High-frequency Magnetic Components

Summary

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. The book supplies high-frequency models of inductors and transformers and addresses the proximity and skin effects on winding and core losses in magnetic components at high freqencies. Other high-frequency phenomena is also covered in detail. End-of-chapter problems aid the readers learning process, with a solutions manual available for use in the classroom. Original in its focus; this book concentrates on the magnetic components of inductors and transformers for high-frequency applications Combines concept-orientated explanations of integrated inductors and the self-capacitance of inductors and transformers, with student-friendly analysis Includes design examples and design procedures, with review questions and problems at the end of each chapter for the reader to test their learning Solutions are provided in an accompanying Solutions Manual

Author Biography

Marian K. Kazimierczuk is Robert J. Kegerreis Distinguished Professor of Electrical Engineering at Wright State University, Dayton, Ohio, USA. He is the author of six books, over 130 archival refereed journal papers, over 150 conference papers, and seven patents. He is a Fellow of the IEEE. He received the Outstanding Teaching Award from the American Society for Engineering Education (ASEE) in 2008. His research interests are in power electronics, including pulse-width modulated dc–dc power converters, resonant dc–dc power converters, modeling and controls, RF power amplifiers and oscillators, semiconductor power devices, high-frequency magnetic devices, renewable energy sources, and evanescent microwave microscopy

Preface
List of Symbols
Fundamentals of Magnetic Devices 1
Introduction
Magnetic Relationships
Magnetic Circuits
Magnetic Laws
Eddy Currents
Core Saturation
Volt-Second Balance
Inductance
Inductance Factor
Magnetic Energy
Self-Resonant Frequency
Classification of Power Losses in Magnetic Components
Noninductive Coils
Summary
References
Review Questions
Problems
Magnetic Cores
Introduction
Properties of Core Materials
Magnetic Dipoles
Magnetic Domains
Curie Temperature
Magnetization
Magnetic Materials
Hysteresis
Core Permeability
Core Geometries
Iron Alloy Cores
Amorphous Alloy Cores
NickelûIron and CobaltûIron Cores
Ferrite Cores
Powder Cores
Nanocrystalline Cores
Superconductors
Hysteresis Core Loss
Eddy-Current Core Loss
Total Core Loss
Complex Permeability
Summary
References
Review Questions
Problems
Skin Effect
Introduction
Skin Depth
Ratio of AC-to-DC Winding Resistance
Skin Effect in Long Single Round Conductor
Current Density in Single Round Conductor
Impedance of Round Conductor
Magnetic Field Intensity for Round Wire
Other Methods of Determining the Round Wire Inductance
Power Density in Round Conductor
Skin Effect on Single Rectangular Plate
Summary
References
Review Questions
Problems
Proximity Effect
Introduction
Proximity and Skin Effects in Two Parallel Plates
Antiproximity and Skin Effects in Two Parallel Plates
Proximity Effect in Multiple-Layer Inductor
Summary
Appendix: Derivation of Proximity Power Loss
References
Review Questions
Problems
Winding Resistance at High Frequencies
Introduction
Winding Resistance
Square and Round Conductors
Winding Resistance of Rectangular Conductor
Winding Resistance of Square Wire
General Equation
Winding Resistance of Round Wire
Leakage Inductance
Solution for Round Conductor Winding in Cylindrical Coordinates
Litz Wire
Winding Power Loss for Inductor Current with Harmonics
Effective Winding Resistance for Nonsinusoidal Inductor Current
Thermal Model of Inductors
Summary
References
Review Questions
Problems
Laminated Cores
Introduction
Low-Frequency Solution
General Solution
Summary
References
Review Questions
Problems
Transformers
Introduction
Ideal Transformer
Voltage Polarities and Current Directions in Transformers
Nonideal Transformers
NeumannÆs Formula for Mutual Inductance
Mutual Inductance
Coupling Coefficient
Dot Convention
Series-Aiding and Series-Opposing Connections
Reflected Impedance
Energy Stored in Coupled Inductors
Magnetizing Inductance
Leakage Inductance
Transformers with Air Gap
Autotransformers
Measurement of Transformer Inductances
Stray Capacitance
High-Frequency Transformer Model
Noninterleaved Windings
Interleaved Windings
AC Current Transformers
Winding Power Losses with Harmonics
Thermal Model of Transformers
Summary
References
Review Questions
Problems
Integrated Inductors
Introduction
Skin Effect
Resistance of Rectangular Trace
Inductance of Straight Rectangular Trace
Construction of Integrated Inductors
Meander Inductors
Inductance of Straight Round Conductor
Inductance of Circular Round Wire Loop
Inductance of Two-Parallel Wire Loop
Inductance of Rectangle of Round Wire
Inductance of Polygon Round Wire Loop
Bondwire Inductors
Single-Turn Planar Inductor
Inductance of Planar Square Loop
Planar Spiral Inductors
Multi-metal Spiral Inductors
Planar Transformers
MEMS Inductors
Inductance of Coaxial Cable
Inductance of Two-Wire Transmission Line
Eddy Currents in Integrated Inductors
Model of RF Integrated Inductors
PCB Inductors
Summary
References
Review Questions
Problems
Self-Capacitance
Introduction
High-Frequency Inductor Model
Self-Capacitance Components
Capacitance of Parallel-Plate Capacitor
Self-Capacitance of Foil Winding Inductors
Capacitance of Two Parallel Round Conductors
Capacitance of Round Conductor and Conducting Plane
Self-Capacitance of Single-Layer Inductors
Self-Capacitance of Multi-layer Inductors
Capacitance of Coaxial Cable
Summary
References
Review Questions
Problems
Design of Inductors
Introduction
Magnet Wire
Wire Insulation
Restrictions on Inductors
Window Utilization Factor
Temperature Rise of Inductors
Mean Turn Length of Inductors
Area Product Method
AC Inductor Design
Inductor Design for Buck Converter in CCM
Inductor Design for Buck Converter in DCM Using Ap Method
Core Geometry Coefficient Kg Method
Inductor Design for Buck Converter in CCM Using Kg Method
Inductor Design for Buck Converter in DCM Using Kg Method
Summary
References
Review Questions
Problems
Design of Transformers
Introduction
Area Product Method
Optimum Flux Density
Transformer Design for Flyback Converter in CCM
Transformer Design for Flyback Converter in DCM
Geometrical Coefficient Kg Method
Transformer Design for Flyback Converter in CCM Using Kg Method
Transformer Design for Flyback Converter in DCM Using Kg Method
Summary
References
Review Questions
Problems
Index
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