Microstrip Leaky-Wave Antennas

IEEETRANSACTIONSONANTENNASANDPROPAGATION,VOL.56,NO.7,JULY2008
1853

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

Abstract—Thespectral-domainapproachisappliedforthe
analysisandthedesignofthecylindricalmicrostripleaky-wave
antenna.Thefirsthigher-orderleaky-modeisthoroughlyinvesti-
gated.Weperformthewell-knownspectral-domainapproachand
Galerkin’smethodtoacquirethecomplexpropagationconstants
ofleakymodes,whichareverifiedwithresultsobtainedbythe
scattering-parameterextractiontechnique.Twopracticalan-
tennasaredesignedandimplemented.Measuredreturnlossand
radiationpatternsshowagoodperformanceofthesecylindrical
antennas,comparedtothatoftheplanarones.

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

I.I
NTRODUCTION

S
PACE-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).Thisworkwassupportedinpartbythe
NationalScienceCouncilunderGrantsNSC95–2218-E-009–041andNSC
95–2752-E-002–009,andinpartbytheKinkiMobileRadioCenter,Foundation
underKMRCR&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.
DigitalObjectIdentifier10.1109/TAP.2008.924693

Fig.1.Thecross-sectionalviewofthecylindricalmicrostripline.
II.T
HEORY

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

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1854IEEETRANSACTIONSONANTENNASANDPROPAGATION,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].Sincethetwoendpoints
and
areactuallythesamepointsandatthesamePECboundary,the
fieldsbetweenthemareperiodicfunctions.
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)