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Pulse-width Modulated DC–DC Power Converters MARIAN K KAZIMIERCZUK Wright State University Dayton, Ohio, USA A John Wiley and Sons, Ltd, Publication Pulse-width Modulated DC–DC Power Converters Pulse-width Modulated DC–DC Power Converters MARIAN K KAZIMIERCZUK Wright State University Dayton, Ohio, USA A John Wiley and Sons, Ltd, Publication This edition first published 2008  2008 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books Designations used by companies to distinguish their products are often claimed as trademarks All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners The publisher is not associated with any product or vendor mentioned in this book This publication is designed to provide accurate and authoritative information in regard to the subject matter covered It is sold on the understanding that the publisher is not engaged in rendering professional services If professional advice or other expert assistance is required, the services of a competent professional should be sought A catalogue record for this book is available from the British Library ISBN: 978-0-470-77301-7 (HB) Typeset by Laserwords Private Limited, Chennai, India Printed and bound by Markono Print Media Pte Ltd Singapore To my family Contents Preface About the Author List of Symbols Introduction 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14 Classification of Power Supplies Basic Functions of Voltage Regulators Power Relationships in DC–DC Converters DC Transfer Functions of DC–DC Converters Static Characteristics of DC Voltage Regulators Dynamic Characteristics of DC Voltage Regulators Linear Voltage Regulators 1.7.1 Series Voltage Regulator 1.7.2 Shunt Voltage Regulator Topologies of PWM DC–DC Converters Relationships among Current, Voltage, Energy, and Power Electromagnetic Compatibility Summary References Review Questions Problems Buck PWM DC–DC Converter 2.1 Introduction 2.2 DC Analysis of PWM Buck Converter for CCM 2.2.1 Circuit Description 2.2.2 Assumptions 2.2.3 Time Interval < t ≤ DT 2.2.4 Time Interval DT < t ≤ T 2.2.5 Device Stresses for CCM 2.2.6 DC Voltage Transfer Function for CCM xix xxi xxiii 1 5 12 13 14 17 18 19 20 20 21 22 23 23 23 23 27 27 28 29 29 viii CONTENTS 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.2.7 Boundary between CCM and DCM 2.2.8 Ripple Voltage in Buck Converter for CCM 2.2.9 Switching Losses with Linear MOSFET Output Capacitance 2.2.10 Switching Losses with Nonlinear MOSFET Output Capacitance 2.2.11 Power Losses and Efficiency of Buck Converter for CCM 2.2.12 DC Voltage Transfer Function of Lossy Converter for CCM 2.2.13 MOSFET Gate-drive Power 2.2.14 Design of Buck Converter for CCM DC Analysis of PWM Buck Converter for DCM 2.3.1 Time Interval < t ≤ DT 2.3.2 Time Interval DT < t ≤ (D + D1 )T 2.3.3 Time Interval (D + D1 )T < t ≤ T 2.3.4 Device Stresses for DCM 2.3.5 DC Voltage Transfer Function for DCM 2.3.6 Maximum Inductance for DCM 2.3.7 Power Losses and Efficiency of Buck Converter for DCM 2.3.8 Design of Buck Converter for DCM Buck Converter with Input Filter Buck Converter with Synchronous Rectifier Buck Converter with Positive Common Rail Tapped-inductor Buck Converters 2.7.1 Tapped-inductor Common-diode Buck Converter 2.7.2 Tapped-inductor Common-transistor Buck Converter 2.7.3 Watkins–Johnson Converter Multiphase Buck Converter Summary References Review Questions Problems Boost PWM DC–DC Converter 3.1 Introduction 3.2 DC Analysis of PWM Boost Converter for CCM 3.2.1 Circuit Description 3.2.2 Assumptions 3.2.3 Time Interval < t ≤ DT 3.2.4 Time Interval DT < t ≤ T 3.2.5 DC Voltage Transfer Function for CCM 3.2.6 Boundary between CCM and DCM 3.2.7 Ripple Voltage in Boost Converter for CCM 3.2.8 Power Losses and Efficiency of Boost Converter for CCM 3.2.9 DC Voltage Transfer Function of Lossy Boost Converter for CCM 3.2.10 Design of Boost Converter for CCM 3.3 DC Analysis of PWM Boost Converter for DCM 3.3.1 Time Interval < t ≤ DT 30 32 37 39 42 46 47 48 51 54 56 57 57 57 59 61 63 69 69 72 74 74 76 76 77 79 81 81 82 85 85 85 85 88 88 89 90 91 93 95 97 99 103 105 B Introduction to MATLAB MATLAB is an abbreviation for MATrix LABoratory It is a very powerful mathematical tool used to perform numerical computation using matrices and vectors to obtain two- and three-dimensional graphs MATLAB can also be used to perform complex mathematical analysis Getting Started Open MATLAB by clicking Start > Programs > MATLAB > R2006a > MATLAB R2006a Open a new M-file by clicking File > New > M-File Type the code in the M-File Save the file as fn.m (e.g., Lab1.m) Simulate the code by doing one of the following: (a) Click on Debug > Run (b) Press F5 (c) On the tool bar, click the icon Run Use HELP by pressing F1 Use % at the beginning of a line for comments Generating x-axis Data x = Initial-Value: Increment:Final-Value; Example: x = 1:0.001:5; or Pulse-width Modulated DC–DC Power Converters Marian K Kazimierczuk  2008 John Wiley & Sons, Ltd 770 PULSE-WIDTH MODULATED DC–DC POWER CONVERTERS x = [list of all the values]; Example: x = [1, 2, 3, 5, 7, 10]; or x = linspace(start-value, stop-value, number-of-points); Example: x = linspace(0, 2*pi, 90); or x = logspace(start-power, stop-power, number-of-points); Example: x = logspace(1, 5, 1000); Semilogarithmic Scale semilogx(x-variable, y-variable); grid on Log-log Scale loglog(x, y); grid on Generate y-axis Data y = f(x); Example: y = cos(x); z = sin(x); Multiplication and Division A dot should be used in front of the operator for matrix multiplication and division c = a.*b; or c = a./b; Symbols and Units Math symbols should be in italic Math signs (like ( ), =, and +) and units should not be in italic Leave one space between a symbol and a unit x-axis and y-axis Labels xlabel(‘{ \it x} (unit) ’) ylabel(‘{ \it y} (unit) ’) INTRODUCTION TO MATLAB Example: xlabel(‘{\it v {GS}} (V)’) ylabel(‘{\it i {DS} } (A)’) set(gca, ‘ylim’, [1, 10]) set(gca, ‘ytick’, [0:2:10]) Greek Symbols Type: \alpha, \beta, \Omega, \omega, \pi, \phi, \psi, \gamma, \theta, and \circ to obtain: α, β, , ω, π , φ, ψ, γ , θ , and ◦ Plot Commands plot (x, y, ‘.-’, x, z, ‘- -’) set(gca, ‘xlim’, [x1, x2]); set(gca, ‘ylim’, [y1, y2]); set(gca, ‘xtick’, [x1:scale-increment:x2]); text(x, y, ‘{\it symbol} = 25 V’); Examples: set(gca, ‘xlim’, [4, 10]); set(gca, ‘ylim’, [1, 8]); set(gca, ‘xtick’, [4:1:10]); text(x, y, ‘{\it V} = 25 V’); 3D Plot Commands plot3(x1, y1, z1); Example: t = linespace(0, 9*pi); xlabel(‘sin(t)’) ylabel(‘cos(t)’) zlabel(‘t’) plot(sin(t), cos(t), t) Bode Plots f = logspace(start-power, stop-power, number-of-points) NumF = [a1 a2 a3]; %Define the numerator of polynomial in s-domain DumF = [a1 a2 a3]; %Define the denominator of polynomial in s-domain [MagF, PhaseF] = bode(NumF, DenF, (2*pi*f)); figure(1) semilogx(f, 20*log10(MagF)) F = tf(NumF, DenF) %Converts the polynomial into transfer function [NumF, DenF] = tfdata(F) %Converter transfer function into polynomial 771 772 PULSE-WIDTH MODULATED DC–DC POWER CONVERTERS Step Response NumFS = D*NumF; t = [0:0.000001:0.05]; [x, y] = step(NumFS, DenF, t); figure(2) plot(t, Initial-Value + y); To Save Figure Go to File, click Save as, go to EPS file option, type the file name, and click Save Example Program clear all clc x = linspace(0, 2*pi, 90); y = sin(x); z = cos(x); grid on xlabel(‘{\it x}’) ylabel(‘ {\it y }, {\it z }’) plot(x , y, ‘-.’, x, z, ‘- -’) Polynomial Curve Fitting x = [0 0.5 1.0 1.5 2.0 2.5 3.0]; y = [10 12 16 24 30 37 51]; p = polyfit(x, y, 2) yc = polyval(p, x); plot(x, y, ‘x’, x, yc) xlabel(‘x’) ylabel(‘y’), grid legend(‘Actual data’, ‘Fitted polynomial’) Answers to Problems 1.1 LNR = 10 mV/V, PLNR = 0.303 % 1.2 LOR = 0.2 mV/mA, PLOR = 0.2 %, Ro = 0.2 , LLR = 1.3 ηFL(min) = 22 %, ηFL(max) = 55 % 1.4 Rin(DC ) = 36 2.2 Lmin = 492.2 µH 2.3 ISMmax = 2.179 A, VSMmax = 32 V 2.4 Vr = 3.214 mV, VCpp = mV, f0 = 1.592 kHz 2.5 Vr = 5.3 mV 2.6 (a) D = 0.5 at η = 100 % (b) D = 0.625 at η = 80 % 2.7 For D = 0.1, PrDS = 0.25 W For D = 0.9, PrDS = 2.25 W 2.8 For D = 0.1, PD = 4.95 W For D = 0.9, PD = 0.55 W 2.9 CJ = 585.95 pF, Cds (VI ) = 25.35 pF, Q(VI ) = 20.32 nC, Psw = 8.112 W, Pturnoff = 5.408 W, Psw (FET ) = 2.704 W 2.10 Lmax = 25.6 µH 2.13 Lmax = 0.2 µH, Cmin = 589 µF, rCmax = m 2.14 Lmax = 8.2 µH, Cmin = 228 µF, rCmax = 37 m 3.2 VSMmax = VDMmax = 380 V, ISMmax = IDMmax = 0.574 A 3.3 Lmin = 44.44 µH 3.4 Lmin = 40.8 µH 3.5 (a) D = 0.5 at η = 100 % (b) D = 0.6 at η = 80 % Pulse-width Modulated DC–DC Power Converters Marian K Kazimierczuk  2008 John Wiley & Sons, Ltd 774 PULSE-WIDTH MODULATED DC–DC POWER CONVERTERS 3.6 PrDS = 0.247 W, PrDS = 0.625 W, PrDS = 1.224 W, PrDS = 2.222 W, PrDS = W, PrDS = 7.5 W, PrDS = 15.556 W, PrDS = 40 W, PrDS = 180 W 3.7 PRF = 2.222 W, PRF = 2.5 W, PRF = W, PRF = 10 W, PRF = 20 W 3.8 PrL = 2.469 W, PrL = 3.125 W, PrL = 4.082 W, PrL = 5.556 W, PrL = W, PrL = 12.5 W, PrL = 22.22 W, PrL = 50 W, PrL = 200 W 3.9 Lmax = 2.22 µH 4.1 Lmin = 304 µH 4.2 Lmin = 283.15 µH 4.3 VSMmax = VDMmax = 235 V, ISMmax = IDMmax = 3.666 A 4.4 Cmin = 61 µF, rCmax = 81.85 m 4.5 PrC = 0.111 W, PrC = 0.25 W, PrC = 0.429 W, PrC = 0.667 W, PrC = W, PrC = 1.5 W, PrC = 2.333 W, PrC = W, PrC = W 4.6 Lmax = 126.39 µH 4.7 Lmax = 115 µH 5.1 n = 1/3, Dmax = 0.6885 5.2 VSMmax = 454 V, VDMmax = 1361 V 5.3 Lm(min) = 711 µH 5.4 ISMmax = 5.183 A, IDMmax = 1.728 A 5.5 Cmin = 1.4 µF, rCmax = 1.736 5.7 (a)Lm(max) = 172.5 µH (b)Lm(max) = 57.849 µH 6.1 (a) DMAX = 0.6667 (b) DMAX = 0.3333 (c) DMAX = 0.2 6.2 (a) VSM = VI (b) VSM = 1.5 VI (c) VSM = 1.25 VI 6.3 (a) VD3M = 1.5 VI (b) VD3M = VI (c) VD3M = VI 6.4 n1 = 6.5 DMAX = 0.5 6.6 Dmin = 0.3119, Dnom = 0.3428, Dmax = 0.381 6.7 VSMmax = 684 V, VD1Mmax = 42.75 V, VD2Mmax = 42.75 V, VD3Mmax = 684 V 6.8 Lmin = 13.762 µH 6.9 Cmin = 229 µF, fo = 2.055 kHz, rCmax = 21.8 m 6.10 ID1Mmax = ID2Mmax = 42.75 A 6.11 Lm(min) = 2.219 mH 6.12 ISMmax = 5.985 A 6.13 Lmax = 12.38 µH 7.2 n = 9, Dmin = 0.3424, Dmax = 0.4193 7.3 VSMmax = 324 V, VDMmax = 38 V ANSWERS 775 7.4 Lmin = 18.9 µH 7.5 Cmin = 41.93 µF, fo = 4.5 kHz 7.6 Lm(min) = 5.08 mH 7.7 Lmax = 0.6858 µH 8.2 n = 2, Dmin = 0.27021, Dmax = 0.3968 8.3 For the transformer center-tapped rectifier, VSMmax = VDMmax = 187 V For the transformer bridge rectifier, VSMmax = VDMmax = 93.5 V 8.4 iLmax = 31.543 A, iLmax /IOmax = 60.6 % 8.5 Lmin = 60.65 µH 8.6 Cmin = 75.58 µF, fo = 1.9 kHz 8.7 Lm(min) = 425.788 µH 8.8 ISM = 35.58 A, IDM = 67.7714 A 8.9 n = 1/10, Dmin = 0.2815, Dmax = 0.4144 8.10 VSMnom = 187 V, VDM = 1870 V 8.11 Lmin = 21.86 mH 8.12 Cmin = 82.88 µF, rCmax = 57.18 9.1 n = 1/5 9.2 Dmin = 0.3509, Dmax = 0.4511 9.3 VSMmax = 108 V, VDMmax = 270 V 9.4 Lmin = mH 9.5 Cmin = 5.639 µF, fo = 1.125 kHz, fripple /fo = 71.11 9.6 IDM = 2.168 A, ISM = 16.26 A 9.8 Lmin = 6.874 µH, Cmin = 24.8 µF, VImax = 31.2 V, ISMmax = 500.52 A, VDMmax = 124.8 V, IDMmax = 54.91 A 9.9 L = 1.5 µH 10.1 IS = 0.4IL , VLD = 0.4 VSD 10.2 rDSAV (S ) = 2.5 , RFAV (D) = 40 m , VFAV (D) = 0.7 V 10.3 rDSAV (L) = 0.4 , RFAV (L) = 14.4 m , VFAV (L) = 0.42 V 10.4 rDSAV (S ) = 2.5 , RFAV (S ) = 90 m , VFAV (S ) = 1.05 V 10.5 rDSAV (D) = 1.1111 , RFAV (D) = 40 m , VFAV (D) = 0.7 V 10.6 r = 0.6144 10.7 rL(S ) = 1.25 , rL(D) = 0.556 10.8 Dil = 0.4il A, IL d = 1.8d A, Dvds = 0.4 vds V, VDS d = 24d V, r = 0.6144 11.1 MVDC = 9.06 dB, η = 98.38 % 776 PULSE-WIDTH MODULATED DC–DC POWER CONVERTERS 11.2 zn = −106 rad/s, zp = 7.1683 krad/s, f0 = 323.55 Hz, ξ = 0.162, Q = 3.086, p1 , p2 = −329.3 ± j 2006.07 rad/s, fd = 319.27 Hz 11.3 Tpo = 61.05 dBV, |Tp (∞)| = −3.84 dBV 11.4 Mvo = dB 11.5 Zi (0) = 220.384 11.6 Zo (0) = 22.216 , Zo (∞) = 11.7 Zo (0) = 3.4 , Zo (0) = 10.96 , Zo (0) = 66.329 , Zo (0) = 238.61 11.8 ξlossy /ξlossless = 1.165, Q = 3.597, ξ = 0.139 12.1 Tm = 0.2 V−1 12.2 VR = 3.25 V 12.3 β = 1/123 = −41.8 dB RB = k , RA = 120 k , h11 = 992 12.4 Tk = 5.162 dB 12.6 Tclo = 41.8 dB 12.7 Ricl (0) = −215 at RLmin , Ricl (0) = −2175 at RLmax 13.1 VI > VO = 10 V 13.2 VI > 11.11 V 13.3 Stable M1 = 76.41 × 103 A/s 13.4 Unstable The converter requires slope compensation 13.5 VTm = 0.664 V, M3opt = 66.45 × 103 A/s 13.6 M3nom = 46.847 × 103 A/s, Ipk = 0.468 A 13.7 Hicl (z ) = 13z /(z + 0.3), Hicl (s) = 120 × 1010 /(s + 323, 076.9s + 12 × 1010 ), Ti(s) = 12 × 1010 /[s(s + 323076.9)] 13.8 VO = −31.154 V 14.1 zi = −1124 rad/s, fzi = 178.8 Hz 14.2 Tpio = 11.19 dBA, Tpix = 142.5 dBA 14.3 Mvio = −46.78 dBA/V, fzi = 89.46 Hz 14.4 Aio = dB, fzn = 159 kHz 15.1 p = 1.5 × 1016 holes/cm3 , ρp = 0.868 cm, σp = 1.152 ( cm)−1 , silicon-to-boron atoms = 3.333 × 106 , p/n = 1012 , ρSi /ρp = 2.058 × 105 15.2 xp = 0.32 µm, xp = 32 µm, W = 32.32 µm, xn /xp = 100 15.3 xp = 0.272 µm, xn = 0.00272 µm, W = 0.2747 µm, xn /xp = 100 15.4 xn = 88 µm, xp = 0.88 µm, W = 88.88 µm, xn /xp = 100, Em = 135.53 kV/cm 15.7 t10 % = 2.3τp 15.8 PRR = W ANSWERS 777 15.9 AJ = 0.05 cm2 , NDmin = 2.1623 × 1016 cm−3 , ln = 5.45 µm, CJ = 864.2 pF, RDR = 0.3849 µ 16.1 µn = 100 cm2 /Vs 16.2 WD = µm, WD = 10 µm, WD = 20 µm, WD = 40 µm 16.3 ND = 2.586 × 1015 cm−3 , ND = 1.293 × 1015 cm−3 , ND = 6.465 × 1014 cm−3 , ND = 3.232 × 1014 cm−3 16.4 VBD = 1295 V, VBD = 129.5 V, VBD = 12.95 V 16.5 VBD = 129.9 kV, VBD = 12.99 kV, VBD = 1.299 kV 16.6 (a) Cox = 34.53 µF/m2 , kp = 2.07 µA/V2 (b) Cox = 345.3 µF/m2 , kp = 20.7 µA/V2 (b) Cox = 3453 µF/m2 , kp = 207 µA/V2 16.7 IDsat = 4.9 A, Rc = 0.714 , Rc(sc) = 1.214 16.8 W = 1.6 × 106 µm, n = 105 , Ac = 3.6 mm, CD = 27, 778 cells/mm2 , SD = 0.444 m/mm2 , U = 0.3556 m/mm2 16.10 Cox = 34.53 nF/cm2 , kp = 13.812 nF/cm2 , (W /L)min = 4.525 × 105 , L = µm, W = 0.4525 m, n = 5.656 × 103 17.1 f0 = MHz, D = 0.667, Lr = 1.2 µH, Cr = 2.7 nF, ISM = A, VSM = 84 V, IDM = A, VDM = 42 V 17.4 f0 = MHz, D = 0.5, Lr = 0.21 µH, Cr = 33 nF, ISM = 20 A, VSM = 24 A, IDM = 10 A, VDM = 48 V INDEX Acceptor, 630, 633, 638 Active clamping, 232, 281, 282, 283 Ambient temperature, 729 Amorphous material, 628 Antiparallel diode, 123, 679 Apparent power, 129 Aspect ratio, 684, 699 Asymmetrical junction, 633 Audio susceptibility, 450, 495, 552, 616 Avalanche breakdown, 637, 642, 668, 699, 701 Average power, 18, 129 Averaged circuit model, 397, 407, 414, 415, 416, 417, 418, 419, 428 Baliga, 704 Band gap energy, 629, 631, 632, 668 Bandwidth, 448, 453 Battery charger, Beveled edge, 645 Bidirectional converter, 123, 174, 229 Bode plots, 448, 449, 451, 452, 474, 475, 477, 482, 492, 533, 538, 570 Body diode, 677, 679, 685, 699, 700, 710, 711, 712, 713, 715 Boost converter, 16, 17, 85, 642, 552, 616 Boost-buck converter, 16, 17, 177, 643 Breakdown voltage, 627, 632, 637, 645, 699, 701, 704, 727 Bridge converter, 17, 289, 325 Bridge rectifier, 132, 290, 326 Buck converter, 16, 23 Buck-boost converter, 16, 17, 129 Built-in potential barrier, 39, 641, 646, 647 Cascade, 73, 178 CCM, 23, 30, 85, 139, 191, 239, 398 Channel-length modulation, 683 Characteristic impedance, 230, 737 Charge carrier, 629, 648, 659, 660, 665, 686 Charge neutrality, 630 Chopper, 24 Circuit averaging, 397 Clamp diode, 233 Class E amplifier, 736 Closed loop, 493, 495, 496, 500, 506, 518, 526, 528, 530, 531, 543, 552, 592, 553, 559 CMOS, 70, 179 Complex power, 129 Comparator, 512 Compensator, 512 Conducted interference, 19 Conduction loss, 43, 49 Conductivity modulation, 636, 680, 727 Constant-frequency control, 512, 561 Continuous conduction mode, 23 Continuous-time model, 399 Control, 257, 469, 512, Controller, 480 Control voltage, 566, 567, 568 Conversion ratio, Converter, 23, 85, 139 Crossover frequency, 484 Current-mode control, 511, 551, 554, 557 Current probe, 512 Current programming, 511 Current ripple, 33, 294 Pulse-width Modulated DC–DC Power Converters Marian K Kazimierczuk  2008 John Wiley & Sons, Ltd 780 INDEX Current source, 25 Current transformer, 512 ´ converter, 16, 17, 177 Cuk DCM, 23, 30, 103, 159, 201, 261, 421 Deadbeat control, 526 Delay time, 448, 576 Depletion region, 633, 638, 683 Diode, 23, 627, 629 Discontinuous conduction mode, 23, 51 Discrete-time model, 530 Displacement factor, 130 Dissipation, 43 Distortion factor, 130 Disturbance, 464, 546 Donor, 630, 633 Drain, 41, 674 Drift current, 629, 660 Drift region, 674, 679, 701, 702, 708, 710, 726 Dual converter, 17, 127 Duality, 127 Duty cycle, 24 Duty ratio, 24, Efficiency, 5, 9, 42, 61, 95, 112, 140, 166, 201, 219, 250, 270, 301, 336, 374 Electromagnetic interference, 19 EMI, 19, 232, 735, 669 Energy, 18, 28, 41, 189, 192, 240, 403, 434, 647 Equivalent series resistance, 33 Error amplifier, 478, 548 Error voltage, 534, 478 ESR, 33, 37, 80, 146 Extrinsic semiconductor, 630, 633, 661 Excess charge, 648, 650, 654 Feedback network, 488, 609 Filter, 24, 69, 192, 530 Flip-flop, 512 Flyback converter, 16, 17, 189 Forced response, 528 Forward converter, 16, 17, 239 Fourier series, 32, 567 Freewheeling diode, 23 Gain margin, 480, 484, 538 Gate, 43, 47, 674 Gate drive, 43, 47 Gate oxide, 674, 701, 784 Gate threshold voltage, 701, 784 Grading coefficient, 647 Half-bridge converter, 17, 289 Harmonics, 32, 411 Heatsink, 728 Heat transfer, 728 conduction, 728 convection, 728 radiation, 728 Hole, 630, 631, 656, 674, 686 Ideal transformer, 190, 193, 242 IGBT, 726 Impact ionization, 637 Incremental capacitance, 646, 649 Inductance, 32, 59, 93, 146, 166, 199, 248, 270, 299, 320, 335, 355, 372, 292 Inductor, 23, 25, 74, 76, 124, 126, 181 Instability, 518, 521 Insulated gate bipolar transistor, 726 Integral control, 480, 485, 488, 611 Integral-lead controller, 480, 485, 488, 611 Intrinsic semiconductor, 628, 667 Inverse converter, 17, 126 Isolated converter, 17, 192, 229 Junction, 632, 637, 645, 647 capacitance, 646, 662 breakdown, 642, 633, 662 temperature, 627, 631, 628, 687, 729 Laplace, 503, 568, 569, 588, 749, 747 Latch, 512, 514 Leakage inductance, 191, 229, 230, 231, 241 Line regulation, 6, Linear model, 411, 415, 417 Linear region, 678, 686 Linearization, 399, 413 Linearized averaged circuit, 397, 415, 417 Load regulation, 7, Loop, 518, 524, 526, 530, 531, 537, 543, 546, 552 Loop gain, 492, 537, 611, 548 Loss, 5, 37, 61, 95, 201, 250, 270, 301, 336, 374, 628 Low-pass filter, 25, 280, 530 Majority carrier device, 656 Metal-oxide-semiconductor field effect transistor, 673 Minority carrier devices, 659 Minority carrier lifetime, 648, 656, 662 Magnetic core, 82, 134, 241 Magnetizing inductance, 191, 198,199, 218, 242, 243, 245, 265, 290, 294, 296, 315, 328, 331, 386 Metal-semiconductor junction, 659 INDEX 781 Mobility, 674, 680, 686, 687, 692, 696, 699, 710 Mobility degradation coefficient, 696 Model, 6, 397, 405, 408, 414, 415, 416, 417, 418 Modulated signal, 567 Modulating signal, 567 MOSFET, 18, 23, 289, 325, 363, 673, 684, 686, 701, 708, 710 Multiphase converter, 77 Multiple outputs, 228, 280 Multi-resonant converter, 759 Quality factor, 442, 446, 574, 575, 743 Quasi-resonant converter, 736, 745, 753 n-type, 630, 633, 638, 640, 648, 659, 661 Natural frequency, 442 Natural response, 526 Noise, 15, 19 Nonlinear capacitance, 39 Nonlinear circuit, 397, 400, 413, 415, 418 Nonlinearity, 39 Nyquist frequency, 413, 433, 531 SH, 526 Sampling-and-hold, 511, 526, 536, 544, 548, 566 Saturation, 635, 678, 685, 678, 692, 695, 696, 698, 710 Saturation region, 678, 686, 715 Sawtooth voltage, 473 Schottky diode, 18, 632, 635, 649, 659, 670 Secondary winding, 190, 296, 329, 363 Second-order filter, 24, 69, 530 Semiconductor, 628, 630 Semiconductor device, 627, 673 SEPIC, 16, 17, 666, 724, 726, 765 Shoot-through, 70 Short-channel effect, 697 Silicon, 627, 628, 631, 673 Silicon carbide, 627, 628, 631, 662, 668, 673, Single-ended converter, 16, 17, 339, 440, 436 Single phase, 17 Slope compensation, 521, 523, 525, 526, 544, 554, 557, 560 Soft switching, 735 Stability, 480, 519, 523, 524, 534 State-space averaging, 397 Stored charge, 650, 679 Stored energy, 28, 220, 240 Switch, 23, 627, 737 Switching frequency, 24 Switching loss, 38, 39, 43, 654, 735 Synchronous rectifier, 69, 124, 178, 179, 180, 281 Off-state, 627 Ohmic region, 678, 679 On-resistance, 42, 403, 627, 705, 708, 727 On-state, 627 On-voltage, 627 Output voltage, 6, 7, 8, 24 Op-amp, 512 Open loop, 437, 440, 450, 453, 455, 458, 571, 576, 581, 585, 588, 590 Overshoot, 459, 462i, 464, 586, 589, 591 p-type, 631, 633, 640, 648, 660, 674 Parasitic capacitances, 710 Perturbation, 413, 518, 519, 520, 521, 525, 526, 527 PFC, 129, 132 Phase, 191, 326, 442, 455, 458, 540, 549 Phase control, 357 Phase margin, 480, 484, 538, 541, 550 Phase shift, 191 Pinch-off region, 678 Pole, 442, 531, 544, 574, 575 Polyphase converter, 77 Polysilicon, 674, 714, 715 Power factor, 129 Power factor correction, 129, 132 Power quality, 131 Primary winding, 190, 229, 230, 290, 330, 363 Punch-through breakdown, 642, 643 Push-pull converter, 17, 263 Pulse-width modulation, 1, 65, 289, 471 PWM, 1, 65, 289, 325, 471, 551 Rational function, 532 Real power, 129 Reference voltage source, 13 Regulation, 6, 7, Reverse recovery, 650, 651, 662, 669 Richardson constant, 661 RHP, 442, 444, 530, 546 Right-hand plane zero, 442, 464 Ripple, 32, 93, 146, 218, 248, 299, 335, 372 THD, 130 Thermal management, 632, 728 Thermal model, 728 Thermal resistance, 728 Thermal resistivity, 728 Threshold voltage, 12, 635, 677, 685, 686 Topology, 17, 727, 736 Total harmonic distortion, 130 Transfer function, 441, 448, 450, 472, 552, 559 782 INDEX Transform, 503, 567, 568, 569, 588, 747, 749 Transformer, 17, 189, 190, 192, 193, 239, 289, 290, 326, 363 Triode region, 678 Transient response, 458, 502, 620 Transition, 37, 39, 40, 651, 657, 665, 710 Turns ratio, 190, 241, 306, 341, 378 Unity power factor, 129, 130, 132, 133 Unstable, 519, 521, 524, 532, 534, 546 Utility, 1, 129, 132 Variable, 531 Voltage clamp, 231 Voltage-mode control, 469 Voltage regulation, 1, 13, 14 Volt-second balance, 29 z -domain, 530 z -transform, 530, 530 ZCS, 736, 751, 760, 763 Zero-current switching, 736, 751, 753 Zero, 442, 444, 574, 579, 583 ZOH, 526, 531 Zero-order hold, 526, 531, 569 ZVS, 736, 745, 760, 763 Zero-voltage switching, 736, 745, 763