Converters, Applications,
`and Design
`
`SECOND EDITION
`
`NED MOHAN
`Depariment of Electrical Engineering
`University of Minnesota
`Minneapolis, Minnesota
`
`TORE M. UNDELAND
`Faculty of Electrical Engineering and Computer Science
`Norwegian Institute of Technology
`Trondheim, Norway
`
`WILLIAM P. ROBBINS
`Department of Electrical Engineering
`University of Minnesota
`Minneapolis, Minnesota
`
`
`
`JOHN WILEY & SONS, INC.
`New York Chichester Brisbane Toronto Singapore
`
`Page 1 of 104
`
`BMW EXHIBIT 1008
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`Page 1 of 104
`
`BMW EXHIBIT 1008
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`
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`
`Copyright © 1989, 1995 by John Wiley & Sons, Inc.
`
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`Reproduction or translation of any part of this work beyond that permitted by Sections 107
`and 108 of the 1976 United States Copyright Act without the permission of the copyright owner
`is unlawful. Requests for permission or further information should be addressed to the
`Permissions Department, John Wiley & Sons, Inc.
`
`Library of Congress Cataloging in Publication Data:
`
`Mohan, Ned.
`Power electronics : converters, applications, and design / Ned
`Mohan, Tore M. Undeland, William P. Robbins,— 2nd ed.
`.
`om.
`
`Includes bibliographical references and indexes.
`ISBN 0-471-58408-8 (cloth)
`3. Power
`1. Power electronics.
`2. Electric current converters.
`semiconductors.
`I. Undeland, Tore M.
`TU. Robbins, William P.
`itl. Title.
`TK7881.15.M64 1995
`621.317—dc20
`
`94-21158
`CIP
`
`Printed in the United States of America.
`
`100987654321
`
`Page 2 of 104
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`

`

`
`
` SONTENTS
`
`
`
`PART 1
`
`INTRODUCTION
`
`Chapter 1 Power Electronic Systems
`1-1 Introduction
`1-2 Power Electronics versus Linear Electronics
`1-3 Scope and Applications
`1-4 Classification of Power Processors and Converters
`1-5 About the Text
`1-6 Interdisciplinary Nature of Power Electronics
`1-7 Convention of Symbols Used
`
`Chapter 2 Overview of Power Semiconductor Switches
`2-1 Introduction
`
`16
`
`2-4 Desired Characteristics in Controllable Switches
`2-5 Bipolar Junction Transistors and Monolithic Darlingtons
`2-6 Metal—Oxide— Semiconductor Field Effect Transistors
`2-7 Gate-Turn-Off Thyristors
`2-8 Insulated Gate Bipolar Transistors
`2-9 MOS-Controlled Thyristors
`2-10 Comparison of Controllable Switches
`2-11 Drive and Snubber Circuits
`2-12 Justification for Using Idealized Device Characteristics
`
`Chapter 3. Review of Basic Electrical and Magnetic Circuit Concepts
`3-1 Introduction
`3.2 Electric Circuits
`3-3 Magnetic Circuits
`
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`
`ix
`
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`

`

`x
`
`CONTENTS
`
`Chapter 4 Computer Simulation of Power Electronic Converters
`and Systems
`4-1 Introduction
`61
`4-2 Challenges in Computer Simulation
`4-3 Simulation Process
`62
`64
`4.4 Mechanics of Simulation
`4-5 Solution Techniques for Time-Domain Analysis
`4-6 Widely Used, Circuit-Oriented Simulators
`69
`4-7 Equation Solvers
`72
`Summary
`74
`Problems
`74
`References
`75
`
`62
`
`65
`
`PART 2 GENERIC POWER ELECTRONIC CIRCUITS
`Chapter 5 Line-Frequency Diode Rectifiers: Line-Frequency ac >
`Uncontrolled de
`5-1 Introduction
`79
`80
`5-2 Basic Rectifier Concepts
`5-3 Single-Phase Diode Bridge Rectifiers
`82
`100
`5-4 Voltage-Doubler (Single-Phase) Rectifiers
`5-5 Effect of Single-Phase Rectifiers on Neutral Currents in Three-Phase,
`Four-Wire Systems
`101
`103
`5-6 Three-Phase, Full-Bridge Rectifiers
`112
`5-7 Comparison of Single-Phase and Three-Phase Rectifiers
`5.8 Inrush Current and Overvoltages at Turn-On
`112
`5-9 Concerns and Remedies for Line-Current Harmonics and Low Power
`Factor
`113
`Summary
`i13
`Problems
`il4
`References
`116
`Appendix
`117
`
`122
`
`Chapter 6 Line-Frequency Phase-Controlled Rectifiers and
`Inverters: Line-Frequency ac <> Controlled de
`6-1 Introduction
`121
`6-2 Thyristor Circuits and Their Control
`6-3 Single-Phase Converters
`126
`6-4 Three-Phase Converters
`138
`6-5 Other Three-Phase Converters
`Summary
`153
`Problems
`154
`References
`137
`Appendix
`158
`Chapter 7 de-de Switch-Mode Converters
`7-1 Introduction
`161
`7-2 Control of dc—de Converters
`
`153
`
`162
`
`ol
`
`T?
`
`79
`
`121
`
`161
`
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`

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`
`
`
`CONTENTS
`
`xi
`
`7-3 Step-Down (Buck) Converter
`7-4 Step-Up (Boost) Converter
`178
`7-5 Buck— Boost Converter
`184
`7-6 Caik de—de Converter
`7-7 Full Bridge dc—dce Converter
`7-8 dc—de Converter Comparison
`Summary
`196
`Problems
`197
`References
`199
`
`164
`172
`
`188
`195
`
`Chapter 8 Switch-Mode dce—ac Inverters: de ~ Sinusoidal ac
`8-1 Introduction
`200
`8-2 Basic Concepts of Switch-Mode Inverters
`8-3 Single-Phase Inverters
`211
`8-4 Three-Phase Inverters
`225
`8-5 Effect of Blanking Time on Output Voltage in PWM Inverters
`8-6 Other Inverter Switching Schemes
`239
`8-7 Rectifier Mode of Operation
`243
`Summary
`244
`Problems
`246
`References
`248
`
`202
`
`236
`
`200
`
`249
`
`299
`
`301
`
`Chapter 9 Resonant Converters: Zero-Voltage and/or Zero-Current
`Switchings
`9-1 Introduction
`249
`9-2 Classification of Resonant Converters
`9-3 Basic Resonant Circuit Concepts
`9-4 Load-Resonant Converters
`258
`9-5 Resonant-Switch Converters
`273
`9-6 Zero-Voltage-Switching, Clamped-Voltage Topologies
`9-7 Resonant-dc-Link Inverters with Zero-Voltage Switchings
`9-8 High-Frequency-Link Integral-Half-Cycle Converters
`Summary
`291
`Problems
`291
`References
`295
`
`252
`
`253
`
`280
`287
`
`289
`
`PART 3 POWER SUPPLY APPLICATIONS
`
`Chapter 10 Switching de Power Supplies
`10-1 Introduction
`301
`301
`10-2 Linear Power Supplies
`10-3 Overview of Switching Power Supplies
`10-4 dce—de Converters with Electrical Isolation
`10-5 Control of Switch-Mode de Power Supplies
`10-6 Power Supply Protection
`341
`344
`10-7 Electrical Isolation in the Feedback Loop
`10-8 Designing to Meet the Power Supply Specifications
`Summary
`349
`
`302
`304
`322
`
`346
`
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`

`

`xii
`
`CONTENTS
`
`Problems
`References
`
`349
`351
`
`Chapter 11 Power Conditioners and Uninterruptible Power
`Supplies
`11-1 Introduction
`354
`11-2 Power Line Disturbances
`11-3 Power Conditioners
`357
`11-4 Uninterruptible Power Supplies (UPSs)
`Summary
`363
`Problems
`363
`References
`364
`
`358
`
`354
`
`PART 4 MOTOR DRIVE APPLICATIONS
`Chapter 12
`Introduction to Motor Drives
`12-1 Introduction
`367
`12-2 Criteria for Selecting Drive Components
`Summary
`375
`Problems
`376
`References
`376
`
`368
`
`de Motor Drives
`Chapter 13
`13-1 Introduction
`377
`377
`13-2 Equivalent Circuit of dc Motors
`380
`13-3 Permanent-Magnet dc Motors
`13-4 de Motors with a Separately Excited Field Winding
`13-5 Effect of Armature Current Waveform
`382
`13-6 dc Servo Drives
`383
`13-7 Adjustable-Speed de Drives
`Summary
`396
`Problems
`396
`References
`398
`
`39]
`
`381
`
`Induction Motor Drives
`Chapter 14
`14-1 Introduction
`399
`400
`14-2 Basic Principles of Induction Motor Operation
`14-3 Induction Motor Characteristics at Rated (Line) Frequency
`and Rated Voltage
`405
`14-4 Speed Control by Varying Stator Frequency and Voltage
`14-5 Impact of Nonsinusoidal Excitation on Induction Motors
`14-6 Variable-Frequency Converter Classifications
`418
`14-7 Variable-Frequency PWM-VSI Drives
`419
`14-8 Variable-Frequency Square-Wave VSI Drives
`
`14-9 Variable-Frequency CSI Drives
`426
`
`14-10 Comparison of Variable-Frequency Drives
`
`
`427
`
`425
`
`406
`415
`
`304
`
`365
`367
`
`377
`
`399
`
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`
`

`

`CONTENTS=xiii
`
`428
`14-11 Line-Frequency Variable-Voltage Drives
`14-12 Reduced Voltage Starting (‘Soft Start’’) of Induction Motors
`14-13 Speed Control by Static Slip Power Recovery
`431
`Summary
`432
`Problems
`433
`References
`434
`
`430
`
`Chapter 15 Synchronous Motor Drives
`15-1 Introduction
`435
`435
`15-2 Basic Principles of Synchronous Motor Operation
`15-3 Synchronous Servomotor Drives with Sinusoidal Waveforms
`15-4 Synchronous Servomotor Drives with Trapezoidal Waveforms
`15-5 Load-Commutated Inverter Drives
`442
`15-6 Cycloconverters
`445
`Summary
`445
`Problems
`446
`References
`447
`
`439
`440
`
`PART 5 OTHER APPLICATIONS
`Chapter 16 Residential and Industrial Applications
`16-1 Introduction
`451
`16-2 Residential Applications
`16-3 Industrial Applications
`Summary
`459
`Problems
`459
`References
`459
`
`451
`455
`
`Chapter 17 Electric Utility Applications
`17-1 Introduction
`460
`17-2 High-voltage dc Transmission
`17-3 Static var Compensators
`471
`17-4 Interconnection of Renewable Energy Sources and Energy Storage
`Systems to the Utility Grid
`475
`17-5 Active Filters
`480
`Summary
`Problems
`References
`
`450
`481
`482
`
`460
`
`Chapter 18 Optimizing the Utility Interface with Power
`Electronic Systems
`18-1 Introduction
`483
`18-2 Generation of Current Harmonics
`485
`18-3 Current Harmonics and Power Factor
`18-4 Harmonic Standards and Recommended Practices
`18-5 Need for Improved Utility Interface
`487
`
`485
`
`484
`
`435
`
`449
`454
`
`460
`
`433
`
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`

`xiv
`
`CONTENTS
`
`18-6 Improved Single-Phase Utility Interface
`18-7 Improved Three-Phase Utility Interface
`18-8 Electromagnetic Interference
`500
`Summary
`502
`Problems
`503
`References
`503
`
`488
`498
`
`PART 6 SEMICONDUCTOR DEVICES
`
`Chapter 19 Basic Semiconductor Physics
`19-1 Introduction
`507
`19-2 Conduction Processes in Semiconductors
`19-3 pn Junctions
`513
`19-4 Charge Control Description of pn-Junction Operation
`19-5 Avalanche Breakdown
`520
`Summary
`522
`Problems
`522
`References
`523
`
`507
`
`518
`
`Chapter 20 Power Diodes
`20-1 Introduction
`524
`20-2 Basic Structure and J—V Characteristics
`20-3 Breakdown Voltage Considerations
`20-4 On-State Losses
`531
`20-5 Switching Characteristics
`20-6 Schottky Diodes
`539
`Summary
`543
`Problems
`543
`References
`545
`
`535
`
`$24
`
`526
`
`546
`
`Chapter 21 Bipolar Junction Transistors
`21-1 Introduction
`$46
`21-2 Vertical Power Transistor Structures
`91-3 I-V Characteristics
`548
`21-4 Physics of BJT Operation
`21-5 Switching Characteristics
`562
`21-6 Breakdown Voltages
`
`563
`21-7 Second Breakdown
`565
`21-8 On-State Losses
`21-9 Safe Operating Areas
`Summary
`568
`Problems
`569
`References
`570
`
`550
`556
`
`567
`
`Chapter 22 Power MOSFETs
`22-1 Introduction
`571
`22-2 Basic Structure
`571
`
`Page 8 of 104
`
`505
`
`507
`
`524
`
`546
`
`571
`
`Page 8 of 104
`
`

`

`CONTENTS
`
`XV
`
`596
`
`613
`
`626
`
`641
`
`374
`99-3 [-V Characteristics
`22-4 Physics of Device Operation
`581
`22-5 Switching Characteristics
`22-6 Operating Limitations and Safe Operating Areas
`Summary
`593
`Problems
`594
`References
`595
`
`576
`
`587
`
`Chapter 23 Thyristers
`23-1 Introduction
`596
`23-2 Basic Structure
`596
`597
`23-3 I-V Characteristics
`599
`23-4 Physics of Device Operation
`603
`23-5 Switching Characteristics
`23-6 Methods of Improving di/dt and dv/dt Ratings
`Summary
`610
`Problems
`6ll
`References
`612
`
`608
`
`Chapter 24 Gate Turn-Off Thyristors
`24-1 Introduction
`613
`24-2 Basic Structure and [-V Characteristics
`24-3 Physics of Turn-Off Operation
`614
`24-4 GTO Switching Characteristics
`616
`24-5 Overcurrent Protection of GTOs
`623
`Summary
`624
`Problems
`624
`References
`625
`
`613
`
`Insulated Gate Bipolar Transistors
`Chapter 25
`25-1 Introduction
`626
`25-2 Basic Structure
`626
`628
`25-3 [-V Characteristics
`25-4 Physics of Device Operation
`
`25-5 Latchup in IGBTs
`631
`25-6 Switching Characteristics
`25-7 Device Limits and SOAs
`Summary
`639
`Problems
`639
`References
`640
`
`634
`637
`
`629
`
`Chapter 26 Emerging Devices and Circuits
`26-1 Introduction
`641
`26-2 Power Junction Field Effect Transistors
`26-3 Field-Controlled Thyristor
`646
`96-4 JFET-Based Devices versus Other Power Devices
`26-5 MOS-Controlled Thyristors
`649
`
`641
`
`648
`
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`
`

`

`xvi
`
`CONTENTS
`
`656
`26-6 Power Integrated Circuits
`26-7 New Semiconductor Materials for Power Devices
`Summary
`664
`Problems
`665
`References
`666
`
`661
`
`669
`
`680
`
`691
`
`PART 7 PRACTICAL CONVERTER DESIGN
`CONSIDERATIONS
`Chapter 27 SnubberCircuits
`77-1 Function and Types of Snubber Circuits
`27-2 Diode Snubbers
`670
`678
`27-3 Snuber Circuits for Thyristors
`27-4 Need for Snubbers with Transistors
`27-5 Turn-Off Snubber
`682
`27-6 Overvoltage Snubber
`686
`688
`21-7 Turn-On Snubber
`27-8 Snubbers for Bridge Circuit Configurations
`97-9 GTO Snubber Considerations
`692
`Summary
`693
`Problems
`694
`References
`695
`Chapter 28 Gate and Base Drive Circuits
`98-1 Preliminary Design Considerations
`696
`28-2 de-Coupled Drive Circuits
`697
`28-3 Electrically Isolated Drive Circuits
`98-4 Cascode-Connected Drive Circuits
`28-5 Thyristor Drive Circuits
`712
`28-6 Power Device Protection in Drive Circuits
`98-7 Circuit Layout Considerations
`722
`Summary
`728
`Problems
`729
`References
`729
`Chapter 29 Component Temperature Control and Heat Sinks
`29-1 Control of Semiconductor Device Temperatures
`730
`29-2. Heat Transfer by Conduction
`731
`29-3 Heat Sinks
`737
`29-4 Heat Transfer by Radiation and Convection
`Summary
`742
`Problems
`743
`References
`743
`Chapter 30 Design of Magnetic Components
`30-1 Magnetic Materials and Cores
`744
`30-2 Copper Windings
`752
`
`703
`710
`
`717
`
`739
`
`667
`669
`
`696
`
`730
`
`744
`
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`
`

`

`756
`
`754
`30-3 Thermal Considerations
`30-4 Analysis of a Specific Inductor Design
`30-5 Inductor Design Procedures
`760
`30-6 Analysis of a Specific Transformer Design
`30-7 Eddy Currents
`771
`7719
`30-8 Transformer Leakage Inductance
`780
`30-9 Transformer Design Procedure
`30-10 Comparison of Transformer and Inductor Sizes
`Summary
`789
`Problems
`790
`References
`792
`
`767
`
`CONTENTS Vii
`
`789
`
`Index
`
`793
`
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`

`

`
`
`
`CHAPTER10
`
`10-1
`
`
`
`SWITCHING dePOWER
`SUPPLIES
`
`
`
`INTRODUCTION
`
`Regulated de power supplies are needed for most analog and digital electronic systems.
`Most power supplies are designed to meet someorall of the following requirements:
`¢ Regulated output. The output voltage must be held constant within a specified
`tolerance for changes within a specified range in the input voltage and the output
`loading.
`° Isolation. The output may be required to be electrically isolated from the input.
`e Multiple outputs. There may be multiple outputs (positive and negative) that may
`differ in their voltage and currentratings. Such outputs may be isolated from each
`other.
`
`In addition to these requirements, common goals are to reduce power supply size and
`weight and improvetheir efficiency. Traditionally, linear power supplies have been used.
`However, advances in the semiconductor technology have lead to switching power sup-
`plies, which are smaller and much moreefficient compared to linear power supplies. The
`cost comparison betweenlinear and switching supplies depends on the power rating.
`
`10-2
`
`LINEAR POWER SUPPLIES
`
`To appreciate the advantages of the switching supplies, it is desirable first to consider the
`linear power supplies. Figure 10-la shows the schematic of a linear supply. in order to
`provide electrical isolation between the input and the output and to deliver the output in
`the desired voltage range, a 60-Hz transformer is needed. A transistor is connected in
`series that operates in its active region.
`Comparing V, with a reference voltage V,.., the control circuit in Fig. 10-1a adjusts
`the transistor base current such that V, (=vgz — vcg) equals V,,.¢. The transistor in a linear
`supply acts as an adjustable resistor where the voltage difference vg — V,, between the
`input and the desired output voltage appears across the transistor and causes power losses
`in it. For a given range of 60 Hz ac input voltage, the rectified andfiltered output v(t) may
`be as shownin Fig. 10-1b. To minimize the transistor powerlosses, the transformer turns
`ratio should be carefully selected such that Vzmin in Fig. 10-15 is greater than V, but does
`not exceed V, by a large margin.
`
`301
`
`
`
`Page 12 of 104
`
`Page 12 of 104
`
`

`

`302
`
`CHAPTER 10
`
`SWITCHING de POWER SUPPLIES
`
`+
`
`vce = ¥g—- Vo
`
`COMMi
`
`—
`
`Jo
`
`
`
`1-¢ or 3-9
`
`
`
`transformer
`Rectifier
`Filter
`capacitor
`
`fa}
`
`ug (t)
`
`vg range
`
`
`
`Figure 10-1 Linear powersupply: (a) schematic; (b) selection of transformer turns ratio
`so that Vymin > VM by a small margin.
`
`two major shortcomings of a linear power
`
`The preceding discussion points out
`supply:
`1. A low-frequency (60-Hz) transformeris required. Such transformers are larger in
`size and weight compared to high-frequency transformers.
`2. Thetransistor operates in its active region, incurring a significant amountof power
`loss. Therefore, the overall efficiencies of linear power supplies are usually in a
`range of 30-60%.
`Onthe positive side, these supplies utilize simple circuitry and therefore may cost less in
`small powerratings (<25 W). Also, these supplies do not produce large EMI with other
`equipment.
`
`10-3
`
`OVERVIEW OF SWITCHING POWER SUPPLIES
`As opposed to linear power supplies, in switching power supplies, the transformation of
`dc voltage from one level to another is accomplished by using de-to-de converter circuits
`(or those derived from them), which were discussed in Chapters 7 and 9. These circuits
`employ solid-state devices (transistors, MOSFETs,etc.), which operate as a switch: either
`completely off or completely on. Since the power devices are not required to operate in
`their active region, this mode of operation results in a lower powerdissipation. Increased
`switching speeds, higher voltage and current ratings, and a relatively lower cost of these
`
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`Page 13 of 104
`
`

`

`
`
`10-3 OVERVIEW OF SWITCHING POWER SUPPLIES
`
`303
`
`devices are the factors that have contributed to the emergence of switching power sup-
`plies.
`Figure 10-2 shows a switching supply with electrical isolation in a simplified block
`diagram form. The input ac voltageis rectified into an unregulated dc voltage by means
`of a dioderectifier of the type discussed in Chapter 5. It should be noted that an EMIfilter,
`as discussed in Chapter 18, is used at the input to prevent the conducted EMI. The de—de
`converter block in Fig. 10-2 converts the input de voltage from one level to another de
`level. This is accomplished by high-frequency switching, which produces high-frequency
`ac across the isolation transformer. The secondary output of the transformeris rectified
`andfiltered to produce V,. The output of the de supply in Fig. 10-2 is regulated by means
`of a feedback control that employs a PWMcontroller as discussed in Chapter 7, where the
`control voltage is compared with a sawtooth waveform at the switching frequency. The
`electrical isolation in the feedback loop is providedeither through an isolation transformer
`as shown or through an optocoupler.
`In many applications, multiple outputs (both positive and negative) are required.
`These outputs may be required to be electrically isolated from each other, depending on
`the application. Figure 10-3 shows the block diagram of a switching supply where only
`one output V,, is regulated and the other two are unregulated. If V,. and/or V,3 needs to
`be regulated, then linear regulator(s) can be used to regulate the other output(s).
`Two major advantages of switching power supplies over linear power supplies are
`now apparent. These are as follows:
`
`° The switching elements (powertransistors or MOSFETs)operate as a switch: either
`completely off or completely on. By avoiding their operation in their active region,
`a significant reduction in power losses is achieved. This results in a higher energy
`efficiency in a 70-90% range. Moreover,a transistor operating in on/off mode has
`a much larger power-handling capability comparedto its linear mode.
`
`dc-dc conversion with isolation
`~T
`
`Isolation boundary
`
`|
`
`
`de
`de
`
`
`
`Rectifier|(unregulated) Rectifier regulated
`sei
`EME
`1. -
`+
`+
`
`Filter
`Filter
`Filter
`
`
`
`
`
`
`
`
`
`
`
`
`
`Base/gate Drive
`Circuit
`
`
`Feedback
`
`Figure 10-2 Schematic of a switch-mode de power supply.
`
`
`
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`Page 14 of 104
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`

`

`304
`
`CHAPTER 10
`
`SWITCHING de POWER SUPPLIES
`
`Voi, ref
`
`.
`
`Feed back
`
`- __
`
`d
`=
`
`(unregulated)
`ic
`
`(unregulated)
`
`
`
`( us
`regulated
`
`)
`
`.
`
`Vo2
`‘(unregulated)
`
`:
`
`Vo3
`
`Figure 10-3 Multiple outputs.
`
`° Since a high-frequency isolation transformeris used (as compared to a 50- or 60-Hz
`transformer in a linear power supply), the size and weight of switching supplies can
`be significantly reduced.
`On the negative side, switching supplies are more complex, and proper measures
`must be taken to prevent EMI due to high-frequency switchings.
`The above-mentioned advantages of switching supplies (over linear supplies) out-
`weigh their shortcomings above a certain power rating. The power rating where this
`breakover occurs is steadily decreasing with time due to advances in semiconductor
`technology.
`Switching de power supplies, in general, utilize modifications of the following two
`classes of converter topologies:
`1. Switch-mode dc—de converters, discussed in Chapter 7, where the switches op-
`erate in a switch mode.
`2. Resonant converters, discussed in Chapter 9, which utilize zero-voltage and/or
`zero-current switchings.
`In this chapter,
`the switch-mode converter topologies are used to described the
`operation of switching power supplies. Many of the basic principles discussed in this
`chapter also apply to the switching power supplies with resonant converters.
`
`10-4
`
`de-de CONVERTERS WITH ELECTRICAL ISOLATION
`
`INTRODUCTION TO de—de CONVERTERS WITH ISOLATION
`10-4-1
`As seen by the block diagram of Fig. 10-2, the electrical isolation in switching de power
`supplies is provided by a high-frequency isolation transformer. Figure 10-4a shows a
`
`typical transformer core characteristic in termsof its B-H (hysteresis) loop. Here B,, is the
`maximum flux density beyond which saturation occurs and B, is the remnantflux density.
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`10-4
`
`de—-de CONVERTERS WITH ELECTRICAL ISOLATION
`
`
`
`305
`
`
`
`(b)
`
`fe)
`
`Figure 10-4 Transformer representation: (a) typical B—H loop of transformer core,
`(b) two-winding transformer; (c) equivalent circuit.
`
`Various types of de—de converters (with isolation) can be divided into two basic cate-
`gories, based on the way they utilize the transformer core:
`1. Unidirectional core excitation where only the positive part (quadrant 1) of the B-H
`loop is used
`2. Bidirectional core excitation where both the positive (quadrant 1) and the negative
`(quadrant 3) parts of the B—H loopare utilized alternatively
`
`10-4-1-1 Unidirectional Core Excitation
`Some ofthe de—dce converters (without isolation) discussed in Chapter 7 can be modified
`to provide electrical
`isolation by means of unidirectional core excitation. Two such
`modifications are as follows:
`
`® Flyback converter (derived from buck~ boost converter)
`® Forward converter (derived from step-down converter)
`The output voltage of these converters is regulated by meansofthe PWMswitching
`scheme discussed in Chapter 7.
`
`10-4-1-2 Bidirectional Core Excitation
`Toprovide electrical isolation by meansof bidirectional core excitation, the single-phase
`switch-modeinverter topologies of Chapter 8 can be used to produce a square-waveac at
`the input of the high-frequency isolation transformer in Fig. 10-2. We will discuss the
`following inverter topologies, which can constitute a switching de power supply:
`
`* Push-pull
`* Half bridge
`¢ Full bridge
`
`
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`306
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`CHAPTER 10
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`SWITCHING de POWER SUPPLIES
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`As in Chapters 7 and 8, for analyzing the following circuits, the switches are treated
`as being ideal and the powerlossesin the inductive, capacitive, and transformer elements
`are neglected. Some ofthese losses limit the operational capabilities of these circuits and
`are discussed separately.
`All of the circuits are analyzed under a steady-state operating condition, and the filter
`capacitor at the output is assumed to be so large (as in Chapter 7) as to allow the
`assumption that the output voltage v,(2) ~ V, (i.e., essentially a pure dc). The analysis is
`presented only for the continuous-conduction mode, and the analysis of the discontinuous-
`conduction modeis left as an exercise.
`
`Isolation Transformer Representation
`10-4-1-3
`A high-frequency transformer is required to provide electrical isolation. Neglecting the
`losses in the transformer of Fig. 10-4b, an approximate equivalent circuit for a two-
`winding transformer is redrawn in Fig. 10-4c, where N,: Nis the transformer winding
`turns ratio, L,, is the magnetizing inductance referred to the primary side, and L;, and Ly
`are the leakage inductances. In the ideal transformer, v/v. = N,/N2 and Nyi, = Noio.
`In a switch-mode de—de converter, it is desirable to minimize the leakage induc-
`tances L,, and Ly by providing a tight magnetic coupling between the two windings. The
`energy associated with the leakage inductances has to be absorbed by the switching
`elements and their snubbercircuits, thus clearly indicating a need to minimize the leakage
`inductances. Similarly, in a switch-mode dc—dce converter, it is desirable to make the
`magnetizing inductanceL,, in Fig. 10-4c as high as possible to minimize the magnetizing
`currenti,, that flows through the switches and thus increases their current ratings.
`It is important to consider the effect of the transformer leakage inductancesin switch
`selection and snubber design. However, these inductances have a minor effect on the
`converter voltage transfer characteristics and therefore have been neglected in the con-
`verter analysis to follow.
`In one of the converter topologies to be discussed, called the flyback converter, the
`transformeris in fact intended to be a two-winding inductor, which has dual functions of
`providing energy storage as in an inductor andelectrical isolation as in a transformer.
`Therefore, the previous comments to make L,, high do not apply to this topology. How-
`ever, the simplified transformer equivalentcircuit canstill be used for analysis purposes.
`The transformer design considerations in resonant power supplies are different than
`the ones discussed before for switch-mode power supplies. There, the leakage inductances
`and/or the magnetizing inductance may in fact be utilized to provide zero-voltage and/or
`zero-current switchings.
`
`19-4-1-4 Control of dc~de Converters with Isolation
`In the single-switch topologies like the flyback and the forward converters, the output
`voltage V, for a given input V, is controlled by PWM in a mannersimilar to that used for
`their nonisolated counterparts discussed in Chapter 7.
`In the push— pull, half-bridge, and full-bridge de—dc converters, where the converter
`output is rectified to produce a dc output, the dc output voltage V, is controlled by using
`the PWM scheme shownin Fig. 10-5, which controls the interval A during which all the
`switches are off simultaneously. This is unlike the PWM schemes used in Chapter 7 to
`control full-bridge de—de converters and in Chapter 8 to control single-phase dc-to-ac
`inverters.
`
`Page 17 of 104
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`10-4
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`de—-de CONVERTERS WITH ELECTRICAL ISOLATION
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`307
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`
` BBEVOA[04]UCDaseyYOAyLoopres
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`aspig-tin4aSpiiq-HeHlind-ysng
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`Page 18 of 104
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`aBpligjing
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`CHAPTER 10
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`SWITCHING de POWER SUPPLIES
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`(a}
`
`(b}
`
`Figure 10-6 Flyback converter.
`
`10-4-2 FLYBACK.CONVERTERS (DERIVED FROM
`BUCK—BOOST CONVERTERS)
`Flyback converters are derived from the buck—boost converter discussed in Chapter 7 and
`redrawn in Fig. 10-6a. By placing a second winding on the inductor, it is possible to
`achieve electrical isolation, as shown in Fig. 10-60.
`Figure 10-7a shows the converter circuit where the two-winding inductor is repre-
`sented by its approximate equivalent circuit. When the switch is on, due to the winding
`polarities, the diode D in Fig. 10-7a becomes reverse biased. The continuous-current-
`conduction mode in a buck—boost converter corresponds to an incomplete demagnetiza-
`tion of the inductor core in the flyback converter. Therefore, as shown by the waveforms
`in Fig. 10-8, the inductor core flux increaseslinearly from its initial value (0), which is
`finite and positive:
`
`b(t) = (0) + nt O<t< ton
`
`1
`
`V,
`
`and the peak flux b at the end of the on interval is given as
`
`(10-1)
`
`(10-2)
`
` /
`
`A
`
`o = (fon) = b(0) + no
`
`Va
`
`After t,,, the switch is turned off and the energy stored in the core causes the current
`to flow in the secondary winding through the diode D, as shown by Fig. 10-7b. The
`
`
`
`Figure 10-7 Flyback converter circuit states: (a) switch on; (6) switch off.
`
`308
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`Page 20 of 104
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`10-4 de-de CONVERTERS WITH ELECTRICAL ISOLATION
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`309
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`
`
`
`Figure 10-8 Flyback converter waveforms.
`
`voltage across the secondary winding v. = —Vo, and therefore, the flux decreaseslinearly
`during tore
`
`A
`Vo
`(2) = ® ~ AG ~ ton)
`2
`
`lon S0< Ts
`
`and
`
`a
`Vo
`oT) = o ~ nts ~ ton)
`2
`
`(10-3)
`
`(10-4)
`
`N; on
`N. (
`5
`= (0) + fon — T, -
`
`fon)
`
`(
`
`ing
`.
`using Eq. 10-2
`
`)
`
`Since the net change offlux through the core over one time period mustbe zero in steady
`state,
`
`(T,) = (0)
`
`(10-6)
`
`Therefore, from Eqs. 10-5 and 10-6
`
`10-7
`Vo Ne
`BD
`(10-7)
`14 Ni -D
`where D = 1,,/T, is the switch duty ratio. Equation 10-7 shows that the voltage transfer
`radio in a flyback converter depends on D in an identical manner as the buck—boost
`The voltage and current waveforms shown in Fig. 10-8 can be obtained from the
`equations below. During the on interval,
`the transformer primary voltage v, = Vie
`
`converter.
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`CHAPTER 10
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`SWITCHING de POWER SUPPLIES
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`Therefore, the inductor current rises linearly from its initial value LAO):
`V
`in(t) = int) = En(O) + at
`0<t<ton
`
`(10-8)
`
`and
`
`A
`
`Aa
`
`(10-9)
`In = Iw = m(O) + mc
`During the off interval, the switch current goes to Zero and v, = —(N,/N,)V,. Therefore,
`i, and the diode current ip can be expressed during t,, <¢< T, as
`im(t) = Lm — ven — ton)
`s
`Vo(NIIN.
`
`Va
`
`(10-10)
`
`and
`
`ip(t) = nin "Ny In (t—ton)L,, (10-11)
`
`VANJN)
`Mi Nils
`
`
`
`Since the average diode current equals L,, from Eq. 10-11
`»
`»
`Nz
`1
`N, (i — DIT,
`
`Im=Iow N.1- Dp? Ny Lm Vo (10-12)
`
`
`= = Ie t+ yp
`-12
`The voltage across the switch during the off interval equals
`
`My.
`Vs
`Vew = Va +
`No
`i-D
`
`(10-13)
`
`10-4-2-1 Other Flyback Converter Topologies
`Two modifications of the flyback converter topology are shown in Fig. 10-9. Another
`flyback topology that is well suited for low-output-voltage applications is discussed in
`
`reference 5.
`Two-Transistor Flyback Converter. Figure 10-9a shows a two-transistor version of a
`flyback converter where T, and T, are turned on and off simultaneously. The advantage
`of such a topology over a single-transistor flyback converter, discussed earlier, is that
`voltage rating of the switches is one-half of the single-transistor version. Moreover, since
`a current path exists through the diodes connected to the primary winding, a dissipative
`snubberacross the primary winding is not needed to dissipate the energy associated with
`the transformer primary-winding leakage inductance (see reference 17).
`Paralleling Flyback Converters. At high power levels, it may be beneficial to parallel
`two or moreflyback converters rather than using a single higher power unit. Some of the
`advantagesof paralleling, which are not limited just to the flyback converter are (a) that
`it provides higher system reliability due to redundancy, (b) that it increases the effective
`switching frequency and hence decreases current pulsationsat the input and/or the output,
`and (c) that it allows low-power modules to be standardized where a numberof these can
`be paralleled to provide a higher power capability.
`The problem of current sharing among the parallel converters can be remedied by
`means of current-mode control, which is discussed later in this chapter.
`Figure 10-9b shows two flyback converters in parallel; these operate at the same
`switching frequency, but the switches in the two converters are sequenced to turn on a
`
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`10-4
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`de—-de CONVERTERS WITH ELECTRICAL ISOLATION
`
`311
`
`——ae
`
`Ni: No
`
`{b)
`
`Figure 10-9 Otherflyback topologies: (a) two-transistor flyback converter; (6) parallelled
`flyback converters.
`
`half-time period apart from one another. This results in improved input and output current
`waveforms (see Problem 10-4).
`
`10-4-3 FORWARD CONVERTER (DERIVED FROM
`STEP-DOWN CONVERTER)
`
`Figure 10-10 shows an idealized forward converter. As will be discussed shortly, the
`transformer magnetizing current must be taken into account in these converters.
`Initially, assuming a transformer to be ideal, when the switch is on, D, becomes
`forward biased and D, reverse biased. Therefore in Fig. 10-10,
`
`v= —VWa- Vo Ot < ton
`
`(10-14)
`
`which is positive.