DETRArla
`
`IPR2022-00716
`Apple EX1008 Page 1
`
`

`

`har80679_FC.qxd 12/11/09 6:23 PM Page ii
`
`Commonly used Power
`and Converter Equations
`
`Instantaneous power:
`
`p(t) ⫽ v(t)i(t)
`
`Energy:
`
`W ⫽ 3
`
`t2
`
`t1
`
`p(t)dt
`
`v(t)i(t) dt
`
`t0⫹T
`
`3
`
`t0
`
`1 T
`
`p(t) dt ⫽
`
`t0⫹T
`
`3
`
`t0
`
`1 T
`
`⫽
`
`W T
`
`Average power:
`
`P ⫽
`
`Average power for a dc voltage source:
`
`Pdc ⫽ Vdc Iavg
`
`Vrms ⫽B 1
`
`T3T
`
`0
`
`rms voltage:
`
`v 2(t)dt
`
`Vrms ⫽2V
`Im13
`Irms ⫽Ba Im13b 2
`
`23
`
`, rms ⫹ Á
`
`22
`
`, rms ⫹V
`
`21
`
`, rms ⫹V
`
`rms for v ⫽ v1 ⫹ v2 ⫹ v3 ⫹ . . . :
`
`rms current for a triangular wave:
`
`Irms ⫽
`
`rms current for an offset triangular wave:
`
`⫹ I 2
`dc
`
`rms voltage for a sine wave or a full-wave rectified sine wave: Vrms ⫽
`
`Vm12
`
`IPR2022-00716
`Apple EX1008 Page 2
`
`

`

`har80679_FC.qxd 12/11/09 6:23 PM Page iii
`
`rms voltage for a half-wave rectified sine wave:
`
`Vrms ⫽
`
`Vm
`2
`
`P
`Vrms Irms
`
`⫽
`
`P S
`
`pf ⫽
`Power factor:
`
`Total harmonic distortion:
`
`DF ⫽A
`
`Distortion factor:
`
`Form factor ⫽
`
`Irms
`Iavg
`
`THD ⫽Aaq
`
`n⫽2
`I1
`
`I 2
`n
`
`1
`1 ⫹ (THD)2
`
`Crest factor ⫽
`
`Ipeak
`Irms
`
`Buck converter:
`Vo ⫽ Vs D
`
`Boost converter:
`
`Vo ⫽
`
`Vs
`1 ⫺ D
`
`Buck-boost and ´Cuk converters:
`
`Vo ⫽ ⫺Vsa D
`1 ⫺ Db
`Vo ⫽ Vsa D
`1 ⫺ Db
`Vo ⫽ Vsa D
`N1b
`1 ⫺ Dba N2
`
`Forward converter: Vo ⫽ VsDa N2N1b
`
`SEPIC:
`
`Flyback converter:
`
`IPR2022-00716
`Apple EX1008 Page 3
`
`

`

`har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page i
`
`Power Electronics
`
`Daniel W. Hart
`Valparaiso University
`Valparaiso, Indiana
`
`IPR2022-00716
`Apple EX1008 Page 4
`
`

`

`har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page ii
`
`POWER ELECTRONICS
`
`Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the
`Americas, New York, NY 10020. Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights
`reserved. No part of this publication may be reproduced or distributed in any form or by any means,
`or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill
`Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission,
`or broadcast for distance learning.
`
`Some ancillaries, including electronic and print components, may not be available to customers outside
`the United States.
`
`This book is printed on acid-free paper.
`
`1 2 3 4 5 6 7 8 9 0 DOC/DOC 1 0 9 8 7 6 5 4 3 2 1 0
`
`ISBN 978-0-07-338067-4
`MHID 0-07-338067-9
`
`Vice President & Editor-in-Chief: Marty Lange
`Vice President, EDP: Kimberly Meriwether-David
`Global Publisher: Raghothaman Srinivasan
`Director of Development: Kristine Tibbetts
`Developmental Editor: Darlene M. Schueller
`Senior Marketing Manager: Curt Reynolds
`Project Manager: Erin Melloy
`Senior Production Supervisor: Kara Kudronowicz
`Senior Media Project Manager: Jodi K. Banowetz
`Design Coordinator: Brenda A. Rolwes
`Cover Designer: Studio Montage, St. Louis, Missouri
`(USE) Cover Image: Figure 7.5a from interior
`Compositor: Glyph International
`Typeface: 10.5/12 Times Roman
`Printer: R. R. Donnelley
`
`All credits appearing on page or at the end of the book are considered to be an extension of the
`copyright page.
`
`This book was previously published by: Pearson Education, Inc.
`
`Library of Congress Cataloging-in-Publication Data
`
`Hart, Daniel W.
`Power electronics / Daniel W. Hart.
`p. cm.
`Includes bibliographical references and index.
`ISBN 978-0-07-338067-4 (alk. paper)
`1. Power electronics. I. Title.
`TK7881.15.H373 2010
`621.31'7—dc22
`
`www.mhhe.com
`
`2009047266
`
`IPR2022-00716
`Apple EX1008 Page 5
`
`

`

`har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page iii
`
`To my family, friends, and the many students
`I have had the privilege and pleasure of guiding
`
`IPR2022-00716
`Apple EX1008 Page 6
`
`

`

`har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page iv
`
`BRIEF CONTENTS
`
`Chapter 1
`Introduction 1
`
`Chapter 7
`DC Power Supplies
`
`265
`
`Chapter 2
`Power Computations 21
`
`Chapter 8
`Inverters 331
`
`Chapter 3
`Half-Wave Rectifiers 65
`
`Chapter 9
`Resonant Converters 387
`
`Chapter 4
`Full-Wave Rectifiers 111
`
`Chapter 5
`AC Voltage Controllers
`
`171
`
`Chapter 6
`DC-DC Converters 196
`
`Chapter 10
`Drive Circuits, Snubber Circuits,
`and Heat Sinks
`431
`
`Appendix A Fourier Series for Some
`Common Waveforms
`461
`Appendix B State-Space Averaging 467
`
`Index
`
`473
`
`iv
`
`IPR2022-00716
`Apple EX1008 Page 7
`
`

`

`har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page v
`
`Chapter 1
`Introduction 1
`1.1 Power Electronics 1
`1.2 Converter Classification 1
`1.3 Power Electronics Concepts 3
`1.4 Electronic Switches 5
`The Diode 6
`Thyristors 7
`Transistors 8
`1.5 Switch Selection 11
`1.6 Spice, PSpice, and Capture 13
`1.7 Switches in Pspice 14
`The Voltage-Controlled Switch
`Transistors
`16
`Diodes
`17
`18
`Thyristors (SCRs)
`Convergence Problems in
`PSpice
`18
`1.8 Bibliography 19
`Problems 20
`
`14
`
`Chapter 2
`Power Computations 21
`2.1
`Introduction 21
`2.2 Power and Energy 21
`Instantaneous Power 21
`Energy 22
`Average Power 22
`2.3
`Inductors and Capacitors 25
`2.4 Energy Recovery 27
`
`CONTENTS
`
`2.5 Effective Values: RMS 34
`2.6 Apparent Power and Power
`Factor 42
`Apparent Power S 42
`Power Factor 43
`2.7 Power Computations for Sinusoidal
`AC Circuits 43
`2.8 Power Computations for Nonsinusoidal
`Periodic Waveforms 44
`Fourier Series 45
`Average Power 46
`Nonsinusoidal Source and
`Linear Load 46
`Sinusoidal Source and Nonlinear
`Load 48
`2.9 Power Computations Using
`PSpice 51
`2.10 Summary 58
`2.11 Bibliography 59
`Problems 59
`
`Chapter 3
`Half-Wave Rectifiers 65
`3.1
`Introduction 65
`3.2 Resistive Load 65
`Creating a DC Component
`Using an Electronic Switch 65
`3.3 Resistive-Inductive Load 67
`3.4 PSpice Simulation 72
`Using Simulation Software for
`Numerical Computations 72
`
`v
`
`IPR2022-00716
`Apple EX1008 Page 8
`
`

`

`har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page vi
`
`vi
`
`Contents
`
`3.6
`
`3.5 RL-Source Load 75
`Supplying Power to a DC Source
`from an AC Source 75
`Inductor-Source Load 79
`Using Inductance to
`Limit Current 79
`3.7 The Freewheeling Diode 81
`Creating a DC Current 81
`Reducing Load Current Harmonics 86
`3.8 Half-Wave Rectifier With a Capacitor
`Filter 88
`Creating a DC Voltage from an
`AC Source 88
`3.9 The Controlled Half-Wave
`Rectifier 94
`Resistive Load 94
`RL Load 96
`RL-Source Load 98
`3.10 PSpice Solutions For
`Controlled Rectifiers 100
`Modeling the SCR in PSpice 100
`3.11 Commutation 103
`The Effect of Source Inductance 103
`3.12 Summary 105
`3.13 Bibliography 106
`Problems 106
`
`Capacitance Output Filter 122
`Voltage Doublers 125
`LC Filtered Output 126
`4.3 Controlled Full-Wave Rectifiers 131
`Resistive Load 131
`RL Load, Discontinuous Current 133
`RL Load, Continuous Current 135
`PSpice Simulation of Controlled Full-Wave
`Rectifiers 139
`Controlled Rectifier with
`RL-Source Load 140
`Controlled Single-Phase Converter
`Operating as an Inverter 142
`4.4 Three-Phase Rectifiers 144
`4.5 Controlled Three-Phase
`Rectifiers 149
`Twelve-Pulse Rectifiers 151
`The Three-Phase Converter Operating
`as an Inverter 154
`4.6 DC Power Transmission 156
`4.7 Commutation: The Effect of Source
`Inductance 160
`Single-Phase Bridge Rectifier 160
`Three-Phase Rectifier 162
`4.8 Summary 163
`4.9 Bibliography 164
`Problems 164
`
`Chapter 4
`Full-Wave Rectifiers 111
`4.1
`Introduction 111
`4.2 Single-Phase Full-Wave Rectifiers 111
`The Bridge Rectifier 111
`The Center-Tapped Transformer
`Rectifier 114
`Resistive Load 115
`RL Load 115
`Source Harmonics 118
`PSpice Simulation 119
`RL-Source Load 120
`
`171
`
`Chapter 5
`AC Voltage Controllers
`5.1
`Introduction 171
`5.2 The Single-Phase AC Voltage
`Controller 171
`Basic Operation 171
`Single-Phase Controller with a
`Resistive Load 173
`Single-Phase Controller with
`an RL Load 177
`PSpice Simulation of Single-Phase
`AC Voltage Controllers 180
`
`IPR2022-00716
`Apple EX1008 Page 9
`
`

`

`har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page vii
`
`5.3 Three-Phase Voltage
`Controllers 183
`Y-Connected Resistive Load 183
`Y-Connected RL Load 187
`Delta-Connected Resistive Load 189
`5.4
`Induction Motor Speed Control 191
`5.5 Static VAR Control 191
`5.6 Summary 192
`5.7 Bibliography 193
`Problems 193
`
`Chapter 6
`DC-DC Converters 196
`6.1 Linear Voltage Regulators 196
`6.2 A Basic Switching Converter 197
`6.3 The Buck (Step-Down)
`Converter 198
`Voltage and Current Relationships 198
`Output Voltage Ripple 204
`Capacitor Resistance—The Effect
`on Ripple Voltage 206
`Synchronous Rectification for the
`Buck Converter 207
`6.4 Design Considerations 207
`6.5 The Boost Converter 211
`Voltage and Current Relationships 211
`Output Voltage Ripple 215
`Inductor Resistance 218
`6.6 The Buck-Boost Converter 221
`Voltage and Current Relationships 221
`Output Voltage Ripple 225
`6.7 The ´Cuk Converter 226
`6.8 The Single-Ended Primary Inductance
`Converter (SEPIC) 231
`6.9
`Interleaved Converters 237
`6.10 Nonideal Switches and Converter
`Performance 239
`Switch Voltage Drops 239
`Switching Losses 240
`
`Contents
`
`vii
`
`6.11 Discontinuous-Current Operation 241
`Buck Converter with Discontinuous
`Current 241
`Boost Converter with Discontinuous
`Current 244
`6.12 Switched-Capacitor Converters 247
`The Step-Up Switched-Capacitor
`Converter 247
`The Inverting Switched-Capacitor
`Converter 249
`The Step-Down Switched-Capacitor
`Converter 250
`6.13 PSpice Simulation of DC-DC
`Converters 251
`A Switched PSpice Model 252
`An Averaged Circuit Model 254
`6.14 Summary 259
`6.15 Bibliography 259
`Problems 260
`
`Chapter 7
`DC Power Supplies
`265
`7.1
`Introduction 265
`7.2 Transformer Models 265
`7.3 The Flyback Converter 267
`Continuous-Current Mode 267
`Discontinuous-Current Mode in the Flyback
`Converter 275
`Summary of Flyback Converter
`Operation 277
`7.4 The Forward Converter 277
`Summary of Forward Converter
`Operation 283
`7.5 The Double-Ended (Two-Switch)
`Forward Converter 285
`7.6 The Push-Pull Converter 287
`Summary of Push-Pull Operation 290
`7.7 Full-Bridge and Half-Bridge DC-DC
`Converters 291
`
`IPR2022-00716
`Apple EX1008 Page 10
`
`

`

`har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page viii
`
`viii
`
`Contents
`
`7.8 Current-Fed Converters 294
`7.9 Multiple Outputs 297
`7.10 Converter Selection 298
`7.11 Power Factor Correction 299
`7.12 PSpice Simulation of DC
`Power Supplies 301
`7.13 Power Supply Control 302
`Control Loop Stability 303
`Small-Signal Analysis 304
`Switch Transfer Function 305
`Filter Transfer Function 306
`Pulse-Width Modulation Transfer
`Function 307
`Type 2 Error Amplifier with
`Compensation 308
`Design of a Type 2 Compensated
`Error Amplifier 311
`PSpice Simulation of Feedback Control 315
`Type 3 Error Amplifier with
`Compensation 317
`Design of a Type 3 Compensated
`Error Amplifier 318
`Manual Placement of Poles and Zeros
`in the Type 3 Amplifier 323
`7.14 PWM Control Circuits 323
`7.15 The AC Line Filter 323
`7.16 The Complete DC Power Supply 325
`7.17 Bibliography 326
`Problems 327
`
`Chapter 8
`Inverters 331
`8.1
`Introduction 331
`8.2 The Full-Bridge Converter 331
`8.3 The Square-Wave Inverter 333
`8.4 Fourier Series Analysis 337
`8.5 Total Harmonic Distortion 339
`8.6 PSpice Simulation of Square Wave
`Inverters 340
`
`8.7 Amplitude and Harmonic
`Control 342
`8.8 The Half-Bridge Inverter 346
`8.9 Multilevel Inverters 348
`Multilevel Converters with Independent
`DC Sources 349
`Equalizing Average Source Power
`with Pattern Swapping 353
`Diode-Clamped Multilevel
`Inverters 354
`8.10 Pulse-Width-Modulated
`Output 357
`Bipolar Switching 357
`Unipolar Switching 358
`8.11 PWM Definitions and
`Considerations 359
`8.12 PWM Harmonics 361
`Bipolar Switching 361
`Unipolar Switching 365
`8.13 Class D Audio Amplifiers 366
`8.14 Simulation of Pulse-Width-Modulated
`Inverters 367
`Bipolar PWM 367
`Unipolar PWM 370
`8.15 Three-Phase Inverters 373
`The Six-Step Inverter 373
`PWM Three-Phase
`Inverters 376
`Multilevel Three-Phase
`Inverters 378
`8.16 PSpice Simulation of
`Three-Phase Inverters 378
`Six-Step Three-Phase
`Inverters 378
`PWM Three-Phase
`Inverters 378
`8.17 Induction Motor Speed
`Control 379
`8.18 Summary 382
`8.19 Bibliography 383
`Problems 383
`
`IPR2022-00716
`Apple EX1008 Page 11
`
`

`

`har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page ix
`
`Chapter 9
`Resonant Converters 387
`9.1
`Introduction 387
`9.2 A Resonant Switch Converter:
`Zero-Current Switching 387
`Basic Operation 387
`Output Voltage 392
`9.3 A Resonant Switch Converter:
`Zero-Voltage Switching 394
`Basic Operation 394
`Output Voltage 399
`9.4 The Series Resonant Inverter 401
`Switching Losses 403
`Amplitude Control 404
`9.5 The Series Resonant
`DC-DC Converter 407
`Basic Operation 407
`Operation for ωs ⬎ ωo 407
`Operation for ω0 /2 ⬍ ωs⬍ ω0
`Operation for ωs ⬍ ω0 /2 413
`Variations on the Series Resonant DC-DC
`Converter 414
`9.6 The Parallel Resonant
`DC-DC Converter 415
`9.7 The Series-Parallel DC-DC
`Converter 418
`9.8 Resonant Converter Comparison 421
`9.9 The Resonant DC Link Converter 422
`9.10 Summary 426
`9.11 Bibliography 426
`Problems 427
`
`413
`
`Contents
`
`ix
`
`Chapter 10
`Drive Circuits, Snubber Circuits,
`and Heat Sinks
`431
`10.1 Introduction 431
`10.2 MOSFET and IGBT Drive
`Circuits 431
`Low-Side Drivers 431
`High-Side Drivers 433
`10.3 Bipolar Transistor Drive
`Circuits 437
`10.4 Thyristor Drive Circuits 440
`10.5 Transistor Snubber Circuits 441
`10.6 Energy Recovery Snubber
`Circuits 450
`10.7 Thyristor Snubber Circuits 450
`10.8 Heat Sinks and Thermal
`Management 451
`Steady-State Temperatures 451
`Time-Varying Temperatures 454
`10.9 Summary 457
`10.10 Bibliography 457
`Problems 458
`
`Appendix A Fourier Series for Some
`Common Waveforms
`461
`Appendix B State-Space Averaging 467
`
`Index
`
`473
`
`IPR2022-00716
`Apple EX1008 Page 12
`
`

`

`This page intentionally left blank
`
`IPR2022-00716
`Apple EX1008 Page 13
`
`

`

`har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page xi
`
`This book is intended to be an introductory text in power electronics, primar-
`
`ily for the undergraduate electrical engineering student. The text assumes
`that the student is familiar with general circuit analysis techniques usually
`taught at the sophomore level. The student should be acquainted with electronic
`devices such as diodes and transistors, but the emphasis of this text is on circuit
`topology and function rather than on devices. Understanding the voltage-current
`relationships for linear devices is the primary background required, and the concept
`of Fourier series is also important. Most topics presented in this text are appropriate
`for junior- or senior-level undergraduate electrical engineering students.
`The text is designed to be used for a one-semester power electronics
`course, with appropriate topics selected or omitted by the instructor. The text
`is written for some flexibility in the order of the topics. It is recommended that
`Chap. 2 on power computations be covered at the beginning of the course in
`as much detail as the instructor deems necessary for the level of students.
`Chapters 6 and 7 on dc-dc converters and dc power supplies may be taken before
`Chaps. 3, 4, and 5 on rectifiers and voltage controllers. The author covers chap-
`ters in the order 1, 2 (introduction; power computations), 6, 7 (dc-dc converters;
`dc power supplies), 8 (inverters), 3, 4, 5 (rectifiers and voltage controllers), fol-
`lowed by coverage of selected topics in 9 (resonant converters) and 10 (drive and
`snubber circuits and heat sinks). Some advanced material, such as the control
`section in Chapter 7, may be omitted in an introductory course.
`The student should use all the software tools available for the solution
`to the equations that describe power electronics circuits. These range from
`calculators with built-in functions such as integration and root finding to
`more powerful computer software packages such as MATLAB®, Mathcad®,
`Maple™, Mathematica®, and others. Numerical techniques are often sug-
`gested in this text. It is up to the student to select and adapt all the readily
`available computer tools to the power electronics situation.
`Much of this text includes computer simulation using PSpice® as a supple-
`ment to analytical circuit solution techniques. Some prior experience with
`PSpice is helpful but not necessary. Alternatively, instructors may choose to use
`a different simulation program such as PSIM® or NI Multisim™ software instead
`of PSpice. Computer simulation is never intended to replace understanding of
`fundamental principles. It is the author’s belief that using computer simulation
`for the instructional benefit of investigating the basic behavior of power elec-
`tronics circuits adds a dimension to the student’s learning that is not possible
`from strictly manipulating equations. Observing voltage and current waveforms
`from a computer simulation accomplishes some of the same objectives as those
`
`PREFACE
`
`xi
`
`IPR2022-00716
`Apple EX1008 Page 14
`
`

`

`har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page xii
`
`xii
`
`Preface
`
`of a laboratory experience. In a computer simulation, all the circuit’s voltages
`and currents can be investigated, usually much more efficiently than in a hard-
`ware lab. Variations in circuit performance for a change in components or oper-
`ating parameters can be accomplished more easily with a computer simulation
`than in a laboratory. PSpice circuits presented in this text do not necessarily rep-
`resent the most elegant way to simulate circuits. Students are encouraged to use
`their engineering skills to improve the simulation circuits wherever possible.
`The website that accompanies this text can be found at www.mhhe
`.com/hart, and features Capture circuit files for PSpice simulation for students
`and instructors and a password-protected solutions manual and PowerPoint®
`lecture notes for instructors.
`My sincere gratitude to reviewers and students who have made many
`valuable contributions to this project. Reviewers include
`Ali Emadi
`Illinois Institute of Technology
`Shaahin Filizadeh
`University of Manitoba
`James Gover
`Kettering University
`Peter Idowu
`Penn State, Harrisburg
`Mehrdad Kazerani
`University of Waterloo
`Xiaomin Kou
`University of Wisconsin-Platteville
`Alexis Kwasinski
`The University of Texas at Austin
`Medhat M. Morcos
`Kansas State University
`Steve Pekarek
`Purdue University
`Wajiha Shireen
`University of Houston
`Hamid Toliyat
`Texas A&M University
`Zia Yamayee
`University of Portland
`Lin Zhao
`Gannon University
`A special thanks to my colleagues Kraig Olejniczak, Mark Budnik, and
`Michael Doria at Valparaiso University for their contributions. I also thank
`Nikke Ault for the preparation of much of the manuscript.
`
`IPR2022-00716
`Apple EX1008 Page 15
`
`

`

`har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page xiii
`
`Preface
`
`xiii
`
`Complete Online Solutions Manual Organization System (COSMOS). Pro-
`fessors can benefit from McGraw-Hill’s COSMOS electronic solutions manual.
`COSMOS enables instructors to generate a limitless supply of problem mate-
`rial for assignment, as well as transfer and integrate their own problems
`into the software. For additional information, contact your McGraw-Hill sales
`representative.
`Electronic Textbook Option. This text is offered through CourseSmart for both
`instructors and students. CourseSmart is an online resource where students can
`purchase the complete text online at almost one-half the cost of a traditional text.
`Purchasing the eTextbook allows students to take advantage of CourseSmart’s Web
`tools for learning, which include full text search, notes and highlighting, and e-mail
`tools for sharing notes among classmates. To learn more about CourseSmart options,
`contact your McGraw-Hill sales representative or visit www.CourseSmart.com.
`Daniel W. Hart
`Valparaiso University
`Valparaiso, Indiana
`
`IPR2022-00716
`Apple EX1008 Page 16
`
`

`

`This page intentionally left blank
`
`IPR2022-00716
`Apple EX1008 Page 17
`
`

`

`C H A P T E R 1
`
`Introduction
`
`1.1 POWER ELECTRONICS
`Power electronics circuits convert electric power from one form to another using
`electronic devices. Power electronics circuits function by using semiconductor
`devices as switches, thereby controlling or modifying a voltage or current. Appli-
`cations of power electronics range from high-power conversion equipment such
`as dc power transmission to everyday appliances, such as cordless screwdrivers,
`power supplies for computers, cell phone chargers, and hybrid automobiles.
`Power electronics includes applications in which circuits process milliwatts or
`megawatts. Typical applications of power electronics include conversion of ac to
`dc, conversion of dc to ac, conversion of an unregulated dc voltage to a regulated
`dc voltage, and conversion of an ac power source from one amplitude and fre-
`quency to another amplitude and frequency.
`The design of power conversion equipment includes many disciplines from
`electrical engineering. Power electronics includes applications of circuit theory,
`control theory, electronics, electromagnetics, microprocessors (for control), and
`heat transfer. Advances in semiconductor switching capability combined with the
`desire to improve the efficiency and performance of electrical devices have made
`power electronics an important and fast-growing area in electrical engineering.
`
`1.2 CONVERTER CLASSIFICATION
`The objective of a power electronics circuit is to match the voltage and current re-
`quirements of the load to those of the source. Power electronics circuits convert one
`type or level of a voltage or current waveform to another and are hence called
`converters. Converters serve as an interface between the source and load (Fig. 1-1).
`
`1
`
`IPR2022-00716
`Apple EX1008 Page 18
`
`

`

`har80679_ch01_001-020.qxd 12/15/09 2:27 PM Page 2
`
`2
`
`C H A P T E R 1 Introduction
`
`Input
`
`Source
`
`Converter
`
`Output
`
`Load
`
`Figure 1-1 A source and load interfaced by a power electronics converter.
`
`Converters are classified by the relationship between input and output:
`ac input/dc output
`The ac-dc converter produces a dc output from an ac input. Average power
`is transferred from an ac source to a dc load. The ac-dc converter is
`specifically classified as a rectifier. For example, an ac-dc converter
`enables integrated circuits to operate from a 60-Hz ac line voltage by
`converting the ac signal to a dc signal of the appropriate voltage.
`dc input/ac output
`The dc-ac converter is specifically classified as an inverter. In the inverter,
`average power flows from the dc side to the ac side. Examples of inverter
`applications include producing a 120-V rms 60-Hz voltage from a 12-V
`battery and interfacing an alternative energy source such as an array of
`solar cells to an electric utility.
`dc input/dc output
`The dc-dc converter is useful when a load requires a specified (often
`regulated) dc voltage or current but the source is at a different or
`unregulated dc value. For example, 5 V may be obtained from a 12-V
`source via a dc-dc converter.
`ac input/ac output
`The ac-ac converter may be used to change the level and/or frequency of
`an ac signal. Examples include a common light-dimmer circuit and speed
`control of an induction motor.
`Some converter circuits can operate in different modes, depending on circuit
`and control parameters. For example, some rectifier circuits can be operated as
`inverters by modifying the control on the semiconductor devices. In such cases,
`it is the direction of average power flow that determines the converter classifica-
`tion. In Fig. 1-2, if the battery is charged from the ac power source, the converter
`is classified as a rectifier. If the operating parameters of the converter are changed
`and the battery acts as a source supplying power to the ac system, the converter
`is then classified as an inverter.
`Power conversion can be a multistep process involving more than one type
`of converter. For example, an ac-dc-ac conversion can be used to modify an ac
`source by first converting it to direct current and then converting the dc signal to
`an ac signal that has an amplitude and frequency different from those of the orig-
`inal ac source, as illustrated in Fig. 1-3.
`
`IPR2022-00716
`Apple EX1008 Page 19
`
`

`

`har80679_ch01_001-020.qxd 12/17/09 12:49 PM Page 3
`
`1.3 Power Electronics Concepts
`
`3
`
`+
`−
`
`Rectifier
`
`P
`
`Converter
`
`P
`
`Inverter
`
`+
`
`−
`
`Figure 1-2 A converter can operate as a rectifier or an inverter, depending on the direction
`of average power P.
`
`Input
`
`Source
`
`Converter 1
`
`Converter 2
`
`Output
`
`Load
`
`Figure 1-3 Two converters are used in a multistep process.
`
`1.3 POWER ELECTRONICS CONCEPTS
`To illustrate some concepts in power electronics, consider the design problem of
`creating a 3-V dc voltage level from a 9-V battery. The purpose is to supply 3 V
`to a load resistance. One simple solution is to use a voltage divider, as shown in
`Fig. 1-4. For a load resistor RL, inserting a series resistance of 2RL results in 3 V
`across RL. A problem with this solution is that the power absorbed by the 2RL
`resistor is twice as much as delivered to the load and is lost as heat, making the
`circuit only 33.3 percent efficient. Another problem is that if the value of the load
`resistance changes, the output voltage will change unless the 2RL resistance
`changes proportionally. A solution to that problem could be to use a transistor in
`place of the 2RL resistance. The transistor would be controlled such that the volt-
`age across it is maintained at 6 V, thus regulating the output at 3 V. However, the
`same low-efficiency problem is encountered with this solution.
`To arrive at a more desirable design solution, consider the circuit in Fig. 1-5a.
`In that circuit, a switch is opened and closed periodically. The switch is a short
`circuit when it is closed and an open circuit when it is open, making the voltage
`
`2RL
`
`+
`
`RL
`
`3 V
`
`−
`
`+ −
`
`9 V
`
`Figure 1-4 A simple voltage divider for creating 3 V from a 9-V source.
`
`IPR2022-00716
`Apple EX1008 Page 20
`
`

`

`har80679_ch01_001-020.qxd 12/15/09 2:27 PM Page 4
`
`4
`
`C H A P T E R 1 Introduction
`
`Average
`
`t
`
`9 V
`
`+
`
`−
`
`(a)
`
`+
`
`vx(t)
`
`−
`
`vx(t)
`
`9 V
`
`3 V
`
`T
`
`(b)
`
`T3
`
`Figure 1-5 (a) A switched circuit; (b) a pulsed voltage waveform.
`
`across RL equal to 9 V when the switch is closed and 0 V when the switch is open.
`The resulting voltage across RL will be like that of Fig. 1-5b. This voltage is
`obviously not a constant dc voltage, but if the switch is closed for one-third of the
`period, the average value of vx (denoted as Vx) is one-third of the source voltage.
`Average value is computed from the equation
`/3
`
`3T
`1 T
`
`avg(vx) ⫽ Vx ⫽
`
`vx(t) dt ⫽
`
`3T
`1 T
`
`9 dt ⫹
`
`0 dt ⫽ 3 V
`
`(1-1)
`
`3T
`1 T
`
`0
`T/3
`0
`Considering efficiency of the circuit, instantaneous power (see Chap. 2)
`absorbed by the switch is the product of voltage and current. When the switch is
`open, power absorbed by it is zero because the current in it is zero. When the
`switch is closed, power absorbed by it is zero because the voltage across it is
`zero. Since power absorbed by the switch is zero for both open and closed con-
`ditions, all power supplied by the 9-V source is delivered to RL, making the cir-
`cuit 100 percent efficient.
`The circuit so far does not accomplish the design object of creating a dc volt-
`age of 3 V. However, the voltage waveform vx can be expressed as a Fourier series
`containing a dc term (the average value) plus sinusoidal terms at frequencies that
`are multiples of the pulse frequency. To create a 3-V dc voltage, vx is applied to a
`low-pass filter. An ideal low-pass filter allows the dc component of voltage to pass
`through to the output while removing the ac terms, thus creating the desired dc
`output. If the filter is lossless, the converter will be 100 percent efficient.
`
`IPR2022-00716
`Apple EX1008 Page 21
`
`

`

`har80679_ch01_001-020.qxd 12/15/09 2:27 PM Page 5
`
`1.4 Electronic Switches
`
`5
`
`+
`
`vx(t)
`−
`
`+
`
`Low-Pass Filter
`
`RL
`
`3 V
`
`−
`
`+ −
`
`9 V
`
`Figure 1-6 A low-pass filter allows just the average value of vx to pass through to the load.
`
`Switch Control
`
`+ −
`
`Vo
`
`+
`
`vx(t)
`
`Low-Pass Filter
`
`−
`
`Vs
`
`+
`
`−
`
`Figure 1-7 Feedback is used to control the switch and maintain the desired output voltage.
`
`In practice, the filter will have some losses and will absorb some power.
`Additionally, the electronic device used for the switch will not be perfect and will
`have losses. However, the efficiency of the converter can still be quite high (more
`than 90 percent). The required values of the filter components can be made smaller
`with higher switching frequencies, making large switching frequencies desirable.
`Chaps. 6 and 7 describe the dc-dc conversion process in detail. The “switch” in this
`example will be some electronic device such as a metal-oxide field-effect transis-
`tors (MOSFET), or it may be comprised of more than one electronic device.
`The power conversion process usually involves system control. Converter
`output quantities such as voltage and current are measured, and operating para-
`meters are adjusted to maintain the desired output. For example, if the 9-V bat-
`tery in the example in Fig. 1-6 decreased to 6 V, the switch would have to be
`closed 50 percent of the time to maintain an average value of 3 V for vx. A feed-
`back control system would detect if the output voltage were not 3 V and adjust
`the closing and opening of the switch accordingly, as illustrated in Fig. 1-7.
`
`1.4 ELECTRONIC SWITCHES
`An electronic switch is characterized by having the two states on and off, ideally
`being either a short circuit or an open circuit. Applications using switching
`devices are desirable because of the relatively small power loss in the device. If
`the switch is ideal, either the switch voltage or the switch current is zero, making
`
`IPR2022-00716
`Apple EX1008 Page 22
`
`

`

`har80679_ch01_001-020.qxd 12/15/09 2:27 PM Page 6
`
`6
`
`C H A P T E R 1 Introduction
`
`the power absorbed by it zero. Real devices absorb some power when in the on
`state and when making transitions between the on and off states, but circuit effi-
`ciencies can still be quite high. Some electronic devices such as transistors can
`also operate in the active range where both voltage and current are nonzero, but
`it is desirable to use these devices as switches when processing power.
`The emphasis of this textbook is on basic circuit operation rather than on
`device performance. The particular switching device used in a power electronics
`circuit depends on the existing state of device technology. The behaviors of
`power electronics circuits are often not affected significantly by the actual device
`used for switching, particularly if voltage drops across a conducting switch are
`small compared to other circuit voltages. Therefore, semiconductor devices are
`usually modeled as ideal switches so that circuit behavior can be emphasized.
`Switches are modeled as short circuits when on and open circuits when off. Tran-
`sitions between states are usually assumed to be instantaneous, but the effects of
`nonideal switching are discussed where appropriate. A brief discussion of semi-
`conductor switches is given in this section, and additional information relating to
`drive and snubber circuits is provided in Chap. 10. Electronic switch technology
`is continually changing, and thorough treatments of state-of-the-art devices can
`be found in the literature.
`
`The Diode
`A diode is the simplest electronic switch. It is uncontrollable in that the on and
`off conditions are determined by voltages and currents in the circuit. The diode
`is forward-biased (on) when the current id (Fig. 1-8a) is positive and reverse-
`biased (off) when vd is negative. In the ideal case, the diode is a short circuit
`
`id
`
`i
`
`On
`
`Off
`
`vd
`
`v
`
`(b)
`
`(c)
`
`Off
`
`t
`
`trr
`(d)
`
`(e)
`
`i
`
`On
`
`Anode
`id
`
`+ −
`
`vd
`
`Cathode
`(a)
`
`Figure 1-8 (a) Rectifier diode; (b) i-v characteristic; (c) idealized i-v characteristic;
`(d) reverse recovery time trr; (e) Schottky diode.
`
`IPR2022-00716
`Apple EX1008 Page 23
`
`

`

`har80679_ch01_001-020.qxd 12/15/09 2:27 PM Page 7
`
`1.4 Electronic Switches
`
`7
`
`when it is forward-biased and is an open circuit when reverse-biased. The actual
`and idealized current-voltage characteristics are shown in Fig. 1-8b and c. The
`idealized characteristic is used in most analyses in this text.
`An important dynamic characteristic of a nonideal diode is reverse recovery
`current. When a diode turns off, the current in it decreases and momentarily
`becomes negative before becoming zero, as shown in Fig. 1-8d. The time trr is
`the reverse recovery time, which is usually less than 1 ␮s. This phenomenon
`may become important in high-frequency applications. Fast-recovery diodes
`are designed to have a smaller trr than diodes designed for line-frequency appli-
`cations. Silicon carbide (SiC) diodes have very little reverse recovery, resulting
`in more efficient circuits, especially in high-power applications.
`Schottky diodes (Fig. 1-8e) have a metal-to-silicon barrier rather than a P-N
`junction. Schottky diodes have a forward voltage drop of typically 0.3 V. These
`are often used in low-voltage applications where diode drops are significant rel-
`ative to other circuit voltages. The reverse voltage for a Schottky diode is limited
`to about 100 V. The metal-silicon barrier in a Schottky diode is not subject to
`recovery transients and turn-on and off faster than P-N junction diodes.
`
`Thyristors
`Thyristors are electronic switches used in some power electronic circuits where
`control of switch turn-on is required. The term thyrist