Electromagnetic Waves and Antennas

419 Pages·2016·22.7 MB·English

by  Sophocles J.Orfanidis

Electromagnetic
Waves and Antennas
Electromagnetic
Waves and Antennas
To Monica and John
Sophocles J. Orfanidis
Rutgers University
viii ElectromagneticWaves&Antennas–S.J.Orfanidis–Feb. 28,2004
4 ReflectionandTransmission 81
4.1 PropagationMatrices, 81
4.2 MatchingMatrices, 85
4.3 ReflectedandTransmittedPower, 88
4.4 SingleDielectricSlab, 91
Contents
4.5 ReflectionlessSlab, 94
4.6 Time-DomainReflectionResponse, 102
4.7 TwoDielectricSlabs, 104
4.8 Problems, 106
5 MultilayerStructures 109
Preface viii
5.1 MultipleDielectricSlabs, 109
5.2 AntireflectionCoatings, 111
1 Maxwell’sEquations 1 5.3 DielectricMirrors, 116
5.4 PropagationBandgaps, 127
1.1 Maxwell’sEquations, 1
5.5 Narrow-BandTransmissionFilters, 127
1.2 LorentzForce, 2
5.6 EqualTravel-TimeMultilayerStructures, 132
1.3 ConstitutiveRelations, 3
5.7 ApplicationsofLayeredStructures, 146
1.4 BoundaryConditions, 6
5.8 ChebyshevDesignofReflectionlessMultilayers, 149
1.5 Currents,Fluxes,andConservationLaws, 8
5.9 Problems, 157
1.6 ChargeConservation, 9
1.7 EnergyFluxandEnergyConservation, 10
6 ObliqueIncidence 160
1.8 HarmonicTimeDependence, 12
1.9 SimpleModelsofDielectrics,Conductors,andPlasmas, 13 6.1 ObliqueIncidenceandSnell’sLaws, 160
1.10 Problems, 21 6.2 TransverseImpedance, 162
6.3 PropagationandMatchingofTransverseFields, 165
2 UniformPlaneWaves 25 6.4 FresnelReflectionCoefficients, 167
6.5 TotalInternalReflection, 169
2.1 UniformPlaneWavesinLosslessMedia, 25
6.6 BrewsterAngle, 175
2.2 MonochromaticWaves, 31
6.7 ComplexWaves, 178
2.3 EnergyDensityandFlux, 34
6.8 GeometricalOptics, 188
2.4 WaveImpedance, 35
6.9 Fermat’sPrinciple, 190
2.5 Polarization, 35
6.10 RayTracing, 192
2.6 UniformPlaneWavesinLossyMedia, 42
6.11 Problems, 203
2.7 PropagationinWeaklyLossyDielectrics, 48
2.8 PropagationinGoodConductors, 49
7 MultilayerFilmApplications 205
2.9 PropagationinObliqueDirections, 50
2.10 ComplexorInhomogeneousWaves, 53 7.1 MultilayerDielectricStructuresatObliqueIncidence, 205
2.11 Problems, 55 7.2 LossyMultilayerStructures, 207
7.3 SingleDielectricSlab, 209
3 PropagationinBirefringentMedia 60 7.4 AntireflectionCoatingsatObliqueIncidence, 211
7.5 OmnidirectionalDielectricMirrors, 215
3.1 LinearandCircularBirefringence, 60
7.6 PolarizingBeamSplitters, 225
3.2 UniaxialandBiaxialMedia, 61
7.7 ReflectionandRefractioninBirefringentMedia, 228
3.3 ChiralMedia, 63
7.8 BrewsterandCriticalAnglesinBirefringentMedia, 232
3.4 GyrotropicMedia, 66
7.9 MultilayerBirefringentStructures, 235
3.5 LinearandCircularDichroism, 67
7.10 GiantBirefringentOptics, 237
3.6 ObliquePropagationinBirefringentMedia, 68
7.11 Problems, 242
3.7 Problems, 75
vii
www.ece.rutgers.edu/∼orfanidi/ewa ix x ElectromagneticWaves&Antennas–S.J.Orfanidis–Feb. 28,2004
8 Waveguides 243 11.6 Quarter-WavelengthTransformerWithShuntStub, 372
11.7 Two-SectionSeriesImpedanceTransformer, 374
8.1 Longitudinal-TransverseDecompositions, 244
11.8 SingleStubMatching, 379
8.2 PowerTransferandAttenuation, 249
11.9 BalancedStubs, 383
8.3 TEM,TE,andTMmodes, 251
11.10DoubleandTripleStubMatching, 385
8.4 RectangularWaveguides, 254
11.11L-SectionLumpedReactiveMatchingNetworks, 387
8.5 HigherTEandTMmodes, 256
11.12Pi-SectionLumpedReactiveMatchingNetworks, 390
8.6 OperatingBandwidth, 258
11.13ReversedMatchingNetworks, 397
8.7 PowerTransfer,EnergyDensity,andGroupVelocity, 259
11.14Problems, 399
8.8 PowerAttenuation, 261
8.9 ReflectionModelofWaveguidePropagation, 264 12 S-Parameters 401
8.10 ResonantCavities, 266
8.11 DielectricSlabWaveguides, 268 12.1 ScatteringParameters, 401
8.12 Problems, 276 12.2 PowerFlow, 405
12.3 ParameterConversions, 406
9 TransmissionLines 278 12.4 InputandOutputReflectionCoefficients, 407
12.5 StabilityCircles, 409
9.1 GeneralPropertiesofTEMTransmissionLines, 278
12.6 PowerGains, 415
9.2 ParallelPlateLines, 284
12.7 GeneralizedS-ParametersandPowerWaves, 421
9.3 MicrostripLines, 285
12.8 SimultaneousConjugateMatching, 425
9.4 CoaxialLines, 289
12.9 PowerGainCircles, 430
9.5 Two-WireLines, 294
12.10UnilateralGainCircles, 431
9.6 DistributedCircuitModelofaTransmissionLine, 296
12.11OperatingandAvailablePowerGainCircles, 433
9.7 WaveImpedanceandReflectionResponse, 298
12.12NoiseFigureCircles, 439
9.8 Two-PortEquivalentCircuit, 300
12.13Problems, 444
9.9 TerminatedTransmissionLines, 301
9.10 PowerTransferfromGeneratortoLoad, 304 13 RadiationFields 446
9.11 Open-andShort-CircuitedTransmissionLines, 306
9.12 StandingWaveRatio, 309 13.1 CurrentsandChargesasSourcesofFields, 446
9.13 DetermininganUnknownLoadImpedance, 311 13.2 RetardedPotentials, 448
9.14 SmithChart, 315 13.3 HarmonicTimeDependence, 451
9.15 Time-DomainResponseofTransmissionLines, 319 13.4 FieldsofaLinearWireAntenna, 453
9.16 Problems, 326 13.5 FieldsofElectricandMagneticDipoles, 455
13.6 Ewald-OseenExtinctionTheorem, 460
10 CoupledLines 335 13.7 RadiationFields, 465
13.8 RadialCoordinates, 468
10.1 CoupledTransmissionLines, 335
13.9 RadiationFieldApproximation, 470
10.2 CrosstalkBetweenLines, 341
13.10ComputingtheRadiationFields, 471
10.3 WeaklyCoupledLineswithArbitraryTerminations, 344
13.11Problems, 473
10.4 Coupled-ModeTheory, 346
10.5 FiberBraggGratings, 348 14 TransmittingandReceivingAntennas 476
10.6 DiffuseReflectionandTransmission, 351
10.7 Problems, 353 14.1 EnergyFluxandRadiationIntensity, 476
14.2 Directivity,Gain,andBeamwidth, 477
11 ImpedanceMatching 354 14.3 EffectiveArea, 482
14.4 AntennaEquivalentCircuits, 486
11.1 ConjugateandReflectionlessMatching, 354
14.5 EffectiveLength, 488
11.2 MultisectionTransmissionLines, 356
14.6 CommunicatingAntennas, 490
11.3 Quarter-WavelengthChebyshevTransformers, 357
14.7 AntennaNoiseTemperature, 492
11.4 Two-SectionDual-BandChebyshevTransformers, 363
14.8 SystemNoiseTemperature, 496
11.5 Quarter-WavelengthTransformerWithSeriesSection, 369
14.9 DataRateLimits, 502
www.ece.rutgers.edu/∼orfanidi/ewa xi xii ElectromagneticWaves&Antennas–S.J.Orfanidis–Feb. 28,2004
14.10SatelliteLinks, 504 17.12LensAntennas, 618
14.11RadarEquation, 507 17.13Problems, 619
14.12Problems, 509
18 AntennaArrays 620
15 LinearandLoopAntennas 510
18.1 AntennaArrays, 620
15.1 LinearAntennas, 510 18.2 TranslationalPhaseShift, 620
15.2 HertzianDipole, 512 18.3 ArrayPatternMultiplication, 622
15.3 Standing-WaveAntennas, 514 18.4 One-DimensionalArrays, 632
15.4 Half-WaveDipole, 516 18.5 VisibleRegion, 634
15.5 MonopoleAntennas, 518 18.6 GratingLobes, 635
15.6 Traveling-WaveAntennas, 519 18.7 UniformArrays, 638
15.7 VeeandRhombicAntennas, 522 18.8 ArrayDirectivity, 642
15.8 LoopAntennas, 525 18.9 ArraySteering, 643
15.9 CircularLoops, 527 18.10ArrayBeamwidth, 645
15.10SquareLoops, 528 18.11Problems, 647
15.11DipoleandQuadrupoleRadiation, 529
15.12Problems, 531 19 ArrayDesignMethods 649
16 RadiationfromApertures 532 19.1 ArrayDesignMethods, 649
19.2 Schelkunoff’sZeroPlacementMethod, 652
16.1 FieldEquivalencePrinciple, 532 19.3 FourierSeriesMethodwithWindowing, 654
16.2 MagneticCurrentsandDuality, 534 19.4 SectorBeamArrayDesign, 655
16.3 RadiationFieldsfromMagneticCurrents, 536 19.5 Woodward-LawsonFrequency-SamplingDesign, 660
16.4 RadiationFieldsfromApertures, 537 19.6 Narrow-BeamLow-SidelobeDesigns, 664
16.5 HuygensSource, 540 19.7 BinomialArrays, 668
16.6 DirectivityandEffectiveAreaofApertures, 542 19.8 Dolph-ChebyshevArrays, 670
16.7 UniformApertures, 544 19.9 Taylor-KaiserArrays, 682
16.8 RectangularApertures, 544 19.10MultibeamArrays, 685
16.9 CircularApertures, 546 19.11Problems, 688
16.10VectorDiffractionTheory, 549
16.11ExtinctionTheorem, 553 20 CurrentsonLinearAntennas 689
16.12VectorDiffractionforApertures, 555
16.13FresnelDiffraction, 556 20.1 Hall´enandPocklingtonIntegralEquations, 689
16.14Knife-EdgeDiffraction, 560 20.2 Delta-GapandPlane-WaveSources, 692
16.15GeometricalTheoryofDiffraction, 566 20.3 SolvingHall´en’sEquation, 693
16.16Problems, 572 20.4 SinusoidalCurrentApproximation, 695
20.5 ReflectingandCenter-LoadedReceivingAntennas, 696
17 ApertureAntennas 575 20.6 King’sThree-TermApproximation, 699
20.7 NumericalSolutionofHall´en’sEquation, 703
17.1 Open-EndedWaveguides, 575 20.8 NumericalSolutionUsingPulseFunctions, 706
17.2 HornAntennas, 579 20.9 NumericalSolutionforArbitraryIncidentField, 710
17.3 HornRadiationFields, 581 20.10NumericalSolutionofPocklington’sEquation, 712
17.4 HornDirectivity, 586 20.11Problems, 718
17.5 HornDesign, 589
17.6 MicrostripAntennas, 592 21 CoupledAntennas 719
17.7 ParabolicReflectorAntennas, 598
17.8 GainandBeamwidthofReflectorAntennas, 600 21.1 NearFieldsofLinearAntennas, 719
17.9 Aperture-FieldandCurrent-DistributionMethods, 603 21.2 SelfandMutualImpedance, 722
17.10RadiationPatternsofReflectorAntennas, 606 21.3 CoupledTwo-ElementArrays, 726
17.11Dual-ReflectorAntennas, 615 21.4 ArraysofParallelDipoles, 729
www.ece.rutgers.edu/∼orfanidi/ewa xiii
21.5 Yagi-UdaAntennas, 738
21.6 Hall´enEquationsforCoupledAntennas, 743
21.7 Problems, 750
22 Appendices 752
Preface
A PhysicalConstants, 752
B ElectromagneticFrequencyBands, 753
C VectorIdentitiesandIntegralTheorems, 755
D Green’sFunctions, 757
E CoordinateSystems, 760
F FresnelIntegrals, 762
G MATLABFunctions, 765 Thistextprovidesabroadandapplications-orientedintroductiontoelectromagnetic
wavesandantennas. Currentinterestintheseareasisdrivenbythegrowthinwireless
References 770 andfiber-opticcommunications,informationtechnology,andmaterialsscience.
Communications,antenna,radar,andmicrowaveengineersmustdealwiththegener-
Index 799 ation,transmission,andreceptionofelectromagneticwaves. Deviceengineersworking
onever-smallerintegratedcircuitsandateverhigherfrequenciesmusttakeintoaccount
wavepropagationeffectsatthechipandcircuit-boardlevels. Communicationandcom-
puternetworkengineersroutinelyusewaveguidingsystems,suchastransmissionlines
andopticalfibers. Novelrecentdevelopmentsinmaterials,suchasphotonicbandgap
structures,omnidirectionaldielectricmirrors,andbirefringentmultilayerfilms,promise
arevolutioninthecontrolandmanipulationoflight. Thesearejustsomeexamplesof
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–Feb. 28,2004
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–Feb. 28,2004
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–Feb. 28,2004
4 ReflectionandTransmission 81
4.1 PropagationMatrices, 81
4.2 MatchingMatrices, 85
4.3 ReflectedandTransmittedPower, 88
4.4 SingleDielectricSlab, 91
Contents
4.5 ReflectionlessSlab, 94
4.6 Time-DomainReflectionResponse, 102
4.7 TwoDielectricSlabs, 104
4.8 Problems, 106
5 MultilayerStructures 109
Preface xiv
5.1 MultipleDielectricSlabs, 109
5.2 AntireflectionCoatings, 111
1 Maxwell’sEquations 1 5.3 DielectricMirrors, 116
5.4 PropagationBandgaps, 127
1.1 Maxwell’sEquations, 1
5.5 Narrow-BandTransmissionFilters, 127
1.2 LorentzForce, 2
5.6 EqualTravel-TimeMultilayerStructures, 132
1.3 ConstitutiveRelations, 3
5.7 ApplicationsofLayeredStructures, 146
1.4 BoundaryConditions, 6
5.8 ChebyshevDesignofReflectionlessMultilayers, 149
1.5 Currents,Fluxes,andConservationLaws, 8
5.9 Problems, 157
1.6 ChargeConservation, 9
1.7 EnergyFluxandEnergyConservation, 10
6 ObliqueIncidence 160
1.8 HarmonicTimeDependence, 12
1.9 SimpleModelsofDielectrics,Conductors,andPlasmas, 13 6.1 ObliqueIncidenceandSnell’sLaws, 160
1.10 Problems, 21 6.2 TransverseImpedance, 162
6.3 PropagationandMatchingofTransverseFields, 165
2 UniformPlaneWaves 25 6.4 FresnelReflectionCoefficients, 167
6.5 TotalInternalReflection, 169
2.1 UniformPlaneWavesinLosslessMedia, 25
6.6 BrewsterAngle, 175
2.2 MonochromaticWaves, 31
6.7 ComplexWaves, 178
2.3 EnergyDensityandFlux, 34
6.8 GeometricalOptics, 188
2.4 WaveImpedance, 35
6.9 Fermat’sPrinciple, 190
2.5 Polarization, 35
6.10 RayTracing, 192
2.6 UniformPlaneWavesinLossyMedia, 42
6.11 Problems, 203
2.7 PropagationinWeaklyLossyDielectrics, 48
2.8 PropagationinGoodConductors, 49
7 MultilayerFilmApplications 205
2.9 PropagationinObliqueDirections, 50
2.10 ComplexorInhomogeneousWaves, 53 7.1 MultilayerDielectricStructuresatObliqueIncidence, 205
2.11 Problems, 55 7.2 LossyMultilayerStructures, 207
7.3 SingleDielectricSlab, 209
3 PropagationinBirefringentMedia 60 7.4 AntireflectionCoatingsatObliqueIncidence, 211
7.5 OmnidirectionalDielectricMirrors, 215
3.1 LinearandCircularBirefringence, 60
7.6 PolarizingBeamSplitters, 225
3.2 UniaxialandBiaxialMedia, 61
7.7 ReflectionandRefractioninBirefringentMedia, 228
3.3 ChiralMedia, 63
7.8 BrewsterandCriticalAnglesinBirefringentMedia, 232
3.4 GyrotropicMedia, 66
7.9 MultilayerBirefringentStructures, 235
3.5 LinearandCircularDichroism, 67
7.10 GiantBirefringentOptics, 237
3.6 ObliquePropagationinBirefringentMedia, 68
7.11 Problems, 242
3.7 Problems, 75
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