fundamentals-of-power-electronics_2nd.pdf

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15 Transformer Design

Fundamentals of Power Electronics SECOND EDITION

Fundamentals of Power Electronics SECOND EDITION Robert W. Erickson Dragan University of Colorado Boulder, Colorado KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

0-306-48048-4 eBook ISBN: Print ISBN: 0-7923-7270-0 ©2004 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2001 Kluwer Academic/Plenum Publishers New York All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at: http://kluweronline.com http://ebooks.kluweronline.com

Dedicated to Linda, William, and Richard Lidija, Filip, Nikola, and Stevan

Contents Preface 1 Introduction to Power Processing Several Applications of Power Electronics Elements of Power Electronics Introduction 1.1 1.2 1.3 References Converters in Equilibrium Principles of Steady State Converter Analysis I 2 2.1 2.2 2.3 2.4 2.5 Introduction Inductor Volt-Second Balance, Capacitor Charge Balance, and the Small-Ripple Approximation Boost Converter Example uk Converter Example Estimating the Output Voltage Ripple in Converters Containing Two-Pole Low-Pass Filters Summary of Key Points 2.6 References Problems 3 Steady-State Equivalent Circuit Modeling, Losses, and Efficiency 3.1 3.2 3.3 The DC Transformer Model Inclusion of Inductor Copper Loss Construction of Equivalent Circuit Model xix 1 1 7 9 11 13 13 15 22 27 31 34 34 35 39 39 42 45

viii Contents 3.6 References Problems 4 Switch Realization 3.4 3.5 4.1 4.2 4.3 4.4 References Problems Inductor Voltage Equation Capacitor Current Equation Complete Circuit Model Efficiency 3.3.1 3.3.2 3.3.3 3.3.4 How to Obtain the Input Port of the Model Example: Inclusion of Semiconductor Conduction Losses in the Boost Converter Model Summary of Key Points Single-Quadrant Switches Current-Bidirectional Two-Quadrant Switches Voltage-Bidirectional Two-Quadrant Switches Four-Quadrant Switches Synchronous Rectifiers Switch Applications 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 A Brief Survey of Power Semiconductor Devices 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 Switching Loss 4.3.1 4.3.2 4.3.3 4.3.4 Summary of Key Points Power Diodes Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) Bipolar Junction Transistor (BJT) Insulated Gate Bipolar Transistor (IGBT) Thyristors (SCR, GTO, MCT) Transistor Switching with Clamped Inductive Load Diode Recovered Charge Device Capacitances, and Leakage, Package, and Stray Inductances Efficiency vs. Switching Frequency 5 The Discontinuous Conduction Mode Origin of the Discontinuous Conduction Mode, and Mode Boundary Analysis of the Conversion Ratio M(D,K) Boost Converter Example Summary of Results and Key Points 5.1 5.2 5.3 5.4 Problems 6 Converter Circuits 6.1 Circuit Manipulations 6.1.1 6.1.2 6.1.3 Inversion of Source and Load Cascade Connection of Converters Rotation of Three-Terminal Cell 46 46 47 48 50 52 56 56 57 63 65 65 67 71 72 73 74 75 78 81 86 88 92 93 96 98 100 101 102 103 107 108 112 117 124 126 131 132 132 134 137

Contents ix Differential Connection of the Load Full-Bridge and Half-Bridge Isolated Buck Converters Forward Converter Push-Pull Isolated Buck Converter Flyback Converter Boost-Derived Isolated Converters Isolated Versions of the SEPIC and the Converter Switch Stress and Utilization Design Using Computer Spreadsheet 6.2 6.3 6.4 6.1.4 A Short List of Converters Transformer Isolation 6.3.1 6.3.2 6.3.3 6.3.4 6.3.5 6.3.6 Converter Evaluation and Design 6.4.1 6.4.2 Summary of Key Points 6.5 References Problems Converter Dynamics and Control AC Equivalent Circuit Modeling II 7 7.1 7.2 7.3 7.4 7.5 Averaging the Inductor Waveforms Discussion of the Averaging Approximation Averaging the Capacitor Waveforms The Average Input Current Perturbation and Linearization Construction of the Small-Signal Equivalent Circuit Model Discussion of the Perturbation and Linearization Step Results for Several Basic Converters Example: A Nonideal Flyback Converter Introduction The Basic AC Modeling Approach 7.2.1 7.2.2 7.2.3 7.2.4 7.2.5 7.2.6 7.2.7 7.2.8 7.2.9 State-Space Averaging 7.3.1 7.3.2 7.3.3 7.3.4 Circuit Averaging and Averaged Switch Modeling 7.4.1 7.4.2 7.4.3 7.4.4 7.4.5 7.4.6 The Canonical Circuit Model 7.5.1 Obtaining a Time-Invariant Circuit Circuit Averaging Perturbation and Linearization Switch Networks Example: Averaged Switch Modeling of Conduction Losses Example: Averaged Switch Modeling of Switching Losses Development of the Canonical Circuit Model The State Equations of a Network The Basic State-Space Averaged Model Discussion of the State-Space Averaging Result Example: State-Space Averaging of a Nonideal Buck–Boost Converter 138 143 146 149 154 159 161 165 168 171 171 174 177 177 179 185 187 187 192 193 194 196 197 197 201 202 204 204 213 213 216 217 221 226 228 229 232 235 242 244 247 248

x Contents 7.5.2 7.6 7.7 References Problems Example: Manipulation of the Buck–Boost Converter Model into Canonical Form Canonical Circuit Parameter Values for Some Common Converters 7.5.3 Modeling the Pulse-Width Modulator Summary of Key Points 8 Converter Transfer Functions 8.1 8.2 8.3 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 Review of Bode Plots 8.1.1 8.1.2 8.1.3 8.1.4 8.1.5 8.1.6 8.1.7 8.1.8 Analysis of Converter Transfer Functions 8.2.1 8.2.2 8.2.3 Graphical Construction of Impedances and Transfer Functions 8.3.1 8.3.2 8.3.3 8.3.4 8.3.5 Graphical Construction of Converter Transfer Functions Measurement of AC Transfer Functions and Impedances Summary of Key Points Series Impedances: Addition of Asymptotes Series Resonant Circuit Example Parallel Impedances: Inverse Addition of Asymptotes Parallel Resonant Circuit Example Voltage Divider Transfer Functions: Division of Asymptotes Example: Transfer Functions of the Buck–Boost Converter Transfer Functions of Some Basic CCM Converters Physical Origins of the RHP Zero in Converters 8.4 8.5 8.6 References Problems 9 Controller Design 9.1 9.2 Introduction Effect of Negative Feedback on the Network Transfer Functions 9.2.1 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 9.2.2 9.3 9.4 Construction of the Important Quantities 1/(1 + T) and T/(1 + T) and the Closed-Loop Transfer Functions Stability 250 252 253 256 257 258 265 267 269 275 276 277 278 282 287 289 293 294 300 300 302 303 305 308 309 311 313 317 321 322 322 331 331 334 335 337 337 340

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