Magnetic Components : Basics and Applications

The book deals with methods for the description and design of electromagnetic components. Both linear and nonlinear components are covered. For electrical simulations the necessary equivalent circuit diagrams are derived and a general methodology is developed. Possible influences on properties via material selection, winding design and premagnetisation of sections are treated. Measurement characterization, modeling, possible errors and model limits are dealt with extensively. In the last chapter examples are discussed. The content Magnetostatics and magnetodynamics Magnetic material properties Optimization of soft magnetic inductive components Transformation of magnetic and electrical circuits Modeling of magnetic field sections Metrological characterization of inductive components Apparent power and volume for inductive components Approximation of empirical characteristic curves Application examples The target groups Engineers and prospective engineers (master course) with a focus on power engineering, mechatronics, medical technology, electromagnetic compatibility Engineers with a focus on marketing and, where appropriate, sales of electrical devices and systems This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation Preface 5 Symbol Directory 7 Coded Notation 7 Operations with Variables 8 Variables Used 8 Latin Letters 9 Greek Letters 10 Circuit Symbols 11 Contents 13 1: The Magnetostatic Field 17 1.1 Magnetic Field Quantities and Characteristics of Magnetic Circuits 19 1.2 The Circular Integral in the Magnetic Field - the Magnetomotive Force (MMF) - the Magnetic Force 28 1.3 The Magnetic Circuit and its Elements 34 1.4 Energy and Forces in the Magnetic Field 38 1.5 The Biot-Savart Law 40 1.6 The Lorentz Force 42 1.7 The Vector Potential 45 References 47 2: The Magnetodynamic Field 48 2.1 The Law of Induction 48 2.2 Self-Induction 54 2.3 Mutual Induction 62 2.4 Transformers 64 2.5 Oscillating Circuits with Concentrated Elements 71 2.6 Energy Propagation Between Lines and in the Space 77 2.7 The Maxwell Equations 93 References 95 3: Magnetic Properties of Materials 96 3.1 Macroscopic Description of Magnetic Properties 96 3.2 Atomistic Models of Magnetism 112 3.3 Temperature Influences on the Magnetic Properties 118 3.4 Loss Mechanisms in Magnetic Components 124 3.5 Energy and Forces in the Magnetic Field 127 3.6 Magnetostriction 136 References 138 4: Optimization of Soft Magnetic Components 140 4.1 Basic Requirements for Soft Magnetic High Performance Materials 140 4.2 Description of Core Losses During Magnetization 144 4.3 Optimization Approach for Transformers 148 4.4 Optimization Approach for Chokes with an Air Gap 154 4.5 Special Material Problems in the Design of Inductive Components 161 4.6 Optimization Approach for Saturable (Switching) Chokes 167 References 170 5: Transformation of Magnetic and Electrical Circuits 171 5.1 Comparison of Magnetic and Electrical Circuits 171 5.2 Magnetization of a Core Section by a Current-Conducting Winding 173 5.3 Duality Principle and Graphic Circuit Inversion 176 5.4 Coupling of an Electrically-Caused Alternating Magnetic Flux into an Electromagnetic Circuit with Interactions Between Bot... 177 5.5 Modeling Example of a Linear ``Leakage Core ́ ́ Transformer 187 5.6 Modelling Approach for Nonlinear Magnetic Sections 191 5.7 Consideration of Hard Magnetic Properties 206 5.8 Variable Magnetic Sections in Inductive Structures 209 References 218 6: Calculation and Modelling of Linear Magnetic Field Sections in Magnetic Devices 219 6.1 Elementary Magnetic Conductance/Permeance 219 6.2 Distributed Magnetic Field Quantities Versus Lumped Equivalent Parameters 225 6.3 Inductance of Conductors and Conductor Arrangements 229 6.4 Inductance of Windings 231 6.5 Leakage Inductance Between Windings 239 6.6 Approaches to Determine the Leakage Inductance with Different Winding Arrangements 246 6.7 Design of Transformers and Chokes with Strong Yoke Leakage 250 6.8 Determination of Parameters of Inductive Components with Toroidal Cores 257 6.9 Permeability as a Complex Parameter 270 6.10 Complex Permeability of Winding Material and Structural Parts 278 References 296 7: Characterization of Inductive Components 298 7.1 Basics 298 7.2 Equivalent Circuits for Inductors 306 7.3 Characterization of Inductive Components by Measuring Sinusoidal Voltage, Current and Their Phase Relation 312 7.4 Bridge Circuits for Determining the Impedance Components of Inductive Components 317 7.5 Measuring the B(H(T)) Characteristic 327 7.6 Transformer Measurement Methods 335 7.7 Calorimetric Methods for Loss Determination 337 References 343 8: Apparent Power and Volume at Inductive Components 344 8.1 Basic Considerations Using the Example of Transformers 344 8.2 Size of Optimized Ferrite Chokes and Transformers 348 8.3 Consideration of Dielectric Properties in the Core 360 8.4 Small Transformers for Mains Frequency 366 8.5 Problems of Increasing the Operating Frequency 370 8.6 Transmission and Distribution Transformers of Power Supply Systems 381 8.7 Windings of Copper or Aluminium 386 References 388 9: Approximation of Empirical Characteristic Curves 390 9.1 Dimensional Analysis for Ordering Influencing and Resulting Values Among Each Other 390 9.2 Linear Regression Analysis 401 9.3 General Approach as Linear Combination of Influences 414 9.4 Planning of Experiments 421 9.5 Determination of an Optimized Functional System for the Approximation of Measurement Data from Random Samples of the Measu... 429 9.6 Properties of the Approximating Basic Vectors 443 9.7 Quality Functionalities for the Approximation 445 9.8 Algorithms for the Numerical Solution of the Approximation Tasks 449 References 462 10: Application Examples 464 10.1 Shunts for Current Measurement 464 10.2 Current Transformers for Current Measurement 479 10.3 Rogowski Coils for Current Measurement 486 10.4 Design Aspects of Chokes 492 10.5 Controllable Inductors 516 10.6 DC/DC Converter with 2 Chokes Without Coupling on One Core 535 10.7 Controllable Harmonic Absorber Filters to Reduce Harmonic Mains Currents 541 10.8 Coupled Inductors for Interleaved Operation 550 10.9 DC/DC Converter with Reduced Voltage Stress at the Switches 567 10.10 Double Pulse Test for Semiconductor Switching Elements 575 10.11 Possibilities of Influencing Leakage Inductances 581 10.12 Single-Phase Transformers for Voltage Adjustment and Insulation 598 10.13 Transformers for Multiphase Voltage Systems 604 10.14 Transmission Line Transformers (TLT) 622 Circuits with Coaxial Lines 626 Transformers with Symmetrical Double Lines 630 10.15 Transformers with Controllable Output Voltage 631 10.16 Electronic ``Direct Current Transformers ́ ́ 638 10.17 Transformerless Grid Connected AC Current Feed in from DC Sources and Storages 645 10.18 Mains Pollutions of Power Converters (EMC) and Non-Linear Loads and Their Influence by Transformers 650 10.19 Pseudo Multilevel Converter 662 10.20 Energy Recovery from a Converter by Choke Transformer 666 10.21 Inverter Based on a T-Filter 671 10.22 Power-Modulated Electronic Power Source for Longitudinal Gas Flow CO2 cw Lasers 676 10.23 Description of Resonant Circuits and Resonant Circuits in the Phase Plane 686 10.24 Magnetic Stabilization of Heating Voltages 695 10.25 Oscillators with Non-Linear Magnetic Components 703 10.26 Circuit Concepts for Generating Short High-Energy Pulses for Pulse Power Applications 709 10.27 Pulse Laser with Semiconductor Switch 720 10.28 Magnetic Amplifier 727 10.29 Rough Dimensioning of a Transformer 736 10.30 Influence of Winding Material on Quality of HF Coils 741 10.31 Large-Signal Power Loss Measurements on Large Cores 749 10.32 Modelling the Dependence of the Inductance of Air Gap Reactors 762 10.33 Dimensioning of a Choke for a Buck Converter with AMCC Core 769 10.34 Current Ripple Cancellation in DC/DC and DC/AC Converters 776 10.35 Controllable Inductors in Parallel Operation 784 References 796 Related Literature 801 Chapter 1 801 Chapter 2 801 Chapter 3 802 Chapter 4 802 Chapter 5 803 Chapter 6 803 Chapter 7 804 Chapter 8 805 Chapter 9 805 Chapter 10.1 805 Chapter 10.2 805 Chapter 10.3 806 Chapter 10.5 806 Chapter 10.7 806 Chapter 10.8 806 Chapter 10.10 807 Chapter 10.13 807 Chapter 10.15 808 Chapter 10.17 808 Chapter 10.22 809 Chapter 10.23 809 Chapter 10.24 809 Chapter 10.26 809 Index 810