necona
`
`.
`Edition
`
`OWE R
`ELECTRONICS
`
`Converters,
`
`Applications,
`
`and Design
`
`Power input
`
`vi
`
`ii
`
`Power
`processor
`
`Power output
`
`Load
`
`'0
`
`Control
`signals
`
`Measurements
`
`Controller
`
`-4— Reference
`
`MOHAN
`
`I UNDELAND
`
`I ROBOIN
`
`Petitioners
`Ex. 1032, p. Cover
`
`

`

`ABOUT THE AUTHORS
`
`Ned Mohan is a professor in the Department of Electrical Engineering at the University
`of Minnesota, where he holds the Oscar A. Schott Chair in Power Electronics. He has
`worked on several power electronics projects sponsored by the industry and the electric
`power utilities, including the Electric Power Research Institute. He has numerous pub-
`lications and patents in this field.
`
`Tore M. Undeland is a Professor in Power Electronics in the Faculty of Electrical
`Engineering and Computer Science at the Norwegian Institute of Technology. He is also
`Scientific Advisor to the Norwegian Electric Power Research Institute of Electricity
`Supply. He has been a visiting scientific worker in the Power Electronics Converter
`Department of ASEA in Vaasteras, Sweden, and at Siemens in Trondheim, Norway, and
`a visiting professor in the Department of Electrical Engineering at the University of
`Minnesota. He has worked on many industrial research and development projects in the
`power electronics field and has numerous publications.
`
`William P. Robbins is a professor in the Department of Electrical Engineering at the
`University of Minnesota. Prior to joining the University of Minnesota, he was a research
`engineer at the Boeing Company. He has taught numerous courses in electronics and
`semiconductor device fabrication. His research interests are in ultrasonics, pest insect
`detection via ultrasonics, and micromechanical devices, and he has numerous publications
`in this field.
`
`Petitioners
`Ex. 1032, p. iv
`
`

`

`POWER
`ELECTRONICS
`Converters, Applications,
`and Design
`
`SECOND EDITION
`
`NED MOHAN
`Department of Electrical Engineering
`University of Minnesota
`Minneapolis, Minnesota
`
`TORE M. UNDELAND
`Faculty of Electrical Engineering and Computer Science
`Norwegian Institute of Technology
`Trondheim, Norway
`
`WILLIAM P. ROBBINS
`Department of Electrical Engineering
`University of Minnesota
`Minneapolis, Minnesota
`
`JOHN WILEY & SONS, INC.
`New York Chichester Brisbane Toronto Singapore
`
`Petitioners
`Ex. 1032, p. v
`
`

`

`Acquisitions Editor
`Developmental Editor
`Marketing Manager
`Senior Production Editor
`Text Designer
`Cover Designer
`Manufacturing Manager
`Illustration Coordinator
`
`Steven M. Elliot
`Sean M. Culhane
`Susan Elbe
`Savoula Amanatidis
`Lynn Rogan
`David Levy
`Lori Bulwin
`Jaime Perea
`
`This book was typeset in Times Roman by The Clarinda Company, and printed and bound
`by Hamilton Printing Company. The cover was printed by NEBC.
`
`Recognizing the importance of preserving what has been written, it is a policy of
`John Wiley & Sons, Inc. to have books of enduring value published in the United States
`printed on acid-free paper, and we exert our best efforts to that end.
`
`PSpice is a registered trademark of MicroSim Corporation.
`MATLAB is a registered trademark of The MathWorks, Inc.
`
`Copyright © 1989, 1995 by John Wiley & Sons, Inc.
`
`All rights reserved. Published simultaneously in Canada.
`
`Reproduction or translation of any part of this work beyond that permitted by Sections 107
`and 108 of the 1976 United States Copyright Act without the permission of the copyright owner
`is unlawful. Requests for permission or further information should be addressed to the
`Permissions Department, John Wiley & Sons, Inc.
`
`Library of Congress Cataloging in Publication Data:
`
`Mohan, Ned.
`Power electronics : converters, applications, and design / Ned
`Mohan, Tore M. Undeland, William P. Robbins.-2nd ed.
`p.
`cm.
`Includes bibliographical references and indexes.
`ISBN 0-471-58408-8 (cloth)
`1. Power electronics. 2. Electric current converters. 3. Power
`II. Robbins, William P.
`semiconductors.
`I. Undeland, Tore M.
`III. Title.
`TK7881.15.M64 1995
`621.317—dc20
`
`94-21158
`CIP
`
`Printed in the United States of America.
`
`10 9 8 7 6 5 4 3 2
`
`Petitioners
`Ex. 1032, p. vi
`
`

`

`PREFACE
`
`SECOND EDITION
`
`The first edition of this book was published in 1989. The basic intent of this edition
`remains the same; that is, as a cohesive presentation of power electronics fundamentals for
`applications and design in the power range of 500 kW or less, where a huge market exists
`and where the demand for power electronics engineers is likely to be. Based on the
`comments collected over a five-year period, we have made a number of substantial
`changes to the text. The key features are as follows:
`
`• An introductory chapter has been added to provide a review of basic electrical and
`magnetic circuit concepts, making it easier to use this book in introductory power
`electronics courses.
`• A chapter on computer simulation has been added that describes the role of com-
`puter simulations in power electronics. Examples and problems based on PSpice®
`and MATLAB® are included. However, we have organized the material in such a
`way that any other simulation package can be used instead or the simulations can
`be skipped altogether.
`• Unlike the first edition, the diode rectifiers and the phase-controlled thyristor con-
`verters are covered in a complete and easy-to-follow manner. These two chapters
`now contain 56 problems.
`• A new chapter on the design of inductors and transformers has been added that
`describes easy-to-understand concepts for step-by-step design procedures. This
`material will be extremely useful in introducing the design of magnetics into the
`curriculum.
`• A new chapter on heat sinks has been added.
`
`ORGANIZATION OF THE BOOK
`
`This book is divided into seven parts. Part 1 presents an introduction to the field of power
`electronics, an overview of power semiconductor switches, a review of pertinent electric
`and magnetic circuit concepts, and a generic discussion of the role of computer simula-
`tions in power electronics.
`Part 2 discusses the generic converter topologies that are used in most applications.
`The actual semiconductor devices (transistors, diodes, and so on) are assumed to be ideal,
`thus allowing us to focus on the converter topologies and their applications.
`Part 3 discusses switch-mode dc and uninterruptible power supplies. Power supplies
`represent one of the major applications of power electronics.
`
`vii
`
`Petitioners
`Ex. 1032, p. vii
`
`

`

`viii
`
`PREFACE
`
`Part 4 considers motor drives, which constitute another major applications area.
`Part 5 includes several industrial and commercial applications in one chapter. An-
`other chapter describes various high-power electric utility applications. The last chapter in
`this part of the book examines the harmonics and electromagnetic interference concerns
`and remedies for interfacing power electronic systems with the electric utilities.
`Part 6 discusses the power semiconductor devices used in power electronic converters
`including diodes, bipolar junction thyristors, metal —oxide —semiconductor (MOS) field
`effect transistors, thyristors, gate turn-off thyristors, insulated gate bipolar transistors, and
`MOS-controlled thyristors.
`Part 7 discusses the practical aspects of power electronic converter design including
`snubber circuits, drive circuits, circuit layout, and heat sinks. An extensive new chapter
`on the design of high-frequency inductors and transformers has been added.
`
`PSPICE SIMULATIONS FOR TEACHING AND DESIGN
`
`As a companion to this book, a large number of computer simulations are available
`directly from Minnesota Power Electronics Research and Education, P.O. Box 14503,
`Minneapolis, MN 55414 (Phone/Fax: 612-646-1447) to aid in teaching and in the design
`of power electronic systems. The simulation package comes complete with a diskette with
`76 simulations of power electronic converters and systems using the classroom (evalua-
`tion) version of PSpice for IBM-PC-compatible computers, a 261-page detailed manual
`that describes each simulation and a number of associated exercises for home assignments
`and self-learning, a 5-page instruction set to illustrate PSpice usage using these simula-
`tions as examples, and two high-density diskettes containing a copy of the classroom
`(evaluation) version of PSpice. This package (for a cost of $395 plus a postage of $4
`within North America and $25 outside) comes with a site license, which allows it to be
`copied for use at a single site within a company or at an educational institution in regular
`courses given to students for academic credits.
`
`SOLUTIONS MANUAL
`
`As with the first edition of this book, a solutions manual with completely worked-out
`solutions to all the problems is available from the publisher.
`
`ACKNOWLEDGMENTS
`
`We wish to thank all the instructors who have allowed us this opportunity to write the
`second edition of our book by adopting its first edition. Their comments have been most
`useful. We are grateful to Professors Peter Lauritzen of the University of Washington,
`Thomas Habetler of the Georgia Institute of Technology, Daniel Chen of the Virginia
`Institute of Technology, Alexander Emanuel of the Worcester Polytechnic Institute, F. P.
`Dawson of the University of Toronto, and Marian Kazimierczuk of the Wright State
`University for their helpful suggestions in the second edition manuscript. We express our
`sincere appreciation to the Wiley editorial staff, including Steven Elliot, Sean Culhane,
`Lucille Buonocore, and Savoula Amanatidis, for keeping us on schedule and for many
`spirited discussions.
`
`Ned Mohan
`Tore M. Undeland
`William P. Robbins
`
`Petitioners
`Ex. 1032, p. viii
`
`

`

`CONTENTS
`
`PART 1
`
`INTRODUCTION
`
`Chapter 1 Power Electronic Systems
`1-1 Introduction
`3
`1-2 Power Electronics versus Linear Electronics
`1-3 Scope and Applications
`7
`1-4 Classification of Power Processors and Converters
`12
`1-5 About the Text
`1-6 Interdisciplinary Nature of Power Electronics
`14
`1-7 Convention of Symbols Used
`Problems
`14
`References
`15
`
`4
`
`13
`
`9
`
`Chapter 2 Overview of Power Semiconductor Switches
`16
`2-1 Introduction
`2-2 Diodes
`16
`18
`2-3 Thyristors
`20
`2-4 Desired Characteristics in Controllable Switches
`2-5 Bipolar Junction Transistors and Monolithic Darlingtons
`2-6 Metal—Oxide—Semiconductor Field Effect Transistors
`26
`2-7 Gate-Turn-Off Thyristors
`2-8 Insulated Gate Bipolar Transistors
`2-9 MOS-Controlled Thyristors
`29
`2-10 Comparison of Controllable Switches
`30
`2-11 Drive and Snubber Circuits
`2-12 Justification for Using Idealized Device Characteristics
`Summary
`32
`Problems
`32
`References
`32
`
`27
`
`29
`
`24
`25
`
`31
`
`1
`
`3
`
`16
`
`Chapter 3 Review of Basic Electrical and Magnetic Circuit Concepts
`3-1 Introduction
`33
`3-2 Electric Circuits
`3-3 Magnetic Circuits
`Summary
`57
`Problems
`58
`60
`References
`
`33
`46
`
`33
`
`Petitioners
`Ex. 1032, p. ix
`
`

`

`x CONTENTS
`
`Chapter 4 Computer Simulation of Power Electronic Converters
`and Systems
`61
`4-1 Introduction
`4-2 Challenges in Computer Simulation
`62
`4-3 Simulation Process
`64
`4-4 Mechanics of Simulation
`4-5 Solution Techniques for Time-Domain Analysis
`69
`4-6 Widely Used, Circuit-Oriented Simulators
`72
`4-7 Equation Solvers
`74
`Summary
`74
`Problems
`References
`75
`
`65
`
`62
`
`PART 2 GENERIC POWER ELECTRONIC CIRCUITS
`
`Chapter 5 Line-Frequency Diode Rectifiers: Line-Frequency ac —>
`Uncontrolled dc
`79
`5-1 Introduction
`80
`5-2 Basic Rectifier Concepts
`82
`5-3 Single-Phase Diode Bridge Rectifiers
`100
`5-4 Voltage-Doubler (Single-Phase) Rectifiers
`5-5 Effect of Single-Phase Rectifiers on Neutral Currents in Three-Phase,
`101
`Four-Wire Systems
`103
`5-6 Three-Phase, Full-Bridge Rectifiers
`5-7 Comparison of Single-Phase and Three-Phase Rectifiers
`112
`5-8 Inrush Current and Overvoltages at Turn-On
`5-9 Concerns and Remedies for Line-Current Harmonics and Low Power
`Factor
`113
`Summary
`113
`Problems
`114
`References
`116
`Appendix
`117
`
`112
`
`Chapter 6 Line-Frequency Phase-Controlled Rectifiers and
`Inverters: Line-Frequency ac 4--> Controlled dc
`6-1 Introduction
`121
`6-2 Thyristor Circuits and Their Control
`6-3 Single-Phase Converters
`126
`6-4 Three-Phase Converters
`138
`6-5 Other Three-Phase Converters
`Summary
`153
`154
`Problems
`157
`References
`Appendix
`158
`
`122
`
`153
`
`Chapter 7 dc—dc Switch-Mode Converters
`7-1 Introduction
`161
`7-2 Control of dc—dc Converters
`
`162
`
`61
`
`77
`
`79
`
`121
`
`161
`
`Petitioners
`Ex. 1032, p. x
`
`

`

`CONTENTS xi
`
`164
`7-3 Step-Down (Buck) Converter
`172
`7-4 Step-Up (Boost) Converter
`178
`7-5 Buck—Boost Converter
`184
`7-6 Ctik dc—dc Converter
`7-7 Full Bridge dc—dc Converter
`7-8 dc—dc Converter Comparison
`196
`Summary
`197
`Problems
`References
`199
`
`188
`195
`
`200
`
`249
`
`299
`
`301
`
`Chapter 8 Switch-Mode dc—ac Inverters: dc H Sinusoidal ac
`8-1 Introduction
`200
`8-2 Basic Concepts of Switch-Mode Inverters
`211
`8-3 Single-Phase Inverters
`8-4 Three-Phase Inverters
`225
`8-5 Effect of Blanking Time on Output Voltage in PWM Inverters
`239
`8-6 Other Inverter Switching Schemes
`243
`8-7 Rectifier Mode of Operation
`244
`Summary
`246
`Problems
`References
`248
`
`202
`
`236
`
`252
`
`Chapter 9 Resonant Converters: Zero-Voltage and/or Zero-Current
`Switchings
`249
`9-1 Introduction
`9-2 Classification of Resonant Converters
`253
`9-3 Basic Resonant Circuit Concepts
`258
`9-4 Load-Resonant Converters
`273
`9-5 Resonant-Switch Converters
`9-6 Zero-Voltage-Switching, Clamped-Voltage Topologies
`9-7 Resonant-dc-Link Inverters with Zero-Voltage Switchings
`289
`9-8 High-Frequency-Link Integral-Half-Cycle Converters
`291
`Summary
`291
`Problems
`References
`295
`
`280
`287
`
`PART 3 POWER SUPPLY APPLICATIONS
`
`Chapter 10 Switching de Power Supplies
`10-1 Introduction
`301
`301
`10-2 Linear Power Supplies
`10-3 Overview of Switching Power Supplies
`10-4 dc—dc Converters with Electrical Isolation
`10-5 Control of Switch-Mode dc Power Supplies
`10-6 Power Supply Protection
`341
`344
`10-7 Electrical Isolation in the Feedback Loop
`10-8 Designing to Meet the Power Supply Specifications
`349
`Summary
`
`302
`304
`322
`
`346
`
`Petitioners
`Ex. 1032, p. xi
`
`

`

`xii CONTENTS
`
`Problems
`References
`
`349
`351
`
`Chapter 11 Power Conditioners and Uninterruptible Power
`Supplies
`354
`11-1 Introduction
`11-2 Power Line Disturbances
`357
`11-3 Power Conditioners
`11-4 Uninterruptible Power Supplies (UPSs)
`363
`Summary
`363
`Problems
`364
`References
`
`358
`
`354
`
`PART 4 MOTOR DRIVE APPLICATIONS
`
`Chapter 12 Introduction to Motor Drives
`367
`12-1 Introduction
`12-2 Criteria for Selecting Drive Components
`Summary
`375
`Problems
`376
`References
`376
`
`368
`
`Chapter 13 dc Motor Drives
`377
`13-1 Introduction
`377
`13-2 Equivalent Circuit of dc Motors
`380
`13-3 Permanent-Magnet dc Motors
`13-4 dc Motors with a Separately Excited Field Winding
`382
`13-5 Effect of Armature Current Waveform
`383
`13-6 dc Servo Drives
`13-7 Adjustable-Speed dc Drives
`396
`Summary
`396
`Problems
`398
`References
`
`391
`
`381
`
`Chapter 14 Induction Motor Drives
`399
`14-1 Introduction
`400
`14-2 Basic Principles of Induction Motor Operation
`14-3 Induction Motor Characteristics at Rated (Line) Frequency
`405
`and Rated Voltage
`14-4 Speed Control by Varying Stator Frequency and Voltage
`14-5 Impact of Nonsinusoidal Excitation on Induction Motors
`418
`14-6 Variable-Frequency Converter Classifications
`419
`14-7 Variable-Frequency PWM-VSI Drives
`14-8 Variable-Frequency Square-Wave VSI Drives
`426
`14-9 Variable-Frequency CSI Drives
`14-10 Comparison of Variable-Frequency Drives
`
`425
`
`427
`
`406
`415
`
`354
`
`365
`
`367
`
`377
`
`399
`
`Petitioners
`Ex. 1032, p. xii
`
`

`

`CONTENTS xiii
`
`428
`14-11 Line-Frequency Variable-Voltage Drives
`14-12 Reduced Voltage Starting ("Soft Start") of Induction Motors
`431
`14-13 Speed Control by Static Slip Power Recovery
`Summary
`432
`Problems
`433
`434
`References
`
`430
`
`Chapter 15 Synchronous Motor Drives
`15-1 Introduction
`435
`15-2 Basic Principles of Synchronous Motor Operation
`435
`15-3 Synchronous Servomotor Drives with Sinusoidal Waveforms
`15-4 Synchronous Servomotor Drives with Trapezoidal Waveforms
`15-5 Load-Commutated Inverter Drives
`442
`15-6 Cycloconverters
`445
`Summary
`445
`Problems
`446
`References
`447
`
`439
`440
`
`PART 5 OTHER APPLICATIONS
`
`Chapter 16 Residential and Industrial Applications
`451
`16-1 Introduction
`16-2 Residential Applications
`16-3 Industrial Applications
`Summary
`459
`Problems
`459
`References
`459
`
`451
`455
`
`460
`
`Chapter 17 Electric Utility Applications
`460
`17-1 Introduction
`17-2 High-voltage dc Transmission
`471
`17-3 Static var Compensators
`17-4 Interconnection of Renewable Energy Sources and Energy Storage
`475
`Systems to the Utility Grid
`17-5 Active Filters
`480
`480
`Summary
`481
`Problems
`482
`References
`
`Chapter 18 Optimizing the Utility Interface with Power
`Electronic Systems
`18-1 Introduction
`483
`484
`18-2 Generation of Current Harmonics
`485
`18-3 Current Harmonics and Power Factor
`18-4 Harmonic Standards and Recommended Practices
`487
`18-5 Need for Improved Utility Interface
`
`485
`
`435
`
`449
`
`451
`
`460
`
`483
`
`Petitioners
`Ex. 1032, p. xiii
`
`

`

`xiv CONTENTS
`
`18-6 Improved Single-Phase Utility Interface
`18-7 Improved Three-Phase Utility Interface
`18-8 Electromagnetic Interference
`500
`Summary
`502
`503
`Problems
`References
`503
`
`488
`498
`
`PART 6 SEMICONDUCTOR DEVICES
`
`Chapter 19 Basic Semiconductor Physics
`19-1 Introduction
`507
`19-2 Conduction Processes in Semiconductors
`19-3 pn Junctions
`513
`19-4 Charge Control Description of pn-Junction Operation
`19-5 Avalanche Breakdown
`520
`522
`Summary
`Problems
`522
`References
`523
`
`507
`
`518
`
`Chapter 20 Power Diodes
`524
`20-1 Introduction
`20-2 Basic Structure and V Characteristics
`526
`20-3 Breakdown Voltage Considerations
`531
`20-4 On-State Losses
`20-5 Switching Characteristics
`539
`20-6 Schottky Diodes
`Summary
`543
`Problems
`543
`545
`References
`
`535
`
`524
`
`546
`
`Chapter 21 Bipolar Junction Transistors
`546
`21-1 Introduction
`21-2 Vertical Power Transistor Structures
`548
`21-3 I— V Characteristics
`21-4 Physics of BJT Operation
`21-5 Switching Characteristics
`562
`21-6 Breakdown Voltages
`563
`21-7 Second Breakdown
`21-8 On-State Losses
`565
`21-9 Safe Operating Areas
`568
`Summary
`Problems
`569
`570
`References
`
`550
`556
`
`567
`
`Chapter 22 Power MOSFETs
`22-1 Introduction
`571
`22-2 Basic Structure
`571
`
`505
`
`507
`
`524
`
`546
`
`571
`
`Petitioners
`Ex. 1032, p. xiv
`
`

`

`574
`22-3 1—V Characteristics
`576
`22-4 Physics of Device Operation
`581
`22-5 Switching Characteristics
`22-6 Operating Limitations and Safe Operating Areas
`593
`Summary
`Problems
`594
`595
`References
`
`587
`
`Chapter 23 Thyristors
`596
`23-1 Introduction
`23-2 Basic Structure
`596
`23-3 1—V Characteristics
`597
`599
`23-4 Physics of Device Operation
`603
`23-5 Switching Characteristics
`23-6 Methods of Improving dildt and dvldt Ratings
`Summary
`610
`Problems
`611
`References
`612
`
`608
`
`Chapter 24 Gate Turn-Off Thyristors
`613
`24-1 Introduction
`24-2 Basic Structure and I—V Characteristics
`614
`24-3 Physics of Turn-Off Operation
`24-4 GTO Switching Characteristics
`616
`24-5 Overcurrent Protection of GTOs
`623
`Summary
`624
`624
`Problems
`625
`References
`
`613
`
`Chapter 25 Insulated Gate Bipolar Transistors
`25-1 Introduction
`626
`25-2 Basic Structure
`626
`25-3 I —V Characteristics
`628
`25-4 Physics of Device Operation
`25-5 Latchup in IGBTs
`631
`25-6 Switching Characteristics
`25-7 Device Limits and SOAs
`Summary
`639
`Problems
`639
`640
`References
`
`634
`637
`
`629
`
`Chapter 26 Emerging Devices and Circuits
`641
`26-1 Introduction
`26-2 Power Junction Field Effect Transistors
`646
`26-3 Field-Controlled Thyristor
`26-4 JFET-Based Devices versus Other Power Devices
`649
`26-5 MOS-Controlled Thyristors
`
`641
`
`648
`
`CONTENTS xv
`
`596
`
`613
`
`626
`
`641
`
`Petitioners
`Ex. 1032, p. xv
`
`

`

`xvi CONTENTS
`
`656
`26-6 Power Integrated Circuits
`26-7 New Semiconductor Materials for Power Devices
`Summary
`664
`665
`Problems
`References
`666
`
`661
`
`PART 7 PRACTICAL CONVERTER DESIGN
`CONSIDERATIONS
`
`Chapter 27 Snubber Circuits
`27-1 Function and Types of Snubber Circuits
`670
`27-2 Diode Snubbers
`678
`27-3 Snuber Circuits for Thyristors
`27-4 Need for Snubbers with Transistors
`682
`27-5 Turn-Off Snubber
`27-6 Overvoltage Snubber
`686
`27-7 Turn-On Snubber
`688
`27-8 Snubbers for Bridge Circuit Configurations
`692
`27-9 GTO Snubber Considerations
`693
`Summary
`694
`Problems
`References
`695
`
`680
`
`669
`
`691
`
`Chapter 28 Gate and Base Drive Circuits
`696
`28-1 Preliminary Design Considerations
`697
`28-2 dc-Coupled Drive Circuits
`28-3 Electrically Isolated Drive Circuits
`28-4 Cascode-Connected Drive Circuits
`712
`28-5 Thyristor Drive Circuits
`28-6 Power Device Protection in Drive Circuits
`722
`28-7 Circuit Layout Considerations
`Summary
`728
`Problems
`729
`References
`729
`
`703
`710
`
`717
`
`Chapter 29 Component Temperature Control and Heat Sinks
`730
`29-1 Control of Semiconductor Device Temperatures
`731
`29-2 Heat Transfer by Conduction
`737
`29-3 Heat Sinks
`29-4 Heat Transfer by Radiation and Convection
`742
`Summary
`Problems
`743
`References
`743
`
`739
`
`Chapter 30 Design of Magnetic Components
`744
`30-1 Magnetic Materials and Cores
`30-2 Copper Windings
`752
`
`667
`
`669
`
`696
`
`730
`
`744
`
`Petitioners
`Ex. 1032, p. xvi
`
`

`

`756
`
`30-3 Thermal Considerations
`754
`30-4 Analysis of a Specific Inductor Design
`30-5 Inductor Design Procedures
`760
`30-6 Analysis of a Specific Transformer Design
`30-7 Eddy Currents
`771
`30-8 Transformer Leakage Inductance
`779
`30-9 Transformer Design Procedure
`780
`30-10 Comparison of Transformer and Inductor Sizes
`Summary
`789
`Problems
`790
`References
`792
`
`767
`
`CONTENTS xvii
`
`789
`
`Index
`
`793
`
`Petitioners
`Ex. 1032, p. xvii
`
`

`

`CHAPTER 7
`
`dc— dc SWITCH-MODE
`CONVERTERS
`
`7-1
`
`INTRODUCTION
`
`The dc—dc converters are widely used in regulated switch-mode dc power supplies and in
`dc motor drive applications. As shown in Fig. 7-1, often the input to these converters is
`an unregulated dc voltage, which is obtained by rectifying the line voltage, and therefore
`it will fluctuate due to changes in the line-voltage magnitude. Switch-mode dc-to-dc
`converters are used to convert the unregulated dc input into a controlled dc output at a
`desired voltage level.
`Looking ahead to the application of these converters, we find that these converters are
`very often used with an electrical isolation transformer in the switch-mode dc power
`supplies and almost always without an isolation transformer in case of dc motor drives.
`Therefore, to discuss these circuits in a generic manner, only the nonisolated converters
`are considered in this chapter, since the electrical isolation is an added modification.
`The following do—dc converters are discussed in this chapter:
`
`1. Step-down (buck) converter
`2. Step-up (boost) converter
`3. Step-down/step-up (buck— boost) converter
`4. Ctik converter
`5. Full-bridge converter
`Of these five converters, only the step-down and the step-up are the basic converter
`topologies. Both the buck—boost and the Cilk converters are combinations of the two
`basic topologies. The full-bridge converter is derived from the step-down converter.
`
`Battery i—
`
`AC
`line volts
`(1-phase or
`3-phase)
`
`Uncontrolled
`Diode
`Rectifier
`
`DC
`(unregulated)
`
`Filter
`Capacitor
`
`DC
`(unregulated)
`
`DC-DC
`Converter
`
`DC
`(regulated)
`
`Load
`
`Figure 7-1 A dc—dc converter system.
`
`t
`ucontrol
`
`161
`
`Petitioners
` Ex. 1032, p. 161
`
`

`

`162
`
`CHAPTER 7
`
`dc—dc SWITCH-MODE CONVERTERS
`
`The converters listed are discussed in detail in this chapter. Their variations, as they
`apply to specific applications, are described in the chapters dealing with switch-mode de
`power supplies and dc motor drives.
`In this chapter, the converters are analyzed in steady state. The switches are treated
`as being ideal, and the losses in the inductive and the capacitive elements are neglected.
`Such losses can limit the operational capacity of some of these converters and are dis-
`cussed separately.
`The dc input voltage to the converters is assumed to have zero internal impedance.
`It could be a battery source; however, in most cases, the input is a diode rectified ac line
`voltage (as is discussed in Chapter 5) with a large filter capacitance, as shown in Fig. 7-1
`to provide a low internal impedance and a low-ripple dc voltage source.
`In the output stage of the converter, a small filter is treated as an integral part of the
`dc-to-dc converter. The output is assumed to supply a load that can be represented by an
`equivalent resistance, as is usually the case in switch-mode dc power supplies. A dc motor
`load (the other application of these converters) can be represented by a dc voltage in series
`with the motor winding resistance and inductance.
`
`7-2 CONTROL OF dc—dc CONVERTERS
`
`In dc—dc converters, the average dc output voltage must be controlled to equal a desired
`level, though the input voltage and the output load may fluctuate. Switch-mode dc—dc
`converters utilize one or more switches to transform dc from one level to another. In a
`dc—dc converter with a given input voltage, the average output voltage is controlled by
`controlling the switch on and off durations (too and toff). To illustrate the switch-mode
`conversion concept, consider a basic dc —dc converter shown in Fig. 7-2a. The average
`value Vo of the output voltage vo in Fig. 7-2b depends on t. and toff. One of the methods
`for controlling the output voltage employs switching at a constant frequency (hence, a
`constant switching time period Ts = t.„ + toff) and adjusting the on duration of the switch
`to control the average output voltage. In this method, called pulse-width modulation
`(PWM) switching, the switch duty ratio D, which is defined as the ratio of the on duration
`to the switching time period, is varied.
`The other control method is more general, where both the switching frequency (and
`hence the time period) and the on duration of the switch are varied. This method is used
`only in dc—dc converters utilizing force-commutated thyristors and therefore will not be
`discussed in this book. Variation in the switching frequency makes it difficult to filter the
`ripple components in the input and the output waveforms of the converter.
`
`U p
`
`0
`
`v0
`
`tan
`
`T,
`
`(b)
`
`Vd
`
`(a)
`
`Figure 7-2 Switch-mode dc—dc conversion.
`
`Petitioners
` Ex. 1032, p. 162
`
`

`

`7-2 CONTROL OF dc—dc CONVERTERS 163
`
`V. (desired)
`
`Vo (actual)-3.-
`
`Amplifier
`—
`
`vcontrol
`
`Comparator
`
`
`
`Switch
`control
`signal
`
`Repetitive
`waveform
`
`(a)
`
`oss = Sawtooth voltage
`
`vcontroi
`(amplified error)
`
`0
`
`Switch
`control
`signal
`
`On
`
`On
`
`ucontroi > vst
`
``"— ton
`
`, ,Off
`
`toff
`
`Oti
`"‘"--vcontrol < vst
`
`(switching frequency fs = 71; )
`
`(b)
`
`Figure 7-3 Pulse-width modulator: (a) block diagram; (b) comparator signals.
`
`In the PWM switching at a constant switching frequency, the switch control signal,
`which controls the state (on or off) of the switch, is generated by comparing a signal-level
`control voltage vco,„„„ with a repetitive waveform as shown in Figs. 7-3a and 7-3b. The
`control voltage signal generally is obtained by amplifying the error, or the difference
`between the actual output voltage and its desired value. The frequency of the repetitive
`waveform with a constant peak, which is shown to be a sawtooth, establishes the switch-
`ing frequency. This frequency is kept constant in a PWM control and is chosen to be in
`a few kilohertz to a few hundred kilohertz range. When the amplified error signal, which
`varies very slowly with time relative to the switching frequency, is greater than the
`sawtooth waveform, the switch control signal becomes high, causing the switch to turn
`on. Otherwise, the switch is off. In terms of vc,„„rO1 and the peak of the sawtooth wave-
`form V„ in Fig. 7-3, the switch duty ratio can be expressed as
`D = ton = Vcontrol
`vs,
`TS
`
`(7-1)
`
`The dc—dc converters can have two distinct modes of operation: (1) continuous
`current conduction and (2) discontinuous current conduction. In practice, a converter may
`operate in both modes, which have significantly different characteristics. Therefore, a
`converter and its control should be designed based on both modes of operation.
`
`Petitioners
` Ex. 1032, p. 163
`
`

`

`164
`
`CHAPTER 7
`
`dc —dc SWITCH-MODE CONVERTERS
`
`7-3 STEP-DOWN (BUCK) CONVERTER
`
`T,
`
`volt) dt
`
`=TS (I t'
`
`n Vd dt
`
`As the name implies, a step-down converter produces a lower average output voltage than
`the dc input voltage Vd. Its main application is in regulated dc power supplies and dc
`motor speed control.
`Conceptually, the basic circuit of Fig. 7-2a constitutes a step-down converter for a
`purely resistive load. Assuming an ideal switch, a constant instantaneous input voltage
`Vd, and a purely resistive load, the instantaneous output voltage waveform is shown in
`Fig. 7-2b as a function of the switch position. The average output voltage can be calcu-
`lated in terms of the switch duty ratio:
`1
`V, = —
`Ts
`
`T,
`
`I on
`
`0 dt) =
`
`ton
`
`Vd = DVd
`
`(7-2)
`
`Substituting for D in Eq. 7-2 from Eq. 7-1 yields
`
`where
`
`Vo =
`
`Vd
`
`Vs(
`
`Vcontrol = kVcontrol
`
`k =
`
`Vd
`
`Vs,
`
`= constant
`
`By varying the duty ratio ton/Ts of the switch, Vo can be controlled. Another important
`observation is that the average output voltage Vo varies linearly with the control voltage,
`as is the case in linear amplifiers. In actual applications, the foregoing circuit has two
`drawbacks: (1) In practice the load would be inductive. Even with a resistive load, there
`would always be certain associated stray inductance. This means that the switch would
`have to absorb (or dissipate) the inductive energy and therefore it may be destroyed. (2)
`The output voltage fluctuates between zero and Vd, which is not acceptable in most
`applications. The problem of stored inductive energy is overcome by using a diode as
`shown in Fig. 7-4a. The output voltage fluctuations are very much diminished by using
`a low-pass filter, consisting of an inductor and a capacitor. Figure 7-4b shows the wave-
`form of the input voi to the low-pass filter (same as the output voltage in Fig. 7-2b without
`a low-pass filter), which consists of a dc component Vo, and the harmonics at the switch-
`ing frequency L and its multiples, as shown in Fig. 7-4b. The low-pass filter character-
`istic with the damping provided by the load resistor R is shown in Fig. 7-4c. The
`corner frequency L of this low-pass filter is selected to be much lower than the switch-
`ing frequency, thus essentially eliminating the switching frequency ripple in the output
`voltage.
`During the interval when the switch is on, the diode in Fig. 7-4a becomes reverse
`biased and the input provides energy to the load as well as to the inductor. During the
`interval when the switch is off, the inductor current flows through the diode, transferring
`some of its stored energy to the load.
`In the steady-state analysis presented here, the filter capacitor at the output is assumed
`to be very large, as is normally the case in applications requiring a nearly constant
`instantaneous output voltage vo(t) = V,. The ripple in the capacitor voltage (output
`voltage) is calculated later.
`From Fig. 7-4a we observe that in a step-down converter, the average inductor
`current is equal to the average output current l o, since the average capacitor current in
`steady state is zero (as discussed in Chapter 3, Section 3-2-5-1).
`
`Petitioners
`Ex. 1032, p. 164
`
`

`

`7-3 STEP-DOWN (BUCK) CONVERTER
`
`165
`
`id
`
`vd
`
`1101
`
`Low-pass
`filter
`
`+
`
`—
`
`vo = Vo
`—
`
`C
`
`'
`
`•
`
`R
`(load)
`
`•
`
`L
`
`(a)
`
`Vd
`
`0
`
`Fe--
`ton —4*— toff—a-I
`1.4— T =
`5
`V°
`
`f,
`
`Vo
`
`t
`
`Frequency spectrum
`of uoi
`
`114
`
`v21,
`
`1 %.•
`
`,
`
`3/:
`
`fa
`
`(=
`
`(b)
`
`0
`
`20 log10
`
`-4O dB
`
`—80 dB
`
`fc
`
`104
`
`(c)
`Figure 7-4 Step-down dc—dc converter.
`
`I
`I
`100f, t,
`
` 1" (log scale)
`
`7-3-1 CONTINUOUS-CONDUCTION MODE
`
`Figure 7-5 shows the waveforms for the continuous-conduction mode of operation where
`the inductor current flows continuously [iL(t) > 0]. When the switch is on for a time
`duration tc,„, the switch conducts the inductor current and the diode becomes reverse
`biased. This results in a positive voltage vL = Vd Vo across the inductor in Fig. 7-5a.
`This voltage causes a linear increase in the inductor current iL. When the switch is turned
`off, because of the inductive energy storage, iL continues to flow. This current now flows
`through the diode, and vL, = —Vo in Fig. 7-5b.
`
`Petitioners
`
`Ex. 1032, p. 165
`
`

`

`166
`
`CHAPTER 7
`
`do—dc SWIT