Fundamentals of applied electromagnetics 6th

FUNDAMENTAL PHYSICAL CONSTANTS VALUE CONSTANT SYMBOL speed of light in vacuum c gravitational constant G 6.67 x 10-11 N·m2/kg2 Boltzmann's constant K 1.38 x 10-23 J/K elementary charge e 1.60 x 10-19 C permittivity of free space EO permeability of free space /-to 4n x 10-7 Him electron mass me 9.11 x 10-31 kg proton mass mp 1.67 x 10-27 kg Planck's constant h 6.63 x 10-34 J·s intrinsic impedance of free space r]() 376.7 ~ 120n MAXWELL'S 2.998 x 108 x 108 m/s ~ 8.85 x 10-12::::: 3JJr x 10-9 F/m n EQUATIONS V·D = a; Gauss's law Faraday's law VxE= aB at Gauss's law for magnetism Ampere's law MULTIPLE VxH=J+- & SUBMULTIPLE an at PREFIXES PREFIX SYMBOL MAGNITUDE PREFIX SYMBOL MAGNITUDE exa E 1018 milli m 10-3 peta P 1015 micro J1 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 W hen this book in draft form, each student was asked to write a brief statement understanding of what role electromagnetics describing his or her plays in science, technology, and society The following statement, submitted by Mr Schaldenbrand, was selected for inclusion here: Electromagnetics has done more than just help science Since we have such advanced communications, our understanding of other nations and nationalities has increased exponentially This understanding has led and will lead the governments of the world to work towards global peace The more knowledge we have about different cultures, the less foreign these cultures will seem A global kinship will result, and the by-product will be harmony Understanding is the first step, and communication is the means Electromagnetics holds the key to this communication, and therefore is an important subject for not only science, but also the sake of humanity Mike Schaldenbrand, 1994 The University of Michigan SOME USEFUL A B = A B cos e A B A x B VECTOR IDENTITIES Scalar (or dot) product = nAB sin8AB Vector (or cross) product it normal to plane containing A (B x C) = B (C x A) = C (A x B) A x (B x C) = B(A C) - C(A x B) V(U + V) VevV) + VV = VU + = UVV VVU v (A + B) = V A + V B V evA) = UV· A + A· V x (U A) = UV x A V x (A + B) = V x A VU + VU +V x A x B V· (A x B) = B· (V x A) - A (V x B) V (V x A) = VxVV=O V x V x A = V(V A) - V2A / (V A) V dv = fA ds Divergence theorem (s encloses V) / (V x A) ds = fA s c dl Stukes's theorem (S bounded by C) A and B FUNDAMENTALS OF APPLIED ELECTROMAGNETICS 6/e Fawwaz T Ulaby University of Michigan, Ann Arbor Eric Michielssen University of Michigan, Ann Arbor Urn bertoRavaioli University of Illinois, Urbana-Champaign PEARSON Upper Saddle River Boston Columbus San Francisco New York Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi· Mexico City· Sao Paulo· Sydney Hong Kong Seoul· Singapore· Taipei· Tokyo Preface to 6/e Building on the core content and style of its predecessor, this sixth edition (6/e) of Applied Electromagnetics introduces new features designed to help students develop a deeper understandi ng of electromagnetic concepts and appl ications Prominent among them is a set of 42 CD simulation modules that allow the user to interactively analyze and design transrnission 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 loss less 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 printing this new edition in full color, graphs and illustrations now more efficiently convey core concepts, and by expanding the scope of topics of the Technology Briefs, additional bridges between electromagnetic fundamentals and their counLless engineering and scientific applications are established In summary: New to this edition • A set of 42 CD-interactive simulation modules • New/updated Technology Briefs • Full-color figures and images • New/updated end-of-chapter problems • Updated bibliography 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 learning from it We hope you enjoy FAWWAZ T ULABY ERIC MICHIELSSEN UMBERTO RAVAIOLJ PREFACE Excerpts From the Preface to the Fifth Edition CONTENT 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 e1ectromagnetics 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 in Chapter I with reviews of complex numbers and phasor analysis 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 Suggested Syllabi Two-Semester Syllabus One-Semester credits (42 contact hours per semester) Chapter Sections Hours Syllabus credits (56 contact hours) Sections Hours Introduction: Waves and Phasors All All Transmission Lines All 12 2-1 to 2-8 and 2-11 Vector Analysis All All Electrostatics All 4-1 to 4-10 Magnetostatics All 5-1 to 5-5 and 5-7 to 5-8 Exams Total for first semester 42 Maxwell's Equations for Time-Varying Fields All 6-1 to 6-3, and 6-6 Plane-wave Propagation All 7-1 to 7-4, and 7-6 Wave Reflection and Transmission All 8-1 to 8-3, and 8-6 Radiation and Antennas All 10 9-1 to 9-6 Satellite Communication Systems and Radar Sensors All None 10 Exams I Total for second semester Extra Hours 40 - Total 56 PREFACE 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 ~oradiation 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 ofthe 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 MESSAGE TO THE STUDENT The interactive CD-ROM accompanying this book was developed with you, the student, in mind Take the time to use it in conjunction with the material in the textbook The multiplewindow feature of electronic displays makes it possible to design interactive modules with "help" buttons to guide the student through the solution of a problem when needed 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 CD-ROM is a useful resource for self-study Use it! ACKNOWLEDGMENTS My sincere gratitude goes to Roger DeRoo, Richard Carnes and Jim Ryan I am indebted to Roger DeRoo for his painstaking review of several drafts of the manuscript Richard Carnes is unquestionably the best technical typist I have ever worked with; his mastery of IbTEX,coupled with his attention to detail, made it possible to arrange the material in a clear and smooth format The artwork was done by Jim Ryan, who skillfully transformed my rough sketches into drawings that are both professional looking and esthetically pleasing I am also grateful to the following graduate students for reading through parts or all of the manuscript and for helping me with the solutions manual: Bryan Hauck, Yanni Kouskoulas, and Paul Siqueira Special thanks are due to the reviewers for their valuable comments and suggestions They include Constantine Balanis of Arizona State University, Harold Mott of the University of Alabama David Pozar ofthe 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 l also would like to thank Mr Ralph Pescatore for copy-editing the manuscript FAWWAZ T ULAllY 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 44 53 92 131 158 173 212 228 234 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 264 284 310 335 345 378 390 434 Contents Preface Photo Credits Chapter 1-1 1-2 1-3 1-4 Introduction: Waves and Phasors TB1 LED Lighting 44 13 1-7 Review of Phasors 49 1-7.1 50 17 1-1 1-1.2 17 EM in the Classical Era EM in the Modern Era 17 Dimensions, Units, and Notation 19 The Nature of Electromagnetism 1-3.1 The Gravitational Force: A Useful Analogue 1-3.2 Electric Fields 1-3.3 Magnetic Fields 1-3.4 Static and Dynamic Fields 26 Traveling Waves 1-4.1 1-5 Sinusoidal Waves in a Lossless Medium 1-4.2 Sinusoidal Waves in a Lossy Medium The Electromagnetic Spectrum 1-6 Review of Complex Numbers 1-7.2 15 Historical Timeline Solution Procedure TB2 Traveling Waves in the Phasor Domain Solar Cells 52 53 Chapter Transmission Lines 61 2-1 26 General Considerations 62 2-1.1 The Role of Wavelength 62 2-1.2 Propagation Modes 64 2-2 Lumped-Element 27 2-3 Transmission-Line 29 30 2-4 70 32 2-5 Wave Propagation on a Transmission Line The Lossless Microstrip Line 33 2-6 The Lossless Transmission Line: General Considerations 2-6.1 Voltage Reflection Coefficient 79 2-6.2 83 37 40 41 Model Equations Standing Waves 65 69 75 80 2-7 Wave Impedance of the Lossless Line 88 TB3 Microwave Ovens 92 APPENDIXD ANSWERS TO SELECTED PROBLEMS 7.22 H = -YO.16e-30x COS(27Cx 109t - 40x - 36.85°) (Nm) 7.27 Say = Y0.48 (W/m2) 7.29 (a) Say = zI25e-o.4z (W/m2) (b) A=-1.74z(dB) (e) z=23.03m 7.34 up = X 108 (m/s) (b) Pay = 7.05 X 9.5 8.5 = -0.67; T = 0.33 (b) S = (e) S~v = 0.52 (W/m~); S~y = 0.24 (W/m2); S~v = 0.28 (W 1m ) (a) Ei = 5Cx + jy)e-j4rrz/3 (VIm) r = -0.2; (b) (e) Ef G = 0.44 = -3.5 dB ( e) 10 = 67.6 A; PI = 269 W 9.9 D 9.11 = -(x + jy)ej4rrz/3 (VIm); EI = 4(x + jY)e-1.26xI0-2ze-j2rrz (VIm); EI = 5(x + jy)[e-j4rrz/3 - 0.2ej4rrz(3) (Vim) 8.9 £f2 = J£fl£q; (VIm); lmax = 1.5 m d = c/[4f(£fl£f3)ij4) 8.11 Zin::::: (lOa - j 127) Q; reflected fraction of incident power = 0.24 8.13 f = 75 MHz 8.15 pi = 1.01 x 10-4 W/m2 8.17 emin = 20.40 8.19 SI -r-r- SI fp = 59.88 (Mb/s) /:) :6 1287C R k2 (fJO Rrad R = 6.4 x 10-3; T = 0.9936 (b) pi = 85 mW; pr = 0.55 mW; pi = 84.45 mW e (W/m2) sin2 (a) ~ = 62% (e) = dB 10 = 95 A; P; = 129.2 W 9.20 PI 259 (mW) 9.22 PI = 75 (J-tW) = 9.26 f3nuJl 5.73° 9.28 (a) f3xz = 0.75°; 9.30 (a) f3e = 1.8°; f3\'z = 1.50 x 104 = 45.6 dB D=3.61 fly = f3aR f3a = 0.18° = 0.96 (a) FaCe) = 4cos2 m [i (4cose + I)] FaCe)=5+4cos(27Ccose) FaCe) = 4cos2(1 cos e (d) Fa(e)=5+4cos(7Ccose+t) (e) Fa(e) = - 4sin(1 cos e) t) (e) 9.34 df): = 1.414 8.43 570 Q (empty); 290 Q (filled) e~o= 57 r = -R- = 2071'2(1/).,)2(Q) (b) (a) 8.47 (a) Q = 8367; (b) Q ~ Io1kr/O (e-JkR) ~~ e, ¢) = OEII = OJ ~ (b) G = 0.93 = -0.3 (b) 8.39 a = 3.33 em; b = em 8.45 9.18 9.32 8.31 et = 18.44° 8.35 (d) (b) 8.24 d = 68.42 em 8.26 ~ (a) E(R, (e) D = 1.5 = 0.85 8.22 d = 15 ern = 1.63 = 2.1 dB /0 = 1.48 A; PI = 80.4 W G (b) ~:~~:) = % of transmitted power = 96% lEI Imax= 85.5 dB (a) ~ = 99.3% (e) 9.14 r = 0.8 = 36.61 (b) (d) % of reflected power = 4%; 8.7 (a) ~ = 29.7% (b) 9.7 Smax= x 10-5 (W/m2) r (a) (J-tW/m2) 9.3 (a) Direction of maximum radiation is a circular cone 1200 wide, centered around the -l-z-axis (b) D =4 = 6dB (e) Qp=7C(sr)=3.14(sr) (d) f3 = 120° 10-4 (W) Chapter 8.1 Chapter 9.1 Smax = 7.6 7.25 (Rae! Rdc) = 143.55 7.31 499 9850 - sin [(157C/4)cose) 9.36 Fan(e) - 25sin2[(37C/4)cose)' 9.39 = -2.72 (rad) = -155.9° f3 - 135 - sme 500 APPENDIX D Chapter 10 10.1 T = 82.97 minutes 10.3 133 channels 10.5 (fp)max = 300 kHz 10.7 Rmax = 4.84 km ANSWERS TO SELECTED PROBLEMS The following list of books, arranged alphabetically by the last name of the first author, provides references for further reading Ramo, S., J.R Whinnery, and T Van Duzer, Fields and Waves in Communication Electronics, 3rd ed., John Wtley & Sons, New York, 1994 Electromagnetics Rao, N.N., Elements of Engineering Electromagnetics, Prentice Hall, Upper Saddle River, New Jersey, 2004 Balanis, c.A., Advanced Engineering Electromagnetics, Wiley & Sons, New York, 1989 John Shen, L'C, and J.A Kong, Applied Electromagnetism, 3rd ed., PWS Engineering, Boston, Mass., 1995 Cheng, D.K., Fundamentals of Engineering Electromagnetics, Addison Wesley, Reading, Reading, MA, 1993 Antennas and Radiowave Propagation Hayt, W.H., Jr and J.A Buck, Engineering Electromagnetics, 7th ed., McGraw-Hill, New York, 2005 Balanis, C.A., Antenna Theory: Analysis and Design, John Wiley & Sons, New York, 2005 Iskander, M.F., Electromagnetic Fields & Waves, Prentice Hall, Upper Saddle River, NJ, 2000 Ishimaru, A., Electromagnetic Wave Propagation, Radiation, and Scattering, Prentice Hall, Upper Saddle River, New Jersey, 1991 King, R.W.P and S Prasad, Fundamental Electromagnetic Theory and Applications, Prentice Hall, Englewood Cliffs, New Jersey, 1986 Stutzman, W.L and G.A Thiele, Antenna Theory and Design, John Wiley & Sons, New York, 1997 502 Optical Engineering Microwave Engineering Bohren, e.F and D.R Huffman, Absorption and Scattering of Light by Small Particles, John Wiley & Sons, New York, 1998 Freeman, J.e., Fundamentals of Microwave Lines, John Wiley & Sons, New York, 1996 Born, M and E Wolf, Principles of Optics, 7th ed., Pergamon Press, New York, 1999 Hecht, E., Optics, Addison-Wesley, Reading, Mass., 2001 Smith, W.J., Modern Optical Engineering, SPIE Press, 2007 Walker, B.H., Optical Engineering Fundamentals, SPIE Press, 2009 Pozar, D.M., Microwave Reading, Mass., 2004 Engineering, Richharia, M., Satellite Communication Hill, New York, 1999 Transmission Addison-Wesley, Systems, McGraw- Scott, A.W., Understanding Microwaves, John Wiley & Sons, New York, 2005 Skolnik, M.I., Introduction to Radar Systems, 3rded., McGrawHill, New York, 2002 Stimson, G.W., Introduction to Airborne Radar, Aircraft Company, EI Segundo, California, 2001 Hughes 3-dB beamwidth, 425 linear phase, 457 pattern multiplication principle, 449 scanning, 456-460 uniform phase, 453-454 broadside direction, 421 directivity D, 425, 445 effective area, 445 far-field (far-zone) region, 417,420-421 gain, 427-429 half-wave dipole, 429 433 inputnnpedance, 416 isotropic, 416, 424 large aperture, 440-446 multiplication principle, normalized radiation intensity, 421 pattern solid angle Up, 424 patterns, 416, 423 beam dimensions, 424 beamwidth {3,424-25 directivity D, 425-427 polarization, 416 receiving, 438-439 reciprocal,416 types, 475 arrays, 475 dipoles, 475 helices, 475 horns, 475 parabolic dishes 475 A Abacus, 24 Ablation, 131 ac motor, 17,21 ac resistance R, 354 Acceptance angle (Ja, 376 Adding machine, 24 Alternating current (ac), 21 AM radio, 22 Ampere, Andre-Marie, 20 Ampere'S law, 268-271, 283 Amplitude-comparison monopulse radar, 481 Amplitude modulation (AM), 22 Analog computer, 24 Angle error signal, 484 Angle of incidence OJ,374 Angle of reflection (Jr, 374 Angle of transmission 8t, 374 Angular frequency co, 35, 71 Angular velocity ro, 35 Antennas, 416-461, 474-475 aperture, 441 rectangular, 443-445 scalar formulation 441 vector formulation 441 arrays, 446-453 503 INDEX 504 Antenna radiation pattern, 416 Arithmometer, 24 Armstrong, Edwin, 22, 23 ARPANET, 23 Array factor Fa ((n, 449 array amplitude distribution, 449 array phase distribution, 449 Atmospheric transmissivity Y, 473 Attenuation constant O!, 70, 348 Average power SaY, 355 Average power density SaY, 355 Auxiliary angle 1/10 342 Axial ratio R, 342 Azimuth angle ¢i 419 Azimuth-difference channel 483 Azimuth plane (cp-plane), 423 Azimuth resolution Llx, 478 B bac-cab rule, 150 Backus John, 24 Band gap energy, 54 Bar-code readers 390-391 Bardcen, John, 23 Base vector, 145 BASIC, 24 Beam dimensions, 424 Beamwidth /3, 424 425, 444-445 Becquerel, Alexandre-Edmond, 53 Bell Alexander 22 Berliner Emil 22 Bemers-Lee, Tim, 25 Bhatia Sabeer, 25 Bioelectrics 132 Biot, Jean-Baptiste, 20,29 Biot-Savart law, 20, 29 257-263, 283 current distributions, 258-261 surface current density Js,258 volume current density J, 258 volume distributions, 258-261 Bistatic radar, 479 Brattain, Walter, 23 Braun, Karl, 22 Brewster (polarizing) angle 385-386 407 Broadside array, 453 Broadside direction, 421 Bush, Vannevar, 24 c Capacitance C, 224-226 capacitor, 224 of a coaxial line, 226 of a parallel-plate capacitor, 225-226 Capacitive sensors, 212, 234-238 Capacitor, 20 as batteries 228-230 electrochemical double-layer (EDLC), 228 Cardullo Mario 335 Carrier frequency f 476 Cartesian coordinate system r , y z 151 152 CAT (CT) scan, 173 Cathode ray tube (CRT), 22 Cavity resonators, 404-406, 407 Cell phone, 23 Charge continuity equation, 316 321 Charge distribution, 193-194, 197 surface distribution, 197 Circulation 176 Circulator 472 Coaxial line, 64 Complex conjugate, 43 Complex feeding coefficient Ai 448 Complex numbers, 41-49 complex conjugate, 43 Euler's identity, 43, 56 polar form, 43 properties, 43, 48 rectangular fOlID 41 rectangular-polar relations 43 56 Compressive stress 310 Conductance G, 109 Conductivity (T 24 31 209 492 Conductors, 207-211 conduction current 207 conduction current density J, 208 conductivity, 209 492 equipotential medium, 209 resistance 209-211 semiconductors, 208, 209 Conservative (irrotational) field 178,203 Constitutive parameters, 207 Convection current, 194 Conversion efficiency, 53 Coordinate systems, 151-160 Cartesian x, y, z 151, 152 cylindrical r, cp, Z, 152, 153-155 spherical R, g,