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Antennas and Propagation for Wireless Communications.pdf

Antennas and Propagation for Wi…

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简介:本文档为《Antennas and Propagation for Wireless Communicationspdf》,可适用于电信技术领域,主题内容包含ChapterIntroductionAcommunicationslinkorchannelconsistsofasourceofinformat符等。

ChapterIntroductionAcommunicationslinkorchannelconsistsofasourceofinformation,transmitterelectronicsincludingmodulators,mixers,poweramplifiers,orothercomponents,atransmittingantennaorarray,thepropagationenvironment,areceivingantennaorarrayandassociatedreceiverelectronics,andsignalprocessingtodetectanddecodeinformationfromthereceivedsignalThepurposeofthisbookistodeveloptheanalyticaltoolsrequiredforanendtoendmodelofsuchacommunicationslink,includingantennaandpropagationeffectsaswellassignalprocessingThekeyfiguresofmeritforthecommunicationslinkarethesignaltonoiseratio(SNR)andchannelcapacityChannelcapacityisthemaximumbitratethatcanbereliablysentfromtransmittertoreceiverForasinglecommunicationschannel,thecapacityisdeterminedbythebandwidthofthechannelandthesignaltonoiseratio(SNR)atthereceiveroutput,whichisinfluencedbythefollowingfactors:Transmitter:Totalradiatedpower,antennaradiationpattern,gain,andpolarizationPropagationenvironment:Distancebetweentransmitterandreceiver,multipath,blockage,loss,noise,andinterferenceReceiver:Antennacharacteristics,amplifiersandreceiverelectronics,andsignalprocessingThegoalistounderstandeachoftheseaspectsoftheelectromagneticpropagationchannelandtomodeltheoverallperformanceofacommunicationschannelintermsofthetransmittercharacteristics,propagationenvironment,andreceiversystemInordertodevelopacompletechannelmodel,wemustconsiderantennatheoryforbothtransmittingandreceivingantennas,specificantennatypesandarrayantennas,noisetheory,propagationchannels,andcommunicationtheoryforbothsingleantennasandmultiantennasystemsThiswillprovidethetoolsnecessarytodeterminetheSNRattheoutputofacommunicationslink,thechannelcapacity,andthebiterrorraterealizedwiththechannelforaspecificmodulationschemeThesetoolswillalsoallowsynthesisofacommunicationssystemwhichmeetsadesiredperformancecriterionLinkBudgetAnalysisAsimpletoolforpropagationanalysisisalinkbudget,whichistherelationshipbetweenthetotaltransmittedpowerandthesignalpoweratthereceiveroutputintermsofantennagainandfreespacepathlossThelinkbudget,togetherwiththenoiselevelatthereceiveroutput,determinestheSNRforacommunicationssystemInthistreatment,wewilldevelopmodelsforthevariouscontributionstoasystemlinkbudgetForcomplexpropagationenvironmentsandmultipleinputmultipleoutput(MIMO)communicationssystems,asimplelinkbudgetanalysisisinadequate,andamoresophisticatedcapacitymodelmustbedevelopedECEn:AntennasandPropagationforWirelessCommunicationsApplicationsApplicationsofantennasandpropagationmodelingincludeeverythingfromabasicpointtopointmicrowavecommunicationslinkorradiobroadcastsystemtomoderntechnologiessuchaswirelesslocalareanetworks,satelliteuplinksanddownlinks,deepspacecommunications,andMIMOsystemsManyofthesameprinciplesareapplicabletootherfieldsbeyondvoiceanddatatransmission,suchasreceiversforradioastronomyobservations,magneticresonanceimaging,radar,globalpositionsystems,andremotesensingWarnickJensenJanuary,ChapterAntennasAsadevicethattransformsawaveonatransmissionlinetoawaveinthespacearoundtheantenna,anantennahastwokeyproperties:theinputimpedanceitpresentstothetransmissionline,andthepatternoftheradiatedfieldsConfiguredasareceiver,theantennacanbemodeledasanequivalentvoltageorcurrentsourceconnectedtoatransmissionline,withanopencircuitvoltageorshortcircuitcurrentinducedbyanincidentfieldandagivensourceimpedanceTypically,anantennaismodeledasatransmitter,anditsreceivingpropertiesareinferredusingtheelectromagneticreciprocityprincipleAnantennaradiationproblemisaboundaryvalueproblem,wherethefieldsradiatedbytheantennaaredeterminedbyMaxwell’sequationswithmaterialpropertiesgivenbytheshapeandcompositionoftheantennastructureandasourceexcitationconnectedtotheantennaterminalsMaxwell’sequationsthendeterminetheelectromagneticfieldsaroundtheantennaFromthesefields,thevoltageandcurrentattheantennaterminalscanbecomputedtodeterminetheantennaimpedance,andthefarfieldsdeterminetheantennaradiationpatternAntennaAnalysisOnewaytofindthefieldsaroundtheantennaistouseanumericalmethodtosolvetheboundaryvalueproblemdirectlyAllantennaparameters,includingtheantennaimpedance,canbefoundinthiswayForsimpleantennatypes,itismoreconvenienttodevelopapproximateformulasfortheantennaparametersusinganalyticaltechniquesOneofthebasicanalyticaltechniquesofantennatheoryistomodeltheantennaasanequivalentcurrentdistribution,whichwhenimpressedinfreespaceradiatesthesamefieldsastheantennastructurewithagivenexcitationattheterminalsTheradiationintegralcanbeusedtofindthefarfields,fromwhichtheradiationpatternandradiationresistancecanbecomputedForalosslessantenna,theradiationresistanceisequaltotherealpartoftheantennaimpedanceThecurrentisalsosometimesusedtoestimatetheadditionalpartoftheantennaresistanceduetoohmiclossesintheantennastructureAmoresophisticatedanalysisoranumericalmethodisusuallyrequiredtomodeltheantennareactanceandobtainanaccuratevaluefortheantennaimpedanceAnalyticalcurrentmodelsaretypicallyapproximateandcanbefoundonlyforsimpleantennageometriesForcomplexantennas,analyticalcurrentmodelsarenotavailable,andnumericalmethodsareusedtosolveMaxwell’sequationsandfindthefieldradiatedbytheantennaCommonanalyticalcurrentmodelsandnumericalmethodsusedforantennaanalysisinclude:Analyticalapproximations:Hertziandipolemodel(deltafunctioncurrent)Linearantennas:triangularorsinusoidalcurrentdistributionsECEn:AntennasandPropagationforWirelessCommunicationsApertureantennas:aperturefieldisapproximatedbytheincidencefieldthatilluminatestheaperturePatchantennas:cavitymodelforfieldsunderthepatchNumericalmethodsDmethodofmoments(MOM)forthinwiresDmethodofmoments(MOM)forperfectelectricconductor(PEC)objectsDmethodofmoments(MOM)forcompositedielectricandconductingstructuresFinitedifferencetimedomain(FDTD)Finiteelementmethod(FEM)Theanalyticalapproximationsprovideanequivalentcurrentrepresentationfortheantenna,fromwhichthefieldsradiatedbythecurrentsourcecanbefoundusingaGreen’sfunctionandtheradiationintegralAGreen’sfunctionisthefieldradiatedbyapointordeltafunctionsourceforagivensetofboundaryconditionsItcanbethoughtofastheimpulseresponseofspaceBoundaryconditionsmayincludedielectricinterfaces,conductors,andtheradiationboundaryconditionatinfinityThemostcommoncaseisthefreespaceGreen’sfunction,whichisavailableinanalyticformThefieldisthengivenbyaradiationintegral,whichistheconvolutionoftheGreen’sfunctionwithacurrentsourceFreeSpaceGreen’sFunctionOneapproachtofindingthefieldsradiatedbyapointsourceistotransformthefirstordersystemofMaxwell’sequationsintoasinglesecondorderpartialdifferentialequation(PDE)Ifwedothis,wefindthattheelectricfieldsatisfiesthePDEkE(r)=jωµJ(r)()Inhomogeneousregionwithnounbalancedcharge,D=togetherwiththeidentityEE=EcanbeusedinthisexpressiontoobtaintheHelmholtzequationkE(r)=jωµJ(r)()TofindaGreen’sfunction,weneedtosolveforEforapointsourceoftheformJ(r)=pˆδ(rr′)()wherer′isthelocationofthesourceandpˆisthepolarizationTherearedifficultiesassociatedwithfindingtheGreen’sfunctionforeitherofthesePDEsThederivativeoperatorin()iscomplicated,soitisdifficulttosolvethisequationdirectlyEquation()hasasimplerderivativeoperator,buttheHelmholtzequationhasmoresolutionsthanMaxwell’sequations(longitudinalwaves),sothosenonphysicalsolutionsmustbeeliminatedfromtheconvolutionoftheGreen’sfunctionwiththesourcetoobtainavalidelectricfieldToovercomethesedifficulties,wecandefineanauxiliarypotentialthatalsosatisfiesaHelmholtztypePDEfromwhichvalidelectricandmagneticfieldscanbederivedGauss’slawforthemagneticfluxdensityisB=()Usingatheoremfromdifferentialgeometry,itfollowsthatBisthecurlofsomevectorfield,sothatB=A()WarnickJensenJanuary,ECEn:AntennasandPropagationforWirelessCommunicationswhereAiscalledthemagneticvectorpotentialUsingthisinFaraday’slaw,(EjωA)=()Usinganothertheoremfromdifferentialgeometry,thequantityinparenthesismustbethegradientofsomescalarfunction,sothatEjωA=φ()Inthestaticcase(ω=),φistheelectricpotentialUsing()inAmpere’slawleadstokA=jωµφµJ()UsinganidentityfortheLaplacianoperator,kA=µJjωµφA()Thelasttwotermsontherightareinconvenient,butwecaneliminatethemUsingthefactthattherearemanyvectorfieldsAthatsatisfy()foragivenB,wecanchoosetheparticularvectorpotentialforwhichA=jωµφ()ThisisknownastheLorenzgaugeUsingthisin()leadstotheHelmholtzequationkA=µJ()Thisissimilarinformto(),butallsolutionsnowrepresentvalidelectromagneticfieldsScalarGreen’sFunctionWenowneedtosolve()forapointsourceWewilllabelthesolutionA(r)forapointsourcelocatedatr′asg(r,r′),sothatkg(r,r′)=δ(rr′)()Sincefreespaceishomogeneous,wecanshiftr′tozero,sothatg(r,)=g(r)=g(r),andwehavekg(r)=δ(r)()WecansimplifytheLaplacianconsiderablysincegisnowonlyafunctionofrForr>,thisbecomesrr(rgr)kg(r)=()Ifweletu(r)=rg(r),thenddru(r)ku(r)=()whichhasthegeneralsolutionu(r)=AejkrBejkr()Theradiationboundaryconditionatinfinityimpliesthatwavesmustbeoutgoing,sowemusthaveB=,andg(r)=Aejkrr()WarnickJensenJanuary,ECEn:AntennasandPropagationforWirelessCommunicationsItnowremainstofindtheconstantAWewilldothisbyensuringthatthelefthandsideof()integratestooveravolumecontainingtheoriginIntegratingbothsidesof()overaballVofradiusrleadstoVkAejkrrdr=()IftheradiusofVissmall,thenthisbecomesVkAejkrrdr'VArdr=AVrdr=ASrdS=ASrrsinθdθdφ=piAfromwhichwehaveA=(pi)Shiftingthesourcepointfromtheoriginbacktor′leadstothefinalresultg(r,r′)=ejk|rr′|pi|rr′|()ThisisthescalarfreespaceGreen’sfunctionRadiationIntegralThemagneticvectorpotentialforanarbitrarysourcedistributionJisgivenbytheintegralofthescalarGreen’sfunctionweightedbythesourcedistributionPhysically,weareusingthelinearityoftheproblemtoaddupthefieldsradiatedbymanysmallpointsourcesthatcombinetomakeupthesourcedistributionThisleadstotheradiationintegralA(r)=µg(r,r′)J(r′)dr′()Sincefreespaceisashiftinvariantmedium,theGreen’sfunctioncanbewrittenintheformg(rr′),whichplacestheradiationintegralintoaconvolutionformTheelectricfieldcanbefoundintermsofthemagneticvectorpotentialusing()andtheLorenzgauge,sothatE=jωAφ=jωAjωµA()=jωkAInserting()forthevectorpotential,E(r)=jωµkg(r,r′)J(r′)dr′()ThisisthefreespaceradiationintegralfortheelectricfieldintermsofthescalarGreen’sfunctionandtheelectriccurrentdensityWarnickJensenJanuary,ECEn:AntennasandPropagationforWirelessCommunicationsFarFieldApproximationOfteninantennaanalysisweareonlyinterestedinthefieldsfarfromtheantennaInthiscase,wecansimplifytheradiationintegralconsiderablyIfthesourceisneartheoriginandthefieldobservationpointrisfarfromtheorigin,then|rr′|=(xx′)(yy′)(xz′)'xxx′yyy′zzz′=rrr′=rrˆr′r'r(rˆr′r)=rrˆr′Usingthisin(),g(r,r′)'ejkrpirejkrˆr′()Tofirstorderinr,thederivativeoperatorsin()canbeapproximatedusingejkrr=rˆrejkrrO(r)=rˆ(jkejkrrejkrr)O(r)'jkrˆejkrrsothat'jkrˆfarfromthesourceUsingtheseresultsin()leadstothefarfieldradiationintegralE(r)=jωµ(rˆrˆ)ejkrpirejkrˆr′J(r′)dr′()Therˆrˆtermsubtractsoutwaveswithelectricfieldintherdirection,sincethesearelongitudinalwavesandarenotvalidsolutionsofMaxwell’sequationTheidentitytermispreciselywhatwewouldhaveobtainedifwehadsolved()directlyTheintegralN(r)=ejkrˆr′J(r′)dr′()ismuchlikeaFouriertransformofthesourceThisquantityiscalledthevectorcurrentmomentIntermsofN,E=jωµ(rˆrˆ)ejkrpir(θˆNθφˆNφrˆNr)=jωµejkrpir(θˆNθφˆNφ)()Whenevaluatingtheintegraloverr′,ifthesourcematchesarectangulargeometry,itisoftenconvenienttousesphericalcoordinatesforrandrectangularcoordinatesforr′,sothatrˆr′=(xˆsinθcosφyˆsinθsinφzˆcosθ)(x′xˆy′xˆz′zˆ)=x′sinθcosφy′sinθsinφz′cosθ()WarnickJensenJanuary,ECEn:AntennasandPropagationforWirelessCommunicationsMagneticCurrentOfteninantennaanalysisitisconvenienttouseequivalentmagneticcurrentsinadditiontoelectriccurrentsThereareapparentlynoisolatedmagneticchargesinnature,butfictitiousmagneticcurrentscanstillbeintroducedmathematicallyintoFaraday’slawbyaddingasourcetermM:E=jωBM()Iftherearenounbalancedelectriccharges,thenD=,andthereforewecanrepresentDasacurlaccordingtoD=F()Followingaderivationsimilartothatof(),aHelmholtzequationforFcanbeobtained,whichleadstotheGreen’sfunctionsolutionE(r)=g(r,r′)M(r′)dr′()Inthefarfieldlimit,E(r)'jkejkrpirrˆL(r)()whereL(r)=ejkrˆr′M(r′)dr′()ElectricandMagneticCurrentsCombining()and()leadstothecompletefarfieldradiationintegralforelectricandmagneticcurrents,E(r)'jkejkrpirθˆ(ηNθLφ)φˆ(ηNφLθ)()ThemagneticfieldisH(r)'jkejkrpirθˆ(NφLθη)φˆ(NθLφη)()Theseexpressionsrepresentthemostgeneralpossibleformforasphericalwave,whichdecaysinamplitudeasrandhassphericalphasefronts(r=constant)ItcanbeseenbyinspectingthesetwoexpressionsthattheelectricandmagneticfarfieldsareorthogonalandhavenolongitudinalcomponentintherˆdirectionWarnickJensenJanuary,ECEn:AntennasandPropagationforWirelessCommunicationsAntennaParametersAnantennaisatransformerbetweenatransmissionlineandfreespaceTodescribeanantenna,wemustcharacterizeitspropertiesasatransmissionlineload(inputimpedance)andthedistributionoftheelectromagneticenergythatitradiatesintospace(radiationpattern)ThereareanumberofkeyparametersandconceptsthatwecanusetodescribeantennapropertiesWewillfirstconsiderantennasastransmitters,andthenwewillusethereciprocitytheoremtodeterminethereceivingpropertiesofanantennaAntennaParameterDefinitionsRadiationpattern:AnantennaradiationpatternistheangulardistributionofthepowerradiatedbyanantennaIfanantennaradiatesfieldsE(r,θ,φ)andH(r,θ,φ),thenthetimeaveragefarfieldpowerdensityradiatedatthepointrhastheformSav(r,θ,φ)=ReE(r)H(r)=|E(r)|ηrˆ'f(θ,φ)rrˆ,r()wherewehavelumpedalltheangledependenceintof(θ,φ)ThisangulardependenceistheradiationpatternoftheantennaItiscustomarytonormalizetheradiationpatterntoamaximumvalueofunity,sothattheradiationpatternisdefinedtobef(θ,φ)fmaxWhilethepowerdensitypatternismostimportant,onecanalsolookatthefieldintensity,phase,orpolarizationpatternsofanantennaIsotropicpattern:Equalpowerisradiatedinalldirections,sothatf(θ,φ)=Norealantennahasthispattern,buttheisotropicradiatorisimportantasareferencepatternwithwhichtocompareotherantennaradiationpatternsinordertodefinedirectivityOmnidirectionalpattern:f(θ,φ)=f(θ),sothepatternisindependentofazimuthalanglePatterncut:Ingeneral,aradiationpatternisatwodimensionalfunctionwhichrequiresaDplottovisualizeForconvenience,itiscommontoplotasliceofthepattern,suchasathetacut,f(θ,φ)withφfixedEplanecut:PatternintheplanecontainingtheelectricfieldvectorradiatedbytheantennaandthedirectionofmaximumradiationHplanecut:PatternintheplanecontainingthemagneticfieldvectorradiatedbytheantennaandthedirectionofmaximumradiationPatternlobes:LocalmaximaintheradiationpatternThemainlobeisthelobewhichreachesfmaxSidelobesaresmallerlobesAbacklobeisapatternlobeneartheoppositedirectionofthemainlobeSidelobelevel:RatiooffmaxtothepeakvalueofthelargestsidelobeBeamwidth:ThereareseveralwaystospecifytheangularwidthofthemainlobeThemostcommonarethehalfpowerbeamwidth(HPBW)andtobeamwidthThehalfpowerhalfbeamwidth(HPBW)isalsousedPencilbeampattern:RadiationpatternwithasmallmainbeamwidthWarnickJensenJanuary,ECEn:AntennasandPropagationforWirelessCommunicationsDirectivity:RatioofradiatedpowerdensityinagivendirectiontothepowerdensityofanisotropicreferenceantennaradiatingthesametotalpowerThetotalradiatedpowerisPrad=SSavdS()whereSisaclosedsurfacecontainingtheantennaThepowerdensityradiatedbyanisotropicantennaisSiso=rˆPradpir()Bythedefinition,thedirectivitypatternisD(θ,φ)=Sav(r)Prad(pir)()ThedirectivityDisthemaximumvalueofthedirectivitypatternDirectivityandbeamwidthareinverselyrelatedPartialdirectivity:Inmanycases,thereceiverdoesnotcaptureallthepowerradiatedbythetransmittingantenna,butinsteadonlythepowerinonepolarizationpˆPartialdirectivityisdefinedtobetheradiationintensitycorrespondingtoagivenpolarizationdividedbythetotalradiatedpoweraveragedoveralldirectionsIEEEStandardWecanmodify()tobethepartialdirectivitywithrespecttothepolarizationpˆbyreplacingtheradiatedpowerdensitywithSav,p=|pˆE(r)|η()inthedefinition()ofdirectivity

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