24005759 introduction to solid state power electronics

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Introduction to

Solid State

Power Electronics

Editor: John William Motto, Jr.

Semiconductor DivisionYoungwood, Pennsylvania 15697


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AcknowledgementThe material for this updated text was originallywritten by Dr. William E. Newell, a noted authorityon power electronics with the aid of his associates atthe Westinghouse Research and DevelopmentCenter. Until his untimely death in 1976, Dr. Newellhad devoted much of his life to helping practicing

engineers and students alike better understand thefield of power electronics. As a teacher withinWestinghouse, as well as at Carnegie MellonUniversity, Dr. Newell tested the materials in this textwell, with over five years of use and refinement.

We dedicate this text to the memory of Dr. Newellfor his unselfish contributions to the field of powerelectronics. In order that future generations ofengineers and students can profit from the efforts ofDr. Newell, The Westinghouse Electric Corporationhas engaged his friends and colleague John W.

Motto, Jr., to edit this work. John brings to this taskover 17 years of applications and ratings experienceon power semiconductor devices.

We hope you find this text a worthwhile addition toyour reference library. We appreciate any commentsyou might have so that your ideas can be reflected insucceeding editions of this text.

POWEREX, Inc.200 Hillis StreetYoungwood, PA 15697-1800

February 1977COPYRIGHT 1977 BY POWEREX, INC.

All Rights Reserved

Information furnished in this text is believed to beaccurate and reliable. However, Powerex can assume

no responsibility for its use; nor any infringements ofpatents, or other rights of third parties which mayresult from its use. No license is granted byimplication or other use under any patent or patentrights of Powerex.


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ForewordAlthough power electronics has a considerablylonger history than many better known areas ofelectrical engineering, its widespread significance isonly now beginning to gain recognition. In a sense,power electronics is the marriage of techniqueswhich are characteristically power. But the

incompatibilities which have traditionally separatedthese two specialties makes the consummation of thismarriage far from simple. Power engineers find itdifficult to adapt their intuitive thought patterns to amicrosecond time scale, and electronics engineershave similar problems in adjusting to the demands ofa megawatt power scale. Thus there is a growingneed for electrical engineers whose capabilitiestranscend the two fields.

At least three current trends dictate that in spite ofits slow rise to prominence, power electronics will

soon emerge as a discipline and profession ofmajor importance:

1. The growing shortage of oil and gas and growingenvironmental concern will stimulate theutilization of clean electrical power in countlessnew areas now predominantly served by otherforms of energy.

2. Efficiency in the manipulation and control ofelectrical power will have increasing priority asthe rising cost of power forces the abandonment

of techniques which are short-term cheap butlong-term wasteful.

3. The evolution of present applications and thecreation of new applications will cause increasingdemands for speed, precision, and reliability inpower control that can be satisfied by no othertechnology.This text seeks to introduce powerelectronics in a way which emphasizes both theshared and the unique aspects of a wide varietyof circuits for power conversion and control. Italso seeks to build on elementary fundamentals

with which all electrical engineers should befamiliar. A review of these fundamental principalsneeded to establish a basic understanding ofpower electronics is concisely stated in AppendixI as the Ten Cornerstones of Power Electronics.

This text is divided into the following majorchapters:

I. IntroductionII. Diodes and Uncontrolled RectifiersIII. Thyristors, AC/DC Converters, and OtherNaturally Commutated CircuitsIV. Turn-off Devices and Self-commutated Circuits

V. Power Semiconductor Device Protection

Each of these chapters is further divided into concisediscussions of the topics and ideas that are felt to be ofgreatest importance in appreciating both thecapabilities and limitations of power electronics. Thisformat should allow the reader to quickly andselectively locate the section(s) of greatest interest tohim.

Although a familiarity with the vocabulary of powerelectronics may result from reading or listening,experience has shown that relatively little usefullearning (defined as the acquisition of new skills)occurs in this way. The problems at the end of eachchapter are the meat of the text. These problemsseek to illustrate important results while encouragingthe reader to think and analyze in terms of broadlyapplicable physical principles. They seek to avoidboth routine formula plugging and excessivemathematical grinding.

Once power electronics has penetrated yourawareness barrier, hopefully you will be aroused tocontinue your involvement with the field, becominga contributor to the profession as well as abenefactor from the technology.


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Table of Contents

CHAPTER 1INTRODUCTION TO POWER ELECTRONICS

Section

1. What is power electronics?

2. Power Converters as Switching Matrices

3. The Role of Power Filters

4. Types of Solid-State Switches

5. Commutation

6. The Internal Functional Sections of a

Generalized Power Converter

7. Power/Frequency Domains of Power Electronics

8. Specialized Technologies of Power Electronics

9. Converter Terminology Defined

10. Operation of an AC/DC Converter

11. Functional Categories of Applications

12. Power Electronics Lab.. Curiosity or

Competitive Necessity?13. Power Electronics Books

14. Problems

CHAPTER 2DIODES AND UNCONTROLLED RECTIFIERS

Section

1. Type 1 Switch or Diode

2. Steady-State V-I Characteristic of a Diode

3. Transient V-I Characteristic of a Diode

4. Pulse Number5. Simplifying Assumptions

6. Single-Phase Half-Wave Diode Rectifier

7. Single-Phase Half-Wave Diode Rectifier R/L Loads

8. Single-Phase Half-Wave Diode Rectifier Other Loads

9. Single-Phase Full-Wave Diode Rectifiers and

Continuous Current

10. Average Voltage Across an Inductance

11. Two-Pulse Rectifier with Inductance Filter

12. Power Relationships

13. Three-Phase Diode Rectifiers

14. Generalized Center-Tap Rectifier

15. Generalized Bridge Rectifier16. Applications of Diode Rectifiers

17. Transformers and Nonsinusoidal Waveforms

18. Problems

CHAPTER 3THYRISTORS, AC/DC CONVERTERS ANDOTHER NATURALLY COMMUTATED CIRCUITS

Section

1. Type 2 Switch Thyristor

2. Steady-State V-I Characteristic of a Thyristor

3. Two-Transistor Analog for Explaining Thyristor Turn On

4. Gate Characteristics5. Transient V-I Characteristic of a Thyristor

6. Thyristor Ratings Design Tradeoffs and

Commercial Availability

7. Circuit Functions Performed by Type 2 Switches

8. Two-Pulse AC/DC Converter Operating as a

Controlled Rectifier

9. Two-Pulse AC/DC Converter Operating as a

Synchronous Inverter

10. AC/DC Converter as a linear Amplifier

11. AC/DC Converter as a DC Motor Drive

12. Two-Pulse Semiconverter

13. Two-Pulse Dual Converter

14. Waveform Derivation for a 3-Phase Bridge

AC/DC Converter

15. Naturally Commutated Cycloconverter

16. Bilateral Solid-State Switches

17. Triac

18. AC Switches and Regulators

19. Varegulators

20. Brushless Machines

21. Summary

22. Problems

CHAPTER 4TURN-OFF DEVICES AND SELFCOMMUTATED CIRCUITS

Section

1. Power Transistor

2. Gate Controlled Switch

3. DC Switching and Regulation

4. Chopper Using Thyristors

5. Fundamentals of Inverters

6. Full-Bridge Inverter7. Half-Bridge Inverter with an Inductive Load

8. Thyristor Inverters with Forced Commutation

9. Types of Forced Commutation

10. Series Inverter

11. Parallel Inverter

12. Complementary Impulse Commutated Inverter

13. Inverter Output Voltage Control

14. Inverter Output Waveform Improvement

15. Frequency and Power Factor Changers

16. Problems


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CHAPTER 5POWER SEMICONDUCTOR DEVICEPROTECTION

Section

1. The Power Module

2. Importance of Junction Temperature

3. Components of Dissipation

4. Average Dissipation at 60 Hz Switching Rate5. Average Dissipation at 40 KHz Switching Rate

6. Simplified Geometry Assumed for the Typical Device

7. Junction-to-Case Thermal Resistance

8. Heat Sink Calculation

9. Selection of Device Package and Type of Heat Sink

10. Natural Connection Air Cooling

11. Forced Air Cooling

12. Water Cooling

13. Using the Data Sheet for Heat Sink Calculations

14. Thermal Capacity

15. Transmission Line for Transient Thermal Analysis

16. Initial Temperature Rise

17. Transient Thermal Impedance of Each Section

18. Calculation of Thermal Time Constant

19. Junction-to-Case Transient Thermal Impedance

20. Using Transient Thermal Impedance

21. Calculation of Pulse and Surge Current Capabilities

22. Turn-On di/dt

23. Transient Overvoltage

24. Off-State dv/dt

25. Series/Parallel Arrays for High-Power Applications

26. Summary

27. Problems

APPENDIX ITen Cornerstones of Power Electronics

APPENDIX IISelected Symbol List

APPENDIX III

Power Electronic Circuit Configurations Voltage andCurrent Relationships


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Chapter 1INTRODUCTION

TO POWER

ELECTRONICS

Section

1. What is power electronics? . . . . . . . . . . . . . . . . . . . . .1-2

2. Power Converters as Switching Matrices . . . . . . . . . . . .1-3

3. The Role of Power Filters . . . . . . . . . . . . . . . . . . . . . .1-3

4. Types of Solid-State Switches . . . . . . . . . . . . . . . . . . . .1-4

5. Commutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-5

6. The Internal Functional Sections of a

Generalized Power Converter . . . . . . . . . . . . . . . . . . .1-5

7. Power/Frequency Domains of Power Electronics . . . . . . .1-6

8. Specialized Technologies of Power Electronics . . . . . . . . .1-7

9. Converter Terminology Defined . . . . . . . . . . . . . . . . . .1-7

10. Operation of an AC/DC Converter . . . . . . . . . . . . . . .1-8

11. Functional Categories of Applications . . . . . . . . . . . . .1-8

12. Power Electronics Lab. Curiosity or

Competitive Necessity? . . . . . . . . . . . . . . . . . . . . . . . .1-9

13. Power Electronics Books . . . . . . . . . . . . . . . . . . . . . .1-10

14. Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-12

Introduction

The objectives of this chapter are to establish aperspective for the entire text which will enablethe reader:

a. To relate and distinguish power electronics fromother fields of electronics and electrical engineering;

b. To recognize the importance of power efficiencyand to understand how it is achieved;

c. To distinguish between the basic types ofsolid-state switching devices;

d. To define the basic functional sections within apower converter, the specialized technologiesinvolved in converter design, and the functionalapplications which converters serve.


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1. What is Power Electronics? (Figure 1.1)

For descriptive purposes, it is frequently useful todivide the overall field of electrical engineering intothree areas of specialization: electronics, power, andcontrol. The electronicsarea deals primarily withdevices and circuits for the processing of

information; thepowerarea deals with both rotatingand static equipment for the generation,transmission, distribution, and utilization of vastquantities of electrical power; and the controlareadeals with the stability and response characteristics ofclosed-loop systems using feedback on either acontinuous or sampled-data basis.

Interstitial to all three of these areas ispowerelectronics, which deals with the use ofelectronicsforthe controland conversion of large amounts ofelectricalpower.

The origins of power electronics can be traced backmany years, at which time mercury-arc devices wereutilized for the rectification of AC to DC or theinversion of DC to AC. However, todays rapidlygrowing usage of power electronics has resulted fromthe development of solid-state power devices.

Specifically, then, we will limit the use of the namepower electronics to those applications in which

electrical power flows through and is controlled byone or more solid-state power devices. (Note that thisdefinition excludes such applications as those wherea low-level electronic control circuit actuates anelectromechanical relay in the power circuit.)

All of the important parameters of the electricalwaveform are subject to regulation or conversion by

solid-state power devices, including effective voltage,effective current, frequency, and/or power factor.Often the control of electrical power is desiredsimply as a means for controlling some non-electricalparameter. For example, drives for controlling thespeed of a motor. In other applications, powerelectronics is used to control the temperature of anoven, the rate of an electrochemical refining process,the intensity of lighting, etc.

The design of power electronics equipment involvesinteractions with the source and the load, and

utilizes small-signal electronic control circuits as wellas power devices. Therefore power electronics drawsupon, and indeed depends upon all of the otherareas of electrical engineering. Obviously, thepotential scope of this field is quite vast!

Despite the growing importance of powerelectronics, very few universities presently offercourses devoted to this area, and few courses in theother areas deals significantly with it either. Thereinlies the motivation for this text. To keep the textwithin bounds, we will assume that you have a basic

knowledge of the other areas of electricalengineering. We will concentrate most heavily onthose important topics which are either ignored orgiven inadequate emphasis in available texts in theother areas.

Probably the single most important distinctionbetween power electronics and small-signalelectronics is the importance attached to overallpower efficiency. In most cases, other factorsoutweigh power efficiency in small-signal electroniccircuits, and power efficiency is calculated as an

interesting after thought, if at all. But in powerelectronics, power efficiency is critical because boththe cost of dissipating the heat and the cost of thewasted power are significant compared to the totalcost of the equipment.

The importance of power efficiency dictates that thebasic control element in power electronics must be aswitch, NOT a continuously variable element.

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POWER

STATIC

EQUIPMENT

ROTATING

EQUIPMENT

ELECTRONIC

S

DEVICES

CIR

CUITS

POWER

ELECTRONICS

CONTROL

CONTINUOUS SAMPLEDDATA

Figure 1.1Power Electronics

Interstitial to all of the major disciplines ofelectrical engineering.


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2. Power Converters as Switching Matrices(Figure 1.2)

Newcomers to power electronics are frequentlybewildered by the hundreds of different circuits whichconfront them when they begin to search typicalreferences in the field. The essential differencesbetween the various circuits are seldom clearlydistinguished from their basic similarities. And if youattempt to understand each of these circuitsindividually, you have a lifetime project before you.

The first fundamental principle which you shouldremember forever is that power efficiency dictatesthat switches be used as control devices. The secondfundamental principle, which is of equal importance,is that all high-power controls or converters aresimply switching matrices. Like a telephoneexchange, a general switching matrix permits anyincoming line to be connected for a specified periodof time to any outgoing line.

If there are m incoming lines and n outgoing lines,the matrix has m x n switches. Because of the factthat most solid-state switches are unilateral, thegeneral solid-state switching matrix has 2 x m x nswitches, one switch of each polarity for eachintersection.

Specific converter circuits may have one linecommon to the input and output, in which case the2 switches associated with the corresponding

intersection degenerate to a short circuit. Othercircuits require only one-way conduction so that 1 ofthe 2 switches at each intersection can be discarded.In summary, the number of solid-state switches in aparticular converter circuit may be less than or equalto 2 x m x n, but any converter circuit can be derivedfrom the general switching matrix.

A power switching matrix synthesizes the desiredvoltages on the output lines from selected chunksof the input voltages as dictated by the switchingcontrol signals.* The functions which a givenconverter circuit can perform are dictated by

(a) which of the switches are omitted from thegeneral matrix,

(b) the switching control signals, and

(c) the types of solid-state switches used.

*In a sense, a power converter is a combination analog/digital circuit. Ituses switches to perform the required processing, like a digital circuit butunlike an analog circuit. On the other hand, the power signal that isprocessed is continuous as in an analog circuit, not quantized as in adigital circuit.

3. The Role of Power Filters

The voltage waveforms which are synthesized by theswitching matrix are usually only an approximation to

the desired output waveforms. Although theapproximation could be improved by usingcontinuously variable devices in place of the switches,this would cause an intolerable loss in powerefficiency. Because of the repetitive nature of theswitching action, the discrepancy in the waveformsappears as spurious frequencies which can beremoved by a filter in the output lines. In otherwords, the output filter absorbs the unwanted ripplevoltages from the output of the matrix.

A secondary effect is that the input current

waveforms to the matrix contain spuriousfrequencies which may be undesirable in the supplylines or the source. Therefore another filter may beneeded on the input lines to provide a local path forthe unwanted ripple currents required by the matrix.

These discrepancies may be viewed as an undesiredripple in the instantaneous power flow through thematrix. The filters reduce this ripple in the inputand output lines by storing energy during intervals of

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Switching Control

Signals

n OutputLines

m InputLines

Figure 1.2mxn Switching Matrix


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excess power flow and returning energy to the circuitduring intervals of insufficient power flow.

Filters contribute significantly to the cost, size, andweight of power electronics equipment, as well as toits performance. The cost and weight of the filtersdepend on the maximum energy storage which isrequired, which depends in turn on both the power

rating of the circuit and the frequency of theundesired ripple. The lower the ripple frequency, thelonger the interval during which the filter must beable to absorb or supply a significant portion of therated power. Conversely, if the ripple frequency canbe increased, comparable performance can beobtained from smaller and less costly filters.

These considerations, together with the relatedsavings on transformers, motivate the selection of apower frequency greater than 60Hz in someapplications. In other applications which are limited

to 60Hz, the ripple frequency can be increased bythe selection of a circuit configuration with a higherpulse number, as we shall see later.

4. Types of Solid-State Switches (Figure 1.3)

Types of Switches:

Type 1 DIODES - Conduct Automatically whenForward Polarity is Applied.

Type 2 THYRISTORS or SCRS - Begin toConduct in the Forward Direction UponCommand of a Control Signal andContinue to Conduct Until the NextCurrent Zero Crossing.

Type 3 TRANSISTORS, GATE CONTROLLEDSWITCHES, FORCE-COMMUTATEDTHYRISTORS - Forward Conduction can beInitiated and Interrupted by Control Signals

As stated previously, one of the factors whichdetermine the performance of a power switching

matrix is the type of switch that is used. For presentpurposes we dont need to get into the physics ofsolid-state switches, but we should distinguishbetween three main types of switches that areavailable to us. All three types are UNILATERAL.They can conduct current in one direction, known asthe forward direction, but they very rapidly ceaseconduction when the reverse polarity is applied. Theother characteristics of these switches are as follows:

Type 1 Switches always conduct whenever aforward polarity of voltage is applied totheir terminals. Type 1 switches are knownas rectifiers or diodes.

Type 2 Switches do not conduct forward currentuntil commanded to do so by a control

signal. Therefore Type 2 switches behave asType 1 switches and continue to conduct aslong as forward current flows. Type 2switches are known as thyristors (the fullofficial name is reverse blocking triodethyristor) or silicon controlled rectifiers(SCRs).

Type 3 Switches can not only turn on forwardconduction when commanded by thecontrol signal, but can also interruptconduction upon command without waitingfor reverse polarity to be applied. Powertransistors and gate controlled switchesexhibit Type 3 behavior. By artificial circuitmeans, thyristors can also be forcecommutated to operate asType 3 switches.

It is probably obvious that the 3 types of switcheshave been listed in the order of increasing generality.That is, with appropriate control signals a Type 3

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Switching ControlSignals

n OutpLinesm InputLines

InputFilter

OutputFilter

Figure 1.3Power Electronic Converter as a Switching Matrix


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switch can replace either a Type 2 or a Type 1 switch,and a Type 2 switch can replace a Type 1 switch. Butthey are not interchangeable in the opposite order.

5. Commutation

Definitions Regarding Commutation:

COMMUTATION Current Interruption orTransfer to an Alternate Path.

NATURAL OR LINE COMMUTATION OccursBecause of the Changing AC Line Voltages.

SELF OR FORCED COMMUTATION OccursBecause of Inherent or Artificial Turn-off Ability.

LOAD COMMUTATION Depends on Inherent orArtificially Produced Load Characteristics.

In the discussion of switches, we have just noted thatit is the ability to interrupt conduction whichdistinguishes the third type from the first two types.The process by which current in a switch is caused tocease is called commutation, and the availablemeans of commutation play an important role indetermining the capabilities of any given circuit.

Classical rectifier or inverter circuits based on mercury-arc devices utilize what is known as natural or linecommutation. Commutation occurs naturallybecause of the changing AC line voltages, either:

(a) because the circuit current goes to zero, or

(b) because the circuit current is transferred toanother switch which is connected to a higherpotential. The analysis of these circuits dates backmore than 30 years, although solid-state powerdevices have made many new applicationstechnically and economically feasible.

In a turn-off circuit, commutation can be caused tooccur at arbitrary times in one of two ways. The mostobvious way is to use a Type 3 switch having inherent

turn-off ability. The second way is to forcecommutate a Type 2 switch, and we willsubsequently explore various methods of doing this.Either of these ways is known as self commutation.

When commutation depends on the load havingcertain characteristics, the process is known as loadcommutation. Load commutation may be similar toeither line or forced commutation according to

whether the required characteristics are inherent inthe load or must be produced artificially.

Most applications of turn-off circuits were notfeasible until the advent of solid-state power devices.This technology is developing rapidly and isproviding many new opportunities for applyingsolid-state power electronics.

6. The Internal Functional Sections of a GeneralizedPower Converter (Figure 1.4)

We stated previously that power electronicsencompasses a vast amount of technology from boththe electronics and power fields, plus considerabletechnology not ordinarily covered by either of thosefields. In the time available, this text will focus onthose topics which will help you to understand howtypical converter circuits operate, what limitations

are encountered in designing such circuits, and howthese limitations are dealt with.

To clarify the emphasis of this text, the componentsof a generalized power converter can be grouped intosix main internal functional sections: power devices,power modules, the power circuit, the switchingcontrol signal generator, and input and output filters.

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Power Circuit

Power Modules

Power

Device

InputFilter

OutputFilter

Output

Lines

To Load

SwitchingControl

Signal

Generator

Input LinesFrom Power

Source

ExternalControl

Signals

1

2

n

Figure 1.4Internal Functional Sections of aGeneralized Power Converter


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Thepower devicesare the solid-state devices whichhave made modern power electronics possible. Wewill emphasize their important terminalcharacteristics, but the details of semiconductorphysics and device fabrication are outside the scopeof this text.

Each power device or group of devices is embedded

within apower modulewhich interfaces it with thesurrounding power circuit. The power moduleimplements the function of a single switch in theswitching matrix. In addition to one or more powerdevices, each power module contains one or moreheat sinks, fuses and other components to protectthe power devices, and sometimes local circuitry forgating and forced commutation.

Thepower circuitinterconnects the power modulesinto the appropriate switching matrix, and includesthe transformers needed for isolation, changing

voltage levels, etc. Starting from simple bridge andcenter-tap arrangements and wye or deltatransformer connections, the number of powercircuit configurations is seemingly endless. Forexample, the ANSI Standard C34.2-1968, Practicesand Requirements for Semiconductor PowerRectifiers, designates some 70 standard circuitconfigurations for rectifiers alone.

The output filtersmooths the discrepancies betweenthe voltage waveform synthesized by the powercircuit and the desired output voltage waveform.

The input filterprovides a path for harmonic currentswhich are required by the power circuit but whichare undesirable in the input supply lines.

The switching control signal generatorreceives signalsfrom the input lines, the output lines, from withinthe power circuit, and/or from external control linesand processes them to generate appropriate gatingpulses to actuate each Type 2 or Type 3 switch. Thesegating pulses usually have a periodicity which isdetermined in one of three ways:

(a) In the simplest case, the gating signals aresynchronized in frequency with the AC supply,but with adjustable relative phase.

(b) When the converter is powered from a DC source,internal time constants or an internal referenceoscillator determine the periodicity of switching.

(c) In a frequency changer, the gating signals mustbe properly synchronized with both the ACsource frequency and the desired outputfrequency. In effect, the smaller of these twofrequencies modulates the larger frequency.

The design of the switching control signal generatorutilizes all of the applicable circuit technology from

both analog and digital electronics.

This text will concentrate most heavily on variouscommon configurations for the power circuit and onsome aspects of the power module. Appropriatetiming of the switching control signals will bediscussed, but the design of the control circuits whichgenerate these signals is outside the scope of the text.

7. Power/Frequency Domains of Power Electronics(Figure 1.5)

The three-dimensional space of voltage-current-frequency provides another interesting way tocategorize power electronics. Within this space, thefirst and by far the most widely useful domain isdefined by voltage and current limits which arewithin the capability of a single solid-state device perpower module. These limits are rather arbitrary, andchange with time as new solid-state devices aredeveloped, but for present purposes they will beshown at 2kV and 1000A. This domain can be calledthe Medium Power Domain, although at its upper

limit it extends to a power of 2 MW!

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HighFrequency(FastDevices)

MediumPower

HighCurrent(ParallelDevices)

HighPower

100k

10k

10

0

100

1k

1GW10MW

100kW

1kW

10k

1k

10

100

20 200 20k2k

Voltage

InAmps

Current

SwitchingFrequencyinHz

200k

100k

HighVoltage(Series

Devices)

Figure 1.5Power Frequency Domains of Power Electronics


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Power devices can be cascaded in series to increasethe voltage limit. When this is necessary, theassociated technology falls within the High VoltageDomain. Similarly power devices can be paralleledto increase the current limit, thereby defining aHigh Current Domain. For some applications,series/parallel arrays are required, leading to aHigh Power Domain.

Conventional solid-state power devices are capable ofmuch faster switching action that a mechanicalswitch, but the switching time is not zero.Consequently there is an upper limit on the switchingfrequency of conventional power devices, which forpresent purposes will be arbitrarily assumed to be 1kHz. However, power devices especially designed forfast switching action are available. The technologyassociated with the use of these fast devices defines aHigh Frequency Domain.

8. Specialized Technologies of Power Electronics(Figure 1.6)

A pinwheel can be used to further extend thespecialized technological categories of powerelectronics without trying to show an n-dimensionalpicture. The Core Discipline incorporates theMedium Power Domain, with the additionalrequirements of natural commutation and other

requirements being nominal. Power electronicsequipment for a particular application incorporatestechnology from the Core Discipline plus technologyfrom one or more of the specialized categories.

The High Voltage, High Current, High Power, andHigh Frequency Domains just discussed constitutesome of these specialized technologies. Forced

Commutation is another category of increasingimportance. Numerous other categories ofspecialized technology could be noted. For example,in some applications the power devices must bespecified on the basis of their transient surge ratingsrather than on their steady-state ratings. In someapplications, such as those for the consumermarket,cost reduction is a critical consideration. Inother applications, such as those for the consumermarket, cost reduction is a critical consideration. Inother applications, such as aerospace, size and weightare critical considerations. And so on and on.

This introductory text will touch lightly upon anumber of these categories, but the Core Disciplineand Forced Commutation form the keyhole whichwe hope will unlock a basic understanding of powerelectronics for you.

9. Converter Terminology Defined

Power Converter Terminology:

CONVERTER General TermSWITCH Full Off or Full On

REGULATOR Intermediate Control of AC or DC

RECTIFIER Converts AC to DC

INVERTER Converts DC to AC

FREQUENCY CHANGER Changes Frequency ofAC Power

POWER FACTOR CHANGER Changes Power

Factor of an AC Load

AC/DC CONVERTER Operates as Rectifieror Inverter

Unfortunately the field of power electronics aboundswith inconsistent and ambiguous usage ofterminology. To maintain internal consistency, we willadopt the following definitions:

1-7

TechnologyAdvancement

Research

2kV &>1000A

HighFrequency

>1kHZ

Pulse &Surge-Limited

Applications

Cost-CriticalApplications

Size/Weight-Critical

Applications

CriticalWaveform

or EMI

Critical LoadInteractions

ForcedCommutation

Figure 1.6Specialized Technologies of Power Electronics


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CONVERTER A general term which can be usedto describe any one of the following circuit types, acombination of several types, or all types as a group.

SWITCH A device or circuit which has two extremestates - full off or full on.

REGULATOR A circuit which permitsintermediate control of AC or DC power. Thedesired output frequency is the same as the inputfrequency. If implemented by switching devices,regulation is achieved by time - averaging with asuitable time constant. A DC regulator is often calleda chopper.

RECTIFIER Converts AC power to DC power.

INVERTER Converts DC power to AC power.

FREQUENCY CHANGER A converter in whichthe desired AC output frequency is generally

different from the AC input frequency.

POWER FACTOR CHANGER A converter whichmanipulates the power factor of an AC load withoutchanging frequency.

In contrast to the previous discussion of the internalfunctions and the specialized technologies of powerelectronics, these terms form the basis forcategorizing power electronics according to externalor application-oriented functions. However, as will beseen, rectifiers and inverters are not exclusive typesof circuits. Certain circuits can perform eitherfunction. Therefore we will define anotherintermediate category:

AC/DC CONVERTER A circuit which may operateeither as a rectifier or as an inverter.

10. Operation of an AC/DC Converter (Figure 1.7)

As the name implies, an AC voltage appears at oneset of terminals of an AC/DC converter, and a DCvoltage appears at the other set of terminals. Theoperation of the converter can be described in termsof 4 quadrants as viewed from the DC terminals. Thehorizontal axis represents the average DC current,and the vertical axis represents the average DCvoltage. In quadrant I, where average voltage andaverage current are both positive, net power flow isfrom the AC terminals to the DC terminals; theprocess is known as positive rectification.

Similarly, if both the average voltage and averagecurrent are negative, net power flow is still from theAC terminals to the DC terminals and the process isknown as negative rectification.

If either the average voltage or the average currentreverses (but not both), power flow also reverses.That is, in Quadrants II and IV, power flows from theDC terminals to the AC terminals. In AC/DCconverters, the AC line provides the current zerosneeded to naturally commutate Type 2 switches. Inquadrants II and IV the process is known assynchronous inversion to distinguish it from the typeof inversion which requires forced commutation.

As will be seen later, some AC/DC converters canoperate only in certain quadrants. If operation isconfined to Quadrant I, the circuit is called a1-Quadrant Converter. A 2-Quadrant Converter canoperate in either Quadrant I or Quadrant IV. And a4-Quadrant Converter can operate in any ofthe 4 quadrants.

11. Functional Categories of Applications (Figure 1.8)

Prior to the advent of solid-state power devices,power converters were limited almost exclusively torectifiers and synchronous inverters. We will nowattempt to meaningfully categorize the variety offunctional applications which are possible withsolid-state power devices.

1-8

Positive Average DC Voltage

PositiveRectification

Positive AverageDC Current

Negative AverageDC Current

SynchronousInversion

Synchronous

Inversion

Negative Average DC Voltage

1-Quadrant Converter - Operates in I Only2-Quadrant Converter - Operates in I or IV3-Quadrant Converter - Operates in I through IV

Negative

Rectification

II I

III IV

Figure 1.7Regions of Operation of an AC/DC Converter


14/111

As we have discussed, 1-Quadrant Rectifiers arelimited to net power flow from the AC to DCterminals. These rectifiers can be implemented using

only Type 1 switches (diodes).2- and 4-Quadrant AC/DC Converters permit powerflow in either direction, but require Type 2 switches.Since power can flow either way, AC/DC convertersbridge the gap between the traditional Rectifierand Inverter categories.

It is also possible to implement AC Switches andRegulators and certain types of Frequency Changerswith naturally commutated Type 2 switches.

With Type 3 switches (or force-commutated Type 2

switches), other types of inverters, DC Switches andRegulators (i.e. choppers), and Frequency and PowerFactor Changers become feasible.

The text will explain the basic principles ofoperation of circuits which serve each of thesefunctions.

12. Power Electronics - Laboratory Curiosity orCompetitive Necessity? (Figure 1.9)

The potential advantages of solid-state power electronicsover electromechanical equipment are well known:increased reliability and service life, and reduced sizeand maintenance. In some cases, there is a sizable costadvantage, while in other cases the performancecapabilities can be achieved in no other way.

For these reasons, power electronics is penetratingmany new application areas and outmoding manytraditional design approaches. Product engineering

departments accustomed to well established designprocedures involving Ward-Leonard drives, or relaylogic, or selenium rectifiers are faced with extinctionovernight if they cannot adapt to the higher levels ofcomplexity and analytical sophistication both madepossible and made necessary by solid-state electronics.

In assessing business risks, a company must try toguard against squandering development funds on apremature attempt to market a laboratory curiosity.

1-9

1-QuadrantRectifiers

Type 1Switches

Type 2Switches

(NaturalCommutation)

AC DC AC DC DC AC

AC AC AC AC DC DC

AC Switches

& Regulators

DC Switches

& Regulators

Type 3 Switches

(Forced Commutation)

Frequency & Power

Factor Changers

Force-CommutatedInverters

2- & 4-QuadrantAC/DC Converters

Figure 1.8Types of Power converters

CompetitiveNecessity

% of Annual Market

Maximum Time AllowableTo Defend Your Share of the Market

(Typically 2-4 Years)

Time

LaboratoryCuriosity

100%

80%

60%

20%

40%

Figure 1.9Universal S-Curve Showing the Capture of a Marketby a Product Which Takes Advantage of Power

Electronics


15/111

It must also guard against being caught withoutadequate competence in a rapidly evolvingtechnology when that technology becomes acompetitive necessity. Many technologies evolve overa period of decades, leaving adequate reaction timefor business planning.

One aspect of power electronics which is not widely

appreciated is that when it captures a market, itfrequently does so with a bang. Solid-state typicallymoves from an insignificant share of the market to adominate share in a period of only 2 to 4 years. Thusa company which does not maintain a nucleus ofcompetence in this new technology can easily lose asecure market position because of inadequatereaction time.

Power electronics has already become a competitivenecessity in many applications, and will soon emergefrom its laboratory curiosity status in many others.

Therefore this text will not dwell on the details ofexisting applications, but will seek to convey anunderstanding of basic principals and techniques whichare equally applicable to countless new applications.

To supplement this brief introduction to power electronics, the followingreview articles are recommended:

A. Kusko, Solid-State Motor-Speed Controls, IEEESpectrum, pp. 50-55; October 1972.

H.F. Storm, Solid-State Power Electronics in the U.S.A.,IEEE Spectrum, pp. 49-59; October 1969.

F.W. Gutzwiller, Thyristors and Rectifier Diodes TheSemiconductor Workhorses, IEEE Spectrum, pp. 102-111;August 1967.

R.G. Hoft, Static Power Converters in the U.S.A., IEEEIntnl. Semiconductor Power Converter Conference Record,pp. 2-8-1 to 8; May 1972.

J.J. Bates and R.E. Colyer, The Impact of SemiconductorDevices on Electrical Power Engineering, Radio &Electronic Engineer, vol. 43, pp. 115-124; Jan./Feb. 1973.

W.E. Newell, Power Electronics - Emerging from Limbo,IEEE Trans., vol. IA-10, pp. 7-11; Jan./Feb. 1974.

A.M. Curry and R.V. Wachter, A User Looks at theSemiconductor Converter, IEEE Trans., vol. IGA-4, pp. 41-46; Jan./Feb. 1968.

A. Ludbrook, Basic Economics of Thyristor AdjustableSpeed Drive Systems, IEEE Industry and GeneralApplications 4th Annual Meeting Record, pp. 591-596; Oct.1969.

D.W. Borst, et. al., Voltage Control by Means of PowerThyristors, IEEE Trans., vol. IGA-2, pp. 102-124; Mar./Apr.1966.

13. Power Electronics Books

A. Power Device Manufacturers Handbooks

1. SCR Designers Handbook (Second Edition, 1970)Westinghouse Semiconductor Div., Youngwood, PA.

2. SCR Manual (Fifth Edition, 1972) General Electric Co.,Syracuse, NY.

3. Solid-State Power Circuits (1971) RCA Technical Series SP-52. RCA Solid-State Division, Somerville, NJ.

4. SCR Applications Handbook (First Printing) InternationalRectifier Corporation;September 1974.

5. Semiconductor Power Circuits Handbook (1968) MotorolaSemiconductor Products Div.,Phoenix, Ariz.

6. Power Semiconductor DATAbook D.A.T.A., Inc., Orange,NJ (A worldwide tabulation of the ratings of commercial

power diodes, transistors, and thyristors, revised twice a

year.)

B. Textbooks and Special Issues on Power Devices

1. Semiconductor Controlled Rectifiers: Principals and Applications ofPNPN Devices(1964) by F.E. Gentry, et. al. (General Electric)Prentice-Hall, Englewood Cliffs, NJ.

2. Special Issue on High-Power Semiconductor DevicesIEEETransactions on Electron Devices, vol. ED-17, no. 9;September 1970.

3. Special Issue on High-Power Semiconductor DevicesProceedings ofthe IEEE, vol. 55, no. 8; August 1967.

C. Textbooks on Power Circuit Analysis1. The Fundamental Theory of Arc Convertors(1939) by H. Rissik.

Chapman & Hall, London. Facsimile reprint available fromUniversity Microfilms, Ann Arbor, Mich. (A classic book,equally applicable today if thyristor converter is substitutedfor arc convertor.)

2. Power Diode and Thyristor Circuits(1971) by R.M. Davis.Cambridge University Press, London.

3. Rectifier Circuits: Theory and Design(1965) by J. Schaefer. JohnWiley, New York.

4. Principles of Inverter Circuits (1964) by B.D. Bedford and

R.G. Hoft (General Electric) John Wiley, New York.

5. Thyristor Phase-Controlled Converters and Cycloconverters(1971)by B.R. Pelly (Westinghouse) Wiley-Interscience, New York.

6. The Theory and Design of Cycloconverters(1972) by W.McMurray (General Electric) MIT Press, Cambridge, Mass.

7. Line-Commutated Thyristor Converters(Second Edition, 1972)by G. Molgen (Siemens) Pitman Publishing, London.

1-10


16/111

8. Semiconductor Devices in Power Engineering(1968) Edited by J.Seymour. Sir Isaac Pitman, London.

9. Power Engineering Using Thyristors: Vol. 1 - Techniques ofThyristor Power Control(1970) Edited by M.J. Rose (Mullard)Mullard Ltd., London.

10. Thyristor Control(1973) by F.F. Mazda (ITT). John Wiley, NewYork.

11. Power Electronics: Thyristor Controlled Power for Electric Motors(1973) by R. Ramshaw (Univ. Waterloo, Ontario) Chapmanand Hall, London. (Distributed in USA by John Wiley, NY.)

12. Power Semiconductor Circuits(1975) by S.B. Dewan and A.Straughen Wiley-Interscience, New York.

13. Theory of SCR Circuit and Application of Motor Control(1968) byT.J. Takeuchi (Tokyo EE College) Tokyo ElectricalEngineering College Press, Tokyo. (This book is unique inits application of Laplace transforms to the analysis of powercontrol circuits.)

14. Rectifier Circuits(1972) Edited by W.F. Waller. Macmillan

Press, Basingstoke, Hampshire, U.K.

15. Transistor Inverters and Converters(1963) by T. Roddam. VanNostrand, Princeton, NJ.

D. Textbooks on Applications

1. Solid-State DC Motor Drives(1969) by A. Kusko, MIT Press,Cambridge, Mass.

2. Design of Solid-State Power Supplies(1971) by E.R. Hnatek(National Semiconductor) Van Nostrand Reinhold, NewYork.

3. Direct Current Transmission - Vol.1 (1971) by E.W. Kimbark

(Bonneville Power Admin.) Wiley-Interscience, New York.

4. High Voltage Direct Current Convertors and Systems(1965)Edited by B.J. Cory, Macdonald, London.

5. Electric Power Utilization by N.N. Hancock (Univ.Manchester) Sir Isaac Pitman, London.

6. Power Semiconductor Applications: Vol. I - General Considerations;Vol. II - Equipment and Systems(1972) Edited by J.D. Harndenand F.B. Golden IEEE Press, New York. (An extensive andinexpensive collection of selected papers reprinted fromliterature.)

7. Thyristor Control of AC Motors(1973) by J.M.D. Murphy,

Pergamon Press, Oxford, England.

E. Elementary Books and Experimenters Guides

1. Understanding Silicon Controlled Rectifiers(1968) by S. Heller(Voorhees Technical Institute) Hayden, New York.

2. RCA SCR Experimenters Manual(1967) RCA Technical SeriesKM-71 (Experimenters Kit KD2105 also available.) RCADistributor Products, Harrison, NJ.

3. 110 Thyristor Projects Using SCRs and Triacs(1972) by R.M.

Marston, lliffe, London.

4. Thyristors(1971) by L.W. Owens (Mullard) Mullard,Mitcham, Surrey, U.K.

5. Thyristors and Their Applications(1972) by P. Atkinson(University of Reading) Mills &Boon, London.

1-11


17/111

14. Problems

Problem 1.1 Power Efficiency of a Series Rheostat as aPower Control

Assume that a series rheostat is used to control the flowof power to a 100-kW oven as shown by the circuitbelow. When RR= 0, full power is delivered to the oven.As R

Ris increased, power to the oven decreases and

ultimately approaches zero as RRbecomes infinite.

(a) On the axes provided, plot the source power, theoven power, and the power dissipated in therheostat as functions of the oven voltage.

(b) Plot the power efficiency, defined as the ratio ofoven power to source power.

(c) How much power must the heat sink attached tothe rheostat be capable of dissipating?____ watts.

(d) Making whatever assumptions seem reasonable toyou, estimate the value of the power wasted by thiscontrol over its useful life, neglecting theadditional cost of dissipating the heat. If a simplebut more efficient control can be purchased for$15 per kW of controlled power, how long will ittake for the better control to completely pay foritself by reducing wasted power? (Assume thiscontrol has a power efficiency of 95%.)

Problem 1.2 Switching Power Efficiency

After working Problem 1.1 and being impressed by thepoor efficiency of a rheostat as a power control, anengineer invents a way to improve the efficiency. Henotes that the rheostat dissipates no power when it is ineither of its limiting positions, zero or infinite resistance.Therefore he devises a mechanism which causes therheostat to spend nearly all of the time in one or theother of these limiting positions, with negligible time atintermediate positions. Average power to the oven iscontrolled by varying the relative time (duty cycle) spentin the two positions. For instance, if half of the time isspent in each position, the average oven voltage is 500 Vand the average oven power is 50 kW. Repeat (a), (b),and (c) of Problem 1.1 for this modified control, andplot results on the axes below. (d) Is oven powerproportional to the square of average oven voltage?

Explain.You have probably observed that the rheostat is no longer arheostat but a switch, and you have just established for yourselfwhy high-power controls use a switching mode of operation.

1-12

0

100

75

50

25

0

Oven Voltage

Source=1000V

Oven =10 ohms

Rheostat = RR

PowerinKW

PowerEffic

iencyin%

Current

250 500 750 1000

0 25 50 75 100

Problem 1.1Power Efficiency

0

100

75

50

25

0

Average Oven Voltage

Source=1000V

Oven =10 ohms

Rheostat = RR

PowerinKW

PowerEfficiencyin%

% Duty Cycle

250 500 750 1000

0 25 50 75 100

Problem 1.2Switching Efficiency


18/111

2-1

Section

1. Type 1 Switch or Diode . . . . . . . . . . . . . . . . . . . . . . .2-2

2. Steady-State V-I Characteristic of a Diode . . . . . . . . . . .2-2

3. Transient V-I Characteristic of a Diode . . . . . . . . . . . .2-2

4. Pulse Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-3

5. Simplifying Assumptions . . . . . . . . . . . . . . . . . . . . . .2-3

6. Single-Phase Half-Wave Diode Rectifier . . . . . . . . . . . .2-4

7. Single-Phase Half-Wave Diode Rectifier R/L Load . . .2-5

8. Single-Phase Half-Wave Diode Rectifier Other Loads . .2-6

9. Single-Phase Full-Wave Diode Rectifiers and

Continuous Current . . . . . . . . . . . . . . . . . . . . . . . . .2-7

10. Average Voltage Across an Inductance . . . . . . . . . . . . .2-8

11. Two-Pulse Rectifier with Inductance Filter . . . . . . . . . .2-8

12. Power Relationships . . . . . . . . . . . . . . . . . . . . . . . . .2-913. Three-Phase Diode Rectifiers . . . . . . . . . . . . . . . . . . .2-10

14. Generalized Center-Tap Rectifier . . . . . . . . . . . . . . . .2-12

15. Generalized Bridge Rectifier . . . . . . . . . . . . . . . . . . .2-12

16. Applications of Diode Rectifiers . . . . . . . . . . . . . . . . .2-13

17. Transformers and Nonsinusoidal Waveforms . . . . . . .2-13

18. Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-15

Chapter 2DIODES AND

UNCONTROLLED

RECTIFIERS

IntroductionThe objectives of this chapter are:

a. To name and describe the important steady-stateand transient terminal characteristics ofsolid-state diodes.

b. To list the simplifying assumptions usually madein rectifier analysis.

c. To explain the operation of a one-pulse rectifierand sketch the voltage and current waveforms forvarious types of loads.

d. To work simple problems related to voltage-

averaging by an inductor in the DC circuit.

e. To explain the real, reactive, and distortioncomponents of total apparent power for thenon-sinusoidal AC line current drawn by a rectifier.

f. To describe the operation of single-phase andthree-phase center-tap and bridge rectifiers.

g. To list several common applications ofuncontrolled rectifiers.


19/111

2-2

1. Type 1 Switch or Diode (Figure 2.1)

A conventional solid-state diode is a Type 1 switch. Ithas two terminals, known as the anode and thecathode. Internally, a simple diode consists of asingle PN junction within a crystal of silicon. The

anode terminal connects to the P side of thejunction, and the cathode connects to the N side.When the anode or P side is positive with respect tothe cathode or N side, the diode conducts forwardcurrent with a relatively low voltage drop. Thetriangle in the schematic symbol for a diodeindicates the polarity of forward current flow.

When the polarity is reversed, a large reverse voltagecan be applied but only a small reverse leakagecurrent will flow.

2. Steady-State V-I Characteristic of a Diode(Figure 2.2)

The highly nonlinear behavior of a diode which hasjust been discussed can best be illustrated by thesteady-state V-I characteristic. The primary steady-state parameters which describe a diode are shown.Theforward voltage dropis determined primarily bythe semiconductor material from which the diode isfabricated, independent of the current rating of thediode. The material is nearly always silicon, and the

voltage drop is about one volt.

The internal or junction temperature is an importantfactor in the operation of all solid-state devices.Power diodes are usually rated for operation atjunction temperatures up to 200C. The forwardpower dissipation of a device is proportional to theforward voltage drop and the forward current. Sincethe voltage drop is nearly constant, it is the ability todissipate the heat without exceeding the maximum

junction temperaturewhich determines theforwardcurrent rating of a device. Larger currents cause moredissipation, leading to physically larger devices to getthe heat out.

The reverse leakage currentof a diode depends on itssize and internal design, and also depends onleakage at the junction surfaces. Reverse leakagecurrent increases rapidly with junction temperature.

In addition to the forward current rating of a diode,another parameter of extreme practical importanceis the reverse breakdown voltage. Together these twoparameters determine the maximum load powerwhich the diode can control. Although the reversebreakdown voltage depends on the internal design(but not the physical size) of the diode, practicalfabrication processes lead to a spread in each batchof devices. Consequently this rating is determined bytesting each individual diode.

3. Transient V-I Characteristic of a Diode (Figure 2.3)

The switching action of a solid-state device is muchfaster than that of a mechanical switch of the samepower capacity. Nevertheless it is not instantaneous.

When forward voltage is applied to a diode, a shortturn-on timeelapses before the charges at the PNjunction reach equilibrium to carry full forwardcurrent. This time is measured in nanoseconds.

Anode

Terminal

Cathode

Terminal

PN JunctionP

N

Figure 2.1Type 1 Switch or Diode

I

V

Reverse Leakage Current

Reverse Breakdown Voltage

Forward Voltage Drop

Rated Forward Current Depends

on Heat Sink and Waveform

Figure 2.2

Steady State V-I Characteristic of a Diode


20/111

2-3

Of greater practical importance is the transient whichoccurs when reverse voltage is applied to turn off adiode which has been conducting forward current.The charges which had been carrying this currentmust be swept out from the junction region beforethe reverse non-conducting state can be established.These charges are called stored charge, and dependon the internal design of the diode and on the

forward current which has been flowing. Theinstantaneous reverse current which flows is usuallylimited by the circuit external to the diode, but theamp-seconds of the reverse current transient dependon the stored charge. The duration of this transient iscalled the reverse recovery time or turn-off time. Thistime is also nanoseconds for fast low voltage computerdiodes, but is measured in tenths of microseconds andmicroseconds for high power diodes.

Elementary descriptions of the physics of solid-statediodes are contained in many textbooks on

electronics. More advanced information on powerdiodes is contained in:

F. E. Gentry, et al, Semiconductor Controlled Rectifiers:Principles and Applications of PNPN Devices, Chapter 1;Prentice-Hall; 1964.

Y. C. Kao, The Design of High-Voltage, High-PowerSilicon Junction Rectifiers, IEEE Trans., vol. ED-17,pp. 657-660; September 1970.

4. Pulse Number

Among the important factors which influence thechoice and design of rectifiers are the magnitudeand frequency of the ripple voltage at the DCterminals. The smaller the magnitude and the higherthe frequency, the cheaper it is to filter the ripple tospecific tolerances.

The ratio of the fundamental frequency of the DCripple to the AC supply frequency is commonlycalled the pulse number. Most single-phase rectifiersare 2-pulse, and most three-phase rectifiers are6-pulse.

5. Simplifying Assumptions

The analysis of a rectifier circuit usually begins withthe study of the idealized version of the circuit. Inmost cases the characteristics of the idealized circuitcan be read directly from design tables as containedin Appendix III. Practical deviations from theidealized circuit can then be added as needed.

The simplifying assumptions involved in theidealized circuits are as follows:

(a) The voltage drop across switching devices isneglected while they are conducting, and theleakage current is neglected while they areblocking.

(b) The turn-on and turn-off times of the switchingdevices are negligible.

(c) The AC line voltage is sinusoidal and there is nostray impedance (line impedance, transformerreactance, ect.).

(d) The DC terminals are connected to an ideal filter

(an infinite inductance) which maintains the DCcurrent constant over each cycle at its averagevalue. We will look at what is involved in thisassumption shortly.

Figure 2.3Transient V-I Characteristic of a Diode

Reverse Recovery Timeor Turn-off Time

Time

Time

Stored Charge

ReverseLeakage Current

Turn-on

Time

Forward Current

Forward Voltage

VoltageReverse

Pulse NumberFundamental Ripple Frequency

AC Supply Frequency =


21/111

2-4

In review the assumptions are:

Simplifying Assumptions

(a) Switches have no voltage drop or leakage current.

(b) Instantaneous switching.

(c) Sinusoidal voltage source.

(d) Constant DC current over each cycle.

It was stated in the Introduction that the ideal voltagewaveforms at the output of the switching matrixconsist of segments selected from the input voltagewaveforms as dictated by the switching control signals.If the input voltages and the switching control signalsare specified, it would seem that the output voltagewaveform from the matrix could easily bedetermined. Once the voltage waveform is known,the current waveform in a specified load can bedetermined by conventional analysis.

Fortunately an adequate analysis is sometimes asstraight-forward as the above discussion implies.However, subtle and unexpected factors can oftenhave significant effects. For example, the loadcurrent waveform may influence the commutationpoints, which in turn modify the voltage waveform.This interaction can lead to an analysis that issomewhat less straightforward. Also, thecommutation of current from one switch to anotherrequires a finite time, even if the dynamic responseof the switching devices is instantaneous. Thiscommutation overlap further complicates the ideal

voltage waveforms.

Therefore the best approach to an analyticalunderstanding of the operation of switched powercircuits is to proceed slowly from basic fundamentals,being careful not to be misled by implicitassumptions which are invalid.

The problems encountered in converter analysis arediscussed in:

S.B. Dewan and G. R. Slemon, Analysis Techniques forThyristor Converters, IEEE Power Electronics

Specialists Conference Record, pp. 141-148; June 1973.

S. B. Dewan and J. B. Forsythe, Techniques of Analysisfor SCR Converters, IEEE Industry & GeneralApplications 4th Annual Meeting Record, pp. 453-468;Oct. 1969.

6. Single-Phase Half-Wave Diode Rectifier(Figure 2.4)

Although the half-wave diode rectifier is not a usefulcircuit for high power applications, it neverthelesspermits a number of useful principles to be explainedin their simplest terms. For the moment we will adoptsimplifying assumptions (a), (b), and (c), butassumption (d) is not valid for this one-pulse circuit.*We will use this circuit to introduce the study ofrectifier waveforms and the effects which the load hason these waveforms.

If the load is purely resistive, the output voltage

waveform consists of half-cycles of a sine waveseparated by half-cycles of zero output voltage, forwhich the average value is:

Vp Vp

Vout

Vout

Vave=

Vout

Vave 0=

Vp

Vp

R

2Vp

L

VpR

L

I

I

R

Iave=

Vout

I

L

Vp

I

Iave=

Figure 2.4Single-Phase Half-Wave Diode Rectifier

V V t dt V

ave p

p= =

20

sin


22/111

2-5

The current waveform is identical in shape to thevoltage waveform, and the average current is:

On the other hand, if the load is purely inductive, the

waveforms change considerably. During the first halfcycle, the current builds up from zero to a peak value,Ip = 2Vp/L. During the half cycle, energy has beentransferred from the AC source to the inductor, and(1/2) LI2pwatt-seconds are stored in the magneticfield. However, the diode cannot interrupt the non-zero current which exists when the source voltagereverses polarity. The diode must wait for the currentto go to zero by itself before conduction ceases. Infact, the diode will continue to conduct throughoutthe second half-cycle, during which the outputvoltage is negative and the total energy stored in the

inductor is returned to the AC line. If the inductor islossless, the diode will conduct continuously, and atthe end of each full cycle the total net energy transferwill be zero. Note that although the instantaneousoutput voltage goes negative, the current never does.If the current did go negative, it would violate theassumed behavior of the ideal diode.

Since the diode conducts continuously, the loadvoltage is identical to the AC source voltage, and hasan average value ofzero. However, the average value ofthe current is Vp/L. This example illustrates that

average voltages and currents must be manipulatedwith care. In general, average current does NOTequal average voltage divided by impedance!

Thought Question: In steady state, the diode in thisideal circuit never becomes reverse biased, and thecurrent is the same as if the diode were shorted.Would the circuit operate in the same way if thediode were not present?

*The terminology one-pulse circuit indicates that the circuit has a pulsenumber of one.

7. Single-Phase Half-Wave Diode Rectifier R/L Load(Figure 2.5)

In practice, the inductor is not lossless, so we mustconsider at least some series resistance. At the end ofthe first half cycle, the current will be less than thepreviously calculated Ip because of the voltage dropand consequent power loss in R. During the secondhalf cycle, R will continue to dissipate power as longas current flows. Since there is less total energy toreturn to the AC line, current will always ceasebefore the second half cycle is completed. That is,commutation does occur, but is delayed until afterthe zero crossing of the AC source voltage. Netpower flow over the full cycle will be from the ACline to the load, as it must be to account for the lossin R.

During the time when the instantaneous voltage andcurrent are both of the same polarity, power flow is

IV

Rave

p=

Vout

I

Vout

I

R

L

Vout

Vout

Vp

2Vp

Vp

LI

I

R

L

Figure 2.5Single-Phase Half-Wave Diode Rectifier R/L Load


23/111

2-6

from the AC line to the load, and the circuit acts as arectifier. During the time when the instantaneousvoltage and current are not of the same polarity,power flow is from the load to the AC line, and thecircuit acts as a synchronous inverter. Since the loadis passive, the net power flow over a full cycle mustbe from the AC line to the load. Since the diodemust conduct for the full half cycle of rectification,

but ceases conduction part way through theinversion half-cycle, the circuit has positive averagevoltage and cannot invert net power from its DCterminals to its AC terminals.

If the L/R time constant of the load is smallcompared to a half-period of the AC source,commutation is delayed very little, and the operationof the circuit approaches that of a circuit with aresistive load. As L/R increases, the delay incommutation increases and the current waveformapproaches a sine wave (plus a DC component).

However, since the peak current cannot exceed2Vp/L, the inductance cannot be increasedsufficiently to hold the current constant as requiredby simplifying assumption (d).

If the intent of the rectifier is to get maximum powertransfer into the load, the flow of power back intothe AC line on alternate half cycles is undesirable.This reverse flow occurs because of the reversal ofthe polarity of the instantaneous output voltage.Both can be prevented by connecting afreewheeling or bypass diode across the output to

conduct whenever the output voltage tries to gonegative. The rectifier diode then commutates off atthe zero-crossing of the AC source voltage. The loadcurrent continues to flow, but is transferred to theloop formed by the freewheeling diode. This diode isforward biased by the kickback voltage of theinductance. The energy stored in L then dischargesinto R rather than being returned to the AC line.The freewheeling diode helps to prevent the loadcurrent from ever going to zero, and thereby reducesthe ripple.

8. Single-Phase Half-Wave Diode Rectifier Other Loads (Figure 2.6)

Two other types of loads should also be notedbriefly capacitive loads and back-emf loads. If acapacitive load can be represented by R and C inseries, the steady-state load voltage charges up to Vpand thereafter current ceases.

However, if the equivalent circuit is a parallelcombination of R and C, the capacitor tends tosmooth the ripple in output voltage, but the current(in the diode) occurs in brief spikes. Note that incontrast to an inductive load which tends topostpone commutation after the voltage zerocrossing, a capacitive load causes commutation tooccur before the voltage zero crossing.

Similarly, a back-emf load of the polarity shown, suchas a battery or a DC motor, also causes current spikesand early commutation. No current flows until theAC line voltage exceeds the back-emf. If the polarityof this load emf is reversed, conduction beginsbefore the first zero crossing of the AC sourcevoltage and commutation is delayed until after thesecond zero crossing. As in the case of the inductiveload, the AC source receives power during part ofeach cycle. But the net power flow over a full cycle inthis and all other diode rectifier circuits is always

from the AC to the DC terminals. Hence they are1-Quadrant rectifiers.

I

R

I

R

VBatt

C

Vout

Vout

VBatt

I

I

Figure 2.6Single-Phase Half-Wave Diode Rectifier - Other Loads


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9. Single-Phase Full-Wave Diode Rectifiers andContinuous Current(Figure 2.7)

Single-phase full-wave diode rectifiers are two-pulsecircuits since the fundamental ripple frequency istwice the AC supply frequency. With a resistive orpartially inductive load, the current in the DC circuitis continuous,* and the diodes always commutate atthe zero crossings of the AC source voltage. Hencethe DC voltage waveform consists of successivehalf-cycles of a sine-wave, independent of the load. Ineffect, the two diodes that are tied to the positive DC

terminal connect it to the AC terminal which isinstantaneously more positive. Similarly, the twodiodes that are tied to the negative DC terminal(in the bridge circuit) connect it to the morenegative AC terminal.

If the load is purely resistive, the DC current has thesame waveform as the voltage except that the

amplitude is multiplied by 1/R. The average value ofthese waveforms constitutes the DC or zero-frequency component, and is given by:

The AC line current is the same as the DC currentexcept that alternate half cycles are reversed inpolarity. Thus the AC line current is purely

sinusoidal with no harmonic content.Two-pulse circuits have limited practical value forhigh-power applications because of the large ripplewhich is contained in the DC output voltage. It isreadily seen that the ripple has a peak-to-peak valueof Vp and contains all even harmonics of the ACsource frequency.

The ripple current is ordinarily reduced by addingseries inductance in the DC circuit to pass the DCcomponent of current while attenuating theharmonics. In practice, part or all of this inductanceis frequently in the load itself, as in the case of amotor armature or field. However for the sake ofdiscussion, the inductance will be considered as afilter which is part of the rectifier, and the resistancewill be considered as the load.

The presence of this inductance will change thecurrent waveform and consequently the voltagewaveform across the resistance. However, as long asthe current is continuous, the presence or the valueof the inductance does not influence thecommutation points of the diodes, and hence doesnot affect the output voltage waveform from thediodes. In particular, the inductance does notchange the average value of this waveform calculatedabove. This average voltage must be equal to the sumof the average voltages across the inductance and theresistance. As we shall see in the next section, theaverage voltage across the inductance must be zero.Therefore, the average voltage across the resistanceis (2/)Vp and the average current is (2/) (Vp/R)

Figure 2.7Two-Pulse Diode Rectifier Circuits and Waveforms

Vp

R

VpVout

Vin

IoutIave=

Vave =

t

Vout

Iout+

RVin

Vpsin t

Iin

VoutVin

Vin

Iout+

R

2Vp

2Vp

R

Iin

RI V V t dt Vave ave p p

= = =

0

2sin


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2-8

independent of the inductance.

It should also be noted that rectifier analysis normallyassumes steady-state conditions. Obviously there is atransient with an L/R time constant which can alterthe waveforms when a rectifier is first started.

*The DC current is said to be discontinuous if it contains finite intervalsof zero current. With a capacitive or back-emf load, the current will be

discontinuous unless the series inductance exceeds some minimum criticalvalue. (See R.J. Distler and S.G. Munshi, Critical Inductance andControlled Rectifiers, IEEE Trans., vol. IECI-12, pp. 34-37; March1965.) With discontinuous current, the commutation points and the DCvoltage waveform from the diodes are load-dependent.

10. Average Voltage Across an Inductance

A fundamental principle which should be remembered isthat in steady-state, the voltage across an inductance,averaged over a full cycle, is always zero.

This principle may be verified as follows. The voltageacross an inductance averaged over a cycle is defined as:

We also know that the defining relationship betweenvoltage and current for an inductance is:

Integrating this equation over a full cycle gives thechange in current:

But, again by definition, the change in current over afull cycle in steady-state is zero. Hence VLave mustalso be zero.

11. Two-Pulse Rectifier with Inductance Filter(Figure 2.8)

Returning to the two-pulse diode rectifier, we canconsider the effects of inductance in series with theload in two cases. In the first case, the inductance isnominal. That is, it is big enough to have anappreciable smoothing effect but small enough thatthe ripple is still significant. An approximate valuefor this inductance is R/.

The load current waveform no longer consists of halfsine waves,* but the average current is still the sameas before, 2Vp/R. The AC line current is no longersinusoidal, but approximates a poor square wave withsuperimposed ripple. The inductance has reducedthe harmonic content of the load current byincreasing the harmonic content of the ACsource current.

V V t dt L

diLave L

i

i

= = =

2 20

0

2

0

2

( )

V V t dt Lave L

=

20

2

( )

V t Ldi

dtor di

LV t dt L L( ) ( )= =

1

i diL

V t dt L

Vi

i

LLave

= = = 0

22

1 2

0

( )

Vp

Vp

VoutVR= RIout

Vin

Iin

VoutVR= Vd= RId= 2Vp/

Vp

Id

Vin

Iin

Waveforms forL >> R/

Waveforms for

L R/

Figure 2.8Effects of Inductance on the Waveforms of aTwo-Pulse Diode Rectifier(Voltage Across Inductance Shown Shaded)


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The voltage which appears across the inductance isshown shaded. In order for the average voltageacross the inductance to be zero, the positive shadedareas must be equal to the negative shaded areas.

In the second case, the series inductance is increaseduntil it is much larger than R/. The ripple acrossthe load is now insignificant, and simplifying

assumption (d) is valid. The load current is constantat its average value. These constant values of loadvoltage and current are designated Vd and Id:

The inductance has totally removed the harmoniccontent of the load voltage and current, but the ACsource current waveform has become a square waveof value Id: Unless otherwise stated, most rectifier

analysis assumes these idealized conditions.*In the one-pulse circuit, the single diode could not commutate until theload current went to zero. Note that in this two-pulse circuit the loadcurrent never goes to zero. Commutation occurs, not because the loadcurrent goes to zero, but because this current is captured when thevoltage in some other diode loop exceeds the voltage in the loop of thediode previously conducting.

12. Power Relationships (Figure 2.9)

The purpose of a rectifier is to convert AC powerinto DC power. The fundamental nature of powertransfer in power electronics makes it essential for usto understand the relationships between the variouscomponents of power. Although these relationshipsare probably quite familiar when the waveforms are

purely sinusoidal, they must be modified to includethe nonsinusoidal waveforms encountered inrectifiers and other types of converters.

The two-pulse rectifier which we have just discussedpresents an opportunity to explain these modifiedrelationships. Under simplifying assumptions (a),there is no power dissipation in the switchingdevices. Therefore the net power flow at the ACterminals averaged over a full cycle must be exactlyequal to the net power flow at the DC terminals.

With a large inductance in the DC circuit, the DCcurrent is constant at Id, and the voltage across theload resistance is constant at Vd. Therefore the realDC power is easily calculated as:

According to simplifying assumptions (c), the ACsource voltage is sinusoidal. Therefore its RMS value,V, is related to its peak value by:

However. as we have seen, the AC current waveformis a square wave of amplitude Id , in phase with theAC voltage. The RMS value of this square wave is Id,and there is no apparent power factor phase angle.We might be led to conclude that the AC power isthe product of the RMS AC voltage, V, and the RMSAC current, I = I:

It is apparent that this total apparent power is notequal to the real DC power calculated above. Wehave been misled by applying relationships derivedfor sinusoidal waves to a case where the current isnonsinusoidal.

V RI V V

d aveP= = =

1

VI1P= Real Power

= DisplacementAngle

=DistortionAngle

VI1Q= Reactive or

Quadrature Power

(VIh)2= Distortion Power

Real Power

Total Apparent Power

I2= I1P2+ I1Q

2+ Ih2

Power Factor = cos cos =

h = 2

h = 2

VI= TotalApparent

Power

VI1= ApparentFundamental Power

Figure 2.9Power Relationships

P V I V I d d d p d

= =( / )2

V Vp= / 2

P VI V I T p d

= =( / )2


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To reconcile this situation, expand the currentwaveform into a Fourier series where the RMS valueof harmonic h is Ih. The RMS value of thewaveform is then:

or

In general, the fundamental current, I1, will consistof an in-phase component, I1p, and a quadraturecomponent, I1Q(if the fundamental current is not inphase with the voltage). Then:

Multiplying both sides of this equation by the squareof the RMS voltage gives:

The left side of the equation is the square of the totalapparent power, but of the three terms on the rightside, only the in-phasecomponent of the samefrequency as the voltage represents realpower(watts). The second term represents the square ofthe reactive power (VARs) which results if thefundamental current is out of phase with the voltage,and the third term is a wattless power caused by theharmonic components (i.e., distortion) of thenonsinusoidal waveform.

For sinusoidal waves, a right triangle displaysgeometrically the mathematical relationship betweenreal power, reactive power, and apparent power. Thephase angle, , is one of the angles of this triangle,and the power factor (ratio of real power to apparentpower) is equal to cos .

Similarly two right triangles can be used to give ageometric representation of the equation above. Thephase angle between the voltage and thefundamental component of current is known as thedisplacement angle, , and cos is called thedisplacement factor. The harmonic term isassociated with a second right triangle and an

angle, , which has little significance. However, cos is known as the distortion factor, and is equal tothe ratio of the apparent fundamental power to thetotal apparent power. The two triangles may becascaded as shown in the figure, and it is apparentthat the power factor is now equal to the product ofthe displacement factor and the distortion factor.

For the two-pulse diode rectifier, the fundamentalcomponent of current is in phase with the voltage.Therefore, = 0, and the displacement factor isunity. However, the RMS value of the fundamentalcomponent of a square wave is equal to 4/ 2 timesthe RMS value of the square wave. Therefore thedistortion factor is 4/ 2.

The real AC power is then the product of thedisplacement factor, the distortion factor, and thetotal apparent power:

The real AC power is seen to be equal to the real DCpower calculated previously, and the desired powerbalance has been verified.

13. Three-Phase Diode Rectifiers (Figure 2.10)

The pulse number of a single-phase rectifier cannot

be increased beyond two unless some artificial meansis available for generating out-of-phase voltages. Onthe other hand, the pulse number of a polyphaserectifier may be made arbitrarily high by variousinterconnections of transformer windings. The mostcommon high-power rectifiers are supplied from athree-phase source and use a three-pulse orsix-pulse circuit.

The easiest way to derive the waveforms of athree-phase bridge rectifier is to consider each halfseparately with respect to the neutral. The upper

three diodes constitute a three-pulse center-tapcircuit, and each diode conducts for 120. Thevoltage from the positive DC terminal to the neutral,V+N, has a positive average value of (3 3/2) VpN,where VpN is the peak phase voltage to the neutral.The waveform is as shown. If a load is connectedbetween the positive DC terminal and the neutral(including enough inductance to maintain thecurrent constant), a current Id+will flow.

I I I I= + + +1

2

2

2

3

2....

I I Ih

h

2

1

2 2

2

= +=

I I I Ip Q hh

2

1

2

1

2 2

2= + +

=

( ) ( ) ( ) ( )VI VI VI VI p Q h

2

1

2

1

2 2= + +

=

VI V I V Ip

p d

p d11 4

2 2

2+

=( )


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2-11

Similarly the lower group of three diodes generates anegative three-pulse waveform between the negativeDC terminal and the neutral, and a load will cause acurrent Id- to flow. As long as the neutral isconnected, the two groups of diodes operateindependently as three-pulse rectifiers, and thecurrents Id+ and Id- need not be equal. Howeverthere will be a net DC component of current in eachwinding, tending to cause DC magnetization of thecores, if these currents are unequal.

If the load is connected directly between the positive

and negative DC terminals without a neutralconnection, the average DC voltage doubles and Id+and Id- must be equal because there is no return pathfor a difference current. Therefore coremagnetization is no longer a problem. However,another significant advantage also occurs. Note thatcommutation occurs alternately, not simultaneously,in the two groups of diodes. When the twothree-pulse groups operate together, a six-pulseoutput waveform results.

The current in each wye-connected secondarywinding supply AC to the bridge is a square wave ofamplitude Id, consisting of a 120 positive pulse, a60 period to zero current, a 120 negative pulse,and another 60 period of zero current. If theprimaries of the transformer are also wye-connected,the AC line currents will have the same waveform.On the other hand, if the primaries are delta-connected, the AC line current becomes different inwaveform although the harmonic content remainsthe same.

Circuits having higher pulse numbers furtherincrease the ripple frequency, making filtering easierand reducing the harmonic content of the ACcurrent. However, these circuits may also reduce theconduction angle of each diode, thereby reducingthe utilization of its capacity. Therefore, circuitshaving pulse numbers higher than six are usuallyused only for special purposes.

We will now state, without proof, several general laws

V+N

V-N

(V+Nave= VPN)

Vout

VCAVBCVAB

t

t

t

VCNVBNVAN

332

(Voutave= Vd = VPN)33

Wye-Connected Primaries

Delta-ConnectedPrimaries

Current in

Line A

Id- VPN3

VPN

Id

Id+

N

+

V+N

Vout

V+N

Figure 2.10Waveforms for a Three-Phase Bridge Rectifer


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concerning the harmonics generated by idealdiode rectifiers:

(1) The ripple voltage at the output has afundamental of pfs, where p is the pulse numberand fs is the source frequency. Because of thelack of symmetry of the positive and negativeparts of the ripple waveform, allharmonics of

this fundamental ripple frequency will bepresent: npfs, n = 1, 2, 3, ... The peak amplitudeof any harmonic of the source frequency whichis present, relative to the uncontrolled DCvoltage, is 2/(n2p2 - 1). That is, the pulsenumber determines which harmonics offs arepresent in the output, butdoes notchange therelative amplitude of a given harmonic if it ispresent.

(2) The only harmonics present in the inputcurrent (in addition to the fundamental current

at fs) occur at (np 1) fs, n = 1, 2, 3, ... Theamplitude of each harmonic current, relative tothe fundamental current, is inverselyproportional to its order (i.e., to np 1).

References:

J. Schaefer, Rectifier Circuits: Theory and Design, p. 257 and p.298, John Wiley, New York; 1965.

B. R. Pelly, Thyristor Phase-Controlled Converters andCycloconverters, pp. 94-107, John Wiley, New York; 1971.

C. J. Amato, A Simple and Speedy Method for Determining

the Fourier Coefficients of Power Converter Waveforms,IEEE Industry & General Applications 4th Annual MeetingRecord, pp. 477-483; Oct. 1969.

I. K. Dortort, Phase Shifting of Harmonics in AC Circuits ofRectifiers, IEEE Trans., vol. IGA-4, pp. 655-658; Nov./Dec.1968.

14. Generalized Center-Tap Rectifier (Figure 2.11)

The two-pulse and three-pulse center tap circuitswhich we have discussed are characterized by the factthat one terminal of the DC circuit is connecteddirectly to a center-tap or neutral point of thetransformer windings which couple the rectifier tothe AC supply. The generalized center-tap rectifierhas q secondaries, with adjacent secondariesseparated by 360/q. The required number of diodesis q, one for each secondary. The pulse number isalso equal to q.

For q = 1, the circuit is a single-phase half-waverectifier. Although widely used for low-current powersupplies, this circuit is not useful at high power levelsbecause of its large ripple voltage and because of theDC current which it draws from the AC line. Circuitsfor which q = 2, 3, or 6 are of greaterpractical importance.

Center-tap rectifiers are also known as single-waycircuits because the current in each transformerwinding is unidirectional. If q is even, currents ineach pair of windings flow in opposite directions so

that the net DC magnetization of transformer coresis zero. However, if q is odd, there is no cancellationand DC magnetization of transformer cores is aproblem. In this case, magnetization is usuallyavoided by a zig-zag series connection of pairs oftransformer secondaries, arranged so that the effectof each winding carrying unidirectional current iscancelled by another winding which carries currentin the opposite direction.

15. Generalized Bridge Rectifier (Figure 2.12)

Bridge rectifiers do not ordinarily have a directconnection between the DC terminals and thetransformer secondaries, but each winding isconnected to two oppositely polarized diodes so thatboth polarities of current flow in each winding.Hence DC magnetization of the transformer cores isnot a problem. Another name for bridge circuits isdouble-way circuits.

24005759 introduction to solid state power electronics

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