Marian K. Kazimierczuk
High-Frequency Magnetic Components
Marian K. Kazimierczuk
High-Frequency Magnetic Components
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A unique text on the theory and design fundaments of inductors and transformers, updated with more coverage on the optimization of magnetic devices and many new design examples
The first edition is popular among a very broad audience of readers in different areas of engineering and science. This book covers the theory and design techniques of the major types of high-frequency power inductors and transformers for a variety of applications, including switching-mode power supplies (SMPS) and resonant dc-to-ac power inverters and dc-to-dc power converters. It describes eddy-current phenomena…mehr
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A unique text on the theory and design fundaments of inductors and transformers, updated with more coverage on the optimization of magnetic devices and many new design examples
The first edition is popular among a very broad audience of readers in different areas of engineering and science. This book covers the theory and design techniques of the major types of high-frequency power inductors and transformers for a variety of applications, including switching-mode power supplies (SMPS) and resonant dc-to-ac power inverters and dc-to-dc power converters. It describes eddy-current phenomena (such as skin and proximity effects), high-frequency magnetic materials, core saturation, core losses, complex permeability, high-frequency winding resistance, winding power losses, optimization of winding conductors, integrated inductors and transformers, PCB inductors, self-capacitances, self-resonant frequency, core utilization factor area product method, and design techniques and procedures of power inductors and transformers. These components are commonly used in modern power conversion applications. The material in this book has been class-tested over many years in the author's own courses at Wright State University, which have a high enrolment of about a hundred graduate students per term. The book presents the growing area of magnetic component research in a textbook form, covering the foundations for analysing and designing magnetic devices specifically at high-frequencies. Integrated inductors are described, and the Self-capacitance of inductors and transformers is examined. This new edition adds information on the optimization of magnetic components (Chapter 5). Chapter 2 has been expanded to provide better coverage of core losses and complex permeability, and Chapter 9 has more in-depth coverage of self-capacitances and self-resonant frequency of inductors. There is a more rigorous treatment of many concepts in all chapters. Updated end-of-chapter problems aid the readers' learning process, with an online solutions manual available for use in the classroom.
Provides physics-based descriptions and models of discrete inductors and transformers as well as integrated magnetic devices
New coverage on the optimization of magnetic devices, updated information on core losses and complex permeability, and more in-depth coverage of self-capacitances and self-resonant frequency of inductors
Many new design examples and end-of-chapter problems for the reader to test their learning
Presents the most up-to-date and important references in the field
Updated solutions manual, now available through a companion website
An up to date resource for Post-graduates and professors working in electrical and computer engineering. Research students in power electronics. Practising design engineers of power electronics circuits and RF (radio-frequency) power amplifiers, senior undergraduates in electrical and computer engineering, and R & D staff.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
The first edition is popular among a very broad audience of readers in different areas of engineering and science. This book covers the theory and design techniques of the major types of high-frequency power inductors and transformers for a variety of applications, including switching-mode power supplies (SMPS) and resonant dc-to-ac power inverters and dc-to-dc power converters. It describes eddy-current phenomena (such as skin and proximity effects), high-frequency magnetic materials, core saturation, core losses, complex permeability, high-frequency winding resistance, winding power losses, optimization of winding conductors, integrated inductors and transformers, PCB inductors, self-capacitances, self-resonant frequency, core utilization factor area product method, and design techniques and procedures of power inductors and transformers. These components are commonly used in modern power conversion applications. The material in this book has been class-tested over many years in the author's own courses at Wright State University, which have a high enrolment of about a hundred graduate students per term. The book presents the growing area of magnetic component research in a textbook form, covering the foundations for analysing and designing magnetic devices specifically at high-frequencies. Integrated inductors are described, and the Self-capacitance of inductors and transformers is examined. This new edition adds information on the optimization of magnetic components (Chapter 5). Chapter 2 has been expanded to provide better coverage of core losses and complex permeability, and Chapter 9 has more in-depth coverage of self-capacitances and self-resonant frequency of inductors. There is a more rigorous treatment of many concepts in all chapters. Updated end-of-chapter problems aid the readers' learning process, with an online solutions manual available for use in the classroom.
Provides physics-based descriptions and models of discrete inductors and transformers as well as integrated magnetic devices
New coverage on the optimization of magnetic devices, updated information on core losses and complex permeability, and more in-depth coverage of self-capacitances and self-resonant frequency of inductors
Many new design examples and end-of-chapter problems for the reader to test their learning
Presents the most up-to-date and important references in the field
Updated solutions manual, now available through a companion website
An up to date resource for Post-graduates and professors working in electrical and computer engineering. Research students in power electronics. Practising design engineers of power electronics circuits and RF (radio-frequency) power amplifiers, senior undergraduates in electrical and computer engineering, and R & D staff.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Verlag: Wiley & Sons
- 2. Aufl.
- Seitenzahl: 760
- Erscheinungstermin: 28. Januar 2014
- Englisch
- Abmessung: 250mm x 175mm x 45mm
- Gewicht: 1237g
- ISBN-13: 9781118717790
- ISBN-10: 1118717791
- Artikelnr.: 39043542
- Verlag: Wiley & Sons
- 2. Aufl.
- Seitenzahl: 760
- Erscheinungstermin: 28. Januar 2014
- Englisch
- Abmessung: 250mm x 175mm x 45mm
- Gewicht: 1237g
- ISBN-13: 9781118717790
- ISBN-10: 1118717791
- Artikelnr.: 39043542
Professor Marian K. Kazimierczuk, Wright State University, Dayton, Ohio, USA Professor Kazimierczuk has been conducting research in the area of power electronics amplifiers for more than thirty years, twice chairing the Technical Committee of Power Electronics and Power Systems for the IEEE Circuits and Systems Society. Over twenty-two years he has taught three graduate courses in high-frequency power electronics, and has won the Excellence in Teaching Award several times. His Science Citation index is one of the highest in the field, at over 1000 citations; he owns seven patents, has published over 110 papers in the IEEE Transactions, and has published more than 150 papers in the IEEE international conferences on power conversion. An IEEE Fellow, he has served as Associate Editor for the IEEE Transactions on Circuits and Systems and is currently an Associate Editor of the IEEE Transactions on Industrial Electronics.
Preface xvii About the Author xix List of Symbols xxi 1 Fundamentals of
Magnetic Devices 1 1.1 Introduction 1 1.2 Fields 2 1.3 Magnetic
Relationships 2 1.4 Magnetic Circuits 6 1.5 Magnetic Laws 9 1.6 Eddy
Currents 29 1.7 Core Saturation 32 1.8 Inductance 40 1.9 Air Gap in
Magnetic Core 51 1.10 Fringing Flux 54 1.11 Inductance of Strip
Transmission Line 62 1.12 Inductance of Coaxial Cable 62 1.13 Inductance of
Two-Wire Transmission Line 63 1.14 Magnetic Energy and Magnetic Energy
Density 64 1.15 Self-Resonant Frequency 69 1.16 Quality Factor of Inductors
69 1.17 Classification of Power Losses in Magnetic Components 69 1.18
Noninductive Coils 71 1.19 Summary 71 1.20 References 74 1.21 Review
Questions 76 1.22 Problems 78 2 Magnetic Cores 81 2.1 Introduction 81 2.2
Properties of Magnetic Materials 81 2.3 Magnetic Dipoles 83 2.4 Magnetic
Domains 89 2.5 Curie Temperature 90 2.6 Magnetic Susceptibility and
Permeability 91 2.7 Linear, Isotropic, and Homogeneous Magnetic Materials
93 2.8 Magnetic Materials 93 2.9 Hysteresis 96 2.10 Low-Frequency Core
Permeability 98 2.11 Core Geometries 99 2.12 Ferromagnetic Core Materials
103 2.13 Superconductors 108 2.14 Hysteresis Loss 109 2.15 Eddy-Current
Core Loss 113 2.16 Steinmetz Empirical Equation for Total Core Loss 129
2.17 Core Losses for Nonsinusoidal Inductor Current 135 2.18 Complex
Permeability of Magnetic Materials 136 2.19 Cooling of Magnetic Cores 151
2.20 Summary 152 2.21 References 157 2.22 Review Questions 160 2.23
Problems 161 3 Skin Effect 163 3.1 Introduction 163 3.2 Resistivity of
Conductors 164 3.3 Skin Depth 166 3.4 AC-to-DC Winding Resistance Ratio 173
3.5 Skin Effect in Long Single Round Conductor 173 3.6 Current Density in
Single Round Conductor 175 3.7 Magnetic Field Intensity for Round Wire 193
3.8 Other Methods of Determining the Round Wire Inductance 195 3.9 Power
Loss Density in Round Conductor 200 3.10 Skin Effect in Single Rectangular
Plate 204 3.11 Skin Effect in Rectangular Foil Conductor Placed Over Ideal
Core 215 3.12 Summary 218 3.13 Appendix 220 3.14 References 222 3.15 Review
Questions 223 3.16 Problems 224 4 Proximity Effect 226 4.1 Introduction 226
4.2 Orthogonality of Skin and Proximity Effects 227 4.3 Proximity Effect in
Two Parallel Round Conductors 227 4.4 Proximity Effect in Coaxial Cable 228
4.5 Proximity and Skin Effects in Two Parallel Plates 230 4.6 Antiproximity
and Skin Effects in Two Parallel Plates 244 4.7 Proximity Effect in
Open-Circuit Conductor 249 4.8 Proximity Effect in Multiple-Layer Inductor
250 4.9 Self-Proximity Effect in Rectangular Conductors 256 4.10 Summary
259 4.11 Appendix 260 4.12 References 261 4.13 Review Questions 263 4.14
Problems 263 5 Winding Resistance at High Frequencies 265 5.1 Introduction
265 5.2 Eddy Currents 265 5.3 Magnetic Field Intensity in Multilayer Foil
Inductors 266 5.4 Current Density in Multilayer Foil Inductors 274 5.5
Winding Power Loss Density in Individual Foil Layers 278 5.6 Complex
Winding Power in nth Layer 281 5.7 Winding Resistance of Individual Foil
Layers 282 5.8 Orthogonality of Skin and Proximity for Individual Foil
Layers 284 5.9 Optimum Thickness of Individual Foil Layers 286 5.10 Winding
Inductance of Individual Layers 291 5.11 Power Loss in All Layers 292 5.12
Impedance of Foil Winding 293 5.13 Resistance of Foil Winding 294 5.14
Dowell's Equation 294 5.15 Approximation of Dowell's Equation 298 5.16
Winding AC Resistance with Uniform Foil Thickness 300 5.17 Transformation
of Foil Conductor to Rectangular, Square, and Round Conductors 308 5.18
Winding AC Resistance of Rectangular Conductor 309 5.19 Winding Resistance
of Square Wire 318 5.20 Winding Resistance of Round Wire 326 5.21
Inductance 335 5.22 Solution for Round Conductor Winding in Cylindrical
Coordinates 338 5.23 Litz Wire 338 5.24 Winding Power Loss for Inductor
Current with Harmonics 351 5.25 Winding Power Loss of Foil Inductors
Conducting DC and Harmonic Currents 364 5.26 Winding Power Loss of Round
Wire Inductors Conducting DC and Harmonic Currents 366 5.27 Effective
Winding Resistance for Nonsinusoidal Inductor Current 367 5.28 Thermal
Effects on Winding Resistance 370 5.29 Thermal Model of Inductors 373 5.30
Summary 374 5.31 Appendix 375 5.32 References 377 5.33 Review Questions 381
5.34 Problems 381 6 Laminated Cores 383 6.1 Introduction 383 6.2
Low-Frequency Eddy-Current Laminated Core Loss 384 6.3 Comparison of Solid
and Laminated Cores 389 6.4 Alternative Solution for Low-Frequency
Eddy-Current Core Loss 389 6.4.1 Sinusoidal Inductor Voltage 391 6.4.2
Square-Wave Inductor Voltage 393 6.4.3 Rectangular Inductor Voltage 393 6.5
General Solution for Eddy-Current Laminated Core Loss 393 6.6 Summary 408
6.7 References 409 6.8 Review Questions 410 6.9 Problems 411 7 Transformers
412 7.1 Introduction 412 7.2 Transformer Construction 413 7.3 Ideal
Transformer 413 7.4 Voltage Polarities and Current Directions in
Transformers 416 7.5 Nonideal Transformers 417 7.6 Neumann's Formula for
Mutual Inductance 422 7.7 Mutual Inductance 424 7.8 Magnetizing Inductance
425 7.9 Coupling Coefficient 427 7.10 Leakage Inductance 429 7.11 Dot
Convention 432 7.12 Series-Aiding and Series-Opposing Connections 435 7.13
Equivalent T Network 435 7.14 Energy Stored in Coupled Inductors 436 7.15
High-Frequency Transformer Model 437 7.16 Stray Capacitances 438 7.17
Transformer Efficiency 438 7.18 Transformers with Gapped Cores 438 7.19
Multiple-Winding Transformers 439 7.20 Autotransformers 439 7.21
Measurements of Transformer Inductances 440 7.22 Noninterleaved Windings
442 7.23 Interleaved Windings 444 7.24 Wireless Energy Transfer 446 7.25 AC
Current Transformers 446 7.26 Saturable Reactors 454 7.27 Transformer
Winding Power Losses with Harmonics 455 7.28 Thermal Model of Transformers
464 7.29 Summary 465 7.30 References 467 7.31 Review Questions 470 7.32
Problems 471 8 Integrated Inductors 472 8.1 Introduction 472 8.2 Skin
Effect 472 8.3 Resistance of Rectangular Trace with Skin Effect 474 8.4
Inductance of Straight Rectangular Trace 477 8.5 Inductance of Rectangular
Trace with Skin Effect 478 8.6 Construction of Integrated Inductors 480 8.7
Meander Inductors 481 8.8 Inductance of Straight Round Conductor 485 8.9
Inductance of Circular Round Wire Loop 486 8.10 Inductance of Two-Parallel
Wire Loop 486 8.11 Inductance of Rectangle of Round Wire 486 8.12
Inductance of Polygon Round Wire Loop 486 8.13 Bondwire Inductors 487 8.14
Single-Turn Planar Inductor 488 8.15 Inductance of Planar Square Loop 490
8.16 Planar Spiral Inductors 490 8.17 Multimetal Spiral Inductors 505 8.18
Planar Transformers 506 8.19 MEMS Inductors 507 8.20 Inductance of Coaxial
Cable 509 8.21 Inductance of Two-Wire Transmission Line 509 8.22 Eddy
Currents in Integrated Inductors 509 8.23 Model of RF-Integrated Inductors
510 8.24 PCB Inductors 512 8.25 Summary 514 8.26 References 515 8.27 Review
Questions 518 8.28 Problems 519 9 Self-Capacitance 520 9.1 Introduction 520
9.2 High-Frequency Inductor Model 520 9.3 Self-Capacitance Components 530
9.4 Capacitance of Parallel-Plate Capacitor 531 9.5 Self-Capacitance of
Foil Winding Inductors 532 9.6 Capacitance of Two Parallel Round Conductors
533 9.7 Capacitance of Round Conductor and Parallel Conducting Plane 539
9.8 Capacitance of Straight Parallel Wire Pair Over Ground 540 9.9
Capacitance Between Two Parallel Straight Round Conductors with Uniform
Charge Density 540 9.10 Capacitance of Cylindrical Capacitor 542 9.11
Self-Capacitance of Single-Layer Inductors 542 9.12 Self-Capacitance of
Multilayer Inductors 545 9.13 Self-Capacitance of Single-Layer Inductors
553 9.14 T-to-Y Transformation of Capacitors 557 9.15 Overall
Self-Capacitance of Single-Layer Inductor with Core 557 9.16 Measurement of
Self-Capacitance 559 9.17 Inductor Impedance 560 9.18 Summary 564 9.19
References 565 9.20 Review Questions 566 9.21 Problems 566 10 Design of
Inductors 568 10.1 Introduction 568 10.2 Magnet Wire 569 10.3 Wire
Insulation 572 10.4 Restrictions on Inductors 572 10.5 Window Utilization
Factor 574 10.6 Temperature Rise of Inductors 581 10.7 Mean Turn Length of
Inductors 585 10.8 Area Product Method 586 10.9 Design of AC Inductors 590
10.10 Inductor Design for Buck Converter in CCM 603 10.11 Inductor Design
for Buck Converter in DCM Using Ap Method 619 10.12 Core Geometry
Coefficient Kg Method 654 10.13 Inductor Design for Buck Converter in CCM
Using Kg Method 658 10.14 Inductor Design for Buck Converter in DCM Using
Kg Method 660 10.15 Summary 663 10.16 References 664 10.17 Review Questions
666 10.18 Problems 666 11 Design of Transformers 668 11.1 Introduction 668
11.2 Area Product Method 668 11.3 Optimum Flux Density 673 11.4 Area
Product Ap for Sinusoidal Voltages 674 11.5 Transformer Design for Flyback
Converter in CCM 675 11.6 Transformer Design for Flyback Converter in DCM
689 11.7 Geometrical Coefficient Kg Method 702 11.8 Transformer Design for
Flyback Converter in CCM Using Kg Method 705 11.9 Transformer Design for
Flyback Converter in DCM Using Kg Method 709 11.10 Summary 714 11.11
References 714 11.12 Review Questions 715 11.13 Problems 715 Appendix A
Physical Constants 717 Appendix B Maxwell's Equations 718 Answers to
Problems 719 Index 725
Magnetic Devices 1 1.1 Introduction 1 1.2 Fields 2 1.3 Magnetic
Relationships 2 1.4 Magnetic Circuits 6 1.5 Magnetic Laws 9 1.6 Eddy
Currents 29 1.7 Core Saturation 32 1.8 Inductance 40 1.9 Air Gap in
Magnetic Core 51 1.10 Fringing Flux 54 1.11 Inductance of Strip
Transmission Line 62 1.12 Inductance of Coaxial Cable 62 1.13 Inductance of
Two-Wire Transmission Line 63 1.14 Magnetic Energy and Magnetic Energy
Density 64 1.15 Self-Resonant Frequency 69 1.16 Quality Factor of Inductors
69 1.17 Classification of Power Losses in Magnetic Components 69 1.18
Noninductive Coils 71 1.19 Summary 71 1.20 References 74 1.21 Review
Questions 76 1.22 Problems 78 2 Magnetic Cores 81 2.1 Introduction 81 2.2
Properties of Magnetic Materials 81 2.3 Magnetic Dipoles 83 2.4 Magnetic
Domains 89 2.5 Curie Temperature 90 2.6 Magnetic Susceptibility and
Permeability 91 2.7 Linear, Isotropic, and Homogeneous Magnetic Materials
93 2.8 Magnetic Materials 93 2.9 Hysteresis 96 2.10 Low-Frequency Core
Permeability 98 2.11 Core Geometries 99 2.12 Ferromagnetic Core Materials
103 2.13 Superconductors 108 2.14 Hysteresis Loss 109 2.15 Eddy-Current
Core Loss 113 2.16 Steinmetz Empirical Equation for Total Core Loss 129
2.17 Core Losses for Nonsinusoidal Inductor Current 135 2.18 Complex
Permeability of Magnetic Materials 136 2.19 Cooling of Magnetic Cores 151
2.20 Summary 152 2.21 References 157 2.22 Review Questions 160 2.23
Problems 161 3 Skin Effect 163 3.1 Introduction 163 3.2 Resistivity of
Conductors 164 3.3 Skin Depth 166 3.4 AC-to-DC Winding Resistance Ratio 173
3.5 Skin Effect in Long Single Round Conductor 173 3.6 Current Density in
Single Round Conductor 175 3.7 Magnetic Field Intensity for Round Wire 193
3.8 Other Methods of Determining the Round Wire Inductance 195 3.9 Power
Loss Density in Round Conductor 200 3.10 Skin Effect in Single Rectangular
Plate 204 3.11 Skin Effect in Rectangular Foil Conductor Placed Over Ideal
Core 215 3.12 Summary 218 3.13 Appendix 220 3.14 References 222 3.15 Review
Questions 223 3.16 Problems 224 4 Proximity Effect 226 4.1 Introduction 226
4.2 Orthogonality of Skin and Proximity Effects 227 4.3 Proximity Effect in
Two Parallel Round Conductors 227 4.4 Proximity Effect in Coaxial Cable 228
4.5 Proximity and Skin Effects in Two Parallel Plates 230 4.6 Antiproximity
and Skin Effects in Two Parallel Plates 244 4.7 Proximity Effect in
Open-Circuit Conductor 249 4.8 Proximity Effect in Multiple-Layer Inductor
250 4.9 Self-Proximity Effect in Rectangular Conductors 256 4.10 Summary
259 4.11 Appendix 260 4.12 References 261 4.13 Review Questions 263 4.14
Problems 263 5 Winding Resistance at High Frequencies 265 5.1 Introduction
265 5.2 Eddy Currents 265 5.3 Magnetic Field Intensity in Multilayer Foil
Inductors 266 5.4 Current Density in Multilayer Foil Inductors 274 5.5
Winding Power Loss Density in Individual Foil Layers 278 5.6 Complex
Winding Power in nth Layer 281 5.7 Winding Resistance of Individual Foil
Layers 282 5.8 Orthogonality of Skin and Proximity for Individual Foil
Layers 284 5.9 Optimum Thickness of Individual Foil Layers 286 5.10 Winding
Inductance of Individual Layers 291 5.11 Power Loss in All Layers 292 5.12
Impedance of Foil Winding 293 5.13 Resistance of Foil Winding 294 5.14
Dowell's Equation 294 5.15 Approximation of Dowell's Equation 298 5.16
Winding AC Resistance with Uniform Foil Thickness 300 5.17 Transformation
of Foil Conductor to Rectangular, Square, and Round Conductors 308 5.18
Winding AC Resistance of Rectangular Conductor 309 5.19 Winding Resistance
of Square Wire 318 5.20 Winding Resistance of Round Wire 326 5.21
Inductance 335 5.22 Solution for Round Conductor Winding in Cylindrical
Coordinates 338 5.23 Litz Wire 338 5.24 Winding Power Loss for Inductor
Current with Harmonics 351 5.25 Winding Power Loss of Foil Inductors
Conducting DC and Harmonic Currents 364 5.26 Winding Power Loss of Round
Wire Inductors Conducting DC and Harmonic Currents 366 5.27 Effective
Winding Resistance for Nonsinusoidal Inductor Current 367 5.28 Thermal
Effects on Winding Resistance 370 5.29 Thermal Model of Inductors 373 5.30
Summary 374 5.31 Appendix 375 5.32 References 377 5.33 Review Questions 381
5.34 Problems 381 6 Laminated Cores 383 6.1 Introduction 383 6.2
Low-Frequency Eddy-Current Laminated Core Loss 384 6.3 Comparison of Solid
and Laminated Cores 389 6.4 Alternative Solution for Low-Frequency
Eddy-Current Core Loss 389 6.4.1 Sinusoidal Inductor Voltage 391 6.4.2
Square-Wave Inductor Voltage 393 6.4.3 Rectangular Inductor Voltage 393 6.5
General Solution for Eddy-Current Laminated Core Loss 393 6.6 Summary 408
6.7 References 409 6.8 Review Questions 410 6.9 Problems 411 7 Transformers
412 7.1 Introduction 412 7.2 Transformer Construction 413 7.3 Ideal
Transformer 413 7.4 Voltage Polarities and Current Directions in
Transformers 416 7.5 Nonideal Transformers 417 7.6 Neumann's Formula for
Mutual Inductance 422 7.7 Mutual Inductance 424 7.8 Magnetizing Inductance
425 7.9 Coupling Coefficient 427 7.10 Leakage Inductance 429 7.11 Dot
Convention 432 7.12 Series-Aiding and Series-Opposing Connections 435 7.13
Equivalent T Network 435 7.14 Energy Stored in Coupled Inductors 436 7.15
High-Frequency Transformer Model 437 7.16 Stray Capacitances 438 7.17
Transformer Efficiency 438 7.18 Transformers with Gapped Cores 438 7.19
Multiple-Winding Transformers 439 7.20 Autotransformers 439 7.21
Measurements of Transformer Inductances 440 7.22 Noninterleaved Windings
442 7.23 Interleaved Windings 444 7.24 Wireless Energy Transfer 446 7.25 AC
Current Transformers 446 7.26 Saturable Reactors 454 7.27 Transformer
Winding Power Losses with Harmonics 455 7.28 Thermal Model of Transformers
464 7.29 Summary 465 7.30 References 467 7.31 Review Questions 470 7.32
Problems 471 8 Integrated Inductors 472 8.1 Introduction 472 8.2 Skin
Effect 472 8.3 Resistance of Rectangular Trace with Skin Effect 474 8.4
Inductance of Straight Rectangular Trace 477 8.5 Inductance of Rectangular
Trace with Skin Effect 478 8.6 Construction of Integrated Inductors 480 8.7
Meander Inductors 481 8.8 Inductance of Straight Round Conductor 485 8.9
Inductance of Circular Round Wire Loop 486 8.10 Inductance of Two-Parallel
Wire Loop 486 8.11 Inductance of Rectangle of Round Wire 486 8.12
Inductance of Polygon Round Wire Loop 486 8.13 Bondwire Inductors 487 8.14
Single-Turn Planar Inductor 488 8.15 Inductance of Planar Square Loop 490
8.16 Planar Spiral Inductors 490 8.17 Multimetal Spiral Inductors 505 8.18
Planar Transformers 506 8.19 MEMS Inductors 507 8.20 Inductance of Coaxial
Cable 509 8.21 Inductance of Two-Wire Transmission Line 509 8.22 Eddy
Currents in Integrated Inductors 509 8.23 Model of RF-Integrated Inductors
510 8.24 PCB Inductors 512 8.25 Summary 514 8.26 References 515 8.27 Review
Questions 518 8.28 Problems 519 9 Self-Capacitance 520 9.1 Introduction 520
9.2 High-Frequency Inductor Model 520 9.3 Self-Capacitance Components 530
9.4 Capacitance of Parallel-Plate Capacitor 531 9.5 Self-Capacitance of
Foil Winding Inductors 532 9.6 Capacitance of Two Parallel Round Conductors
533 9.7 Capacitance of Round Conductor and Parallel Conducting Plane 539
9.8 Capacitance of Straight Parallel Wire Pair Over Ground 540 9.9
Capacitance Between Two Parallel Straight Round Conductors with Uniform
Charge Density 540 9.10 Capacitance of Cylindrical Capacitor 542 9.11
Self-Capacitance of Single-Layer Inductors 542 9.12 Self-Capacitance of
Multilayer Inductors 545 9.13 Self-Capacitance of Single-Layer Inductors
553 9.14 T-to-Y Transformation of Capacitors 557 9.15 Overall
Self-Capacitance of Single-Layer Inductor with Core 557 9.16 Measurement of
Self-Capacitance 559 9.17 Inductor Impedance 560 9.18 Summary 564 9.19
References 565 9.20 Review Questions 566 9.21 Problems 566 10 Design of
Inductors 568 10.1 Introduction 568 10.2 Magnet Wire 569 10.3 Wire
Insulation 572 10.4 Restrictions on Inductors 572 10.5 Window Utilization
Factor 574 10.6 Temperature Rise of Inductors 581 10.7 Mean Turn Length of
Inductors 585 10.8 Area Product Method 586 10.9 Design of AC Inductors 590
10.10 Inductor Design for Buck Converter in CCM 603 10.11 Inductor Design
for Buck Converter in DCM Using Ap Method 619 10.12 Core Geometry
Coefficient Kg Method 654 10.13 Inductor Design for Buck Converter in CCM
Using Kg Method 658 10.14 Inductor Design for Buck Converter in DCM Using
Kg Method 660 10.15 Summary 663 10.16 References 664 10.17 Review Questions
666 10.18 Problems 666 11 Design of Transformers 668 11.1 Introduction 668
11.2 Area Product Method 668 11.3 Optimum Flux Density 673 11.4 Area
Product Ap for Sinusoidal Voltages 674 11.5 Transformer Design for Flyback
Converter in CCM 675 11.6 Transformer Design for Flyback Converter in DCM
689 11.7 Geometrical Coefficient Kg Method 702 11.8 Transformer Design for
Flyback Converter in CCM Using Kg Method 705 11.9 Transformer Design for
Flyback Converter in DCM Using Kg Method 709 11.10 Summary 714 11.11
References 714 11.12 Review Questions 715 11.13 Problems 715 Appendix A
Physical Constants 717 Appendix B Maxwell's Equations 718 Answers to
Problems 719 Index 725
Preface xvii About the Author xix List of Symbols xxi 1 Fundamentals of
Magnetic Devices 1 1.1 Introduction 1 1.2 Fields 2 1.3 Magnetic
Relationships 2 1.4 Magnetic Circuits 6 1.5 Magnetic Laws 9 1.6 Eddy
Currents 29 1.7 Core Saturation 32 1.8 Inductance 40 1.9 Air Gap in
Magnetic Core 51 1.10 Fringing Flux 54 1.11 Inductance of Strip
Transmission Line 62 1.12 Inductance of Coaxial Cable 62 1.13 Inductance of
Two-Wire Transmission Line 63 1.14 Magnetic Energy and Magnetic Energy
Density 64 1.15 Self-Resonant Frequency 69 1.16 Quality Factor of Inductors
69 1.17 Classification of Power Losses in Magnetic Components 69 1.18
Noninductive Coils 71 1.19 Summary 71 1.20 References 74 1.21 Review
Questions 76 1.22 Problems 78 2 Magnetic Cores 81 2.1 Introduction 81 2.2
Properties of Magnetic Materials 81 2.3 Magnetic Dipoles 83 2.4 Magnetic
Domains 89 2.5 Curie Temperature 90 2.6 Magnetic Susceptibility and
Permeability 91 2.7 Linear, Isotropic, and Homogeneous Magnetic Materials
93 2.8 Magnetic Materials 93 2.9 Hysteresis 96 2.10 Low-Frequency Core
Permeability 98 2.11 Core Geometries 99 2.12 Ferromagnetic Core Materials
103 2.13 Superconductors 108 2.14 Hysteresis Loss 109 2.15 Eddy-Current
Core Loss 113 2.16 Steinmetz Empirical Equation for Total Core Loss 129
2.17 Core Losses for Nonsinusoidal Inductor Current 135 2.18 Complex
Permeability of Magnetic Materials 136 2.19 Cooling of Magnetic Cores 151
2.20 Summary 152 2.21 References 157 2.22 Review Questions 160 2.23
Problems 161 3 Skin Effect 163 3.1 Introduction 163 3.2 Resistivity of
Conductors 164 3.3 Skin Depth 166 3.4 AC-to-DC Winding Resistance Ratio 173
3.5 Skin Effect in Long Single Round Conductor 173 3.6 Current Density in
Single Round Conductor 175 3.7 Magnetic Field Intensity for Round Wire 193
3.8 Other Methods of Determining the Round Wire Inductance 195 3.9 Power
Loss Density in Round Conductor 200 3.10 Skin Effect in Single Rectangular
Plate 204 3.11 Skin Effect in Rectangular Foil Conductor Placed Over Ideal
Core 215 3.12 Summary 218 3.13 Appendix 220 3.14 References 222 3.15 Review
Questions 223 3.16 Problems 224 4 Proximity Effect 226 4.1 Introduction 226
4.2 Orthogonality of Skin and Proximity Effects 227 4.3 Proximity Effect in
Two Parallel Round Conductors 227 4.4 Proximity Effect in Coaxial Cable 228
4.5 Proximity and Skin Effects in Two Parallel Plates 230 4.6 Antiproximity
and Skin Effects in Two Parallel Plates 244 4.7 Proximity Effect in
Open-Circuit Conductor 249 4.8 Proximity Effect in Multiple-Layer Inductor
250 4.9 Self-Proximity Effect in Rectangular Conductors 256 4.10 Summary
259 4.11 Appendix 260 4.12 References 261 4.13 Review Questions 263 4.14
Problems 263 5 Winding Resistance at High Frequencies 265 5.1 Introduction
265 5.2 Eddy Currents 265 5.3 Magnetic Field Intensity in Multilayer Foil
Inductors 266 5.4 Current Density in Multilayer Foil Inductors 274 5.5
Winding Power Loss Density in Individual Foil Layers 278 5.6 Complex
Winding Power in nth Layer 281 5.7 Winding Resistance of Individual Foil
Layers 282 5.8 Orthogonality of Skin and Proximity for Individual Foil
Layers 284 5.9 Optimum Thickness of Individual Foil Layers 286 5.10 Winding
Inductance of Individual Layers 291 5.11 Power Loss in All Layers 292 5.12
Impedance of Foil Winding 293 5.13 Resistance of Foil Winding 294 5.14
Dowell's Equation 294 5.15 Approximation of Dowell's Equation 298 5.16
Winding AC Resistance with Uniform Foil Thickness 300 5.17 Transformation
of Foil Conductor to Rectangular, Square, and Round Conductors 308 5.18
Winding AC Resistance of Rectangular Conductor 309 5.19 Winding Resistance
of Square Wire 318 5.20 Winding Resistance of Round Wire 326 5.21
Inductance 335 5.22 Solution for Round Conductor Winding in Cylindrical
Coordinates 338 5.23 Litz Wire 338 5.24 Winding Power Loss for Inductor
Current with Harmonics 351 5.25 Winding Power Loss of Foil Inductors
Conducting DC and Harmonic Currents 364 5.26 Winding Power Loss of Round
Wire Inductors Conducting DC and Harmonic Currents 366 5.27 Effective
Winding Resistance for Nonsinusoidal Inductor Current 367 5.28 Thermal
Effects on Winding Resistance 370 5.29 Thermal Model of Inductors 373 5.30
Summary 374 5.31 Appendix 375 5.32 References 377 5.33 Review Questions 381
5.34 Problems 381 6 Laminated Cores 383 6.1 Introduction 383 6.2
Low-Frequency Eddy-Current Laminated Core Loss 384 6.3 Comparison of Solid
and Laminated Cores 389 6.4 Alternative Solution for Low-Frequency
Eddy-Current Core Loss 389 6.4.1 Sinusoidal Inductor Voltage 391 6.4.2
Square-Wave Inductor Voltage 393 6.4.3 Rectangular Inductor Voltage 393 6.5
General Solution for Eddy-Current Laminated Core Loss 393 6.6 Summary 408
6.7 References 409 6.8 Review Questions 410 6.9 Problems 411 7 Transformers
412 7.1 Introduction 412 7.2 Transformer Construction 413 7.3 Ideal
Transformer 413 7.4 Voltage Polarities and Current Directions in
Transformers 416 7.5 Nonideal Transformers 417 7.6 Neumann's Formula for
Mutual Inductance 422 7.7 Mutual Inductance 424 7.8 Magnetizing Inductance
425 7.9 Coupling Coefficient 427 7.10 Leakage Inductance 429 7.11 Dot
Convention 432 7.12 Series-Aiding and Series-Opposing Connections 435 7.13
Equivalent T Network 435 7.14 Energy Stored in Coupled Inductors 436 7.15
High-Frequency Transformer Model 437 7.16 Stray Capacitances 438 7.17
Transformer Efficiency 438 7.18 Transformers with Gapped Cores 438 7.19
Multiple-Winding Transformers 439 7.20 Autotransformers 439 7.21
Measurements of Transformer Inductances 440 7.22 Noninterleaved Windings
442 7.23 Interleaved Windings 444 7.24 Wireless Energy Transfer 446 7.25 AC
Current Transformers 446 7.26 Saturable Reactors 454 7.27 Transformer
Winding Power Losses with Harmonics 455 7.28 Thermal Model of Transformers
464 7.29 Summary 465 7.30 References 467 7.31 Review Questions 470 7.32
Problems 471 8 Integrated Inductors 472 8.1 Introduction 472 8.2 Skin
Effect 472 8.3 Resistance of Rectangular Trace with Skin Effect 474 8.4
Inductance of Straight Rectangular Trace 477 8.5 Inductance of Rectangular
Trace with Skin Effect 478 8.6 Construction of Integrated Inductors 480 8.7
Meander Inductors 481 8.8 Inductance of Straight Round Conductor 485 8.9
Inductance of Circular Round Wire Loop 486 8.10 Inductance of Two-Parallel
Wire Loop 486 8.11 Inductance of Rectangle of Round Wire 486 8.12
Inductance of Polygon Round Wire Loop 486 8.13 Bondwire Inductors 487 8.14
Single-Turn Planar Inductor 488 8.15 Inductance of Planar Square Loop 490
8.16 Planar Spiral Inductors 490 8.17 Multimetal Spiral Inductors 505 8.18
Planar Transformers 506 8.19 MEMS Inductors 507 8.20 Inductance of Coaxial
Cable 509 8.21 Inductance of Two-Wire Transmission Line 509 8.22 Eddy
Currents in Integrated Inductors 509 8.23 Model of RF-Integrated Inductors
510 8.24 PCB Inductors 512 8.25 Summary 514 8.26 References 515 8.27 Review
Questions 518 8.28 Problems 519 9 Self-Capacitance 520 9.1 Introduction 520
9.2 High-Frequency Inductor Model 520 9.3 Self-Capacitance Components 530
9.4 Capacitance of Parallel-Plate Capacitor 531 9.5 Self-Capacitance of
Foil Winding Inductors 532 9.6 Capacitance of Two Parallel Round Conductors
533 9.7 Capacitance of Round Conductor and Parallel Conducting Plane 539
9.8 Capacitance of Straight Parallel Wire Pair Over Ground 540 9.9
Capacitance Between Two Parallel Straight Round Conductors with Uniform
Charge Density 540 9.10 Capacitance of Cylindrical Capacitor 542 9.11
Self-Capacitance of Single-Layer Inductors 542 9.12 Self-Capacitance of
Multilayer Inductors 545 9.13 Self-Capacitance of Single-Layer Inductors
553 9.14 T-to-Y Transformation of Capacitors 557 9.15 Overall
Self-Capacitance of Single-Layer Inductor with Core 557 9.16 Measurement of
Self-Capacitance 559 9.17 Inductor Impedance 560 9.18 Summary 564 9.19
References 565 9.20 Review Questions 566 9.21 Problems 566 10 Design of
Inductors 568 10.1 Introduction 568 10.2 Magnet Wire 569 10.3 Wire
Insulation 572 10.4 Restrictions on Inductors 572 10.5 Window Utilization
Factor 574 10.6 Temperature Rise of Inductors 581 10.7 Mean Turn Length of
Inductors 585 10.8 Area Product Method 586 10.9 Design of AC Inductors 590
10.10 Inductor Design for Buck Converter in CCM 603 10.11 Inductor Design
for Buck Converter in DCM Using Ap Method 619 10.12 Core Geometry
Coefficient Kg Method 654 10.13 Inductor Design for Buck Converter in CCM
Using Kg Method 658 10.14 Inductor Design for Buck Converter in DCM Using
Kg Method 660 10.15 Summary 663 10.16 References 664 10.17 Review Questions
666 10.18 Problems 666 11 Design of Transformers 668 11.1 Introduction 668
11.2 Area Product Method 668 11.3 Optimum Flux Density 673 11.4 Area
Product Ap for Sinusoidal Voltages 674 11.5 Transformer Design for Flyback
Converter in CCM 675 11.6 Transformer Design for Flyback Converter in DCM
689 11.7 Geometrical Coefficient Kg Method 702 11.8 Transformer Design for
Flyback Converter in CCM Using Kg Method 705 11.9 Transformer Design for
Flyback Converter in DCM Using Kg Method 709 11.10 Summary 714 11.11
References 714 11.12 Review Questions 715 11.13 Problems 715 Appendix A
Physical Constants 717 Appendix B Maxwell's Equations 718 Answers to
Problems 719 Index 725
Magnetic Devices 1 1.1 Introduction 1 1.2 Fields 2 1.3 Magnetic
Relationships 2 1.4 Magnetic Circuits 6 1.5 Magnetic Laws 9 1.6 Eddy
Currents 29 1.7 Core Saturation 32 1.8 Inductance 40 1.9 Air Gap in
Magnetic Core 51 1.10 Fringing Flux 54 1.11 Inductance of Strip
Transmission Line 62 1.12 Inductance of Coaxial Cable 62 1.13 Inductance of
Two-Wire Transmission Line 63 1.14 Magnetic Energy and Magnetic Energy
Density 64 1.15 Self-Resonant Frequency 69 1.16 Quality Factor of Inductors
69 1.17 Classification of Power Losses in Magnetic Components 69 1.18
Noninductive Coils 71 1.19 Summary 71 1.20 References 74 1.21 Review
Questions 76 1.22 Problems 78 2 Magnetic Cores 81 2.1 Introduction 81 2.2
Properties of Magnetic Materials 81 2.3 Magnetic Dipoles 83 2.4 Magnetic
Domains 89 2.5 Curie Temperature 90 2.6 Magnetic Susceptibility and
Permeability 91 2.7 Linear, Isotropic, and Homogeneous Magnetic Materials
93 2.8 Magnetic Materials 93 2.9 Hysteresis 96 2.10 Low-Frequency Core
Permeability 98 2.11 Core Geometries 99 2.12 Ferromagnetic Core Materials
103 2.13 Superconductors 108 2.14 Hysteresis Loss 109 2.15 Eddy-Current
Core Loss 113 2.16 Steinmetz Empirical Equation for Total Core Loss 129
2.17 Core Losses for Nonsinusoidal Inductor Current 135 2.18 Complex
Permeability of Magnetic Materials 136 2.19 Cooling of Magnetic Cores 151
2.20 Summary 152 2.21 References 157 2.22 Review Questions 160 2.23
Problems 161 3 Skin Effect 163 3.1 Introduction 163 3.2 Resistivity of
Conductors 164 3.3 Skin Depth 166 3.4 AC-to-DC Winding Resistance Ratio 173
3.5 Skin Effect in Long Single Round Conductor 173 3.6 Current Density in
Single Round Conductor 175 3.7 Magnetic Field Intensity for Round Wire 193
3.8 Other Methods of Determining the Round Wire Inductance 195 3.9 Power
Loss Density in Round Conductor 200 3.10 Skin Effect in Single Rectangular
Plate 204 3.11 Skin Effect in Rectangular Foil Conductor Placed Over Ideal
Core 215 3.12 Summary 218 3.13 Appendix 220 3.14 References 222 3.15 Review
Questions 223 3.16 Problems 224 4 Proximity Effect 226 4.1 Introduction 226
4.2 Orthogonality of Skin and Proximity Effects 227 4.3 Proximity Effect in
Two Parallel Round Conductors 227 4.4 Proximity Effect in Coaxial Cable 228
4.5 Proximity and Skin Effects in Two Parallel Plates 230 4.6 Antiproximity
and Skin Effects in Two Parallel Plates 244 4.7 Proximity Effect in
Open-Circuit Conductor 249 4.8 Proximity Effect in Multiple-Layer Inductor
250 4.9 Self-Proximity Effect in Rectangular Conductors 256 4.10 Summary
259 4.11 Appendix 260 4.12 References 261 4.13 Review Questions 263 4.14
Problems 263 5 Winding Resistance at High Frequencies 265 5.1 Introduction
265 5.2 Eddy Currents 265 5.3 Magnetic Field Intensity in Multilayer Foil
Inductors 266 5.4 Current Density in Multilayer Foil Inductors 274 5.5
Winding Power Loss Density in Individual Foil Layers 278 5.6 Complex
Winding Power in nth Layer 281 5.7 Winding Resistance of Individual Foil
Layers 282 5.8 Orthogonality of Skin and Proximity for Individual Foil
Layers 284 5.9 Optimum Thickness of Individual Foil Layers 286 5.10 Winding
Inductance of Individual Layers 291 5.11 Power Loss in All Layers 292 5.12
Impedance of Foil Winding 293 5.13 Resistance of Foil Winding 294 5.14
Dowell's Equation 294 5.15 Approximation of Dowell's Equation 298 5.16
Winding AC Resistance with Uniform Foil Thickness 300 5.17 Transformation
of Foil Conductor to Rectangular, Square, and Round Conductors 308 5.18
Winding AC Resistance of Rectangular Conductor 309 5.19 Winding Resistance
of Square Wire 318 5.20 Winding Resistance of Round Wire 326 5.21
Inductance 335 5.22 Solution for Round Conductor Winding in Cylindrical
Coordinates 338 5.23 Litz Wire 338 5.24 Winding Power Loss for Inductor
Current with Harmonics 351 5.25 Winding Power Loss of Foil Inductors
Conducting DC and Harmonic Currents 364 5.26 Winding Power Loss of Round
Wire Inductors Conducting DC and Harmonic Currents 366 5.27 Effective
Winding Resistance for Nonsinusoidal Inductor Current 367 5.28 Thermal
Effects on Winding Resistance 370 5.29 Thermal Model of Inductors 373 5.30
Summary 374 5.31 Appendix 375 5.32 References 377 5.33 Review Questions 381
5.34 Problems 381 6 Laminated Cores 383 6.1 Introduction 383 6.2
Low-Frequency Eddy-Current Laminated Core Loss 384 6.3 Comparison of Solid
and Laminated Cores 389 6.4 Alternative Solution for Low-Frequency
Eddy-Current Core Loss 389 6.4.1 Sinusoidal Inductor Voltage 391 6.4.2
Square-Wave Inductor Voltage 393 6.4.3 Rectangular Inductor Voltage 393 6.5
General Solution for Eddy-Current Laminated Core Loss 393 6.6 Summary 408
6.7 References 409 6.8 Review Questions 410 6.9 Problems 411 7 Transformers
412 7.1 Introduction 412 7.2 Transformer Construction 413 7.3 Ideal
Transformer 413 7.4 Voltage Polarities and Current Directions in
Transformers 416 7.5 Nonideal Transformers 417 7.6 Neumann's Formula for
Mutual Inductance 422 7.7 Mutual Inductance 424 7.8 Magnetizing Inductance
425 7.9 Coupling Coefficient 427 7.10 Leakage Inductance 429 7.11 Dot
Convention 432 7.12 Series-Aiding and Series-Opposing Connections 435 7.13
Equivalent T Network 435 7.14 Energy Stored in Coupled Inductors 436 7.15
High-Frequency Transformer Model 437 7.16 Stray Capacitances 438 7.17
Transformer Efficiency 438 7.18 Transformers with Gapped Cores 438 7.19
Multiple-Winding Transformers 439 7.20 Autotransformers 439 7.21
Measurements of Transformer Inductances 440 7.22 Noninterleaved Windings
442 7.23 Interleaved Windings 444 7.24 Wireless Energy Transfer 446 7.25 AC
Current Transformers 446 7.26 Saturable Reactors 454 7.27 Transformer
Winding Power Losses with Harmonics 455 7.28 Thermal Model of Transformers
464 7.29 Summary 465 7.30 References 467 7.31 Review Questions 470 7.32
Problems 471 8 Integrated Inductors 472 8.1 Introduction 472 8.2 Skin
Effect 472 8.3 Resistance of Rectangular Trace with Skin Effect 474 8.4
Inductance of Straight Rectangular Trace 477 8.5 Inductance of Rectangular
Trace with Skin Effect 478 8.6 Construction of Integrated Inductors 480 8.7
Meander Inductors 481 8.8 Inductance of Straight Round Conductor 485 8.9
Inductance of Circular Round Wire Loop 486 8.10 Inductance of Two-Parallel
Wire Loop 486 8.11 Inductance of Rectangle of Round Wire 486 8.12
Inductance of Polygon Round Wire Loop 486 8.13 Bondwire Inductors 487 8.14
Single-Turn Planar Inductor 488 8.15 Inductance of Planar Square Loop 490
8.16 Planar Spiral Inductors 490 8.17 Multimetal Spiral Inductors 505 8.18
Planar Transformers 506 8.19 MEMS Inductors 507 8.20 Inductance of Coaxial
Cable 509 8.21 Inductance of Two-Wire Transmission Line 509 8.22 Eddy
Currents in Integrated Inductors 509 8.23 Model of RF-Integrated Inductors
510 8.24 PCB Inductors 512 8.25 Summary 514 8.26 References 515 8.27 Review
Questions 518 8.28 Problems 519 9 Self-Capacitance 520 9.1 Introduction 520
9.2 High-Frequency Inductor Model 520 9.3 Self-Capacitance Components 530
9.4 Capacitance of Parallel-Plate Capacitor 531 9.5 Self-Capacitance of
Foil Winding Inductors 532 9.6 Capacitance of Two Parallel Round Conductors
533 9.7 Capacitance of Round Conductor and Parallel Conducting Plane 539
9.8 Capacitance of Straight Parallel Wire Pair Over Ground 540 9.9
Capacitance Between Two Parallel Straight Round Conductors with Uniform
Charge Density 540 9.10 Capacitance of Cylindrical Capacitor 542 9.11
Self-Capacitance of Single-Layer Inductors 542 9.12 Self-Capacitance of
Multilayer Inductors 545 9.13 Self-Capacitance of Single-Layer Inductors
553 9.14 T-to-Y Transformation of Capacitors 557 9.15 Overall
Self-Capacitance of Single-Layer Inductor with Core 557 9.16 Measurement of
Self-Capacitance 559 9.17 Inductor Impedance 560 9.18 Summary 564 9.19
References 565 9.20 Review Questions 566 9.21 Problems 566 10 Design of
Inductors 568 10.1 Introduction 568 10.2 Magnet Wire 569 10.3 Wire
Insulation 572 10.4 Restrictions on Inductors 572 10.5 Window Utilization
Factor 574 10.6 Temperature Rise of Inductors 581 10.7 Mean Turn Length of
Inductors 585 10.8 Area Product Method 586 10.9 Design of AC Inductors 590
10.10 Inductor Design for Buck Converter in CCM 603 10.11 Inductor Design
for Buck Converter in DCM Using Ap Method 619 10.12 Core Geometry
Coefficient Kg Method 654 10.13 Inductor Design for Buck Converter in CCM
Using Kg Method 658 10.14 Inductor Design for Buck Converter in DCM Using
Kg Method 660 10.15 Summary 663 10.16 References 664 10.17 Review Questions
666 10.18 Problems 666 11 Design of Transformers 668 11.1 Introduction 668
11.2 Area Product Method 668 11.3 Optimum Flux Density 673 11.4 Area
Product Ap for Sinusoidal Voltages 674 11.5 Transformer Design for Flyback
Converter in CCM 675 11.6 Transformer Design for Flyback Converter in DCM
689 11.7 Geometrical Coefficient Kg Method 702 11.8 Transformer Design for
Flyback Converter in CCM Using Kg Method 705 11.9 Transformer Design for
Flyback Converter in DCM Using Kg Method 709 11.10 Summary 714 11.11
References 714 11.12 Review Questions 715 11.13 Problems 715 Appendix A
Physical Constants 717 Appendix B Maxwell's Equations 718 Answers to
Problems 719 Index 725