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Commonly used Power
and Converter Equations
Instantaneous power: p(t) ϭ v(t)i(t)
t2

Energy: W ϭ

3

p(t)dt

t1

t0 ϩT

t0 ϩT

t0

t0

W 1

1
p(t) dt ϭ
v(t)i(t) dt
Average power: P ϭ ϭ
T T3
T3
Average power for a dc voltage source: Pdc ϭ Vdc Iavg
rms voltage: Vrms ϭ

1 T 2
v (t)dt
BT3
0

rms for v ϭ v1 ϩ v2 ϩ v3 ϩ . . . : Vrms ϭ 2V 1,2 rms ϩ V 2,2 rms ϩ V 3,2 rms ϩ Á
rms current for a triangular wave: Irms ϭ

Im
13

rms current for an offset triangular wave: Irms ϭ

Im 2
2
b ϩ I dc
B 13
a

rms voltage for a sine wave or a full-wave rectified sine wave: Vrms ϭ


Vm
12


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rms voltage for a half-wave rectified sine wave: Vrms ϭ
Power factor: pf ϭ

P
P
ϭ
S Vrms Irms
q

Aa
Total harmonic distortion: THD ϭ nϭ2
I1
Distortion factor: DF ϭ
Form factor ϭ

Irms
Iavg


Crest factor ϭ

Ipeak
Irms

I 2n

1
A 1 ϩ (THD)2

Buck converter: Vo ϭ Vs D
Boost converter: Vo ϭ

Vs
1ϪD

´ converters: Vo ϭ Ϫ Vs a
Buck-boost and Cuk
SEPIC: Vo ϭ Vs a

D
b
1ϪD

Flyback converter: Vo ϭ Vs a

D
N
b a 2b
1 Ϫ D N1


Forward converter: Vo ϭ Vs D a

N2
b
N1

D
b
1ϪD

Vm
2


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Page i

Power Electronics
Daniel W. Hart
Valparaiso University
Valparaiso, Indiana


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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
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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
2009047266
www.mhhe.com


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To my family, friends, and the many students

I have had the privilege and pleasure of guiding


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BRIEF CONTENTS

Chapter 1
Introduction

Chapter 7
DC Power Supplies

1

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 10
Drive Circuits, Snubber Circuits,
and Heat Sinks 431

Chapter 5
AC Voltage Controllers

Appendix A Fourier Series for Some
Common Waveforms 461

Chapter 6
DC-DC Converters 196

iv

171

Appendix B State-Space Averaging
Index

473


467


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CONTENTS

Chapter 1
Introduction
1.1
1.2
1.3
1.4

2.5
2.6

1

Power Electronics 1
Converter Classification 1
Power Electronics Concepts 3
Electronic Switches 5
The Diode 6

Thyristors 7
Transistors 8

1.5
1.6
1.7

1.8

Bibliography 19
Problems 20

Chapter 2
Power Computations 21
2.1
2.2

Introduction 21
Power and Energy 21
Instantaneous Power 21
Energy 22
Average Power 22

2.3
2.4

Apparent Power S 42
Power Factor 43

2.7

2.8

Inductors and Capacitors 25
Energy Recovery 27

Power Computations for Sinusoidal
AC Circuits 43
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

Switch Selection 11
Spice, PSpice, and Capture 13
Switches in Pspice 14
The Voltage-Controlled Switch
Transistors 16
Diodes 17
Thyristors (SCRs) 18
Convergence Problems in
PSpice 18

Effective Values: RMS 34
Apparent Power and Power
Factor 42


14

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
3.2

Introduction 65
Resistive Load 65
Creating a DC Component
Using an Electronic Switch 65

3.3
3.4

Resistive-Inductive Load 67
PSpice Simulation 72
Using Simulation Software for
Numerical Computations 72

v



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Contents

Capacitance Output Filter 122
Voltage Doublers 125
LC Filtered Output 126

RL-Source Load 75
Supplying Power to a DC Source
from an AC Source 75

3.6

Inductor-Source Load 79

4.3

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

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


4.4
4.5

Resistive Load 94
RL Load 96
RL-Source Load 98

3.10 PSpice Solutions For
Controlled Rectifiers 100
Modeling the SCR in PSpice 100

4.6
4.7

4.1
4.2

Introduction 111
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

DC Power Transmission 156
Commutation: The Effect of Source

Inductance 160
Single-Phase Bridge Rectifier 160
Three-Phase Rectifier 162

The Effect of Source Inductance 103

Chapter 4
Full-Wave Rectifiers 111

Three-Phase Rectifiers 144
Controlled Three-Phase
Rectifiers 149
Twelve-Pulse Rectifiers 151
The Three-Phase Converter Operating
as an Inverter 154

3.11 Commutation 103
3.12 Summary 105
3.13 Bibliography 106
Problems 106

Controlled Full-Wave Rectifiers 131

4.8
4.9

Summary 163
Bibliography 164
Problems 164


Chapter 5
AC Voltage Controllers
5.1
5.2

171

Introduction 171
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


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Contents

5.3


Three-Phase Voltage
Controllers 183
Y-Connected Resistive Load 183
Y-Connected RL Load 187
Delta-Connected Resistive Load 189

5.4
5.5
5.6
5.7

Induction Motor Speed Control 191
Static VAR Control 191
Summary 192
Bibliography 193
Problems 193

Chapter 6
DC-DC Converters 196
6.1
6.2
6.3

Linear Voltage Regulators 196
A Basic Switching Converter 197
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
6.5

Design Considerations 207
The Boost Converter 211
Voltage and Current Relationships 211
Output Voltage Ripple 215
Inductor Resistance 218

6.6

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
7.1
7.2
7.3

´
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

Introduction 265
Transformer Models 265
The Flyback Converter 267
Continuous-Current Mode 267

Discontinuous-Current Mode in the Flyback
Converter 275
Summary of Flyback Converter
Operation 277

The Buck-Boost Converter 221
Voltage and Current Relationships 221
Output Voltage Ripple 225

265

7.4

The Forward Converter 277
Summary of Forward Converter
Operation 283

7.5
7.6

The Double-Ended (Two-Switch)
Forward Converter 285
The Push-Pull Converter 287
Summary of Push-Pull Operation 290

7.7

Full-Bridge and Half-Bridge DC-DC
Converters 291


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Contents

7.8
7.9
7.10
7.11
7.12

Current-Fed Converters 294
Multiple Outputs 297
Converter Selection 298
Power Factor Correction 299
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
7.15
7.16
7.17

PWM Control Circuits 323
The AC Line Filter 323
The Complete DC Power Supply 325
Bibliography 326
Problems 327

Chapter 8
Inverters 331
8.1

8.2
8.3
8.4
8.5
8.6

Introduction 331
The Full-Bridge Converter 331
The Square-Wave Inverter 333
Fourier Series Analysis 337
Total Harmonic Distortion 339
PSpice Simulation of Square Wave
Inverters 340

8.7
8.8
8.9

Amplitude and Harmonic
Control 342
The Half-Bridge Inverter 346
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


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Contents

Chapter 9
Resonant Converters 387
9.1
9.2

Introduction 387
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 Ͼ ωo 407
Operation for ω0 /2 Ͻ ωsϽ ω0 413
Operation for ωs Ͻ 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

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
Index

473

467


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PREFACE

T

his book is intended to be an introductory text in power electronics, primarily 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 chapters 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), followed 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 suggested 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 supplement 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 electronics 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
xi



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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 hardware lab. Variations in circuit performance for a change in components or operating parameters can be accomplished more easily with a computer simulation
than in a laboratory. PSpice circuits presented in this text do not necessarily represent 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.


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Page xiii

Preface

Complete Online Solutions Manual Organization System (COSMOS). Professors can benefit from McGraw-Hill’s COSMOS electronic solutions manual.
COSMOS enables instructors to generate a limitless supply of problem material 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

xiii


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Page 1

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. Applications 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 frequency 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 requirements 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


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C H A P T E R 1 Introduction

Source

Input

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 classification. 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 original ac source, as illustrated in Fig. 1-3.



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1.3
Rectifier

Power Electronics Concepts

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.

Source

Input

Converter 1

Output

Converter 2

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 voltage 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

+
9V

−

+

2RL
RL

3V

−

Figure 1-4 A simple voltage divider for creating 3 V from a 9-V source.

3


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C H A P T E R 1 Introduction

+

+

vx(t)

9V

−

−
(a)

vx(t)

9V

3V

Average
T
3

t

T

(b)

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
T

T/3

T

1
1
1
vx(t) dt ϭ
9 dt ϩ
0 dt ϭ 3 V
avg(vx) ϭ Vx ϭ
T3
T3
T3
0

0

(1-1)


T/3

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 conditions, all power supplied by the 9-V source is delivered to RL, making the circuit 100 percent efficient.
The circuit so far does not accomplish the design object of creating a dc voltage 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.


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1.4

+

+


9V

+

vx(t) Low-Pass Filter

−

Electronic Switches

−

RL

3V
−

Figure 1-6 A low-pass filter allows just the average value of vx to pass through to the load.

Switch Control

+

+
vx(t) Low-Pass Filter

Vs
−

−


+
Vo
−

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 transistors (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 parameters are adjusted to maintain the desired output. For example, if the 9-V battery 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 feedback 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

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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 efficiencies 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. Transitions between states are usually assumed to be instantaneous, but the effects of
nonideal switching are discussed where appropriate. A brief discussion of semiconductor 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 reversebiased (off) when vd is negative. In the ideal case, the diode is a short circuit
Anode
id
+
vd
−

i

id

On

Off
vd

Cathode
(a)

v

(b)

i

(c)

On
Off
t

trr
(d)

(e)

Figure 1-8 (a) Rectifier diode; (b) i-v characteristic; (c) idealized i-v characteristic;
(d) reverse recovery time trr; (e) Schottky diode.


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1.4

Electronic Switches

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 applications. 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 relative 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 thyristor often refers to a family
of three-terminal devices that includes the silicon-controlled rectifier (SCR), the
triac, the gate turnoff thyristor (GTO), the MOS-controlled thyristor (MCT), and
others. Thyristor and SCR are terms that are sometimes used synonymously. The
SCR is the device used in this textbook to illustrate controlled turn-on devices in
the thyristor family. Thyristors are capable of large currents and large blocking
voltages for use in high-power applications, but switching frequencies cannot be
as high as when using other devices such as MOSFETs.
The three terminals of the SCR are the anode, cathode, and gate (Fig.1-9a).
For the SCR to begin to conduct, it must have a gate current applied while it has
a positive anode-to-cathode voltage. After conduction is established, the gate signal is no longer required to maintain anode current. The SCR will continue to
conduct as long as the anode current remains positive and above a minimum
value called the holding level. Figs. 1-9a and b show the SCR circuit symbol and
the idealized current-voltage characteristic.
The gate turnoff thyristor (GTO) of Fig. 1-9c, like the SCR, is turned on by
a short-duration gate current if the anode-to-cathode voltage is positive. However, unlike the SCR, the GTO can be turned off with a negative gate current.
The GTO is therefore suitable for some applications where control of both
turn-on and turnoff of a switch is required. The negative gate turnoff current
can be of brief duration (a few microseconds), but its magnitude must be very
large compared to the turn-on current. Typically, gate turnoff current is onethird the on-state anode current. The idealized i-v characteristic is like that of
Fig. 1-9b for the SCR.


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Anode
A
i

Anode

A

+
vAK
−

Gate
G


iA

On
Off
vAK

K
Cathode
(a)

Gate
Cathode
(c)

(b)
Anode
A

MT2

A
G

Gate

or

G


Gate
MT1
(d)

K

K
Cathode
(e)

Figure 1-9 Thyristor devices: (a) silicon-controlled rectifier (SCR); (b) SCR idealized i-v
characteristic; (c) gate turnoff (GTO) thyristor; (d) triac; (e) MOS-controlled thyristor (MCT).

The triac (Fig. 1-9d) is a thyristor that is capable of conducting current in
either direction. The triac is functionally equivalent to two antiparallel SCRs
(in parallel but in opposite directions). Common incandescent light-dimmer circuits use a triac to modify both the positive and negative half cycles of the input
sine wave.
The MOS-controlled thyristor (MCT) in Fig. 1-9e is a device functionally
equivalent to the GTO but without the high turnoff gate current requirement. The
MCT has an SCR and two MOSFETs integrated into one device. One MOSFET
turns the SCR on, and one MOSFET turns the SCR off. The MCT is turned on
and off by establishing the proper voltage from gate to cathode, as opposed to establishing a gate current in the GTO.
Thyristors were historically the power electronics switch of choice because
of high voltage and current ratings available. Thyristors are still used, especially
in high-power applications, but ratings of power transistors have increased
greatly, making the transistor more desirable in many applications.

Transistors
Transistors are operated as switches in power electronics circuits. Transistor drive
circuits are designed to have the transistor either in the fully on or fully off state.

This differs from other transistor applications such as in a linear amplifier circuit
where the transistor operates in the region having simultaneously high voltage
and current.