Pulse-Width Modulated DC-DC Power Converters Second Edition

Transcription

1 Pulse-Width Modulated DC-DC Power Converters Second Edition Marian K. Kazimierczuk

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3 Pulse-Width Modulated DC DC Power Converters

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5 Pulse-Width Modulated DC DC Power Converters Second Edition MARIAN K. KAZIMIERCZUK Wright State University, Dayton, Ohio, USA

6 This edition first published John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought Library of Congress Cataloging-in-Publication Data Kazimierczuk, Marian K. Pulse-width modulated DC DC power converters / Marian K. Kazimierczuk. Second edition. pages cm Includes bibliographical references and index. ISBN (cloth) 1. DC-to-DC converters. 2. Pulse circuits. 3. PWM power converters. I. Title. TK7872.C8K dc A catalogue record for this book is available from the British Library. ISBN: Set in 9.5/11.5pt Times by Aptara Inc., New Delhi, India

7 To my wife Alicja

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9 Contents About the Author Preface Nomenclature xxi xxiii xxv 1 Introduction Classification of Power Supplies Basic Functions of Voltage Regulators Power Relationships in DC DC Converters DC Transfer Functions of DC DC Converters Static Characteristics of DC Voltage Regulators Dynamic Characteristics of DC Voltage Regulators Linear Voltage Regulators Series Voltage Regulator Shunt Voltage Regulator Topologies of PWM DC DC Converters Relationships Among Current, Voltage, Energy, and Power Summary 19 References 19 Review Questions 20 Problems 21 2 Buck PWM DC DC Converter Introduction DC Analysis of PWM Buck Converter for CCM Circuit Description Assumptions Time Interval: 0 < t DT Time Interval: DT < t T Device Stresses for CCM DC Voltage Transfer Function for CCM Boundary Between CCM and DCM Capacitors Ripple Voltage in Buck Converter for CCM Switching Losses with Linear MOSFET Output Capacitance Switching Losses with Nonlinear MOSFET Output Capacitance Power Losses and Efficiency of Buck Converter for CCM DC Voltage Transfer Function of Lossy Converter for CCM MOSFET Gate-Drive Power 48

10 viii Contents Gate Driver Design of Buck Converter for CCM DC Analysis of PWM Buck Converter for DCM Time Interval: 0 < t DT Time Interval: DT < t (D + D 1 )T Time Interval: (D + D 1 )T < t T Device Stresses for DCM DC Voltage Transfer Function for DCM Maximum Inductance for DCM Power Losses and Efficiency of Buck Converter for DCM Design of Buck Converter for DCM Buck Converter with Input Filter Buck Converter with Synchronous Rectifier Buck Converter with Positive Common Rail Quadratic Buck Converter Tapped-Inductor Buck Converters Tapped-Inductor Common-Diode Buck Converter Tapped-Inductor Common-Transistor Buck Converter Watkins Johnson Converter Multiphase Buck Converter Switched-Inductor Buck Converter Layout Summary 85 References 87 Review Questions 88 Problems 88 3 Boost PWM DC DC Converter Introduction DC Analysis of PWM Boost Converter for CCM Circuit Description Assumptions Time Interval: 0 < t DT Time Interval: DT < t T DC Voltage Transfer Function for CCM Boundary Between CCM and DCM Ripple Voltage in Boost Converter for CCM Power Losses and Efficiency of Boost Converter for CCM DC Voltage Transfer Function of Lossy Boost Converter for CCM Design of Boost Converter for CCM DC Analysis of PWM Boost Converter for DCM Time Interval: 0 < t DT Time Interval: DT < t (D + D 1 )T Time Interval: (D + D 1 )T < t T Device Stresses for DCM DC Voltage Transfer Function for DCM Maximum Inductance for DCM Power Losses and Efficiency of Boost Converter for DCM Design of Boost Converter for DCM 120

11 Contents ix 3.4 Bidirectional Buck and Boost Converters Synchronous Boost Converter Tapped-Inductor Boost Converters Tapped-Inductor Common-Diode Boost Converter Tapped-Inductor Common-Load Boost Converter Duality Power Factor Correction Power Factor Boost Power Factor Corrector Electronic Ballasts for Fluorescent Lamps Summary 141 References 142 Review Questions 143 Problems Buck Boost PWM DC DC Converter Introduction DC Analysis of PWM Buck Boost Converter for CCM Circuit Description Assumptions Time Interval: 0 < t DT Time Interval: DT < t T DC Voltage Transfer Function for CCM Device Stresses for CCM Boundary Between CCM and DCM Ripple Voltage in Buck Boost Converter for CCM Power Losses and Efficiency of the Buck Boost Converter for CCM DC Voltage Transfer Function of Lossy Buck Boost Converter for CCM Design of Buck Boost Converter for CCM DC Analysis of PWM Buck Boost Converter for DCM Time Interval: 0 < t DT Time Interval: DT < t (D + D 1 )T Time Interval: (D + D 1 )T < t T Device Stresses of the Buck Boost Converter in DCM DC Voltage Transfer Function of the Buck Boost Converter for DCM Maximum Inductance for DCM Power Losses and Efficiency of the Buck Boost Converter in DCM Design of Buck Boost Converter for DCM Bidirectional Buck Boost Converter Synthesis of Buck Boost Converter Synthesis of Boost Buck (Ćuk) Converter Noninverting Buck Boost Converters Cascaded Noninverting Buck Boost Converters Four-Transistor Noninverting Buck Boost Converters Tapped-Inductor Buck Boost Converters Tapped-Inductor Common-Diode Buck Boost Converter Tapped-Inductor Common-Transistor Buck Boost Converter Tapped-Inductor Common-Load Buck Boost Converter Tapped-Inductor Common-Source Buck Boost Converter 191

12 x Contents 4.9 Summary 192 References 192 Review Questions 193 Problems Flyback PWM DC DC Converter Introduction Transformers DC Analysis of PWM Flyback Converter for CCM Derivation of PWM Flyback Converter Circuit Description Assumptions Time Interval: 0 < t DT Time Interval: DT < t T DC Voltage Transfer Function for CCM Boundary Between CCM and DCM Ripple Voltage in Flyback Converter for CCM Power Losses and Efficiency of Flyback Converter for CCM DC Voltage Transfer Function of Lossy Converter for CCM Design of Flyback Converter for CCM DC Analysis of PWM Flyback Converter for DCM Time Interval: 0 < t DT Time Interval: DT < t (D + D 1 )T Time Interval: (D + D 1 )T < t T DC Voltage Transfer Function for DCM Maximum Magnetizing Inductance for DCM Ripple Voltage in Flyback Converter for DCM Power Losses and Efficiency of Flyback Converter for DCM Design of Flyback Converter for DCM Multiple-Output Flyback Converter Bidirectional Flyback Converter Ringing in Flyback Converter Flyback Converter with Passive Dissipative Snubber Flyback Converter with Zener Diode Voltage Clamp Flyback Converter with Active Clamping Two-Transistor Flyback Converter Summary 243 References 244 Review Questions 244 Problems Forward PWM DC DC Converter Introduction DC Analysis of PWM Forward Converter for CCM Derivation of Forward PWM Converter Time Interval: 0 < t DT Time Interval: DT < t DT + t m Time Interval: DT + t m < t T Maximum Duty Cycle 253

13 Contents xi Device Stresses DC Voltage Transfer Function for CCM Boundary Between CCM and DCM Ripple Voltage in Forward Converter for CCM Power Losses and Efficiency of Forward Converter for CCM DC Voltage Transfer Function of Lossy Converter for CCM Design of Forward Converter for CCM DC Analysis of PWM Forward Converter for DCM Time Interval: 0 < t DT Time Interval: DT < t DT + t m Time Interval: DT + t m < t (D + D 1 )T Time Interval: (D + D 1 )T < t T DC Voltage Transfer Function for DCM Maximum Inductance for DCM Power Losses and Efficiency of Forward Converter for DCM Design of Forward Converter for DCM Multiple-Output Forward Converter Forward Converter with Synchronous Rectifier Forward Converters with Active Clamping Two-Switch Forward Converter Forward Flyback Converter Summary 292 References 293 Review Questions 293 Problems Half-Bridge PWM DC DC Converter Introduction DC Analysis of PWM Half-Bridge Converter for CCM Circuit Description Assumptions Time Interval: 0 < t DT Time Interval: DT < t T Time Interval: T 2 < t T 2 + DT Time Interval: T 2 + DT < t T Device Stresses DC Voltage Transfer Function of Lossless Half-Bridge Converter for CCM Boundary Between CCM and DCM Ripple Voltage in Half-Bridge Converter for CCM Power Losses and Efficiency of Half-Bridge Converter for CCM DC Voltage Transfer Function of Lossy Converter for CCM Design of Half-Bridge Converter for CCM DC Analysis of PWM Half-Bridge Converter for DCM Time Interval: 0 < t DT Time Interval: DT < t (D + D 1 )T Time Interval: (D + D 1 )T < t T DC Voltage Transfer Function for DCM Maximum Inductance for DCM 326

14 xii Contents 7.4 Summary 326 References 327 Review Questions 327 Problems Full-Bridge PWM DC DC Converter Introduction DC Analysis of PWM Full-Bridge Converter for CCM Circuit Description Assumptions Time Interval: 0 < t DT Time Interval: DT < t T Time Interval: T 2 < t T 2 + DT Time Interval: T 2 + DT < t T Device Stresses DC Voltage Transfer Function of Lossless Full-Wave Converter for CCM Boundary Between CCM and DCM Ripple Voltage in Full-Bridge Converter for CCM Power Losses and Efficiency of Full-Bridge Converter for CCM DC Voltage Transfer Function of Lossy Converter for CCM Design of Full-Bridge Converter for CCM DC Analysis of PWM Full-Bridge Converter for DCM Time Interval: 0 < t DT Time Interval: DT < t (D + D 1 )T Time Interval: (D + D 1 )T < t T DC Voltage Transfer Function for DCM Maximum Inductance for DCM Phase-Controlled Full-Bridge Converter Summary 362 References 362 Review Questions 362 Problems Small-Signal Models of PWM Converters for CCM and DCM Introduction Assumptions Averaged Model of Ideal Switching Network for CCM Averaged Values of Switched Resistances Model Reduction Large-Signal Averaged Model for CCM DC and Small-Signal Circuit Linear Models of Switching Network for CCM Large-Signal Circuit Model of Switching Network for CCM Linearization of Switching Network Model for CCM Block Diagram of Small-signal Model of PWM DC DC Converters Family of PWM Converter Models for CCM PWM Small-Signal Switch Model for CCM Modeling of Ideal Switching Network for DCM Relationships Among DC Components for DCM Small-Signal Model of Ideal Switching Network for DCM 395

15 Contents xiii 9.12 Averaged Parasitic Resistances for DCM Summary 400 References 402 Review Questions 405 Problems Small-Signal Characteristics of Buck Converter for CCM Introduction Small-Signal Model of the PWM Buck Converter Open-Loop Transfer Functions Open-Loop Control-to-Output Transfer Function Delay in Control-to-Output Transfer Function Open-Loop Input-to-Output Transfer Function Open-Loop Input Impedance Open-Loop Output Impedance Open-Loop Step Responses Open-Loop Response of Output Voltage to Step Change in Input Voltage Open-Loop Response of Output Voltage to Step Change in Duty Cycle Open-Loop Response of Output Voltage to Step Change in Load Current Open-Loop DC Transfer Functions Summary 436 References 436 Review Questions 437 Problems Small-Signal Characteristics of Boost Converter for CCM Introduction DC Characteristics Open-Loop Control-to-Output Transfer Function Delay in Open-Loop Control-to-Output Transfer Function Open-Loop Audio Susceptibility Open-Loop Input Impedance Open-Loop Output Impedance Open-Loop Step Responses Open-Loop Response of Output Voltage to Step Change in Input Voltage Open-Loop Response of Output Voltage to Step Change in Duty Cycle Open-Loop Response of Output Voltage to Step Change in Load Current Summary 467 References 467 Review Questions 468 Problems Voltage-Mode Control of PWM Buck Converter Introduction Properties of Negative Feedback Stability Single-Loop Control of PWM Buck Converter Closed-Loop Small-Signal Model of Buck Converter Pulse-Width Modulator 478

16 xiv Contents 12.7 Feedback Network Transfer Function of Buck Converter with Modulator and Feedback Network Control Circuits Error Amplifier Proportional Controller Integral Controller Proportional-Integral Controller Integral-Single-Lead Controller Loop Gain Closed-Loop Control-to-Output Voltage Transfer Function Closed-Loop Input-to-Output Transfer Function Closed-Loop Input Impedance Closed-Loop Output Impedance Closed-Loop Step Responses Response to Step Change in Input Voltage Response to Step Change in Reference Voltage Closed-Loop Response to Step Change in Load Current Closed-Loop DC Transfer Functions Summary 518 References 519 Review Questions 519 Problems Voltage-Mode Control of Boost Converter Introduction Circuit of Boost Converter with Voltage-Mode Control Transfer Function of Modulator, Boost Converter Power Stage, and Feedback Network Integral-Double-Lead Controller Design of Integral-Double-Lead Controller Loop Gain Closed-Loop Control-to-Output Voltage Transfer Function Closed-Loop Audio Susceptibility Closed-Loop Input Impedance Closed-Loop Output Impedance Closed-Loop Step Responses Closed-Loop Response to Step Change in Input Voltage Closed-Loop Response to Step Change in Reference Voltage Closed-Loop Response to Step Change in Load Current Closed-Loop DC Transfer Functions Summary 552 References 552 Review Questions 552 Problems Current-Mode Control Introduction Principle of Operation of PWM Converters with Peak CMC Relationship Between Duty Cycle and Inductor-Current Slopes Instability of Closed-Current Loop 560

17 Contents xv 14.5 Slope Compensation Analysis of Slope Compensation in Time Domain Boundary of Slope Compensation for Buck and Buck Boost Converters Boundary Slope Compensation for Boost Converter Sample-and-Hold Effect on Current Loop Natural Response of Inductor Current to Small Perturbation in Closed-Current Loop Forced Response of Inductor Current to Step Change in Control Voltage in Closed-Current Loop Relationship Between s-domain and z-domain Transfer Function of Closed-Current Loop in z-domain Closed-Loop Control Voltage-to-Inductor Current Transfer Function in s-domain Approximation of H icl by Rational Transfer Function Step Responses of Closed-Inner Loop Loop Gain of Current Loop Loop Gain of Inner Loop in z-domain Loop Gain of Inner Loop in s-domain Gain-Crossover Frequency of Inner Loop Phase Margin of Inner Loop Maximum Duty Cycle for Converters Without Slope Compensation Maximum Duty Cycle for Converters with Slope Compensation Minimum Slope Compensation for Buck and Buck Boost Converter Minimum Slope Compensation for Boost Converter Error Voltage-to-Duty Cycle Transfer Function Closed-Loop Control Voltage-to-Duty Cycle Transfer Function of Current Loop Alternative Representation of Current Loop Current Loop with Disturbances Modified Approximation of Current Loop Voltage Loop of PWM Converters with Current-Mode Control Control-to-Output Transfer Function for Buck Converter Block Diagram of Power Stages of PWM Converters Closed-Voltage Loop Transfer Function of PWM Converters with Current-Mode Control Closed-Loop Audio Susceptibility of PWM Converters with Current-Mode Control Closed-Loop Output Impedance of PWM Converters with Current-Mode Control Feedforward Gains in PWM Converters with Current-Mode Control without Slope Compensation Feedforward Gains in PWM Converters with Current-Mode Control and Slope Compensation Control-to-Output Voltage Transfer Function of Inner Loop with Feedforward Gains Audio-Susceptibility of Inner Loop with Feedforward Gains Closed-Loop Transfer Functions with Feedforward Gains Slope Compensation by Adding a Ramp to Inductor Current Waveform Relationships for Constant-Frequency Current-Mode On-Time Control Summary 639 References 640 Review Questions 644 Problems 644

18 xvi Contents Appendix: Sample-and-Hold Modeling Sampler of the Control Voltage Zero-Order Hold of Inductor Current Approximations of e st s Current-Mode Control of Boost Converter Introduction Open-Loop Small-Signal Transfer Functions Open-Loop Duty Cycle-to-Inductor Current Transfer Function High-Frequency Open-Loop Duty Cycle-to-Inductor Current Transfer Function Open-Loop Input Voltage-to-Inductor Current Transfer Function Open-Loop Inductor-to-Output Current Transfer Function Open-Loop Step Responses of Inductor Current Open-Loop Response of Inductor Current to Step Change in Input Voltage Open-Loop Response of the Inductor Current to Step Change in the Duty Cycle Open-Loop Response of Inductor Current to Step Change in Load Current Closed-Current-Loop Transfer Functions Forward Gain Loop Gain of Current Loop Closed-Loop Gain of Current Loop Control-to-Output Transfer Function Input Voltage-to-Duty Cycle Transfer Function Load Current-to-Duty Cycle Transfer Function Output Impedance of Closed-Current Loop Closed-Voltage-Loop Transfer Functions Control-to-Output Transfer Function Control Voltage-to-Feedback Voltage Transfer Function Loop Gain of Voltage Loop Closed-Loop Gain of Voltage Loop Closed-Loop Audio Susceptibility with Integral Controller Closed-Loop Output Impedance with Integral Controller Closed-Loop Step Responses Closed-Loop Response of Output Voltage to Step Change in Input Voltage Closed-Loop Response of Output Voltage to Step Change in Load Current Closed-Loop Response of Output Voltage to Step Change in Reference Voltage Closed-Loop DC Transfer Functions Summary 711 References 711 Review Questions 712 Problems Open-Loop Small-Signal Characteristics of PWM Boost Converter for DCM Introduction Small-Signal Model of Boost Converter for DCM Open-Loop Control-to-Output Transfer Function Open-Loop Input-to-Output Voltage Transfer Function Open-Loop Input Impedance Open-Loop Output Impedance 725

19 Contents xvii 16.7 Step Responses of Output Voltage of Boost Converter for DCM Response of Output Voltage to Step Change in Input Voltage Response of Output Voltage to Step Change in Duty Cycle Response of Output Voltage to Step Change in Load Current Open-Loop Duty Cycle-to-Inductor Current Transfer Function Open-Loop Input Voltage-to-Inductor Current Transfer Function Open-Loop Output Current-to-Inductor Current Transfer Function Step Responses of Inductor Current of Boost Converter for DCM Step Response of Inductor Current to Step Change in Input Voltage Step Response of Inductor Current to Step Change in Duty Cycle Step Response of Inductor Current to Step Change in Load Current DC Characteristics of Boost Converter for DCM DC-to-DC Voltage Transfer Function of Lossless Boost Converter for DCM DC-to-DC Voltage Transfer Function of Lossy Boost Converter for DCM Efficiency of Boost Converter for DCM Summary 745 References 745 Review Questions 746 Problems Silicon and Silicon-Carbide Power Diodes Introduction Electronic Power Switches Atom Electron and Hole Effective Mass Semiconductors Intrinsic Semiconductors Extrinsic Semiconductors n-type Semiconductor p-type Semiconductor Maximum Operating Temperature Wide Band Gap Semiconductors Physical Structure of Junction Diodes Formation of Depletion Layer Charge Transport Static I V Diode Characteristic Breakdown Voltage of Junction Diodes Depletion-Layer Width Electric Field Intensity Distribution Avalanche Breakdown Voltage Punch-Through Breakdown Voltage Edge Terminations Capacitances of Junction Diodes Junction Capacitance Diffusion Capacitance Reverse Recovery of pn Junction Diodes Qualitative Description Reverse Recovery in Resistive Circuits 790

20 xviii Contents Charge-Continuity Equation Reverse Recovery in Inductive Circuits Schottky Diodes Static I V Characteristic of Schottky Diodes Breakdown Voltages of Schottky Diodes Junction Capacitance of Schottky Diodes Switching Characteristics of Schottky Diodes Solar Cells Light-Emitting Diodes SPICE Model of Diodes Summary 811 References 815 Review Questions 816 Problems Silicon and Silicon-Carbide Power MOSFETs Introduction Integrated MOSFETs Physical Structure of Power MOSFETs Principle of Operation of Power MOSFETs Cutoff Region Formation of MOSFET Channel Linear Region Saturation Region Antiparallel Diode Derivation of Power MOSFET Characteristics Ohmic Region Pinch-off Region Channel-Length Modulation Power MOSFET Characteristics Mobility of Charge Carriers Effect of Doping Concentration on Mobility Effect of Temperature on Mobility Effect of Electric Field on Mobility Short-Channel Effects Ohmic Region Pinch-off Region Aspect Ratio of Power MOSFETs Breakdown Voltage of Power MOSFETs Gate Oxide Breakdown Voltage of Power MOSFETs Specific On-Resistance Figures-of-Merit of Semiconductors On-Resistance of Power MOSFETs Channel Resistance Accumulation Region Resistance Neck Region Resistance Drift Region Resistance Capacitances of Power MOSFETs Gate-to-Source Capacitance 862

21 Contents xix Drain-to-Source Capacitance Gate-to-Drain Capacitance Switching Waveforms SPICE Model of Power MOSFETs IGBTs Heat Sinks Summary 886 References 888 Review Questions 888 Problems Electromagnetic Compatibility Introduction Definition of EMI Definition of EMC EMI Immunity EMI Susceptibility Classification of EMI Sources of EMI Safety Standards EMC Standards Near Field and Far Field Techniques of EMI Reduction Insertion Loss EMI Filters Feed-Through Capacitors EMI Shielding Interconnections Summary 903 References 903 Review Questions 903 Problem 904 A Introduction to SPICE 907 B Introduction to MATLAB 910 C Physical Constants 915 Answers to Problems 917 Index 925

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23 About the Author Marian K. Kazimierczuk is Frederick A. White Distinguished Professor of Electrical Engineering at Wright State University, Dayton, Ohio, USA. He received the M.S., Ph.D., and D.Sc. degrees from Warsaw University of Technology, Department of Electronics, Warsaw, Poland. He is the author of six books, over 180 archival refereed journal papers, over 210 conference papers, and seven patents. His research interests are in power electronics, including RF high-efficiency power amplifiers and oscillators, PWM dc dc power converters, resonant dc dc power converters, modeling and controls of power converter, highfrequency magnetic devices, electronic ballasts, active power factor correctors, semiconductor power devices, wireless charging systems, renewable energy sources, energy harvesting, green energy, and evanescent microwave microscopy. Professor Kazimierczuk is a Fellow of the IEEE. He served as Chair of the Technical Committee of Power Systems and Power Electronics Circuits, IEEE Circuits and Systems Society. He served on the Technical Program Committees of the IEEE International Symposium on Circuits and Systems (ISCAS) and the IEEE Midwest Symposium on Circuits and Systems. He also served as Associate Editor of the IEEE Transactions on Circuits and Systems, Part I, Regular Papers, IEEE Transactions on Industrial Electronics, International Journal of Circuit Theory and Applications, andjournal of Circuits, Systems, and Computers, and as Guest Editor of the IEEE Transactions on Power Electronics. He was an IEEE Distinguished Lecturer. Professor Kazimierczuk received the Presidential Award for Outstanding Faculty Member at Wright State University in He was Brage Golding Distinguished Professor of Research at Wright State University in He received the Trustees Award from Wright State University for Faculty Excellence in He received the Outstanding Teaching Award from the American Society for Engineering Education (ASEE) in He was also honored with the Excellence in Research Award, Excellence in Teaching Awards, and Excellence in Professional Service Award in the College of Engineering and Computer Science, Wright State University. He is listed in Top Authors in Engineering and Top Authors in Electrical & Electronic Engineering. Professor Kazimierczuk is the author or co-author of six books: Resonant Power Converters, 2nd Ed., Wiley, Pulse-Width Modulated DC DC Power Converters, IEEE Press/Wiley, High-Frequency Magnetic Components, 2nd Ed. (translated in Chinese), Wiley, RF Power Amplifiers, 2nd Ed. (translated in Chinese), Wiley, Electronic Devices, A Design Approach, Pearson/Prentice Hall, and Laboratory Manual to Accompany Electronic Devices, A Design Approach, 2nd Ed., Pearson/Prentice Hall.

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25 Preface This book is about switching-mode dc dc power converters with pulse-width modulation (PWM) control. It is intended as a power electronics textbook at the senior and graduate levels for students majoring in electrical engineering, as well as a reference for practicing engineers in the area of power electronics. The purpose of the book is to provide foundations for semiconductor power devices, topologies of PWM switching-mode dc dc power converters, modeling, dynamics, and controls of PWM converters. The book is devoted to energy conversion. The first part of the book covers topologies of transformerless and isolated PWM converters, such as buck, boost, and buck boost, flyback, forward, half-bridge, and full-bridge converters. The second part covers small-signal circuit models of PWM converters, transfer functions of PWM converter power stages, voltage-mode control, and current-mode control of PWM converters. The third part presents silicon and silicon carbide power devices. The textbook assumes that the student is familiar with general circuit analysis techniques and electronic circuits. Complete solutions for all problems are included in the Solutions Manual, which is available from the publisher for those instructors who adopt the book for their courses. I am pleased to express my gratitude to Dr. Nisha Kondrath and Agasthya Ayachit for MATLAB figures, proofreading, suggestions, and critical evaluation of the manuscript. Throughout the entire course of this project, the support provided by John Wiley & Sons was excellent. I wish to express my sincere thanks to Ella Mitchell, Associate Commissioning Editor, Electrical Engineering; Peter Mitchell, Publisher, Engineering Technology; and Richard Davis, Senior Project Editor. It has been a real pleasure working with them. Last but not least, I wish to thank my family for the support. The author would welcome and greatly appreciate suggestions and corrections from the readers, for the improvements in the technical content as well as the presentation style. Marian K. Kazimierczuk

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27 Nomenclature A A i A J BW C C b C c C ds C gd C gs C iss C min C o C oss C ox C rss c D d d m d T ESR f c f z f 0 f p f s f 180 H sh I Crms I pk I rms I D I DM I Drms I I I L I LB I O I Omax I Omin Transfer function of forward path in negative feedback system Inductor-to-load current transfer function Cross-sectional area of junction Bandwidth Filter capacitance Blocking capacitance Coupling capacitance Drain source capacitance of MOSFET Gate drain capacitance of MOSFET Gate source capacitance of MOSFET MOSFET input capacitance at V DS = 0, C iss = C gs + C gd Minimum value of filter capacitance C Transistor output capacitance MOSFET output capacitance at V GD = 0, C oss = C gs + C ds Oxide capacitance per unit area MOSFET transfer capacitance, C rss = C gd Speed of light DC component of on-duty cycle of switch AC component of on-duty cycle of switch Amplitude of small-signal component of on-duty cycle of switch Total on-duty cycle of switch Equivalent series resistance of capacitors and inductors Gain-crossover frequency Frequency of zero of transfer function Corner frequency Frequency of pole of transfer function Switching frequency Phase-crossover frequency Transfer function of sampler and zero-order hold rms value of capacitor current i C Magnitude of cross-conduction current rms value of current i Average diode current Peak diode current rms value of diode current DC input current of converter Average current through inductor L Average current through inductor L at CCM/DCM boundary DC output current of converter Maximum value of dc load current I O Minimum value of dc load current I O

28 xxvi Nomenclature I OB DC output current at the boundary between CCM and DCM I SM Peak switch current I Srms rms value of switch current i S i i AC component of input current i 0 i (t) Zero-order-hold AC component of input current i o AC component of load current i C Current through filter capacitor C i D Diode current i L Current through inductor L i O Total load current i S Switch current K i Input feedforward gain K o Output feedforward gain k Boltzmann constant L Inductance, Channel length L e Effective channel length L n Electron diffusion length L p Hole diffusion length L m Magnetizing inductance of transformer L max Maximum inductance L for DCM operation L min Minimum inductance L for CCM operation LNR Line regulation LOR Load regulation M IDC DC current transfer function of converter M VDC DC voltage transfer function of converter M v Open-loop input-to-output voltage function of converter M vcl Closed-loop input-to-output voltage function of converter M vi Open-loop input voltage-to-inductor current transfer function M vo Open-loop input-to-output voltage function of converter at f = 0 m e Mass of free electron m e Effective mass of electron m h Mass of hole m h Effective mass of hole N A Concentration of acceptors N D Concentration of donors N p Number of turns of primary winding N s Number of turns of secondary winding n Transformer turns ratio, electron concentration density n + Electron concentration of heavily doped semiconductor by donors n i Intrinsic carrier concentration n n Majority electron concentration n p Minority electron concentration n p0 Thermal equilibrium minority electron concentration p n Minority hole concentration p n0 Thermal equilibrium minority hole concentration p p Majority hole concentration PM Phase margin P ton Turn-on switching losses Total diode conduction loss P D

29 Nomenclature xxvii P FET Overall power dissipation in MOSFET (excluding gate-drive power) P G Gate-drive power P I DC input power of converter P LS Overall power dissipation of converter PM Phase margin P O DC output power of converter P RF Conduction loss in diode forward resistance R F P rc Conduction loss in filter capacitor ESR P VF Conduction loss in diode offset voltage V F p Hole concentration p + Hole concentration of heavily doped semiconductor by acceptors Q Quality factor Q g Gate charge Q F Forward stored charge Q rr Reverse recovery charge q Magnitude of electron charge R DR Resistance of drift region R F Diode forward resistance R L DC load resistance R LB DC load resistance at CCM/DCM boundary R Lmax Maximum value of load resistance R L R Lmin Minimum value of load resistance R L r C Equivalent series resistance (ESR) of filter capacitor r DS On-resistance of MOSFET q Electron charge S Specific resistance of drift region S max Maximum percentage overshoot SR Slew rate of op-amps T Switching period, Loop gain T A Ambient temperature T c Voltage transfer function of controller T cl Closed-loop control-to-output transfer function T i Loop gain of current loop T J Junction temperature T m Transfer function of pulse-width modulator T p Open-loop control-to-output transfer function T pi Open-loop duty cycle-to-inductor current transfer function T po Open-loop control-to-output transfer function at f = 0 THD Total harmonic distortion t f Fall time t r Rise time t rr Reverse recovery time V bi Built-in potential V C DC component of control voltage V cm Amplitude of small-signal component of control voltage V Cpp Peak-to-peak ripple voltage of the filter capacitance V E DC component of error voltage V t Gate-to-source threshold voltage Breakdown voltage V BD

30 xxviii V BR V DM V DS V DSS V F V GD V GSpp V I V O V R V r V rcpp V SM V T V Tm v C v c v c (t) v c (jω) v DS v E v F v e v d v f v L v i v o v sat v r v rc v th v sat W W C W L Z i Z icl Z o Z ocl β Δi L η θ μ μ p μ n ξ ρ Nomenclature Reverse blocking (breakdown) voltage Reverse peak voltage of diode Drain source dc voltage of MOSFET Drain source breakdown voltage of MOSFETs Diode offset voltage, dc component of feedback voltage Gate-to-drain voltage of MOSFET Peak-to-peak gate-to-source voltage DC component of input voltage of converter DC output voltage of converter DC reference voltage Peak-to-peak value of output ripple voltage Peak-to-peak ripple voltage across ESR Peak switch voltage Thermal voltage Peak ramp voltage of pulse-width modulator Total control voltage AC component of control voltage Sampled AC component of control voltage Spectrum of sampled AC component of control voltage Drain source voltage of MOSFET Total error voltage Total feedback voltage AC component of error voltage Average drift velocity AC component of feedback voltage Voltage across inductance L AC component of converter input voltage AC component of converter output voltage Saturation velocity of carriers AC component of reference voltage Voltage across ESR of filter capacitor Thermal velocity of electron Saturated average drift velocity Channel width Energy stored in capacitor Energy stored in inductor Open-loop input impedance of converter Closed-loop input impedance of converter Open-loop output impedance of converter Closed-loop output impedance of converter Transfer function of feedback network Peak-to-peak of inductor ripple current Efficiency of converter Thermal resistance Carrier mobility Mobility of holes Mobility of electrons Damping ratio Resistivity