Fundamentals of Power Electronics

Preface 1
I 2
Contents
xix Introduction 1
1.1 Introduction to Power Processing 1
1.2 Several Applications of Power Electronics 7
1.3 Elements of Power Electronics 9
References
Converters in Equilibrium 11
Principles of Steady State Converter Analysis 13
2.1 Introduction 13
2.2 Inductor Volt-Second Balance, Capacitor Charge Balance, and the Small-Ripple
Approximation 15
2.3 Boost Converter Example 22
2.4 uk Converter Example 27
2.5 Estimating the Output Voltage Ripple in Converters Containing Two-Pole
Low-Pass Filters 31
2.6 Summary of Key Points 34
References 34 Problems 35
Steady-State Equivalent Circuit Modeling, Losses, and Efficiency 39
3.1 The DC Transformer Model 39
3.2 Inclusion of Inductor Copper Loss 42
3.3 Construction of Equivalent Circuit Model 45
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Contents
3.3.1 Inductor Voltage Equation 46
3.3.2 Capacitor Current Equation 46
3.3.3 Complete Circuit Model 47
3.3.4 Efficiency 48
3.4 How to Obtain the Input Port of the Model 50
3.5 Example: Inclusion of Semiconductor Conduction Losses in the Boost
Converter Model 52
3.6 Summary of Key Points 56
References 56 Problems 57
Switch Realization 63
4.1 Switch Applications 65
4.1.1 Single-Quadrant Switches 65
4.1.2 Current-Bidirectional Two-Quadrant Switches 67
4.1.3 Voltage-Bidirectional Two-Quadrant Switches 71
4.1.4 Four-Quadrant Switches 72
4.1.5 Synchronous Rectifiers 73
4.2 A Brief Survey of Power Semiconductor Devices 74
4.2.1 Power Diodes 75
4.2.2 Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) 78
4.2.3 Bipolar Junction Transistor (BJT) 81
4.2.4 Insulated Gate Bipolar Transistor (IGBT) 86
4.2.5 Thyristors (SCR, GTO, MCT) 88
4.3 Switching Loss 92
4.3.1 Transistor Switching with Clamped Inductive Load 93
4.3.2 Diode Recovered Charge 96
4.3.3 Device Capacitances, and Leakage, Package, and Stray Inductances 98
4.3.4 Efficiency vs. Switching Frequency 100
4.4 Summary of Key Points 101
References 102 Problems 103
The Discontinuous Conduction Mode 107
5.1 Origin of the Discontinuous Conduction Mode, and Mode Boundary 108
5.2 Analysis of the Conversion Ratio M(D,K) 112
5.3 Boost Converter Example 117
5.4 Summary of Results and Key Points 124
Problems 126
Converter Circuits 131
6.1 Circuit Manipulations 132
6.1.1 Inversion of Source and Load 132
6.1.2 Cascade Connection of Converters 134
6.1.3 Rotation of Three-Terminal Cell 137
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Contents ix
6.1.4 Differential Connection of the Load 138
6.2 A Short List of Converters 143
6.3 Transformer Isolation 146
6.3.1 Full-Bridge and Half-Bridge Isolated Buck Converters 149
6.3.2 Forward Converter
6.3.3 Push-Pull Isolated Buck Converter
6.3.4 Flyback Converter
6.3.5 Boost-Derived Isolated Converters
6.3.6 Isolated Versions of the SEPIC and the
6.4 Converter Evaluation and Design
6.4.1 Switch Stress and Utilization
6.4.2 Design Using Computer Spreadsheet
6.5 Summary of Key Points
References Problems
II Converter Dynamics and Control 7 AC Equivalent Circuit Modeling
7.1 Introduction
7.2 The Basic AC Modeling Approach
7.2.1 Averaging the Inductor Waveforms
7.2.2 Discussion of the Averaging Approximation
7.2.3 Averaging the Capacitor Waveforms
7.2.4 The Average Input Current
7.2.5 Perturbation and Linearization
7.2.6 Construction of the Small-Signal Equivalent Circuit Model 201
7.2.7 Discussion of the Perturbation and Linearization Step 202
7.2.8 Results for Several Basic Converters 204
7.2.9 Example: A Nonideal Flyback Converter 204
154 159 161 165
Converter 168 171 171 174 177 177 179
185
187
7.3 State-Space Averaging 213
7.3.1 The State Equations of a Network 213
7.3.2 The Basic State-Space Averaged Model 216
7.3.3 Discussion of the State-Space A veraging Result 217
7.3.4 Example: State-Space Averaging of a Nonideal Buck–Boost Converter 221
7.4 Circuit Averaging and Averaged Switch Modeling 226
7.4.1 Obtaining a Time-Invariant Circuit 228
7.4.2 Circuit Averaging 229
7.4.3 Perturbation and Linearization 232
7.4.4 Switch Networks 235
7.4.5 Example: Averaged Switch Modeling of Conduction Losses 242
7.4.6 Example: Averaged Switch Modeling of Switching Losses 244
7.5 The Canonical Circuit Model 247
7.5.1 Development of the Canonical Circuit Model 248
187 192 193 194 196 197 197
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Contents
7.5.2 Example: Manipulation of the Buck–Boost Converter Model
into Canonical Form 250
7.5.3 Canonical Circuit Parameter Values for Some Common Converters 252
Modeling the Pulse-Width Modulator 253 Summary of Key Points 256
8
References 257 Problems 258
Converter Transfer Functions 265
8.1 Review of Bode Plots 267
8.1.1 Single Pole Response 269
8.1.2 Single Zero Response 275
8.1.3 Right Half-Plane Zero 276
8.1.4 Frequency Inversion 277
8.1.5 Combinations 278
8.1.6 Quadratic Pole Response: Resonance 282
8.1.7 The Low-Q Approximation 287
8.1.8 Approximate Roots of an Arbitrary-Degree Polynomial 289
8.2 Analysis of Converter Transfer Functions 293
8.2.1 Example: Transfer Functions of the Buck–Boost Converter 294
8.2.2 Transfer Functions of Some Basic CCM Converters 300
8.2.3 Physical Origins of the RHP Zero in Converters 300
8.3 Graphical Construction of Impedances and Transfer Functions 302
8.3.1 Series Impedances: Addition of Asymptotes 303
8.3.2 Series Resonant Circuit Example 305
8.3.3 Parallel Impedances: Inverse Addition of Asymptotes 308
8.3.4 Parallel Resonant Circuit Example 309
8.3.5 Voltage Divider Transfer Functions: Division of Asymptotes 311
8.4 Graphical Construction of Converter Transfer Functions 313
8.5 Measurement of AC Transfer Functions and Impedances 317
8.6 Summary of Key Points 321
References 322 Problems 322
Controller Design 331
9.1 Introduction 331
9.2 Effect of Negative Feedback on the Network Transfer Functions 334
9.2.1 Feedback Reduces the Transfer Functions
from Disturbances to the Output 335
9.2.2 Feedback Causes the Transfer Function from the Reference Input
to the Output to be Insensitive to Variations in the Gains in the
Forward Path of the Loop 337
9.3 Construction of the Important Quantities 1/(1 + T) and T/(1 + T)
and the Closed-Loop Transfer Functions 337
9.4 Stability 340
9
7.6 7.7
Contents xi
9.4.1 The Phase Margin Test 341
9.4.2 The Relationship Between Phase Margin
and Closed-Loop Damping Factor 342
9.4.3 Transient Response vs. Damping Factor 346
9.5 Regulator Design 347
9.5.1 Lead (PD) Compensator 348
9.5.2 Lag (PI) Compensator 351
9.5.3 Combined (PID) Compensator 353
9.5.4 Design Example 354
9.6 Measurement of Loop Gains 362
9.6.1 Voltage Injection 364
9.6.2 Current Injection 367
9.6.3 Measurement of Unstable Systems 368
9.7 Summary of Key Points 369
References 369 Problems 369
10 Input Filter Design 377
10.1 Introduction 377
10.1.1 Conducted EMI 377
10.1.2 The Input Filter Design Problem 379
10.2 Effect of an Input Filter on Converter Transfer Functions 381
10.2.1 Discussion 382
10.2.2 Impedance Inequalities 384
10.3 Buck Converter Example 385
10.3.1 Effect of Undamped Input Filter 385
10.3.2 Damping the Input Filter 391
10.4 Design of a Damped Input Filter 392
Parallel Damping 395 Parallel Damping 396 Series Damping 398
Cascading Filter Sections 398
10.4.1 10.4.2 10.4.3 10.4.4 10.4.5
11 AC and DC Equivalent Circuit Modeling of the Discontinuous Conduction Mode 409
11.1 DCM Averaged Switch Model 410
11.2 Small-Signal AC Modeling of the DCM Switch Network 420
11.2.1 Example: Control-to-Output Frequency Response
of a DCM Boost Converter 428
11.2.2 Example: Control-to-output Frequency Responses
of a CCM/DCM SEPIC 429
Example: Two Stage Input Filter 400 10.5 Summary of Key Points 403 References 405 Problems 406
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11.3 High-Frequency Dynamics of Converters in DCM 431
11.4 Summary of Key Points 434
References 434 Problems 435
Current Programmed Control 439
12.1 Oscillation for D > 0.5 441
12.2 A Simple First-Order Model 449
12.2.1 Simple Model via Algebraic Approach: Buck–Boost Example 450
12.2.2 Averaged Switch Modeling 454
12.3 A More Accurate Model 459
12.3.1 Current-Programmed Controller Model 459
12.3.2 Solution of the CPM Transfer Functions 462
12.3.3 Discussion 465
12.3.4 Current-Programmed Transfer Functions of the CCM Buck Converter 466
12.3.5 Results for Basic Converters 469
12.3.6 Quantitative Effects of Current-Programmed Control
on the Converter Transfer Functions 471
12.4 Discontinuous Conduction Mode 473
12.5 Summary of Key Points 480
References 481 Problems 482
III Magnetics 489 13 Basic Magnetics Theory 491
13.1 Review of Basic Magnetics 491
13.1.1 Basic Relationships 491
13.1.2 Magnetic Circuits 498
13.2 Transformer Modeling 501
13.2.1 The Ideal Transformer 502
13.2.2 The Magnetizing Inductance 502
13.2.3 Leakage Inductances 504
13.3 Loss Mechanisms in Magnetic Devices 506
13.3.1 Core Loss 506
13.3.2 Low-Frequency Copper Loss 508
13.4 Eddy Currents in Winding Conductors 508
13.4.1 Introduction to the Skin and Proximity Effects 508
13.4.2 Leakage Flux in Windings 512
13.4.3 Foil Windings and Layers 514
13.4.4 Power Loss in a Layer 515
13.4.5 Example: Power Loss in a Transformer Winding 518
13.4.6 Interleaving the Windings 520
13.4.7 PWM Waveform Harmonics 522
14
13.5.1 Filter Inductor
13.5.2 AC Inductor
13.5.3 Transformer
13.5.4 Coupled Inductor
13.5.5 Flyback Transformer
13.6 Summary of Key Points References
Problems
Inductor Design
14.1 Filter Inductor Design Constraints
14.1.1 Maximum Flux Density
14.1.2 Inductance
14.1.3 Winding Area
14.1.4 Winding Resistance
14.1.5 The Core Geometrical Constant
14.2 A Step-by-Step Procedure
14.3 Multiple-Winding Magnetics Design via the
14.3.1 Window Area Allocation
14.3.2 Coupled Inductor Design Constraints
14.3.3 Design Procedure
15
14.4 Examples
14.4.1 Coupled Inductor for a Two-Output Forward Converter
14.4.2 CCM Flyback Transformer
14.5 Summary of Key Points
References Problems
Transformer Design
15.1 Transformer Design: Basic Constraints
15.1.1 Core Loss
15.1.2 Flux Density
15.1.3 Copper Loss
15.1.4 Total Power Loss vs.
15.1.5 Optimum Flux Density
15.2 A Step-by-Step Transformer Design Procedure
15.3 Examples
13.5 Several Types of Magnetic Devices, Their B–H Loops, and Core vs. Copper Loss
Contents xiii
525 525 527 528 529 530 531 532 533
539
539 541 542 542 543 543
544
545
545 550 552
554 554 557 562 562 563
565
565
566 566 567 568 569 570 573 573 576 580 580 582
Method
15.3.1 Example 1: Single-Output Isolated
Converter
15.3.2 Example 2: Multiple-Output Full-Bridge Buck Converter
15.4 AC Inductor Design
15.4.1 Outline of Derivation
15.4.2 Step-by-Step AC Inductor Design Procedure
xiv
IV 16
Contents
15.5 Summary 583 References 583 Problems 584
Modern Rectifiers and Power System Harmonics 587
Power and Harmonics in Nonsinusoidal Systems 589
16.1 Average Power 590
16.2 Root-Mean-Square (RMS) Value of a Waveform 593
16.3 Power Factor 594
16.3.1 Linear Resistive Load, Nonsinusoidal Voltage 594
16.3.2 Nonlinear Dynamic Load, Sinusoidal Voltage 595
16.4 Power Phasors in Sinusoidal Systems 598
16.5 Harmonic Currents in Three-Phase Systems 599
16.5.1 Harmonic Currents in Three-Phase Four-Wire Networks 599
16.5.2 Harmonic Currents in Three-Phase Three-Wire Networks 601
16.5.3 Harmonic Current Flow in Power Factor Correction Capacitors 602
16.6 AC Line Current Harmonic Standards 603
16.6.1 International Electrotechnical Commission Standard 1000 603
16.6.2 IEEE/ANSI Standard 519 604
17
Line-Commutated Rectifiers 609
17.1 The Single-Phase Full-Wave Rectifier 609
17.1.1 Continuous Conduction Mode 610
17.1.2 Discontinuous Conduction Mode 611
17.1.3 Behavior when C is Large 612
17.1.4 Minimizing THD when C is Small 613
17.2 The Three-Phase Bridge Rectifier 615
17.2.1 Continuous Conduction Mode 615
17.2.2 Discontinuous Conduction Mode 616
17.3 Phase Control 617
17.3.1 Inverter Mode 619
17.3.2 Harmonics and Power Factor 619
17.3.3 Commutation 620
17.4 Harmonic Trap Filters 622
17.5 Transformer Connections 628
17.6 Summary 630
References 631 Problems 632
Pulse-Width Modulated Rectifiers 637
18.1 Properties of the Ideal Rectifier 638
18
Bibliography Problems
605 605
18.2 Realization of a Near-Ideal Rectifier
18.2.1 CCM Boost Converter
18.2.2 DCM Flyback Converter
18.3 Control of the Current Waveform
18.3.1 Average Current Control
18.3.2 Current Programmed Control
18.3.3 Critical Conduction Mode and Hysteretic Control
18.3.4 Nonlinear Carrier Control
18.4 Single-Phase Converter Systems Incorporating Ideal Rectifiers
18.4.1 Energy Storage
18.4.2 Modeling the Outer Low-Bandwidth Control System
18.5 RMS Values of Rectifier Waveforms
18.5.1 Boost Rectifier Example
18.5.2 Comparison of Single-Phase Rectifier Topologies
18.6 Modeling Losses and Efficiency in CCM High-Quality Rectifiers
18.6.1 Expression for Controller Duty Cycle d(t)
18.6.2 Expression for the DC Load Current
18.6.3 Solution for Converter Efficiency
18.6.4 Design Example
18.7 Ideal Three-Phase Rectifiers
18.8 Summary of Key Points
References Problems
V Resonant Converters 19 Resonant Conversion
19.1 Sinusoidal Analysis of Resonant Converters
19.1.1 Controlled Switch Network Model
19.1.2 Modeling the Rectifier and Capacitive Filter Networks
19.1.3 Resonant Tank Network
19.1.4 Solution of Converter Voltage Conversion Ratio
19.2 Examples
19.2.1 Series Resonant DC–DC Converter Example
19.2.2 Subharmonic Modes of the Series Resonant Converter
19.2.3 Parallel Resonant DC–DC Converter Example
19.3 Soft Switching
19.3.1 Operation of the Full Bridge Below Resonance: Zero-Current Switching
19.3.2 Operation of the Full Bridge Above Resonance: Zero-Voltage Switching
19.4 Load-Dependent Properties of Resonant Converters
19.4.1 Inverter Output Characteristics
19.4.2 Dependence of Transistor Current on Load
19.4.3 Dependence of the ZVS/ZCS Boundary on Load Resistance
Contents xv
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642 646
648 648 654 657 659 663 663 668 673 674 676 678
679 681 683 684 685 691 692 696
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705
709 710 711 713 714
715
715 717 718 721
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726
727 729 734
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Contents
19.4.4 Another Example 737
19.5 Exact Characteristics of the Series and Parallel Resonant Converters 740
19.5.1 Series Resonant Converter 740
19.5.2 Parallel Resonant Converter 748
19.6 Summary of Key Points 752
References 752 Problems 755
Soft Switching 761
20.1 Soft-Switching Mechanisms of Semiconductor Devices 762
20.1.1 Diode Switching 763
20.1.2 MOSFET Switching 765
20.1.3 IGBT Switching 768
20.2 The Zero-Current-Switching Quasi-Resonant Switch Cell 768
20.2.1 Waveforms of the Half-Wave ZCS Quasi-Resonant Switch Cell 770
20.2.2 The Average Terminal Waveforms 774
20.2.3 The Full-Wave ZCS Quasi-Resonant Switch Cell 779
20.3 Resonant Switch Topologies 781
20.3.1 The Zero-Voltage-Switching Quasi-Resonant Switch 783
20.3.2 The Zero-Voltage-Switching Multi-Resonant Switch 784
20.3.3 Quasi-Square-Wave Resonant Switches 787
20.4 Soft Switching in PWM Converters 790
20.4.1 The Zero-Voltage Transition Full-Bridge Converter 791
20.4.2 The Auxiliary Switch Approach 794
20.4.3 Auxiliary Resonant Commutated Pole 796
20.5 Summary of Key Points 797
References 798 Problems 800
20
Appendices 803
Appendix A
A.1 A.2
RMS Values of Commonly-Observed Converter Waveforms 805
Some Common Waveforms 805 General Piecewise Waveform 809
Appendix B Simulation of Converters 813
B.1
Averaged Switch Models for Continuous Conduction Mode 815
B.1.1 Basic CCM Averaged Switch Model 815
B.1.2 CCM Subcircuit Model that Includes Switch Conduction Losses 816
B.1.3 Example: SEPIC DC Conversion Ratio and Efficiency 818
B.1.4 Example: Transient Response of a Buck–Boost Converter 819
B.2 Combined CCM/DCM Averaged Switch Model 822
B.2.1 Example: SEPIC Frequency Responses 825
B.2.2 Example: Loop Gain and Closed-Loop Responses
of a Buck Voltage Regulator 827
B.2.3 Example: DCM Boost Rectifier B.3 Current Programmed Control
B.3.1 Current Programmed Mode Model for Simulation
B.3.2 Example: Frequency Responses of a Buck Converter with
Contents xvii
832 834 834
837 840
843
843 846 849 850 850
855 857 859 861
863
864 865 866 866 867 868 869 871
References
Appendix C
C.1 C.2 C.3 C.4
References
Appendix D
Magnetics Design Tables
Current Programmed Control
Middlebrook’s Extra Element Theorem
Basic Result Derivation Discussion Examples
C.4.1 A Simple Transfer Function
C.4.2 An Unmodeled Element
C.4.3 Addition of an Input Filter to a Converter
C.4.4 Dependence of Transistor Current on Load in a Resonant Inverter
D.1 Pot Core Data
D.2 EE Core Data
D.3 EC Core Data
D.4 ETD Core Data
D.5 PQ Core Data
D.6 American Wire Gauge Data
References
Index