Electromagnetic Waves and Antennas Electromagnetic ToMonicaandJohn Waves and Antennas Copyright©1999–2008bySophoclesJ.Orfanidis Allrightsreserved. Nopartsofthispublicationmaybereproduced,storedinaretrieval system,ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopy- ing,recordingorotherwise,withoutthepriorwrittenpermissionoftheauthor. Sophocles J. Orfanidis MATLAB(cid:2)R isaregisteredtrademarkofTheMathWorks,Inc. Rutgers University Webpage: www.ece.rutgers.edu/~orfanidi/ewa vi CONTENTS 3.5 PulsePropagationandGroupVelocity, 92 3.6 GroupVelocityDispersionandPulseSpreading, 95 3.7 PropagationandChirping, 100 3.8 DispersionCompensation, 101 3.9 Slow,Fast,andNegativeGroupVelocities, 103 Contents 3.10 ChirpRadarandPulseCompression, 110 3.11 FurtherReading, 120 3.12 Problems, 120 4 PropagationinBirefringentMedia 129 4.1 LinearandCircularBirefringence, 129 Preface xiii 4.2 UniaxialandBiaxialMedia, 130 4.3 ChiralMedia, 132 4.4 GyrotropicMedia, 135 1 Maxwell’sEquations 1 4.5 LinearandCircularDichroism, 136 1.1 Maxwell’sEquations, 1 4.6 ObliquePropagationinBirefringentMedia, 137 1.2 LorentzForce, 2 4.7 Problems, 144 1.3 ConstitutiveRelations, 3 5 ReflectionandTransmission 150 1.4 BoundaryConditions, 7 1.5 Currents,Fluxes,andConservationLaws, 9 5.1 PropagationMatrices, 150 1.6 ChargeConservation, 10 5.2 MatchingMatrices, 154 1.7 EnergyFluxandEnergyConservation, 11 5.3 ReflectedandTransmittedPower, 157 1.8 HarmonicTimeDependence, 13 5.4 SingleDielectricSlab, 160 1.9 SimpleModelsofDielectrics,Conductors,andPlasmas, 16 5.5 ReflectionlessSlab, 163 1.10 Kramers-KronigDispersionRelations, 26 5.6 Time-DomainReflectionResponse, 171 1.11 GroupVelocity,EnergyVelocity, 29 5.7 TwoDielectricSlabs, 173 1.12 Problems, 31 5.8 ReflectionbyaMovingBoundary, 175 5.9 Problems, 178 2 UniformPlaneWaves 36 6 MultilayerStructures 183 2.1 UniformPlaneWavesinLosslessMedia, 36 2.2 MonochromaticWaves, 42 6.1 MultipleDielectricSlabs, 183 2.3 EnergyDensityandFlux, 45 6.2 AntireflectionCoatings, 185 2.4 WaveImpedance, 46 6.3 DielectricMirrors, 190 2.5 Polarization, 46 6.4 PropagationBandgaps, 201 2.6 UniformPlaneWavesinLossyMedia, 52 6.5 Narrow-BandTransmissionFilters, 201 2.7 PropagationinWeaklyLossyDielectrics, 58 6.6 EqualTravel-TimeMultilayerStructures, 206 2.8 PropagationinGoodConductors, 59 6.7 ApplicationsofLayeredStructures, 220 2.9 PropagationinObliqueDirections, 61 6.8 ChebyshevDesignofReflectionlessMultilayers, 223 2.10 ComplexorInhomogeneousWaves, 63 6.9 Problems, 231 2.11 DopplerEffect, 66 2.12 PropagationinNegative-IndexMedia, 70 7 ObliqueIncidence 238 2.13 Problems, 73 7.1 ObliqueIncidenceandSnel’sLaws, 238 3 PulsePropagationinDispersiveMedia 80 7.2 TransverseImpedance, 240 7.3 PropagationandMatchingofTransverseFields, 243 3.1 PropagationFilter, 80 7.4 FresnelReflectionCoefficients, 245 3.2 FrontVelocityandCausality, 82 7.5 MaximumAngleandCriticalAngle, 247 3.3 ExactImpulseResponseExamples, 85 7.6 BrewsterAngle, 256 3.4 TransientandSteady-StateBehavior, 88 v CONTENTS vii viii CONTENTS 7.7 ComplexWaves, 258 10.6 DistributedCircuitModelofaTransmissionLine, 412 7.8 TotalInternalReflection, 261 10.7 WaveImpedanceandReflectionResponse, 414 7.9 ObliqueIncidenceonaLossyMedium, 262 10.8 Two-PortEquivalentCircuit, 416 7.10 ZenneckSurfaceWave, 267 10.9 TerminatedTransmissionLines, 417 7.11 SurfacePlasmons, 269 10.10PowerTransferfromGeneratortoLoad, 420 7.12 ObliqueReflectionfromaMovingBoundary, 272 10.11Open-andShort-CircuitedTransmissionLines, 422 7.13 GeometricalOptics, 276 10.12StandingWaveRatio, 425 7.14 Fermat’sPrinciple, 279 10.13DetermininganUnknownLoadImpedance, 427 7.15 RayTracing, 281 10.14SmithChart, 431 7.16 Snel’sLawinNegative-IndexMedia, 292 10.15Time-DomainResponseofTransmissionLines, 435 7.17 Problems, 295 10.16Problems, 442 8 MultilayerFilmApplications 300 11 CoupledLines 453 8.1 MultilayerDielectricStructuresatObliqueIncidence, 300 11.1 CoupledTransmissionLines, 453 8.2 LossyMultilayerStructures, 302 11.2 CrosstalkBetweenLines, 459 8.3 SingleDielectricSlab, 304 11.3 WeaklyCoupledLineswithArbitraryTerminations, 462 8.4 FrustratedTotalInternalReflection, 306 11.4 Coupled-ModeTheory, 464 8.5 SurfacePlasmonResonance, 310 11.5 FiberBraggGratings, 466 8.6 PerfectLensinNegative-IndexMedia, 319 11.6 DiffuseReflectionandTransmission, 469 8.7 AntireflectionCoatingsatObliqueIncidence, 327 11.7 Problems, 471 8.8 OmnidirectionalDielectricMirrors, 330 8.9 PolarizingBeamSplitters, 341 12 ImpedanceMatching 473 8.10 ReflectionandRefractioninBirefringentMedia, 343 8.11 BrewsterandCriticalAnglesinBirefringentMedia, 347 12.1 ConjugateandReflectionlessMatching, 473 8.12 MultilayerBirefringentStructures, 350 12.2 MultisectionTransmissionLines, 475 8.13 GiantBirefringentOptics, 352 12.3 Quarter-WavelengthChebyshevTransformers, 476 8.14 Problems, 357 12.4 Two-SectionDual-BandChebyshevTransformers, 482 12.5 Quarter-WavelengthTransformerWithSeriesSection, 488 9 Waveguides 359 12.6 Quarter-WavelengthTransformerWithShuntStub, 491 12.7 Two-SectionSeriesImpedanceTransformer, 493 9.1 Longitudinal-TransverseDecompositions, 360 12.8 SingleStubMatching, 498 9.2 PowerTransferandAttenuation, 365 12.9 BalancedStubs, 502 9.3 TEM,TE,andTMmodes, 367 12.10DoubleandTripleStubMatching, 504 9.4 RectangularWaveguides, 370 12.11L-SectionLumpedReactiveMatchingNetworks, 506 9.5 HigherTEandTMmodes, 372 12.12Pi-SectionLumpedReactiveMatchingNetworks, 509 9.6 OperatingBandwidth, 374 12.13ReversedMatchingNetworks, 516 9.7 PowerTransfer,EnergyDensity,andGroupVelocity, 375 12.14Problems, 518 9.8 PowerAttenuation, 377 9.9 ReflectionModelofWaveguidePropagation, 380 13 S-Parameters 522 9.10 ResonantCavities, 382 9.11 DielectricSlabWaveguides, 384 13.1 ScatteringParameters, 522 9.12 Problems, 392 13.2 PowerFlow, 526 13.3 ParameterConversions, 527 10 TransmissionLines 394 13.4 InputandOutputReflectionCoefficients, 528 13.5 StabilityCircles, 530 10.1 GeneralPropertiesofTEMTransmissionLines, 394 13.6 PowerGains, 536 10.2 ParallelPlateLines, 400 13.7 GeneralizedS-ParametersandPowerWaves, 542 10.3 MicrostripLines, 401 13.8 SimultaneousConjugateMatching, 546 10.4 CoaxialLines, 405 13.9 PowerGainCircles, 551 10.5 Two-WireLines, 410 13.10UnilateralGainCircles, 552 CONTENTS ix x CONTENTS 13.11OperatingandAvailablePowerGainCircles, 554 17 RadiationfromApertures 658 13.12NoiseFigureCircles, 560 17.1 FieldEquivalencePrinciple, 658 13.13Problems, 565 17.2 MagneticCurrentsandDuality, 660 14 RadiationFields 568 17.3 RadiationFieldsfromMagneticCurrents, 662 17.4 RadiationFieldsfromApertures, 663 14.1 CurrentsandChargesasSourcesofFields, 568 17.5 HuygensSource, 666 14.2 RetardedPotentials, 570 17.6 DirectivityandEffectiveAreaofApertures, 668 14.3 HarmonicTimeDependence, 573 17.7 UniformApertures, 670 14.4 FieldsofaLinearWireAntenna, 575 17.8 RectangularApertures, 670 14.5 FieldsofElectricandMagneticDipoles, 577 17.9 CircularApertures, 672 14.6 Ewald-OseenExtinctionTheorem, 582 17.10VectorDiffractionTheory, 675 14.7 RadiationFields, 587 17.11ExtinctionTheorem, 679 14.8 RadialCoordinates, 590 17.12VectorDiffractionforApertures, 681 14.9 RadiationFieldApproximation, 592 17.13FresnelDiffraction, 682 14.10ComputingtheRadiationFields, 593 17.14Knife-EdgeDiffraction, 686 14.11Problems, 595 17.15GeometricalTheoryofDiffraction, 694 17.16Rayleigh-SommerfeldDiffractionTheory, 700 15 TransmittingandReceivingAntennas 598 17.17Plane-WaveSpectrumRepresentation, 703 17.18FresnelDiffractionandFourierOptics, 708 15.1 EnergyFluxandRadiationIntensity, 598 17.19Problems, 719 15.2 Directivity,Gain,andBeamwidth, 599 15.3 EffectiveArea, 604 18 ApertureAntennas 723 15.4 AntennaEquivalentCircuits, 608 15.5 EffectiveLength, 610 18.1 Open-EndedWaveguides, 723 15.6 CommunicatingAntennas, 612 18.2 HornAntennas, 727 15.7 AntennaNoiseTemperature, 614 18.3 HornRadiationFields, 729 15.8 SystemNoiseTemperature, 618 18.4 HornDirectivity, 734 15.9 DataRateLimits, 624 18.5 HornDesign, 737 15.10SatelliteLinks, 626 18.6 MicrostripAntennas, 740 15.11RadarEquation, 629 18.7 ParabolicReflectorAntennas, 746 15.12Problems, 631 18.8 GainandBeamwidthofReflectorAntennas, 748 18.9 Aperture-FieldandCurrent-DistributionMethods, 751 16 LinearandLoopAntennas 634 18.10RadiationPatternsofReflectorAntennas, 754 18.11Dual-ReflectorAntennas, 763 16.1 LinearAntennas, 634 18.12LensAntennas, 766 16.2 HertzianDipole, 636 16.3 Standing-WaveAntennas, 638 19 AntennaArrays 768 16.4 Half-WaveDipole, 642 16.5 MonopoleAntennas, 643 19.1 AntennaArrays, 768 16.6 Traveling-WaveAntennas, 645 19.2 TranslationalPhaseShift, 768 16.7 VeeandRhombicAntennas, 647 19.3 ArrayPatternMultiplication, 770 16.8 LoopAntennas, 650 19.4 One-DimensionalArrays, 780 16.9 CircularLoops, 652 19.5 VisibleRegion, 782 16.10SquareLoops, 654 19.6 GratingLobes, 784 16.11DipoleandQuadrupoleRadiation, 655 19.7 UniformArrays, 786 16.12Problems, 657 19.8 ArrayDirectivity, 790 19.9 ArraySteering, 791 19.10ArrayBeamwidth, 794 19.11Problems, 796 CONTENTS xi 20 ArrayDesignMethods 799 D Green’sFunctions, 944 E CoordinateSystems, 947 20.1 ArrayDesignMethods, 799 F Fresnel,Exponential,Sine,andCosineIntegrals, 949 20.2 Schelkunoff’sZeroPlacementMethod, 802 G Gauss-LegendreQuadrature, 955 20.3 FourierSeriesMethodwithWindowing, 804 H LorentzTransformations, 961 20.4 SectorBeamArrayDesign, 805 I MATLABFunctions, 969 20.5 Woodward-LawsonFrequency-SamplingDesign, 809 20.6 DiscretizationofContinuousLineSources, 814 References 974 20.7 Narrow-BeamLow-SidelobeDesigns, 818 20.8 BinomialArrays, 822 20.9 Dolph-ChebyshevArrays, 823 Index 1021 20.10TaylorOne-ParameterSource, 836 20.11ProlateArray, 840 20.12TaylorLineSource, 842 20.13VilleneuveArrays, 846 20.14MultibeamArrays, 847 20.15Problems, 850 21 CurrentsonLinearAntennas 852 21.1 Hall´enandPocklingtonIntegralEquations, 852 21.2 Delta-Gap,FrillGenerator,andPlane-WaveSources, 855 21.3 SolvingHall´en’sEquation, 856 21.4 SinusoidalCurrentApproximation, 858 21.5 ReflectingandCenter-LoadedReceivingAntennas, 859 21.6 King’sThree-TermApproximation, 862 21.7 EvaluationoftheExactKernel, 869 21.8 MethodofMoments, 874 21.9 Delta-FunctionBasis, 877 21.10PulseBasis, 881 21.11TriangularBasis, 886 21.12NECSinusoidalBasis, 888 21.13Hall´en’sEquationforArbitraryIncidentField, 891 21.14SolvingPocklington’sEquation, 896 21.15Problems, 900 22 CoupledAntennas 902 22.1 NearFieldsofLinearAntennas, 902 22.2 SelfandMutualImpedance, 905 22.3 CoupledTwo-ElementArrays, 911 22.4 ArraysofParallelDipoles, 914 22.5 Yagi-UdaAntennas, 923 22.6 Hall´enEquationsforCoupledAntennas, 929 22.7 Problems, 936 23 Appendices 938 A PhysicalConstants, 938 B ElectromagneticFrequencyBands, 939 C VectorIdentitiesandIntegralTheorems, 941 xiv PREFACE Thebookisbasedonlecturenotesforafirst-yeargraduatecourseon“Electromag- neticWavesandRadiation”thatIhavebeenteachingatRutgersformorethantwenty years. Thecoursedrawsstudentsfromavarietyoffields,suchassolid-statedevices, wireless communications, fiber optics, biomedical engineering, and digital signal and arrayprocessing. Undergraduateseniorshavealsoattendedthegraduatecoursesuc- Preface cessfully. Thebookrequiresaprerequisitecourseonelectromagnetics,typicallyofferedatthe junioryear.Suchintroductorycourseisusuallyfollowedbyasenior-levelelectivecourse on electromagnetic waves, which covers propagation, reflection, and transmission of waves,waveguides,transmissionlines,andperhapssomeantennas. Thisbookmaybe usedinsuchelectivecourseswiththeappropriateselectionofchapters. Thistextprovidesabroadandapplications-orientedintroductiontoelectromagnetic At the graduate level, there is usually an introductory course that covers waves, wavesandantennas. Currentinterestintheseareasisdrivenbythegrowthinwireless guides, lines, and antennas, and this is followed by more specialized courses on an- andfiber-opticcommunications,informationtechnology,andmaterialsscience. tennadesign,microwavesystemsanddevices,opticalfibers,andnumericaltechniques Communications,antenna,radar,andmicrowaveengineersmustdealwiththegen- in electromagnetics. No single book can possibly cover all of the advanced courses. eration,transmission,andreceptionofelectromagneticwaves. Deviceengineerswork- Thisbookmaybeusedasatextintheinitialcourse,andasasupplementarytextinthe ing on ever-smaller integrated circuits and at ever higher frequencies must take into specializedcourses. accountwavepropagationeffectsatthechipandcircuit-boardlevels. Communication andcomputernetworkengineersroutinelyusewaveguidingsystems,suchastransmis- ContentsandHighlights sionlinesandopticalfibers. Novelrecentdevelopmentsinmaterials,suchasphotonic bandgap structures, omnidirectional dielectric mirrors, birefringent multilayer films, The first eight chapters develop waves concepts and applications. The material pro- surface plasmons, negative-index metamaterials, slow and fast light, promise a revo- gresses from Maxwell equations, to uniform plane waves in various media, such as lutioninthecontrolandmanipulationoflightandotherapplications. Thesearejust losslessandlossydielectricsandconductors,birefringentandchiralmedia,including some examples of topics discussed in this book. The text is organized around three negative-indexmedia, toreflectionandtransmissionproblemsatnormalandoblique maintopicareas: incidence,includingreflectionfrommovingboundariesandtheDopplereffect,tomul- tilayerstructures. • The propagation, reflection, and transmission of plane waves, and the analysis Chapterthreedealswithpulsepropagationindispersivemedia,withdiscussionsof anddesignofmultilayerfilms. groupandfrontvelocityandcausality,groupvelocitydispersion,spreadingandchirp- • Waveguides,transmissionlines,impedancematching,andS-parameters. ing,dispersioncompensation,slow,fast,andnegativegroupvelocity,andanintroduc- • Linearandapertureantennas,scalarandvectordiffractiontheory,antennaarray tiontochirpradarandpulsecompression. design,numericalmethodsinantennas,andcoupledantennas. Someoftheobliqueincidenceapplicationsincludeinhomogeneouswaves,totalin- ternalreflection,surfaceplasmons,raytracingandatmosphericrefraction,andSnel’s Thetextemphasizesconnectionstoothersubjects. Forexample,themathematical lawinnegative-indexmedia. techniquesforanalyzingwavepropagationinmultilayerstructuresandthedesignof Thematerialonmultilayerstructuresincludesthedesignofantireflectioncoatings, multilayeropticalfiltersarethesameasthoseusedindigitalsignalprocessing, such omnidirectionaldielectricmirrors,broadbandreflectionlessmultilayers,frustratedto- asthelatticestructuresoflinearprediction,theanalysisandsynthesisofspeech,and talinternalreflectionandsurfaceplasmonresonance,perfectlensesinnegative-index geophysical signal processing. Similarly, antenna array design is related to the prob- media,polarizingbeamsplitters,andbirefringentmultilayerstructures. lemofspectralanalysisofsinusoidsandtodigitalfilterdesign,andButlerbeamsare Chapters9–13dealwithwaveguidesandtransmissionlines.Wecoveronlyrectangu- equivalenttotheFFT. larwaveguides,resonantcavities,andsimpledielectricwaveguides. Thetransmission line material includes a discussion of microstrip and coaxial lines, terminated lines, Use standing wave ratio and the Smith chart, and examples of time-domain transient re- sponseoflines. Wehaveincludedsomematerialoncoupledlinesandcrosstalk,aswell Thebookisappropriateforfirst-yeargraduateorseniorundergraduatestudents. There assomeoncoupledmodetheoryandfiberBragggratings. isenoughmaterialinthebookforatwo-semestercoursesequence. Thebookcanalso We devote one chapter to impedance matching methods, including multisection beusedbypracticingengineersandscientistswhowantaquickreviewthatcoversmost Chebyshevquarter-wavelengthtransformers,quarter-wavelengthtransformerswithse- ofthebasicconceptsandincludesmanyapplicationexamples. PREFACE xv xvi PREFACE riesorshuntstubs,singlestubtuners,aswellasL-sectionandΠ-sectionreactivematch- lutionofasystemofcoupledHall´enequations. Wepresentvariousexamples,including ingnetworks. thedesignofYagi-Udaantennas. Chapter13presentsanintroductiontoS-parameterswithadiscussionofinputand OurMATLAB-basednumericalsolutionsarenotmeanttoreplacesophisticatedcom- outputreflectioncoefficients,two-portstabilityconditions,transducer,operating,and mercialfieldsolvers. Theinclusionofnumericalmethodsinthisbookwasmotivatedby availablepowergains,powerwaves,simultaneousconjugatematching,noisefigurecir- thedesiretoprovidethereaderwithsomesimpletoolsforself-studyandexperimenta- cles,illustratingtheconceptswithanumberoflow-noisehigh-gainmicrowaveamplifier tion. Thestudyofnumericalmethodsinelectromagneticsisasubjectinitselfandour designsincludingthedesignoftheirinputandoutputmatchingcircuits. treatmentdoesnotdojusticetoit. However,wefeltthatitwouldbefuntobeableto Chapters14–22dealwithradiationandantennaconcepts. Webeginbyderivingex- quicklycomputefairlyaccurateradiationpatternsinvariousantennaexamples, such pressionsfortheradiationfieldsfromcurrentsources,includingmagneticcurrents,and asYagi-Udaandothercoupledantennas,aswellhornsandreflectorantennas. thenapplythemtolinearandapertureantennas. Chapter15coversgeneralfundamen- Theappendixincludessummariesofphysicalconstants,electromagneticfrequency tal antenna concepts, such as radiation intensity, power density, directivity and gain, bands,vectoridentities,integraltheorems,Green’sfunctions,coordinatesystems,Fres- beamwidth, effective area, effective length, Friis formula, antenna noise temperature, nel integrals, sine and cosine integrals, the stationary phase approximation, Gauss- powerbudgetsinsatellitelinks,andtheradarequation. Legendrequadrature,Lorentztransformations,andadetailedlistoftheMATLABfunc- Wehaveincludedanumberoflinearantennaexamples,suchasHertzianandhalf- tions. wavedipoles,traveling,vee,andrhombicantennas,aswellasloopantennas. Finally, there is a large (but inevitably incomplete) list of references, arranged by Twochaptersaredevotedtoradiationfromapertures. ThefirstdiscussesSchelku- topicarea,aswellasseveralweblinks,thatwehopecouldserveasastartingpointfor noff’sfieldequivalenceprinciple,magneticcurrentsandduality,radiationfieldsfrom furtherstudy. apertures,vectordiffractiontheory,includingtheKottler,Stratton-Chu,andFranzfor- mulations,extinctiontheorem,Fresneldiffraction,Fresnel,zones,Sommerfeld’ssolu- MATLABToolbox tiontotheknife-edgediffractionproblem,geometricaltheoryofdiffraction,Rayleigh- Sommerfelddiffractiontheoryanditsconnectiontotheplane-wavespectrumrepresen- ThetextmakesextensiveuseofMATLAB.Wehavedevelopedan“ElectromagneticWaves tationwithapplicationstoFourieroptics. &Antennas”toolboxcontaining170MATLABfunctionsforcarryingoutallofthecom- Thesecondpresentsanumberofapertureantennaexamples,suchasopen-ended putations and simulation examples in the text. Code segments illustrating the usage waveguides,hornantennas,includingoptimumhorndesign,microstripantennas,para- of these functions are found throughout the book, and serve as a user manual. The bolicanddualreflectors,andlensantennas. functionsmaybegroupedintothefollowingcategories: Twootherchaptersdiscussantennaarrays. Thefirstintroducesbasicconceptssuch asthemultiplicativearraypattern,visibleregion,gratinglobes,directivityincludingits 1. Design and analysis of multilayer film structures, including antireflection coat- optimization,arraysteering,andbeamwidth. ings, polarizers, omnidirectionalmirrors, narrow-bandtransmissionfilters, sur- Theotherdiscussesseveralarraydesignmethods,suchasbyzeroplacement,Fourier faceplasmonresonance,birefringentmultilayerfilmsandgiantbirefringentop- series method with windowing, sector beam design, Woodward-Lawson method, and tics. severalnarrow-beamlow-sidelobedesigns,suchasbinomial,Dolph-Chebyshev,Taylor’s 2. Designofquarter-wavelengthimpedancetransformersandotherimpedancematch- one-parameter, Taylor’sn¯ distribution, prolate, andVilleneuvearraydesign. Wehave ingmethods,suchasChebyshevtransformers,dual-bandtransformers,stubmatch- expandedontheanalogieswithtime-domainDSPconceptsandfilterdesignmethods. ingandL-,Π-andT-sectionreactivematchingnetworks. Wefinallygivesomeexamplesofmultibeamdesigns,suchasButlerbeams. 3. Designandanalysisoftransmissionlinesandwaveguides,suchasmicrostriplines Thelasttwochaptersdealwithnumericalmethodsforlinearantennas. Chapter21 anddielectricslabguides. developstheHall´enandPocklingtonintegralequationsfordeterminingthecurrenton 4. S-parameter functions for gain computations, Smith chart generation, stability, alinearantenna,discussesKing’sthree-termapproximations,andthenconcentrateson gain,andnoise-figurecircles,simultaneousconjugatematching,andmicrowave numerical solutions for delta-gap input and arbitrary incident fields. We discuss the amplifierdesign. methodofmoments,implementedwiththeexactortheapproximatethin-wirekernel and using various bases, such as pulse, triangular, and NEC bases. These methods 5. Functionsforthecomputationofdirectivitiesandgainpatternsoflinearantennas, requiretheaccurateevaluationoftheexactthin-wirekernel,whichweapproachusing suchasdipole,vee,rhombic,andtraveling-waveantennas,includingfunctionsfor anellipticfunctionrepresentation. theinputimpedanceofdipoles. InChapter22wediscusscoupledantennas,inparticular,paralleldipoles. Initially, 6. Aperture antenna functions for open-ended waveguides, horn antenna design, weassumesinusoidalcurrentsandreducetheproblemtothecalculationofthemutual diffractionintegrals,andknife-edgediffractioncoefficients. impedancematrix. Then,weconsideramoregeneralformulationthatrequirestheso- 7. Antenna array design functions for uniform, binomial, Dolph-Chebyshev, Tay- lorone-parameter,Taylorn¯distribution,prolate,Villeneuvearrays,sector-beam, PREFACE xvii multi-beam,Woodward-Lawson,andButlerbeams. Functionsforbeamwidthand directivitycalculations,andforsteeringandscanningarrays. 8. NumericalmethodsforsolvingtheHall´enandPocklingtonintegralequationsfor singleandcoupledantennas,computingtheexactthin-wirekernel,andcomputing selfandmutualimpedances. 9. Severalfunctionsformakingazimuthalandpolarplotsofantennaandarraygain patternsindecibelsandabsoluteunits. 10. TherearealsoseveralMATLABmoviesshowingpulsepropagationindispersive mediaillustratingslow,fast,andnegativegroupvelocity;thepropagationofstep signalsandpulsesonterminatedtransmissionlines;thepropagationoncascaded lines; stepsignalsgettingreflectedfromreactiveterminations; faultlocationby TDR;crosstalksignalspropagatingoncoupledlines;andthetime-evolutionofthe fieldlinesradiatedbyaHertziandipole. TheMATLABfunctionsaswellasotherinformationaboutthebookmaybedown- loadedfromthewebpage: www.ece.rutgers.edu/~orfanidi/ewa. Acknowledgements I would like to thank the many generations of my students who shaped the content ofthisbookandthefollowingpeoplefortheirusefulcommentsandsuggestionsfor improvement: M.Abouowf,L.Alekseyev,S.Bang,R.Balder-Navarro,C.Christodoulou, C.Collister,A.Dane,G.Fano,H.Fluhler,K.Foster,S.Fuhrman,J.Hudson,F.Innes,W. G.Krische,M.Maybell,P.Matusov,K.T.McDonald,K.Michalski,J-S.Neron,V.Niziev,F. D.Nunes,H.Park,E.Perrin,D.Phillips,R.Rosensweig,M.Schuh,A.Siegman,P.Simon, K. Subramanian, V. Turkovic, P. Whiteneir, A. Young, and C. Zarowski. Any errors or shortcomingsare,ofcourse,entirelymyown. SophoclesJ.Orfanidis February2008