the lack of adequate theoretical analysis techniques, many of these power supplies only marginally met their desired performance require- ments. In many cases, they were considered to be unreliable. Although they appeared to be very simple in concept, these switching regulators exhibited phenomena that were not understood and certainly could not be analyzed. Things began to improve, however, in the early 1970s, when Dr. R.D. Mid- dlebrook and his group of students at the California Institute of Technology developed the powerful circuit-averaging techniques, thus opening the door for the application of conventional linear circuit analysis methods. With these tools brought to bear, the many subtle complexities of the conceptually “simple” switching regulator were soon understood, allowing engineers to design SMPSs with improved performance and higher reliability. At this point, the power electronics field began to expand rapidly as better components were developed, power conversion technology advancements were made, and sophisticated computer-aided design and analysis methods were utilized. Having been in the power electronics field for many years, I have had the good fortune to be involved with the design and analysis of many different types of power supplies. Here in this book, one of my goals is to provide the reader with a good understanding of the essential requirements for analyzing the switching regulated power supply performance characteristics. Another goal is to further demonstrate the power of the circuit-averaging technique by using computer circuit simulation programs to provide the desired performance analyses. At this point, I would like to reference the very important work of Dr. Vincent Bello, who, in his seminal paper,9 pointed the way to using the SPICE-based computer circuit simulator to perform linear small signal analysis and nonlinear large signal transient performance analysis as well. The simula- tion techniques presented in this book are based almost entirely on Dr. Bello’s approach. There have been several theoretical and practical contributors to the advancement of the circuit-averaging techniques over the years and I hope that the information presented here can help to further these advancements. • Chapter 1 is a refresher of the basics of SMPS fundamentals and circuit-averaging modeling. This may also be a primer for the new- comer, but it is recommended that the beginner read the referenced works to obtain a more complete understanding. Copyright 2005 by Taylor & Francis Group, LLC DK1137_C000.fm Page vi Monday, June 20, 2005 2:18 PM • Chapter 2 provides information on the general analysis requirements of a power supply. This is deemed necessary because it is equally important to know what questions to ask as it is to provide the answers. • Chapter 3 gives information on how to develop the general types of SMPS models and demonstrates the analysis approach using a SPICE-based circuit simulator. • Chapter 4 looks, in a practical way, at most of the basic first-order types of analysis generally associated with SMPS performance. • Chapter 5 provides more practical and detailed information on developing an SMPS and SMPS component models. • In Chapter 6, three power supplies are analyzed in practical detail. In these examples, emphasis is placed on using the circuit-averaging macromodel of the integrated circuit PWM controller. This is felt to simplify and expedite the analysis of a particular design that uses these commercially available controllers. As circuits and systems become larger and more complex, the macromodel approach will continue to increase in importance in almost all areas of electronic circuit analysis. The PWM macromodeling effort presented here will hopefully lead to the future development of many more such mac- romodels for commercially available PWM controllers, as has been the case with macromodels for transistors, op amps, etc. • Appendix A deals with the optimal design of SMPS input filters. This is included here simply because of the fundamental importance of this subject to any power supply. • Appendix B provides the first-order approach used in developing the macromodel for two commercially available PWM controllers. As was stated earlier, this is only a first step and hopefully will lead to the advancement and further development of these macros. Although they are very important aspects of any switch mode power supply, the analyses of actual switching circuits per se are not specifically addressed in this book. For our purposes, these switching circuits are con- sidered to be in the realm of conventional electronic circuit transient analysis and not implicitly related to the performance of an SMPS. There may be exceptions to this, of course. I would like to express my thanks and appreciation to all the wonderful people with whom I have worked over the years who have shared their invaluable knowledge and experiences. I would also like to expressly thank Col. William T. McLyman of the Jet Propulsion Laboratory for his encour- agement and for being instrumental in producing this book. Johnny C. Bennett Copyright 2005 by Taylor & Francis Group, LLC DK1137_C000.fm Page vii Monday, June 20, 2005 2:18 PM Author Johnny C. Bennett is a native of the state of Louisiana and is a graduate of Louisiana Tech University. He received his BSEE in 1964 and has worked as an electronics engineer over the past 40 years specializing in analog and power electronics circuit design. He has worked for many of the top tech- nological companies both as an employee and as a consultant. Johnny’s hobbies are reading, music, genealogy, and traveling. He currently resides in the city of South Lake Tahoe, California, and is the father of two adult sons. Copyright 2005 by Taylor & Francis Group, LLC DK1137_C000.fm Page ix Monday, June 20, 2005 2:18 PM Contents 1 Review of Switch Mode Power Supply Fundamentals 1.1 Basic Topologies 1.1.1 Buck Converter — Continuous Mode 1.1.2 Buck Converter — Discontinuous Mode 1.1.3 Boost Converter — Continuous Mode 1.1.4 Boost Converter — Discontinuous Mode 1.1.5 Buck–Boost Converter — Continuous Mode 1.1.6 Buck–Boost Converter — Discontinuous Mode 1.2 Basic Control Methods 1.2.1 Frequency of Operation Factors (FOFs) 1.2.2 Voltage Mode Control 1.2.3 Current Mode Control 1.2.4 Feedback and Feedforward Control Additions 1.3 Conclusion 2 SMPS Analysis Requirements 2.1 DC Requirements 2.1.1 Output Regulation 2.1.2 Cross Regulation with Multiple Outputs 2.1.3 Efficiency 2.1.4 Miscellaneous Range and Threshold Considerations 2.2 AC Requirements 2.2.1 AC Control Loop Stability Margins 2.2.2 Input Filter Stability Margins 2.2.3 Source and Load Stability Margins 2.2.4 Electromagnetic Compatibility 2.3 Transient Requirements 2.3.1 Load Transients 2.3.2 Line Transients 2.3.3 Power-Up and Power-Down Transients 2.3.4 Energy Storage for Line Dropouts 2.4 Summary 3 Fundamental Switch Mode Converter Model Development 3.1 Buck and Boost Converter Continuous Mode Large Signal Models Copyright 2005 by Taylor & Francis Group, LLC DK1137_C000.fm Page x Monday, June 20, 2005 2:18 PM 3.2 Buck and Boost Converter Discontinuous Mode Large Signal Models 3.3 Buck and Boost Continuous and Discontinuous Mode Unified Models 3.4 Buck–Boost (Flyback) Converter Continuous Mode Large Signal Model 3.5 Buck–Boost (Flyback) Converter Discontinuous Mode Large Signal Model 3.6 Buck–Boost Continuous and Discontinuous Mode Unified Model 3.7 Cuk Converter Continuous Mode Large Signal Model 3.8 Cuk Converter Discontinuous Mode Large Signal Model 3.9 Cuk Converter Continuous and Discontinuous Mode Unified Model 3.10 Boost Converter Model Analysis Example 3.11 Summary 4 Analyzing the Fundamental SMPS Model 4.1 Buck Converter SMPS Analysis (Voltage Mode) 4.1.1 Voltage Mode Converter Model Setup 4.1.2 Open Loop Analysis (Continuous and Discontinuous Modes) 4.1.2.1 Forward Transfer Function 4.1.2.2 Output Impedance (Voltage Mode) 4.1.2.3 Control to Output (Voltage Mode) 4.1.3 SMPS Closed Loop Analysis (Continuous and Discontinuous Modes) 4.1.3.1 AC Loop Gain (Voltage Mode) 4.1.3.2 SMPS Output Impedance (Voltage Mode) 4.1.3.3 SMPS Line Regulation (Voltage Mode) 4.1.3.4 SMPS Feedforward Analysis 4.1.4 SMPS Combined Feedback and Feedforward Analysis (Line Regulation) 4.2 Buck Converter SMPS Analysis (Current Mode) 4.2.1 Current Mode Converter Model Setup 4.2.2 Open Voltage Loop AC Analysis (Continuous and Discontinuous Modes) 4.2.2.1 Open Voltage Loop AC Output Impedance (Current Mode) 4.2.2.2 Open Voltage Loop Forward Transfer Function (Current Mode) 4.2.2.3 Control to Output Analysis (Current Mode) 4.2.2.4 Inner Inductor Current Control Loop Gain Copyright 2005 by Taylor & Francis Group, LLC DK1137_C000.fm Page xi Monday, June 20, 2005 2:18 PM 4.2.3 SMPS Closed Loop Analysis (Current Mode) 4.2.3.1 SMPS Output Impedance (Current Mode) 4.2.3.2 SMPS Line Regulation (Current Mode) 4.3 Summary 5 SMPS Component Models 5.1 Component Model Development 5.1.1 Real-World Capacitor Macro. 5.1.2 Real-World Inductor Macro 5.1.3 SMPS Diode Macro 5.1.4 Integrated Circuit Controllers 5.2 Parasitic Resistance Effects 5.3 Peripheral Circuit Additions 5.3.1 Input Filter 5.3.2 Inrush Current Limiter 5.3.3 Undervoltage Lockout and Soft Start Circuits 5.3.4 Power Factor Correction Circuits 5.3.5 Multiple Outputs 5.3.6 Postregulated Output Circuits 5.3.7 Synchronous Rectifier Circuits 5.3.8 Energy Storage Systems 5.4 Summary 6 Analyzing the Advanced SMPS Model 6.1 Pulse Width Modulator (PWM) Controller Macromodel 6.2 Practical Flyback SMPS Analysis 6.2.1 Flyback SMPS Model Setup 6.2.2 Flyback SMPS Large Signal Power ON/OFF Analysis 6.2.3 Flyback SMPS Large Signal Load and Line Transient Analysis 6.2.4 Flyback SMPS Current-Limiting Performance 6.2.5 Flyback SMPS AC Stability Analysis 6.2.6 Flyback SMPS AC Line Rejection Analysis 6.3 Practical Buck SMPS Analysis with Parasitic Resistances 6.3.1 Practical Buck Converter Model Development with Parasitic Resistances 6.4 Practical “Loop-Opening” Techniques for AC Analysis 6.5 Buck SMPS Soft Start and “Hiccup” Current Limit Analysis 6.6 Summary Appendix A Design Fundamentals of SMPS Input Filters A.1 General Requirements A.2 Fundamental Single-Stage LC Section Examples Copyright 2005 by Taylor & Francis Group, LLC DK1137_C000.fm Page xii Monday, June 20, 2005 2:18 PM A.3 Parallel Damped Single-Stage Input Filter A.4 Series Damped Single Stage Input Filter A.5 Two-Stage Input Filter Design Appendix B Pulse Width Modulator Controller Macromodeling B.1 UC 1844 Circuit-Averaging Macromodel Development B.2 UC 1825A Circuit-Averaging Macromodel Development References Copyright 2005 by Taylor & Francis Group, LLC