船载卫星tv天线座设计的性能

PROPERTIESOF ANTENNA EFFECTIVE PATH RADARRANGEEQUATIONANDCROSS WHYUSEAN 天线的性 天线辐 增 有效面 路径损 距离方程和截 为什么要使用一个天线 PROPERTIESOFOneapproachtoanantennabookstartswithadiscussionofhowantennasradiate.BeginningwithMaxwell’sequations,wederiveelectromagneticwaves.Afterthatlengthydiscussion,whichcontainsalotofmathematics,wediscusshowthesewavesexcitecurrentsonconductors.Thesecondhalfofthestoryisthatcurrentsradiateandproduceelectromagneticwaves.Youmayalreadyhavestudiedthatsubject,orifyouwishtofurtheryourbackground,consultbooksonelectromagnetics.Thestudyofelectromagneticsgivesinsightintothemathematicsdescribingantennaradiationandprovidestherigortopreventmistakes.Weskipthediscussionofthoseequationsandmovedirectlytopracticalaspects.Itisimportanttorealizethatantennasradiatefromcurrents.Designconsistsofcontrollingcurrentstoproducethedesiredradiationdistribution,calleditspattern.Inmanysituationstheproblemishowtopreventradiationfromcurrents,suchasincircuits.Wheneveracurrentesseparatedindistancefromitsreturncurrent,itradiates.Simplystated,wedesigntokeepthetwocurrentsclosetogether,toreduceradiation.Somediscussionswillignorethecurrentdistributionandinstead,considerderivedties,suchasfieldsinanapertureormagneticcurrentsinaslotoraroundtheedgesofamicrostrippatch.Youwilldiscoverthatweuseanyconceptthatprovidesinsightorsimplifiesthemathematics.Anantennaconvertsboundcircuitfieldsintopropagatingelectromagneticwavesand,byreciprocity,collectspowerfrompassingelectromagneticwaves.Maxwell’sequationspredictthatanytime-varyingelectricormagneticfieldproducestheoppositefieldandformsanelectromagneticwave.Thewavehasitstwofieldsorientedorthogonally,anditpropagatesinthedirectionnormaltothenedefinedbytheperpendicularelectricandmagneticfields.Theelectricfield,themagneticfield,andthedirectionofpropagationformaright-handedcoordinatesystem.Thepropagatingwavefieldintensitydecreasesby1/Rawayfromthewhereasastaticfielddropsoffby1/R2.Anycircuitwithtime-varyingfieldshasthecapabilityofradiatingtosomeextent.Weconsideronlytime-harmonicfieldsandusephasornotationwithtimeejwt.Anoutward-propagatingwaveisgivenbyej(kRwt),wherek,thewavenumber,isby2π/λ.λisthewavelengthofthewavegivenbyc/f,wherecisthevelocityoflight(3m/sinspace)andfisthefrequency.Increasingthedistancefromthesourcedecreasesthephaseofthewave.Consideratwo-wiretransmissionlinewithfieldsboundtoit.Thecurrentsonasinglewirewillradiate,butaslongasthegroundreturnpathisnear,itsradiationwillnearlycanceltheotherline’sradiationbecausethetwoare180°outofphaseandthewavestravelaboutthesamedistance.Asthelines efartherandfartherapart,intermsofwavelengths,thefieldsproducedbythetwocurrentswillnolongercancelinalldirections.Insomedirectionsthephasedelayisdifferentforradiationfromthecurrentoneachline,andpowerescapesfromtheline.Wekeepcircuitsfromradiatingbyprovidingclosegroundreturns.Hence,high-speedlogicrequiresgroundnestoreduceradiationanditsunwantedcrosstalk.ANTENNAAntennasradiatesphericalwavesthatpropagateintheradialdirectionforacoordinatesystemcenteredontheantenna.Atlargedistances,sphericalwavescanbeapproximatedbynewaves.newavesareusefulbecausetheysimplifytheproblem.Theyarenotphysical,however,becausetheyrequireinfinitepower.ThePoyntingvectordescribesboththedirectionofpropagationandthepowerdensityoftheelectromagneticwave.ItisfoundfromthevectorcrossproductoftheelectricandmagneticfieldsandisdenotedS:S=E W/Rootmeansquare(RMS)valuesareusedtoexpressthemagnitudeofthefields.H*isthecomplexconjugateofthemagneticfieldphasor.Themagneticfieldisproportionaltotheelectricfieldinthefarfield.Theconstantofproportionisη,theimpedanceofspace(η=ESSE

W/

BecausethePoyntingvectoristhevectorproductofthetwofields,itisorthogonaltobothfieldsandthetripletdefinesaright-handedcoordinatesystem:(E,H,S).Considerapairofconcentricspherescenteredontheantenna.Thefieldsaroundtheantennadecreaseas1/R,1/R2,1/R3,andsoon.Constant-ordertermswouldrequirethatthepowerradiatedgrowwithdistanceandpowerwouldnotbeconserved.ForfieldtermsproportionaltoTheenergyontheinnersphereislargerthanthatontheoutersphere.Theenergiesarenotradiatedbutareinsteadconcentratedaroundtheantenna;theyarenear-fieldterms.OnlytheR2termofthePoyntingvector(1/Rfieldterms)representsradiatedpowerbecausetheareagrows R2andgivesaconstantproduct.Alltheradiatedpowerflowingthroughinnerspherewillpropagatetotheoutersphere.Thesignoftheinputreactancedependsonthenear-fieldpredominanceoffieldtype:electric(capacitive)ormagnetic(inductive).Atresonance(zeroreactance)thestoredenergiesduetothenearfieldsareequal.IncreasingthestoredfieldsincreasesthecircuitQandnarrowstheimpedancebandwidth.Farfromtheantennaweconsideronlytheradiatedfieldsandpowerdensity.Thepowerflowisthesamethroughconcentricspheres:44R

44RTheaveragepowerdensityisproportionalto1/R2.Considerdifferentialareasonthetwospheresatthesamecoordinateangles.Theantennaradiatesonlyintheradialdirection;therefore,nopowermaytravelintheθorφdirection.Powertravelsinfluxtubesbetweenareas,anditfollowsthatnotonlytheaveragePoyntingvectorbutalsoeverypartofthepowerdensityisproportionalto1/R2:1 2SR2sinddSR2sin1 2SinceinaradiatedwaveSisproportionalto1/R2,Eisproportionalto1/R.Itisconvenientdefineradiationintensitytoremovethe1/R2U(θ,φ)=S(R,θ,φ)R W/solidRadiationintensitydependsonlyonthedirectionofradiationandremainsthesameatalldistances.Aprobeantennameasurestherelativeradiationintensity(pattern)bymovinginacircle(constantR)aroundtheantenna.Often,ofcourse,theantennarotatesandtheprobeisSomepatternshaveestablishednames.Patternsalongconstantanglesofthesphericalcoordinatesarecalledeitherconical(constantθ)orgreatcircle(constantφ).Thegreatcirclecutswhenφ=0°orφ=90°aretheprincipalnepatterns.Othernamedcutsarealsoused,buttheirnamesdependontheparticularmeasurementpositioner,anditisnecessarytoannotatethesepatternscarefullytoavoidconfusionbetweenpeoplemeasuringpatternsondifferentpositioners.Patternsaremeasuredbyusingthreescales:(1)linear(power),(2)squareroot(fieldintensity),and(3)decibels(dB).ThedBscaleisusedthemostbecauseitrevealsofthelow-levelresponsesFigure1.1demonstratesmanycharacteristicsofpatterns.Thehalf-powerbeamwidthissometimescalledjustthebeamwidth.Thetenth-powerandnullbeamwidthsareusedinsomeapplications.Thispatterncomesfromaparabolicreflectorwhosefeedismovedofftheaxis.Thevestigiallobeoccurswhenthefirstsidelobe esjoinedtothemainbeamandformsashoulder.Forafeedlocatedontheaxisoftheparabola,thefirstsidelobesareequal. Gainisameasureoftheabilityoftheantennatodirecttheinputpowerintoradiationinaparticulardirectionandismeasuredatthepeakradiationintensity.ConsiderthepowerdensityradiatedbyanisotropicantennawithinputpowerPoatadistanceR:S=Po/4πR2.Anisotropicantennaradiatesequallyinalldirections,anditsradiatedpowerdensitySisfoundbydividingthe ESP0GE

Gainisachievedbydirectingtheradiationawayfromotherpartsoftheradiationsphere.Ingeneral,gainisdefinedasthegain-biasedpatternoftheantenna:

powerradiation FIGURE1.1AntennapatternThesurfaceintegraloftheradiationintensityovertheradiationspheredividedbytheinputpowerPoisameasureoftherelativepowerradiatedbytheantenna,ortheantennaPr2G,sindd

00 0wherePristheradiatedpower.Materiallossesintheantennaorreflectedpowerduetopoorimpedancematchreducetheradiatedpower.Inthisbook,integralsintheequationaboveandthosethatfollowexpressconceptsmorethanoperationsweperformduringdesign.Onlyfortheoreticalsimplificationsoftherealworldcanwefindclosed-formsolutionsthatwouldcallforactualintegration.Wesolvemostintegralsbyusingnumericalmethodsthatinvolvebreakingtheintegrandintosmallsegmentsandperformingaweightedsum.However,itishelpfulthatintegralsusingmeasuredvaluesreducetherandomerrorsbyaveraging,whichimprovestheresult.Inasystemthetransmitteroutputimpedanceorthereceiverinputimpedancemaynotmatchtheantennainputimpedance.Peakgainoccursforareceiverimpedanceconjugatematchedtotheantenna,whichmeansthattheresistivepartsarethesameandthereactivepartsarethesamemagnitudebuthaveoppositesigns.Precisiongainmeasurementsrequireatunertheantennaandreceivertoconjugate-matchthetwo.Alternatively,themismatchlossmustberemovedbycalculationafterthemeasurement.Eithertheeffectofmismatchesisconsideredseparayforagivensystem,ortheantennasaremeasuredintothesystemimpedanceandmismatchlossisconsideredtobepartoftheefficiency.ExampleComputethepeakpowerdensityat10kmofanantennawithaninputpowerof3Wandagainof15dB.FirstconvertdBgaintoaratio:G

10

=31.62.Thepowerspreadsovertheareawithradius10kmoranareaof4π(104 m2.ThepowerdensityS3W(31.62)75.5nW/WecalculatetheelectricfieldintensityusingEq.(1-75.510975.5109Althoughgainisusuallyrelativetoanisotropicantenna,someantennagainsarereferredtoaλ/2dipolewithanisotropicgainof2.14dB.Ifweapproximatetheantennaasapointsource,wecomputetheelectricfieldradiatedbyusingEq.(1.2):eReRThisrequiresonlythattheantennabesmallcomparedtotheradialdistanceR.Equation(1.4)ignoresthedirectionoftheelectricfield,whichwedefineaspolarization.Theunitsoftheelectricfieldarevolts/meter.Wedeterminethefar-fieldpatternbymultiplyingEq.(1.4)byandremovingthephase

e

sincephasehasmeaningonlywhenreferredtopointinthefarfield.Thefar-fieldelectric

E

unitisP0G,P0G,E

,

G, EP

,

0 Duringysis,weoftennormalizeinputpowerto1Wandcancomputegaineasilyfrom4electricfieldbymultiplyingbya =4EFFECTIVEAntennascapturepowerfrompassingwavesanddeliversomeofittotheterminals.Giventhepowerdensityofthewaveandtheeffectiveareaoftheantenna,thepowertotheterminalsisthe

Pd

Foranapertureantennasuchasahorn,parabolicreflector,orflat-tearray,effectiveareaisphysicalareamultipliedbyapertureefficiency.Ingeneral,lossesduetomaterial,distribution,andmismatchreducetheratiooftheeffectiveareatothephysicalarea.Typicalestimatedapertureefficiencyforaparabolicreflectoris55%.Evenantennaswithinfinitesimalphysicalareas,suchasdipoles,haveeffectiveareasbecausetheyremovepowerfrompassingwaves.PATHWecombinethegainofthetransmittingantennawiththeeffectiveareaofthereceivingantennatodeterminedeliveredpowerandpathloss.ThepowerdensityatthereceivingantennaisgivenbyEq.(1.3),andthereceivedpowerisgivenbyEq.(1.6).Bycombiningthetwo,weobtainthepathloss:t tAntenna1transmits,andantenna2receives.Ifthematerialsintheantennasarelinearandisotropic,thetransmittingandreceivingpatternsareidentical(reciprocal)[2,p.116].Whenweconsiderantenna2asthetransmittingantennaandantenna1asthereceivingantenna,thepathlossist tSincetheresponsesarereciprocal,thepathlossesareequalandwecangatherandeliminateG1G2= Becausetheantennaswerearbitrary,thisquotientmustequalaconstant.Thisconstantwasfoundbyconsideringtheradiationbetweentwolargeapertures[3]:G

WesubstitutethisequationintopathlosstoexpressitintermsofthegainsoreffectivePdGG

A1

2t 124R 2t

2WemakequickevaluationsofpathlossforvariousunitsofdistanceRandforfrequencyfinmegahertzusingtheformula.pathloss(dB)=KU20logfRG1dBG2whereKudependsonthelength

Computethegainofa3-m-diameterparabolicreflectorat4GHzassuming55%apertureefficiency.GainisrelatedtoeffectiveareabyEq.G4WecalculatetheareaofacircularaperturebyAD/22.Bycombiningtheseequations,wehave DfG

a

whereDisthediameterandweobtainthe

istheapertureefficiency.Onsubstitutingthevalues34109G

0.55

ExampleCalculatethepathlossofa50-kmcommunicationlinkat2.2GHzusingatransmitterantennawithagainof25dBandareceiverantennawithagainof20dB.Pathloss=32.45+20log[2200(50)]-25-20=88.3Whathappenstotransmissionbetweentwoaperturesasthefrequencyisincreased?Ifweassumethattheeffectivearearemainsconstant,asinaparabolicreflector,thetransmissionincreasesasthesquareoffrequency: A AAfd1 12

Bft R22 R2ctwhereBisaconstantforafixedrange.Thereceivingaperturecapturesthesamepowerregardlessoffrequency,butthegainofthetransmittingantennaincreasesasthesquareoffrequency.Hence,thereceivedpoweralsoincreasesasfrequencysquared.Onlyforantennas,whosegainisafixedvaluewhenfrequencychanges,doesthepathlossincreaseasthesquareoffrequency.RADARRANGEEQUATIONANDCROSSRadaroperatesusingadoublepathloss.Theradartransmittingantennaradiatesafieldthatilluminatesatarget.Thesefieldsexcitesurfacecurrentsthatalsoradiatetoproduceasecondfield.Thesefieldspropagatetothereceivingantenna,wheretheyarecollected.Mostradarsusethesameantennabothtotransmitthefieldandtocollectthesignalreturned,calledamonostaticsystem,whereasweuseseparateantennasforbistaticradar.Thereceivingsystemcannotbedetectedinabistaticsystembecauseitdoesnottransmitandhasgreatersurvivabilityinamilitaryapplication.Wedeterminethepowerdensityilluminatingthetargetatarange

byusingEq.

TTThetarget’sradarcrosssection(RCS),thescatteringareaoftheobject,isexpressedinsquaremetersordBm2:10log(squaremeters).TheRCSdependsonboththeandreflectedwavedirections.Wemultiplythepowercollectedbythetargetwithitsreceivingpatternbythegainoftheeffectiveantennaduetothecurrentsinduced:RCS

InacommunicationsystemwecallPstheequivalentisotropicradiatedpower(EIRP),whichequalstheproductoftheinputpowerandtheantennagain.The esthesourceandweapplyEq.(1.2)tofindthepowerdensityatthereceivingantennaatarangefromthetarget.Finally,thereceivingantennacollectsthepowerdensitywithaneffectiveAR.Wecombinetheseideastoobtainthepowerdeliveredtothe S

R

4R24R2WeapplyEq.(1.7)toeliminatetheeffectiveareaofthereceivingantennaandgathertermstodeterminethebistaticradarrangeequation: GG2,,,recT

43R2R2 TWereduceEq.(1.13)andcollecttermsformonostaticradar,wherethesameantennaisusedforbothtransmittingandreceiving: G2TrecT 43Radarreceivedpowerisproportionalto1/R

and

G2WefindtheapproximateRCSofaflattebyconsideringtheteasanantennawithaneffectivearea.Equation(1.11)givesthepowerdensityonthetethatcollectsthispoweroveranareaAR:TT Thepowerscatteredbytheteisthepowercollected,PC,timesthegainoftheteasanantenna,GP:PP

,T CT

R Thisscatteredpoweristheeffectiveradiatedpowerinaparticulardirection,whichinanantennaistheproductoftheinputpowerandthegaininaparticulardirection.Wecalculatethetegainbyusingtheeffectiveareaandfindthescatteredpowerintermsofarea:PG4PsTWedeterminetheRCSσbyEq.(1.12),thescatteredpowerdividedbythepower G,G, R

P T TherightexpressionofEq.(1.14)dividesthegainintotwopiecesforbistaticscattering,wherethescattereddirectionisdifferentfromthedirection.Monostaticscatteringusesthesameandreflecteddirections.Wecansubstituteanyobjectfortheflatteandusetheideaofaneffectiveareaanditsassociatedantennagain.AnantennaisanobjectwithuniqueRCScharacteristicbecausepartofthepowerreceivedwillbedeliveredtotheantennaterminals.Ifweprovideagoodimpedancematchtothissignal,itwillnotreradiateandtheRCSisreduced.Whenweilluminateanantennafromanarbitrarydirection,someofthepowerdensitywillbescatteredbythestructureandnotdeliveredtotheantennaterminals.ThisleadstothedivisionofantennaRCSintotheantennamodeofreradiatedsignalscausedbyterminalmismatchandthestructuralmode,thefieldsreflectedoffthestructureforpowerdensitynotdeliveredtotheterminals.WHYUSEANWeuseantennastotransfersignalswhennootherwayispossible,such withamissileoroverruggedmountainterrain.Cablesareexpensiveandtakealongtimeto Aretheretimeswhenwewoulduseantennasoverlevelground?Thelargepathlossesofantennasystemsleadustobelievethatcablerunsarebetter.

重要的是要天线辐射电流。设计由控制电流来产生所需的辐射分布,称为模1/R2。随时间变化的磁场会引起任何电路具有辐射在一定程度上的能力。我们只考虑时间谐波领域和使用相符号与时间依