JOHN R. BRAUER, PhD, PE, is Adjunct Professor in the Department of Electrical Engineering and Computer Science at the Milwaukee School of Engineering. A Life Fellow of the IEEE, he received their Third Millennium Medal in 2000 for his service, and has served on the boards of the Applied Computational Electromagnetics Society and the International Compumag Society. In addition, Dr. Brauer has published 160 technical papers and contributed to several books.

PREFACE xi
PREFACE TO THE FIRST EDITION xiii
LIST OF 66 EXAMPLES xv
PART I MAGNETICS 1
1 Introduction 3
1.1 Overview of Magnetic Actuators 3
1.2 Overview of Magnetic Sensors 4
1.3 Actuators and Sensors in Motion Control Systems 5
1.4 Magnetic Actuators and Sensors in Mechatronics 7
References 8
2 Basic Electromagnetics 9
2.1 Vectors 9
2.2 Ampere's Law 14
2.3 Magnetic Materials 17
2.4 Faraday's Law 22
2.5 Potentials 25
2.6 Maxwell's Equations 28
Problems 29
References 31
3 Reluctance Method 33
3.1 Simplifying Ampere's Law 33
3.2 Applications 37
3.3 Fringing Flux 40
3.4 Complex Reluctance 41
3.5 Limitations 41
Problems 42
References 42
4 Finite-Element Method 43
4.1 Energy Conservation and Functional Minimization 43
4.2 Triangular Elements for Magnetostatics 45
4.3 Matrix Equation 46
4.4 Finite-Element Models 49
Problems 53
References 53
5 Magnetic Force 55
5.1 Magnetic Flux Line Plots 55
5.2 Magnetic Energy 60
5.3 Magnetic Force on Steel 61
5.4 Magnetic Pressure on Steel 65
5.5 Lorentz Force 66
5.6 Permanent Magnets 67
5.7 Magnetic Torque 72
5.8 Magnetic Volume Forces on Permeable Particles 73
Problems 75
References 76
6 Other Magnetic Performance Parameters 79
6.1 Magnetic Flux and Flux Linkage 79
6.2 Inductance 82
6.3 Capacitance 86
6.4 Impedance 88
Problems 91
References 91
PART II ACTUATORS 93
7 Magnetic Actuators Operated by DC 95
7.1 Solenoid Actuators 95
7.2 Voice Coil Actuators 106
7.3 Other Actuators Using Coils and Permanent Magnets 108
7.4 Proportional Actuators 109
7.5 Rotary Actuators 112
7.6 Magnetic Bearings and Couplings 114
7.7 Magnetic Separators 117
Problems 125
References 127
8 Magnetic Actuators Operated by AC 129
8.1 Skin Depth 129
8.2 Power Losses in Steel 130
8.3 Force Pulsations 135
8.4 Cuts in Steel 139
References 145
9 Magnetic Actuator Transient Operation 147
9.1 Basic Timeline 147
9.2 Size, Force, and Acceleration 148
9.3 Linear Magnetic Diffusion Times 150
9.4 Nonlinear Magnetic Infusion Times 156
9.5 Nonlinear Magnetic Effusion Time 164
9.6 Pulse Response of Nonlinear Steel 169
Problems 171
References 174
PART III SENSORS 175
10 Hall Effect and Magnetoresistive Sensors 177
10.1 Simple Hall Voltage Equation 177
10.2 Hall Effect Conductivity Tensor 179
10.3 Finite-Element Computation of Hall Fields 182
10.4 Hall Sensors for Position or Current 190
10.5 Magnetoresistance 193
10.6 Magnetoresistive Heads for Hard Disk Drives 194
10.7 Giant Magnetoresistive Spin Valve Sensors 195
Problems 198
References 198
11 Other Magnetic Sensors 201
11.1 Speed Sensors Based on Faraday's Law 201
11.2 Inductive Recording Heads 203
11.3 Proximity Sensors Using Impedance 206
11.4 Linear Variable Differential Transformers 210
11.5 Magnetostrictive Sensors 213
11.6 Fluxgate Sensors 215
11.7 Chattock Coil Field and Current Sensor 219
11.8 Squid Magnetometers 222
11.9 Magnetoimpedance and Miniature Sensors 223
11.10 MEMS Sensors 224
Problems 225
References 226
PART IV SYSTEMS 229
12 Coil Design and Temperature Calculations 231
12.1 Wire Size Determination for DC Currents 231
12.2 Coil Time Constant and Impedance 234
12.3 Skin Effects and Proximity Effects for AC Currents 235
12.4 Finite-Element Computation Of Temperatures 239
Problems 246
References 246
13 Electromagnetic Compatibility 249
13.1 Signal-To-Noise Ratio 249
13.2 Shields and Apertures 250
13.3 Test Chambers 255
Problems 260
References 260
14 Electromechanical Finite Elements 263
14.1 Electromagnetic Finite-Element Matrix Equation 263
14.2 0D and 1D Finite Elements for Coupling Electric Circuits 266
14.3 Structural Finite-Element Matrix Equation 272
14.4 Force and Motion Computation by Time Stepping 273
14.5 Typical Electromechanical Applications 275
Problems 286
References 286
15 Electromechanical Analysis Using Systems Models 289
15.1 Electric Circuit Models of Magnetic Devices 289
15.2 VHDL-AMS/Simplorer Models 296
15.3 MATLAB/Simulink Models 301
15.4 Including Eddy Current Diffusion Using a Resistor 307
15.5 Magnetic Actuator Systems for 2D Planar Motion 312
15.6 Optimizing Magnetic Actuator Systems 313
Problems 324
References 325
16 Coupled Electrohydraulic Analysis Using Systems Models 327
16.1 Comparing Hydraulics and Magnetics 327
16.2 Hydraulic Basics and Electrical Analogies 328
16.3 Modeling Hydraulic Circuits in Spice 330
16.4 Electrohydraulic Models in Spice and Simplorer 334
16.5 Hydraulic Valves and Cylinders in Systems Models 341
16.6 Magnetic Diffusion Resistor in Electrohydraulic Models 348
16.7 Optimization of an Electrohydraulic System 352
16.8 Magnetic Actuators for Digital Hydraulics 353
Problems 357
References 357
APPENDIX A: SYMBOLS, DIMENSIONS, AND UNITS 359
APPENDIX B: NONLINEAR B-H CURVES 361
APPENDIX C: FINAL ANSWERS FOR ODD-NUMBERED PROBLEMS 367
INDEX 371