Electromagnetic Waves and Antennas

537 Pages·2012·10.56 MB·English

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