dipole and mono pole antenna gain

8/12/2019 Dipole and Mono pole antenna gain

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Techn ica lRepor t1756 Sep t ember1997

D i p o l e a n d M o n o p o l e A n t e n n a G a i n a n d E f f e c t i v e A r e a forC o m m u n i c a t i o n F o r m u l a s J .C .Logan J .W .R o c k w a y

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W8FBC1VB*


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Technica lReport1756 September1997

D i p o l e a n d M o n o p o l e A n t e n n a G a i n a n d E f f e c t i v e A r e a forC o m m u n i c a t i o n F o r m u l a s J .C .Logan J .W .Roc kw a y

Approved for publicrelease;distributionisunlimited.

VNavalCommand,Controlan dOceanSurveillance CenterRDT EDivision,Sa nDiego,CA 92152-5001


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NAVALC OM M A N D,C O N T R O LA ND OC E A NSU RV E I L L A N C EC E N TE R R D T & EDIVISIONS a nDiego ,Ca l i f o rn i a 92152-5001 H -A.WILL IAMS,C AP T ,US NrrmaCo m m and i ngOfficer Lbs xecut iveDirector

ADMINISTRATIVEINFORMATION T heworkdescribedin thisreportw as performedby th eElectromagneticsandA dvancedTechnologyDivisiono fth eNavalCom m and,Controlan dOcea nSurveil lanceCenterR D T E Division.heworkw as fundedbyth eOfficeo fNavalResearch,Code334,under th eEM CTask

EM CommunicationSensorConceptsfo rIntegratedCompositeTopsideSubtaskofth eFY96Sur-faceShipHull,Mechanical ,andElectricalTechnologyProgram(program element0602121N).

Releasedby nderauthorityo fL.CRussell,Head .J.Sayre,H e a d AppliedElectromagnetics lectromagneticsA dvancedTechnology Division

SB


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C O N T E N T S INT RODUCT IONA N T E N N AP A R A M E T E R SA N T E N N AGAINA N T E N N AEFFECTIVEA R E AA N T E N N AEFFECTIVEHEIGHTTRANSMISSIONEQUATIONT RANSM ISS IONFOR S E V E R A L ANT ENNA CONFIGURATIONSDIPOLE TODIPOLEINFREE SPACE 7 M O N O P O L ETO M O N O P O L E ONAC O N D U C T I N GS U R F A C EM O N O P O L ETODIPOLE ABOVE AC O N D U C T I N GS U R F A C EDIPOLE TOM O N O P O L EO NAC O N D U C T I N GS U R F A C E0DIPOLE TODIPOLE ABOVEAC O N D U C T I N GS U R F A C E0S U M M A R Y 3R E F E R E N C E S 5

T a b l e s 1.alf-wavedipoleantenna configuration(paralleldipolesinfreespace)2.uarter-wavemonopoleantennaconfiguration(parallelmonopolesonagroundplane)3.uarter-wavemonopoleantennaconfiguration(parallelmonopolesonaground

plane)4.alf-wavedipoleantennaconfiguration(paralleldipolesaboveaconducting surface) 1


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INTRODUCTION A comparisoninvolvingantennameasurementsan dperformancepredictionshassome-t imesrevealeda6-dB discrepancybetweenth eground-wave transmissionmeasurementsand

th ecorrespondingcalculations.T hesourceofthis6-dB discrepancy isattributableto an in -correctdefinitionof th eeffectiveareaofth ereceivingverticalmonopoleantenna.Thiserro-neousdefinitionisthatth eeffectiveareaofth everticalreceivingm onopoleistwiceaslarge as thatofacorrespondingreceivingdipoleinfreespace(Wolf,1966).Thi sreportshowsthatth eeffectiveareaofamonopole isone-half thatofth ecorrespondingdipole.Itisthisvalueofeffectivearea thatresolvesth e6-dB discrepancybetweenm easurem entsan danalysis.Thi sdefinitionhasmeaningin th egeneralformsofth etransmission formulafo rcommuni-cationan dradarsystems.


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A N TE N N APA R A M E T E R S ANTE NNA GAIN

T hedirectivityan dgainof an antennaar eimportantmeasuresofits performanceasatransmittingsystem.If atransmitting antennaradiatesisotropically,th epowerdensityormagnitudeof th ePoyntingvector,P is o,atadistance,r,fromth etransmitterisP is o=W T/47 r r2, 1)

whereW Tis th eradiatedpower.Antennasgenerally don otradiatepower equallyinal ldirections.T hemagnitudeofth e

Poynting vectorisnotaconstant,butisusuallysomefunctionofth eangles0an d orP(0, ) ) .T heratioof th epower density radiatedafixeddistancein agivendirection to Pj S0sth egainofth eantenna.Thus,th etransmittinggaindescribesth evariationinp ow e rdensitywithangelandis

G T e, .)=p e ,


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T heavailablepower,W R ,atth ereceiverloadisW R=I 2RL

=V A 2R L/[( R A+ R L)2+(X A+ X L )2]2.6)T oobtainth em axi m ump ow e ravailableto th ereceivesystemload,th ei m pedanceof th e systemloadm ustbe equalto th ecomplexconjugateof th eimpedanceofth ereceiveantenna. Thus,fo rthisspecialcaseofm axi m ump ow e rtransfer,th em axi m umavailable p o w e ratth e receivesystem loadis

W Rm =V A 2/[4 R L ]. 7)Foran yotherm atchedcondition,th etransferredpower willbe smallerbyth eloadmis-matchlossfactor,L M :

LM=R L 2/[( R A+R L)2+(X A+ X L )2] .8)T hereceivedpower,W R ,isalsoequalto th escalarproductofth ep ow e rdensityofth ein -cidentwave,P(0,< j > ) ,an dth eeffectivearea,A ee,< | > ) ,ofth ereceiveantenna.T hepolarization mismatchistakenintoaccount withth efactorLPOL:

W R=L PO LP(0,(|))Ae(e,(j)). 9)T h epolarizationmismatchfactorisequalto1whenth epolarizationofth eincoming wave coincideswithth eantenna polarization.Thisisth econdition fo rmaximumreceivepower:

W Rm =P(0,(|))Ae(e,(()). 10)Usingequations(7 )and(10),th em axi m umeffectiveareais

A em (9,(j>)= V A 2/[4 R LP(e ,ft]. 11)ANTE NNA EFFECTIVEHE I G HT

F orlinearorwireantennas,anantennaparametersimilartoeffectiveareaisth econceptofeffectiveheight.For th eeffectiveheightof areceiveantenna,itissom eti m esconvenient to expressth einducedopen-circuit voltage,V A ,in termsofth eincidentpeakfieldintensity,E(9,< | > ) ,andeffectiveheight,he(9 , j > ) ,ofth eantenna,orV A=E q,f)heq,f). 12)

Again,th eeffectiveheightismaximumwhenth epolarizationmismatch factoris1 .Ifth e propagationm edi umh as an intrinsicimpedance,T |, p(e,


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Substitutingequations(12)an d(13)intoequation(11),th em axi m umeffectiveheightish em e,4 > ) =2[R L A em (G ,4 0 /ri] 1/2.14)

T h econceptsofeffectiveareaan deffectiveheightar eintrinsicallyrelated.TRANSMISSIONEQUATION

Equation(3 )ca nbe rearrangedtosolvefo rth epowerdensity availableat th ereceivean -tenna:

P(e,4 > )=Gr


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T R ANS M IS S IO NFOR SE V E RA LA N TE N N ACONFIGURATIONS T h etransmissionequationsar en ow appliedto th efollowingconfigurationsof transmitan dreceiveantennas.

DIPOLE TO DIPOLE FREE SP EConsidertw odipolesinfreespacethatar eorientedparalleltoeachother an dsituatedadistanceof10 0wavelengthsapart.A t10 0wavelengths,th etw oantennasarein th efa rfield

ofeachother.B o t hdipolesar ehalf-waveinlengthan dhavearadiusof0.0001wavelengths. O nedipoleantennaisacenter-fed transmitting dipole.T heotherantennaisareceivingdi- polethatisloadedinth ecenter withaconjugatematchedload.T h ehalf-wavedipolegainis2.16dB (Kraus,1950).Sinceth ereceivedipolehasaconju- gateloadimpedance,equation(18)ca nbeusedtocalculateth etransmission betweenth e dipoles.Thesecalculationscan thenbe verifiedbynumericalcomputationusing th emethod

ofmoments.F orthisanalysis,MININECProfessional isused(Rockwayetal.,1995).MINMEC Professionalisafrequency-domain,method-of-moments computer codefo rth eanalysisof wireantennas.U si ngth emethodof moments,MININEC Professionalsolvesan electricfieldformulation fo rth ecurrentsonelectricallythinwiresusingaGalerkinproce-durewithtriangular basisfunctions.Radiation patterns,nearfields,chargedistribution,im -pedancean dotherusefulparametersar ecomputedfromth ecurrentsolution.Thisformula-tionresultsinan unusuallycompactan defficientcomputeralgorithm.InthisnewestMININECeffort,th eformulation h as beenchangedtous etriangular basisfunctions,result-in gin greateraccuracy.T helimitationsofpreviousversionsofMININEChavebeenelimi-nated.T hecomputationalenginesar ewrittenin F O R T R A Nfo rgreaterspeedan dto m akemaximum us eofavailablem e m or y tose tarraysizes.T heuserinterfacerunsunderth e MicrosoftWindowsenvi ronm ent .Thisrepresentsasignificanti m provem entin th eM I N I N E Cantennamodelingcapability.T heuserinterfaceprovidesma nyconveni entoptionsfor defin-in gantennageometry.Built-ingraphics,onlinecontext-sensitive help,andproblemdiagnos-ticsai dth euserin problemdefinition.Outputgraphicsan dlinkagetospreadsheetsandwordprocessorsofotherWindowsapplicationsgreatlyenhance th einterpretation an danalysisofMININEC computations.

T heresultsofMININECProfessionalan dequation(18)fo rth efree-space,half-wavedi- poleantennaproblemar egivenintable1 .T heMININECProfessional resultsverifyth euse ofequation (18)andth ehalf-wavedipoleantennagainof approximately2.17dB .

Table Half-wavedipoleantennaconfiguration(paralleldipolesinfreespace).T h e o r y (dB) MININE Professional(dB)

Gain 2.16(Kraus) 2.17 T r a n s m i s s i o n -57.7(Eq.18 ) -57.6


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MONOPOLE TO MONOPOLE ON ONDU TING SURF EConsidertw overticalm onopoleson an infinite,perfectly conductinggroundplaneandsituatedadistance of10 0wavelengthsapart.Bothm onopolesar equarter-waveinlengthandhavearadiusof 0.0001wavelengths.Again,MININECProfessional can be applied.A gai n,th eantennasar ethinan dar einth efa rfieldsofeachother.O neantennaisa bottom-fed

transmitting monopole.T heotherantennaisa receivingmonopolethatisbase-loaded withaconjugatematchedload.T hegainofahemisphericsourceistwiceth egainofth ecorrespondingisotropicsource,a

sourceradiating inal ldirections(Kraus,1950).Thus,th egain,G TM (9 , > ) ,ofatransmittingm onopolehastwiceth egain,G TD (6 ,< | > ) ,ofth ecorresponding transmitting dipoleorGiM q,f)= 2GiD q,f). (20)

Thus,th egainofaquarter-wavemonopoleshouldhavetwiceth egainofacorresponding half-wavedipole,or5.16dB .MININECProfessional isagainusedtoverifyth eassumedgainof th em onopole .MININECProfessionalisalsousedtoverifyth euse ofequation(18)inth ecalculationoftransmission betweenth etransmitan dreceivemonopoles.Theseresultsar esummarizedin table2.

Table2.Quarter-wavemonopoleantennaconfiguration(parallelmonopolesonagroundplane).T h e o r y(dB) MININE Professional(dB)Gain 5.16(Kraus) 5.17 T r a n s m i s s i o n -51.7(Eq.18 ) -57.6

MININEC ProfessionalndKraus(1950)agreeon th egainofth etransmitting antenna.A sindicatedintable2,th etransmission resultsofequation(18)an dMININECProfessionaldo notagree.However,th etransmission prediction ofequation(18)isapproximately6dB orfourt imesgreaterthanth ecalculationofMININEC Professional.Comparing th eMININECProfessionalresultsoftables1an d2,th etransmission fo rth e tw odipolesinfreespaceisth esameasth etransmissionfo rth etw oequivalentmonopoleson aconductingsurface.Again,th egainof atransmitting monopoleistwiceth egainof th e

equivalenttransmittingdipole.Consideringequation(18)an dth eequivalenceofth edipole problemandmonopole problemtransmission,th erelationshipof th eeffectiveareaofam o-nopole,A em M (0 ,< 1 > ) ,to th eeffectiveareaofan equivalentdipole,A em D (6 ,< > ) ,isA e m D(6 ,< | > ) =4A em Me,< | > ) . (21)

T heeffectiveareaofth ereceivemonopoleisone-fourthth eeffectiveareaofth ecorre-spondingreceivedipole.Thus,ifamonopolean dadipolear eimmersedinidenticalfields


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th edipolewilldeliverto amatchedloadfourtimesth epowerasisavailablefromamonopole.

Forth edipole,equation(17)isrewritten as GRD(9,(t))=47rAe m D(e,()))/X 2. 22)Substitutingequations(20)an d(21)intoequation (17)fo ramonopole,

G R M ( 6 ,4 0 = 6T IA em M (9 ,< j > )/X 2. 23)Usingequation(23)in equation(16),th etransmissionbetweenmonopoleantennas

becom esW RM/WTM =GTM(e,)GRM(e,(|>)L R/4.24)

MININEC Professional isusedtoverifyth eus eof equation(24)in th ecalculationoftransmission between transmitan dreceivemonopoles.Theseresultsar esummarizedin table3.T heMINMECresultverifiesth eus eofequation(24)fo rth etransmission betweentransmitting an dreceiving monopoles.

Table3 (paralle Quarter-wavemonopoleantennaconfigurationmonopolesonagroundplane).Theory( dB ) MININE Professional( dB )

Ga in 5.16(Kraus) 5.17 Transmission -57.7(Eq.24 ) 57.6

MONOPOLET ODIPOLEABOVEACONDUCTINGSU R F A C EConsideraquarter-wavemonopolem ountedvertically on an infinite,perfectly conducting groundplane.T hemonopoleisabottom-fedtransmittingantenna.Ahalf-wave,receivingdipoleantennaissituated10 0wavelengthsfromth etransmittingmonopoleandiscenter-loadedwithaconjugatem atchedload.T h ereceivingdipoleantennaisoriented vertically to th egroundpanean dissituatedat variouselevationsaboveth egroundplane.Theseeleva-tionsar emeasured fromth ebottomof th edipolean dinclude0.5,1 ,3,5,7,and9wave-lengths.Bothantennashavearadiusof0.0001wavelengths.Extrapolatingth eresultsof th eprevioussections,equation(16)ca nbeadapted to calculate th etransmission.Forthisconfiguration,G T (9 ,< | > ) ecomesGTM 6,|> ) fo rth etransmitting monopole.Equation(21)isusedfo rth ereceivingdipolewithagainofGTD 9, > ) F orthisconfiguration,th e transmissionequationbecom es

W RD /W T M=GTM ( 9 ,< J 0 G R D ( 9 , |> ) LR. (25)


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Equation(25)givesatransmissionvalueof-54.7dBfo rthisconfiguration.T heMININEC Professionalcalculationisalso-54.7dB fo ral lofth ereceivedipoleelevations. DIPOLET OMONOPOLEONACONDUCTI NGS URFACE

Consider ahalf-wave,transmittingdipolesituatedverticallyatvariousdistancesabovean infinite,perfectly conductinggroundplane. heseelevationsar em easuredfromth ebottom ofth edipoleandinclude0.5,1,3,5,7,an d9wavelengths.T hehalf-wavedipoleisacenter -fe dtransmitting antenna.A quarter-wave,receivingmonopoleissituated10 0wavelengthsfromth etransmittingdipolean disbottom-loadedwithaconjugateload.B o t hantennashave aradiusof0.0001wavelengths.Equation(16)ca nagainbeusedtocalculateth etransmission.F orthisconfiguration,th e existenceofth eground planeresultsinadoubleincreasein th efieldatth emonopole overafree-spacefieldfromth edipole.Equation(23)isusedfo rth ereceivingmonopole withagain

ofG T M (0 ,< ) . orthisconfiguration, th etransmission equationbecom esW RM/WTD-2GT D(e,


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Table4 .Half wavedipoleantennaconfigurationparalleldipolesaboveaconductingsurface).

TransmitterHeight

FTGTDq,f )( dB )Eq.(27)

Transmission( d B )

MININEProfessionalTransmission( d B )

.5 7 .8 -5 2 -5 21 7 .3 -52.5 52.53 1 .8 -5 8 -585 -8 67.9 67.97 5 .3 -54.6 54.69 8 -51.9 51.9


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S U M M A R YInth eabovediscussionan u m b e rofdifferentantennaconfigurationshavebeenconsid-ered.ro mthesestudiesageneralformofth etransmissionformulafo racommunication

circuitca nbe derived.Thisgeneralform isW R/W T =FTGT0,4 0RGRMCO,4 0 R.28)T ouse thisequation,th egainofamonopoleistwiceth egainof th ecorrespondingdipole(i.e.,equation(19)).W h e nth etransmittingdipoleisinfreespaceorth etransmittingantenna isamonopole,Fjisunity.W h e nth etransmitting antennaisadipoleantennaan dislocatedaboveagroundplane,FTm aynotbe unityan dwilldependon th eelevationof th etransmit- tingantennaaboveth egroundplaneandth elocationat which th eradiatedfieldisdeter-mined(e.g.,th elocationofth everticalreceiveantenna).Ifth ereceiveantennaisam o-nopole,FRwillbe0.25.If th ereceiveantennaisadipoleorientedaboveagroundplane,FRwillbeunity.T h emaximum effectiveareaofareceivemonopoleisone-fourthth em axi m umeffectiveareaofth ecorrespondingdipole.T herelationship of gaintom axi m umeffectiveareafor adipoleis

G t o( e , 4 0=4 7 iA em D (6,(t))/X 2.29)T h erelationshipof gainandmaximum effectiveareafo racorrespondingm onopoleis

G e,4 > ) -16T IA em M (e ,4 0 /x2.3 0)T h econceptsof effectiveareaan deffectiveheightar eintrinsically relatedby

hem(9,4=[2R LA em e,4 > ) /r \ ]m. 31)T hemaximum effectiveheightofareceivemonopoleisone-half th em axi m umeffectiveheightof th ecorrespondingdipole.

13


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RE F E RE N C E S Kraus,J.D.1950.Antennas.McGraw-Hi l lB o o kCo.,N ew York,N Y .Rockway,J.W .an dJ.C.Logan.1995.MININECProfessional forWindows.EM Scientific,

Inc.,CarsonCity,N V .Wolff,E.A.1966.AntennaAnalysis.JohnWileyandSons.,N e w York,N Y .

15


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13 .A B S T R A C T Maximum200words)

Acomparisoninvolvingantennameasurementsandperformancepredictionsh assometimesrevealeda6-dBdiscrepancyb et ween th egr o und - wa v et ransmissionmeasurementsandth ecorrespondingcalculat ions. h esource ofthis6-dBdiscrepancyisattributabletoan incorrectdefinitionofth eeffectiveareaofth ereceivingverticalm o n o -piea nt enna .h is erroneousdefinit ionisthatth eeffectiveareaofth everticalreceivingm on opl eistwiceaslargeasthatofacorrespondingreceivingdipolein freespace.hisreports h o w sthatth eeffectiveareaofamonopoleisone-halfthatofthecorrespondingdipole.t isthisvalueofeffectivearea thatresolvesthe6 -dBdiscrepancybetween m e as u re m e n tsan danalysis. h isdefinit ionh asmeaningin th egeneralformsofth etransmissionformulaforcommunicaitionandradars ys t em s .

14 .SUBJECTT E R M S MissionArea:C o m m a n d ,Control,an dC o m m unica t io nsantennagain a nt ennaeffectivearea transmissionformulas a nt ennaconfigurations

15 .N U M B E ROFP A G E S 19

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dipole and mono pole antenna gain

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