Power Electronics by M H Rashid

-

PEARSON

l l: ll: CtL~Q Ll tCS 1 Q \ 1\_1l: L'-

v

I

Contents viii

Abnnt the Author

Chapter 1

I n tro d uction

1

1.1

I Applications of Power Electronics 1.1.l History of Power E lectronics

]2

Po,ver Semiconductor Devices 12 1 1.2.2

Power D iodes Thyristors 6

2

s

5

1 2 3 Pn,vcr Transistors 9 1 3 Con trol Characteristics of Power Devices 1.4

Characteristics and Specifications of Switches I 4 1 Ideal Cbaractetistics 16 1 4 2 Cbaracleristics nf Practical Devices 1.4.3 Switch Specifications 18

]44 Device Choices 1.5 1.6 1.7 1.8 19

1.10 1 11

10 16

]7

12

Types of Power E lectronic Circuits 20 Design o r Power E lectronics Equipment 23 Determining the Root-Mean-Square Values of Waveforms 24 Peripheral E ffects Power Modules 26 Intelligent Modules 26 Power Electronics Iaurnals and Conferences ?8 S ummary 29

References 29 Review Questions

24

30

Ch a pter 2 Power Semiconductor Diodes and Ci rcuits ? 1 lo1codur tian 31 2 2 Sen1iconductar Basics 31 ? 3 Diode Cbaractccistirs 11

31

vii

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viii

Contents

2.4 2.5

Reve rse Recovery Characteristics 35 Power D iode Types 38 2.5.l General-Purpose Diodes 38 2.5.2 Fast-Recovery Diodes 38 2.5.3 Schollky Diodes 39

? 6 Si licon Carbide Diodes 2.7

Spice Diode Model

39 40

2 8 Secies-Cooncc1ed Diodes 2 9 Parallel-Connected Diodes

42 4S

2 IQ Diodes ,Yi tb RC and RI I oads 46 2 11 Diodes with I C and RI CI oads 49 2.12 Freewheeling D iodes 56 2.13 Recovery of Trapped Energv with a Diode Summarv

References 61 Revje,v Questions Proh)em, 64 Chapter 3

61

Diod e Rectifiers

68

1]

ln1rod11rtioo

3.2

Single-Phase Half-Wave Rectifiers

6.8

11 Performance Parameters 3.4

3.5 3.6 3.7 · 3.8 3.9 3.10 3.11 3.12

119

Power lransistors

Intcadurtino

82

119

Review Questions Prablcros 12Q

4) 4.2

68

69

Single-Phase Full-Wave Rectifiers 77 Single-Phase Full-Wave Rectifier with RL Load Multiphase Star Rectifiers 87 Three-Phase Bridge Rectifiers 92 Three-Phase Bridge Rectifier with RL Load 95 Comparison of Diode Rectifiers 101 Rectifier Circuit Design 101 Output Voltage with LC Filter 112 Effects of Source and Load Inductances 1 6

ummarv References

Chapter 4

58

62

122

122

Bipolar Junction Transistors 123 4.2.1 Steady-State Characteristics 124 4.2.2 Switching Characteristics 128 4.2.3 Switching Limits 135

43 Power MQSEEis 4.3.1 4.3.2

J'.37

Steadv-State Characteristics 141 142 Switching Characteristics

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Contents 44

ma, MOS

45

STis

48 49

4.10

)44

J45

46 IOBis 4.7

142

Series and Parallel Operation 150 dVdt and du/dt I imitations 151 SPICE Models 155 4 9 I BU SPICE Madel I 'i5 4 2 2 MQSEEI SPICE Madel t •;, 4 9 3 JOBI SPICE Model 158 160 Comparisons of Transistors Summarv 160

References

16'

Review Questions

Pcnbleros Chapter 5 51

ix

163

164

DC-DC Converters Introd uctinn

166

166

5.2

Principle of Step-Down Operation 166 5.2.1 Generation of Dutv Cycle 170 171 5.3 Step-Down Converter with RL Load 176 5.4 Principle of Step-Up Operation 5.5 Step-Up Converter with a Resistive Load 179 "l 6 Performance Parameters 181 5 7 Converter Classifica tion 182 5.8 Switching-Mode Regulators 186 5.8.1 Buck Regulators 186 5.8.2 Boost Regulators 190 5.8.3 Buck- Boost Regulators 194 I98 5.8.4 Cuk Regulators 5.8.5 Limitations of Single-Stage Conversion 205 5.9 Comparison of Regulators 5.10 Multioutput Boost Converter 206 5 11 Diode Rec1 ificr·Eed Boast Converter 208 5.1 2 Chopper Circuit Design 211 5.13 State-Space Analysis of Regulators 217 Summary 221 Bcfc rc orcs 221 Review Questions 223 Problems 224 · Chapter 6 6]

6.2

Pulse-Wid th-Modulated Inverters Int roduction 226 Principle of Operatio n

63 Pcrforn1anc:c Pora1nercrs 6.4

204

226

227

230

Sinelc-Phasc Bridec Inverters

232

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x

Contents

6 5 Three-Phase inverters

237

6.5.l 6.5.2

6.6

6.7 6.8

180-Degree Conduction 237 120-Degree Conduction 246 Voltage Control of Single-Phase Inverters 248 6.6.1 Single-Pulse-Width Modulation 248 6.6.2 Multiple-Pulse-Width Modulation 250 6 6 3 Sinusoidal Pulse-Width Modulation 253 6.6.4 Modified Sinusoidal Pulse·Width Modulation 6.6.5 Phase-Displacement Control 258 Advanced Modulation Techniques 260 Voltage Control of Three -Phase Inverters 264 6 8 ] Sinusoidal PWM 265 6.8.2 60-D egrec PWM 268

6 8 3 Thjrd-Harmooic PWM 6.8.4 6.8.5

257

268

Space Vector Modulation 271 Comparison of PWM Techniques

279

6 9 Harmonic Reductions 280 610 Cuaeot-Source Inverters 285 6 ] ] Variable DC-I ink In verter 288 6.12 Boost Inverter 289 6.13 In verter Circuit Design Summary

294

299

References

299 Review Questions

PcobJems Chapter 7

Thyristors

7 1 Introduction 7.2 7.3

7.4 7.5 7.6

300

301 304 304

304 Thyristor Characteristics Two-Transistor Model ofThvristor 307 Thyristor Tum-O n 309 Thyristor Turn-Off 311 Thyristor Tvpes 3 13 7.6.1 Phase-Controlled Thyristors 314

Z6,2 BCTs 7.6.3 764 7.6.5 766

767

ll 4

Fast-SwitchingThyristors 315 I A$CBs 316 Bidirectional Triode Thyristors 31 6 BCTs 111

oms

3]8

MTQs

123

7.6 8 FET-CTHs 7.6 9

122

7.6.10 ETOs 2 6 11 ,acrs

321

Z 612

325

MCfs

324

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Contents

xi

7 613 SIIlis 328 7.6.14 Comparisons of1l1yristors 330 330 7.7 Series Operation of'Thvristors 7.8 Parallel Operation of Thyristors 337 7 9 dildt Protection 338 7 1Q du/dt Protection 339 7.11 SPICE Thyristor Model 341 7.11.1 Thyristor SPICE Model 341 2 I I 2 GTQ SPICE Madel 343 2 ]] 3 MCI SPICE Madel 345 7 ]] 4 S ITH SPICE Model 345 Summary 346 References 347 Review Questions 350 350 Problems Chapter 8

BI

Reso nant Pulse Inverters lntrodnction

352

352

352 8 2 Series Resonant Inverters 8 7 1 Series Resonant lnverrers with 1Jnidirectianal Switches 8.3

353 8 2 2 Series Resonant lnverrers with Bidirectional Switches 361 Frequency Response of Series-Re'sonant Inverters 368 8.3.1 Frequency Response for Series Loaded 368 8.3.2 Frequency Response for Parallel Loaded 370 8.33 Frequency Response for Series-Parallel Loaded 372

84

Parallel Resonant Inverters

8.5 86

Voltage Control of Resonant Inverters Oass E Resonant lnvecrec 380

8 7 Class E Resonant Rectifi er 8.8 8.9 8.10

374 383

Zero-Current-Switching Resonant Converters 388 8.8.1 L-Type ZCS Resonant Converter 389 8.8.2 M-Type ZCS Resonant Converter 391 393 Zero·Voltage-Switching Resonant Converters Comparisons Between ZCS and ZVS Resonant Converters

8 J1 Two-Ouadrant zvs Rewoam Converters 812 Resonant DC·l ink Inverters 399 Summary

References Problems

91 9.2

396

396

402

401

Review Questions

Chapter 9

377

403

404

406

Multilevel Inverters Introd11ctiao 406 Multilevel Concept

407

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xii

Contents

9.3 9.4

9.5

JYpes of Multilevel Inverters 408 Diode-Clamped Multilevel Inverter 409 9.4.1 Principle of Operation 410 9.4.2 Features of Diode-Clamped Inverter 411 9.4.3 Improved Diode-Clamped Inverter 412 Flying-Capacitors Multilevel Inverter 414 9.5.1 Principle of Operation 415 9.5.2 Features of Flying-Capacitors Inverter 417

96 Cascaded Multilevel Inverter 9.6.1 9.7

9. 11

Chapter 10 JO I 10.2 10.3

10.4

10.5 10.6

10.7 10.8

10.9

418

9,6.2 features of Cascaded lovecler

412

Applications 421 9.7.1 Reactive Power Compensation

422

9 72 9.8 9.9 910

417

Principle of O peration

Rack·tn·Back lnlcrtic

423

9.7.3 Adjustable Speed Drives 424 Switching Device Currents 424 DC· Link Capacitor Voltage Balancing 425

Feau1res of Multilevel Inverters

427

Comparisons of Multilevel Converters Summary 428 References 429 Review Questions 430 Problems 430

Controlled Rectifiers lntrod11c1ion

428

431

431

Principle of Phase-Controlled Converter Operation 432 Single-Phase Full Converters 434 10.3.1 Single-Phase Full Converter with RL Load 438 Single-Phase Dual Converters 440 Principle of Three-Phase Half· Wave Converters 443 Three-Phase Full Converters 447 45] JO 6 I Three-Phase f un Convener with RI J oad Three-Phase Dual Converters 453 Power Factor Improvements 456 10.8.1 Extinction Angle Control 456 457 10.82 Symmetric Angle Control 10.8.3 PWM Control 461 10.8,4 Single-Phase Sinusoidal PWM 463

JO.a 5

Three-Phase PWM Rectifier

465

Single-Phase Semiconvcrtcrs 467 10.9.J Single-Phase Scmiconvcrter with RL Load 474 IO.IO Three-Phase Semiconverters 10.10.1 Three-Phase Semiconverters with RL Load 480 JO.I 1 Single-Phase Series Converters' 10.12 Twelve-Pulse Converters 485

472 479

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Contents

10.13

D esign of Converter Circuits

10 14

Effects oft oad and Source lnd11crances Summary 494 Rcfen:nccs 495 R eview Questions

Problems

487

49?

496

497

11 I

AC Voltage Controllers Introduction ~00

11.2 11.3 11.4 11.5

Principle of On-Off Control 501 Principle o f Phase Control 503 Single-Phase Bidirectional Controllers with Resisti ve Loads Single-Phase Controllers with Inductive Loads 509

Chapter 11

500

) ).6 Three-Phase Fun. Wave Conrronecs 11.7 11.8 11.9

11.10 JI JI 11.12 11.13

Chapter 12 )2

Matrix Converter

12 3 Three-Phase AC Switches

554

12.9

545

551 551

12.5 12.6 12.7 12.8

537

551

Single-Phase AC Switches

12.4

518

i:;1n

Design of AC Voltage-Contro ller Circuits Effects of Source an d Load I nductances Summary 546 547 References Review Questions 54 7 Problems 548

Static Switches

506

SJ4

Three-Phase Bidirectional Delta-Connected Controllers Single-Phase Transformer Connection C hangers 522 Cycloconverters 526 11.9.l Single-Phase Cycloconverters 527 11.9.2 Three-Phase Cycloconvcrtcrs 530 ll .9.3 Reduction of Output H armonics 530 AC Voltage Controllers with PWM Control 534

1 lnrroductioo

12.2

xiii

Three-Phase Rcversine Switches 554 AC Switches fo r Bus Transfer 556 D C Switches 557 Solid-State Re lays 561 Microelectronic Relays 563 563 12.8.1 Photovoltaic Re lay I 2.8.2 Photovoltaic Isolators 565 Design of Static Switches 566 Summary 567 References 567 568 Review Questions Problems 568

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xiv

Contents Chapter 13

13.1 13.2 13.3 13.4

13.5 13.6

13.7 13.8 13.9 13.10

Ch apter 14

Flexible AC Transmission Systems

570

Introduction 570 Principle of Power Transmission 571 Principle of Shunt Compensation 573 Shunt Compensators 575 13.4.1 Thyristor-Controlled Reactor 575 13.4.2 Thyristor-Switched Capacitor 577 13.4.3 Static VAR Compensator 580 13.4.4 Advanced Static VAR Compensator 581 Principle of Series Compensation 582 Series Compensators 585 13.6.1 Thyristor-Switched Series Capacitor 585 13.6.2 Thyristor-Controlled Series Capacitor 586 13.6.3 Forced-Commutation-Controlled Series Capacitor 13.6.4 Series Static VAR Compensator 589 589 13.6.5 Advanced SSVC Principle of Phase-Angle Compensation 592 Phase-Angle Compensator 594 Unified Power Flow Controller 596 Comparisons of Compensators 597 Summary 598 References 598 Review Questions 599 Problems 599 Power Supplies

601

14 I

Introduction

14.2

14.4

DC Power Supplies 602 14.2.1 Switched-Mode DC Power Supplies 602 14.2.2 Flyback Converter 602 14.2.3 Forward Converter 606 14.2.4 Push-PulJ Converter 611 14.2.5 Half-Bridge Converter 613 14.2.6 Full-Bridge Converter 616 14.2.7 Resonant DC Power Supplies 619 14.2.8 Bidirc'ctional Power Supplies 619 AC Power Supplies 621 14.3.1 Switched-Mode AC Power Supplies 623 14.3.2 Resonant AC Power Supplies 623 14.3.3 Bidirectional AC Power Supplies 624 Multistage Conversions 625

)4 5

Control Circuits

14.6

Magnetic Design Considerations 630 14.6.1 Transformer Design 630 14.6.2 • DC Inductor 634

14.3

587

©J

626

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Conti,nts

14.6.3 Magnetic Saturation Summary 636 Rcfcrcnrr:s

1S 1

635

636

Review Questions Problems 637

Chapter 15

xv

DC Drives Introduction

637

640 640

15 2 15.3 15.4

Basic Cba ractccislics of DC Motors 641 Operating Modes 645 Single-Phase Drives 648 }5.4.1 Single-Phase Half-Wave-Converter Drives 649 15.4.2 Single-Phase Semiconverter Drives 650 15.4.3 Single-Phase Full-Converter Drives 651 15.4.4 Single-Phase Dual-Converter Drives 652 15.5 Three-Phase Drives 656 15.5.1 Three-Phase Half-Wave-Converter Drives 657 15.5.2 Three-Phase Semiconverter Drives 657 15.5.3 Three-Phase Full-Converter Drives 657 15 5 4

15 6

15.7

Three·Phase Dnal·C-Onverter Drives

ReviewQuestions Problems

Chapter 16

658

DC-DC Converter Drives 662 15.6.1 Principle of Power Control 662 15.6.2 Principle of Regenerative Brake Control 664 15.6,3 Principle of Rheostatic Brake Control 667 15.6.4. Principle of Combined Regenerative and Rheostatic Brake Control 668 15.6.5 1\vo- and Four-Quadrant DC-DC Converter Drives 15.6.6 Multiphase DC-DC Converters 670 Closed-Loop Control of DC Drives 673 15.7.1 Open-Loop lransfer Function 673 15.7.2 a osed-Loop Transfer Function 678 15.7.3 Phase-Locked-Loop Control 684 15.7.4 Microcomputer Control of DC Drives 685 Summary 6'i!/7 References 682

669

688

688

AC Drives

692

16 1 Introduction 692 16 2 Induction Motor Drives

693

16.2.1 Performance Characteristics 694 16.2.2 Stator Voltage Control 701 16.2.3 Rotor Voltage Control 703 16.2.4 Frequency Control 711

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xvi

Contents

16.3 16.4

16.2.5 Voltage and Frequency Control 713 16.2.6 Current Control 716 16.2.7 Voltage. Current, and Frequency Control 720 Closed-Loop Control of Induction Motors 721 Vector Controls 726 16.4.I Basic Principle of Vector Control 727 16.4.2 Direct and Quadrature-Axis Transformation 728 16 4 3

16.5

16.6

I ndi rect Yertor Control

References Problems

745

756

Review Questions

Chapt er 17

734

16.4.4 Director Vector Control 736 Synchronous Motor Drives 738 16.5.l Cylindrical Rotor Motors 738 16.5.2 Salient-Pole Motors 741 16.5.3 Reluctance Motors 743 16.5.4 Permanent-Magnet Motors 743 16.5.5 Switched Reluctance Motors 744 16.5.6 Closed-Loop Control of Synchronous Motors 16.5.7 Brushless DC and AC Motor Drives 747 Stepper Motor Control 749 16.6. I Variable-Reluctance Stepper Motors 750 16.6.2 Permanent-Magnet Stepper Motors 753 Summarv 756 757

758

Gate Drive Circuits

761

17.1 Introduction 761 17.2 MOSFET Gate Drive 761 17.3 BJT Base Drive 763 17.4 Isolation of Gate and Base Drives 767 17.4. 1 Pulse Transformers 769 17.4.2 Op1ocouplcrs 769 17.5 Thyristor Firing Circuits 770 17.6 Unijunction Transistor 772 17.7 Programmable Unijunction Transistor 775 17.8 Thyristor Converter Gating Circuits 777 17.9 Gate Drive ICs 777 17.9.1 Drive IC for Converters 781 17.9.2 High-Voltage IC for Motor Drives 784 Summary 788 References 789 Review Questions 789 Problems 790

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Contents Chapter 18

Protection of Devices and Circuits

791

18.l lntroduction 791 18.2 C-Ooling and Heat Sinks 791 18.3 Thermal Modeling of Power Switching Devices 797 18.3.1 Electrical Equivalent Thermal Model 798 18.3.2 Mathematical Thermal Equivalent Circuit 800 18.3.3 Coupling of Electrical and Thermal Components 803 18.4 Snubber Circuits 804 18.5 Reverse Recovery Transients 18.6 Supply- and Load-Side Transients 810 18.7 Voltage Proteclion by Selenium Diodes and Metal Oxide Varistors 813 18.8 Current Protections 815 18.8.1 Fusing 815 18.8.2 Fault Curreot with AC Source 822 18.8.3 i'ault Current with DC Source 824 18.9 Electromagnetic Interference 827 18.9.1 Sources of EMI 828 18.9.2 Minimizing EMI Generation 828 18.9.3 EMI Shielding 829 18.9.4 EMI Standards 829 Summary 830 References 831 Review Questions 831 Problems 832 Appendix A

Three-Phase Circuits

Appendix B

Magnetic Circuits

AppendixC

Switching Functions of Converters

AppendixD

DC Transient Analysis

AppendixE

Fourier Analysis

Bibliography

801

835 839

847

853

857

860

Answers to Selected Problems Index

xvii

863

871

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Preface The third edition of Power Electronics is intended as a textbook for a course on power electronics/static power converters for junior or senior undergraduate students in elec· trical and electronic engineering. It can also be used as a textbook for graduate stu· dents and as a reference book for practicing engineers involved in the design and applications of power electronics. The prerequisites are courses on basic electronics and basic electrical circuits. The content of Power Electronics is beyond the scope of a one-semester course. The time allocated to a course on power electronics in a typical undergraduate curriculum is normally only one semester. Power electronics has aJ. ready advanced to the point where it is difficult to cover the entire subject in a onesemester course. For an undergraduate course, Chapters 1 to 11 should be adequate to provide a good background on power electronics. Chapters 12 to 16 could be left for other courses or included in a graduate course. Table P.1 shows suggested topics for a one-semester course on "Power Electronics" and Table P.2 for one semester course on "Power Electronics and Motor Drives."' TABI f PJ Suggested Topics for One Scme.stcr Course on Pnwcr Elcarnoics

t mutes

ln1mduccinn Power srmimndnctnr diodes and circuits

J 110 1 12 2.1102.4. 2.7.2.10 102.13

3

Diode rtttifica

3.11039

4

Power rransistnrs PC..-DC con·•erter:s J>WM iovcr1ca Thyristors

l 2

s

6 1 8

lll

u

12

Reson;1nt pulse inverters

Controlled u:ctifica

AC ,•oltage conuoUen Static switcbcs Mid·tcrm exams and quizzes

final exam Tntal tcctnrcs in a IS·s·ctk serotstt r

4.2 4.10 4.11 5110 S7 6.l 10 6.6.6.8 10 6.ll

2 2

s

2.

5 1

7 Jlo 75. 7.9.7 JO

2

81 to 85 JQJ 10 106 11 I to JI S 12 I to 128

3

6 l

2 3 l

45 xix

Copyrighled malcria

xx

Preface TARI E P2 Suggested Topics ror One Semester Course on fnwer EJecrrnnirs and Morar Prlxes I ectures

2 3

Introduction Power stmironduc1nr dindes and circuits Diode rcclifica

1 1 10 1 12 2.1 to 2.4, 2.7,2.10 10 2.13

2 2

31to38

Q

Power transisrnrs

4.2.4.10, 4.11 5.1 to 5.1 6.t 10 6.6, 6.8 10 6.11 7.1 to 1.5. 1.9. 7.10

4 I 4

I

PC-PC ron,.·crtGU

~

Appendix

PWM inverters Thvristors Controlled rcctificn AC voltage controllers Magnetic circuits

DC dci ..·cs

1SJtolS7

Appendix

Three-phase circuits

u

AC drives

A 1.610 16.6 16.1 to 16.6

6 7 Ul

u

u

s I

101 ro 107

5

11.110 11.5

2 I

8 1610 166

~tid·tcrm exams and qu.i.zzcs

fi.nal exam Total lectures in a 15-week semester

s I

6 3 3

45

The fundamentals of power electronics are well established and they do not change rapidly. However, the device characteristics are continuously being improved and new devices arc added. Power Eltctronics, which employs the bottom-up approach, covers device characteristics conversion techniques first and then applications. It emphasizes the fundamental principles of power conversions. This third edition of

Power Electronics is a complete revision of the second edition, and (i) features bottom· up approach rather than top-down approach; (ii) introduces the state-of-the-art advanced Modulation Techniques: (iii) presents three new chapters on "Multilevel Inverters" (Chapter 9), "Flexible AC Transmission Systems" (Chapter 13), and "Gate Drive Circuits" (Chapter 17) and covers state-of-the-art techniques; (iv) integrates the industry standard software, SPICE, and design examples that are verified by SPICE simulation; (v) examines converters with RL-loads under both continuous and discon· tinuous current conduction: and (vi) has expanded sections and/or paragraphs to add explanations. The book is divided i.n to five parts: 1. 2. 3. 4. S.

Introduction-Chapter 1 Devices and gate-drive circuits-Chapters 2, 4, 7, and 17 Power conversion techniques-Chapters 3, 5, 6, 8, 9, 10, and 11 Applications-Chapters 12.13, 14, 15, and 16 Protection and thermal modeling-Chapter 18

Topics like three-phase circuits, magnetic circuits, switching functions of converters, DC transient analysis, and Fourier analysis arc reviewed in the Appendices. Power electronics deals with the applications of solid-state electronics for the control and conversion of electric power. Conversion techniques require the switching oo and off of power semiconductor devices. Low-level electronics circuits, which nor· malJy consist of integrated circuits and discrete componenu, generate the required

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Preface

xxi

gating signals for the powe r devices. Integrated circuits and discrete components are being replaced by microprocessors and signal processing !Cs. An ideal power device should have no switching-on and -off limitations in terms of tum-on time, turn-off time, current, and voltage handling capabilities. Power semiconductor technology is rapidly developing fast switching power devices with increasing voltage and current limits. Power switching devices such as power BJTs, power MOSFETs. S!Ts. IGBTs. MCTs. SITHs. SCRs, T RIACs. GTOs. MTOs, ETOs, IGCTs, and other semiconductor devices are finding increasing applications in a wide range of products. With the availability of faster switching devices, the applications of modem microprocessors and digital signal processing in synthesizing the control strategy for gating power devices to meet the conversion specifications are widening the scope of power electronics. The power electronics revolution has gained momentum, since the early 1990s. Within the next 20 years, power electronics will shape and condition the electricity somewhere between its generation and all its users. The potential applications of power electronics are yet to be fully explored but we've made every effort to cover as many applications as possible in this book. Any comments and suggestions regarding this book are welcomed and should be sent to the author. Dr. Muhammad H. Rashid Professor and Director Electrical and Computer Engineering University of West Florida 11000 University Parkway Pensacola, FL 32514-5754 E-mail: [email protected]

PSPICE SOFTWARE AND PROGRAM FILES The student version PSpice schematics and/or Orcad capture software can be obtained or downloaded from Cadence Design Systems, Inc. 2655 Seely Avenue San Jose, CA 95134 Websites: http://www.cadence.com http://www.orcad.com http://www.pspice.com The website http://uwf.edu/mrashid contains all PSpice circuits, PSpice schematics, Orcad capture, and Mathcad files for use with this book. Important Note: The PSpice circuit files (with an extension .CIR) are selfcontained and each file contains any necessary device or component.models. However, the PSpice schematic files (with an extension .SCH) need the user-defined model library file Rashld_PEJ...MODELLIB, which is included ,vith the schematic files, and must be Included from the Analysis menu of PSpice Schematics. Similarly, the Orcad

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xxll

Preface schematic files (with extensions .OPJ and .DSN) new the user-defined model library file Rashld..)'EJ...J,IODELUB, which is included with the Orcad schematic files, must

be Included from the PSpice Simulation settings menu of Orcad Capture. Without these files being included while running the simulation, it will not run and will.give errors.

ACKNOWLEDGMENTS Many people have contributed to this edition and made suggestions based on their classroom experience as a professor or a student. I would like to thank the following persons for their comments and suggestions: Mazen Abdel-Salam, King Fahd University of Petroleum and Minerals, Saudi Arabia Johnson Asumadu, Western Michigan University Ashoka K. S. Bhat, University ofVictoria, Canada Fred Brockhurst, Rose-Hu/man Institution of Technology Jan C Cochrane, Tlze University of Melbourne.Australia Ovidiu Crisan, University of Houston Joseph M. Crowley, University of lllinois, Urbana-Champaign Mehrad Ehsani, Texas A&M University Alexander E. Emanuel, Worcester Polytechnic Institute George Gela, Ohio State University Herman W. Hill, Ohio University Constantine J. Hatziadoniu, Sowhern lllinois University, Carbondale Wahid Hubbi, New Jersey lnstitllle of Technology Murrija Ilic-Spong, University of Illinois, Urbana-Champaign Shahidul I. Khan, Concordia University, Canada Hussein M. ~ojabadi, Sahand University of Technology, Iran Peter Lauritzen, University ofWashington Jack Lawler, University of Tennessee Arthur R. Miles, North Dakota State University Medhat M. Morcos, Kansas State University Hassan Moghbelli, Purdue University Calumet H. Ramezani-Ferdowsi, University of Mashhad, Iran Prasad Enjeti, Taas A &M University Saburo Mastsusaki, TDK Corporation, Japan Vedula V. Sastry, Iowa State University Elias G. Straogas, Michigan State University Selwyn Wright, The University of Huddersfield, Queensgate, UK S. Yu.varajan, North Dakota State University It has been a great pleasure working with the editor, Alice Dworkin and the production edi· tor, Donna Kmg. Finally, I would thank my family for their love, patience, and understanding.

MUHAMMAD H. RAsHID

P_ensacola, Florida

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About the Author Muhammad ff. Rashid received the B.S,.. I

I

IOBT

l'i-Oamid

'•

MOSFET

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12 Copyrghlcd malcria

1.3 Control Characteristics of Power Devices 13 r-• • •

•• ••

lOOM

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FIGURE 1.8

Applications of po"·cr dc\'iCCS. (C.Ourtesy of Powcrex, Inc.)

When a power semiconduc1or device is in a normal conduction mode, there is a small voltage drop across the device. In the o u1put vohage waveforms in Figure 1.9, these voltage drops are considered negligible, and unless specified this assumption is made throughout the following chapters. The power _semiconductor switching devices can be classified on the basis of:

1. Uncontrolled turn on and off (e.g., diode); 2. Controlled tum on and uncontrolled tum off (e.g., SCR); 3. Controlled turn-on and -off characteristics (e.g.. BJT, MOSFET, GTO, SITH, IGBT, SIT, MCT); 4. Continuous gate signal requirement (BIT, MOSFET, IGBT, SIT); 5. Pulse gate r equire ment (e.g.•SCR. GTO. M CT): 6. Bipolar voltage-withstanding capability (SCR, GTO); 7. Unipolar voltage-withstanding capability (BJ'f, MOSFET, GTO, IGBT. MCT); 8. Bidirectional curre nt capability (TRIAC. RCT); 9. Unidirectional current capability (SCR, GTO, BJT, MOSFET. MCT, IGBT, SITH, SIT, diode).

Table 1.4 shows the switching characteristics in terms of its voltage, current, and gate signals.

Copyrghicd matcria

14

Chapter 1

Introduction

Oate

signal +

Vo

+er--~ ~ -t>f:.._..::....--, Input

Thyris1or

voltage

R

v,

+ Outpu1 voltage

••

r

-~ _________o__ n

n

' t

vr

(•)Thyristor •~i•ch SITH..)) A~

K

+

J~_ _ _ _ _ n vr

,,

n

[.

(b) GTOIMTO/ETO/IGCT/MCT/SITH swilch (For MCT, the polarity olVo is reversed as shown)

+ -----

v,

+ R

(c) TrantiSlor switch

(d) MOSFET/JGBT swi1ch

,,

[.

FIGURE 1.9

Control characteristics or power sv.itching de\'ices.

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TABLE 1.4 Switching Characteristics of Po"·cr Semiconductors Continuous

Device Type

Device

Diodes

Power diode BIT MOSFET COOLMOS IGBT SIT SCR RCT TRIAC OTO MTO ETO IGC r SITH MCT

Transistors

1hyristors

() 0

~

c5::r ~ 3

~

§.

"'-

~

u,

Gate

Pulse Gate

Controlled

'I\Jm-On

Turn·Orl

x

x x x

x x x x

x x

x x x x x

Unipolar Voltiding a rapid feedback loop, which can terminate chip operation harmlessly when the system conditions exceed the 11om1al operating conditions. For example, smart power chips must be designed 10 shut down wi1hou1 damage when a short circuit occurs across a load such as a motor winding. With sman power technology, the load current is monitored, and whenever this current exceeds a preset limit, the drive voltage to the power switches is shut off. In addition to this over-current protection features such as

Sniart po,vcru:cl1001ogy

,

I

,

,,

I

/

i

,I ,,

I

l""'IU1pol:i.r power transistors

1

l_ PoY.·er

control

Power ~ HPower MOSFETs

dc\lite~

f

-lnsulated-uatr binolnr transiuors

YMOS-controlled thvristors

I

JO-VCMOS l.fitb·VOIHll,!C level shirt

Load

'

I Analog 1 OICUll'i Sonsmg and r,otection I-

Ooerauonal nmnlifiers

~ - - ~ r-lQvcrvolt:ii.!.elundef'\Oh:.te_c

: loc1~11rinl

\

1

\

\

l-fie.h·5nrcd bin,,,(a.r 1ru1l!U1ors

''

''

C'IJCUllS J HO\"cttem"'"r'J.turc

YOvercunenl/no,lo.1d

\

'

\ \

'

Interface

Logic L.rH"oh..S ' CMOS ciicult~ 1 ensov

' 'i..::=::=::::'.........::====:_~~~~~~~_J

FIGURE 1. 19 FunC'l.ionnJblock diagram or a snu,n po"·c r. l Rcf. 7. J. Balig-.11

Co ,yr ;hi

m

ri,1

28

Olapter 1

Introduction

overvollage and overtemperature protection are commonly included to prevent destructive failures. Some manufacturers of devices and modules and their Web sites are as follows: Advanced Power Technology, Inc. ABB Semiconductors Eupec Fuji Electric Collmer Semiconductor, Inc. Dynex Semiconductor Harris Corp. Hitachi, Ltd. Power Devices Infineon Technology International Rectifier Marconi Electronic Devices, Inc. Mitsubishi Semiconductors Mite! Semiconductors Motorola, Inc. National Semiconductors, Inc. Nihon International Electronics Corp. On Semiconductor Philips Semiconductors Power Integrations. Inc. Powerex, Inc. PowerTech, Inc. RCA Corp. Rockwell Inc. Reliance Electric Siemens Silicon Power Corp. Semikron International Siliconix, Inc. Tokio, Inc. Toshiba America Electronic Components, Inc. Unitrode Integrated Circuits Corp. Westcode Semiconductors Ltd .

1.11

www.advancedpowcr.com/ www.abbsem.com/ www.eupec.com/p/index.hlm www.fujielectric.co.jp/eng/denshi/scd/index.htm www.collmer.com www.dynexsemi.com www.harris.com/ www.hitachi.co.jplpse www.infineon.com/ www.irf.com www.marconi.com/ www.mitsubishielectric.com/ www.mitelsemi.com www.motorola.com www.national.com/ wwv.:,abbscm.corn/english/salesb.htm www.onsemi.com www.semiconductors.philips.com/catalog/ www.powerint.com/ www.pwrx.com/ www.powcr-tech.com/ www.rca.com/ www.rockwell.com www.reliance.com www.siemens.com www.siliconpower.com/ www.semikron.com/ www.siliconix.com www.tokin.com/ www.toshiba.com/taec/ www.unitrode.com/ www.westcode.com/ws-prod.html

POWER ELECTRONICS JOURNALS AND CONFERENCES There are many professional journals and conferences in which the new developments are published. The Institute of Electrical and Electronics Engineers (IEEE) c·library Explore is an excellent tool in finding articles published in the IEE journals

Copyrghlcd malcria

References

29

and magazines, and in the IEEE journals. magazines, and sponsored conferences.

Some of them are: IEEE e_Library ieeexplore.ieee.org/ IEEE Transactions on Aerospace and Systems www.iece.org/ IEEE Transactions on Industrial Electronics www.ieee.org/ IEEE Tnmsactions 011 Industry Applications www.ieee.org/ IEEE Transactions on Power Delivery www.iece.org/ IEEE Transactions on Power Electronics www.iccc.org/ IEE Proceedings 011 Electric Power www.ice.org/Publish/ Journal of Electrical Machinery 111,d Power Systems Applied Power Electronics Conference (APEC) European 'Power Electronics Conference (EPEC) IEEE Industrial Electronics Conference (IECON) IEEE Industry Applications Society (!AS) Annual Meeting International Conference on Electrical Machines (lCEM) International Power Electronics Conference (IPEC) International Power Electronics Congress (CIEP) International Telecommunications Energy Conference (INTELEC) Power Conversion Intelligent Motion (PCIM) Power Electronics Specialist Conference (PESC)

SUMMARY As the technology for the power semiconductor devices and integrated circuits develops, the potential for the applications of power electronics becomes wider. There arc already many power semiconductor devices that arc commercially available; however, the development in this direction is continuing. 11te power converters fall generally into six categories:(!) rectifiers, (2) ac-dc conver1ers, (3) ac- ac converlers, (4) de-de converters, (5) dc-ac converters. and (6) static switches. The design of power electronics circuits requires designing the power and control circuits. The voltage and current harmon.ics that arc generated by the power conver1crs can be reduced (or minimized) with a proper choice of the control strategy.

REFERENCES

.

[l) E. I. Carroll. "Power electronics: where next?" Power E11gi11eeri11g /011rnal, December 1996, pp. 242- 243. (2) S. Bernet. ''Recent developments of high power converters for industry and traction appli· cations." IEEE Tra11sactiom 011 Power Electronics, Vol. 15, No. 6, November 2000, pp. 1102-1117. [3] E. l. Carroll. "PO\VCT electronics for very high power applications,.. Power Engineering l our·

1101.April 1999,pp.81-87. (4) P. K. Steimer. H. E. Gruning. J. Wcminger. E. Carroll. S. Klada. and S. Linder, "IGCT-a new emerging ror hig.h po,1,·er. lo,v cos1 inverters;· IEEE Industry Applico1ions Maga7.ine, July/August 1999, pp.12-18. [SI R. G. Horr, Se111ico11tl11c1or Po1vtr £tcc1ro11ics. Ne\\' York: Van Nostrand Reinhold. 1986.

Copyrghtcd matcria

30

Chapter 1

Introduction

(6) K. Gndi. "Power electronics in action," IEEE Sp,ctrum,July 1995, p. 33. (7) J. Baliga, " Power )Cs in the daddlc." IEEE SptcJnim, July 1995, pp. 34-49. [8) I. Zvcrev and J. Hancock, "CoolMOS Select.ion Guide; Application note: AN-CoolMOS· 02, lnfm,on Tcdmologies, June 2000. [9J "Power Electronics Books." SMPS Technology Knowledge Base, March I , 1999. www.smpstech.com/bookslbooklist.htm (10) "Power Communities; Darnell.Com Inc., March I, 2002. www.damell.com/

REVIEW QUESTIONS Lt 1.2 1.3 1A

1.6 1.7 1.8 1.9 1.10 1,11 LU 1.13 Ll4

What are power electronics? What are the various types of thyristors? What is a commutation circuit? What are the conditions for a thyristor to conduct? How can a conducting thypstor he turned off? What is a line commutation? What is a forced commutation? What is the difference. between a thyristor and a TRIAC? What is the gating characteristic of a GTO? WbAt is the gating characteristic of an MTO? What is the gating characteristic of an ETO? What is the gating characteristic of an IGCT? What is tum-off time or a thyristor? What is a converter?

1..15 1.16 Ll7 L18 1.19 1.20 l.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29

What is the principle o( ac-dc conversion? What is the principle of ac-ac conversion? What i.s the principle of de-de conversion? Whal is the p rinciple of dc-ac conversion? Whal are the steps invo lved in designing power electronics equipment? What arc the peripheral effects of power electronics equipment? Whal are the differences in the gating characteristics of GTOs and thyristor..? What arc the djffcrcnccs in the gating characteristics of thyristors and transistors? What arc the differences in the gating characteristics of BJTs and MOSFETs? Whal is the gating characteristic of an IGBT? Whal is the gating characteristic of an MCT? Whal is the gating characteristic of an SIT? Whal arc the differences between BJTs and JGBTs? What are the diflcrcnccs between MCT, and GTOs? Whal are the differences between SITHs and GTOs?

LS

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CHAP T ER

2

Power Semiconductor Diodes and Circuits The /earning objectives of this chapter are as follo ws: • • • • • • 2.1

To understand the diode characteristics and its models To learn the types of diodes To learn the series and parallel operation of diodes To learn the SPICE diode model To study the efrects of a unidirectional device like a diode on RLC circuits To study the applications of diodes in freewheeling and stored-energy recovery INTRO DUCTION

Many applications have been found for diodes in electronics and electrical engineering circuits. Power diodes play a significant role in power electronics circuits for conversion of electric power. Some diode circuits that are commonly encountered in power electronics for power processing are reviewed in this chapter. A diode acts as a switch to perform various functions. such as switches in recti· Ciers, freewheeling in switching regulators. charge reversal of capacitor and energy transfer between components, voltage isolation. energy feedback from the load to the power sou,ce, and trapped energy recovery. Power diodes can be assumed as ideal switches for most applications but practical diodes differ from the ideal characteristics and have certain limitations. The power diodes are similar to p11-j unction signal diodes. However, the power diodes have larger power-, voltage-, and current-handling capabilities than those of ordinary signal d iodes. The frequency response (or switching speed) is low compared witli that of signal diodes. 2.2

SEMICONDUCTOR BA SICS

Power semiconductor devices are based on high-purity. single-crystal silicon. Single crystals of several meters long and "ith the required diameter (up to 150 mm) arc 31 Copyrighlcd maleria

32

Chapter 2

Power Semiconductor Diodes and Circuits

grown in the so-called float w11e furnaces. Each huge crystal is sliced into thin wafers, which then go through numerous process steps to turn into power devices. Silicon, is a member of Group IV of the periodic table of elements, that is. having four electrons per atom in its outer orbit. A pure silicon material is known as an intri11sic semico11ductor with resistivity that is too low to be an insulator and too high to be a conductor. It has high resistivity and very high dielectric strength (over 200 kV/cm). The resistivity of an intrinsic semiconductor and its charge carriers that arc available for conduction can be changed, shaped in layers, and graded by implantation of specific impurities. The process of adding impurities is called doping, which involves a single atom of the added impurity per over a million silicon atoms. With different impurities, levels and shapes of doping, high technology of photolithography, laser cutting, etching, insulation, and packaging, the finished power devices are produced from various structures of n-type and p-type semiconductor layers. n· Type material: If pure silicon is doped with a small amount of a Group V ele· ment, such as phosphorus. arsenic, or antimony, each atom of the dopant forms a covalent bond within the silicon lattice, leaving a loose electron. These loose electrons greatly increase the conductivity of the material. When the silicon is lightly doped with an impurity such as phosphorus, the doping is denoted as n doping and the resultant material is referred to as n·type semiconductor. When it is heavily doped, it is denoted as n + doping and the material is referred to as n +-type semiconductor. p· Type material: If pure silicon is doped with a small amount of a Group HI element. such as boron, gallium. or indium. a vacant location called a hole is introduced into the silicon lattice. Analogous to an electron, a hole can be considered a mobile charge carrier as it can be filled by an adjacent electron, which in this way leaves a hole behind. These holes greatly increase the conductivity of the material. When the silicon is lightly doped with an impurity such as boron, the doping is denoted as p-dopi11g and the resultant material is referred to as p -type semiconductor. When it is heavily doped, it is denoted as p+ doping and the material is referred to as p+-type semiconductor.

Therefore, there are free eleclrons available in an rt-type material and free holes available in ap-type material. In a p-type material the holes are called the majority carriers and electrons are called the minority carriers. In the 11-type material, the electrons are called the majority carriers, and holes are called the minority carriers. These carriers are continuously generated by thermal agitations, \hey combine and recombine in accordance to their lifetime, and they achieve an equilibrium density of carriers from about 1010 to 1013/cm3 over a range of about O •c to 1000 •c. Thus, an applied c lcclric field can cause a current flow in an n-type or p -type material. Key Points of Section 2.2

• Free e lectrons or holes are made available by adding impurities to the pure silicon or germanium lhrough a doping process. The electrons are the majority carriers in the n-type material whereas the holes are the majority carriers in a p-type

Copyrghtcd matcria

2.3

Diode Characteristics

33

material. Thus, the application of electric field can cause a current flow in an n-type or a p-type material. 2.3

DIODE CHARACTERISTICS

A power diode is a two-terminal pn-junction device [l, 2) and a pn-junction is normally formed by alloying, diffusion, and epitaxial growth. The modern control techniques in diffusion and epitaxial processes permit the desired device characteristics. Figure 2.1 shows the sectional view of a pn-junction and diode symbol. When the anode potential is positive with respect to the cathode, the diode is said to be forward biased and the diode conducts. A conducting diode has a relatively small forward voltage drop across it; and the magnitude of this drop depends on the manufacturing process and junction temperature. When the cathode potential is positive with respect to the anode, the diode is said to be reverse biased. Under reverse-biased conditions, a small reverse current (also known as leakage currelll) in the range of micro- or milliampere, flows and this leakage current increases slowly in magnitude with the reverse voltage until the avalanche or zener voltage is reached. Figure 2.2a shows the steady-state v -i characteristics of a diode. For most practical purposes, a diode can be regarded as an ideal switch. whose characteristics are shown in Figure 2.2b. ' The v-i characteristics shown in Figure 2.2a can be expressed by an equation known as Schockley diode equation. and it is given under de steady-slate operation by lo = l,(eV,{nVr - I)

(2.1)

where 10 = current through the diode, A; V0 = diode voltage with anode positive with respect to cathode, V; I, = leakage (or reverse saturation) current, t)'Pically in the range 10-6 to 10-15 A; n = empirical constant known as emission coefficiem, or idealiry factor, whose value varies from 1 to 2. Toe emission coefficient n depends on the material and the physical construction of the diode. For germanium diodes, 11 is considered to be 1. For silicon diodes, the predicted value of II is 2, but for most practical silicon diodes, the value of II falls in the range 1.1 to 1.8.

Anode ___..,. p

Cathode n ,__ ..

+ " (a) pn·junclion

Anode

Cathode

"

+ 1, -

'----1,1 , ----' (b) Diode symbol

FIGURE Z.1 pn·lu.nction and diode symbol.

Copyrghlcd malcria

34

Chapter 2

Power Semiconductor Diodes and Circuits

lo -VoR

O

v

0

v

Rc\'ersc

leakage currcnl

FIGURE 2.2

(b) Ideal

(•) Practical

v-i Otaracteristics of diode.

V7 in Eq. (2.1) is a constant called thermal voltage and it is given by kT Vr= IJ

(2.2)

where q = electron charge: 1.6022 x 10- 19 coulomb (C); T = absolute temperature in Kelvin ( K = 273 + °C}; k ~ Boltzmann's constant: 1.3806 x 10- 23 J/K. At a junction temperature of 25 °C, Eq. (2.2) gives

kT

Vr

= - wo. the roots are real and the circuit is said to be over-damped. The solution takes the form (2.44) Case 3. If a < wo. the roots arc complex and the circuit is said to be 1mderdamped. The roots arc s 1.,2

=

-o ± jw,

(2.45)

Copyrighlcd maleria

2.11

Diodes with LC and RLC Loads

53

where w, is called the ri11gi11g freq11e11cy (or damped resonant frequency) and

w, : ~ · The solution takes the form

i(t) = e""'( A 1 cos ••,I

+ A2sin w,t)

(2.46)

which is a damped or decaying si1111soidnl.

Note:The constants A 1 and A 2 can be determined from the initial conditions of

the circuit. The ratio of cx.lwc, is commonly kno,vn as the da,nping rat;o, 6 = R/2 \lcii.

Power e lectronic circuits are generally underdamped such that the circuit current becomes near sinusoidal, to cause a nearly sinusoidal ac output or to turn off a power semiconductor device. Example 2.6

Finding the Current in an RLC Circuit

The second-order RLC circuil or Figure 2. 17 has the de source \'Oltage V, = 220 V, inductance L = 2 mH. capacitance C = 0.05 µF. and resistance R = 160 n. The initial value or the capacitor "oltage is v,(1 = 0) = Vc0 = Oand conductor current /(1 = 0) = O. If switch S1 is closed at 1 = 0. determine (a) an cxprc.. ion for 1hc currcn1 i(1). and (b) 1hc conduction time or diode. (c) Draw a ske1ch or i(r). (d) Use PSpice to plot the instantaneous current i for R = 50 n. 160 n, and 320

n.

Solution ~ 160 x lo'/(2 x 2) = 40.000 rad/s, and from Eq. (2.41), w0 = 1/vLC = 10-' rad/s. 1l1e ringing frec1uency becomes

a. From Eq. (2.40), " = RJ2L w, =

\/1010

-

16 X 10" • 91.652 rad/s

Bcc11usc o < wi:r ii is an undcrdnmpcd circuit and the solution is of the Corn, i(1) =

l'- 0 '( A 1cosw,t

+ A?sinw,t}

Att = 0. i(r = 0) = 0 and 1his gives A1 = 0. The solution becomes

The dcrivati"c of i(r) becomes

\Vhcn the s,vitch is closed at t = 0. the capacitor offers a lo,v impedance and the inductor orrcrs a high impedance. The initinl ra1e or rise of the current is 1in,i1ed only by

the inductor l. Thus at 1 • 0. the circuit dVdt is ~IL. Therefore,

didi l

t• O

=

w A, ; V, r

-

L

which gives the constant as

v,

220 x 1,000

A , = w,I., = 91.652 X 2 ; 1. 2 /\

Copyrghtcd matcria

54

Chapter 2

Power Semiconductor Diodes and Circuits

i.amp

1.2 0.8 0.4 O i • 0.9549Vm x 2/(35 x \12) = 6.56 V and its frequency is / 6 = 6/ = 360 Hz. Key Points of Sedlon 3.6

• A multiphase rectifier increases the amount of de component and lowers the amount of the harmonic components. The output voltage of a p-phase rectifier contains harmonics whose frequencies arc multiples of p (p times the supply frequency),p/.

3.7

THREE-PHASE BRIDGE RECTIFIERS A three· phasc bridge rectifier is commonly used in high-power applications and it is shown in Figure 3.13. This is a full-wave rectifier. It can operate with or without a transformer and gives six-pulse ripples on the output voltage. The diodes are numbered in order or conduction sequences and each one conducts for 120°. The conduction sequence for diodes is D1 - Di, Di - Di, Di - D,, Ds - D,. Ds - D6, and Di - D,,. The pair of diodes which are connected between that pair of supply lines having the highest amount of instantaneous line·to·line voltage will conduct The line-to-line volt· age is V3 times the phase voltage of a three-phase Y-connected source. The waveforms and conduction times of diodes are shown in Figure 3.14 [4] . If Vm is the peak value of the phase voltage, then the instantaneous. phase voltages can be described by

v,. = Vm sin(wt)

Vt,,,=

V01 sin(wt - 120°)

Ven=

;,,,

;.

~

c

o, R

n -

Vao

b

c

-+

Secondary

Prinury

a

Vm sin(wt - 240°)

b

i,

+

"·

o,

FIGURE 3.13

Three-phase. bridge rectifier.

Copyrighted m~leria

3.7

0

2,r

ir

i, V3Vm - R-

4,r

':

T

3I

T

I I I

I I

Three-Phase Bridge Rectifiers

s..

2,r

T

93

wt

Une curre.nt

------.!..I

01--~~+-~ ~-!-~~--!e-~~+-~~-!-,--~-+~-,/, 2ir ~ 2ff a.it 3 T ,

- V3Vftl I I I ~R~ - - - ---~------~----- - ~-------- -

: : : Diodecurrr:=tj

·~~1

3"

7rr

"'

T

2ir wt

FIGURE 3.14 Wavlforms and conduction times of diodes.

Because the line-line voltage leads the phase voltage by 30°, the instantaneous line-line voltages can be described by

= \/3 Vm sin( wt + 30°) Vco = V3 Vm sin(wt - 210') v••

Vi,,

=

\/3 Vm sin( wr - 90' )

The average output voltage is found from

Vdc

= 211'216 1·16 V3Vmcoswtd(wt) 0

= J\/3Vm = 1T

1.654Vm

(3.40)

Copyrighted m~leria

94

Chapter 3

Diode Rectifiers

where V.,. is the peak phase voltage. The nns output voltage is

r/63V; cos

v.... = [ 2..216 lo

2

"9v'3)

3

+( 241'

a

-

wt d( wt)

]'n

112

...1 6554V.'"

V.

(3.41)

m

If the load is purely resistive, the peak current through a diode is/.., the nns value of the diode current is

= Y3 V,./R and

r/6

I, = [ 24,r lo I; cos2 wt d(wt) ]'n

1 21')]'12 -1 (1T - +-sin[ "' 1r 6 2 6

=I a

0.5518/.,.

(3.42)

and the rms value of the trnnsformer secondary current,

11

= [2~

1~

16 /~

cos2 wt d(wt )

rn

112

[! (.!

= I '"1r6 + .!.2 sin 261r) ] = 0.78041...

(3.43)

where /.,. is the peak secondary line current. For a three-phase rectifier q = 6, Eq. (3.38) gives the instantaneous output voltage as

1-1>(1) = 0.9549V.,. ( l +

ts

cos(6r) -

!

1 3

cos(l2wr) + ·· · )

(3.44)

Example 3.10 Finding the Performance Parameters of a Three-Phase Bridge Rectifier A three-phase bridge rectifier bas a purely resistive load of R. Delcnnine (a) the efficiency, (b) lhe FF,(c) the RF,(d) theTUF,(e) the peak inverse (or reverse) vollage (PJV) of each diode.and (0 the peak current through a diode. The rectifier delivers J.,. - 60 A at an output voltage of V.,. • 280.7 V and the source frequency is 60 Hz.

Solution a. From Eq.(3.40), v.,. • l.654V.,. and I.,.• l.654V.,JR. From Eq.(3.41), V,,.. • l.6554V.,. and /..., = t.6554V.,JR. From Eq. (3.1), P.,. ~ (1.6S4V.,) 2/R, from Eq. (3.2), P., = ( l.6554V.,) 2/R, and from Eq. (33) the efficiency 11

=

(t.654V.,.)2 (t.6S54V.,)'

= 99.83%

Copyr ghtcd matcria

3.8

b, From Eq. (3.5), the FF

Thr~·Phase Bridge Rectifier with RL Load

= 1.6554/1.654 = 1.0008 =

V

95

100.08%.

2

c. From Eq. (3.6), the RF = 1.0008 - I = 0.04 = 4%. d. From Eq. (3.15), therms voltage of the transformer secondary, V, = 0.107V.,. From Eq. (3.43), the rms current of the transformer secondary, . r.

v..

,, • 0.18041., s 0.1804 x v3 "'ii The VA rating of the transformer,

VA = 3V,l, = 3

. r. v.. X 0.7804 X v 3 R

x 0.707V.,

From Eq. (3.8) , TUF =

3

l.6S4'

x v3 x 0.707 x 0.7804

c

0.9542

e. From Eq. (3.40), the peak line-to-neutral voltage is V., • 280.7/1.654 - 169.7 V. The peak inverse voltage of each diode is equal to the peak value of the secondary line-toline voltage, PlV • v3 V., • v3 X 169.7 • 293.9 V. t The average current through each diode is

,, = £''\ .. = 2:

cos wt d(wt)

The average current through each diode is 14 I., = 20/0.3183 = 62.83 A.

m

=,..

~sin

f

= 0.3183/.,

60/3 • 20 A; therefore, the peak current is

Nott: This rectifier bas considerably improved performances compared with those of the multiphase rectifier in Figure 3.12 with six pulses.

Key Points or Sedloa 3.6 • A three-phase bridge rectifier has considerably improved performances compared with those of single-phase rectifiers.

3.8

THREE·PHASE BRIDGE RECTIFIER WITH RL LOAD Equations that are derived in Section 3.5 can be applied to determine the load current of a three-phase rectifier with an RL load (similar to Figure 3.15). It can be noted from Figure 3.14 that the output voltage becomes

V,o =

vi V,o sin wl

for

11'

211' .

3

3

- :s wt :s -

where V,o is the line-to-line rms input voltage. The load current i0 can be.found from

"" . L dio dt +Rio+ E = •v2 V,osm wt

Copyr ghtcd matcria

96

Chaptl!r 3

Dlodl! Rel - 8) + A,e- (RIL), - E Z R 2 112 where load impedance Z = (R + (wL)2} and load impedance angle i0 =

(3.45)

e = tan-•

(o>UR). The constant A 1 in Eq. (3.45) can be determined from the condition: at wt • .,,13, i0 • lo,

A = [1 + ! - v:.i, sin(f- 8) 1

0

]e - 0 R z · Z 3 R (3.46) Under a steady-state condition, i0 (w1 = 21'/3) = i0 (o>t = 'IT/3). That is, i0 (w1 21r/3) = 10• Applying this condition, we get the value of / 0 as

l0 -

viV.i, sin(21f/3 - 8) - sin(1r/3 - 0)e-(R/Ll (• l3w) E Z 1 - e-(R/L)(•l3w) R

for / 0

.,,

0

a

(3.47)

which, after substitution in Eq. (3.46) and simplification, gives .

ro a

V2Vo1,[ . ( -

2-

SID

wt -

)

8 +

sin(21f/3 - 8) - sin(1r/3 - 8)

1

_

e-; I (VX) JOOV+---+-- --h----+----.+- --+---t---;---;r-----+ 100 A

280V

260V 240V +-- -+------f----'i---+---+---+--'--+-- --+ 19ru ~ru Dru nms ~ru ~ru 16ms 17ms 18ms oV(4,7) Cl • 18.062 m, I0-1.885

w~ lime

C2 • 19.$92 m. 110.911 di! = -1.8300 m -6.0260

FIGURE 3.17

PSpice plot for Example 3.1 1.

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100

Chapter 3

Diode Rectifiers

+ 211) = f(x), the input current can

becomes zero. Thus, for satisfying the condition of f(x be d escribed by

11 s,, for - :s "" :s -

i,(1) • 1. i,(1)

=-

6

6

71f

1. for

6

:s"" :s

1111

6

which can be expres,ed in a Fourier series as ~

i,(1) = J.,_

+

~

L (a. cos(n"'1) + b. sin(n"'1)) = L c. sin(n"'1 + 4>.) 11•t n• I

where the coefficients arc

a.

b.

=;J. =;1. 1

h

,.

i, (t) cos(n"'1) d(wt) 2 • l,(t) cos(n"'1)

d(wt)

0

~

=;[II, •

cos(n"'1) d("'1) -

f'

}1f

I,

cos(n"'1) d ("'1)] = 0

=;1 [ J~r2t/ sin(nwt) d ("'1) - j,Tr"tI, sin(n"'1) d("'1) ] 4

•

•

whi~ after integration and simplification, gives b,._ as

-41, cos ( n1r )Stn . b,. • ~ b. = 0

(n") . (m') T sin 3

n = 2, 3, 4, 6, 8, 9, .. .

for

. ., c. = ,y I (a.)2 + (b.) 2 = -4/, n'ff cos(mr)Stn

4>. -' arctan (::) =

for n = I, 5, 7, 11, 13, ...

(n") . (=) 2 3 sin

0

Thus, the Fourier series of the input current is given by 1

'

=

f 4.v'3l, ••,

211

(sin(wt) _ sin(5"'1) _ sin(7wt) 1 5 7

+ sin(11"'1 ) + sin(l3"'1) _ sin(17"'1) _ .. . ) 11

13

17

(3.50)

The rms value of the nth harmonic input cuncnt is given by I

I 2~1. nir 2 2 112 -sin., .. = -vi (a" + b") = - n1r 3

(3.51)

The rms value of the fundamental current is

v'6

1, 1 = - I, 1f

= 0.7797 I,

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3.10

Rectifier Circuit Design

101

The nns input current

[z: 1:·

16

I,

=

HF • [ (::,

112

I: d(b>I) ]

= 10

'3 =

r- (fr -

OF = cos cj,1

1 ]'" = [

= cos(O)

,,,

PF = - cos(O)

/,

1]

0.8165/•

112

= 0.3108

or 31.08%

= I

o.n97 a -- •

0.8165

0.9549

Nott: If we compare the PF with that of Example 3.10, where the load is purely resistive, we can notice that the input PF depends on the load angle. For a purely resistive load, PF = 0.8166.

Key Points or Section 3.8 • An inductive load can make the load current continuous. The critical value of the load electromotive force (emf) constant x for a given load impedance angle 6 is higher than that of a single-phase rectifier; that is. x = 86.68% at 6 = 0. • With a highly inductive load, the input current of a rectifier becomes an ac square wave. The input power factor of a three-phase rectifier is 0.955, which is higher than 0.9 for a single-phase rectifier. 3.9

COMPARISONS OF DIODE RECTIFIERS The goal of a rectifier is to yield a de output voltage at a given de output power. Therefore, it is more convenient to express the performance parameters in terms of V.sc and P.i.,. For example, the rating and turns ratio of the transformer in a rectifier circuit can easily be determined if therms input voltage.to the rectifier is in terms of the required output voltage Vi1c. The important parameters arc summarized in Table 3.2 (3). Due to their rel· ative merits, the single-phase and three-phase bridge rectifiers are commonly used. Key Points or Section 3.9

• The single-phase and three-phase bridge rectifiers. which have relative merits. are commonly used for dc-ac conversion.

3.10

RECTIFIER CIRCUIT DESIGN The design of a rectifier involves determining the ratings of semiconductor diodes. The ratings of diodes are normally specified in terms of average current, rms current, peak current, and peak inverse voltage. There arc no standard procedures for the design, but it is required to determine the shapes of the diode currents and voltages. We have noticed in Eqs. (3.20), (3.22), and (3.39) that the output of the rectifiers contain harmonics. Filters can be used to smooth out the de output voltage of

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102

Chapter 3

Diode Rectifiers

TABL£3.2 Pcrfonnanoe Parameters of Diode Rectifiers with a Resistive Load

Performance Pvametcn

Single-Phase Rectifier with CenterTapped 'll-ans!ormer

Bridse Rectifier

Six-Phase St.Ir Rectifier

Bridge Rectifier

3.14V..,

1.s1v...

2.09V..,

1.0SV"'

1.uv.. 0.5-01..,

l.llV,..

0.501"'

0.74V« 0.1671"

0.428V"' 03331"'

1.571.., 0.785/"'

1.57/"' 0.7851"'

6.281.., 0.409/"

3.141.., 0.5791.,.

l.S7 0.81

1.57 0.81 I.II 0.482 123P"' 123P"' 2/,

2.45 0.998

1.74 0.998

Peat repetitive revenc voltage. V«RN Rm, i.nput voltage per tnns(ormcr leg. V, Diode ave"'ge l,c•Vl

=~

Peak repetitive fort¥Vd c:unent, J,..,., Diode mu cunent, 11(«.USJ Form factor of diode current,

1,

(3.61)

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3.10

Rectifier Circuit Design

107

D

v,

+

+

c,

v,

R

•o

wl

(•) Circuit model

II I I I

1 1

I I

.,,

v,

(b) Waveforms for full-w::tYC·rectifier

o, + >

c,

'>R >

wl

(c) Charging

(d) Discharging

FIGURE 3.22

Single-phase bridge rectifier ,,ith C filter.

Since,,-, "' I - .r, Eq. (3.61) can be simplified to Vmtz

12 )

Vm

V,cpp) • Vm ( I - I + RC, • RC, • 2/RC,

Therefore, the average load voltage v., is given by (assuming 12 = 1/2 /)

v...- = v -

"'

V,,,

V,( pp)

- - - =v. - - 2

"'

4/RC,

(3.62)

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108

Chapter 3

Diode .Rectifiers

Thus, the nns output ripple voltage v.. can be found approximately from V,,,. 4V2/RC,

V. • V,tpp) •

"

2V2

The RF can be found from V,,. V., 4/RC, I RF = - = = ~~-"---Vole 4v'1.fRC, V.,(4/RC, - 1) v'1. (4/RC, - I}

(3.63)

which can be solved for C,: 1 C, • 4;R ( I + v'2 RF) = 4 x

~ x 500 ( I + v'2 ~ 0.05) = lZ6.2 µ.F

b. From Eq. (3.62), the average load voltage V"' is

v.., = 169.7 -

169.7 1'

~ =

x 60 x 500 x 126.2 x 10

169.7 - 11.21

= 158.49 V

Example 3.17 Finding the Values of an LC Output Filter to Umit the Amount of Output RIPPie Voltage An LC filter as shown in Figure 3.18c is used to reduce the ripple content of the output voltage for a single-phase full-wave rectifier. The load resistance is R = 40 0, load inductance is L = 10 m.H, and source (requency is 60 Hz (or 377 rad/a). (a) Determine 1hc vnluc:s of L~ and C~ w that the RF of the output voltage is 10%. (b) Use PSpicc to calculate Fourier components of

the output voltage 1.\)- Assume diode parameters IS

= 2-22E - 15, BV

=

1800 V.

Solution a. The. equivalent circuit for the hannonics is shown in Figure 3.23. To make it easier for the nth harmonic ripple current to pass through the filter capacitor, the load impedance must be much greater than that of the capacitor. That is.

VR2+ (nwL) 2 >> _1_ n..C, This condition is generally satisfied by the relation

VR2 + (no,L)'

R _

V ..(no,)

X,, • n~C,

c.

= __!Q__

(3.64)

n..C,

+ v .,.(no,)

L

FIGURE 3.23

Equivalent cil'"t'Uit for harmonics.

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3.10

Rectifier Circuit Design

109

and under this condition, the effect o r the load is negligible. Therms value or the nth harmonic com ponent appearing on the output can be found by using the voltage· divider rule and is expressed as

V00

.

~

I I

I

I

-1/(nwC,) -1 V,i,j = V".11 (nwl,) - 1/(nwC,) (11w)2L, C, - I

(3.65)

The total amount or ripple voltage due to all harmonics is

v. = ac

( L..

v2

),n

(3.66)

on

11•2,,4.6, . . .

For a specified value of V" and with the value ol C, from Eq. (3.64). the value or L, can be computed. We can simplify the computation by considering only the dominant harmonic. From Eq. (3.22) we find that the second harmonic is the dominant one and its rms value is = 4V..,1(3"11r) and the de value. V"' = 2V.,f,r. For n = .2, E qs. (3.65) and (3.66) give

v,,.

v • v02 - I

- I 1\/.2 (2w) 2L,C, - I •

"'

The value of the filter capacitor C, is calculated from

VR

2

+ (2wl )2

=

__!!!... 2..C,

or

C, =

10 41rfV R 2

+ (4,rfl)2

= 326µF

From Eq. (3.6) the RF is defined as RF =

v"

v"'

=

v., = v,. v.,

= "11

1

v"' (41rf)2L,C, -

I

t

3 ((4,rf) 2L,C, - I]

I = o. J

or (4-rrf) 2L,C, - I = 4.714 and L, = 30.83 mH. b. The single-phase bridge rectifier for PSpicc simulation is shown in Figure 3.24. The list or the circuit file is as follows: - l e 3.17 . vs 1 LE

)

CE

7

RX

8 5

L R

7

S ingle- Phae,e Bridge Ractifiot' ,..,ith LC Fil ter 0 SIN (0 169.7V 60HZ)

8 4

6

326UF SOM lOMH DC CN

7

vx

6

5 4

V'i

l 2

2 3

Dl

30.83MH

Used to converge the 'solution

40 DC

CN

r:t10D

Vol tage source to measure the oucput current Voltage source to measure the ifll'.)Ut current ; Diode rrodels

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110

Chapter3

Diode Rectifiers 0 3 2

03 04

4 0 4

.MODEL

IM)[)

D (IS=2. 22E-15 BV=1800V}

•TRAN .FOUR

lOUS

SOMs 33MS V(6 . 5 }

ll2

120HZ

. options

I'l'LS=O

sous

; Diode DK>del parameters

Transient analysis ; Fourier analysis of output voltage

abstol = 1. OOOU reltol = . 05 vntol = O. Olm

.END

The results of PSpice simulation for the output voltage V(6, 5) are as follows:

FOURIER CCMl'ONEm'S OF TRANSIENI' RESl'CfiSE V(6,5) . DC CCMPONEtn' = l.140973E+02 l'.l®IJNIC FIIEl:lUm:'i N:>Rlll\LIZEI> FOURIER N)

(HZ)

1 2 3 4 5 6

1.200E+02 2 . 4008+02 3.600E+02 4.8008+02 6.000E+02 7.2008+02 8. 4008+02 9 . 600E+02 1. 080E+03

7

8 9

TCfrAL HARMONIC

CCtlPCmm'

CCt!PONmI'

Pl!ASE

OORl!l\LIZED

(DB1}

PHl\SE (DID)

l.3048+01 1.000E+OO 1.038E+02 1.2368+02 6. 4968- 01 4.9818- 02 9.2268+01 2.277E-01 1. 7468-02 l.5668- 01 1.201E- 02 4 .8758+01 l.274E-01 9.7678-03 2 .2328+01 l.0208-01 7.8228- 03 8.358E+OO 1 . 9978+00 8.2728-02 6.3438- 03 -1.0612+00 6.982E-02 5.3548-03 6.0158- 02 4.61.28° 03 - 3. 4361!+00 DISTORTICN • 5.6360708+00 PERCENT

O.OOOE•OO 1.9888+01 - 1.1508+01 -5.501.E+Ol - 8.144E+Ol -9.540E+Ol - 1.0188+02 -1.048E+02

-1. 072E+02

which verifies t he design.

i..

3

v, ~

30.83mH

o,

ov

R,

7

80m0

R

03

+

2

••

v,

0

8

o,

o,

400

s

c,

3261< - Vo:2· Toe result is that the anode voltages of diodes D 1 and ~ are equal;

c

L.,

..

- Vu ..

1.,

o,

o,

...,p,

t"'

i4.1

o, b

o,

o.

- "u+

(a) Circuit diagram •1.2

-Vm

·:r

I

..., . I

x

3"

x x=. ii11

2..

T

I

4,,

"H T Q

•

5,,

i111

2,r

T

(b) Wa,•crorms FIGURE 3.27

Three~phase bridge reclifier with source inductances.

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3.12

Effects of Source and Load Inductances

117

and both diodes conduct for a cenain period which is called commutation (or overlap) angle µ.. This transfer or current from one diode to another is called commutation. The reactance corresponding to the inductance is known as commutating reactance. The effect of this overlap is to reduce the average output voltage of conveners. The voltage across I,z is

Vu=

di

Lz -dt

(3.77)

Assuming a linear rise of current i from Oto I& (or a constant dildt = tiiltit), we can write Eq. (3.77) as

Vu tit = /.,z {ij

(3.78)

and this is repeated six times for a three-phase bridge rectifier. Using Eq. (3.78), the average voltage reduction due to the commutating inductances is

V,

=

1

7

2(vL1 +Vu+ v1..3)tit

= 2/(Lt + Lz + y

. ) ti,

= 2/(Lt + Lz + L3) /c1c

(3.79)

lf all the inductances are equal and L, = Lt = I,z = L 3, Eq. (3.79) becomes V, = 6/L,l""

(3.80)

where /is the supply frequency in hertz.

Example 3.20 Finding the Effect of Line Inductance on the Output Voltage of a Rectifier A three-phase bridge rectifier is supplied (rom a Y-connected 208-V 60-Hz supply. The average load current is 60 A and has negligible ripple. Calculate the percentage reduction or output volt· age due to commutation i( the line inductance per phase is 0.5 mH.

Solution L , = 0.5 mH, V, = 208/v':i = 120 V, f = 60 Hz, l0c = 60 A, and Vm = vi x 120 = 169.7 V. From Eq. (3.40). V"' = 1.654 x 169.7 = 280.7 V. Equation (3.80) gives the output voltage reduction,

_ 100 V, • 6 x 60 x 0.5 x 10 3 x 60 • 10.8 V or 10.8 x 'iiio.7 = 3.85% and the effective output voltage is (280.7 - 10.8) = 269.9 V.

Example 3.21 Finding the Effect of Diode Recovery Time on the Output Voltage of a Rectifier The diodes in the single-phase rull,wave rectifier in Figure 3.6a have a reverse recovery time or t,, = 50 fLS and therms input voltage i, V, = 120 V. Determine the effect or the reverse recovery time on the average output voltage if the supply frequency is (a)/, e 2 kHz. and (b) /, = 60 Hz.

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118

Chapter 3

Diode RectifieB

FIGURE 3.28

Effect of reverse recovery time on output voltage.

Solution The reverie recovery time would affect the output voltage of the rectifier. In the Cull-wave recti· fier of Figure 3.6a, the diode Di is not off at "" • 'IT; imtead, it continues to conduct until t = "'"' + t,r As aresult of the reverie recovery time, the average output voltage is reduced and the output voltage waveform is shown in Figure 3.28. If the input voltage is v • V"' sin u>t • v2 V, sin cJll, the average output voltage reduction is

If.'"

V. = V. sin Oll dt = ZVm [- ~]'" "To"' T a>o

v.,

= -:;;- (1 - cos""")

v_ - v'2 v. - v'2 x

120 - 169.7 v

(3.81)

Without any reveBO recovery time, Eq. (311) gives the average output voltage v., = 0.6366V., = 1()8.03 v. 1.

For 1,. = SO f1.S and/, - 2000 Hz. the reduction of the average output voltage is Vm

V,, = -(I - cos 2Tr/,t")

" = 0.061Vm a JO.J V or 9.Sl%otV.,.

b. For'" = 50 f1.S and/, • 60 Hz, the reduction of the output de voltage

v,, •

v"'(t - cos2,r/,1.,) = 5.65 x 10-sv., 'ff

= 9.6 x 10-3 v

or 8.88 x 10-1% of v..,

Note: The effect of 1,, is significant for high-frequency source and for the case of normal 60-Hz source, its effect can be considered negligible.

Key Points or Section 3.U • A practical supply has a source reactance. As a result, the transfer of current from · one diode to another one cannot be instantaneous. There is an overl!'P known as

Copyrghlcd m~leria

Review Questions

119

commutation angle, which Jowers the effective output voltage of the rectifier. The effect of the diode reverse time may be significant for a high-frequency source.

SUMMARY There are different types of rectifiers depending on the connections of diodes and input transformer. The performance parameters of rectifiers are defined and it bas been shown that the performances of rectifiers vary with their types. The rectifiers generate harmonics into the load and the supply line; and these harmonics can be reduced by filters. The performances of the rectifiers are also influenced by the source and load inductances.

REFERENCES (11 J. Schaefer, Rtctifior Circuits-Tlreory and Design, New York: John W~cy & Sons, 1975. (21 R. W. Lee, Power Convert

I

p•

n

n

p

Collector

Emitter

(a) NPN·transisior

(b) PNP-transis1or

FIGURE 4.3

Cross sections ol BJTs.

the emitter side p·layer is made wide, the 11-base is narrow, and the collector side p-layer is narrow and heavily doped. Toe base and collector currents flow through two parallel paths, resulting in a low on-state collector-emitter resistance., RcE(ON)·

4 .2.1

Steady-State Characteristics Although there are three possible configurations--> 1, the collector current can be expressed as (4.6)

le "' aFlc where the c9nstant aF is related to J3 by

(4.7) or (4.8)

Let us consider the circuit of Figure 4.7, where the transistor is operated as a switch.

Is

= Va -

VaE

Ve

= VCE = Vee -

(4.9)

Rs .

~-~+~

IeRc

= Vee

ppRe

- ~(Va - Va£l B

~·~

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4.2 Bipolar Junction Transistors

127

Re le

'• +

v.

Rn +

+

Vee

-+-

YcE

v••

le

FIGURe 4.7

Transistor S\\'llch.

or (4.11) Equation ('4.11 ) indicates that as long as VCE 2: V8£, the CBJ is reverse biased and the transistor is in the active region. The maximum collector current in the active region, which can be obtained by setting Vc 8 = 0 and V8 E = VcE, is Vee - VeE

le..,=

Vee - VaE

Re

Re

(4.12)

and the corresponding value of base current

I

_ lc.11

BM -

13F

(4.13)

If the base current is increased above / 8M, V8 E increases, the collector current increases, and the VCE falls below VaE· This continues until the CBJ is forward biased with V8c of about 0.4 to 0.5 V. The transistor then goes into saturation. The transistor saturation may be defined as the point above which any increase in the base current does not increase the collector current significantly. In the satura tion, the collector current remains almost constant. If the collector-emitter saturation voltage is Vc£1..,,, the collector current is' _ Vee - VeE(sa1) 1cs Re

(4.14)

and tJ1c corresponding v3lue of ba.sc c urrent is

Ics las= -

13F

(4.15)

Normally. the circuit is designed so that 18 is higher than I BS· The ratio of I 8 to I as is called the overdrive facto r (ODF): ODF=~

l as

(4.16)

Copyrghtcd matcria

128

Chapter 4

Power Transistors

and the ratio of !cs to I 8 is called as forced 13, 13ror

-

- ~ Yoo -= +

O

lo

u Vo,

s

+ Basic structure (b) p-Channel depletion-lype MOSFET

+

Symbol

FIGURE 4.15

Depleiion-type MOSFET&

The two types of MOSFETs are (I) depletion MOSFETs, and (2) enhancement MOSFETs [HJ. An 11-channel depletion-type MOSFET is formed on a p-type silicon substrate as shown in Figure 4.15a, with two heavily doped 11+ silicon for low-resistance connections. The gate is isolated from the channel by a thin oxide layer. The three terminals are called gate, drai11, and source. The substrate is normally connected to the source. The gate-to-source voltage Yes could be either positive or negative. If Yes is negative. some of the electrons in the 11-channel area are repelled and a depletion region is created below the oxide layer, resulting in a narrower effective channel and a high resistance from the drain to source R 0 5. lf Ye s is made negative enough, the channel becomes completely depleted, offering a high value of Ros, and no current flows from the drain to source, Ios = 0. The value of Ye s when this happens is called pinchoff voltage Yr, On the other hand, Yes is made positive, the channel becomes wider, and / 05 increases due to reduction in Ros· With a p-channel depletion-type MOSFET, the polarities of Yos, los, and Yes arc reversed as shown in Figure 4.15b. An 11-channel enhancement-type MOSFET has no physical channel, as shown in Figure 4.16a. If YGs is positive, an induced voltage attracts the electrons from the

.

\

Copyrighlcd m~leria

4.3 Power MOSFETs

Met•I!bstrale

D Meta.I

RD

p-Type

0

139

substrate

+

D

Yoo

lo

s Oxide Basie structure (a) n-Channcl cnhancemenl-lypc MOSFET

D Mctnl

n-Type ,ub5tratc

0

Ll

s Oxide

Vn, +

s

Voo

+

Basic structure Symbol (b) p·Channcl cnhanccmenMypc MOSFET FIGURE 4.16

Enhanccmenl-lype MOSFETs.

p·subslrale and accumula1e them at the surface beneath the oxide layer. If VGs is greater than or equal to a value known as threshold voltage Vr, a sufficient number of electrons are accumulated 10 form a virtual n-on model

c c 1,.

I

C1,c

arlE

l1,c1IJJR

.......?

Ra

(I,.1 - l"'1)1Kq,

I

B

Ro B

11,.,t/lF

lh(1

E (b) De model

le E (c) Ebcrs-Moll model

FIGURE 4.38

PSpic:c BJT model

Copyrghlcd m~leria

4.9 SPICE Models

D

Dntin Ro

c..,

D

c,,,

Ro

+ VJd -

- vbd +

- Vw +

G

'•

Ros

Oa1c

t+

v ..

1-

B G

Bulk

'•

Ros l

- vbl + +

157

VP -

- Vm

B

+

Rs

c,,.

Cp

s (b) De model

c,. S

Source

( a) SPICE model FIGURE 4.39

PSpice n-channel MOSFET model.

•

of n-channel MOSFETs has the general form . M:JDEL MNA.liE ?MJS (Pl • Vl P2=V2 P3 =V3 . . . PN•VN)

and the statement for p-channel MOSFETs has the form . M)OEL MW.ME PMOS (Pl=\/1 P2=V2 P3=V3 ••• PN=VNJ

where MNAME is the model name. NMOS and PMOS are the type symbols of n-channel and p-cbannel MOSFETs. respectively. The parameters that affect the switching behavior of an MOSFET in power electronics are L, W, vro,KP, IS, CGSO, and CGDO. The symbol for an MOSFET is M. The name of MOSFETs must start with M and it takes the general form M

~m I L• > T or Lf >> R. In case of discontinuous load current, / 1 = 0 and Eq. (5.11) becomes i1(1) and Eq. (5.13) is valid for O :s t

E

R

(1 - e- •RIL)

:s 12 such that i 2(1 = 12

Because 1

= v:' -

=

L

R In

(

l

+

12) = / 3 = / 1 =

0, which gives

R/2) E

= kT, we get i1(1)

= 12 = V, ;

E

(1 - e-t,)

which after substituting for Ii becomes

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174

Chapter 5

Dc-Oc Converters

Condition fo r continuous current: For / 1

-"

0, Eq. (5.17) gives

- 1 _ E) ( e-t' e' - 1 V,

"" 0

which gives the value of the load electromotive force (emf) ratio x = EIV, as E V,

x= - s

e-t'-1

(5.23)

e'- 1

Example 5.2 Finding the Currents of a De Converter with an RL Load A convener is feeding an RL load as shown in Figure S.3 with V, = 220 V, R = Sn , l = 7.S mH, / • 1 kHz. k • O.S. and E • 0 V. Calculate (a) the minimum instantaneous load cunent J,. {b) the peak instantaneous load current / 2, (c) the maximum peak-to-peak load ripple current, (d ) the average value of load current /~ (e) the rms load current /0 , ( [ ) the effective input resistance R1 seen by the source, (g) the nns chopper current JR , and (b) the critical value or the load inductance for continuous load current. Use PSpice to plot the load current, the supply current, and the freewheeling diode currenL

Solution V, = 220 V, R = S 0 , L = 7.S mH, E = 0 V, k = 0.5, and f = 1000 Hz. From Eq. (S.15), / 2 = 0.7165/1 + 12.473 and from Eq. (S.16), / 1 = 0.7165/2 + 0. Solving these two equations yields / 1 • 18.37 A. b. ,, • 25.63 A. c. A/ = / 2 - / 1 = 25.63 - 18.37 = 7.26 A. From Eq. (5.21), A/mu Eq. (S.22) gives the approximate value, Al ,..,. = 7.33 A .

L

= 7.26 A

and

d. The average load cuncnt is. approximately, I,= /2 + /1 = 25.63

2

+ 18.37 = 22 A 2

e. Assuming that the load current rises linearly from / 1 to I,. the instantaneous load cur·

rent can be expressed as .

I

'1 -

Alt I+

kT

for O <

t

< kT

The rrns value of load current can be found from

!."

1 o lo= ( kT

i} dt

)'n = [11 + (I2 -3

1

I I)

+ /1(/2 -

/1) ] "'

(5.24) =

f.

22.1 A

The average source current

I, • kl, • O.S x 22 • 11 A and the effective input resistance R1 = V,JI,

= 220111 = 20 n.

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5.3 Step-Dow n Converter wit h RL l oad

175

30A -,------- --------- --- ---- ----- ------------------ :- --I - -, J _J

,.. I

'

I I

SEL>> :

OA

--- -------------------- ----- --- -

i:_oJ l(R)

~5..155

,\I

-

9.50901,

,\2

-

901lXlni.

17.qlz =

fL

(5.108)

V.

2 cl

or

t::. '2 = -

V0 (l - k} f~

kV,

(5.109)

= -

fL2

When transistor Q, is off. the energy transfer cap'acitor C 1 is charged by the input cur· rent for time t = 12 • The average charging current for C 1 is 1, 1 = I, and the peak-topeak ripple voltage of the capacitor C1 is I

t::,. V.:i = C1

(''

lo

1' ' dt =

l

(''

c,lo 1' tit =

l,t

c.2

(5.110)

Equation (5.102) gives 12 = V,/l(V, - V,)fl and Eq. (5.110} becomes (5.111) or (5.112) If we assume that the load current ripple t,./0 is negligible, l>iu = M a . The average charging current of C 2, which nows for time T/2, is 1, 2 = l>lz/4 and the peak-to-peak ripple voltage of capacitor C2 is · l>Vc2 = -

I

1TIZ fc2 dt = - I 1Tf2-!!/,· cit = -t::,.fi-

C2 o

Cz o

4

8fC2

(5.113)

or (5.114)

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5.8 Switching-Mode Regulators

203

Condition for continuous inductor current and capacitor voltage. If h, is the average current of inductor Li, the inductor ripple current 1H 1 = 2/u, Using Eqs. (5.103) and (5.106). we get kVs -fL = 2fi1 = 2/s = 1

2k/0 - 1- k

=2

(

k

2

) Vs 1- k R

--

which gives the critical value of the inductor Ltt as ·

Ltt

=

L,

If hz is_the average current of inductor Using Eqs. (5.100) and (5.109), we get kVs

-f lz - =

2ft2

=

(l - k )1R 2kf

Lz, the

(5.115)

inductor ripple current /J./1 = 2lu.

2v. 2kVs = 21. = -R- = (1 - k)R

which gives the critical value of the inductor L a as

L,2 = L2 =

( 1 - k)R / 2

(5.116)

U V. 1 is the average capacitor voltage, the capacitor ripple voltage 6 V, 1 = 2V0 • Using 6 Vtt = 2 V0 into Eq. (5.112), we get I ( I - k)

s

JC,

= 2V = 21 R

•

•

which, after substituting for Is, gives the critical value of the capacitor Cc1 as

k Cr1 = C, = 2/R

(5.117)

If V,2 is the average capacitor voltage, the capacitor ripple voltage 6 Vc2 = 2V0 • Using Eq. (5.100) and (5.114), we get kVs 8C2 Lif2

which, arter substituting for C,2 as

=

zv.

=

0

2kVs 1- k

Lz from Eq. (5 .11 6).gives the critical value of the capacitor Ca = Ci= -

I

8/R

(5.118)

The Ctik regulator is based on the capacitor energy transfer. As a result, the input current is continuous. The circuit has low switching losses and has high efficiency. When transistor Q1 is turned on, it has to carry the currents of inductors L 1 and Lz. As a result a high peak current flows through transistor Q 1• Because the capacitor provides

Copynghlcd m~leria

204

Chapter 5

Dc-Oc Converters

the energy transfer, the ripple current of the capacitor C 1 is also high. This ci.r cuit also requires an additional capacitor and inductor. ·

Example 5.8 Finding the Currents and Voltages In the Cuk Regulator The inp111 vollage or a C~k convcrlcr in Figure S.19a, V, a 12 V. lbe du1y cycle k = 0.25 and 1he . switching frequency is 25 kHt. The filter inductance is L:, = 150 µHand filter capaci1ance is Ci = 220 µF. lbe energy iransfer capaciiancc is C 1 = 200 µF and inductance L 1 a 180 µH. The average load current is I. = 1.25 A. Determine (a) the average output voltage V,; (b) the average input currcnl I,; (c) the peak·to-peak ripple current of inductor Li, /J./1; (d) the peak-lo· peak ripple voltage or capacitor C 1, d v,,; (e) the peak-to-peak ripple current or inductor Li. dfi; (!) the pcak-10-pcak ripple voltage of capacitor C1, d V, 1; and (g) the peak current or the lransistor Ip·

Solution V, = 12 V, k = 0.25. /, C, = 220 µ.F.

= 1.25 A .f = 25 kHz. L

1

= 180 µH, C1 = 200 µF. L1

= 150 µ.H,

and

From Eq. (5.100). V0 • - 0.25 X 12/(1 - 0.25) = - 4 V. From Eq. (5.103). /, = 1.25 X 0.25/( 1 - 0.25) a 0.42 A. From Eq. (5.106). d/ 1 e 12 X 0.25/(25.000 X 180 X 10...) = 0.67 A. From Eq. (5.112).dV,i a 0.42 x (I - 0.25)/(25.000 x 200 x 10-) = 63mV. c. From Eq. (5. 109), d/2 • 0.25 x 12/(25.000 x 150 x 10... ) = 0.8 A. f. From E