Fundamentals of Power Electronics

Preface
1
Introduction
1.1 Introduction to Power Processing
1.2 Several Applications of Power Electronics
Elements of Power Electronics
1.3
1
7
9
References
I Converters in Equilibrium 11
2 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
Boost Converter Example
Cuk Converter Example 15
22
2.3
2.4
2.5 Estimating the Output Voltage Ripple in Converters Containing Two-Pole
Low-Pass Filters
2.6 Summary of Key Points
31
Problems 34
34
35
Steady-State Equivalent Circuit Modeling, Losses, and Efficiency 39
References
3
27
3.1 The DC Transformer Model 39
3.2 Inclusion of Inductor Copper Loss 42
3.3 Construction of Equivalent Circuit Model 45viii
Contents
3.3.1
3.3.2
3.3.3
3.3.4
4
3.4 How to Obtain the Input Port of the Model
3.5 Example: Inclusion of Semiconductor Conduction Losses in the Boost
Converter Model
6
46
46
47
48
50
52
56
Summary of Key Points
3.6
References 56
Problems 57
Switch Realization 63
4.1 Switch Applications 65
4.1.1
4.1.2
4.1.3
4.1.4
4.1.5 65
67
71
72
73
4.2
5
Inductor Voltage Equation
Capacitor Current Equation
Complete Circuit Model
Efficiency
Single-Quadrant Switches
Current-Bidirectional Two-Quadrant Switches
Voltage-Bidirectional Two-Quadrant Switches
Four-Quadrant Switches
Synchronous Rectifiers
A Brief Survey of Power Semiconductor Devices 74
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5 75
78
81
86
88
Power Diodes
Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET)
Bipolar Junction Transistor (BJT)
Insulated Gate Bipolar Transistor (IGBT)
Thyristors (SCR, GTO, MCT)
4.3 Switching Loss
Transistor Switching with Clamped Inductive Load
4.3.1
4.3.2
Diode Recovered Charge
4.3.3
Device Capacitances, and Leakage, Package, and Stray Inductances
Efficiency vs. Switching Frequency
4.3.4
4.4
Summary of Key Points
References
Problems 92
93
96
98
100
101
102
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
Inversion of Source and Load
6.1.1
Cascade Connection of Converters
6.1.2
6.1.3
Rotation of Three-Terminal Cell
132
132
134
137Contents
6.1.4
ix
Differential Connection of the Load
A Short List of Converters
Transformer Isolation
6.3.1 Full-Bridge and Half-Bridge Isolated Buck Converters
6.3.2 Forward Converter
6.3.3 Push-Pull Isolated Buck Converter
6.3.4 Fly back Converter
6.3.5 Boost-Derived Isolated Converters
6.3.6 Isolated Versions of the SEPIC and the Cuk Converter
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 138
143
146
149
154
159
161
165
168
171
171
174
177
177
179
II Converter Dynamics and Control 185
7 AC Equivalent Circuit Modeling 187
7.1
7.2 187
192
193
194
196
197
197
201
202
204
204
213
213
216
217
221
226
228
229
232
235
242
244
247
248
6.2
6.3
7.3
7.4
7.5
Introduction
The Basic AC Modeling Approach
Averaging the Inductor Waveforms
7.2.1
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
7.2.7 Discussion of the Perturbation and Linearization Step
7.2.8 Results for Several Basic Converters
7.2.9 Example: A Nonideai Flyback Converter
State-Space Averaging
7.3.1 The State Equations of a Network
7.3.2 The Basic State-Space Averaged Model
7.3.3 Discussion of the State-Space Averaging Result
7.3.4 Example: State-Space Averaging of a Nonideal Buck-Boost Converter
Circuit Averaging and Averaged Switch Modeling
7.4.1 Obtaining a Time-Invariant Circuit
7.4.2 Circuit Averaging
7.4.3 Perturbation and Linearization
7.4.4 Switch Networks
7.4.5 Example: Averaged Switch Modeling of Conduction Losses
7.4.6 Example: Averaged Switch Modeling of Switching Losses
The Canonical Circuit Model
7.5.1 Development of the Canonical Circuit Modelx
Contents
7.5.2
7.5.3
8
Example: Manipulation of the Buck-Boost Converter Model
into Canonical Form
Canonical Circuit Parameter Values for Some Common Converters
7.6 Modeling the Pulse-Width Modulator 253
7.7 Summary of Key Points 256
References 257
Problems 258
Converter Transfer Functions 265
8.1 Review of Bode Plots 267
8.1.1
8.1.2
8.1.3
8.1.4
8.1.5
8.1.6
8.1.7
8.1.8 269
275
276
277
278
282
287
289
8.2
Single Pole Response
Single Zero Response
Right Half-Plane Zero
Frequency Inversion
Combinations
Quadratic Pole Response: Resonance
The Low-Q Approximation
Approximate Roots of an Arbitrary-Degree Polynomial
Analysis of Converter Transfer Functions
8.2.1
8.2.2
8.2.3
Example: Transfer Functions of the Buck-Boost Converter
Transfer Functions of Some Basic CCM Converters
Physical Origins of the RHP Zero in Converters
293
294
300
300
8.3 Graphical Construction of Impedances and Transfer Functions 302
303
305
308
309
311
8.4 8.3.1
Series Impedances: Addition of Asymptotes
Series Resonant Circuit Example
8.3.2
8.3.3
Parallel Impedances: Inverse Addition of Asymptotes
Parallel Resonant Circuit Example
8.3.4
8.3.5
Voltage Divider Transfer Functions: Division of Asymptotes
Graphical Construction of Converter Transfer Functions
Measurement of AC Transfer Functions and Impedances
8.5
Summary of Key Points
8.6
References
9
250
252
313
317
321
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
9.2.2
Feedback Reduces the Transfer Functions
from Disturbances to the Output
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
9.3 Construction of the Important Quantities 11( 1 + T) and Tl( 1 + T)
and the Closed-Loop Transfer Functions
9.4 Stability
335
337
337
340Contents
9.4.1
9.4.2
9.4.3
9.5
9.6
9.7
10
The Phase Margin Test
The Relationship Between Phase Margin
and Closed-Loop Damping Factor
Transient Response vs. Damping Factor
341
342
346
Regulator Design 347
9.5.1
9.5.2
9.5.3
9.5.4 348
351
353
354
Lead (PD) Compensator
Lag (PI) Compensator
Combined (P/D) Compensator
Design Example
Measurement of Loop Gains 362
9.6.1
9.6.2
9.6.3 364
367
368
Voltage Injection
Current Injection
Measurement of Unstable Systems
Summary of Key Points
369
References 369
Problems 369
Input Filter Design 377
10.1 377
377
Introduction
10.1.1
10.1.2
Conducted EMI
The Input Filter Design Problem
379
10.2 Effect of an Input Filter on Converter Transfer Functions 381
10.3 10.2.1 Discussion
10.2.2 Impedance Inequalities
Buck Converter Example 382
384
385
10.3.1 Effect of Undamped Input Filter
10.3.2 Damping the Input Filter
10.4 Design of a Damped Input Filter
10.4.1 RrCb Parallel Damping
10.4.2 RrLb Parallel Damping
10.4.3 RrLb Series Damping
10.4.4 Cascading Filter Sections
10.4.5 Example: Two Stage Input Filter
10.5 Summary of Key Points
References
11
xi
385
391
392
395
396
398
398
400
403
405
Problems 406
AC and DC Equivalent Circuit Modeling of the Discontinuous Conduction Mode 409
11.1 DCM Averaged Switch Model 11.2 Small-Signal AC Modeling of the DCM Switch Network
11.2.1 Example: Control-to-Output Frequency Response
of a DCM Boost Converter
11.2.2 Example: Control-to-Output Frequency Responses
of a CCM/DCM SEPIC 410
420
428
429Contents
xii
11.3
11.4
12
High-Frequency Dynamics of Converters in DCM
Summary of Key Points
431
References
Problems 434
434
435
Current Programmed Control 439
12.1 Oscillation forD> 0.5 441
12.2 A Simple First-Order Model
12.2.1 Simple Model via Algebraic Approach: Buck-Boost Example
12.2.2 Averaged Switch Modeling 12.3 A More Accurate Model
12.3.1 Current-Programmed Controller Model
12.3.2 Solution of the CPM Transfer Functions
12.3.3 Discussion
12.3.4 Current-Programmed Transfer Functions of the CCM Buck Converter
12.3.5 Results for Basic Converters
12.3.6 Quantitative Effects of Current-Programmed Control
on the Converter Transfer Functions 449
450
454
459
12.4
Discontinuous Conduction Mode
12.5 Summary of Key Points
References
Problems
459
462
465
466
469
471
473
480
481
482
III Magnetics 489
13 Basic Magnetics Theory 491
13.1 491
491
498
501
502
502
504
506
506
508
508
508
512
514
515
518
520
522
13.2
13.3
13.4
Review of Basic Magnetics
13.1.1 Basic Relationships
13.1.2 Magnetic Circuits
Transformer Modeling
13.2.1 The Ideal Transformer
13.2.2 The Magnetizing Inductance
13.2.3 Leakage Inductances
Loss Mechanisms in Magnetic Devices
13.3.1 Core Loss
13.3.2 Low-Frequency Copper Loss
Eddy Currents in Winding Conductors
13.4.1 Introduction to the Skin and Proximity Effects
13.4.2 Leakage Flux in Windings
13.4.3 Foil Windings and Layers
13.4.4 Power Loss in a Layer
13.4.5 Example: Power Loss in a Transformer Winding
13.4.6 Interleaving the Windings
13.4.7 PWM Waveform HarmonicsContents
xiii
Several Types of Magnetic Devices, Their B-H Loops,
and Core vs. Copper Loss
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 525
525
527
528
529
530
531
532
533
Inductor Design 539
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 Kg 539
541
542
542
543
543
14.2
14.3 A Step-by-Step Procedure
Multiple-Winding Magnetics Design via the Kg Method 544
545
14.3.1 Window Area Allocation
14.3.2 Coupled Inductor Design Constraints
14.3.3 Design Procedure
14.4 Examples
14.4.1 Coupled Inductor for a Two-Output Forward Converter
14.4.2 CCM Fly back Transformer
14.5 Summary of Key Points
References
Problems 545
550
552
554
554
557
562
562
563
Transformer Design 565
15.1 565
566
566
567
568
569
570
573
573
576
580
580
582
13.5
14
15
15.2
15.3
15.4
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. till
15.1.5 Optimum Flux Density
A Step-by-Step Transformer Design Procedure
Examples
15.3.1 Example 1: Single-Output Isolated Cuk Converter
15.3.2 Example 2: Multiple-Output Full-Bridge Buck Converter
AC Inductor Design
15.4.1 Outline of Derivation
15.4.2 Step-by-Step AC Inductor Design Procedurexiv
Contents
15.5
Summary
583
Problems 584
IV Modern Rectifiers and Power System Harmonics
16
Power and Harmonics in Nonsinusoidal Systems
16.1 Average Power
16.2 Root-Mean-Square (RMS) Value of a Waveform
16.3 Power Factor
16.3.1 Linear Resistive Load, Nonsinusoidal Voltage
16.3.2 Nonlinear Dynamic Load, Sinusoidal Voltage
589
590
593
594
594
595
16.4 Power Phasors in Sinusoidal Systems 598
Harmonic Currents in Three-Phase Systems 599
16.6
Harmonic Currents in Three-Phase Four-Wire Networks
Harmonic Currents in Three-Phase Three-Wire Networks
Harmonic Current Flow in Power Factor Correction Capacitors
AC Line Current Harmonic Standards
16.6.1
16.6.2
Bibliography
Problems
International Electrotechnical Commission Standard 1000
IEEE/ ANSI Standard 519
Line-Commutated Rectifiers
17.1
17.2
The Single-Phase Full-Wave Rectifier
17.1.1 Continuous Conduction Mode
17.1.2 Discontinuous Conduction Mode
17.1.3 Behavior when Cis Large
17.1.4 Minimizing THD when C is Small
The Three-Phase Bridge Rectifier
17.2.1 Continuous Conduction Mode
17.2.2 Discontinuous Conduction Mode
599
601
602
603
603
604
605
605
609
609
610
611
612
613
615
615
616
617
17.4 Phase Control
17.3.1 Inverter Mode
17.3.2 Harmonics and Power Factor
17.3.3 Commutation
Harmonic Trap Filters 622
17.5 Transformer Connections 628
17.6 Summary Problems 630
631
632
Pulse-Width Modulated Rectifiers 637
17.3
References
18
587
16.5
16.5.1
16.5.2
16.5.3
17
583
References
18.1
Properties of the Ideal Rectifier
619
619
620
638Contents
18.2
Realization of a Near-Ideal Rectifier
xv
640
CCM Boost Converter
DCM Flyback Converter 642
646
18.3 Control of the Current Waveform 648
18.4 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
Single-Phase Converter Systems Incorporating Ideal Rectifiers 648
654
657
659
663
663
668
18.5 18.4.1 Energy Storage
18.4.2 Modeling the Outer Low-Bandwidth Control System
RMS Values of Rectifier Waveforms 674
676
18.6 18.5.1 Boost Rectifier Example
18.5.2 Comparison of Single-Phase Rectifier Topologies
Modeling Losses and Efficiency in CCM High-Quality Rectifiers 679
681
683
684
18.7 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 11
18.6.4 Design Example
Ideal Three-Phase Rectifiers 18.8 Summary of Key Points 691
18.2.1
18.2.2
673
678
685
References 692
Problems 696
v Resonant Converters 703
19 Resonant Conversion 705
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 M = V!Vg 709
710
711
713
714
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 715
715
717
718
721
19.3.1
19.3.2
19.4
Operation of the Full Bridge Below Resonance:
Zero-Current Switching
Operation of the Full Bridge Above Resonance:
Zero-Voltage Switching
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
722
723
726
727
729
734xvi
Contents
19.4.4
20
Another Example
19.5 Exact Characteristics of the Series and Parallel Resonant Converters
19.6 19.5.1 Series Resonant Converter
19.5.2 Parallel Resonant Converter
Summary of Key Points
737
740
740
748
References 752
752
Problems 755
Soft Switching 761
20.1 Soft-Switching Mechanisms of Semiconductor Devices 762
763
765
768
20.2 20.1.1 Diode Switching
20.1.2 MOSFET Switching
20.1.3 IGBT Switching
The Zero-Current-Switching Quasi-Resonant Switch Cell
20.2.1
20.2.2
20.2.3
Waveforms of the Half-Wave ZCS Quasi-Resonant Switch Cell
The Average Terminal Waveforms
The Full-Wave ZCS Quasi-Resonant Switch Cell
768
770
774
779
20.3 Resonant Switch Topologies 781
783
784
787
20.4 20.3.1 The Zero-Voltage-Switching Quasi-Resonant Switch
20.3.2 The Zero-Voltage-Switching Multi-Resonant Switch
20.3.3 Quasi-Square-Wave Resonant Switches
Soft Switching in PWM Converters
20.4.1 The Zero-Voltage Transition Full-Bridge Converter
20.4.2 The Auxiliary Switch Approach
20.4.3 Auxiliary Resonant Commutated Pole
20.5 Summary of Key Points
References
Problems
Appendices
Appendix A
790
791
794
796
797
798
800
803
RMS Values of Commouly-Observed Converter Waveforms
805
A.l Some Common Waveforms 805
A.2 General Piecewise Waveform 809
Appendix B
B.l
B.2
Simulation of Converters
Averaged Switch Models for Continuous Conduction Mode
B.l.l
Basic CCM Averaged Switch Model
B.l.2
CCM Subcircuit Model that Includes Switch Conduction Losses
B.l.3
Example: SEPIC DC Conversion Ratio and Efficiency
B.l.4
Example: Transient Response of a Buck-Boost Converter
Combined CCM/DCM Averaged Switch Model
B.2.l
Example: SEPIC Frequency Responses
B.2.2
Example: Loop Gain and Closed-Loop Responses
of a Buck Voltage Regulator
813
815
815
816
818
819
822
825
827Contents
B.2.3 Example: DCM Boost Rectifier
Current Programmed Control
Current Programmed Mode Model for Simulation
B.3.1
B.3.2 Example: Frequency Responses of a Buck Converter with
Current Programmed Control
References
B.3
AppendixC
Middlebrook's Extra Element Theorem
Basic Result
Derivation
Discussion
Examples
A Simple Transfer Function
C.4.1
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
References
C.l
C.2
C.3
C.4
AppendixD
Magnetics Design Tables
Pot Core Data
D.l
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
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