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1、CHAPTER 2 FundamentalParametersofAntennas2.1 INTRODUCTION.32.2 RADIATION PATTERN.32.2.1RadiationPatternLobes.52.2.2Isotropic,Directional,andOmnidirectionalPatterns.72.2.3PrincipalPatterns.72.2.4FieldRegions.92.2.5Radian（弧度）andSteradian（立体弧度）.132.3 RADIATION POWER DENSITY.152.4 RADIATION INTENSITY.20
2、2.5 BEAMWIDTH.222.6 DIRECTIVITY.252.6.1DirectionalPatterns.352.7 ANTENNA EFFICIENCY.402.8 GAIN.442.9 BEAM EFFICIENCY.492.10 BANDWIDTH.51中国科学技术大学朱旗中国科学技术大学朱旗2.11 POLARIZATION.522.11.1Linear,Circular,andEllipticalPolarizations.552.11.2PolarizationLossFactorandEfficiency.612.12 INPUT IMPEDANCE.672.14 A
3、NTENNA RADIATION EFFICIENCY.712.15 ANTENNA VECTOR EFFECTIVE LENGTH AND EQUIVALENT AREAS.742.15.1VectorEffectiveLength.742.15.2AntennaEquivalentAreas.782.16 MAXIMUM DIRECTIVITY AND MAXIMUM EFFECTIVE AREA.852.17 FRIIS TRANSMISSION EQUATION AND RADAR RANGE EQUATION.882.17.1FriisTransmissionEquation.882
4、.17.2RadarRangeEquation.912.17.3AntennaRadarCrossSection.98Problems.100 中国科学技术大学朱旗中国科学技术大学朱旗2p2“rtIddd2.1 INTTo dparamete2.2 RADAnan“a mathrepresenttheantenIn mostdetermineRadiadensity,directivityAcon AmTRODUCdescribeersarenecDIATIOntennaraematicaltation ofnnaasafucases,edintheation proradiationy,ph
5、aseonvenientmplitude fCTIONthe perfcessary.ON PATadiationpfunctionthe radiaunctionothe radfarfieldroperties in intensitorpolarizasetofcoofield patteN formanceTTERNpatternisn or aation profspacecodiation pregion.nclude pty,fieldation.”ordinatesern.e of andefinedagraphicaoperties ooordinatepattern ipo
6、wer flustrengthisshownantenna,asalofes.isuxh,inFigure Amplitu,definitio2.1.ude powerons of vr pattern.various中国科学技术大学朱旗中国科学技术大学朱旗Oftenthefieldandpowerpatternsarenormalizedtothemaximumvalue,yieldingnormalizedfieldandpowerpatterns.Thepatternisusuallyplottedonalogarithmicscale(dB).Thisscaleisdesirableb
7、ecausealogarithmicscalecanaccentuateinmoredetailsthosepartsofthepatternofverylowvalues.Field pattern typicallyrepresents a plot of themagnitudeoftheelectricormagneticfieldasafunctionoftheangularspace.Power pattern typicallyrepresents a plot of thesquareofthemagnitudeoftheelectricormagneticfieldasafu
8、nctionoftheangularspace.Powerpattern(indB)representsthemagnitudeoftheelectricormagneticfield,indecibels,asafunctionoftheangularspace.中国科学技术大学朱旗中国科学技术大学朱旗2mspStFtFc2.2.1RaVariominor,sidFigursymmetripatternwSome arethanotheFiguretwodimeFigure 2.characteradiationouspartsde,andbare2.3(calthrewithanue of
9、 greers,buta2.3(b)ensional.3(a)whisticsarenPatternofaradiaacklobes.(a)demeedimemberofeater radallareclaillustratepatternhere theindicatednLobesationpattemonstrateensionalradiationiation inssifiedasesaone plasame pd.ernarereesapolarlobes.ntensityslobes.linearane ofpatterneferredtooaslobes：majororrmai
10、n,中国科学技术大学朱旗中国科学技术大学朱旗瓣瓣lmIsi1b Amajo瓣瓣)isdefobecontmaximumInFigure2suchassp Amino A sideintended Aback180owithMinobeminimrlobe(mfinedas“tainingthmradiation2.3themplitbeamorlobe(旁旁lobe(副副瓣瓣lobe.”Uslobeis“arespecttorlobesuized.Sidemain beam“theradiaedirection.”majorlobeantennas旁旁瓣瓣)isany瓣瓣)is“auallya
11、sidaradiatiotothebeausuallyrepelobesarem，主，主ationonofeispointins,theremylobeexca radiatiodelobeisonlobewamofanapresentraethelargnginthemayexistmceptamaon lobe iadjacenthoseaxisantenna.”adiationiestminor=0diremorethanajorlobe.in any dtothemmakesan”nundesirrlobes.ection.Innonemajirection oainlobenangl
12、eoreddirectsomeantjorlobe.other thafapproxiionsandtennas,an thematelyshould中国科学技术大学朱旗中国科学技术大学朱旗2.2.2Isotropic,Directional,andOmnidirectionalPatterns Anisotropicradiatorisdefinedas“ahypotheticallosslessantennahavingequal radiation in all directions.”Although it is ideal and not physicallyrealizable,i
13、tisoftentakenasareferenceforexpressingthedirectivepropertiesofactualantennas.Adirectionalantennaisonehavingthepropertyofradiatingorreceivingelectromagneticwavesmoreeffectivelyinsomedirectionsthaninothers.An omnidirectional antenna is defined as one“having an essentiallynondirectional pattern in a gi
14、ven plane and a directional pattern in anyorthogonal plane.An omnidirectional pattern is then a special type of adirectionalpattern.2.2.3PrincipalPatternsForalinearlypolarizedantenna,performanceisoftendescribedintermsofitsprincipalEandHplanepatterns.中国科学技术大学朱旗中国科学技术大学朱旗 Than ThanAn2.5.For(elevatioEp
15、laneplane;=Other coselected.Figure 2principalc)andoplane;=eEplanedthedireeHplanedthedireillustratiothis exaonplane;and the=/2)isoordinate.Theomn2.6 has aEplanesoneprinci=90o).eisdefineectionofmeisdefineectionofmon is shoample,th=0)isxy plantheprince orientatnidirectionan infinite(elevatiopalHplaneda
16、s“themaximumedas“themaximumwn in Fighe xz ptheprincne(azimucipalHpltions cannalpattere numbeonplanes;ne(azimueplanecmradiationeplanecomradiationgureplanecipaluthalane.n bernofer of;=uthalontainingn.”ontainingtn.”gtheelecthemagnctricfieldeticfieldvectorvector中国科学技术大学朱旗中国科学技术大学朱旗2r(1b0Daab2.2.4FieThes
17、reactive(Fraunhof1.ReacForboundary0.62?/D is theantenna.a.Therb.Forequivboun/2eldRegispacesurnearfieldfer 夫琅和ctivenearmost any of thi/?,?istlargesteactivefia veryvalent radary is c.ionsroundingd,radiatin和费)regirfieldregntennas,s regionthewaveldimensioeldpredoshort dadiator,tcommonlyanantenng nearfon
18、sgionthe outen is?lengthanon of thominatesdipole,othe outey taken tnnaisusufield(Freser?deorertoallysubdisnel 菲涅ividedint涅耳)regioothreereon and faegions:arfield中国科学技术大学朱旗中国科学技术大学朱旗2nabmwtml2.RadiatiDefinnearfielda.Radiatib.TheandependfromthIftmaximumwhichisthe wavemay notimitedby0.62ingnearfnedas“td
19、regionanonfieldsgularfielddent upoheantenntheantmoveraverysmaelength,tt exist.y2?/?field(Freshatregiondthefarpredominddistribuon the dina.tennahalldimallcompahis fieldThe reg?2?snel)regionoftherfieldregnate utionisstancehasaensionredtoregionion is?/?.onfieldofagion。anantennnabetwe eenthereeactive中国科
20、学技术大学朱旗中国科学技术大学朱旗3abttf3.FarfielDefinea.Theantheantb.The fa2?/?Asththeregion(Frto smootfarfieldpatternconsistingone,ormd(Fraunhedas“thagularfieldtenna.rfield regfromtheheobservradiatinesnel),thth and foregion(is wellg of fewmore,majohofer)regatregionddistribugion is coeantennavationismgnhe patterorm
21、 lobe(Fraunhofformed,minor loorlobes.gionofthefieutionisesommonly.movedtonearfieldrn beginss.In thefer),the usuallyobes andldofanassentiallyy taken tontennaindependo exist atdentoftht distanceedistances greateefromer than中国科学技术大学朱旗中国科学技术大学朱旗pc2pepnBrcmoFigurpatternscalculated2D2/,4DItipatternsexcept
22、fopatternstnull andBecauseirealizablecommonlyminimumobservatiore2.9of a pard at disD2/,andsobserare almrsomedtructureat a leveinfinitede in pracyused distanconsis 2?showsrabolic retances oinfinity.rvedthamost idifferencesaroundtel belowistancesactice,thecriterioce of f?/.threeeflectorof R=attheentic
23、al,sinthehefirst25 dB.arenote mostonforfarfieldFFig.2.9中国科学技术大学朱旗中国科学技术大学朱旗2.2.5Radian（弧度）（弧度）andSteradian（立体弧度）（立体弧度）Themeasureofaplaneangleisaradian.Sincethecircumferenceofacircleofradius?is?2?,thereare 2 radinafullcircle.Themeasureofasolidangleisasteradian.Onesteradianisdefinedasthesolid angle wi
24、th its vertex at thecenterofasphereofradius?thatissubtended by a spherical surfaceareaequaltothatofasquarewitheachsideoflength r.AgraphicalillustrationisshowninFigure2.7(b).Sincethearea of a sphere of radius?is?4?,there are 4 sr?4?/?in aclosedsphere.Theinfinitesimalarea?onthesurfaceofasphereisgivenb
25、y?(m2)(21)Therefore,thesolidangle d canbewrittenas中国科学技术大学朱旗中国科学技术大学朱旗?/?(sr)(22)Example2.1Forasphereofradiusr,findthesolidangle(insquareradiansorsteradians)ofasphericalcaponthesurfacesphereoverthenorthpoleregiondefinedbysphericalanglesof030o,0360o.Dothisa.exactly.b.usingA12,where1and2aretwoperpendi
26、cularangularseparationsofthesphericalcappassingthroughthenorthpole.Comparethetwo.Solution:a.Using(22),wecanwritethat?/?0.83566b.?|?1.09662 Theapproximatebeamsolidangleisabout31.23%inerror.中国科学技术大学朱旗中国科学技术大学朱旗2.3 RADIATION POWER DENSITY The quantity used to describe the power associated with anelectr
27、omagneticwaveistheinstantaneousPoyntingvectordefinedas?(23)?：instantaneousPoyntingvector (W/m2)?：instantaneouselectricfieldintensity (V/m)?：instantaneousmagneticfieldintensity (A/m)SincethePoyntingvectorisapowerdensity,thetotalpower,crossingaclosedsurfacecanbeobtainedbyintegratingthenormalcomponento
28、fthePoyntingvectorovertheentiresurfaceP?(24)P:instantaneoustotalpower?W?;n?:unitvectornormaltothesurfaceda:infinitesimalareaoftheclosedsurface?m?中国科学技术大学朱旗中国科学技术大学朱旗Fortimevaryingfields,itisdesirabletofindtheaveragepowerdensity,whichisobtainedbyintegratingtheinstantaneousPoyntingvectoroveroneperioda
29、nddividingbytheperiod.Fortheform?,?,?;?,?,?25?,?,?;?,?,?26?Usingthedefinitionsof(25)and(26)andtheidentityRe?,?,?,?,?/2(23)canbewrittenas?(23)?(27)Finally,thetimeaveragePoyntingvector(averagepowerdensity)canbewrittenas?,?,?,?,?;?/2 (W/m2)(28)Note:Therealpartof?/2representstheaverage(real)powerdensity
30、 Theimaginarypartrepresentsthereactive(stored)powerdensity中国科学技术大学朱旗中国科学技术大学朱旗Baseduponthedefinitionof(28),theaveragepowerradiatedpowercanbewrittenas?Re?(29)Example2.1Theradialcomponentoftheradiatedpowerdensityofanantennais?(W/m2)?isthepeakvalueofthepowerdensity,isthesphericalcoordinate,anda?isthera
31、dialunitvector.Determinethetotalradiatedpower.SOLUTIONFor a closed surface,a sphere of radius?is chosen.To find thetotalradiatedpower,theradialcomponentofthepowerdensityisintegratedoveritssurface.中国科学技术大学朱旗中国科学技术大学朱旗np?2?Anormalizepowerde?1 m2.6.?threeedplotofensityatam is show?edimensioftheaveadist
32、ancwn in Fig?onalrageeofgure?中国科学技术大学朱旗中国科学技术大学朱旗An isotropic radiator is an ideal source that radiates equally in alldirections.Becauseofitssymmetricradiation,itsPoyntingvectorwillnotbeafunctionofthesphericalcoordinateangles and.Inaddition,itwillhaveonlyaradialcomponent.Thusthetotalpowerradiatedbyi
33、tisgivenby?4?(210)andthepowerdensityby?(W/m2)(211)whichisuniformlydistributedoverthesurfaceofasphereofradius?.中国科学技术大学朱旗中国科学技术大学朱旗2.4 RADIATION INTENSITY Radiationintensityinagivendirectionisdefinedasthepowerradiatedfrom an antenna per unit solid angle.The radiation intensity is a farfieldparameter,
34、anditcanbeobtainedbysimplymultiplyingtheradiationdensitybythesquareofthedistance.?(212)Where:?=radiationintensity(W/unitsolidangle);W?=radiationdensity(W/m2)Theradiationintensityisalsorelatedtothefarzoneelectricfieldofanantennaby?,?2?,?,?2?|?,?,?|?,?,?|?,?|?|?,?|?(212a)Where?:farzoneelectricfieldint
35、ensityoftheantenna?,?:farzoneelectricfieldcomponentsoftheantenna?:intrinsicimpedanceofthemediumThusthepowerpatternisalsoameasureoftheradiationintensity.中国科学技术大学朱旗中国科学技术大学朱旗Thetotalpowerisobtainedbyintegratingtheradiationintensity,asgivenby(212),overtheentiresolidangleof 4.Thus?(213)Comparison:?Examp
36、le2.2ForExample2.I,findthetotalradiatedpowerusing(213).SOLUTIONUsing(212)?andby(213)?Foranisotropicsource,?willbeindependentoftheangles and,aswasthecasefor?.Thus(213)canbewrittenas?4?(214)ortheradiationintensityofanisotropicsourceasU?P?/4(215)中国科学技术大学朱旗中国科学技术大学朱旗2i12ubTlaa2.5 BEAThebidenticalp1.Half
37、Po2.FirstNu Ofusuallyre ThbetweenThebeamobeincre ThantennaiadjacentrThemAMWIDeamwidthpointsonowerBeamullBeamwften,theferstoHPhebeamwitandthmwidthdeeasesandhebeamsalsouseradiatingmostcommDTH hofapatoppositemwidth(Hwidth(FN term bePBW.widthisahesideloecreases,viceversmwidthedtodessourcesomonresoternis
38、desideofthHPBW).BW).eamwidthtradeoffobelevel.thesidea.ofthescribetheortargets.olutioncriefined:thehepatternhf.eeeresolutio.iterioniseangularnmaximuoncapabFNBW/2,separatioum.bilitiestowhichisonbetweedistinguisusuallyuentwoshtwousedto中国科学技术大学朱旗中国科学技术大学朱旗approximateHPBW.Thatis,twosourcesseparatedbyangu
39、lardistancesequalorgreaterthanFNBW/2 HPBWofanantennacanberesolved.Iftheseparationissmaller,thentheantennawilltendtosmooththeangularseparationdistance.Example2.4ThenormalizedradiationintensityofanantennaisrepresentedbyU?cos?cos?3?,?0?90?,0?360?Findthea.halfpowerbeamwidthHPBW(inradiansanddegrees)b.fir
40、stnullbeamwidthFNBW(inradiansanddegrees)Solution:a.Since the?represents the power pattern,to find the halfpower中国科学技术大学朱旗中国科学技术大学朱旗beamwidth.LetU?|?3?|?0.5?cos?3?0.707?0.25rad?14.3250Since?issymmetricalaboutthemaximumat?0,thentheHPBWisHPBW?2?0.5rad?28.65?b.Tofindthefirstnullbeamwidth(FNBW),letthe?eq
41、ualtozeroU?|?cos?cos?3?|?0Thisleadstotwosolutionsfor?2?90?,?6?30?Theonewiththe smallestvalue leadstotheFNBW.Again,because of thesymmetryofthepattern,theFNBWisFNBW?2?3radians?60?中国科学技术大学朱旗中国科学技术大学朱旗2.6 DIRECTIVITY Thedirectivityofanantennadefinedastheratiooftheradiationintensityinagivendirectionfromt
42、heantennatotheradiationintensityaveragedoveralldirections.Theaverageradiationintensityisequaltothetotalpowerradiatedbytheantennadividedby 4.Ifthedirectionisnotspecified,thedirectionofmaximumradiationintensityisimplied.DirectivitycanbewrittenasD?,?|?D=directivity(dimensionless);D0=maximumdirectivity(
43、dimensionless)U=radiationintensity(W/unitsolidangle);?=totalradiatedpower(W)?=maximumradiationintensity(W/unitsolidangle);?=radiationintensityofisotropicsource(W/unitsolidangle);中国科学技术大学朱旗中国科学技术大学朱旗Forantennaswithorthogonalpolarizationcomponents,definethepartialdirectivityofanantennaforagivenpolariz
44、ationinagivendirectionas:Partialdirectivity?PartoftheradiationintensitywithagivenpolarizationinagivendirectionthetotalradiationintensityaveragedoveralldirectionsWiththisdefinitionforthepartialdirectivity,theninagivendirection“thetotaldirectivity is the sum of the partial directivities for any two or
45、thogonalpolarizations.”Forasphericalcoordinatesystem,thetotalmaximumdirectivity?fortheorthogonal and componentsofanantennacanbewrittenas?whilethepartialdirectivities?and?areexpressedas?,?where?=radiationintensityinagivendirectioncontainedin fieldcomponent?=radiationintensityinagivendirectioncontaine
46、din fieldcomponent中国科学技术大学朱旗中国科学技术大学朱旗?=radiatedpowerinalldirectionscontainedin fieldcomponent?=radiatedpowerinalldirectionscontainedin fieldcomponentExample2.5FindthemaximumdirectivityoftheantennawhoseradiationintensityisthatofExample2.2.Writeanexpressionforthedirectivityasafunctionofthedirectional
47、angles and.Solution:Theradiationintensityisgivenby?Themaximumradiationisdirectedalong?/2Thus?InExample2.2itwasfoundthat P?A?中国科学技术大学朱旗中国科学技术大学朱旗Wefindthatthemaximumdirectivityisequalto?4?4?1.27 Sincetheradiationintensityisonlyafunctionof,thedirectivityasafunctionofthedirectionalanglesisrepresentedby
48、?1.27?Example2.6Theradialcomponentoftheradiatedpowerdensityofaninfinitesimallineardipoleoflengthl isgivenby?(W/m2)where?is the peak value of the power density,is the usual sphericalcoordinate,and?is the radial unit vector.Determine the maximumdirectivity of the antenna and express the directivity as
49、 a function of thedirectionalangles and.中国科学技术大学朱旗中国科学技术大学朱旗Solution:Theradiationintensityisgivenby?2?Themaximumradiationisdirectedalong?/2.Thus?Thetotalradiatedpowerisgivenby?8?/3Using(216a),themaximumdirectivityisequalto?4?4?8?/3?1.5 greaterthan1.27inExample2.5.Thusthedirectivityisrepresentedby?1.
50、5?中国科学技术大学朱旗中国科学技术大学朱旗(abFigure(U?A?sa.Bothpb.Exampelevate 2.12 ssin)andpatternsaple 2.6 htionplaneshows thExampleareomnidhas moree.he relativ2.6(U?directionae directiove radiatA?sin?l onal chartion inte)racteristicnsities ocs(is naof Examprrower)ple 2.5in the中国科学技术大学朱旗中国科学技术大学朱旗AaTo21dthdAnothereap