DEVELOPMENT OF MAGNETIC COMPONENTS FOR 1-10 MHZ DC/DC CONVERTERS by ANDREW FRANKLIN GOLDBERG S.B., Massachusetts Institute of Technology (1982) S.M., Massachusetts Institute of Technology (1985) E.E., Massachusetts Institute of Technology (1985) Submitted to the Department of Electrical Engineering and Computer Science in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF SCIENCE at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 1988 © Mas;achusetts Institute of Technology 1988 Signature of Author: Department of Electrical Engineerikg and Computer Science September 1, 1988 Certified by: Prof. Martin F. Schlecht Thesis Supervisor Accepted by: .. Prof. Arthur C. Smith Chairman, Department Committee on Graduate Students i :hAbA9uU$ ISTmJuTE OF T nIA.O Y JAN 0 4 1989 LIBRARIES Archives DEVELOPMENT OF MAGNETIC COMPONENTS FOR 1-10 MHZ DC/DC CONVERTERS by ANDREW FRANKLIN GOLDBERG Submitted to the Department of Electrical Engineering and Computer Science on September 1, 1988 in partial fulfillment of the requirements for the Degree of Doctor of Science ABSTRACT Recent efforts to miniaturize one common type of power supply, the dc/dc converter, raise the internal switching frequency of the power circuit from the 20-200 kHz range to the 1-10 MHz range in an effort to reduce the size of the energy storage components that dominate the converter volume. Because of the difficulty of analyzing the power dissipation in the magnetic components, it has been unclear whether present designs represent the smallest components that can be achieved, or whether their size can be reduced further. This thesis, which is part of an MIT project to develop a miniaturized 10 MHz dc/dc converter, shows that by carefully analyzing copper and core loss, the physical size of the magnetic components can indeed be reduced significantly. Both types of power dissipation, winding loss and core loss, are difficult to analyse. Above 1 MHz skin and proximity effects in the conductors greatly increase the copper loss and are difficult to analyse in closed form. Core loss predictions, unlike copper loss predictions, cannot be made from theory alone, but rather require measured data. Such data is generally unavailable for magnetic materials at these frequencies (1-10 MHz) and flux densities (above 50 G). In order to make quantitative predictions of the copper loss, finite element analyses were employed. In order to make quantitative predictions of the core loss in the ferrite magnetic materials, whose permeability and loss vary greatly with flux density and fre- quency, a detailed measurement and analysis procedure was developed and used to measure 2 the properties of eight commercially available nickel-zinc ferrites. The copper and core loss analyses were used to choose a core and winding geometry for the transformer of a prototype 10 MHz, 50 W dc/dc converter under development at MIT. The winding geometry discussed in this thesis, planar spirals on flexible printed circuit board, is much more amenable to economical mass production than the conventional technology of magnet wire and bobbins. The analyses were also used to derive a lumped parameter model of the transformer, and the model was verified by experimental measurements using a 6:1 transformer that was fabricated with planar spiral windings. Even with a thorough understanding of the origins of power dissipation, careful design optimization is necessary in order to achieve the minimum size. The analytic models of copper and core loss were combined in a computer program that designed the transformer with the smallest footprint for a given energy storage, power dissipation, and frequency. This program was used both to produce a design for the transformer of the prototype MIT converter and to investigate the design tradeoffs. It was found that if the copper loss is not reduced by a strategy such as interleaving layers of primary and secondary, then the footprint area of the transformer can increase with increasing frequency, thereby negating one of the motivations for operating at high frequency. It was also found that the curve relating footprint area with the allowable power dissipation has a pronounced knee, so that constraining the power dissipation to be too low results in an unreasonably large transformer, while allowing the power dissipation to be unnecessarily large hardly buys any reduction in the transformer footprint. Thesis Supervisor: Dr. Martin F. Schlecht Title: Associate Professor of Electrical Engineering 3 ACKNOWLEDGEMENTS I would like first to thank my thesis supervisor, Professor Martin F. Schlecht, for his guidance. I have learned a tremendous amount from Marty and am grateful for our many long discussions. I am also grateful for his patience and understanding. I owe an immeasurable debt to Professor John G. Kassakian, who has guided me for almost a decade, supervising my undergraduate research, Bachelor's Thesis, and Master's Thesis, as well as actively participating in my doctoral work. I am grateful to him for the many opportunities he has given me, for our countless technical discussions, and for his wise personal advice. I thank the other members of my thesis committee, Professors Jeffrey H. Lang and David J. Epstein, for the great care they took in reading and commenting on my thesis. I also thank my graduate adviser, Professor Richard D. Thornton, for his guidance, and Professor James R. Kirtley and Dr Stephen D. Umans for their technical advice. I am very grateful to have studied electromagnetic field theory from Professor James R. Melcher. I thank Digital Equipment Corporation, General Electric Corporate Research and Development, and Prime Computer for their financial support of this work. I thank Dr Ming Kuo of General Electric and Mr John Cross of Digital for their technical advice and assistance. I thank the staff of the Barker Engineering Library, especially Mr Richard Hines, for their many data base searches and for hunting down ludicrously obscure technical journals. I thank my pals Mr David Otten and Dr Leo Casey for their invariably excellent technical advice, and more importantly, for all the hours of enjoyably wasted time. I thank my parents for their love and support. Most of all I thank my beloved wife, Dina, for everything. 4 TABLE OF CONTENTS Chapter 1 INTRODUCTION .......................... ............ 8 1.1 The Need for High Density Dc/Dc Converters ................... ........ 8 1.2 Basic Attributes of the Dc/Dc Converter ................................ 9 1.3 The Impact of Parasitic Elements on High Frequency Converters ..... 12 1.4 The Challenges of Miniaturizing Magnetic Components .............. 14 1.5 Overview of Thesis ...................... ............................. 16 Chapter 2 THE USE OF MAGNETIC MATERIAL ............................. 18 2.1 Magnetic Material vs. Air Core ...................................... 18 2.2 Gapped Magnetic Material ........................................... 21 2.3 Conclusions ........................................................... 23 Chapter 3 PREVIOUS WORK .................................................. 24 3.1 Miniaturized Inductors for Signal Processing ......................... 24 3.2 Miniaturized Transformers for Dc/Dc Converters ..................... 28 3.3 Conclusions ....................................... 30 Chapter 4 DISCUSSION OF MAGNETIC COMPONENT GEOMETRY ....... 32 4.1 Finite Element Analysis .............................................. 36 4.2 Sandwich Transformer ................................................ 38 4.2.1 Magnetizing Current Distribution in the Sandwich Inductor ......... 40 4.2.2 Magnetizing Current Distribution in the Sandwich Transformer ...... 45 4.3 Cofired Transformer .................................................. 46 4.4 Slotted Gapped Transformer ......................................... 48 4.5 Slotted Ungapped Transformer ....................................... 55 4.6 Selection of Transformer Geometry ................................... 55 4.7 Conclusions ........................................................... 60 Chapter 5 A LUMPED PARAMETER MODEL OF THE SLOTTED GAPPED TRANSFORMER ............................. 61 5.1 Magnetizing Inductance .............................................. 61 5.2 Leakage Inductance .................... .................... 61 5 5.3 Computing Copper Loss .............................................. 62 5.4 Magnetizing Current Resistance ...................................... 63 5.5 Load Current Resistance ............................................. 64 5.6 Comparison of Analytic Model with Finite Element Analysis ........ 65 5.7 Capacitive Effects . ...................................... 65 5.7.1 Voltage Distribution .................................................. 65 5.7.2 Stored Electric Energy ............................................... 67 5.7.3 Differential and Common Mode Capacitance ......................... 68 5.7.4 Effect of Ground Impedance ......................................... 72 Chapter 6 SELECTION AND CHARACTERIZATION OF 'HE MAGNETIC MATERIAL ............................................. 75 6.1 Survey of Magnetic Materials ......................................... 75 6.1.1 Powdered Iron and Amorphous Metal ................................ 75 6.1.2 Ferrites .............................................................. 77 6.2 Characterization of Permeability and Loss ............................ 78 6.2.1 Experimental Procedure ....................................... 79 6.2.2 Mathematical Analysis ............................................... 82 6.2.2.1 Harmonic Analysis of Voltage and Current Waveforms ............... 83 6.2.2.2 Determination of Material Permeability .............................. 83 6.2.2.3 Determination of Loss Density ....................................... 86 6.2.2.4 Fitting Data to Models ............................................... 87 6.2.3 Experimental Measurements .......................................... 88 6.2.3.1 AC Excitation ........................................ ....... 88 6.2.3.2 Excitation with DC Offset ........................................ 96 6.2.4 Error Analysis ........................................................ 96 6 Chapter 7 DESIGN ANALYSIS ................................................ 103 7.1 The Dual Resonant Forward Converter ......................... ..... 104 7.2 Copper Loss .................................................... 106 7.2.1 Copper Loss in the Primary Winding ............................... 108 7.2.2 Copper Loss in the Secondary Winding ............................. 110 7.3 Description of Design Study Computer Program .................... 111 7.4 The Importance of A Single Turn Secondary ........................ 118 7.5 Dependence of Transformer Size on Frequency ...................... 119 7.6 Multiple Winding Layers ............................................ 122 7.7 Leakage Inductance and Interwinding Capacitance ................. . 126 7.8 Thermal Dependence ................................................ 127 7.9 Scaling Issues ..................................................... 131 7.10 Comparison Between Minimum Area Design and Existing .......... 133 7.11 Conclusion ........................................ .............. 134 Chapter 8 EXPERIMENTAL MEASUREMENTS ON A SLOTTED GAPPED TRANSFORMER ............................ 135 Chapter 9 CONCLUSIONS AND DIRECTIONS FOR FUTURE WORK ................................................... 139 APPENDICES 142 .............. ........... .. . . ...... .. ... ... .... .... ............ Appendix A: Calculations of Winding Loss ........................................ 142 Appendix B: Calculations of Lumped Parameter Model ........................... 145 Appendix C: Derivation of Chapter 6 Results ..................................... 149 Appendix D: Material Measurement Software ..................................... 150 Appendix E: Loss in Secondary Winding .......................................... 155 Appendix F: Derivation of Ph/IP, Constraint ..................................... 156 Appendix G: ZZCHAP7.C ........................................................ 157 Appendix H: Fabrication Techniques .............................................. 181 7 Chapter 1 INTRODUCTION While the physical size of digital and analog electronic circuits has been drastically reduced over the past twenty years, the size of their associated power supplies has been reduced at a much slower rate. As a result, the power supply represents an increasing proportion of the size and cost of electronic equipment.1 Recent efforts to miniaturize one common type of power supply, the dc/dc converter, raise the internal switching frequency of the power circuit from the 100-200 kHz range to the 1-10 MHz range in an effort to reduce the size of the energy storage components that dominate the converter volume. Because of the difficulty of analyzing the power dissipation in the magnetic compo- nents, it has been unclear whether present designs represent the smallest components that can be achieved, or whether their size can be reduced further. The difficulty of analysing both core and copper loss at high frequency has forced designers to make conservative de- signs with cores and windings that may be much larger than they need to be for a given power dissipation. In fact, one prominent member of the power electronics community has written that "...the magnetics design is the main bottleneck to the successful reduction of the overall converter size and weight," and suggests that, because of the limitations of the magnetic components, operation below 500 kHz might yield smaller converters than operation above 1 MHz.2 This thesis, which is part of an MIT project to develop a miniaturized 10 MHz dc/dc converter, investigates the issues involved in miniaturizing magnetic components for dc/dc converters, and employs both theoretical analyses and experimental measurements to develop appropriate designs.3 The work presented in this thesis shows that with careful attention to both core and copper loss, increasing the switching frequency to 10 MHz does indeed reduce the size of the magnetic components. 1 W. W. Burns, III and J. Kociecki, "Power Electronics in the Minicomputer Industry," IEEE Proceedings, 76, 4 (1988), pp. 311-324. 2 S. Cuk, Z. Zhang, and L. A. Kajouke, Low Profile, 50 W/in3 Integrated Magnetics PWM Cuk Converter," Technical Papers of the Third International High Frequency Power Conversion Conference, Intertec Communications, Ventura, California (1988), pp. 442-463. 3 J. G. Kassakian, M. F. Schlecht, "High-Frequency High-Density Converters for Dis- tributed Power Supply Systems," IEEE Proceedings, 76, 4 (1988), pp. 362-376. 8 1.1 The Need for High Density Dc/Dc Converters One of the most active areas of research in power electronics today is the development of very high power density dc/dc converters. Dc/dc converters are a basic type of power supply that transform power from one dc voltage and current level to another in order to match power sources with their loads. The new high density converters promise power densities of over 50 W/in3, a ten-fold increase in power density over current technology.4. 5 One application for these miniaturized converters is in equipment whose size and weight must be minimized, such as satellites and aircraft. These aerospace products are produced in low volume, and their performance and reliability take precedence over cost, especially for military applications. Despite the sophistication of this new technology, these new converters are not limited to application in such speialized, low production volume applications. The converters are small enough to be fabricated by thick and thin film techniques, which permit their mass production and inclusion in high production volume products requiring inexpensive and standardized power supplies. Examples of such high volume products include mid-range and mainframe computers, telecommunications products, and automobiles. In these products miniaturized power supplies would not just replace present-day equipment, but rather permit the use of a new distributed power supply architecture instead of today's centralized power supplies. In computers, for example, large currents must be bussed at low logic voltages from the centralized power supply to each logic card. In order to avoid ohmic drops in the distribution bus, large and expensive copper bars must be employed. A distributed power supply architecture, made possible by the availability of very high power d3nsity dc/dc converters, would greatly reduce the bus size by distributing power at a higher voltage and lower current than in a centralized power supply architecture. In the distributed architecture the conversion from the bus voltage (typically about 42 V in order to satisfy safety standards) to the logic supply voltage would be performed on each logic board. Since space on tightly packed logic boards is extremely valuable, the dc/dc converter that performs this voltage conversion must be as small as possible. 4 Kassakian and Schlecht 5 F. M. Magalhaes, F. T. Dickens, G. R. Westerman, and N. G. Ziesse, "'Zero-Voltage- Switched Resonant Half-Bridge High-Voltage Dc-Dc Converter," Technical Papers of the Third International High Frequency Power Conversion Conference, Intertec Communica- tions, Ventura, California (1988), pp. 332-343. 9 15 A <I> = 15A 20A <I>=1S~~~~A 20i V Fig. 1.1 Interfacing two dc systems. (Figure reproduced from Principles of Power Elec- tronics). 1.2 Basic Attributes of the Dc/Dc Converter This section describes the basic attributes of the conventional, low power density dc/dc converter, explains the role of the magnetic components, and discusses how increasing the internal switching frequency can decrease the volume of the magnetic components. 6 A dc/dc converter is a two-port device which connects a power source that provides dc voltage and current to a load that requires its power at a different dc voltage and current. Figure 1.1 shows the basic configuration of such a two-port that connects a source that provides 200 V and 15 A and a load that requires 150 V at 20 A. The two-port must at least-contain a series element to absorb the voltage difference, and a shunt element to balance the current difference. The series element is realized with an ideal switch that continously opens and closes at a fixed frequency. The required dc, or average, voltage across the switch (in this example 50 V) is achieved by choosing an appropriate ratio of its on-time to its off-time (in this example 0.75). This ratio is known as the duty cycle. Similarly, the shunt element is realized with an ideal switch that achieves the required dc, or average, current (in this example 5 A) by opening when the series switch is closed and by closing when the series switch is open. The waveforms of these switches are shown in Fig. 1.2. Energy storage components must be added to the basic circuit of Fig. 1.1 in order 6 J. G. Kassakian, M. F. Schlecht, and G. C. Verghese, Principles of Power Electronics, Addison-Wesley Publishing Co., Reading, Massachusetts (1989), chap. 6. 10