# power electronics - d.hart mcgraw, Formulas and forms for Electric Machines. Bahcesehir University

PDF (13 MB)
494 pages
29Number of visits
Description
the book of d.hart mcgraw of power electronics
20 points
this document
Preview3 pages / 494
Power Electronics

Instantaneous power:

Energy:

Average power:

Average power for a dc voltage source:

rms voltage:

rms for v  v1  v2  v3  . . . :

rms current for a triangular wave:

rms current for an offset triangular wave:

rms voltage for a sine wave or a full-wave rectified sine wave: Vrms  Vm12

Irms  B a Im13 b

2

 I 2dc

Irms  Im13

Vrms  2V 21, rms V 22, rms V 23, rms  Á

Vrms  B 1 T3

T

0

v2(t)dt

Pdc  Vdc Iavg

P  W

T 

1 T 3

t0T

t0

p(t) dt  1 T 3

t0T

t0

v(t)i(t) dt

W  3 t2

t1

p(t)dt

p(t)  v(t)i(t)

Commonly used Power and Converter Equations

har80679_FC.qxd 12/11/09 6:23 PM Page ii

rms voltage for a half-wave rectified sine wave:

Power factor:

Total harmonic distortion:

Distortion factor:

Buck converter:

Boost converter:

Buck-boost and Ćuk converters:

SEPIC:

Flyback converter:

Forward converter: Vo  VsD a N2 N1

b

Vo  Vs a D

1  D b a

N2 N1

b

Vo  Vs a D

1  D b

Vo  Vs a D

1  D b

Vo  Vs

1  D

Vo  Vs D

Crest factor  Ipeak Irms

Form factor  Irms Iavg

DF  A 1

1  (THD)2

THD  Aa

q

n2

I 2n

I1

pf  P

S 

P

Vrms Irms

Vrms  Vm 2

har80679_FC.qxd 12/11/09 6:23 PM Page iii

Power Electronics

Daniel W. Hart Valparaiso University Valparaiso, Indiana

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page i

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.

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

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page ii

To my family, friends, and the many students I have had the privilege and pleasure of guiding

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page iii

iv

Chapter 1 Introduction 1

Chapter 2 Power Computations 21

Chapter 3 Half-Wave Rectifiers 65

Chapter 4 Full-Wave Rectifiers 111

Chapter 5 AC Voltage Controllers 171

Chapter 6 DC-DC Converters 196

Chapter 7 DC Power Supplies 265

Chapter 8 Inverters 331

Chapter 9 Resonant Converters 387

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

BRIEF CONTENTS

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page iv

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 14 Transistors 16 Diodes 17 Thyristors (SCRs) 18 Convergence Problems in

PSpice 18

1.8 Bibliography 19 Problems 20

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

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

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

CONTENTS

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page v

vi Contents

3.5 RL-Source Load 75 Supplying Power to a DC Source

from an AC Source 75

3.6 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

3.10 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

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

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 5 AC Voltage Controllers 171

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

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page vi

Contents 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 Ćuk 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

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

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page vii

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

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page viii

Contents 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 413 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

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

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page ix

xi

This book is intended to be an introductory text in power electronics, primar-ily for the undergraduate electrical engineering student. The text assumesthat 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

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page xi

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.

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page xii

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

har80679_FM_i-xiv.qxd 12/17/09 12:38 PM Page xiii

C H A P T E R 1

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).

har80679_ch01_001-020.qxd 12/15/09 2:27 PM Page 1

2 CHAPTER 1 Introduction

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.

Source OutputInput

Figure 1-1 A source and load interfaced by a power electronics converter.

har80679_ch01_001-020.qxd 12/15/09 2:27 PM Page 2

1.3 Power Electronics Concepts 3

Figure 1-2 A converter can operate as a rectifier or an inverter, depending on the direction of average power P.

Inverter

Rectifier

Converter

P

P

+ +

− −

1.3 POWER ELECTRONICS CONCEPTS

Source OutputInput

Figure 1-3 Two converters are used in a multistep process.

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

3 V9 V

+

RL

2RL +

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

har80679_ch01_001-020.qxd 12/17/09 12:49 PM Page 3

4 CHAPTER 1 Introduction

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

(1-1)

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.

avg(vx)  Vx  1 T3

T

0

vx(t) dt  1 T3

T/3

0

9 dt  1 T3

T

T/3

0 dt  3 V

9 V

9 V

3 V

+

vx(t)

vx(t)

+

Average

t TT

3

(a)

(b)

Figure 1-5 (a) A switched circuit; (b) a pulsed voltage waveform.

har80679_ch01_001-020.qxd 12/15/09 2:27 PM Page 4

1.4 Electronic Switches 5

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

+

− 3V

+

+

RLvx(t)9V Low-Pass Filter

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

+

+

+

vx(t)Vs VoLow-Pass Filter

Switch Control

Figure 1-7 Feedback is used to control the switch and maintain the desired output voltage.

har80679_ch01_001-020.qxd 12/15/09 2:27 PM Page 5

6 CHAPTER 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

trr

id

vd

Cathode

Anode

On

Off

+

t

i

(a)

(d)

id

vd

i On

Off v

(b) (c)

(e)

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

har80679_ch01_001-020.qxd 12/15/09 2:27 PM Page 6

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 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 sig- nal 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. How- ever, 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 one- third the on-state anode current. The idealized i-v characteristic is like that of Fig. 1-9b for the SCR.

har80679_ch01_001-020.qxd 12/15/09 2:27 PM Page 7

8 CHAPTER 1 Introduction

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 cir- cuits 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 es- tablishing 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.

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).

vAK

iA

vAK

Cathode

Gate

Anode A

G K

+

(a)

or Gate

Anode

(e) Cathode

A

G

K

(b)

iA On

Off

(d)

Gate

MT1

MT2 A

K

G

Gate

Cathode

Anode

(c)

har80679_ch01_001-020.qxd 12/15/09 2:27 PM Page 8