Pulse-Width Modulated DC-DC Power Converters Second Edition

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

3 Pulse-Width Modulated DC DC Power Converters

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

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

Pulse-Width Modulated DC-DC Power Converters Second Edition

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