20
R. Bausiere · E Labrique · G. Seguier
Power Electronic Converters DC-DC Conversion
With 268 Figures
Springer-Verlag Berlin Heidelberg GmbH
Professor Dr. Robert Bausiere
Universite des Sciences et Techniques de Lille 59655 Villeneuve d'Ascq Cedex France
Professor Dr. Francis Labrique
Universite Catholique de Louvain 1348 Louvain-la-Neuve Belgique
Professor Dr. Guy Seguier Universite des Sciences et Techniques de Lille 59655 Villeneuve d'Ascq Cedex France
Translated from the French by the authors with the help of N. Quayle
This is the third volume in a series. The first two were published in English by McGraw Hill the first-on AC/DC conversion, in !986, the second-an AC/ AC conversion, in 1987.
These two volumes are often referred to in the present work.
ISBN 978-3-642-52456-1 ISBN 978-3-642-52454-7 (eBook) DOI 10.1007/978-3-642-52454-7
Library of Congress Cataloging-in-Publication Data
Bausiere, R. (Robert), 194 7 [Convertisseurs de l'electronique de puissance. English] Power electronic converters: DC-DC conversion/R. Bausiere, F. Labrique, G. Seguier. p. cm. - (Electric energy systems and engineering series). Translation of: Les convertisseurs de l'electronique de puissance. Includes bibliographical references and index.
1. Electric current converters. I. Labrique, F. (Francis), 1946- Il. Seguier, Guy. III. Title. IV. Series. TK7872.C8B39 1993 92-10524 621.3815'322-dc20 CIP
This work is subject to copyright. Ali rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright La w of September 9, 1965, in its current version and a copyright fee must always be paid. Violations fali under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heide1berg 1993 Originally pub1ished by Springer-Verlag Berlin Heide1berg New York in 1993
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
Typesetting: Macmillan (India) Ltd., Bangalore, India 61/3020 - 5 4 3 2 1 O - Printed on acid-free paper
Series Editors:
Prof. J.G. Kassakian Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA
Prof. D.H. Naunin Institut ftir Elektronik, Technische Universtiit Berlin, Einsteinufer 19, W-1000 Berlin 10, FRG
Introduction to the Electric Energy Systems and Engineering Series
Concerns for the continued supply and efficient use of energy have recently become important forces shaping our lives. Because of the influence which energy issues have on the economy, international relations, national security, and individual well-being, it is necessary that there exists a reliable, available and accurate source of information on energy in the broadest sense. Since a major form of energy is electrical, this new book series titled Electric Energy Systems and Engineering has been launched to provide such an information base in this important area.
The series coverage will include the following areas and their interaction and coordination: generation, transmission, distribution, conversion, storage, utilization, economics.
Although the series is to include introductory and background volumes, special emphasis will be placed on: new technologies, new adaptations of old technologies, materials and components, measurement techniques, controlincluding the application of microprocessors in control systems, analysis and planning methodologies, simulation, relationship to, and interaction with, other disciplines.
The aim of this series is to provide a comprehensive source of information for the developer, planner, or user of electrical energy. It will also serve as a visible and accessible forum for the publication of selected research results and monographs of timely interest. The series is expected to contain introductory level material of a tutorial nature, as well as advanced texts and references for graduate students, engineers and scientists.
The editors hope that this series will fill a gap and find interested readers.
John G. Kassakian ·Dietrich H. Naunin
Preface
This book is the third in a series of four devoted to POWER ELECTRONIC CONVERTERS:
The first of these concerns AC to DC conversion. The second concerns AC to AC conversion. This volume examines DC to DC conversion. The fourth is devoted to DC to AC conversion.
Converters which carry out the DC-DC conversion operate by chopping the input voltage or current: they are called choppers or switch-mode power converters. Their operating frequency is not imposed by either the input or the output, both of which are at zero frequency. A frequency which is much greater than that of the industrial network can be chosen, provided that suitable configurations and semiconductor devices are used. This is the first difference compared to the rectifiers and AC-AC converters, analyzed in the previous volumes and which often operate at the industrial network frequency.
The second difference concerns the commutation mode. Choppers operate in forced commutation. The beginning of an operating phase does not automatically turn off the semiconductor devices which were conducting during the previous phase and which have to be brought to the blocking state. This turn-off must be carried out autonomously.
These two differences - the higher frequency of commutations and, especially, the different mode of commutation -justify the first two chapters in this work: - Chapter 1 examines general notions concerning converters, supplies and
loads, and more especially, how they can be characterized with regard to commutations.
- Chapter 2 presents semiconductor devices during commutation. The notions concerning the diode and the thyristor outlined at the beginning of Vol. 1 are insufficient, when commutations become an essential phenomenon. Moreover, other components, specially adapted to forced commutation, have to be presented. These two chapters provide an introduction to the analysis of choppers as
well as of inverters. The latter are the subject of the fourth volume in this series.
The following four chapters are devoted to the detailed analysis of DC-DC converters.
X Preface
- Chapter 3 gives a general presentation of chopper structures. - Chapter 4 provides a quantitative analysis of the most common types of
choppers with direct energy transfer. - Chapter 5 examines the most commonly used procedures employed for
turning off thyristors in choppers. - The most widely used configurations of switch-mode power supplies form the
basis of the analysis in Chap. 6.
We thank Robert Bausiere and Francis Labrique for their valuable contributions to the preparation of this volume. R. Bausiere was responsible for Chaps. 2 and 6, as well as for the Appendix on snubbers. F. Labrique was responsible for Chaps. 4 and 5.
As we noted at the beginning of the previous volume, it is somewhat artificial to divide the whole group of converters into four groups according to the conversions each carries out. Different conversions can be obtained with the same structure and can be analyzed together.
This is especially true in the case of choppers and inverters. When controlled in a different way, reversible choppers can operate as inverters. In the part concerning the thyristor turn-off circuits, the analysis of circuits common to two thyristors, connected in series under the same voltage will not be analyzed in detail. Nor will the study of the switching DC power supplies consisting of the cascade association of an inverter, a transformer and a rectifier. Both topics will be taken up in the following volume.
The guiding principle of this collection is to provide a useful and practical tool to power electronics specialists - whether they are designers or users of power converters, in activity or graduating. We have tried to remain faithful to this principle.
The chapter on semiconductor devices in no way lays claim to being a summary of power components physics. It only uses the aspects of this topic which are indispensable for explaining the operation of semiconductor devices in the circuits into which they are embedded, for understanding how they are characterized and the way in which they can be most efficiently used.
Before developing the quantitative analysis of DC-DC converters, we give a very brief description of their basic principles in order to focus on the topics which are to be dealt with; this is the main aim of Chap. 3.
In the detailed further analysis of the most common types of choppers and of switch-mode power supplies, we have developed the computations as far as necessary to obtain the characteristics which are of most immediate interest to users. 1
Lille, August 1992 G. Seguier
1We are very grateful to Mrs. Reine Del Vitto for typing the manuscript and to Mr. Paul Leroy for drawing the figures of this book.
Notes
In order to limit the bibliography to a reasonable length, we have only quoted publications from 1970 onwards.
Insofar as articles are concerned, we have limited the references to those published in the Proceedings and Transactions of the Institute of Electrical and Electronic Engineers (U.S.A.), the Proceedings of the Institute of Electrical Engineers (G.B.), and the Revue Gimerale de /'Electricite (France).
The bibliography concerning: • Power Semiconductor devices is to be found at the end of Chap. 2. • Choppers, at the end of Chap. 4. • Switch-Mode Power Supplies, at the end of Chap. 6. Articles concerning commutation circuits of thyristors are to be found at the
end of chapter 5 and those concerning snubbers at the end of Appendix.
Contents
Chapter 1 Converters, Supplies and Loads: Introductory Remarks.
1.1 Commutation Modes .............. . 1.1.1 1.1.2 1.1.2.1 1.1.2.2 1.2 1.2.1 1.2.1.1 1.2.1.2 1.2.1.3 1.2.2 1.2.2.1 1.2.2.2 1.2.2.3 1.2.3 1.2.3.1 1.2.3.2 1.2.3.3 1.3 1.3.1 1.3.2
Natural Commutation. Forced Commutation. Nature of the Path to be Opened ....... . The Semiconductor Switch ........... . The Semiconductor Switch Incorporated in the Converter Sources ................ . Voltage/Current Generator or Load Definitions and Representations . Real Generators and Loads . . . . . Operating Conditions ........ . Generator and Load Reversibility. Sources. Examples . Instantaneous Reversibility. DC Source Examples ............... . AC Source Examples ............... . Improving or Changing the Nature of a Source. DC Sources ............ . AC Sources ............ . Frequency Increase: Advantages. Time Intervals .......... . Example .............. . Differences in Time Intervals: Consequences.
Chapter 2
2 2 3 3 4 4 5 6 6 8 8 8 9 9
10 10 12 13 13 13 15
Switching Power Semiconductor Devices. . . . . . . . . . . . . . . 17
2.1 Diodes . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.1 2.1.1.1 2.1.1.2 2.1.1.3 2.1.2 2.1.2.1
Remarks on the P-N Semiconductor Junction . Doping, Junction, Space Charge. Forward-Biased Junction ..... . Reverse-Biased Junction. . . . . . . Diode Steady-State Characteristics On-State ............... .
17 17 18 19 19 19
XIV
2.1.2.2 2.1.2.3 2.1.2.4 2.1.3 2.1.3.1 2.1.3.2 2.1.3.3 2.1.4 2.1.4.1 2.1.4.2 2.1.4.3 2.1.4.4 2.2 2.2.1 2.2.1.1 2.2.1.2 2.2.1.3 2.2.2 2.2.2.1 2.2.2.2 2.2.2.3
2.2.3 2.2.3.1 2.2.3.2 2.2.3.3 2.2.4 2.2.4.1 2.2.4.2 2.2.4.3 2.2.4.4 2.2.5 2.2.5.1 2.2.5.2 2.2.5.3 2.2.5.4 2.2.5.5 2.2.6 2.2.6.1 2.2.6.2 2.2.6.3 2.2.6.4 2.2.6.5 2.3 2.3.1
On-State Losses ...... . The Surge Factor: Remarks Off State .......... . Switching Characteristics . Turn-on Transient . Turn-off Transient ... . Switching Losses .... . Notes on Special Diodes High-Voltage Diodes .. Controlled Avalanche Diodes Fast Diodes .......... . Low on-State-Voltage-Drop-Diodes. Bipolar Transistors ..... . Principle: Off-State. On-State The Transistor Effect Off State ........... . Saturation .......... . Steady-State Characteristics Output Characteristics ... Drive Characteristics, Current Limitation Avalanche Breakdown at the C-B 1 unction, Voltage Limitation ............ . Safe Operating Areas . . . . . . ON-State Safe Operating Area. Switch-Mode Operating Areas. Accidental Overload Areas . Turn-on Commutation .... . Establishing the Current ... . Description of a Commutation. Turn-on Losses ....... . Reducing the Turn-on Time Turn-off Commutation .. . Current Turn-off ...... . Description of a Commutation. Turn-off Losses ...... . Reducing Turn-off Time .. Reverse Current: Remarks The Darlington Circuit . Current Gain ...... . Stabilization Resistances Turn-on Switching ... . Turn-off Switching ... . The Monolithic Darlington Circuit . Field Effect Transistors .. . Description and Operation ..... .
Contents
20 21 21 22 23 24 27 28 28 28 29 29 29 29 30 31 32 33 33 34
36 38 38 39 40 41 42 43 44 45 46 46 47 47 49 51 52 52 53 55 55 57 58 59
Contents
2.3.1.1 2.3.1.2 2.3.1.3 2.3.2 2.3.2.1 2.3.2.2 2.3.2.3 2.3.2.4 2.3.2.5 2.3.3 2.3.3.1 2.3.3.2 2.3.3.3 2.3.4 2.3.4.1 2.3.4.2 2.3.4.3 2.3.5 2.4 2.4.1 2.4.1.1 2.4.1.2 2.4.1.3 2.4.1.4 2.4.1.5 2.4.2 2.4.2.1 2.4.2.2 2.4.3 2.4.3.1 2.4.3.2 2.4.3.3 2.4.3.4 2.4.3.5 2.4.4 2.4.4.1 2.4.4.2 2.4.4.3 2.4.4.4 2.4.5 2.4.5.1 2.4.5.2 2.4.5.3 2.4.5.4 2.4.5.5
Low-Power MOSFET. Operating Principle .. "Power" MOSFETS .. Steady-State Characteristics Output Characteristics .. . Input Characteristics .... . Apparent Resistance in the on-State Safe Operating Area ...... . The Parasitic Diode: Remarks ... . Commutations ............ . Stray Capacitances and Their Charge Turn-on-Switching ........... . Turn-off-Switching ........... . MOS Transistor-Bipolar Transistor Associations. BIPMOS Circuit. Cascode Circuit .................. . Parallel Circuit ................... . Notes on the Insulated Gate Bipolar Transistor Thyristors .......... . Description and Operation ...... . Description ............... . Forward-Biased Thyristor Triggering. Thyristor Turn-off .... Two-Transistor Analogy .. Reverse-Bias . . . . . . . . . Steady-State Characteristics Output Current-Voltage Characteristics Gate Characteristics ... . Switching Characteristics ........ . Turn-on Transient ............ . Limitation of the Current Rate of Rise (di/dt). Turn-off Transient ................ . Reapplied Forward Voltage Rate of Rise (du/dt): Limitation . Overvoltage Protection . . . Special Thyristors ........ . Amplifying Gate Thyristor ... . Gate-Assisted Turn-off Thyristor Asymmetrical Thyristor . . . . . . Reverse-Conducting Thyristor .................. . Triacs ............ . Description . . . . . . . . . . Steady-State Characteristics Gate Pulse Triggering ... . Switchings .......... . Increasing the dvjdt ........................ .
XV
59 59 60 60 60 61 62 63 63 64 64 66 67 68 68 69 69 70 71 72 72 73 74 74 75 76 76 77 78 78 80 80 82 83 84 84 84 84 85 86 86 86 87 88 89
XVI
2.5 2.5.1 2.5.2 2.5.2.1 2.5.2.2 2.5.2.3 2.5.3
GTO Thyristors ..... . Description ........ . Operation. Characteristics Turn-on ......... . Turn-off .......... . Outstanding Parameters . Remarks on the Gate Control .
Contents
90 90 91 91 92 97 98
2.5.4 Remarks Concerning the Losses. 100 101 Bibliography ................................... .
Chapter 3 DC-DC Converter Circuits: An Overview. 110
3.1 3.1.1 3.1.1.1 3.1.1.2 3.1.2 3.1.3 3.2 3.2.1 3.2.1.1 3.2.1.2
3.2.2 3.2.2.1 3.2.2.2 3.2.2.3 3.2.3 3.2.3.1 3.2.3.2 3.2.3.3 3.3 3.3.1 3.3.1.1 3.3.1.2 3.3.1.3 3.3.2
3.3.3 3.3.3.1
3.3.3.2
3.4
"Switches" Classification . . . . . . . 110 Unidirectional ''Switches". . . . . . . 110 Naturally Commutated Converters . 111 Force-Commutated Converters 111 Bidirectional "Switches". . . . . . . . 112 Remarks. . . . . . . . . . . . . . . . . 113 Directly Linked DC-DC Converters with Two "Switches" 114 Common Properties. . . . . . . . . . . . . . . . . . . . . . 114 Directly Linked DC-DC Converters . . . . . . . . . . . . 114 Configuration and Transformation Ratio of Converters with Two Switches. . . . . . . . . . . 115 Non-Reversible DC-DC Converters 116 Buck Converter. . 116 Boost Converter . . . . . . . . . 118 Remark . . . . . . . . . . . . . . 119 Reversible DC-DC Converters 119 General Remarks. . . . . . . . . 119 Presentation of the Three Structures 120 Analysis of the Current-Reversible Chopper. . . . . . . . . 122 Full-Bridge DC-DC Converters. 125 Most Usual Configuration . 125 Sequential Control. . . . . . . . . 126 Continuous Control . . . . . . . . 129 Comparison of the Two Control Methods. 131 Remarks on Choppers with Two Controlled Switches Series-Connected Across the DC Voltage Source . . . . 132 Other Types of Full-Bridge DC-DC Converters . . . . 133 Chopper Connecting a Current-Reversible Voltage Source to a Voltage-Reversible Current Source . . . . . . . . . . . . 134 Chopper Connecting a Voltage-Reversible Voltage Source to a Current- and Voltage Reversible Current Source . 135 Indirectly Linked DC-DC Converters . . . . . . . . . . . . . . 139
Contents
3.4.1 3.4.2 3.4.2.1 3.4.2.2 3.4.2.3 3.4.3 3.4.4 3.4.4.1 3.4.4.2 3.4.4.3 3.4.5
XVII
Non-Reversible Chopper with Inductive Energy Storage 140 Reversible Choppers with Inductive Energy Storage. 142 Voltage-Reversible Chopper . . . . . . . . . 142 Current-Reversible Chopper . . . . . . . . . . . . . . . 143 Current- and Voltage-Reversible Chopper . . . . . . . 146 Non-Reversible Chopper with Capacitive Energy Storage. 146 Reversible Choppers with Capacitive Energy Storage 149 Voltage-Reversible Chopper . . . . . . . . . 149 Current-Reversible Chopper . . . . . . . . . . . . . . . 149 Current- and Voltage-Reversible Chopper. . . . . . . 149 Remarks on Choppers with Intermediate Energy Storage Stage 152
Chapter 4 Operation and Characteristics of Directly Linked Choppers . ........................... .
4.1 4.1.1 4.1.1.1 4.1.1.2 4.1.1.3 4.1.2 4.1.3 4.1.3.1 4.1.3.2 4.1.4 4.1.4.1 4.1.4.2 4.1.5 4.1.5.1 4.1.5.2 4.2 4.2.1 4.2.2 4.2.2.1 4.2.2.2 4.2.3 4.2.4 4.2.5 4.3 4.3.1 4.3.1.1 4.3.1.2 4.3.1.3 4.3.2
Effects of Current Source Imperfection ......... . Continuous Conduction: Straightforward Calculation . Current Expressions ...... . Characteristics . . . . . . . . . . . . . . . . . . . . . . Continuous Conduction Limit ............ . Continuous Conduction. "First harmonic" Method Discontinuous Conduction. Straightforward Calculation Current Analysis .................... . Characteristics . . . . . . . . . . . . . . . . . . . . . . Discontinuous Conduction. Simplified Calculation. Equations ....... . Characteristics . . . . . Full-Bridge Choppers . Sequential Control ... Continuous Control .. Correcting the Voltage Source . Operation. Equations ..... . Ripple in Voltage u and Current is Step-down Chopper ......... . Step-up Chopper ........... . Characteristics. Choice of C and Ls . Full-Bridge Choppers ..... . The "First-Harmonic" Method ... . Multiphase Choppers ........ . Switch Operation. Output Waveforms . Output Current Expression. Ripple ... Approximate Calculation of the Output Current Ripple. Current in the Elementary Choppers . Input-Filter Behaviour ................... .
154
154 155 156 157 163 168 170 170 172 176 176 178 179 179 180 184 187 188 189 193 193 195 197 199 200 200 203 204 207
XV Ill
4.3.3 4.3.3.1
Contents
Characteristics ............ . Output Current Ripple t..i' ..... .
4.3.3.2 Current Ripple M in the Choppers.
208 209 210 211 211
4.3.3.3 Output Voltage Ripple t..u in the Filter. 4.3.3.4 Supply Current Ripple t..i5 ....... .
4.3.4 Remarks about the Filter Common to Several Separate Choppers ..................... .
4.4 Notes on Choppers in Traction Applications . 211 212 213 213 216 217 217 219 221 224
4.4.1 Traction Operation ............ . 4.4.1.1 Determination of the Motor Current .. . 4.4.1.2 Choice of Chopper Frequency: Remarks. 4.4.2 Rheostatic Braking ............. . 4.4.2.1 Current Build-up: Operational Boundaries. 4.4.2.2 Controlling the Mean Current ....... . 4.4.3 Regenerative Braking ............ . Bibliography ................................... .
Chapter 5 Forced Commutation of Thyristors . . . . . . . . . . . . . . . . . . . 229
229 231 231 233 234 237
5.1 Parallel Commutation by Capacitor 5.1.1 Operation ................. . 5.1.1.1 Successive Phases. Waveforms ..... . 5.1.1.2 5.1.1.3 5.1.1.4 5.!.2 5.1.2.1 5.1.2.2 5.!.2.3 5.1.3 5.2 5.2.1 5.2.1.1 5.2.1.2 5.2.2 5.2.2.1 5.2.2.2 5.2.2.3 5.2.3 5.3 5.3.1 5.3.2 5.3.2.1 5.3.2.2
Commutation Time. Reverse-Bias Time Addition of an Auxiliary Discharge Circuit The Anti-Return Diode ........... . Effects of the Turn-off Circuit . . . . . . . . 237 Influence on the Voltage Across the Load . 237 Influence on the Current Supplied by the Generator. 238 Influence on the Semiconductor Device Ratings 239 Characteristics . . . . . . . . . . . . . . . . . . 239 Parallel Commutation by Oscillating Circuit 240 Operation. . . . . . . . . . . . . . . . . . . . . 241 Successive Phases, Waveforms. . . . . . . . . 241 Role of the Damping Circuit Da-Ra: Choice of Resistance Ra 245 Effects of the Turn-off Circuit . . . . . . . . . . . . . . 250 Influence on the Voltage Across the Load . . . . . . . 250 Influence on the Current Supplied by the Generator. 251 Influence on the Semiconductor Device Ratings 251 Characteristics . . . . . . . . . . 251 Series Commutation: Principle. 252 Operation . . . . . . . . . . . . . 253 Effects of the Turn-off Circuit . 258 Influence on the Voltage Across the Load . 258 Influence on the Current Supplied by the Generator. 258
Contents
5.3.2.3 5.3.3 5.4 5.4.1 5.4.2 5.4.2.1 5.4.2.2 5.4.2.3 5.4.2.4 5.4.3 5.5
5.5.1 5.5.1.1 5.5.1.2 5.5.2 5.5.2.1 5.5.2.2 5.5.2.3 5.6 5.6.1 5.6.2 5.7
Influence on the Semiconductor Device Ratings Characteristics . . . . . . . . . . . . . . . . . . . . Comparison of the Main Commutation Modes. Reverse-Bias Time .. , ..... . Parasitic Effects .................. . Limitation of the Control Range ........ . Modification of the Average Value of the Output Voltage Overloads Imposed on Semiconductor Devices . Commutation Losses ..................... . Concluding Remarks ..................... . Modification of the Forced Commutation Circuits in the Case of the Step-Down Chopper ............... . Modification of the Type of Semiconductor Switch Replacing a Diode by a Thyristor .......... . Replacing a Thyristor by a Diode .......... . Modifications in the Topological Disposition of the Elements First Modification ...... . Second Modification ................ . Other Possible Modifications .......... . Extension of the Study to the Step~up Chopper. Presentation of the Method ........... . Application to The Three Basic Commutation Circuits Notes on the Turn-off Circuits in the Current-Reversible Chopper and the Full-Bridge Chopper ........... .
5.7.1 Two Thyristors Sharing the Same Forced-Commutation Circuit 5.7.1.1 Sequential Control. ........................ . 5.7.1.2 Complementary Control ..................... . 5.7.2 Mutual Turn-off Procedure of the Main Thyristors: Example 5.7.2.1 Operation. Waveforms .. 5.7.2.2 Other Operational Modes .................... . 5.7.2.3 Remark ............................... . Bibliography ................................... .
Chapter6 Switch-mode Power Supplies
6.1 6.1.1 6.1.2 6.2 6.2.1 6.2.1.1 6.2.1.2 6.2.1.3 6.2.1.4
Introduction .............. . Development of DC Power Supplies . Organisation of the Analysis . . . . . Circuits Without Transformer ..... Buck Converter or Series Chopper .. Average Values of Voltage u' and Current i1•
Current i1 and Voltage u' Ripples .. . Semiconductor Device Ratings .... . Notes on Discontinuous Conduction .
XIX
258 259 260 260 261 261 262 262 262 263
263 264 264 265 268 268 269 269 272 272 273
275 276 277 279 280 280 283 283 285
286
286 286 288 289 289 289 291 293 295
XX
6.2.2 6.2.2.1 6.2.2.2 6.2.2.3 6.2.2.4 6.2.3 6.2.3.1 6.2.3.2 6.2.3.3 6.2.3.4 6.2.4 6.2.4.1 6.2.4.2 6.2.4.3 6.2.4.4 6.3 6.3.1 6.3.2 6.3.2.1 6.3.2.2 6.3.2.3 6.3.2.4 6.3.2.5 6.3.3 6.3.3.1 6.3.3.2 6.3.3.3 6.3.3.4 6.3.3.5 6.4 6.4.1 6.4.1.1
6.4.1.2 6.4.2 6.5 6.5.1 6.5.1.1
6.5.1.2 6.5.1.3 6.5.2 6.6 6.6.1 6.6.2
Boost Converter or Parallel Chopper ..... Average Values of Voltage u' and Current i . Current i and Voltage u' Ripples .. . Semiconductor Device Ratings .... . Notes on Discontinuous Conduction . Buck-Boost Converter. ........ . Average Values of Voltage u' and Current i1•
Current i1 and Voltage u' Ripples .. Semiconductor Device Ratings .... Notes on Discontinuous Operation. Cuk Converter ............ . Voltage u' and u1 , Current i and i2 Average Values Current i and i2 , Voltage u' and u1 Ripples . Semiconductor Device Ratings ...... . Remark ................... . Asymmetrical Circuits with Transformer. General Remarks .............. . Flyback Converter ............. . Average Values of Voltage u' and Magnetomotive Force at Magnetomotive Force and Output Voltage Ripples Semiconductor Device Ratings ..... Operation in the Free-Running Mode Remarks ................. . Forward Converter .......... . Average Values of Voltage u' and Current it. Current it and Voltage u' Ripples Demagnetization Period . . . . . . . . . . . . Semiconductor Device Ratings. . . . . . . . . Remarks on the Half-Bridge Isolated Buck Circuit. Multiphase Asymmetrical Circuits .......... . Multiphase Flyback Circuits ............. . Average Values of Output Voltage and of Magnetomotive Forces .......................... . Magnetomotive Force and Output Voltage Ripples Multiphase Forward Circuits ...... . Asymmetrical Multiple-Output Circuits ... . Multiple-Output Flyback Circuit ....... . Average Values of the Magnetomotive Force and of Output Voltages .... Magnetomotive-Force Ripple .. . Output Voltage Ripples ...... . Multiple-Output Forward Circuit. Notes on Symmetrical Circuits. Various Possible Structures. The Push-Pull Circuit . . . . . .
Contents
297 297 299 302 303 305 305 308 309 309 311 313 317 318 319 319 319 320 322 324 325 326 330 330 331 333 334 336 338 339 339
339 342 343 345 346
346 349 350 350 352 352 353
Content
6.6.2.1 Average Value of the Output Voltage .. 6.6.2.2 Magnetomotive-Force Amplitude .... 6.6.2.3 Current i1 and Voltage u' Ripples . . . . . ..... . 6.6.2.4 Remark on the Simultaneous Diode Conduction ... . Bibliography .................................... .
Appendix Snubbers.
A.l Bipolar Transistors: Switching Losses. A.2 Turn-on Snubber ............ . A.2.1 Reduction of Losses in the Transistor A.2.2 Overvoltage, Total Losses . A.2.3 Using a Saturable Reactor . A.2.4 Switching Energy Recovery. AJ Turn-off Snubber ...... . A.3.1 Reduction of Losses in the Transistor A.3.l.l First Case: y > C0 (Fig. A.l Oa). . . A.3.1.2 Second Case: y < C0 (Fig. A.l Ob) . A.3.2 Overcurrent. Total Losses .... . A.3.3 Switching Energy Recovery .... . A.4 Combination of the two Snubbers Without Energy Recovery A.4.1 Turn-on: Discharge of y. A.4.2 Turn-off: Discharge of I . .................... . A.4.3 Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . A.5 Combination of the two Snubbers with Energy Recovery .. A.5.1 Turn-on ............... . A.5.2 Turn-off ............... . A.6 GTO Thyristor, Turn-off Snubber. A.6.1 Turn-off ............... . A.6.2 Approximate Calculation of the Overvoltage . A.6.3 Overvoltage Reduction ............. . A.6.4 Energy Recovery . . . . . . . . . . . . . . . . . . Bibliography ...
Subject Index.
XXI
355 355 357 357 359
363
363 365 365 366 368 369 371 372 372 374 375 377 378 378 381 383 385 385 388 393 393 394 396 397 399
401
Nomenclature
Prime are used to distinguish quantities relating to the output from the corresponding quantities relating to the input
at AT A B BV c c D D
DAR
e E E f G
I I IH IL I2t
J j k k K K t, Lor!£' m n N N
magnetomotive force average value of a magnetomotive force anode base breakdown voltage collector capacitor drain diode anti-return diode electromotive force constant electromotive force emitter frequency gate instantaneous current special values of a current through a device average value of a direct current holding current latching current overcurrent factor junction positive integers positive intergers or zero ratio cathode switch inductance related value of an e.m.f. number of paralled choppers N-type layer speed
XXIV Nomenclature
p instantaneous power p power p P-type layer Q transistor
Q ratio Lw/R r orR resistance Rh rheostat
time tc commutation time td delay time
tr fall time
trr forward recovery time tgq gate recovery time t p reverse-bias time tq turn-off time t, rise time t,, reverse recovery time T cycle T transistor, thyristor T temperature TC controlled turn-on/off switch
Toff turn-off time
Ton turn-on time u voltage u average voltage or constant voltage v voltage v special value a voltage across a device V0 or VT threshold voltage w energy z damping ratio Cl. switch duty ratio Cl. current gain {3 current gain {3 turn-on relative value }' capacitor 11at magnetomotive force ripple L1i current ripple L1u voltage ripple ( damping factor ). inductance ratio cp flux w angular chopping frequency Wo angular resonant frequency
Nomenclature XXV
Subscripts
a of rotor armature
a of damping circuit AV average B of base BE between base and emitter BR breakdown c of commutation c of case Cory of capacitor C or y c of collector CE between collector and emitter
D of diode D of drain DS between drain and source f of filter f of field winding for F forward G of gate GS between gate and source
J of junction K of switch K max or M max1mum min or m mm1mum mean average nom rated off or OFF off-state on or ON on-state 0 at initial instant 0 with zero current base p peak R orr reverse R repetitive RMS root mean square s of smoothing inductor s surge T of thyristor or transistor T
Q of transistor Q
