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This book introduces the fundamental principles of antenna theory and explains how to apply them to the analysis, design, andmeasurements of antennas. Due to the variety of methods of analysis and design, and the different antenna structures available, theapplications covered in this book are made to some of the most basic and practical antenna configurations. Among these antennaconfigurations are linear dipoles; loops; arrays; broadband antennas; aperture antennas; horns; microstrip antennas; and reflectorantennas. The text contains sufficient mathematical detail to enable undergraduate and beginning graduate students in electricalengineering and physics to follow the flow of analysis and design. Readers should have a basic knowledge of undergraduateelectromagnetic theory, including Maxwell’s equations and the wave equation, introductory physics, and differential and integralcalculus
www.Technicalbookspdf.com ANTENNA THEORY www.Technicalbookspdf.com www.Technicalbookspdf.com ANTENNA THEORY ANALYSIS AND DESIGN FOURTH EDITION Constantine A Balanis www.Technicalbookspdf.com Cover Image: Courtesy NASA/JPL-Caltech Copyright © 2016 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic formats For more information about Wiley products, visit our web site at www.wiley.com Library of Congress Cataloging-in-Publication Data: Balanis, Constantine A., 1938– Modern antenna handbook / Constantine A Balanis.—4th ed p cm Includes index ISBN 978-1-118-642060-1 (cloth) Antennas (Electronics) I Title TK7871.6.B354 2016 621.382′ 4—dc22 2016050162 Printed in the United States of America 10 www.Technicalbookspdf.com To the memory of my parents, uncle and aunt Στη μν´ημη των γoν´εων, τoυ θε´ιoυ και τη𝜍 θε´ια𝜍 μoυ www.Technicalbookspdf.com www.Technicalbookspdf.com Contents Preface xiii About the Companion Website xix Antennas 1.1 1.2 1.3 1.4 1.5 1.6 Introduction Types of Antennas Radiation Mechanism Current Distribution on a Thin Wire Antenna Historical Advancement Multimedia References Fundamental Parameters and Figures-of-Merit of Antennas 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 Introduction Radiation Pattern Radiation Power Density Radiation Intensity Beamwidth Directivity Numerical Techniques Antenna Efficiency Gain, Realized Gain Beam Efficiency Bandwidth Polarization Input Impedance Antenna Radiation Efficiency Antenna Vector Effective Length and Equivalent Areas Maximum Directivity and Maximum Effective Area Friis Transmission Equation and Radar Range Equation Antenna Temperature Multimedia References Problems 15 18 21 22 25 25 25 35 37 40 41 55 60 61 65 65 66 75 79 81 86 88 96 100 103 105 vii www.Technicalbookspdf.com viii CONTENTS Radiation Integrals and Auxiliary Potential Functions 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Introduction The Vector Potential A for an Electric Current Source J The Vector Potential F for A Magnetic Current Source M Electric and Magnetic Fields for Electric (J) and Magnetic (M) Current Sources Solution of the Inhomogeneous Vector Potential Wave Equation Far-Field Radiation Duality Theorem Reciprocity and Reaction Theorems References Problems Linear Wire Antennas Introduction Infinitesimal Dipole Small Dipole Region Separation Finite Length Dipole Half-Wavelength Dipole Linear Elements Near or On Infinite Perfect Electric Conductors (PEC), Perfect Magnetic Conductors (PMC) and Electromagnetic Band-Gap (EBG) Surfaces 4.8 Ground Effects 4.9 Computer Codes 4.10 Multimedia References Problems Loop Antennas 131 132 136 137 138 143 143 145 145 155 158 164 176 179 203 216 216 218 220 235 Introduction Small Circular Loop Circular Loop of Constant Current Circular Loop with Nonuniform Current Ground and Earth Curvature Effects for Circular Loops Polygonal Loop Antennas Ferrite Loop Mobile Communication Systems Applications Multimedia References Problems Arrays: Linear, Planar, and Circular 6.1 6.2 6.3 6.4 6.5 6.6 6.7 127 128 130 145 4.1 4.2 4.3 4.4 4.5 4.6 4.7 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 127 Introduction Two-Element Array N-Element Linear Array: Uniform Amplitude and Spacing N-Element Linear Array: Directivity Design Procedure N-Element Linear Array: Three-Dimensional Characteristics Rectangular-to-Polar Graphical Solution www.Technicalbookspdf.com 235 236 250 259 268 269 270 272 272 275 277 285 285 286 293 312 318 319 322 APPENDIX VIII 1059 b If 4AB < C2 , then A′ B′ < 0, and A′ and B′ have different signs Summarizing the results we can write that If 4AB > C2 and A > 0, then A′ and B′ are both positive If 4AB > C2 and A < 0, then A′ and B′ are both negative If 4AB < C2 , then A′ and B′ have different signs Using the preceding deductions, we can write the sign information of (VIII-18a) as ⎧ +1 if 4AB > C and A > ⎪ 𝛿 = ⎨ −1 if 4AB > C and A < ⎪ −j if 4AB < C2 ⎩ (VIII-21) in the evaluation of the integral in +∞ I(k) ≃ F(xs , ys )ejkf (xs ,ys ) jkf (xs ,ys ) I(k) ≃ F(xs , ys )e +∞ ∫−∞ ∫−∞ j2𝜋𝛿 ejk(A𝜉 √ k |4AB − C2 | +B𝜂 +C𝜉𝜂) d𝜉 d𝜂 (VIII-22) APPENDIX IX Television, Radio, Telephone, and Radar Frequency Spectrums IX.1 TELEVISION IX.1.1 Very High Frequency (VHF) Channels Channel number Frequency (MHz) 54 ↑ 60 ↑ 66 ↑ 72 76 ↑ 82 ↑ 88 10 11 12 13 174 ↑ 180 ↑ 186 ↑ 192 ↑ 198 ↑ 204 ↑ 210 ↑ 216 IX.1.2 Ultra High Frequency (UHF) Channels∗ Channel number Frequency (MHz) 14 15 16 17 18 19 20 82 83 470 ↑ 476 ↑ 482 ↑ 488 ↑ 494 ↑ 500 ↑ 506 ↑ 512 … 878 ↑ 884 ↑ 890 For both VHF and UHF channels, each channel has a 6-MHz bandwidth For each channel, the carrier frequency for the video part is equal to the lower frequency of the bandwidth plus 1.25 MHz while the carrier frequency for the audio part is equal to the upper frequency of the bandwidth minus 0.25 MHz Examples: Channel (VHF): f0 (video) = 54 + 1.25 = 55.25 MHz f0 (audio) = 60 − 0.25 = 59.75 MHz Channel 14 (UHF): f0 (video) = 470 + 1.25 = 471.25 MHz f0 (audio) = 476 − 0.25 = 475.75 MHz *In top ten urban areas in the United States, land mobile is allowed in the first seven UHF TV channels (470–512 MHz) Antenna Theory: Analysis and Design, Fourth Edition Constantine A Balanis © 2016 John Wiley & Sons, Inc Published 2016 by John Wiley & Sons, Inc Companion Website: www.wiley.com/go/antennatheory4e 1061 1062 IX.2 APPENDIX IX RADIO IX.2.1 Amplitude Modulation (AM) Radio Number of channels: 107 (each with 10-kHz separation) Frequency range: 535–1605 kHz IX.2.2 Frequency Modulation (FM) Radio Number of channels: 100 (each with 200-kHz separation) Frequency range: 88–108 MHz IX.3 AMATEUR BANDS Band Frequency (MHz) Band Frequency (MHz) 160-m 80-m 40-m 20-m 15-m 10-m 6-m 1.8–2.0 3.5–4.0 7.0–7.3 14.0–14.35 21.0–21.45 28.0–29.7 50.0–54.0 2-m — — — — — — 144.0–148.0 220–225 420–450 1215–1300 2300–2450 3300–3500 5650–5925 IX.4 CELLULAR TELEPHONE IX.4.1 Land Mobile Systems Uplink: MS to BS (mobile station to base station) Downlink: BS to MS (base station to mobile station) System Uplink (MHz)** Downlink (MHz)* CDMA IS-95 824–849 869–894 North America, Korea, China GSM 890–915 935–960 North America, Europe, China, Japan Extended-GSM 880–915 925–960 North America, Europe, China, Japan DCS 1800 1710–1785 1805–1880 Europe US PCS 1900 1850–1910 1930–1990 North America WCDMA 1920–1980 2110–2170 Everywhere CDMA2000 All existing CDMA system frequencies Major Covered Areas Everywhere *Downlink is the channel from the base station to the mobile unit, which is also called forward-link **Uplink is the channel from the mobile unit to the base station, which is also called reverse-link IX.4.2 Cordless Telephone United States of America: 46–49 MHz Digital European Cordless Telecommunications (DECT): 1.880–1.990 GHz APPENDIX IX IX.5 RADAR IEEE BAND DESIGNATIONS HF (High Frequency): VHF (Very High Frequency): UHF (Ultra High Frequency): L-band: S-band: C-band: X-band: Ku -band: K-band: Ka -band: Millimeter wave band: 3–30 30–300 300–1,000 1–2 2–4 4–8 8–12 12–18 18–27 27–40 40–300 MHz MHz MHz GHz GHz GHz GHz GHz GHz GHz GHz 1063 Index adaptive beamforming, 950–953, 951f, 952f, 969–971, 970f, 971f, 972f amplitude pattern shape, 32–33, 33f amplitude pattern shape, radiation pattern (antenna pattern), 32–33, 33f analysis methods, 20–21 antena, radiation mechanism dipole, 13, 14f E-plane sectoral horn, unbounded medium (te horn), 15 infinite line source, unbounded medium (tm open), 15 radiation problems, computer animated-visualization, 13–15 single wire, 7–10, 8f, 10f two-wires, 10–11, 11f, 12f antenna current distribution, thin wire antenna, 15–18, 16f, 17f, 18f defined, overview, as transition device, 2f transmitting mode, transmission-line Thevenin equivalent, 1, 2f antenna beamforming adaptive beamforming, 950–953, 951f, 952f direction-of-arrival (DOA) algorithms, 947–950, 947f, 950f optimal beamforming techniques, least mean square (LMS) algorithm, 956–959, 957f, 958f, 959f optimal beamforming techniques, minimum mean square error (MMSE) criterion, 955–956 antenna efficiency, 60–61, 61f antenna elements, 19–20 antenna equivalent areas, 83–86 antenna, historical advancement, 18 analysis methods, 20–21 antenna elements, 19–20 future challenges, 21 antenna measurements current measurements, 1014 directivity measurements, 1010–1012 impedance measurements, 1012–1014 overview, 981–982, 982f polarization measurements, 1014–1019, 1015f, 1016f, 1017f, 1018f radiation efficiency, 1012 antenna measurements, antenna ranges, 982 compact ranges, 986–987, 986f compact ranges, CATR designs, 989–992, 991f, 992f compact ranges, CATR performance, 987–989, 988f, 989f, 990f free-space ranges, anechoic chambers, 984–986 985f free-space ranges, elevated ranges, 983–984, 984f free-space ranges, slant ranges, 984, 984f near-field/far-field methods, measurements and computations, 997–1000, 999f near-field/far-field methods, modal-expansion method for planar systems, 996–997 reflection ranges, 983, 983f antenna measurements, gain measurements, 1003, 1005–1006 realized-gain measurements, extrapolation method, 1008 realized-gain measurements, gain-transfer (gain-comparison), measurements, 1009–1010 realized-gain measurements, ground-reflection range method, 1008–1009 realized-gain measurements, three-antenna method, 1007–1008 realized-gain measurements, two-antenna method, 1006, 1007f antenna measurements, near-field/far-field methods, 992–996, 993f, 994f, 995f Antenna Theory: Analysis and Design, Fourth Edition Constantine A Balanis © 2016 John Wiley & Sons, Inc Published 2016 by John Wiley & Sons, Inc Companion Website: www.wiley.com/go/antennatheory4e 1065 1066 INDEX antenna measurements, radiation patterns, 1000–1001, 1000f amplitude pattern, 1001f, 1003, 1004f, 1005f instrumentation, 1001–1003, 1001f, 1002f phase measurements, 1003, 1005f antenna measurements, scale model measurements, 1019, 1019t echo area (RCS) measurements, simulations and comparisons, 1021–1024, 1022f, 1023f gain (amplitude) measurements, simulations and comparisons, 1020–1021, 1020f antenna miniaturization, 619 folding, 624–626, 624f, 626f metamaterials, 626–627 monopole antenna, impedance loading, 620–622, 620f monopole antenna, materials loading, 622–624, 622f patch antennas, 626 antenna radar cross section (RCS), 92–96, 92t, 96f, 97f antenna radiation efficiency, 80 antenna synthesis, continuous sources continuous aperture sources, 417 continuous aperture sources, circular aperture, 418–419, 419t continuous aperture sources, rectangular aperture, 418 discretization of continuous sources, 387, 387f Fourier transform method, linear array, 395–398, 398f Fourier transform method, line-source, 392–394, 395f line-source, 386–387, 387f line-source phase distributions, 416–417, 417f overview, 385 Schelkunoff polynomial method, 387–391, 389f, 390f, 391f, 392f Taylor line-source (one-parameter), 408–414, 411f, 413f, 414f Taylor line-source (Tschebyscheff-error), 404–405 Taylor line-source (Tschebyscheff-error), design procedure, 406–407, 408f triangular, cosine, cosine-squared amplitude distributions, 415–416, 415t Woodward-Lawson method, 398 Woodward-Lawson method, linear array, 403–404 Woodward-Lawson method, line-source, 399–402, 402f antenna temperature, 96, 98–1, 99f antenna types aperture antennas, 3, 4f, 6f array antennas, 5, 6f lens antennas, 6–7, 8f microstrip antennas, 5, 5f, 6f reflector antennas, 6, 7f wire antennas, 3, 4f, 6f antenna vector effective length, equivalent areas antenna equivalent areas, 83–86 maximum directivity, maximum effective area, 86–88, 86f vector effective length, 81–83, 81f aperture antennas, 3, 4f, 6f Babinet’s principle, 680–684 , 680f, 681f, 682f, 683f directivity, 648 field equivalence principle, Huygen’s principle, 639–645, 640f, 641f, 645f ground plane edge effects, geometrical theory of diffraction, 702–703, 703f, 704f, 705–707, 705f, 706f radiation equations, 645–647 aperture antennas, circular apertures, 667–669, 668f beam efficiency, 675, 677f TE11 -mode distribution on infinite ground plane, 671, 672–673t, 674, 674f, 676f uniform distribution on infinite ground plane, 669–671, 671f aperture antennas, design considerations, 676 circular aperture, 678–679, 679t rectangular aperture, 677 aperture antennas, Fourier transforms aperture admittance, 695–702, 698f, 700f asymptotic evaluation of radiated field, 689–694 dielectiric-covered apertures, 694–695, 696f Fourier transforms-spectral domain, 685 radiated fields, 685–689, 685f aperture antennas, rectangular apertures, 648–650, 649f beam efficiency, 666–667, 666f, 677f TE10 -mode distribution on infinite ground plane, 663, 663f, 664f, 665f uniform distribution in space, 658–659t, 661–663, 662f uniform distribution on infinite ground plane, 650–652, 650f, 653f, 654–657, 654f, 658–659t, 660 array antennas, 5, 6f arrays, array design, 285 See also mutual coupling in arrays design considerations, 361–362 design procedure, 318–319 linear array design, 967–968, 968f planar array design, 968–969 arrays, circular array array factor, 363–365, 363f, 367366f arrays, feed networks microstrip and mobile communications antennas, 832–837, 835f, 836f, 837f, 838f INDEX arrays, N-element linear array: directivity, 312 broadside, end-fire arrays, 313–314, 318t Hansen-Woodyard end-fire array, 317–318 ordinary end-fire array, 315–317, 318t arrays, N-element linear array: three-dimensional characteristics N-elements along X- or Y-axis, 320–322, 320f, 321f N-elements along Z-axis, 319–320 arrays, N-element linear array: uniform amplitude/spacing, 293–297, 294f broadside array, 297–299, 298f, 299f Hansen-Woodyard end-fire array, 304–312, 309f, 311f, 312t, 313t ordinary end-fire array, 299–300, 300t, 301f, 303t 302f, 304t phased (scanning) array, 302–304, 303f, 305f, 306f arrays, N-element linear array: uniform spacing, nonuniform amplitude, 323–324 array factor, 325–326, 325f binomial array, design procedure, 327–329, 328f binomial array, excitation coeffecients, 326–327 Dolph-Tschebyscheff array broadside, array design, 331–338, 332f, 334f, 336f, 336t, 339f Dolph-Tschebyscheff array broadside, array factor, 330–331 Dolph-Tschebyscheff array broadside, beamwidth and directivity, 338, 340–341, 340f Dolph-Tschebyscheff array broadside, design, 341–343, 343f Tschebyscheff design, scanning, 344–345, 345f arrays, planar array, 348f array factor, 348–354, 350f, 353f, 354f, 355f, 356f beamwidth, 354, 357–359, 358f directivity, 359–350 arrays, rectangular-to-polar graphical solution, 322–333, 324f arrays, superconductivity, 345 designs with constraints, 346–348 efficiency, directivity, 346 arrays, two-element array, 286–293, 287f, 291f, 292f, 293f Babinets principle, 680–684 baluns, transformers, 521–523, 522f, 523f bandwidth, 65–66 beam efficiency, 65 beamforming, diversity combining, Raleigh-fading, trellis coded modulation, 972–975, 972t, 973f, 974f beamwidth, 40 broadband antennas See also traveling wave antennas electric-magnetic dipole, 559, 560f 1067 helical antenna, 549–550, 550f, 551f Yagi-Uda array of linear elements, 559–561, 560f broadband dipoles, matching techniques See also cylindrical dipole; folded dipole; matching techniques; triangular sheet, bow-tie, and wire simulation of biconical antenna; Vivaldi antenna biconical antenna, input impedance for unipole, 491–492 biconical antenna, input impedance for finite cones, 491 biconical antenna, input impedance for infinite cones, 490–491, 492f biconical antenna, radiated fields, 487, 488f, 489–490 overview, 485–487, 486f, 487f Cassegrain reflectors, 915–916, 917f Cassegrain and Gregorian forms, 919–920, 919f classical form, 917–919, 918f cellular radio systems evolution omnidirectional systems, 933, 933f omnidirectional systems, cell splitting, 934, 934f omnidirectional systems, sectorized systems, 934–936, 935f smart-antenna systems, adaptive array systems, 937–938, 937f, 938f smart-antenna systems, spatial division multiple access (SDMA), 938–939, 939f smart-antenna systems, switch-beam systems, 936–937, 936f, 937f circular loop of constant current, loop antennas power density, radiation intensity, radiation resistance, directivity, 252–253, 253f, 254f, 255–259, 257f, 258f radiated fields, 250–252, 251f circular loop of nonuniform current, loop antennas, 259–260, 260f, 261f, 262–266, 262f, 263f, 264f, 265f arrays, 266 design procedure, 267–268 circular patch, microstrip and mobile communications antennas, 815, 815f conductance, directivity, 821–822, 822f, 823f design, 818–819, 819f electric and magnetic fields - TMzmnp , 816–817 equivalent current densities, fields related, 819–821, 820f resonant frequencies, 817–818 resonant input resistance, 822–823 coordinate system for antenna analysis, 25–26, 26f corner reflector, 876–878, 876f, 877f, 878f, 880–884, 881f, 882f, 883f cross-polarization, reflector antennas (front-fed parabolic), 896–897, 896f, 897f 1068 INDEX current distribution method, reflector antennas (front-fed parabolic), 897–901, 898f, 900f current distribution, thin wire antenna, 15–18, 16f, 17f, 18f cylindrical dipole See also folded dipole bandwidth, 501 equivalent radii, 504–505, 506t input impedance, 501–502, 502f radiation patterns, 503–504, 505f resonance, ground plane simulation, 503, 503t, 504f dielectric resonator antennas (DRAs), 847–848 analysis and design methods, 849–850 basic geometries, 848, 848f, 849f cavity model resonant frequencies (TE, TM modes), 850–852 hybrid modes: resonant frequencies, quality factors, 852–853, 853f, 854t radiated fields, 855–859, 856f, 858f 857f dipole array design, 608–609, 609f computer program, 613–614 design equations, 609–612, 611f design procedure, 611–613, 613f dipole, See also linear wire antennas, dipole array, 13, 14f, 602–605, 603f, 606f, 607–608, 607f, 607t, 608f directional patterns, 47–48, 47f, 49f, 50–51, 51t direction-of-arrival (DOA) algorithms, 947–950, 947f, 950f directivity, 41–46, 44f, 45f aperture efficiency, 898f, 900f, 901–909, 903f, 906f, 908f, 909t, 910f, 911f directional patterns, 47–48, 47f, 49f, 50–51, 51t omnidirectional patterns, 51–52, 52f, 53f, 54 discone, conical skirt model, 512–513, 512f, 513t duality theorem, 138–139, 139t electric and magnetic fields, electric (J) and magnetic (M) current sources, 131–132 electrically small antennas, fundamental limits, 614–619, 615f, 617f, 618f, 618t electric-magnetic dipole, 559, 560f electrostatic charge distribution, 432 bent wire, 437–439, 438f finite straight wire, 433–437, 437f 433f E-plane sectoral horn, 720f, 721f aperture fields, 719–722 directivity, 728–733, 730f, 731f, 732f E-plane sectoral horn, unbounded medium (te horn), 15 equiangular spiral antennas, 593–594 conical spiral, 598, 599f planar spiral, 593–598, 596f, 597f far-field radiation, 136–137 feed design, reflector antennas (front-fed parabolic), 913–915, 915f ferrite loop, loop antennas ferrite-loading receiving loop, 271–272 radiation resistance, 270–271, 271f field regions, 31–33, 32f, 33f folded dipole, 505–512, 507f, 509f, 511f 4×4 vs 8×8 planar array, 969 fractal antennas, 627–633, 628f, 629f, 630f, 631f, 632f frequency independent antennas See also antenna miniaturization; electrically small antennas, fundamental limits; equiangular spiral antennas; fractal antennas; log-periodic antennas overview, 591–592 theory, 592–593 Friis transmission equation, 88–90, 88f future challenges, 21 gain, realized gain, 61–64 ground effects, 203–216 half wavelength dipole, 176–179 Hall´en’s integral equation, 444–445 helical antenna, 549–550, 550f, 551f design procedure, 553–558, 557f end-fire mode, 553 feed design, 558–559, 559f normal mode, 550–553, 552f horizontal electric dipole, 195–203 horn antennas aperture-matched horns, 766–769, 767f, 768f conical horn, 756–759, 757f, 758f, 759f, 760f, 761t corrugated horn, 761–764, 762f, 763f, 765f, 766 dielectric-loaded horns, 771, 773 multimode horns, 769–771, 769f, 772–773f phase center, 773–774 horn antennas, E-plane sectoral horn, 720f, 721f aperture fields, 719–722 directivity, 728–733, 730f, 731f, 732f horn antennas, H-plane sectoral horn, 734f aperture fields, 733 directivity, 738–741, 741f, 742f, 743 radiated fields, 734–738, 737f, 738f, 739f horn antennas, pyramidal horn, 743, 744f aperture fields, equivalent, radiated fields, 744–748, 746f, 747f, 748f, 749f design procedure, 754–756 directivity, 748–754, 751f, 752f INDEX H-plane sectoral horn, 734f aperture fields, 733 directivity, 738–741, 741f, 742f, 743 radiated fields, 734–738, 737f, 738f, 739f important parameters, associated formulas, equation numbers, 101–103t induced EMF method, 458 near-field of dipole, 458–460, 458f self-impedance, 460–463, 460f, 462f, 463f induced EMF method, mutual impedance between linear elements, 467–473, 470f 468f, 471f, 473f 472f infinite line source, unbounded medium (tm open), 15 inhomogeneous vector potential wave solution, 132–136, 133f input impedance, 75–79, 75f, 78f integral equation-moment method, 455–457, 457f, 457t Mini-Numerical Electromagnetic Code (MININEC), 467 mutual impedance between linear elements, 465 Numerical Electromagnetic Code (NEC), 466 integral equations, 431 See also moment method solution integral equations, finite diameter wires Hall´en’s integral equation, 444–445 Pocklington’s integral equation, 440–444, 440f source modeling, delta gap, 445, 446f, 448t source modeling, magnetic-frill generator, 446–448, 446f, 448t integral equations, Integral Equation (IE) method electrostatic charge distribution, 432 electrostatic charge distribution, bent wire, 437–439, 438f electrostatic charge distribution, finite straight wire, 433–437, 437f 433f integral equation, 439 inverted-F antenna (IFA), 843–845, 843f, 845f isotropic, directional, omnidirectional patterns, 30, 31f least mean square (LMS) algorithm, optimal beamforming techniques, 956–959, 957f, 958f, 959f lens antennas, 6–7, 8f linear, circular, elliptical polarization, 68–71 linear elements near/on infinite perfect electric conductors (PEC), perfect magnetic conductors (PMC), and electromagnetic band-gap (EBG) surfaces, 179 ground effects, 203 ground planes: electric, magnetic, 180–182, 182f, 183f 1069 horizontal electric dipole, 195, 196f, 197–203, 198f, 200f, 201f , 202f, 203f image theory, 182–183, 184f, 185f mobile communication devices, antennas for mobile communication, 192–195, 195f, 196f rapid calculations and design, approximate formulas, 191–192 vertical electric dipole, 183–187, 184f, 185f, 187f, 188f, 189, 189f, 190f, 191, 191f linear wire antennas See also linear elements near/on infinite perfect electric conductors (PEC), perfect magnetic conductors (PMC), and electromagnetic band-gap (EBG) surfaces computer codes, 216 dipole in far field, parameters, formulas, equation numbers, 217–218t linear wire antennas, finite length dipole current distribution, 164 directivity, 172–173 input resistance, 173–175, 174f, 176f power density, radiation intensity, radiation resistance, 166–172, 167f, 168f, 169f, 171f radiated fields: element, space, and pattern multiplication, 164–166 linear wire antennas, ground effects, 203 earth curvature, 211–216, 212f, 213f, 215f horizontal electric dipole, 205, 207, 207f, 208f, 209f, 210f PEC, PMC, EBG surfaces, 207, 210 verticle electric dipole, 204–205, 206f linear wire antennas, half-wavelength dipole, 176–177, 178f, 179, 179t linear wire antennas, infinitesimal dipole directivity, 154–155, 155f far-field (kr ≫ 1)region, 153–154 intermediate-field (kr >1) region, 152 near-field (kr ≪ 1) region, 151–152 power density, radiation resistance, 148–150 radian distance, radian sphere, 150–151, 151f radiated fields, 145–148, 146f linear wire antennas, region separation far-field (Fraunhofer) region, 160–162 radiating near-field (Fresnel) region, 162–163 reactive near-field region, 163–164 linear wire antennas, small dipole, 155, 156t, 157f, 158 log-periodic antennas, 598 dipole array, 602–605, 603f, 606f, 607–608, 607f, 607t, 608f dipole array design, 608–609, 609f dipole array design, computer program, 613–614 dipole array design, design equations, 609–612, 611f 1070 INDEX log-periodic antennas (Continued) dipole array design, design procedure, 611–613, 613f planar, wire surfaces, 599–602, 600f, 601f long wire amplitude patterns, maxima, nulls, 538–539, 539f, 540f, 541f input impedance, 541–542 resonant wires, 542–543 loop antennas, 235, 236f circular loops ground/earth curvature effects, 268–269, 268f, 269f loop in far field paramaters, formulas, equation numbers, 274–275t mobile communications applications, 272, 273f polygonal loop antennas, 269–270 loop antennas, circular loop of constant current power density, radiation intensity, radiation resistance, directivity, 252–253, 253f, 254f, 255–259, 257f, 258f radiated fields, 250–252, 251f loop antennas, circular loop of nonuniform current, 259–260, 260f, 261f, 262–266, 262f, 263f, 264f, 265f arrays, 266 design procedure, 267–268 loop antennas, ferrite loop ferrite-loading receiving loop, 271–272 radiation resistance, 270–271, 271f loop antennas, small circular loop equivalent circuit, receiving mode, 249–250, 249f equivalent circuit, transmitting mode, 247–249, 248f far-field (kr ≫ 1) region, 245–246 near-field (kr ≪ 1) region, 246 power density, radiation resistance, 241–245, 244f radiated fields, 236–241, 237f radiation intensity, directivity, 246–247 small loop, infinitesimal magnetic dipole, 241 matching techniques baluns, transformers, 521–523, 522f, 523f quarter-wavelength transformer, binomial design, 515–518 quarter-wavelength transformer, multiple sections, 515 quarter-wavelength transformer, single section, 514–515 quarter-wavelength transformer, Tschebyscheff design, 518–522, 518f, 520f stub-matching, 513 maximum directivity, maximum effective area, 86–88, 86f microstrip and mobile communications antennas analysis methods, 787–788 arrays, feed networks, 832–837, 835f, 836f, 837f, 838f basic characteristics, 784–785, 784f, 785f circular polarization, 830–832, 832f, 832t, 833f, 834f coupling, 827–830, 828f, 829f dielectric resonator antennas (DRAs), 847–848 feeding methods, 785–787, 786f, 787f input impedance, 826–827, 826f inverted-F antenna (IFA), 843–845, 843f, 845f multiband antennas for mobile units, 846–847, 846f overview, 783–784, 784t parameters, formulas, equation numbers, 859t planar inverted-F antenna (PIFA), 838f, 839–840, 839f, 841f quality factor, bandwidth, efficiency, 823–826, 825f slot antenna, 841–843, 842f microstrip and mobile communications antennas, circular patch, 815, 815f conductance, directivity, 821–822, 822f, 823f design, 818–819, 819f electric and magnetic fields - TMzmnp , 816–817 equivalent current densities, fields radiated, 819–821, 820f resonant frequencies, 817–818 resonant input resistance, 822–823 microstrip and mobile communications antennas, rectangular patch cavity model, 799, 799f cavity model, equivalent current densities, 804–807, 805f, 806f, 807 cavity model, field configurations (modes) - TMx , 800–803, 801f, 804f directivity, double slot (k0 h ≪ 1), 812–815, 814f directivity, single slot k0 h ≪ 1), 811–812, 812f nonradiating slots, 810–811 radiating slots, 807–810, 809f transmission-line model effective length, conductance, 793–794, 793f, 795f transmission-line model effective length, design, 791–792, 792f transmission-line model effective length, matching techniques, 796–799, 796f, 799f transmission-line model effective length, resonant frequency, effective width, 790–791, 790f transmission-line model effective length, resonant input resistance, 794–796 transmission-line model, fringing effects, 788–789, 789f microstrip antennas, 5, 5f, 6f Mini-Numerical Electromagnetic Code (MININEC), 467 INDEX mobile ad hoc networks (MANETs) MANETs employing smart-antenna systems, protocol, 962–964, 963f MANETs employing smart-antenna systems, wireless network, 961–962, 962f overview, 960–961, 960f moment method solution, 448 basis (expansion) functions, entire-domain functions, 453 basis (expansion) functions, subdomain functions, 449–452, 450f, 451f, 452f weighting (testing) functions, 453, 454f, 455 multiband antennas for mobile units, 846–847, 846f mutual coupling in arrays active element pattern in array, 478–480, 478f, 480f infinite regular array coupling, 476–478 mutual coupling on array performance, 476 receiving mode coupling, 476 transmitting mode coupling, 474–476, 475f mutual impedance between linear elements, 463–465, 464f, 466f See also self-impedance induced EMF method, 467–473, 470f 468f, 471f, 473f 472f integral equation-moment method, 465 integral equation-moment method, Mini-Numerical Electromagnetic Code (MININEC), 467 integral equation-moment method, Numerical Electromagnetic Code (NEC), 466 mutual impedance between linear elements, integral equation-moment method, 465 90◦ corner reflector, 878–880, 879f Numerical Equivalent Code (NEC), 466 omnidirectional patterns, 51–52, 52f, 53f, 54 omnidirectional systems, 933, 933f cell splitting, 934, 934f sectorized systems, 934–936, 935f optimal beamforming techniques least mean square (LMS) algorithm, 956–959, 957f, 958f, 959f minimum mean square error (MMSE) criterion, 955–956 optimal beamforming techniques, minimum mean square error (MMSE) criterion, 955–956 phase errors, reflector antennas (front-fed parabolic), 910–913, 914f planar inverted-F antenna (PIFA), 838f, 839–840, 839f, 841f planar, wire surfaces, 599–602, 600f, 601f plane reflector, 875–876, 876f Pocklington’s integral equation, 440–444, 440f polarization, 66–68, 67f 1071 linear, circular, elliptical polarization, 68–71 polarization loss factor (PLF), efficiency, 71–75, 71f, 74f pyramidal horn, 743, 744f aperture fields, equivalent, radiated fields, 744–748, 746f, 747f, 748f, 749f design procedure, 754–756 directivity, 748–754, 751f, 752f quarter-wavelength transformer binomial design, 515–518 multiple sections, 515 single section, 514–515 Tschebyscheff design, 518–522, 518f, 520f radar cross section (RCS), 92–96, 92t, 96f, 97f radar range equation, 90–92, 91f radian, steradian, 33, 34f radiating far-field (Fraunhofer) region, 32, 32f radiating near-field (Fresnel) region, 31–32, 32f radiation integrals, auxilliary potential functions electric and magnetic sources, computing fields block diagram, 128f overview, 127–128 radiation intensity, 37–38, 39f radiation pattern (antenna pattern), 25–26, 26f, 27f amplitude pattern shape, 32–33, 33f coordinate system for antenna analysis, 25–26, 26f field regions, 31–33, 32f, 33f isotropic, directional, omnidirectional patterns, 30, 31f principle patterns, 30–31 radiation pattern lobes, 26–30, 28f radiation pattern lobes, 26–30, 28f radiation patterns, numerical techniques, 55–57, 56f, 58f, 59–60, 60f radiation power density, 35–37 radiation problems, computer animation-visualization, 13–15 reactive near-field region, 31, 32f reciprocity, reaction theorems, 138–140 for antenna radiation patterns, 141–143, 142f for two antennas, 140–141, 140f, 141f rectangular patch, 965–966, 966f, 967f, 968f rectangular patch, microstrip and mobile communications antennas nonradiating slots, 810–811 reflector antennas, 6, 7f 90◦ corner reflector, 878–880, 879f corner reflector, 876–878, 876f, 877f, 878f, 880–884, 881f, 882f, 883f plane reflector, 875–876, 876f reflector antennas, front-fed parabolic aperture distribution method, 890–896, 891f, 893f, 895f Cassegrain reflectors, 915–916, 917f 1072 INDEX reflector antennas, front-fed parabolic (Continued) Cassegrain reflectors, Cassegrain and Gregorian forms, 919–920, 919f Cassegrain reflectors, classical form, 917–919, 918f cross-polarization, 896–897, 896f, 897f current distribution method, 897–901, 898f, 900f directivity and aperture efficiency, 898f, 900f, 901–909, 903f, 906f, 908f, 909t, 910f, 911f feed design, 913–915, 915f induced current, 890 phase errors, 910–913, 914f surface geometry, 887–890, 888f reflector antennas, parabolic, 884–887, 885f, 886f reflector antennas, spherical reflector, 920–922, 920f, 922f rhombic antenna geometry, design equations, 549 self-impedance See also mutual impedances between linear elements induced EMF method, 458 induced EMF method, near-field of dipole, 458–460, 458f induced EMF method, self-impedance, 460–463, 460f, 462f, 463f integral equation-moment method, 455–457, 457f, 457t slot antenna, 841–843, 842f smart antennas antenna, array design, 943 antenna, linear array, 944–945, 944f, 945f antenna, planar array, 945–946, 946f beamforming, diversity combining, Raleigh-fading, trellis code modulation, 972–975, 972t, 973f, 974f other geometries, 975–976, 975f signal propagation, 939–941, 940f, 941f, 942f smart antennas’ benefits, 942–943 smart antennas’ drawbacks, 942–943 smart antenna analogy, 931–932, 932f smart antennas, antenna beamforming, 946 adaptive beamforming, 950–953, 951f, 952f direction-of-arrival (DOA) algorithms, 947–950, 947f, 950f optimal beamforming techniques, least mean square (LMS) algorithm, 956–959, 957f, 958f, 959f optimal beamforming techniques, minimum mean square error (MMSE) criterion, 955–956 smart antennas, cellular radio systems evolution omnidirectional systems, 933, 933f omnidirectional systems, cell splitting, 934, 934f omnidirectional systems, sectorized systems, 934–936, 935f smart-antenna systems, adaptive array systems, 937–938, 937f, 938f smart-antenna systems, spatial division multiple access (SDMA), 938–939, 939f smart-antenna systems, switch-beam systems, 936–937, 936f, 937f smart antennas, mobile ad hoc networks (MANETs) MANETs employing smart-antenna systems, protocol, 962–964, 963f MANETs employing smart-antenna systems, wireless network, 961–962, 962f overview, 960–961, 960f smart antennas, system design/simulation/results 4×4 vs 8×8 planar array, 969 adaptive beamforming, 969–971, 970f, 971f, 972f array design, linear array design, 967–968, 968f array design, planar array design, 968–969 design process, 964–965 rectangular patch, 965–966, 966f, 967f, 968f single element, microstrip design, 965 stub-matching, 513 surface geometry, reflector antennas (front-fed parabolic), 887–890, 888f transmitting mode, transmission-line Thevenin equivalent, 1, 2f traveling wave antennas, 533–535, 534f, 535f long wire amplitude patterns, maxima, nulls, 538–539, 539f, 540f, 541f long wire, input impedance, 541–542 long wire, resonant wires, 542–543 rhombic antenna geometry, design equations, 549 V antenna, 543–547, 544f, 545f, 546f, 547f triangular sheet, bow-tie, and wire simulation of biconical antenna, 492–496, 493f, 494f, 495f, 496f two-wires, 10–11, 11f, 12f V antenna, 543–547, 544f, 545f, 546f, 547f vector effective length, 81–83, 81f vector potential A, electric current source J, 129–130 vector potential F, magnetic current source M, 130–131 vertical electric dipole, 183–195 Vivaldi antenna, 496–499, 497f, 499f, 500f wire antennas, 3, 4f, 6f Yagi-Uda array of linear elements, 559–561, 560f computer program and results, 568–571, 569f, 570f design procedure, 575–578, 576t, 577f, 579f far-field pattern, 566–567 impedance and matching techniques, 572, 575, 575t integral equation-moment method, 562–565, 566f optimization, 571–572, 572t, 573t, 574f Yagi-Uda array of loops, 579–580, 579f WILEY END USER LICENSE AGREEMENT Go to www.wiley.com/go/eula to access Wiley’s ebook EULA