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Electromagnetic Waves and Antennas Electromagnetic ToMonicaandJohn Waves and Antennas Copyright©1999–2010bySophoclesJ.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 2.13 Problems, 73 3 PulsePropagationinDispersiveMedia 82 3.1 PropagationFilter, 82 3.2 FrontVelocityandCausality, 84 Contents 3.3 ExactImpulseResponseExamples, 87 3.4 TransientandSteady-StateBehavior, 90 3.5 PulsePropagationandGroupVelocity, 94 3.6 GroupVelocityDispersionandPulseSpreading, 97 3.7 PropagationandChirping, 102 3.8 DispersionCompensation, 103 Preface vi 3.9 Slow,Fast,andNegativeGroupVelocities, 105 3.10 ChirpRadarandPulseCompression, 112 3.11 FurtherReading, 122 1 Maxwell’sEquations 1 3.12 Problems, 122 1.1 Maxwell’sEquations, 1 4 PropagationinBirefringentMedia 131 1.2 LorentzForce, 2 1.3 ConstitutiveRelations, 3 4.1 LinearandCircularBirefringence, 131 1.4 NegativeIndexMedia, 7 4.2 UniaxialandBiaxialMedia, 132 1.5 BoundaryConditions, 7 4.3 ChiralMedia, 134 1.6 Currents,Fluxes,andConservationLaws, 9 4.4 GyrotropicMedia, 137 1.7 ChargeConservation, 10 4.5 LinearandCircularDichroism, 138 1.8 EnergyFluxandEnergyConservation, 11 4.6 ObliquePropagationinBirefringentMedia, 139 1.9 HarmonicTimeDependence, 13 4.7 Problems, 146 1.10 SimpleModelsofDielectrics,Conductors,andPlasmas, 16 1.11 Dielectrics, 17 5 ReflectionandTransmission 152 1.12 Conductors, 20 1.13 ChargeRelaxationinConductors, 22 5.1 PropagationMatrices, 152 1.14 PowerLosses, 23 5.2 MatchingMatrices, 156 1.15 Plasmas, 25 5.3 ReflectedandTransmittedPower, 159 1.16 EnergyDensityinLosslessDispersiveDielectrics, 25 5.4 SingleDielectricSlab, 162 1.17 Kramers-KronigDispersionRelations, 26 5.5 ReflectionlessSlab, 165 1.18 GroupVelocity,EnergyVelocity, 29 5.6 Time-DomainReflectionResponse, 173 1.19 Problems, 31 5.7 TwoDielectricSlabs, 175 5.8 ReflectionbyaMovingBoundary, 177 2 UniformPlaneWaves 36 5.9 Problems, 180 2.1 UniformPlaneWavesinLosslessMedia, 36 6 MultilayerStructures 185 2.2 MonochromaticWaves, 42 2.3 EnergyDensityandFlux, 45 6.1 MultipleDielectricSlabs, 185 2.4 WaveImpedance, 46 6.2 AntireflectionCoatings, 187 2.5 Polarization, 46 6.3 DielectricMirrors, 192 2.6 UniformPlaneWavesinLossyMedia, 53 6.4 PropagationBandgaps, 203 2.7 PropagationinWeaklyLossyDielectrics, 59 6.5 Narrow-BandTransmissionFilters, 203 2.8 PropagationinGoodConductors, 60 6.6 EqualTravel-TimeMultilayerStructures, 208 2.9 PropagationinObliqueDirections, 61 6.7 ApplicationsofLayeredStructures, 222 2.10 ComplexorInhomogeneousWaves, 64 6.8 ChebyshevDesignofReflectionlessMultilayers, 225 2.11 DopplerEffect, 66 6.9 Problems, 233 2.12 PropagationinNegative-IndexMedia, 70 v CONTENTS vii viii CONTENTS 7 ObliqueIncidence 240 10 TransmissionLines 397 7.1 ObliqueIncidenceandSnel’sLaws, 240 10.1 GeneralPropertiesofTEMTransmissionLines, 397 7.2 TransverseImpedance, 242 10.2 ParallelPlateLines, 403 7.3 PropagationandMatchingofTransverseFields, 245 10.3 MicrostripLines, 404 7.4 FresnelReflectionCoefficients, 247 10.4 CoaxialLines, 408 7.5 MaximumAngleandCriticalAngle, 249 10.5 Two-WireLines, 413 7.6 BrewsterAngle, 258 10.6 DistributedCircuitModelofaTransmissionLine, 415 7.7 ComplexWaves, 260 10.7 WaveImpedanceandReflectionResponse, 417 7.8 TotalInternalReflection, 263 10.8 Two-PortEquivalentCircuit, 419 7.9 ObliqueIncidenceonaLossyMedium, 264 10.9 TerminatedTransmissionLines, 420 7.10 ZenneckSurfaceWave, 269 10.10PowerTransferfromGeneratortoLoad, 423 7.11 SurfacePlasmons, 271 10.11Open-andShort-CircuitedTransmissionLines, 425 7.12 ObliqueReflectionfromaMovingBoundary, 274 10.12StandingWaveRatio, 428 7.13 GeometricalOptics, 278 10.13DetermininganUnknownLoadImpedance, 430 7.14 Fermat’sPrinciple, 281 10.14SmithChart, 434 7.15 RayTracing, 283 10.15Time-DomainResponseofTransmissionLines, 438 7.16 Snel’sLawinNegative-IndexMedia, 294 10.16Problems, 445 7.17 Problems, 297 11 CoupledLines 456 8 MultilayerFilmApplications 302 11.1 CoupledTransmissionLines, 456 8.1 MultilayerDielectricStructuresatObliqueIncidence, 302 11.2 CrosstalkBetweenLines, 462 8.2 LossyMultilayerStructures, 304 11.3 WeaklyCoupledLineswithArbitraryTerminations, 465 8.3 SingleDielectricSlab, 306 11.4 Coupled-ModeTheory, 467 8.4 FrustratedTotalInternalReflection, 308 11.5 FiberBraggGratings, 469 8.5 SurfacePlasmonResonance, 312 11.6 DiffuseReflectionandTransmission, 472 8.6 PerfectLensinNegative-IndexMedia, 321 11.7 Problems, 474 8.7 AntireflectionCoatingsatObliqueIncidence, 329 8.8 OmnidirectionalDielectricMirrors, 332 12 ImpedanceMatching 476 8.9 PolarizingBeamSplitters, 343 8.10 ReflectionandRefractioninBirefringentMedia, 345 12.1 ConjugateandReflectionlessMatching, 476 8.11 BrewsterandCriticalAnglesinBirefringentMedia, 349 12.2 MultisectionTransmissionLines, 478 8.12 MultilayerBirefringentStructures, 352 12.3 Quarter-WavelengthChebyshevTransformers, 479 8.13 GiantBirefringentOptics, 354 12.4 Two-SectionDual-BandChebyshevTransformers, 485 8.14 Problems, 359 12.5 Quarter-WavelengthTransformerWithSeriesSection, 491 12.6 Quarter-WavelengthTransformerWithShuntStub, 494 9 Waveguides 361 12.7 Two-SectionSeriesImpedanceTransformer, 496 12.8 SingleStubMatching, 501 9.1 Longitudinal-TransverseDecompositions, 362 12.9 BalancedStubs, 505 9.2 PowerTransferandAttenuation, 367 12.10DoubleandTripleStubMatching, 507 9.3 TEM,TE,andTMmodes, 369 12.11L-SectionLumpedReactiveMatchingNetworks, 509 9.4 RectangularWaveguides, 372 12.12Pi-SectionLumpedReactiveMatchingNetworks, 512 9.5 HigherTEandTMmodes, 374 12.13ReversedMatchingNetworks, 519 9.6 OperatingBandwidth, 376 12.14Problems, 521 9.7 PowerTransfer,EnergyDensity,andGroupVelocity, 377 9.8 PowerAttenuation, 379 13 S-Parameters 525 9.9 ReflectionModelofWaveguidePropagation, 382 9.10 ResonantCavities, 384 13.1 ScatteringParameters, 525 9.11 DielectricSlabWaveguides, 386 13.2 PowerFlow, 529 9.12 Problems, 395 13.3 ParameterConversions, 530 CONTENTS ix x CONTENTS 13.4 InputandOutputReflectionCoefficients, 531 16.10SquareLoops, 657 13.5 StabilityCircles, 533 16.11DipoleandQuadrupoleRadiation, 658 13.6 PowerGains, 539 16.12Problems, 660 13.7 GeneralizedS-ParametersandPowerWaves, 545 13.8 SimultaneousConjugateMatching, 549 17 RadiationfromApertures 661 13.9 PowerGainCircles, 554 13.10UnilateralGainCircles, 555 17.1 FieldEquivalencePrinciple, 661 13.11OperatingandAvailablePowerGainCircles, 557 17.2 MagneticCurrentsandDuality, 663 13.12NoiseFigureCircles, 563 17.3 RadiationFieldsfromMagneticCurrents, 665 13.13Problems, 568 17.4 RadiationFieldsfromApertures, 666 17.5 HuygensSource, 669 14 RadiationFields 571 17.6 DirectivityandEffectiveAreaofApertures, 671 17.7 UniformApertures, 673 14.1 CurrentsandChargesasSourcesofFields, 571 17.8 RectangularApertures, 673 14.2 RetardedPotentials, 573 17.9 CircularApertures, 675 14.3 HarmonicTimeDependence, 576 17.10VectorDiffractionTheory, 678 14.4 FieldsofaLinearWireAntenna, 578 17.11ExtinctionTheorem, 682 14.5 FieldsofElectricandMagneticDipoles, 580 17.12VectorDiffractionforApertures, 684 14.6 Ewald-OseenExtinctionTheorem, 585 17.13FresnelDiffraction, 685 14.7 RadiationFields, 590 17.14Knife-EdgeDiffraction, 689 14.8 RadialCoordinates, 593 17.15GeometricalTheoryofDiffraction, 697 14.9 RadiationFieldApproximation, 595 17.16Rayleigh-SommerfeldDiffractionTheory, 703 14.10ComputingtheRadiationFields, 596 17.17Plane-WaveSpectrumRepresentation, 706 14.11Problems, 598 17.18FresnelDiffractionandFourierOptics, 711 17.19Lenses, 716 15 TransmittingandReceivingAntennas 601 17.20Problems, 722 15.1 EnergyFluxandRadiationIntensity, 601 18 ApertureAntennas 726 15.2 Directivity,Gain,andBeamwidth, 602 15.3 EffectiveArea, 607 18.1 Open-EndedWaveguides, 726 15.4 AntennaEquivalentCircuits, 611 18.2 HornAntennas, 730 15.5 EffectiveLength, 613 18.3 HornRadiationFields, 732 15.6 CommunicatingAntennas, 615 18.4 HornDirectivity, 737 15.7 AntennaNoiseTemperature, 617 18.5 HornDesign, 740 15.8 SystemNoiseTemperature, 621 18.6 MicrostripAntennas, 743 15.9 DataRateLimits, 627 18.7 ParabolicReflectorAntennas, 749 15.10SatelliteLinks, 629 18.8 GainandBeamwidthofReflectorAntennas, 751 15.11RadarEquation, 632 18.9 Aperture-FieldandCurrent-DistributionMethods, 754 15.12Problems, 634 18.10RadiationPatternsofReflectorAntennas, 757 18.11Dual-ReflectorAntennas, 766 16 LinearandLoopAntennas 637 18.12LensAntennas, 769 16.1 LinearAntennas, 637 19 AntennaArrays 771 16.2 HertzianDipole, 639 16.3 Standing-WaveAntennas, 641 19.1 AntennaArrays, 771 16.4 Half-WaveDipole, 645 19.2 TranslationalPhaseShift, 771 16.5 MonopoleAntennas, 646 19.3 ArrayPatternMultiplication, 773 16.6 Traveling-WaveAntennas, 648 19.4 One-DimensionalArrays, 783 16.7 VeeandRhombicAntennas, 650 19.5 VisibleRegion, 785 16.8 LoopAntennas, 653 19.6 GratingLobes, 787 16.9 CircularLoops, 655 19.7 UniformArrays, 789 CONTENTS xi 19.8 ArrayDirectivity, 793 23 Appendices 949 19.9 ArraySteering, 794 A PhysicalConstants, 949 19.10ArrayBeamwidth, 797 B ElectromagneticFrequencyBands, 950 19.11Problems, 799 C VectorIdentitiesandIntegralTheorems, 952 20 ArrayDesignMethods 802 D Green’sFunctions, 955 E CoordinateSystems, 958 20.1 ArrayDesignMethods, 802 F Fresnel,Exponential,Sine,andCosineIntegrals, 960 20.2 Schelkunoff’sZeroPlacementMethod, 805 G Gauss-LegendreQuadrature, 966 20.3 FourierSeriesMethodwithWindowing, 807 H LorentzTransformations, 972 20.4 SectorBeamArrayDesign, 808 I MATLABFunctions, 980 20.5 Woodward-LawsonFrequency-SamplingDesign, 812 20.6 DiscretizationofContinuousLineSources, 817 References 985 20.7 Narrow-BeamLow-SidelobeDesigns, 821 20.8 BinomialArrays, 825 Index 1033 20.9 Dolph-ChebyshevArrays, 826 20.10TaylorOne-ParameterSource, 839 20.11ProlateArray, 843 20.12TaylorLineSource, 845 20.13VilleneuveArrays, 849 20.14MultibeamArrays, 850 20.15Problems, 853 21 CurrentsonLinearAntennas 855 21.1 Hall´enandPocklingtonIntegralEquations, 855 21.2 Delta-Gap,FrillGenerator,andPlane-WaveSources, 858 21.3 SolvingHall´en’sEquation, 859 21.4 SinusoidalCurrentApproximation, 861 21.5 ReflectingandCenter-LoadedReceivingAntennas, 862 21.6 King’sThree-TermApproximation, 865 21.7 EvaluationoftheExactKernel, 872 21.8 MethodofMoments, 877 21.9 Delta-FunctionBasis, 880 21.10PulseBasis, 884 21.11TriangularBasis, 889 21.12NECSinusoidalBasis, 891 21.13Hall´en’sEquationforArbitraryIncidentField, 894 21.14SolvingPocklington’sEquation, 899 21.15Problems, 903 22 CoupledAntennas 905 22.1 NearFieldsofLinearAntennas, 905 22.2 ImprovedNear-FieldCalculation, 908 22.3 SelfandMutualImpedance, 916 22.4 CoupledTwo-ElementArrays, 922 22.5 ArraysofParallelDipoles, 925 22.6 Yagi-UdaAntennas, 934 22.7 Hall´enEquationsforCoupledAntennas, 939 22.8 Problems, 947 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: http://www.ece.rutgers.edu/~orfanidi/ewa Acknowledgements Iwouldliketothankthemanygenerationsofmystudentswhoshapedthecontentof thisbookandthefollowingpeoplefortheirfeedback, usefulcomments, andsugges- tionsforimprovement: M.Abouowf,S.Adhikari,L.Alekseyev,P.Apostolov,F.Avino,S. Bang,R.Balder-Navarro,K-S.Chen,C.Christodoulou,C.Collister,A.Dana,N.Derby,S. Diedenhofen,G.Fano,H.Fluhler,K.Foster,S.Fuhrman,J.Heebl,J.Hudson,C-IG.Hsu, R.Ianconescu,F.Innes,M.Jabbari,S.Kaul,W.G.Krische,A.Lakshmanan,R.Larice,E.M. Lau,R.Leone,M.Maybell,P.Matusov,K.T.McDonald,K.Michalski,J-S.Neron,V.Niziev, F.D.Nunes, H.Park, U.Paz, E.Perrin, A.Perrin, D.Phillips, K.Purchase, D.Ramaccia, R.Rosensweig,M.Schuh,A.Siegman,P.Simon,K.Subramanian,L.Tarof,A.Toscano, E.Tsilioukas,V.Turkovic,Y.Vives,P.Whiteneir,A.Young,C.Zarowski,andG.Zenger. Anyerrorsorshortcomingsare,ofcourse,entirelymyown. SophoclesJ.Orfanidis August2010 2 1. Maxwell’sEquations thereceivingantennas. Awayfromthesources,thatis,insource-freeregionsofspace, 1 Maxwell’sequationstakethesimplerform: ∂B ∇∇∇×E=− Maxwell’s Equations ∂t ∂D ∇∇∇×H= ∂t (source-freeMaxwell’sequations) (1.1.2) ∇∇∇·D=0 ∇∇∇·B=0 The qualitative mechanism by which Maxwell’s equations give rise to propagating electromagneticfieldsisshowninthefigurebelow. 1.1 Maxwell’s Equations Maxwell’sequationsdescribeall(classical)electromagneticphenomena: ∂B ∇∇∇×E=− ∂t For example, a time-varying current J on a linear antenna generates a circulating andtime-varyingmagneticfieldH,whichthroughFaraday’slawgeneratesacirculating ∂D ∇∇∇×H=J+ electricfieldE,whichthroughAmp`ere’slawgeneratesamagneticfield,andsoon. The ∂t (Maxwell’sequations) (1.1.1) cross-linked electric and magnetic fields propagate away from the current source. A ∇∇∇·D=ρ moreprecisediscussionofthefieldsradiatedbyalocalizedcurrentdistributionisgiven ∇∇∇·B=0 inChap.14. ThefirstisFaraday’slawofinduction,thesecondisAmp`ere’slaw asamendedby 1.2 Lorentz Force Maxwelltoincludethedisplacementcurrent∂D/∂t,thethirdandfourthareGauss’laws fortheelectricandmagneticfields. Theforceonachargeqmovingwithvelocityv inthepresenceofanelectricandmag- Thedisplacementcurrentterm∂D/∂tinAmp`ere’slawisessentialinpredictingthe neticfieldE,B iscalledtheLorentzforceandisgivenby: existenceofpropagatingelectromagneticwaves. Itsroleinestablishingchargeconser- vationisdiscussedinSec.1.7. F=q(E+v×B) (Lorentzforce) (1.2.1) Eqs. (1.1.1) are in SI units. The quantities E and H are the electric and magnetic field intensities and are measured in units of [volt/m] and [ampere/m], respectively. Newton’sequationofmotionis(fornon-relativisticspeeds): ThequantitiesDandB aretheelectricandmagneticfluxdensities andareinunitsof [coulomb/m2]and[weber/m2],or[tesla]. D isalsocalledtheelectricdisplacement,and mdv =F=q(E+v×B) (1.2.2) B,themagneticinduction. dt The quantities ρ and J are the volume charge density and electric current density wheremisthemassofthecharge. TheforceF willincreasethekineticenergyofthe (charge flux) of any external charges (that is, not including any induced polarization chargeataratethatisequaltotherateofworkdonebytheLorentzforceonthecharge, chargesandcurrents.) Theyaremeasuredinunitsof[coulomb/m3]and[ampere/m2]. thatis,v·F. Indeed,thetime-derivativeofthekineticenergyis: Theright-handsideofthefourthequationiszerobecausetherearenomagneticmono- polecharges. Eqs.(1.3.17)–(1.3.19)displaytheinducedpolarizationtermsexplicitly. Wkin= 12mv·v ⇒ dWdtkin =mv·ddvt =v·F=qv·E (1.2.3) Thechargeandcurrentdensitiesρ,J maybethoughtofasthesourcesoftheelectro- magneticfields. Forwavepropagationproblems,thesedensitiesarelocalizedinspace; Wenotethatonlytheelectricforcecontributestotheincreaseofthekineticenergy— forexample,theyarerestrictedtoflowonanantenna. Thegeneratedelectricandmag- themagneticforceremainsperpendiculartov,thatis,v·(v×B)=0. neticfieldsareradiatedawayfromthesesourcesandcanpropagatetolargedistancesto

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14.10 Computing the Radiation Fields, 596 . and fiber-optic communications, information technology, and materials science. on electromagnetic waves, which covers propagation, reflection, and transmission of . Antennas” toolbox containing 170 MATLAB functions for carrying out all of the com-.
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