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Contents18.2Realization of a Near-Ideal Rectifierxv640CCM Boost ConverterDCM Flyback Converter64264618.3Control of the Current Waveform64818.418.3.1 Average Current Control18.3.2 Current Programmed Control18.3.3 Critical Conduction Mode and Hysteretic Control18.3.4 Nonlinear Carrier ControlSingle-Phase Converter Systems Incorporating Ideal Rectifiers64865465765966366366818.518.4.1 Energy Storage18.4.2 Modeling the Outer Low-Bandwidth Control SystemRMS Values of Rectifier Waveforms67467618.618.5.1 Boost Rectifier Example18.5.2 Comparison of Single-Phase Rectifier TopologiesModeling Losses and Efficiency in CCM High-Quality Rectifiers67968168368418.718.6.1 Expression for Controller Duty Cycle d(t)18.6.2 Expression for the DC Load Current18.6.3 Solution for Converter Efficiency 1118.6.4 Design ExampleIdeal Three-Phase Rectifiers18.8Summary of Key s696vResonant Converters70319Resonant Conversion70519.1Sinusoidal Analysis of Resonant Converters19.1.1 Controlled Switch Network Model19.1.2 Modeling the Rectifier and Capacitive Filter Networks19.1.3 Resonant Tank Network19.1.4 Solution of Converter Voltage Conversion Ratio M V!Vg70971071171371419.2Examples19.2.1 Series Resonant DC-DC Converter Example19.2.2 Subharmonic Modes of the Series Resonant Converter19.2.3 Parallel Resonant DC-DC Converter Example19.3Soft Switching71571571771872119.3.119.3.219.4Operation of the Full Bridge Below Resonance:Zero-Current SwitchingOperation of the Full Bridge Above Resonance:Zero-Voltage SwitchingLoad-Dependent Properties of Resonant Converters19.4.1 Inverter Output Characteristics19.4.2 Dependence of Transistor Current on Load19.4.3 Dependence of the ZVS/ZCS Boundary on Load Resistance722723726727729734

xviContents19.4.420Another Example19.5Exact Characteristics of the Series and Parallel Resonant Converters19.619.5.1 Series Resonant Converter19.5.2 Parallel Resonant ConverterSummary of Key Points737740740748References752752Problems755Soft Switching76120.1Soft-Switching Mechanisms of Semiconductor Devices76276376576820.220.1.1 Diode Switching20.1.2 MOSFET Switching20.1.3 IGBT SwitchingThe Zero-Current-Switching Quasi-Resonant Switch Cell20.2.120.2.220.2.3Waveforms of the Half-Wave ZCS Quasi-Resonant Switch CellThe Average Terminal WaveformsThe Full-Wave ZCS Quasi-Resonant Switch Cell76877077477920.3Resonant Switch Topologies78178378478720.420.3.1 The Zero-Voltage-Switching Quasi-Resonant Switch20.3.2 The Zero-Voltage-Switching Multi-Resonant Switch20.3.3 Quasi-Square-Wave Resonant SwitchesSoft Switching in PWM Converters20.4.1 The Zero-Voltage Transition Full-Bridge Converter20.4.2 The Auxiliary Switch Approach20.4.3 Auxiliary Resonant Commutated Pole20.5 Summary of Key PointsReferencesProblemsAppendicesAppendix A790791794796797798800803RMS Values of Commouly-Observed Converter Waveforms805A.lSome Common Waveforms805A.2General Piecewise Waveform809Appendix BB.lB.2Simulation of ConvertersAveraged Switch Models for Continuous Conduction ModeB.l.lBasic CCM Averaged Switch ModelB.l.2CCM Subcircuit Model that Includes Switch Conduction LossesB.l.3Example: SEPIC DC Conversion Ratio and EfficiencyB.l.4Example: Transient Response of a Buck-Boost ConverterCombined CCM/DCM Averaged Switch ModelB.2.lExample: SEPIC Frequency ResponsesB.2.2Example: Loop Gain and Closed-Loop Responsesof a Buck Voltage Regulator813815815816818819822825827

ContentsB.2.3 Example: DCM Boost RectifierCurrent Programmed ControlCurrent Programmed Mode Model for SimulationB.3.1B.3.2 Example: Frequency Responses of a Buck Converter withCurrent Programmed ControlReferencesB.3AppendixCMiddlebrook's Extra Element TheoremBasic ResultDerivationDiscussionExamplesA Simple Transfer FunctionC.4.1C.4.2 An Unmodeled ElementC.4.3 Addition of an Input Filter to a ConverterC.4.4 Dependence of Transistor Current on Load in a Resonant InverterReferencesC.lC.2C.3C.4AppendixDMagnetics Design TablesPot Core DataD.lD.2 EE Core DataD.3 EC Core DataD.4 . ETD Core DataD.5 PQ Core DataD.6 American Wire Gauge 850850855857859861863864865866866867868869871

PrefaceThe objective of the First Edition was to serve as a textbook for introductory power electronics courseswhere the fundamentals of power electronics are defined, rigorously presented, and treated in sufficientdepth so that students acquire the knowledge and skills needed to design practical power electronic systems. The First Edition has indeed been adopted for use in power electronics courses at a number ofschools. An additional goal was to contribute as a reference book for engineers who practice power electronics design, and for students who want to develop their knowledge of the area beyond the level ofintroductory courses. In the Second Edition, the basic objectives and philosophy of the First Edition havenot been changed. The modifications include addition of a number of new topics aimed at better servingthe expanded audience that includes students of introductory and more advanced courses, as well aspracticing engineers looking for a reference book and a source for further professional development.Most of the chapters have been significantly revised and updated. Major additions include a new Chapter10 on input filter design, a new Appendix B covering simulation of converters, and a new Appendix C onMiddlebrook's Extra Element Theorem. In addition to the introduction of new topics, we have mademajor revisions of the material to improve the flow and clarity of explanations and to provide additionalspecific results, in chapters covering averaged switch modeling, dynamics of converters operating in discontinuous conduction mode, current mode control, magnetics design, pulse-width modulated rectifiers,and resonant and soft-switching converters.A completely new Chapter 10 covering input filter design has been added to the second addition. The problem of how the input filter affects the dynamics of the converter, often in a manner thatdegrades stability and performance of the converter system, is explained using Middlebrook's Extra Element Theorem. This design-oriented approach is explained in detail in the new Appendix C. Simple conditions are derived to allow filter damping so that converter transfer functions are not changed. Completeresults for optimum filter damping are presented. The chapter concludes with a discussion about thedesign of multiple-section filters, illustrated by a design example.Computer simulation based on the averaged switch modeling approach is presented in Appendix B, including PSpice models for continuous and discontinuous conduction mode, and current-modecontrol. Extensive simulation examples include: finding the de conversion ratio and efficiency of aSEPIC, plotting the transient response of a buck-boost converter, comparing the control-to-output transfer functions of a SEPIC operating in CCM and DCM,determining the loop gain, line-to-output transferfunction, and load transient response of a closed-loop buck voltage regulator, finding the input current

xxPrefacewaveform and THD of a DCM boost rectifier, and comparing the transfer functions and output impedances of buck converters operating with current programmed control and with duty cycle control. Themajor purpose of Appendix B is to supplement the text discussions, and to enable the reader to effectively use averaged models and simulation tools in the design process. The role of simulation as a designverification tool is emphasized. In our experience of teaching introductory and more advanced powerelectronics courses, we have found that the use of simulation tools works best with students who havemastered basic concepts and design-oriented analytical techniques, so that they are able to make correctinterpretations of simulation results and model limitations. This is why we do not emphasize simulationin introductory chapters. Nevertheless, Appendix B is organized so that simulation examples can beintroduced together with coverage of the theoretical concepts of Chapters 3, 7, 9, 10, 11, 12, and 18.Middlebrook's Extra Element Theorem is presented in Appendix C, together with four tutorialexamples. This valuable design-oriented analytical tool allows one to examine effects of adding an extraelement to a linear system, without solving the modified system all over again. The theorem has manypractical applications in the design of electronic circuits, from solving circuits by inspection, to quicklyfinding effects of unmodeled parasitic elements. In particular, in the Second Edition, Middlebrook'sExtra Element Theorem is applied to the input filter design of Chapter 10, and to resonant inverter designin Chapter 19.In Chapter 7, we have revised the section on circuit averaging and averaged switch modeling.The process of circuit averaging and deriving averaged switch models has been explained to allow readers not only to use the basic models, but also to construct averaged models for other applications of interest. Examples of extensions of the averaged switch modeling approach include modeling of switchconduction and switching losses. Related to the revision of Chapter 7, in Appendix B we have includednew material on simulation of converters based on the averaged switch modeling approach.Chapter 8 contains a new substantial introduction that explains the engineering design processand the need for design-oriented analysis. The discussions of design-oriented methods for constructionof frequency response have been revised and expanded. A new example has been added, involvingapproximate analysis of a damped input filter.Chapter 11 on dynamics of DCM (discontinuous conduction mode) converters, and Chapter 12on current-mode control, have been thoroughly revised and updated. Chapter 11 includes a simplifiedderivation of DCM averaged switch models, as well as an updated discussion of high-frequency DCMdynamics. Chapter 12 includes a new, more straightforward explanation and discussion of current-modedynamics, as well as new complete results for transfer functions and model parameters of all basic converters.The chapters on magnetics design have been significantly revised and reorganized. Basic magnetics theory necessary for informed design of magnetic components in switching power converters ispresented in Chapter 13. The description of the proximity effect has been completely revised, to explainthis important but complex subject in a more intuitive manner. The design of magnetic components basedon the copper loss constraint is described in Chapter 14. A new step-by-step design procedure is givenfor multiple-winding inductors, and practical design examples are included for the design of filter inductors, coupled inductors and fly back transformers. The design of magnetic components (transformers andac inductors) based on copper and core loss considerations is described in Chapter 15.To improve their logical flow, the chapters covering pulse-width modulated rectifiers have beencombined into a single Chapter 18, and have been completely reorganized. New sections on current control based on the critical conduction mode, as well as on operation of the CCM boost and DCM fly backas PWM rectifiers, have been added.Part V consists of Chapter 19 on resonant converters and Chapter 20 on soft-switching converters. The discussion of resonant inverter design, a topic of importance in the field of high-frequency electronic ballasts, has been expanded and explained in a more intuitive manner. A new resonant inverter

xxidesign example has also been added to Chapter 19. Chapter 20 contains an expanded tutorial explanationof switching loss mechanisms, new charts illustrating the characteristics of quasi-square-wave and multiresonant converters, and new up-to-date sections about soft-switching converters, including the zerovoltage transition full-bridge converter, the auxiliary switch approach, and the auxiliary resonant commutated pole approach for de-de converters and dc-ac inverters.The material of the Second Edition is organized so that chapters or sections of the book can beselected to offer an introductory one-semester course, but yet enough material is provided for a sequenceof more advanced courses, or for individual professional development. At the University of Colorado, wecover the material from the Second Edition in a sequence of three semester-long power electronicscourses. The first course, intended for seniors and first-year graduate students, covers Chapters 1 to 6,Sections 7.1, 7.2, 7.5, and 7.6 from Chapter 7, Chapters 8 and 9, and Chapters 13 to 15. A project-oriented power electronics design laboratory is offered in parallel with this course. This course serves as aprerequisite for two follow-up courses. The second course starts with Section 7.4, proceeds to Appendices B and C, Chapters 10, 11 and 12, and concludes with the material of Chapters 16 to 18. In the thirdcourse we cover resonant and soft-switching techniques of Chapters 19 and 20.The website for the Second Edition contains comprehensive supporting materials for the text,including solved problems and slides for instructors. Computer simulation files can be downloaded fromthis site, including a PSpice library of averaged switch models, and simulation examples.This text has evolved from courses developed over seventeen years of teaching power electronics at the University of Colorado. These courses, in tum, were heavily influenced by our previous experiences as graduate students at the California Institute of Technology, under the direction of Profs.Slobodan Cuk and R. D. Middlebrook, to whom we are grateful. We appreciate the helpful suggestionsof Prof. Arthur Witulski of the University of Arizona. We would also like to thank the many readers ofthe First Edition, students, and instructors who offered their comments and suggestions, or who pointedout errata. We have attempted to incorporate these suggestions wherever possible.ROBERTW. ERICKSONDRAGAN MAKSIMOVICBoulder, Colorado

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