A Geometrically-Appropriate Cavity Model for a Spherical Inverted-F Antenna (SIFA)

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2404IEEETRANSACTIONSONANTENNASANDPROPAGATION,VOL.61,NO.5,MAY2013

AGeometrically-AppropriateCavityModelfora

SphericalInverted-FAntenna(SIFA)

DavidL.Rolando,StudentMember,IEEE,andGregoryH.Huff,SeniorMember,IEEE

Abstract—Acavitymodelforasphericalinverted-Fantenna(SIFA)isproposedusingacustomcurvilinearcoordinatesystem.Thecoordinatetransformationmapsthesphericalstructureintoanequivalentrectangulartopologytowhichconventionalcavitymethodprocedurescanbeapplied.Thewaveequationunderthistransformationissolvedtopredictthemodalcharacteristics,inputimpedance,andradiationbehavioroftheantenna.Analyti-cally-obtainedresultsarecomparedtosimulatedmodelsandthemeasuredresultsfromonefabricatedmodel.

IndexTerms—Cavitymodel,conformalantenna,patchantenna,sphericalinverted-Fantenna(SIFA).

I.INTRODUCTIONTHECAVITYMODELforplanarmicrostrippatchan-

tennas[1]–[5]hasbeenappliedtoawiderangeof

conformalantennas,includingthosewithcylindrical[6]–[9],

spherical[9]–[14],andconical[15]geometries.Cavityanalysis

providesphysicalinsightintotheoperationoftheseantennas

andenablesaccuratepredictionofmodalcharacteristics,input

impedance,andradiationbehavior.

Well-definedsolutionscantypicallybeobtainedfromcavity

analysisusingCartesianorcommonnon-Euclideancoordinate

systemssuchascylindricalandspherical.Thegeometryof

thesphericalinverted-Fantenna(SIFA)[16],[17]presents

aslightlydifferentopportunitytoapplythecavitymodel.In

itsmostbasicconceptualform,theSIFAcomprisesaplanar

inverted-Fantenna(PIFA)conformedontoaquadrantofa

sphereandrecessedintoitsvolume(similarinthisregardto

[8],[10],[11]).Therefore,itislumpedintothebroadcategory

ofconformalmicrostripantennas.Itspatchtopology,however,

doesnotleadtoaseparablesolutionforthewaveequationin

anystandardcoordinatesystem.Theproposedcavityanalysis

fortheSIFAmitigatesthisgeometriccomplexitythrough

acustomcoordinatetransformationthatyieldsaseparable

solutiontothewaveequation.

First,thebasicphysicalmodeloftheSIFAisreviewed.Then,

acustomcurvilinearcoordinatesystemisintroducedtoconve-

nientlydescribetheSIFAcavity.Intermsofthisnewcoordinate

system,thewaveequationissolvedinsidethecavity.Cavity

ManuscriptreceivedApril19,2012;revisedDecember04,2012;acceptedJanuary22,2013.DateofpublicationFebruary11,2013;dateofcurrentversionMay01,2013.Thismaterialisbaseduponworksupportedby,orinpartby,theU.S.ArmyResearchLaboratoryandtheU.S.ArmyResearchOfficeunderagreementnumberW911NF-09-1-0429.TheauthorsarewiththeElectromagneticsandMicrowaveLaboratoryintheDepartmentofElectricalandComputerEngineeringatTexasA&MUniversity,CollegeStation,TX77843-3128USA(web:www.ghhuff.com;e-mail:prof.ghuff@gmail.com).Colorversionsofoneormoreofthefiguresinthispaperareavailableonlineathttp://ieeexplore.ieee.org.DigitalObjectIdentifier

10.1109/TAP.2013.2246533Fig.1.SimulatedmodeloftheSIFAwith(a)generalizedpatchgeometryand(b)canonicalpatchgeometry.

fields,radiationpatterns,andinputimpedancearecomputed.

Theresultsofthecavitymodelarecomparedtosimulationsand

measurements.Finally,abriefdiscussionofthecurrentshort-

comingsinthemodelandpossiblefutureworkarediscussed.

II.SPHERICALINVERTEDF-ANTENNA

AsimulatedmodeloftheSIFAisshowninFig.1alongwith

importantgeometricparameters.Themostgeneralizedgeom-

etryisshowninpart(a)ofthefigure.Theresonantstructure

consistsofametallicpatchconformedontoanoutersphereand

ametallicgroundplaneconformedontoasmallerinnersphere.

Thepatchstructureoccupieslessthanone-quarterofthesur-

faceareaofthesphere.Thegroundplaneisextendedtoinclude

theremainingportionoftheoutersphericalsurface.Asmall

metallicshortingstripconnectsthepatchtothegroundplane.

TheSIFAconsideredinthisworkisfedbyaradially-directed

coaxialprobe.

AsimplifiedversionoftheSIFAgeometry,showninFig.1(b),hasashortingstripthatisthesamewidthasthepatchstruc-

ture(i.e.,).Thisparticulargeometrymostresembles

thestructureofaPIFAandisconsideredinthisworktobe

the“canonical”versionoftheSIFA.Forsimplicity,thecavity

analysisdevelopedhereinisappliedonlytodesignssatisfying

.TableIliststhespecificdimensionsandsubstrate

parametersforthreesuchcanonicalSIFAdesignsreferredto

throughoutthispaper.Theyareofvarioussizesandoperateat

differingresonantfrequencies.

III.CAVITYMODEL

A.SIFACavityandBoundaryConditions

Fig.2(a)showstheproposedgeometryfortheSIFAcavity.

Thegeometryisachievedbyextrudingthetwo-dimensional

patchstructureontheoutersphereradiallyinwardtothe

groundplane.Themetallicpatchandgroundplanearegiven

0018-926X/$31.00©2013IEEEROLANDOANDHUFF:AGEOMETRICALLY-APPROPRIATECAVITYMODELFORASIFA2405

TABLEISIFADESIGNPARAMETERS

Fig.2.(a)ProposedSIFAcavitygeometrywithboundaryconditions.(b)Sim-ulatedelectricfieldundertheSIFApatch.Thequarter-wavevariationofthefieldalongthelengthofthepatchreinforcestheboundaryconditionsofthecavity.