Fundamentals of Applied Electromagnetics

Coordinate Systems 123 3-3.1 Cartesian to Cylindrical Transformations 123 3-3.2 Cartesian to Spherical Transformations 125 3-3.3 Cylindrical to Spherical Transformations 127 3-3.4 Distance between Two Points 127 3-4 Gradient of a Scalar Field 130 3-4.1 Gradient Operator in Cylindrical and Spherical Coordinates 131 3-4.2 Properties of the Gradient Operator 132 3-5 Divergence of a Vector Field 133 3-5.1 Divergence Theorem 135 3-5.2 Remarks on Notation 135 3-6 Curl of a Vector Field 139 3-6.1 Vector Identities Involving the Curl 140 3-6.2 Stokes's Theorem 141 3-7 Laplacian Operator 142 Problems 144 4 Electrostatics 150 4-1 Maxwell's Equations 151 4-2 Charge and Current Distributions 152 4-2.1 Charge Densities 152 4-2.2 Current Density 154 4-3 Coulomb's Law 155 4-3.1 Electric Field due to Multiple Point Charges 156 4-3.2 Electric Field due to a Charge Distribution 157 4-4 Gauss's Law 160 4-5 Electric Scalar Potential 163 4-5.1 Electric Potential as a Function of Electric Field 163 4-5.2 Electric Potential due to Point Charges 165 4-5.3 Electric Potential due to Continuous Distributions 165 4-5.4 Electric Field as a Function of Electric Potential 165 4-5.5 Poisson's Equation 167 4-6 Electrical Properties of Materials 168 4-7 Conductors 169 4-7.1 Resistance 170 4-7.2 Joule's Law 172 4-8 Dielectrics 173 4-9 Electric Boundary Conditions 177 4-9.1 Dielectric--Conductor Boundary 180 4-9.2 Conductor--Conductor Boundary 181 4-10 Capacitance 182 4-11 Electrostatic Potential Energy 190 4-12 Image Method 191 Problems 194 5 Magnetostatics 204 5-1 Magnetic Forces and Torques 205 5-1.1 Magnetic Force on a Current-Carrying Conductor 207 5-1.2 Magnetic Torque on a Current-Carrying Loop 210 5-2 The Biot--Savart Law 213 5-2.1 Magnetic Field due to Surface and Volume Current Distributions 214 5-2.2 Magnetic Field of a Magnetic Dipole 217 5-3 Magnetic Force between Two Parallel Conductors 218 5-4 Maxwell's Magnetostatic Equations 219 5-4.1 Gauss's Law for Magnetism 219 5-4.2 Amp'ere's Law 220 5-5 Vector Magnetic Potential 226 5-6 Magnetic Properties of Materials 228 5-6.1 Orbital and Spin Magnetic Moments 228 5-6.2 Magnetic Permeability 229 5-6.3 Magnetic Hysteresis of Ferromagnetic Materials 230 5-7 Magnetic Boundary Conditions 233 5-8 Inductance 234 5-8.1 Magnetic Field in a Solenoid 235 5-8.2 Self-inductance 238 5-8.3 Mutual Inductance 240 5-9 Magnetic Energy 241 Problems 245 6 Maxwell's Equations for Time-Varying Fields 254 6-1 Faraday's Law 255 6-2 Stationary Loop in a Time-Varying Magnetic Field 257 6-3 The Ideal Transformer 261 6-4 Moving Conductor in a Static Magnetic Field 262 6-5 The Electromagnetic Generator 265 6-6 Moving Conductor in a Time-Varying Magnetic Field 267 6-7 Displacement Current 268 6-8 Boundary Conditions for Electromagnetics 270 6-9 Charge--Current Continuity Relation 271 6-10 Free-Charge Dissipation in a Conductor 273 6-11 Electromagnetic Potentials 276 6-11.1 Retarded Potentials 276 6-11.2 Time-Harmonic Potentials 277 Problems 281 7 Plane-Wave Propagation 286 7-1 Time-Harmonic Fields 288 7-1.1 Complex Permittivity 289 7-1.2 Wave Equations for a Charge-Free Medium 289 7-2 Plane-Wave Propagation in Lossless Media 290 7-2.1 Uniform Plane Waves 290 7-2.2 General Relation between E and H 294 7-3 Wave Polarization 295 7-3.1 Linear Polarization 296 7-3.2 Circular Polarization 297 7-3.3 Elliptical Polarization 299 7-4 Plane-Wave Propagation in Lossy Media 304 7-4.1 Low-Loss Dielectric 306 7-4.2 Good Conductor 306 7-5 Current Flow in a Good Conductor 308 7-6 Electromagnetic Power Density 311 7-6.1 Plane Wave in a Lossless Medium 312 7-6.2 Plane Wave in a Lossy Medium 313 7-6.3 Decibel Scale for Power Ratios 314 Problems 316 8 Reflection, Transmission, and Waveguides 320 8-1 Wave Reflection and Transmission at Normal Incidence 322 8-1.1 Boundary between Lossless Media 322 8-1.2 Transmission-Line Analogue 325 8-1.3 Power Flow in Lossless Media 326 8-1.4 Boundary between Lossy Media 329 8-2 Snell's Laws 331 8-3 Fiber Optics 334 8-4 Wave Reflection and Transmission at Oblique Incidence 336 8-4.1 Perpendicular Polarization 337 8-4.2 Parallel Polarization 341 8-4.3 Brewster Angle 343 8-5 Reflectivity and Transmissivity 346 8-6 Waveguides 349 8-7 General Relations for E and H 351 8-8 TM Modes in Rectangular Waveguide 352 8-9 TE Modes in Rectangular Waveguide 357 8-10 Propagation Velocities 358 8-11 Cavity Resonators 363 8-11.1 Resonant Frequency 364 8-11.2 Quality Factor 364 Problems 366 9 Radiation and Antennas 372 9-1 The Short Dipole 375 9-1.1 Far-Field Approximation 377 9-1.2 Power Density 378 9-2 Antenna Radiation Characteristics 380 9-2.1 Antenna Pattern 381 9-2.2 Beam Dimensions 383 9-2.3 Antenna Directivity 383 9-2.4 Antenna Gain 386 9-2.5 Radiation Resistance 386 9-3 Half-Wave Dipole Antenna 387 9-3.1 Directivity of lambda/2 Dipole 389 9-3.2 Radiation Resistance of lambda/2 Dipole 389 9-3.3 Quarter-Wave Monopole Antenna 390 9-4 Dipole of Arbitrary Length 391 9-5 Effective Area of a Receiving Antenna 392 9-6 Friis Transmission Formula 395 9-7 Radiation by Large-Aperture Antennas 397 9-8 Rectangular Aperture with Uniform Aperture Distribution 400 9-8.1 Beamwidth 401 9-8.2 Directivity and Effective Area 402 9-9 Antenna Arrays 403 9-10 N-Element Array with Uniform Phase Distribution 410 9-11 Electronic Scanning of Arrays 412 9-11.1 Uniform-Amplitude Excitation 414 9-11.2 Array Feeding 415 Problems 418 10 Satellite Communication Systems and Radar Sensors 424 10-1 Satellite Communication Systems 425 10-2 Satellite Transponders 427 10-3 Communication-Link Power Budget 430 10-4 Antenna Beams 432 10-5 Radar Sensors 433 10-5.1 Basic Operation of a Radar System 433 10-5.2 Unambiguous Range 434 10-5.3 Range and Angular Resolutions 435 10-6 Target Detection 436 10-7 Doppler Radar 439 10-8 Monopulse Radar 440 Problems 444 A Symbols, Quantities, and Units 445 B Material Constants of Some Common Materials 447 C Mathematical Formulas 449 D Answers to Odd-Numbered Problems 451 Bibliography 457 Index 459