Electromagnetic Waves and Antennas

406 Pages·2005·11.35 MB·English

Electromagnetic
Waves and Antennas
Electromagnetic
Waves and Antennas
To Monica and John
Sophocles J. Orfanidis
Rutgers University
viii ElectromagneticWaves&Antennas–S.J.Orfanidis–June21,2004
4 ReflectionandTransmission 86
4.1 PropagationMatrices, 86
4.2 MatchingMatrices, 90
4.3 ReflectedandTransmittedPower, 93
4.4 SingleDielectricSlab, 96
Contents
4.5 ReflectionlessSlab, 99
4.6 Time-DomainReflectionResponse, 107
4.7 TwoDielectricSlabs, 109
4.8 ReflectionbyaMovingBoundary, 111
4.9 Problems, 114
Preface xiv 5 MultilayerStructures 117
5.1 MultipleDielectricSlabs, 117
1 Maxwell’sEquations 1 5.2 AntireflectionCoatings, 119
5.3 DielectricMirrors, 124
1.1 Maxwell’sEquations, 1
5.4 PropagationBandgaps, 135
1.2 LorentzForce, 2
5.5 Narrow-BandTransmissionFilters, 135
1.3 ConstitutiveRelations, 3
5.6 EqualTravel-TimeMultilayerStructures, 140
1.4 BoundaryConditions, 6
5.7 ApplicationsofLayeredStructures, 154
1.5 Currents,Fluxes,andConservationLaws, 8
5.8 ChebyshevDesignofReflectionlessMultilayers, 157
1.6 ChargeConservation, 9
5.9 Problems, 165
1.7 EnergyFluxandEnergyConservation, 10
1.8 HarmonicTimeDependence, 12
6 ObliqueIncidence 168
1.9 SimpleModelsofDielectrics,Conductors,andPlasmas, 13
1.10 Problems, 21 6.1 ObliqueIncidenceandSnell’sLaws, 168
6.2 TransverseImpedance, 170
2 UniformPlaneWaves 25 6.3 PropagationandMatchingofTransverseFields, 173
6.4 FresnelReflectionCoefficients, 175
2.1 UniformPlaneWavesinLosslessMedia, 25
6.5 TotalInternalReflection, 177
2.2 MonochromaticWaves, 31
6.6 BrewsterAngle, 183
2.3 EnergyDensityandFlux, 34
6.7 ComplexWaves, 186
2.4 WaveImpedance, 35
6.8 ObliqueReflectionbyaMovingBoundary, 196
2.5 Polarization, 35
6.9 GeometricalOptics, 199
2.6 UniformPlaneWavesinLossyMedia, 42
6.10 Fermat’sPrinciple, 202
2.7 PropagationinWeaklyLossyDielectrics, 48
6.11 RayTracing, 204
2.8 PropagationinGoodConductors, 49
6.12 Problems, 215
2.9 PropagationinObliqueDirections, 50
2.10 ComplexorInhomogeneousWaves, 53
7 MultilayerFilmApplications 217
2.11 DopplerEffect, 55
2.12 Problems, 59 7.1 MultilayerDielectricStructuresatObliqueIncidence, 217
7.2 LossyMultilayerStructures, 219
3 PropagationinBirefringentMedia 65 7.3 SingleDielectricSlab, 221
7.4 AntireflectionCoatingsatObliqueIncidence, 223
3.1 LinearandCircularBirefringence, 65
7.5 OmnidirectionalDielectricMirrors, 227
3.2 UniaxialandBiaxialMedia, 66
7.6 PolarizingBeamSplitters, 237
3.3 ChiralMedia, 68
7.7 ReflectionandRefractioninBirefringentMedia, 240
3.4 GyrotropicMedia, 71
7.8 BrewsterandCriticalAnglesinBirefringentMedia, 244
3.5 LinearandCircularDichroism, 72
7.9 MultilayerBirefringentStructures, 247
3.6 ObliquePropagationinBirefringentMedia, 73
7.10 GiantBirefringentOptics, 249
3.7 Problems, 80
vii
www.ece.rutgers.edu/∼orfanidi/ewa ix x ElectromagneticWaves&Antennas–S.J.Orfanidis–June21,2004
7.11 Problems, 254 11.4 Two-SectionDual-BandChebyshevTransformers, 375
11.5 Quarter-WavelengthTransformerWithSeriesSection, 381
8 Waveguides 255 11.6 Quarter-WavelengthTransformerWithShuntStub, 384
11.7 Two-SectionSeriesImpedanceTransformer, 386
8.1 Longitudinal-TransverseDecompositions, 256 11.8 SingleStubMatching, 391
8.2 PowerTransferandAttenuation, 261 11.9 BalancedStubs, 395
8.3 TEM,TE,andTMmodes, 263 11.10DoubleandTripleStubMatching, 397
8.4 RectangularWaveguides, 266 11.11L-SectionLumpedReactiveMatchingNetworks, 399
8.5 HigherTEandTMmodes, 268 11.12Pi-SectionLumpedReactiveMatchingNetworks, 402
8.6 OperatingBandwidth, 270 11.13ReversedMatchingNetworks, 409
8.7 PowerTransfer,EnergyDensity,andGroupVelocity, 271 11.14Problems, 411
8.8 PowerAttenuation, 273
8.9 ReflectionModelofWaveguidePropagation, 276 12 S-Parameters 413
8.10 ResonantCavities, 278
8.11 DielectricSlabWaveguides, 280 12.1 ScatteringParameters, 413
8.12 Problems, 288 12.2 PowerFlow, 417
12.3 ParameterConversions, 418
9 TransmissionLines 290 12.4 InputandOutputReflectionCoefficients, 419
12.5 StabilityCircles, 421
9.1 GeneralPropertiesofTEMTransmissionLines, 290 12.6 PowerGains, 427
9.2 ParallelPlateLines, 296 12.7 GeneralizedS-ParametersandPowerWaves, 433
9.3 MicrostripLines, 297 12.8 SimultaneousConjugateMatching, 437
9.4 CoaxialLines, 301 12.9 PowerGainCircles, 442
9.5 Two-WireLines, 306 12.10UnilateralGainCircles, 443
9.6 DistributedCircuitModelofaTransmissionLine, 308 12.11OperatingandAvailablePowerGainCircles, 445
9.7 WaveImpedanceandReflectionResponse, 310 12.12NoiseFigureCircles, 451
9.8 Two-PortEquivalentCircuit, 312 12.13Problems, 456
9.9 TerminatedTransmissionLines, 313
9.10 PowerTransferfromGeneratortoLoad, 316 13 RadiationFields 458
9.11 Open-andShort-CircuitedTransmissionLines, 318
9.12 StandingWaveRatio, 321 13.1 CurrentsandChargesasSourcesofFields, 458
9.13 DetermininganUnknownLoadImpedance, 323 13.2 RetardedPotentials, 460
9.14 SmithChart, 327 13.3 HarmonicTimeDependence, 463
9.15 Time-DomainResponseofTransmissionLines, 331 13.4 FieldsofaLinearWireAntenna, 465
9.16 Problems, 338 13.5 FieldsofElectricandMagneticDipoles, 467
13.6 Ewald-OseenExtinctionTheorem, 472
10 CoupledLines 347 13.7 RadiationFields, 477
13.8 RadialCoordinates, 480
10.1 CoupledTransmissionLines, 347 13.9 RadiationFieldApproximation, 482
10.2 CrosstalkBetweenLines, 353 13.10ComputingtheRadiationFields, 483
10.3 WeaklyCoupledLineswithArbitraryTerminations, 356 13.11Problems, 485
10.4 Coupled-ModeTheory, 358
10.5 FiberBraggGratings, 360 14 TransmittingandReceivingAntennas 488
10.6 DiffuseReflectionandTransmission, 363
10.7 Problems, 365 14.1 EnergyFluxandRadiationIntensity, 488
14.2 Directivity,Gain,andBeamwidth, 489
11 ImpedanceMatching 366 14.3 EffectiveArea, 494
14.4 AntennaEquivalentCircuits, 498
11.1 ConjugateandReflectionlessMatching, 366 14.5 EffectiveLength, 500
11.2 MultisectionTransmissionLines, 368 14.6 CommunicatingAntennas, 502
11.3 Quarter-WavelengthChebyshevTransformers, 369 14.7 AntennaNoiseTemperature, 504
www.ece.rutgers.edu/∼orfanidi/ewa xi xii ElectromagneticWaves&Antennas–S.J.Orfanidis–June21,2004
14.8 SystemNoiseTemperature, 508 17.10RadiationPatternsofReflectorAntennas, 618
14.9 DataRateLimits, 514 17.11Dual-ReflectorAntennas, 627
14.10SatelliteLinks, 516 17.12LensAntennas, 630
14.11RadarEquation, 519 17.13Problems, 631
14.12Problems, 521
18 AntennaArrays 632
15 LinearandLoopAntennas 522
18.1 AntennaArrays, 632
15.1 LinearAntennas, 522 18.2 TranslationalPhaseShift, 632
15.2 HertzianDipole, 524 18.3 ArrayPatternMultiplication, 634
15.3 Standing-WaveAntennas, 526 18.4 One-DimensionalArrays, 644
15.4 Half-WaveDipole, 528 18.5 VisibleRegion, 646
15.5 MonopoleAntennas, 530 18.6 GratingLobes, 647
15.6 Traveling-WaveAntennas, 531 18.7 UniformArrays, 650
15.7 VeeandRhombicAntennas, 534 18.8 ArrayDirectivity, 654
15.8 LoopAntennas, 537 18.9 ArraySteering, 655
15.9 CircularLoops, 539 18.10ArrayBeamwidth, 657
15.10SquareLoops, 540 18.11Problems, 659
15.11DipoleandQuadrupoleRadiation, 541
15.12Problems, 543 19 ArrayDesignMethods 661
16 RadiationfromApertures 544 19.1 ArrayDesignMethods, 661
19.2 Schelkunoff’sZeroPlacementMethod, 664
16.1 FieldEquivalencePrinciple, 544 19.3 FourierSeriesMethodwithWindowing, 666
16.2 MagneticCurrentsandDuality, 546 19.4 SectorBeamArrayDesign, 667
16.3 RadiationFieldsfromMagneticCurrents, 548 19.5 Woodward-LawsonFrequency-SamplingDesign, 672
16.4 RadiationFieldsfromApertures, 549 19.6 Narrow-BeamLow-SidelobeDesigns, 676
16.5 HuygensSource, 552 19.7 BinomialArrays, 680
16.6 DirectivityandEffectiveAreaofApertures, 554 19.8 Dolph-ChebyshevArrays, 682
16.7 UniformApertures, 556 19.9 Taylor-KaiserArrays, 694
16.8 RectangularApertures, 556 19.10MultibeamArrays, 697
16.9 CircularApertures, 558 19.11Problems, 700
16.10VectorDiffractionTheory, 561
16.11ExtinctionTheorem, 565 20 CurrentsonLinearAntennas 701
16.12VectorDiffractionforApertures, 567
16.13FresnelDiffraction, 568 20.1 Hall´enandPocklingtonIntegralEquations, 701
16.14Knife-EdgeDiffraction, 572 20.2 Delta-GapandPlane-WaveSources, 704
16.15GeometricalTheoryofDiffraction, 578 20.3 SolvingHall´en’sEquation, 705
16.16Problems, 584 20.4 SinusoidalCurrentApproximation, 707
20.5 ReflectingandCenter-LoadedReceivingAntennas, 708
17 ApertureAntennas 587 20.6 King’sThree-TermApproximation, 711
20.7 NumericalSolutionofHall´en’sEquation, 715
17.1 Open-EndedWaveguides, 587 20.8 NumericalSolutionUsingPulseFunctions, 718
17.2 HornAntennas, 591 20.9 NumericalSolutionforArbitraryIncidentField, 722
17.3 HornRadiationFields, 593 20.10NumericalSolutionofPocklington’sEquation, 724
17.4 HornDirectivity, 598 20.11Problems, 730
17.5 HornDesign, 601
17.6 MicrostripAntennas, 604
17.7 ParabolicReflectorAntennas, 610
17.8 GainandBeamwidthofReflectorAntennas, 612
17.9 Aperture-FieldandCurrent-DistributionMethods, 615
www.ece.rutgers.edu/∼orfanidi/ewa xiii
21 CoupledAntennas 731
21.1 NearFieldsofLinearAntennas, 731
21.2 SelfandMutualImpedance, 734
21.3 CoupledTwo-ElementArrays, 738
21.4 ArraysofParallelDipoles, 741
Preface
21.5 Yagi-UdaAntennas, 750
21.6 Hall´enEquationsforCoupledAntennas, 755
21.7 Problems, 762
22 Appendices 764
A PhysicalConstants, 764
Thistextprovidesabroadandapplications-orientedintroductiontoelectromagnetic
B ElectromagneticFrequencyBands, 765
wavesandantennas. Currentinterestintheseareasisdrivenbythegrowthinwireless
C VectorIdentitiesandIntegralTheorems, 767
andfiber-opticcommunications,informationtechnology,andmaterialsscience.
D Green’sFunctions, 770
Communications,antenna,radar,andmicrowaveengineersmustdealwiththegener-
E CoordinateSystems, 773
ation,transmission,andreceptionofelectromagneticwaves. Deviceengineersworking
F FresnelIntegrals, 775
G LorentzTransformations, 778 onever-smallerintegratedcircuitsandateverhigherfrequenciesmusttakeintoaccount
H MATLABFunctions, 785 wavepropagationeffectsatthechipandcircuit-boardlevels. Communicationandcom-
puternetworkengineersroutinelyusewaveguidingsystems,suchastransmissionlines
References 790 andopticalfibers. Novelrecentdevelopmentsinmaterials,suchasphotonicbandgap
structures,omnidirectionaldielectricmirrors,andbirefringentmultilayerfilms,promise
arevolutioninthecontrolandmanipulationoflight. Thesearejustsomeexamplesof
Index 820
topicsdiscussedinthisbook. Thetextisorganizedaroundthreemaintopicareas:
• The propagation, reflection, and transmission of plane waves, and the analysis
anddesignofmultilayerfilms.
• Waveguides,transmissionlines,impedancematching,andS-parameters.
• Linearandapertureantennas,scalarandvectordiffractiontheory,antennaarray
design,andcoupledantennas.
Thetextemphasizesconnectionstoothersubjects. Forexample,themathematical
techniquesforanalyzingwavepropagationinmultilayerstructuresandthedesignof
multilayeropticalfiltersarethesameasthoseusedindigitalsignalprocessing, such
asthelatticestructuresoflinearprediction,theanalysisandsynthesisofspeech,and
geophysical signal processing. Similarly, antenna array design is related to the prob-
lemofspectralanalysisofsinusoidsandtodigitalfilterdesign,andButlerbeamsare
equivalenttotheFFT.
Use
Thebookisappropriateforfirst-yeargraduateorseniorundergraduatestudents. There
isenoughmaterialinthebookforatwo-semestercoursesequence. Thebookcanalso
beusedbypracticingengineersandscientistswhowantaquickreviewthatcoversmost
ofthebasicconceptsandincludesmanyapplicationexamples.
Thebookisbasedonlecturenotesforafirst-yeargraduatecourseon“Electromag-
neticWavesandRadiation”thatIhavebeenteachingatRutgersoverthepasttwenty
xiv
www.ece.rutgers.edu/∼orfanidi/ewa xv xvi ElectromagneticWaves&Antennas–S.J.Orfanidis–June21,2004
years. Thecoursedrawsstudentsfromavarietyoffields,suchassolid-statedevices, inhomogeneousmedia. Wepresentseveralexactlysolvableray-tracingexamplesdrawn
wirelesscommunications,fiberoptics,abiomedicalengineering,anddigitalsignaland fromapplicationssuchasatmosphericrefraction,mirages,ionosphericrefraction,prop-
arrayprocessing. Undergraduateseniorshavealsoattendedthegraduatecoursesuc- agationinastandardatmosphere, theeffectofEarth’scurvature, andpropagationin
cessfully. graded-indexopticalfibers.
Thebookrequiresaprerequisitecourseonelectromagnetics,typicallyofferedatthe Weapplythetransfermatrixapproachtotheanalysisanddesignofomnidirectional
junioryear.Suchintroductorycourseisusuallyfollowedbyasenior-levelelectivecourse dielectricmirrorsandpolarizingbeamsplitters. Wediscussreflectionandrefractionin
on electromagnetic waves, which covers propagation, reflection, and transmission of birefringentmedia,birefringentmultilayerfilms,andgiantbirefringentoptics.
waves,waveguides,transmissionlines,andperhapssomeantennas. Thisbookmaybe Chapters8–10dealwithwaveguidingsystems. Webeginwiththedecompositionof
usedinsuchelectivecourseswiththeappropriateselectionofchapters. Maxwell’sequationsintolongitudinalandtransversecomponentsandfocusprimarily
At the graduate level, there is usually an introductory course that covers waves, on rectangular waveguides, resonant cavities, and dielectric slab guides. We discuss
guides, lines, and antennas, and this is followed by more specialized courses on an- issues regarding the operating bandwidth, group velocity, power transfer, and ohmic
tennadesign,microwavesystemsanddevices,opticalfibers,andnumericaltechniques losses. Then, we go on to discuss various types of TEM transmission lines, such as
in electromagnetics. No single book can possibly cover all of the advanced courses. parallelplateandmicrostrip,coaxial,andparallel-wirelines.
Thisbookmaybeusedasatextintheinitialcourse,andasasupplementarytextinthe Weconsidergeneralpropertiesoflines,suchaswaveimpedanceandreflectionre-
specializedcourses. sponse, howtoanalyzeterminatedlinesandcomputepowertransferfromgenerator
to load, matched-line and reflection losses, Th´evenin and Norton equivalent circuits,
standingwaveratios,determiningunknownloadimpedances,theSmithchart,andthe
ContentsandHighlights
transientbehavioroflines.
Inthefirstfourchapters,wereviewMaxwell’sequations,boundaryconditions,charge Wediscusscoupledlines,developtheeven-oddmodedecompositionforidentical
and energy conservation, and simple models of dielectrics, conductors, and plasmas, matched or unmatched lines, and derive the crosstalk coefficients. The problem of
anddiscussuniformplanewavepropagationinvarioustypesofmedia,suchaslossless, crosstalkonweakly-couplednon-identicallineswitharbitraryterminationsissolvedin
lossy,isotropic,birefringent,andchiralmedia. Weintroducethemethodsoftransfer general. Wepresentalsoashortintroductiontocoupled-modetheory, co-directional
and matching matrices for analyzing propagation, reflection, and transmission prob- couplers,fiberBragggratingsasexamplesofcontra-directionalcouplers,andquarter-
lems. Suchmethodsareusedextensivelylateron. wave phase-shifted fiber Bragg gratings as narrow-band transmission filters. We also
Inchapterfiveonmultilayerstructures,wedevelopatransfermatrixapproachto presentbrieflytheSchuster-Kubelka-Munktheoryofdiffusereflectionandtransmission
the reflection and transmission through a multilayer dielectric stack and apply it to asanexampleofcontra-directionalcoupling.
antireflectioncoatings. Wediscussdielectricmirrorsconstructedfromperiodicmulti- Chapters11and12discussimpedancematchingandS-parametertechniques. Sev-
layers,introducetheconceptsofBlochwavenumberandreflectionbands,anddevelop eralmatchingmethodsareincluded,suchaswidebandmulti-sectionquarter-wavelength
analyticalandnumericalmethodsforthecomputationofreflectionbandwidthsandof impedancetransformers,two-sectiondual-bandtransformers,quarter-wavelengthtrans-
the frequency response. We discuss the connection to the new field of photonic and formerswithseriessectionsorwithshuntstubs,two-sectiontransformers,single-stub
otherbandgapstructures. Weconsidertheapplicationofquarter-wavephase-shifted tuners, balanced stubs, double- and triple-stub tuners, L-, T-, and Π-section lumped
Fabry-Perotresonatorstructuresinthedesignofnarrow-bandtransmissionfiltersfor reactivematchingnetworksandtheirQ-factors.
densewavelength-divisionmultiplexingapplications. WehaveincludedanintroductiontoS-parametersbecauseoftheirwidespreaduse
Wediscussequaltravel-timemultilayerstructures,developtheforwardandback- inmicrowavemeasurementsandinthedesignofmicrowavecircuits. Wediscusspower
wardlatticerecursionsforcomputingthereflectionandtransmissionresponses, and flow,parameterconversions,inputandoutputreflectioncoefficients,stabilitycircles,
maketheconnectiontosimilarlatticestructuresinotherfields,suchasinlinearpre- powergaindefinitions(transducer,operating,andavailablegains),powerwavesandgen-
diction and speech processing. We apply the equal travel-time analysis to the design eralizedS-parameters,simultaneousconjugatematching,powergainandnoise-figure
ofquarter-wavelengthChebyshevreflectionlessmultilayers. Suchdesignsarealsoused circles on the Smith chart and their uses in designing low-noise high-gain microwave
laterinmulti-sectionquarter-wavelengthtransmissionlinetransformers. Thedesigns amplifiers.
areexactandnotbasedonthesmall-reflection-coefficientapproximationthatisusually Therestofthebookdealswithradiationandantennas. Inchapters13and14,we
madeintheliterature. considerthegenerationofradiationfieldsfromchargeandcurrentdistributions. We
Inchapterssixandseven,wediscussobliqueincidenceconceptsandapplications, introducetheLorenz-gaugescalarandvectorpotentialsandsolvetheresultinginhomo-
suchasSnell’slaws,TEandTMpolarizations,transverseimpedances,transversetrans- geneousHelmholtzequations. Weillustratethevectorpotentialformalismwiththree
fermatrices,Fresnelreflectioncoefficients,totalinternalreflectionandBrewsterangles. applications: (a)thefieldsgeneratedbyalinearwireantenna,(b)thenearandfarfields
Thereisabriefintroductionofhowgeometricalopticsarisesfromwavepropagation ofelectricandmagneticdipoles,and(c)theEwald-Oseenextinctiontheoremofmolec-
inthehigh-frequencylimit. Fermat’sprincipleisappliedtoderivetherayequationsin
www.ece.rutgers.edu/∼orfanidi/ewa xvii xviii ElectromagneticWaves&Antennas–S.J.Orfanidis–June21,2004
ular optics. Then, we derive the far-field approximation for the radiation fields and mulas,wedevelopasystematicmethodfordesigningsector-beampatterns—aproblem
introducetheradiationvector. equivalenttodesigningabandpassFIRfilter. WeapplytheWoodward-Lawsonmethod
Wediscussgeneralcharacteristicsoftransmittingandreceivingantennas,suchas to the design of shaped-beam patterns. We view the problem of designing narrow-
energy flux and radiation intensity, directivity, gain, beamwidth, effective area, gain- beamlow-sidelobearraysasequivalenttotheproblemofspectralanalysisofsinusoids.
beamwidthproduct,antennaequivalentcircuits,effectivelength,polarizationandload Choosingdifferentwindowfunctions,wearriveatbinomial,Dolph-Chebyshev,andTay-
mismatches, communicating antennas and Friis formula, antenna noise temperature, lor arrays. We also discuss multi-beam arrays, Butler matrices and beams, and their
systemnoisetemperature,limitsonbitrates,powerbudgetsofsatellitelinks,andthe connectiontotheFFT.
radarequation. Inchapters20and21,weundertakeamoreprecisestudyofthecurrentsflowing
Chapter15isanintroductiontolinearandloopantennas. StartingwiththeHertzian onalinearantennaanddeveloptheHall´enandPocklingtonintegralequationsforthis
dipole,wepresentstanding-waveantennas,thehalf-wavedipole,monopoleantennas, problem. The nature of the sinusoidal current approximation and its generalizations
traveling wave antennas, vee and rhombic antennas, circular and square loops, and byKingarediscussed,andcomparedwiththeexactnumericalsolutionsoftheintegral
dipoleandquadrupleradiationingeneral. equations. Wediscusscoupledantennas,definethemutualimpedancematrix,anduse
Chapters 16 and 17 deal with radiation from apertures. We start with the field ittoobtainsimplesolutionsforseveralexamples,suchasYagi-Udaandotherparasitic
equivalenceprincipleandtheequivalentsurfaceelectricandmagneticcurrentsgiven ordrivenarrays. Wealsoconsidertheproblemofsolvingthecoupledintegralequations
intermsoftheaperturefields,andextendthefar-fieldapproximationtoincludemag- foranarrayofparalleldipoles,implementitwithMATLAB,andcomparetheexactresults
netic current sources, leading eventually to Kottler’s formulas for the fields radiated withthosebasedontheimpedancematrixapproach.
fromapertures. Dualitytransformationssimplifythediscussions. Thespecialcasesof OurMATLAB-basednumericalsolutionsarenotmeanttoreplacesophisticatedcom-
uniformrectangularandcircularaperturesarediscussedindetail. mercialfieldsolvers. Theinclusionofnumericalmethodsinthisbookwasmotivated
Then, we embark on a long justification of the field equivalent principle and the by the desire to provide the reader with some simple tools for self-study and experi-
derivationoftheStratton-ChuandKottler-Franzformulas,anddiscussvectordiffrac- mentation. Thestudyofnumericalmethodsinelectromagneticsisasubjectinitself
tiontheory. Thismaterialisratherdifficultbutwehavebrokendownthederivations andourtreatmentdoesnotdojusticetoit. However,wefeltthatitwouldbefuntobe
intologicalstepsusingseveralvectoranalysisidentitiesfromtheappendix. Oncethe abletoquicklycomputefairlyaccurateradiationpatternsofYagi-Udaandothercoupled
ramificationsoftheKottlerformulasarediscussed,weapproximatetheformulaswith antennas,aswellasradiationpatternsofhornandreflectorantennas.
theconventionalKirchhoffdiffractionintegralsanddiscussthescalartheoryofdiffrac- Theappendixincludessummariesofphysicalconstants,electromagneticfrequency
tion. WeconsiderFresneldiffractionthroughaperturesandknife-edgediffractionand bands,vectoridentities,integraltheorems,Green’sfunctions,coordinatesystems,Fres-
presentanintroductiontothegeometricaltheoryofdiffractionthroughSommerfeld’s nelintegrals,andadetailedlistoftheMATLABfunctions. Finally,thereisalarge(but
exactsolutionofdiffractionbyaconductinghalf-plane. inevitably incomplete) list of references, arranged by topic area, that we hope could
We apply the aperture radiation formulas to various types of aperture antennas, serveasastartingpointforfurtherstudy.
suchasopen-endedwaveguides,horns,microstripantennas,andparabolicreflectors.
Wepresentacomputationalapproachforthecalculationofhornradiationpatternsand
MATLABToolbox
optimumhorndesign. Weconsiderparabolicreflectorsinsomedetail,discussingthe
aperture-field and current-distribution methods, reflector feeds, gain and beamwidth ThetextmakesextensiveuseofMATLAB.Wehavedevelopedan“ElectromagneticWaves
properties, and numerical computations of the radiation patterns. We also discuss &Antennas”toolboxcontaining130MATLABfunctionsforcarryingoutallofthecom-
brieflydual-reflectorandlensantennas. putations and simulation examples in the text. Code segments illustrating the usage
Chapters18and19discussantennaarrays. Westartwiththeconceptofthearray of these functions are found throughout the book, and serve as a user manual. The
factor,whichdeterminestheangularpatternofthearray. Weemphasizetheconnection functionsmaybegroupedintothefollowingcategories:
toDSPandviewthearrayfactorasthespatialequivalentofthetransferfunctionofan
FIRdigitalfilter. Weintroducebasicarrayconcepts,suchasthevisibleregion,grating 1. Design and analysis of multilayer film structures, including antireflection coat-
lobes,directivity,beamwidth,arrayscanningandsteering,anddiscusstheproperties ings,polarizers,omnidirectionalmirrors,narrow-bandtransmissionfilters,bire-
of uniform arrays. We present several array design methods for achieving a desired fringentmultilayerfilmsandgiantbirefringentoptics.
angular radiation pattern, such as Schelkunoff’s zero-placement method, the Fourier 2. Designofquarter-wavelengthimpedancetransformersandotherimpedancematch-
seriesmethodwithwindowing,anditsvariant,theWoodward-Lawsonmethod,known ingmethods,suchasChebyshevtransformers,dual-bandtransformers,stubmatch-
inDSPasthefrequency-samplingmethod. ingandL-,Π-andT-sectionreactivematchingnetworks.
Theissuesofproperlychoosingawindowfunctiontoachievedesiredpassbandand 3. Designandanalysisoftransmissionlinesandwaveguides,suchasmicrostriplines
stopbandcharacteristicsarediscussed. WeemphasizetheuseoftheTaylor-Kaiserwin- anddielectricslabguides.
dow,whichallowsthecontrolofthestopbandattenuation. UsingKaiser’sempiricalfor-
www.ece.rutgers.edu/∼orfanidi/ewa xix
4. S-parameter functions for gain computations, Smith chart generation, stability,
gain,andnoise-figurecircles,simultaneousconjugatematching,andmicrowave
amplifierdesign.
5. Functionsforthecomputationofdirectivitiesandgainpatternsoflinearantennas,
suchasdipole,vee,rhombic,andtraveling-waveantennas.
6. Aperture antenna functions for open-ended waveguides, horn antenna design,
diffractionintegrals,andknife-edgediffractioncoefficients.
7. Antennaarraydesignfunctionsforuniform,binomial,Dolph-Chebyshev,Taylor
arrays,sector-beam,multi-beam,Woodward-Lawson,andButlerarrays. Functions
forbeamwidthanddirectivitycalculations,andforsteeringandscanningarrays.
8. NumericalmethodsforsolvingtheHall´enandPocklingtonintegralequationsfor
singleandcoupledantennasandcomputingselfandmutualimpedances.
9. Severalfunctionsformakingazimuthalandpolarplotsofantennaandarraygain
patternsindecibelsandabsoluteunits.
10. TherearealsoseveralMATLABmoviesshowingthepropagationofstepsignals
andpulsesonterminatedtransmissionlines;thepropagationoncascadedlines;
stepsignalsgettingreflectedfromreactiveterminations; faultlocationbyTDR;
crosstalksignalspropagatingoncoupledlines;andthetime-evolutionofthefield
linesradiatedbyaHertziandipole.
TheMATLABfunctionsaswellasotherinformationaboutthebookmaybedown-
loadedfromthewebpage: www.ece.rutgers.edu/~orfanidi/ewa.
Acknowledgements
SophoclesJ.Orfanidis
April2003
viii ElectromagneticWaves&Antennas–S.J.Orfanidis–June21,2004
4 ReflectionandTransmission 86
4.1 PropagationMatrices, 86
4.2 MatchingMatrices, 90
4.3 ReflectedandTransmittedPower, 93
4.4 SingleDielectricSlab, 96
Contents
4.5 ReflectionlessSlab, 99
4.6 Time-DomainReflectionResponse, 107
4.7 TwoDielectricSlabs, 109
4.8 ReflectionbyaMovingBoundary, 111
4.9 Problems, 114
Preface xiv 5 MultilayerStructures 117
5.1 MultipleDielectricSlabs, 117
1 Maxwell’sEquations 1 5.2 AntireflectionCoatings, 119
5.3 DielectricMirrors, 124
1.1 Maxwell’sEquations, 1
5.4 PropagationBandgaps, 135
1.2 LorentzForce, 2
5.5 Narrow-BandTransmissionFilters, 135
1.3 ConstitutiveRelations, 3
5.6 EqualTravel-TimeMultilayerStructures, 140
1.4 BoundaryConditions, 6
5.7 ApplicationsofLayeredStructures, 154
1.5 Currents,Fluxes,andConservationLaws, 8
5.8 ChebyshevDesignofReflectionlessMultilayers, 157
1.6 ChargeConservation, 9
5.9 Problems, 165
1.7 EnergyFluxandEnergyConservation, 10
1.8 HarmonicTimeDependence, 12
6 ObliqueIncidence 168
1.9 SimpleModelsofDielectrics,Conductors,andPlasmas, 13
1.10 Problems, 21 6.1 ObliqueIncidenceandSnell’sLaws, 168
6.2 TransverseImpedance, 170
2 UniformPlaneWaves 25 6.3 PropagationandMatchingofTransverseFields, 173
6.4 FresnelReflectionCoefficients, 175
2.1 UniformPlaneWavesinLosslessMedia, 25
6.5 TotalInternalReflection, 177
2.2 MonochromaticWaves, 31
6.6 BrewsterAngle, 183
2.3 EnergyDensityandFlux, 34
6.7 ComplexWaves, 186
2.4 WaveImpedance, 35
6.8 ObliqueReflectionbyaMovingBoundary, 196
2.5 Polarization, 35
6.9 GeometricalOptics, 199
2.6 UniformPlaneWavesinLossyMedia, 42
6.10 Fermat’sPrinciple, 202
2.7 PropagationinWeaklyLossyDielectrics, 48
6.11 RayTracing, 204
2.8 PropagationinGoodConductors, 49
6.12 Problems, 215
2.9 PropagationinObliqueDirections, 50
2.10 ComplexorInhomogeneousWaves, 53
7 MultilayerFilmApplications 217
2.11 DopplerEffect, 55
2.12 Problems, 59 7.1 MultilayerDielectricStructuresatObliqueIncidence, 217
7.2 LossyMultilayerStructures, 219
3 PropagationinBirefringentMedia 65 7.3 SingleDielectricSlab, 221
7.4 AntireflectionCoatingsatObliqueIncidence, 223
3.1 LinearandCircularBirefringence, 65
7.5 OmnidirectionalDielectricMirrors, 227
3.2 UniaxialandBiaxialMedia, 66
7.6 PolarizingBeamSplitters, 237
3.3 ChiralMedia, 68
7.7 ReflectionandRefractioninBirefringentMedia, 240
3.4 GyrotropicMedia, 71
7.8 BrewsterandCriticalAnglesinBirefringentMedia, 244
3.5 LinearandCircularDichroism, 72
7.9 MultilayerBirefringentStructures, 247
3.6 ObliquePropagationinBirefringentMedia, 73
7.10 GiantBirefringentOptics, 249
3.7 Problems, 80
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