Fundamentals of applyed etromagnetics 7th ulaby

FUNDAMENTALS OF APPLIED ELECTROMAGNETICS Seventh Edition Fawwaz T Ulaby University of Michigan, Ann Arbor Umberto Ravaioli University of Illinois, Urbana–Champaign Pearson Boston · Columbus · Indianapolis · New York · San Francisco · Upper Saddle River · Amsterdam Cape Town · Dubai · London · Madrid · Milan · Munich · Paris · Montreal · Toronto Delhi · Mexico City · Sau Paula · Sydney · Hong Kong · Seoul · Singapore · Taipei · Tokyo Library of Congress Cataloging-in-Publication Data on File Vice President and Editorial Director, ECS: Marcia J Horton Acquisitions Editor: Julie Bai Editorial Assistant: Sandra Rodriguez Managing Editor: Scott Disanno Production Editor: Rose Kernan Art Director: Marta Samsel Art Editor: Gregory Dulles Manufacturing Manager: Mary Fischer Manufacturing Buyer: Maura Zaldivar-Garcia Product Marketing Manager: Bram Van Kempen Field Marketing Manager: Demetrius Hall Marketing Assistant: Jon Bryant Cover Designer: Black Horse Designs c 2015, 2010 Pearson Education, Inc Upper Saddle River, New Jersey 07458 All rights reserved No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher The author and publisher of this book have used their best efforts in preparing this book These efforts include the development, research, and testing of theories and programs to determine their effectiveness The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book The author and publisher shall not be liable in any event for incidental or consequential damages with, or arising out of, the furnishing, performance, or use of these programs Previous editions copyright c 2007 by Pearson Education, Inc Pearson Education Ltd., London Pearson Education Australia Pty Ltd., Sydney Pearson Education Singapore, Pte Ltd Pearson Education North Asia Ltd., Hong Kong Pearson Education Canada, Inc., Toronto Pearson Education de Mexico, S.A de C.V Pearson Education–Japan, Tokyo Pearson Education Malaysia, Pte Ltd Pearson Education, Inc., Upper Saddle River, New Jersey 10 www.pearsonhighered.com ISBN-13: ISBN-10: 978-0-13-335681-6 0-13-335681-7 We dedicate this book to Jean and Ann Lucia This page intentionally left blank Preface to Seventh Edition Building on the core content and style of its predecessor, this seventh edition (7/e) of Applied Electromagnetics introduces new features designed to help students develop a deeper understanding of electromagnetic concepts and applications Prominent among them is a set of 52 web-based simulation modules that allow the user to interactively analyze and design transmission line circuits; generate spatial patterns of the electric and magnetic fields induced by charges and currents; visualize in 2-D and 3-D space how the gradient, divergence, and curl operate on spatial functions; observe the temporal and spatial waveforms of plane waves propagating in lossless and lossy media; calculate and display field distributions inside a rectangular waveguide; and generate radiation patterns for linear antennas and parabolic dishes These are valuable learning tools; we encourage students to use them and urge instructors to incorporate them into their lecture materials and homework assignments Additionally, by enhancing the book’s graphs and illustrations, and by expanding the scope of topics of the Technology Briefs, additional bridges between electromagnetic fundamentals and their countless engineering and scientific applications are established In summary: NEW TO THIS EDITION • A set of 10 additional interactive simulation modules, bringing the total to 52 • Updated Technology Briefs • Enhanced figures and images • New/updated end-of-chapter problems • The interactive modules and Technology Briefs can be found at the Student Website on http://www.pearsonhighered.com/ulaby ACKNOWLEDGMENTS As authors, we were blessed to have worked on this book with the best team of professionals: Richard Carnes, Leland Pierce, Janice Richards, Rose Kernan, and Paul Mailhot We are exceedingly grateful for their superb support and unwavering dedication to the project We enjoyed working on this book We hope you enjoy learning from it Fawwaz T Ulaby Umberto Ravaioli vi PREFACE CONTENT in Chapter with reviews of complex numbers and phasor analysis The book begins by building a bridge between what should be familiar to a third-year electrical engineering student and the electromagnetics (EM) material covered in the book Prior to enrolling in an EM course, a typical student will have taken one or more courses in circuits He or she should be familiar with circuit analysis, Ohm’s law, Kirchhoff’s current and voltage laws, and related topics Transmission lines constitute a natural bridge between electric circuits and electromagnetics Without having to deal with vectors or fields, the student uses already familiar concepts to learn about wave motion, the reflection and transmission of power, phasors, impedance matching, and many of the properties of wave propagation in a guided structure All of these newly learned concepts will prove invaluable later (in Chapters through 9) and will facilitate the learning of how plane waves propagate in free space and in material media Transmission lines are covered in Chapter 2, which is preceded The next part of the book, contained in Chapters through 5, covers vector analysis, electrostatics, and magnetostatics The electrostatics chapter begins with Maxwell’s equations for the time-varying case, which are then specialized to electrostatics and magnetostatics, thereby providing the student with an overall framework for what is to come and showing him or her why electrostatics and magnetostatics are special cases of the more general time-varying case Chapter deals with time-varying fields and sets the stage for the material in Chapters through Chapter covers plane-wave propagation in dielectric and conducting media, and Chapter covers reflection and transmission at discontinuous boundaries and introduces the student to fiber optics, waveguides and resonators In Chapter 9, the student is introduced to the principles of radiation by currents flowing in wires, such as dipoles, as well as Suggested Syllabi 10 Chapter Introduction: Waves and Phasors Transmission Lines Vector Analysis Electrostatics Magnetostatics Exams Maxwell’s Equations for Time-Varying Fields Plane-wave Propagation Wave Reflection and Transmission Radiation and Antennas Satellite Communication Systems and Radar Sensors Exams Extra Hours Two-semester Syllabus credits (42 contact hours per semester) Sections Hours All All All All All One-semester Syllabus credits (56 contact hours) Sections Hours All 12 8 42 2-1 to 2-8 and 2-11 All 4-1 to 4-10 5-1 to 5-5 and 5-7 to 5-8 8 6-1 to 6-3, and 6-6 All All 7-1 to 7-4, and 7-6 8-1 to 8-3, and 8-6 All All 10 9-1 to 9-6 None — Total for second semester 40 Total 56 Total for first semester All PREFACE to radiation by apertures, such as a horn antenna or an opening in an opaque screen illuminated by a light source To give the student a taste of the wide-ranging applications of electromagnetics in today’s technological society, Chapter 10 concludes the book with overview presentations of two system examples: satellite communication systems and radar sensors The material in this book was written for a two-semester sequence of six credits, but it is possible to trim it down to generate a syllabus for a one-semester four-credit course The accompanying table provides syllabi for each of these two options vii ACKNOWLEDGMENTS Special thanks are due to reviewers for their valuable comments and suggestions They include Constantine Balanis of Arizona State University, Harold Mott of the University of Alabama, David Pozar of the University of Massachusetts, S N Prasad of Bradley University, Robert Bond of New Mexico Institute of Technology, Mark Robinson of the University of Colorado at Colorado Springs, and Raj Mittra of the University of Illinois I appreciate the dedicated efforts of the staff at Prentice Hall and I am grateful for their help in shepherding this project through the publication process in a very timely manner MESSAGE TO THE STUDENT The web-based interactive modules of this book were developed with you, the student, in mind Take the time to use them in conjunction with the material in the textbook Video animations can show you how fields and waves propagate in time and space, how the beam of an antenna array can be made to scan electronically, and examples of how current is induced in a circuit under the influence of a changing magnetic field The modules are a useful resource for selfstudy You can find them at the Student Website link on http://www.pearsonhighered.com/ulaby Use them! Fawwaz T Ulaby This page intentionally left blank List of Technology Briefs TB1 TB2 TB3 TB4 TB5 TB6 TB7 TB8 TB9 LED Lighting Solar Cells Microwave Ovens EM Cancer Zappers Global Positioning System X-Ray Computed Tomography Resistive Sensors Supercapacitors as Batteries Capacitive Sensors 20 38 82 112 150 164 196 214 218 TB10 TB11 TB12 TB13 TB14 TB15 TB16 TB17 Electromagnets Inductive Sensors EMF Sensors RFID Systems Liquid Crystal Display (LCD) Lasers Bar-Code Readers Health Risks of EM Fields 256 268 292 322 336 368 382 424 Index arrays, 435–442 linear phase, 446 pattern multiplication principle, 438 scanning, 444–449 uniform phase, 442–443 broadside direction, 409 directivity D, 414, 434 effective area, 434 far-field (far-zone) region, 405, 408–409 gain, 416–417 half-wave dipole, 417–422 input impedance, 404 isotropic, 404, 413 large aperture, 429–435 multiplication principle, 438 normalized radiation intensity, 409 pattern solid angle p , 412 patterns, 404, 411 beam dimensions, 412 beamwidth β, 413–414 directivity D, 414–415 polarization, 404 receiving, 422–427 reciprocal, 404 types, 464 arrays, 464 dipoles, 464 helices, 464 3-dB beamwidth, 414 A Abacus, Ablation, 10, 112 ac motor, 3, ac resistance R, 341 Acceptance angle θa , 365 Adding machine, Admittance Y , 96 Alternating current (ac), AM radio, Amp`ere, Andr´e-Marie, Amp`ere’s law, 252–255, 273 Amplitude-comparison monopulse radar, 470 Amplitude modulation (AM), Analog computer, Angle error signal, 471 Angle of incidence θi , 363 Angle of reflection θr , 363 Angle of transmission θt , 363 Angular frequency ω, 25, 58 Angular velocity ω, 25 Antennas, 404–449, 463–464 aperture, 429 rectangular, 432–434 scalar formulation 430 vector formulation 430 493 494 horns, 464 parabolic dishes, 464 Antenna radiation pattern, 404 Arithmometer, Armstrong, Edwin, 6, ARPANET, Array factor Fa (θ), 438 array amplitude distribution, 438 array phase distribution, 438 Atmospheric transmissivity ϒ, 462 Attenuation constant α, 57, 331 Average power Sav , 343 Average power density Sav , 343 Auxiliary angle ψ0 , 329 Axial ratio R, 329 Azimuth angle φ, 407 Azimuth-difference channel, 471 Azimuth plane (φ-plane), 412 Azimuth resolution x, 466 B bac-cab rule, 139 Backus, John, Band gap energy, 39 Bar-code readers, 382–383 Bardeen, John, Base vector, 134 BASIC, Beam dimensions, 412 Beamwidth β, 413, 414, 433–434 Becquerel, Alexandre-Edmond, 38, 293 Bell, Alexander, Berliner, Emil, Berners–Lee, Tim, Bhatia, Sabeer, Bioelectrics, 113 Biot, Jean-Baptiste, 4, 16 Biot–Savart law, 4, 16, 244–251, 273 current distributions, 244–248 surface current density Js , 244 volume current density J, 244 volume distributions, 244–248 Bistatic radar, 467 Bounce diagram, 118 Boundary conditions, 203–210 Brattain, Walter, Braun, Karl, Brewster (polarizing) angle, 375–376, 396 Broadside array, 442 INDEX Broadside direction, 409 Bush, Vannevar, C Capacitance C, 210–213 capacitor, 210 of a coaxial line, 212 of a parallel-plate capacitor, 211–213 Capacitive sensors, 196, 218–222 Capacitor, 4, as batteries, 214–216 electrochemical double-layer (EDLC), 214 Cardullo, Mario, 322 Carrier frequency f , 465 Cartesian coordinate system x, y, z 141, 142 CAT (CT) scan, 164 Cathode ray tube (CRT), Cavity resonators, 392–394, 396 Cell phone, Charge continuity equation, 301, 307 Charge dissipation, 302 Charge distribution, 180–181, 184 surface distribution, 185 Circular polarization, 324, 326–328 Circulation, 162 Circulator, 460 Cladding, 365 Coaxial line, 51 Complex conjugate, 34 Complex feeding coefficient Ai , 437 Complex numbers, 32–36 complex conjugate, 34 Euler’s identity, 32, 43 polar form, 32 properties, 34 rectangular form, 32 rectangular-polar relations, 32, 43 Complex permittivity c , 315 Compressive stress, 292 Conductance G, 96 Conductivity σ , 8, 18, 198, 477 Conductors, 195–201 conduction current, 195 conduction current density J, 195 conductivity, 198, 477 equipotential medium, 198 resistance, 199–200 semiconductors, 195, 198 Conservative (irrotational) field, 166, 191 INDEX Constitutive parameters, 195 Convection current, 182 Conversion efficiency, 38 Coordinate systems, 140–154 Cartesian x, y, z 141, 142 cylindrical r, φ, z, 140, 142–145 spherical R, θ, φ, 140, 145–147 Coplanar waveguide, 51 Cormack, Allan, 164 Coulomb (C), 13 Coulomb, Charles-Augustin de, 3, 4, 13 Coulomb’s law, 13, 182–187 charge distribution, 184 circular disk of charge, 186 infinite sheet of charge, 187 line distribution, 185 relative permittivity (dielectric constant) r , 183 ring of charge, 185 surface distribution, 185 two-point charges, 184 volume distribution, 185 Critical angle θc , 364 Cross (vector) product, 138–139 CT (CAT) scan, 164 Curie, Paul-Jacques, 292 Curie, Pierre, 292 Curl operator, 162, 163 Current density, 195, 244, 297 Cutoff frequency fmn , 386 Cutoff wavenumber kc , 384 Cylindrical coordinate system r, φ, z, 140, 142–145 D dc motor, De Forest, Lee, Deep Blue, Del (gradient operator) ∇, 155 Detection, 467–469 maximum detectable range Rmax , 468 threshold detection level Prmin , 468 Diamagnetic, 260 Dielectric constant (relative permittivity) r , 15, 183, 202, 479 Dielectrics, 195, 201–203 anisotropic, 202 breakdown, 203–203 breakdown voltage Vbr , 203 electric polarization field P, 202 electric susceptibility χe , 203 homogeneous, 202 495 isotropic, 202 linear, 202 nonpolar, 201 perfect, 195, 198 permanent dipole moments, 202 polar materials, 201 polarization, 201 strength Eds , 203 tables, 204, 479 Difference channel, 471 Digital computer, Dimensions, 11 Dipole, 14, 82, 192, 248, 252 electric, 14, 82, 192 half-wave, 417–422, 451 Hertzian, 406–409 linear, 420–422 moment, 193 short, 427, 451 vertical, 435 Direct current (dc), Directional derivative dT /dl, 155 Directivity D, 414, 434 Dispersive, 50 Displacement current Id , 297–299 Displacement current density Jd , 297 Distance vector, 136 Divergence operator, 158–162 Divergence theorem, 159 Dominant mode, 386 Doppler frequency shift fd , 464, 469 Doppler radar, 469–470 Dot (scalar) product, 136–137 Downlink, 460 Drift velocity ue , 198 du Fay, Charles Fran¸cois, 3, Duplexer (T/R switch), 460, 465 E e electron charge, 13 Echo satellite, Eckert, J Presper, Edison, Thomas, 6, 20 Effective aperture, 422, See also Effective area Effective area Ae , 422 Einstein, Albert, 3, 5, 38 Electric, 3, 496 Electric charge, 3, 4, 13–14 law of conservation of electric charge, 14 principle of linear superposition, 14 Electric dipole, 14, 82, 192 moment, 193 Electric-field aperture distribution Ea (xa , ya ), 430 Electric field intensity E, 14, 179 Electric field phasor E, 319 Electric fields, 13–15, 179, 183–187 dipole, 14, 192 e charge, 13 polarization, 14, 201 Electric flux density D, 15, 179 Electric generator, Electric potential V , 189 Electric scalar potential, 189–194 as a function of electric field, 189–191 due to continuous distributions, 191 due to point charges, 191, 223 electric dipole, 192 Kirchhoff’s voltage law, 190 Laplace’s equation, 193 line distribution, 191 Poisson’s equation, 193 potential energy, 189 Electric susceptibility χe , 203 Electric typewriter, Electrical force Fe , 13 Electrical permittivity , 13, 66, 183–184, 203 of free space , 13 Electrical sensors, 196 capacitive, 196 emf, 196 inductive, 196 resistive, 196–197 Electromagnetic (EM) force, 12, 237 Electromagnetic (EM) spectrum, 30–32 gamma rays, 30, 32 infrared, 30, 32 microwave band, 32, 32 EHF, 32 millimeter-wave band, 32 SHF, 32 UHF, 32 monochromatic, 30 properties, 30 radio spectrum, 30, 32, 32 ultraviolet, 32, 32 visible, 32, 32 INDEX X-rays, 30, 32 Electromagnetic generator, 294–296 Electromagnetic induction, 283 Electromagnetic telegraph, Electromagnetic waves, 5, 82, 353–394 Electromagnets, 256–258 ferromagnetic core, 256 horseshoe, 256 loudspeaker, 257–258 magnetic levitation, 258 magnetically levitated trains (maglevs), 258–258 reed relay, 256 step-down transformer, 256 switch, 256 Electromotive force (emf) Vemf , 5, 283 Electron, 3, 5, 13 Electronic beeper, Electronic steering, 436 EM, Electrostatics, 17, 179 Elevation angle (θ-plane), 412 Elevation-difference channel, 471 Elevation plane (θ-plane), 412 Elliptical polarization, 324, 328–330 Ellipticity angle χ , 328 Emf sensor, 196 End-fire direction, 445 Engelbart, Douglas, ENIAC, Equipotential, 198 Euler’s identity, 32, 43 Evanescent wave, 385 Explorer I satellite, 458 F Faraday, Michael, 3, 5, 283 Faraday’s law, 282–284, 307 motional emf, 289, 307 transformer emf, 284, 307 Far-field (far-zone) region, 405 approximation, 408–409 power density, 409 False alarm probability, 467 Feeding coefficient Ai , 437 Felt, Dorr, Ferromagnetic, 260, 262–264 Fessenden, Reginald, Fiber, 7, 51, 365 Fiber optics, 365–367 INDEX Field lines, 158 Floppy disk, Fluorescence, 20 Fluorescent bulb, 20-23 Flux density, 158 Flux sensor, 293 FORTRAN, Franklin, Benjamin, 3, Free space, 13 velocity of light c, 16 magnetic permeability μ0 , 16 electric permittivity , 13 Frequency, 25 Frequency-division multiple access (FDMA), 460 Frequency modulation (FM), Frequency scanning, 445–449 Friis transmission formula, 427–429, 462 Fundamental forces electromagnetic, 12, 179 nuclear, 12 weak-interaction, 12 gravitational, 12 G Gamma rays, 30, 32 Gauss, Carl Friedrich, Gauss’s law, 5, 187–189 differential form, 187 of infinite line charge, 189 integral form, 187 Gaussian surface, 187 Gauss’s law for magnetism, 251, 252, 273 Geostationary orbit, 458 Gilbert, William, 3, Global Positioning System (GPS), 150–151 Grad (gradient) ∇T , 155 Gradient operator, 155–158 Gravitational force, 12 gravitational field ψ , 12 Grazing incidence, 375 Group velocity ug , 387 H Half-power angle, 413 Half-power beamwidth, 413 Half-wave dipole, 417–422 Henry, Joseph, 3, 5, 283 Hertz, Heinrich, 3, 5, 6, 25 497 Hertzian dipole, 406–409 High-power amplifier, 461 Hoff, Ted, Hole drift velocity uh , 198 Hole mobility μh , 198 Homogeneous material, 195 Homogeneous wave equation, 316 Horn antenna, 405 Hotmail, Hounsfield, Godfrey, 164 Humidity sensor, 219 I Illumination Ea (xa , ya ), 430 Image method, 223–224 Imaginary part Im , 32 Impedance, 49, 58, 66, 68, 75, 76, 93 Impedance matching, 101–110 lumped element matching, 102–108 matching points, 107 network, 102 shunt stub, 108 single-stub matching, 108–111 stub, 108 Impulse period Tp , 465 In-phase, 69 Incandescence, 20 Incandescent bulb, 20–23 Inclination angle ψ, 325 Incremental phase delay δ, 446 Index of refraction, 363 Inductance, 5, 265–271, 273 of a coaxial line, 267 mutual, 266, 270–271 self, 266, 267 solenoid, 265 Inductive sensors, 196, 268–269 eddy-current proximity sensor, 268 ferromagnetic core, 268 linear variable differential transformer (LVDT), 268 proximity detection, 268 Infrared rays, 30, 32 In-phase, 69 Input impedance Zin , 416 Integrated circuit (IC), Intercepted power Pint , 422 Internal (surface) impedance Zs , 341 International System of Units (SI), 11 Internet, 7, 498 Intrinsic impedance η, 318 Isotropic, 195 Isotropic antenna, 404, 413 Isotropic material, 195 J Java, Joule’s law, 201 K Kapany, Narinder, Kemeny, John, Kilby, Jack, Kirchhoff’s laws 49, current, 49, 301, 302 voltage, 49, 190 Kurtz, Thomas, L Laplace’s equation, 193 Laplacian operator, 167–169 Lasers, 368–369 Law of conservation of electric charge, 14 LED bulb, 20-23 LED lighting, 20–23 Left-hand circular (LHC) polarization, 326 Leibniz, Gottfried von, Lenz’s law, 285, 286–287 Leyden Jar, Lidars, 464 Light emitting diode (LED), 22 Lightning rod, Line charge, 180 Line charge density ρ , 180 Linear phase distribution, 444 Liquid crystal display (LCD), 2, 336–338 Liquid crystals, Logarithm, Lorentz force, 237, 273 Loss resistance Rloss , 416 Lossless media, 358, 376–380 Lossy media, 28 Loudspeaker, 257–258 Low-loss dielectric, 333 Luminous efficacy (LE), 23 INDEX M Macintosh, Maiman, Theodore, 368 Maglevs, 258–258 Magnetic dipole, 248 Magnetic energy Wm , 271–272 Magnetic field intensity H, 16, 236 Magnetic field phasor H, 319 Magnetic field, 244–250 between two parallel conductors, 250–251 in a solenoid, 265 inside a toroidal coil, 254–255 of a circular loop, 247–248, 273 of a linear conductor, 244–247 of a long wire, 253–254, 273 of a magnetic dipole, 248 of an infinite current sheet, 255 Magnetic flux , 260 Magnetic flux density B, 15, 236 Magnetic flux linkage , 267 Magnetic force Fm , 16, 236–241 Magnetic hysteresis, 262 Magnetic levitation, 258 Magnetic moment m, 261–262 Magnetic monopole, 252 Magnetic permeability μ, 16, 262 Magnetic potential A, 259–260 Magnetic properties of materials, 260–264 Magnetic sound recorder, Magnetic susceptibility χm , 261 Magnetic torque, 241–244 Magnetite, 3, 15 Magnetization vector M, Magnetized domains, 262 Magnetron tube, 83 Magnus, Marconi, Guglielmo, Mars Pathfinder, Maser, 368 Matched filter, 467 Matched line, 71, 85 Maximum detectable range Rmax , 468 Maxwell, James Clerk, 3, 5, 179 Maxwell’s equations, 251–255, 273, 282 Mauchley, John, Microprocessor, Microstrip line, 51 Microwave band, 32, 32 Mobility μe , 198 INDEX Modal dispersion, 366 Mode, 365, 386 Modem, Moment, 193, 202, 261–262 Monochromatic, 30, 368 Monopulse radar, 470–472, 473 amplitude-comparison monopulse, 470 phase-comparison monopulse, 470 Monostatic radar, 467 Morse, Samuel, 5, m , 284, 289, 307 Motional emf Vemf MS-DOS, Multiple-beam generation, 436 Multiple-PRF, 466 Multiplexer, 461 N n-type layer, 38 Nakama, Yoshiro, Nanocapacitor, 214 Napier, John, Negative electric charge, Neutrons, 13 Newton, Isaac, Noise power, 468, 473 Normal incidence, 356, 396 Normalized load impedance zL , 68 Normalized load reactance xL , 90 Normalized load resistance rL , 90 Notation, 11 Noyce, Robert, Nuclear force, 12 Null beamwidth, 414 O Oblique incidence, 362–364, 396 Oersted, Hans Christian, 4, 15, 282 Ohm, Georg Simon, Ohm’s law, 5, 195 Optical fiber, 7, 51, 365–367 Orbital magnetic moment, 261–262 P p–n junction, 38 p-type layer, 38 Pager, Parallel-plate transmission line, 51 499 Parallel polarization, 374–376 Paramagnetic, 260 Pascal, Blaise, Pattern multiplication principle, 438 Pattern solid angle p , 413 Perfect conductor, 195, 198 Perfect dielectric, 195, 198 Permittivity , 183, 203, 477 Perpendicular polarization, 370–374 Phase, 24 Phase constant β, 57, 331 Phase constant (wavenumber) k, 305 Phase lag, 26 Phase lead, 26 Phase-matching condition, 372 Phase velocity (propagation velocity) up , 318 Phasor representation, 11 Phasors 36–43 Photoelectric effect, 3, 5, 38 Photovoltaic (PV), 38 Photovoltaic effect, 38 Piezein, 196, 292 Piezoelectric transducer, 292 Piezoresistivity, 196–197 Planck, Max, Plane-wave propagation, 313–346 attenuation rate A, 346 circular polarization, 324, 326–328 left-hand circular (LHC), 326 right-hand circular (RHC), 326–328 complex permittivity c , 315 imaginary part , 316 real part , 316 elliptical polarization, 324, 328–330 auxiliary angle ψ0 , 329 axial ratio R, 329 ellipticity angle χ , 328 rotation angle γ , 328 electromagnetic power density, 343 linear polarization, 324, 325–326 lossy medium, 314, 331–339 attenuation constant α, 331 skin depth δs , 333 low-loss dielectric, 333 Pocket calculator, Poisson’s equation, 193 Polarization, 14, 324, 370 parallel polarization, 370, 374–376 perpendicular polarization, 370–374 500 transverse electric (TE) polarization, 370 transverse magnetic (TM) polarization, 370 unpolarized, 376 Polarization diversity, 462 Polarization field P, 202 Polarization state, 324 Position vector, 136 Potential energy We , 213, 217 Poulsen, Valdemar, Power density S(R, θ, φ), 409 Power transfer ratio Prec /Pt , 428 Poynting vector (power density) S, 343, 409 Pressure sensor, 219 Principle of linear superposition, 14 Principal planes, 412 Propagation constant γ , 316 Propagation velocity (phase velocity) up , 25 Pulse code modulation (PCM), Pulse length τ , 465 Pulse repetition frequency (PRF) fp , 465 Q Quality factor Q, 393 Quarter-wavelength transformer, 84 Quasi-conductor, 333 R Radar (radio detection and ranging), 7, 467–469 azimuth resolution x, 466 cross-section, 467 bistatic, 467 detection, 467–469 Doppler, 469–470 monopulse, 470–472, 473 monostatic, 467 multiple-PRF, 466 operation, 464 pulse, 465 range, 465 range resolution R, 466 unambiguous range Ru , 466 Radar cross-section, 467 Radar equation, 468 Radial distance, 16, 142, 464 Radial velocity ur , 464 Radiation efficiency ξ , 416 Radiation intensity, 409 Radiation pattern, 404 INDEX Radiation resistance Rrad , 416 Radio frequency identification (RFID) systems, 322–323 Radio telegraphy, Radio waves, 6, 32, Radius of geostationary orbit, 459, 473 Range R, 145 Range resolution R, 466 RC relation, 211, 226 Real part Re, 32 Received power, 463, 473 Receiving cross section, 422, See also Effective area Rectangular aperture, 432–434 Rectangular waveguide, 51 Reeves, H A., Reflection coefficient, 66–68 Reflectivity R, 377–380 Refraction angle, 363 Reinitzer, Friedrich, 336 Relaxation time constant τr , 302 Resistive sensor, 196–197 Resonant frequency f0 , 392, 393–394 Retarded potentials, 303–304 Right-hand circular (RHC) polarization, 326–328 Răontgen, Wilhelm, 3, Rotation angle , 328 S Satellite, 458–469 antennas, 463–464 elliptical orbit, 459 geostationary, 458 transponders, 460–462 Savart, F´elix, 4, 16 Scalar (dot) product, 136–137 Scalar quantity, 11 Scan angle δ, 446 Score satellite, 458 Seebeck, Thomas, 293 Seebeck potential Vs , 293 Semiconductor, 195, 198 Sensors, 196 capacitive, 196, 218–222 emf, 196, 292–293 inductive, 196, 268–269 resistive, 196–197 Shockley, William, Signal-to-noise ratio Sn , 428, 468, 473 Signal waveform, 465 Skin depth δs , 333 INDEX Smith chart, 52, 88–101 admittance Y , 96 admittance transformation, 96–100 angle of reflected coefficient, 91 characteristic admittance Y0 , 96 conductance G, 96 constant-SWR (-| |) circle, 93 matching points, 107 normalized admittance y, 96 normalized conductance g, 96 normalized susceptance b, 96 normalized load admittance yL , 96 normalized load impedance zL , 90 normalized load reactance xL , 90 normalized load resistance rL , 90 normalized wave impedance z(d), 92 parametric equations, 89–91 phase-shifted coefficient d , 92 standing-wave ratio (SWR), 93–95 susceptance B, 96 unit circle, 90 voltage maxima |V |max , 93–96 voltage minima |V |min , 93–96 wavelengths toward generator (WTG), 93 wavelengths toward load (WTL), 93 Smith, Jack, Smith, P.H., 88 Snell’s laws, 362–364 of reflection, 363, 372, 396 of refraction, 363, 372, 396 Solar cell, 38 Solenoid, 256 Solid angle d , 411 Spherical propagation factor (e−j kR/R), 407 Spherical wave, 314 Spin magnetic moment, 261 Spontaneous emission, 368 Sputnik I satellite, 458 Standing wave, 59, 70–75 first voltage maximum, 72 first voltage minimum, 72 in-phase, 69 interference, 71 minimum value, 71 maximum value, 71 pattern, 71, 83 phase-opposition, 71 properties, 85 voltage standing wave ratio [(VSWR) or (SWR)] S, 72 501 Static conditions, 179 Steradians (sr), 411 Stimulated emission, 368 Stokes’s theorem, 166–167 Strip line, 51 Sturgeon, William, 6, 7, 256 Sum channel, 471 Sun beam, 470 Supercapacitor, 214 Superconductor, 198 Superheterodyne radio receiver, Surface charge density ρs , 180 Surface current density Js , 244 Surface (internal) impedance Zs , 341 Surface resistance Rs , 341 SWR (standing-wave ratio), 93–95 Synchronizer–modulator, 464 System noise temperature Tsys , 428, 463 T Tapered aperture distribution, 433 Telegraph, Telephone, Television (TV), TEM (transverse electromagnetic), 51–52 Tensile stress, 292 Tesla, Nikola, 3, 5, 16 Thales of Miletus, 3, Thermocouple, 292, 293 Thomas de Colmar, Charles Xavier, Thompson, Joseph, 3, Threshold detection level Prmin , 468 Tomography, 164 Toroidal coil, 254–255 Torque, 241–244 Total internal reflection, 364 Townes, Charles, 368 tr , 283 Transformer emf Vemf Transient response, 111–115 Transistor, Transmission coefficients τ , 356 Transmission lines, 48–121 admittance Y , 96 air line, 55, 59 bounce diagram, 118 characteristic impedance Z0 , 58 characteristic parameters, 67 coaxial line, 51, 53, 61 502 complex propagation constant γ , 57 attenuation constant α, 57 phase constant β, 57 conductance G, 96 current maxima and minima, 72 definition, 49 dispersive transmission line, 52 distortionless line, 52 effective relative permittivity eff , 62 load impedance ZL , 66 guide wavelength λ, 59 input impedance Zin , 76, 93 input reactance Xin , 79 input resistance Rin , 79 lossless line, 65–75 lossless microstrip line, 60–65 lumped-element model, 52–53 matched load, 68 matching network, 102 microstrip line, 51, 60–65 nondispersive, 66 open-circuited line, 81 parallel-plate line, 51 parameters, 52–53 phase-shifted coefficient d , 92 power loss, 50 power flow, 86–88 quarter-wavelength transformer, 84 slotted line, 74 Smith chart, 52, 88–101 standing wave, 59, 70–75 Transmission lines (continued) standing wave pattern, 71, 83 SWR circle, 93 TEM (transverse electromagnetic) transmission lines, 51–52 transient response, 111–115 transmission line parameters, 52 capacitance C , 53 conductance G , 53 inductance L , 53 resistance R , 52 voltage maxima |V |max , 93–96 voltage minima |V |min , 93–96 voltage reflection coefficient , 66–68 voltage standing wave ratio [(VSWR) or (SWR)] S, 72 wave impedance Z(d), 75–78 Transmissivity ϒ(θ ), 377–380, 462 Transmitter/receiver (T/R) switch, 465 Transponder, 460–462 INDEX Transverse electric (TE), 370 Transverse electric (TE) polarization, 370 Transverse electromagnetic (TEM) wave, 318 Transverse magnetic (TM), 370 Transverse magnetic (TM) polarization, 370 Travelling waves, 18–32, See also Waves Triode tube, Two-wire line, 51 U Ultracapacitor, 214 Ultraviolet rays, 31, 32 Unambiguous range Ru , 466 Uniform field, 162–163 Uniform field distribution, 432 Units, 11 Unit vectors, 11, 134 Uplink, 460 V van Musschenbroek, Pieter, Vector analysis, 133–169 transformations between coordinate systems, 147–154 Vector magnetic potential, 259–260, 273 Vector Poisson’s equation, 259, 273 Vector (cross) product, 138–139 Vector quantities, 11 Velocity of light in free space c, 16 Video processor/display, 464 Visible light, 32, 32 Volta, Alessandro, 3, VSWR (voltage standing wave ratio) S, 72 See also SWR Volume charge density ρv , 180 Volume current density J, 244 W Walton, Charles, 322 Watson-Watt, Robert, Wave polarization, 324 circular, 324, 326–328 elliptically, 324, 328–330 electric field phasor E, 325 inclination angle ψ, 325 linear, 324, 325–326 INDEX Wave polarizer, 337 Wavefront, 314 Waveguides 380–383, 396 Wavelength, 25, 31 Wavenumber (phase constant) k, 305, 316 Waves, 18–32 Weak-interaction force, 12 White light, Wireless transmission, World Wide Web (WWW), 503 X X-rays, 3, 5, 30, 32 Z Zenith angle θ, 145, 407 Zuse, Konrad, Zworykin, Vladimir, ω-β diagram, 390 This page intentionally left blank F U N D A M E N T A L P HY S I C A L C O N S T A N T S CONSTANT SYMBOL VALUE speed of light in vacuum c 2.998 × 108 ≈ × 108 m/s gravitational constant G 6.67 × 10−11 N·m2 /kg2 Boltzmann’s constant K 1.38 × 10−23 J/K elementary charge e 1.60 × 10−19 C permittivity of free space ε0 permeability of free space μ0 4π electron mass me 9.11 × 10−31 kg proton mass mp 1.67 × 10−27 kg Planck’s constant h 6.63 × 10−34 J·s intrinsic impedance of free space η0 376.7 ≈ 120π 8.85 × 10−12 ≈ −9 36π × 10 × 10−7 H/m F/m F U N D A M E NT A L S I U N IT S DIMENSION UNIT SYMBOL Length meter m Mass kilogram kg Time second s Electric current ampere A Temperature kelvin K Amount of substance mole mol Luminous Intensity candela cd M U LT I P L E & S U B M U LT I P L E P R E F I X E S PREFIX SYMBOL MAGNITUDE PREFIX SYMBOL MAGNITUDE exa E 1018 milli m 10−3 peta P 1015 micro μ 10−6 tera T 1012 nano n 10−9 giga G 109 pico p 10−12 mega M 106 femto f 10−15 kilo k 103 atto a 10−18 Book Website: www.pearsonhighered.com/ulaby G R A D I E NT , D IV E R G E N C E , C U R L , & L A P L A C I A N O P E R AT O R S C A RT E S I A N ( R E CT A N G U L A R ) C O O R D I N AT E S (x, y, z) ∇V = xˆ ∂V ∂V ∂V + yˆ + zˆ ∂x ∂y ∂z ∇ ·A= ∂Ay ∂Az ∂Ax + + ∂x ∂y ∂z xˆ ∂ ∇ ×A= ∂x Ax ∇ 2V = yˆ ∂ ∂y Ay zˆ ∂ ∂Ay ∂Az = xˆ − ∂z ∂y ∂z Az + yˆ ∂Ax ∂Az − ∂z ∂x ∂Ay ∂Ax − ∂x ∂y + zˆ ∂ 2V ∂ 2V ∂ 2V + + 2 ∂x ∂y ∂z2 CY L I N D R I C A L C O O R D I N AT E S ( r , φ , z ) ∂V ∂V ∂V + φˆ + zˆ ∂r r ∂φ ∂z ∂Aφ ∂Az ∂ (rAr ) + + ∇ ·A= r ∂r r ∂φ ∂z ∇V = rˆ ˆ rˆ φr ∂ ∂ ∇ ×A= r ∂r ∂φ Ar rAφ ∇2V = ∂ r ∂r r ∂V ∂r zˆ ∂Aφ ∂Az ∂ = rˆ − r ∂φ ∂z ∂z Az + + φˆ ∂Az ∂Ar − ∂z ∂r + zˆ ∂ ∂Ar (rAφ ) − r ∂r ∂φ ∂ 2V ∂ 2V + r ∂φ ∂z2 S P H E R I C A L C O O R D I N AT E S ( R , θ , φ ) ∂V ∂V ∂V + θˆ + φˆ ∂R R ∂θ R sin θ ∂φ 1 ∂Aφ ∂ ∂ (R AR ) + (Aθ sin θ) + ∇ ·A= R ∂R R sin θ ∂θ R sin θ ∂φ ˆ ∇V = R ˆ R ∂ ∇ ×A= R sin θ ∂R AR ˆ =R ∇2V = R sin θ ∂ R ∂R R2 ˆ ˆ sin θ θR φR ∂ ∂ ∂θ ∂φ RAθ (R sin θ)Aφ ∂ ∂Aθ (Aφ sin θ) − ∂θ ∂φ ∂V ∂R + R sin θ ∂ ∂θ + θˆ sin θ ∂AR 1 ∂ ∂AR ∂ − (RAφ ) + φˆ (RAθ ) − R sin θ ∂φ ∂R R ∂R ∂θ ∂V ∂θ + R sin2 θ ∂ 2V ∂φ S O M E U S E F U L V E CT O R I D E NT IT I E S A · B = AB cos θAB Scalar (or dot) product ˆ A × B = nAB sin θAB Vector (or cross) product, nˆ normal to plane containing A and B A · (B × C) = B · (C × A) = C · (A × B) A × (B × C) = B(A · C) − C(A × B) ∇(U + V ) = ∇U + ∇V ∇(U V ) = U ∇V + V ∇U ∇ · (A + B) = ∇ · A + ∇ · B ∇ · (U A) = U ∇ · A + A · ∇U ∇ × (U A) = U ∇ × A + ∇U × A ∇ × (A + B) = ∇ × A + ∇ × B ∇ · (A × B) = B · (∇ × A) − A · (∇ × B) ∇ · (∇ × A) = ∇ × ∇V = ∇ · ∇V = ∇ V ∇ × ∇ × A = ∇(∇ · A) − ∇ A (∇ · A) d V = V A · ds S (∇ × A) · ds = S Divergence theorem (S encloses V ) A · dl C Stokes’s theorem (S bounded by C) ... Balanis of Arizona State University, Harold Mott of the University of Alabama, David Pozar of the University of Massachusetts, S N Prasad of Bradley University, Robert Bond of New Mexico Institute of. . .FUNDAMENTALS OF APPLIED ELECTROMAGNETICS Seventh Edition Fawwaz T Ulaby University of Michigan, Ann Arbor Umberto Ravaioli University of Illinois, Urbana–Champaign... Institute of Technology, Mark Robinson of the University of Colorado at Colorado Springs, and Raj Mittra of the University of Illinois I appreciate the dedicated efforts of the staff at Prentice Hall