Microstrip Leaky-Wave Antennas

IEEETRANSACTIONSONANTENNASANDPROPAGATION,VOL.56,NO.7,JULY20081853

CharacterizationandDesignofCylindrical

MicrostripLeaky-WaveAntennas

Lieh-ChuanLin,HayatoMiyagawa,ToshihideKitazawa,SeniorMember,IEEE,RueyBingHwang,SeniorMember,IEEE,andYu-DeLin,Member,IEEE

Abstract—Thespectral-domainapproachisappliedfortheanalysisandthedesignofthecylindricalmicrostripleaky-waveantenna.Thefirsthigher-orderleaky-modeisthoroughlyinvesti-gated.Weperformthewell-knownspectral-domainapproachandGalerkin’smethodtoacquirethecomplexpropagationconstantsofleakymodes,whichareverifiedwithresultsobtainedbythescattering-parameterextractiontechnique.Twopracticalan-tennasaredesignedandimplemented.Measuredreturnlossandradiationpatternsshowagoodperformanceofthesecylindricalantennas,comparedtothatoftheplanarones.

IndexTerms—Cylindricalmicrostrip,leaky-wave,spectral-domainapproach(SDA).

I.INTRODUCTION

SPACE-WAVEleakymodesonmanykindsofplanar

transmissionlineshavebeenwidelystudiedandalsore-

ceivednumerousattentions[1]–[6].Leaky-waveantennasare

well-knownfortheiradvantagessuchashigh-gain,wide-band,

etc.Theyalsohavethefrequency-scanningfeature.Although

cylindricaltransmissionlineshavebeenresearchedin[7]–[14],

printedleaky-waveantennasbasedoncylindricalsubstrates

haveyettobestudiedthoroughlyintheliteratures[15]–[17],

whichmayfindapplicationsinsystemsthatrequireconformal

antennasincylindricalshapes.

Thispaperfirstpresentsananalysistoobtainthepropaga-

tioncharacteristicsofthefirsthigherorderleakymodeonthe

cylindricalmicrostripantennas.InSectionII,weusethespec-

traldomainapproach(SDA)[18]tocharacterizethefirsthigher

ordermodeofthecylindricalmicrostripline.Odd-symmetry

andeven-symmetrycurrentbasisfunctionsarechoseninthe

longitudinalandtransversedirections,combinedwiththeedge

conditions.SectionIIIcontainsthenumericalresultsthatchar-

acterizetheeffectsofdifferentouterradiiofcylinders,substrate

thicknesses,andstripwidths.Theleaky-modescatteringparam-

eterextractiontechnique[19]isalsousedtoprovideaverifi-

cationofthenumericalresultsobtainedbySDA.SectionIV

showstheimplementationandmeasurementsoftwocylindrical

leaky-waveantennaswithaperture-couplingfeedingstructures.

Bothoftheseantennashavehighgainsandwidebandwidth.

ManuscriptreceivedDecember8,2006;revisedJanuary25,2008.Pub-lishedJuly7,2008(projected).ThisworkwassupportedinpartbytheNationalScienceCouncilunderGrantsNSC95–2218-E-009–041andNSC95–2752-E-002–009,andinpartbytheKinkiMobileRadioCenter,FoundationunderKMRCR&DGrantforMobileWireless.L-.C.Lin,R.B.Hwang,andY.-D.LinarewithNationalChiaoTungUni-versity,Hsinchu,Taiwan,R.O.C.(e-mail:cm_doglin@hotmail.com).H.MiyagawaandT.KitazawaarewithRitsumeikanUniversity,Kusatsu,Shiga525-8577,Japan.DigitalObjectIdentifier

10.1109/TAP.2008.924693Fig.1.Thecross-sectionalviewofthecylindricalmicrostripline.

II.THEORY

Fig.1showsthecrosssectionofthecylindricalmicrostrip

line.RegionIisthecylindricalsubstratewithapermittivityof

andathicknessof.RegionIIisfreespace.The

stripwithacircumferentialwidthisplacedontopofthesub-

strate.Andtheinnergroundconductorislocatedatacircumfer-

enceofradius.Thepermeabilitiesofallmaterialsare.The

thicknessofthestripandthegroundconductorareassumedto

bezeros.Weexpandthez-componentsoffieldsincylindrical

coordinatesbyinverseFourierseries(suppressingthetime-har-

monicexpressionandz-dependence)[12]as(1)(2)(3)

(4)where

anddefinethe-directionpropagationconstantsuchthat

,whereandaretheattenuationcon-

stantandthephaseconstant,respectively.isthe-directed

propagationconstant.Thecanbeexpressed

intermsoffromMaxwell’sequationsincylindrical

coordinates.

Toanalyzethefirsthigherorderleakymodewithanodd

symmetry,weplaceaPECboundaryatthebottom

0018-926X/$25.00©2008IEEE1854IEEETRANSACTIONSONANTENNASANDPROPAGATION,VOL.56,NO.7,JULY2008

Fig.2.ThePECboundaryrepresentationandtransformation.

inFig.2.ThelongitudinalfieldsbetweenthePEC

sidewallsarethestandingwaves,inthecircumferentialdirec-

tionasopposedtothecreepingwavesin[15].Inthestructure

underconsiderationinthispaper,thepropagationdirectionof

themicrostripleaky-waveantennaisalongthe-directionofthe

cylinder.Shouldsomeapplicationsdemandthatthepropagation

directionofthemicrostripleaky-waveantennasbealongthe

-directionofthecylinder,theanalysismethodin[15]thatim-

plementedWatsontransformtotakeintoaccount,thecreeping

waves,surfacewaves,andspace-waveleakywavesshouldbe

employed.

Thecross-sectiononthe-planecanbetransformedinto

thatoftheplanarmicrostriplinewiththePECsidewalls,like

shieldedmicrostriplines.Thisdirectmappingissimilartothat

usedin[20].Sincethetwoendpointsand

areactuallythesamepointsandatthesamePECboundary,thefieldsbetweenthemareperiodicfunctions.

Tocomputethefieldsinthesidewalls,thevariablesof

theinverseFourierseries(1)–(4)areintegersontherealaxis(-axis)ofthe-plane.Insolvingplanarmicrostripleaky-wave

structures[21]–[24],thevariablesusedinintegrationsover

therealaxisarecontinuous;however,variablesarediscretein

solvingcylindricalstructures.Sincethesurface-waveleakage

phenomenoninplanartransmissionlineswillnotoccurin

cylindricalsubstrates,noconsiderationofthesurfacewave

leakageisneededinthisanalysis.Thebranchpointsinsolving

planarmicrostripleaky-wavestructures[21]–[24]arenot

neededinsolvingcylindricalstructuresbecausethevariables

areirrelevantto.

Thesignof-directionwavenumberinfreespace

intheseries(1)–(4)shouldbechosenproperlytosat-

isfytheexponentialgrowthconditionofthespace-waveleakage

inthepositive-direction,andthissquarerootisattheimproper

Riemannsheet.Thesimilarchoiceofbranchisdefinedin[25].

Resortingtotheorthogonalityoftheeigenfunctionindi-

rection,boundaryconditionsinspectraldomainareusedtode-

terminetheunknowns

Onthegroundconductor

(5)

Ontheboundarybetweenthesubstrateandtheair(6)

(7)Onthestrip(8)

(9)wherearetheFouriertransformsofthecurrentden-sity,onthestrip.From(1)–(4)and(5)–(9)withsomealgebraicoperations,

aresolvedandweobtaintherelationshipsbetweenand(10)

(11)

Thecurrentdensities,areexpandedintermsofbasisfunctions,as

(12)

withunknowncoefficients.Thebasisfunctionsusedinthecomputationsare(13a)

(13b)

consideringthatz-componentand-componentcurrentsareoddandevenandfunctionsof,respectively.Thenumbersofbasisfunctionsand,areand,respectively.TakingtheinverseFouriertransformof(10)–(11),wecanob-tainthetangentialfieldinRegionII.Thenweapplythere-mainingboundaryconditionsthatthetangentialfieldsvanishonthestrip(14)

(15)

Fornumericalcomputation,wetaketheinnerproductoftheaboveequationswiththebasisfunctionsandastestingfunctions(Galerkin’smethod)overthestrip

(16)