IEEE Transactions on Antennas and Propagation

436 Pages·2012·73.696 MB·English

JANUARY2012 VOLUME60 NUMBER1 IETPAK (ISSN0018-926X)
PAPERS
Antennas
MaximumGainofaLossyAntenna............................................................ A.ArbabiandS.Safavi-Naeini 2
ExperimentalValidationofPerformanceLimitsandDesignGuidelinesforSmallAntennas ................................
........................... D.F.Sievenpiper,D.C.Dawson,M.M.Jacob,T.Kanar,S.Kim,J.Long,andR.G.Quarfoth 8
SubstrateIntegratedWaveguide(SIW)Leaky-WaveAntennaWithTransverseSlots ........................................
...............................................................................................J.Liu,D.R.Jackson,andY.Long 20
SubwavelengthSubstrate-IntegratedFabry-PérotCavityAntennasUsingArtificialMagneticConductor..................
....................................................................... Y.Sun,Z.N.Chen,Y.Zhang,H.Chen,andT.S.P.See 30
AReconfigurableWidebandandMultibandAntennaUsingDual-PatchElementsforCompactWirelessDevices........
................ H.F.Abutarboush,R.Nilavalan,S.W.Cheung,K.M.Nasr,T.Peter,D.Budimir,andH.Al-Raweshidy 36
Frequency-ReconfigurableMonopoleAntennas............................................ A.TariqandH.Ghafouri-Shiraz 44
LowProfileFullyPlanarFoldedDipoleAntennaonaHighImpedanceSurface..............................................
....................................................................A.Vallecchi,J.R.DeLuis,F.Capolino,andF.DeFlaviis 51
CrumplingofPIFATextileAntenna ...................................................................... Q.BaiandR.Langley 63
HigherOrderModeExcitationforHigh-GainBroadsideRadiationFromCylindricalDielectricResonatorAntennas ...
......................................................................... D.Guha,A.Banerjee,C.Kumar,andY.M.M.Antar 71
OntheCharacteristicsoftheHighlyDirectiveResonantCavityAntennaHavingMetalStripGratingSuperstrate........
.......................................................................................................A.ForoozeshandL.Shafai 78
Nature of Cross-Polarized Radiations from Probe-Fed Circular Microstrip Antennas and Their Suppression Using
DifferentGeometriesofDefectedGroundStructure(DGS)........................................C.KumarandD.Guha 92
Single, Dual and Tri-Band-Notched Ultrawideband (UWB) Antennas Using Capacitively Loaded Loop (CLL)
Resonators ............................................................................ C.-C.Lin,P.Jin,andR.W.Ziolkowski 102
LeakyWaveEnhancedFeedsforMultibeamReflectorstobeUsedforTelecomSatelliteBasedLinks ....................
.............................................................................. A.Neto,M.Ettorre,G.Gerini,andP.DeMaagt 110
Arrays
94GHzSubstrateIntegratedMonopulseAntennaArray .................................. Y.J.Cheng,W.Hong,andK.Wu 121
ThePlanarUltrawidebandModularAntenna(PUMA)Array............................ S.S.HollandandM.N.Vouvakis 130
ATwo-ChannelTimeModulatedLinearArrayWithAdaptiveBeamforming ..................... Y.TongandA.Tennant 141
AperiodicArrayLayoutOptimizationbytheConstraintRelaxationApproach ...............................................
.................................. T.N.Kaifas,D.G.Babas,G.S.Miaris,K.Siakavara,E.E.Vafiadis,andJ.N.Sahalos 148
TimeReversalBasedBroadbandSynthesisMethodforArbitrarilyStructuredBeam-SteeringArrays .....................
.......................................................................................D.Zhao,Y.Jin,B.-Z.Wang,andR.Zang 164
AGeneralizedHybridApproachfortheSynthesisofUniformAmplitudePencilBeamRing-Arrays ......................
.................................................................................................... O.M.BucciandD.Pinchera 174
PolarimetryWithPhasedArrayAntennas:TheoreticalFrameworkandDefinitions ..........................................
.............................................................K.F.Warnick,M.V.Ivashina,S.J.Wijnholds,andR.Maaskant 184
AnAmplifyingReconfigurableReflectarrayAntenna ............................................ K.K.KishorandS.V.Hum 197
DesignofRetrodirectiveAntennaArraysforShort-RangeWirelessPowerTransmission .......... Y.LiandV.Jandhyala 206
(ContentsContinuedonp.1)
(ContentsContinuedfromFrontCover)
AnisotropicImpedanceSurfacesforLineartoCircularPolarizationConversion .............................................
..................................................E.Doumanis,G.Goussetis,J.L.Gómez-Tornero,R.Cahill,andV.Fusco 212
Imaging andPropagation
Transmitting-ModeTimeReversalImagingUsingMUSICAlgorithmforSurveillanceinWirelessSensorNetwork.....
........................................................................................... X.-F.Liu,B.-Z.Wang,andJ.L.-W.Li 220
UWBMicrowaveImagingofObjectsWithCanonicalShape...................................................................
.................................................................... N.Ghavami,G.Tiberi,D.J.Edwards,andA.Monorchio 231
ExperimentalCharacterizationofanUWBPropagationChannelinUndergroundMines....................................
............................................................................................ Y.Rissafi,L.Talbi,andM.Ghaddar 240
StatisticalPredictionofSiteDiversityGainonEarth-SpacePathsBasedonRadarMeasurementsintheUK...............
.....................................................................................................C.NagarajaandI.E.Otung 247
WidebandCharacterizationofBackscatterChannels:DerivationsandTheoreticalBackground ............................
......................................................................................D.Arnitz,U.Muehlmann,andK.Witrisal 257
CalibrationofElectricFieldSensorsOnboardtheResonanceSatellite ........................................................
............................................ M.Sampl,W.Macher,C.Gruber,T.Oswald,H.O.Rucker,andM.Mogilevsky 267
NumericalandAnalyticalTechniques
ASecond-OrderAsymptoticApproximationfortheSommerfeldHalf-SpaceProblem ..............................W.Lihh 274
DirectRationalFunctionFittingMethodforAccurateEvaluationofSommerfeldIntegralsinStratifiedMedia...........
........................................................................................................................T.N.Kaifas 282
IntegralEquationModelingofDoublyPeriodicStructuresWithanEfficientPMCHWTFormulation .....................
...........................................................................................S.Nosal,P.Soudais,andJ.-J.Greffet 292
Reduced-Order Models of Finite Element Approximations of Electromagnetic Devices Exhibiting Statistical
Variability .................................................................. P.Sumant,H.Wu,A.Cangellaris,andN.Aluru 301
SphericalADIFDTDMethodWithApplicationtoPropagationintheEarthIonosphereCavity ............................
......................................................................................................D.L.PaulandC.J.Railton 310
AnalysisofDirectionalLoggingToolsinAnisotropicandMultieccentricCylindrically-LayeredEarthFormations ......
...................................................................................... G.-S.Liu,F.L.Teixeira,andG.-J.Zhang 318
Analytic Transient Analysis of Radiation From Ellipsoidal Reflector Antennas for Impulse-Radiating Antennas
Applications ............................................................ S.-C.Tuan,H.-T.Chou,K.-Y.Lu,andH.-H.Chou 328
An Analytic Solution of Transient Scattering From Perfectly Conducting Ellipsoidal Surfaces Illuminated by an
ElectromagneticPlaneWave .......................................... H.-T.Chou,S.-C.Tuan,K.-Y.Lu,andH.-H.Chou 340
Green’sFunctionExtractionforInterfacesWithImpedanceBoundaryConditions............. E.SlobandK.Wapenaar 351
ElectromagneticFieldofaHorizontalInfinitelyLongWireOvertheDielectric-CoatedEarth ..............................
................................................................................................... Y.J.Zhi,K.Li,andY.T.Fang 360
DecomposableMediumConditionsinFour-DimensionalRepresentation ...... I.V.Lindell,L.Bergamin,andA.Favaro 367
COMMUNICATIONS
NovelUHFRFIDTagAntennaforMetallicFoilPackages ..................................J.Ryoo,J.Choo,andH.Choo 377
DesignofaBroadbandAll-TextileSlottedPIFA ............P.J.Soh,G.A.E.Vandenbosch,S.L.Ooi,andN.H.M.Rais 379
AnUltrawideband(UWB)SlotlineAntennaUnderMultiple-ModeResonance ..............................................
......................................................................................... X.D.Huang,C.H.Cheng,andL.Zhu 385
ACompactHepta-BandLoop-InvertedFReconfigurableAntennaforMobilePhone........................................
........................................................................ Y.Li,Z.Zhang,J.Zheng,Z.Feng,andM.F.Iskander 389
Hybrid Monopole-DRAs Using Hemispherical/Conical-Shaped Dielectric Ring Resonators: Improved Ultrawideband
Designs .............................................................................. D.Guha,B.Gupta,andY.M.M.Antar 393
AHalfMaxwellFish-EyeLensAntennaBasedonGradient-IndexMetamaterials ...........................................
.......................................................................................Z.L.Mei,J.Bai,T.M.Niu,andT.J.Cui 398
Dual-PolarizedPlanarFeedforLow-ProfileHemisphericalLuneburgLensAntennas ........ A.R.WeilyandN.Nikolic 402
TMScatteringbyPerfectlyConductingPolygonalCross-SectionCylinders:ANewSurfaceCurrentDensityExpansion
RetaininguptotheSecond-OrderEdgeBehavior............................G.Coluccini,M.Lucido,andG.Panariello 407
AModificationoftheKummer’sMethodforEfficientComputationofthe2-Dand3-DGreen’sFunctionsfor1-DPeriodic
Structures .........................................................................................................S.P.Skobelev 412
ASpatialBeamSplitterConsistingofaNear-ZeroRefractiveIndexMedium ................................................
....................................................................................... R.-B.Hwang,N.-C.Hsu,andC.-Y.Chin 417
ExtendedMode-BasedBandwidthAnalysisforAsymmetricNear-FieldCommunicationSystems ....Y.TakandS.Nam 421
ERRATA
Erratato“Three-DimensionalNear-FieldMicrowaveHolographyUsingReflectedandTransmittedSignals” ............
.................................................................R.K.Amineh,M.Ravan,A.Khalatpour,andN.K.Nikolova 425
ListofReviewersfor2011 ........................................................................................................ 426
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DigitalObjectIdentifier10.1109/TAP.2011.2181917
2 IEEETRANSACTIONSONANTENNASANDPROPAGATION,VOL.60,NO.1,JANUARY2012
Maximum Gain of a Lossy Antenna
Amir Arbabi,StudentMember,IEEE, and SafieddinSafavi-Naeini,Member,IEEE
Abstract—Anupperboundontheachievablegainofalossyan- or,ashasrecentlybeenreported,byexploitingengineeredma-
tennaisderived.Thislimitdependsontheantennasizeandanewly terialsasapartofthematchingcircuit[8].Furthermore,inmil-
defined“lossmeritfactor,”whichisshowntobeameasureofthe
limeterwave,Tetrahertz,andopticalfrequencyantennas,radi-
antenna material loss. The derived limit extends the well-known
ationefficiencyreductionduetotheantennalossesismorere-
upperlimitontheratioofantennadirectivitytoitsqualityfactor
tothelossyantennas.Optimalantennacurrentdistributionforthe strictivethanthebandwidth.Basedonthesefacts,thestudyof
maximumgainisfound,andtheradiationpatternandantennaef- the material loss and optimizing the antenna current distribu-
ficiencyarealsopresented. tion in a way to minimize its material loss and maximize the
gainallowustooptimizetheantennastructureundermorere-
Index Terms—Antenna maximum gain, lossy antenna, quality
factor,smallantenna. alisticconditions.Toourknowledge,thisinvestigationhasnot
been performed yet. Although [9] considered the effect of en-
ergylossduetosurroundingmediumofanantenna,theantenna
I. INTRODUCTION itselfwasstillassumedtobelosslessandenclosedinalossless
sphere.Therefore,theantennamateriallossthatresultedfrom
ahighreactivenearfieldwasnotconsidered.
A N ANTENNA is an essential component of a wireless In this paper, the effect of the antenna material loss on the
system.Small-sizeantennaswithoptimalgainandband- maximumachievablegainisanalyzed.Tothisend,theantenna
widthareonhighdemandforcompactpower-efficientportable isassumedtobeenclosedinavirtualsphereanditsfieldsout-
radios.However,thereisawell-knowntradeoffbetweenthean- side the sphere are expanded in terms of orthogonal vectorial
tenna gain, its size, and its achievable bandwidth. It is shown spherical modes whose coefficients are related to the current
thatarbitraryhighgaincanbeachievedfromanarbitrarysmall distributioninsidethesphere.Itisshownthateachofthevec-
perfectelectricconductor(PEC)sphereifthecurrentdistribu- torial spherical modes has its own radiation efficiency which
tiononthesphereisselectedinaproperway[1].Chuderived dependsontheantennasizeandanewlydefinedmaterialloss
an upper limit on the antenna directivity and ratio of antenna meritfactor.Itisobservedthatthemodeefficiencies,exceptfor
directivitytoqualityfactorforomnidirectionalantennaswitha afewlowestordermodes,areverysmall.Thisresultisaman-
finitenumberofvectorialsphericalmodes[2].Indeed,regard- ifestation of the finite rank of the free space Green’s function
lessofsize,thereisnolimitonthegain ofa losslessantenna, whosemoregeneralformisdiscussedin[10].
but for achieving high gain, the current amplitude on the an-
tenna surface should be large. Large current amplitude on the
II. PROBLEMDESCRIPTION
antenna generates large reactive stored energy around the an-
tenna.Thisreactiveenergyincreasestheantennaqualityfactor. Itis assumed thatthe antenna radiatesinfreespace and the
FollowingChu,severalresearcherstriedtoquantifythetradeoff smallestspherethatenclosestheantennahasaradiusof .The
between the antenna directivity and the large reactive energy coordinatesystemischoseninawaythattheoriginisthecenter
storedaroundtheantenna[1],[3]–[6].In[5]and[6],itisshown ofthesphereandits axisisorientedintheantenna’smaximum
thatthereisalimitontheratioofdirectivitytoqualityfactorof radiationdirection.Itisalsoassumedthattheantennaisfedbya
a general lossless antenna. In all of these studies, the antenna lumpedsourceand,therefore,thedirectradiationoftheapplied
isassumedtobelosslessanditsqualityfactorisregardedasa source is ignored. The electric and magnetic field satisfy the
measureoftheantennainputimpedancebandwidth.Although Maxwell’sequationsintheentirespace
alargequalityfactorrepresentshighreactiveenergyandsmall
bandwidth,therelationbetweentheconventionalqualityfactor
(1a)
andbandwidthbecomeslessusefulforlowandmoderatevalues
(1b)
ofqualityfactor[7].Inaddition,low- antennascanbematched
toadesiredimpedanceoverabandwidthwiderthanwhatisde-
where istheequivalentcurrentdensity
terminedbytheirqualityfactorsbyusinglumped,quasilumped
(2)
ManuscriptreceivedJanuary30,2011;revisedMay01,2011;acceptedJuly
02,2011.DateofpublicationSeptember15,2011;dateofcurrentversionJan-
and ispositiondependent.Itshould benoticed
uary05,2012. Thisworkwassupportedby theNationalScienceandEngi-
neeringCouncil(NSERC)ofCanadaandResearchInMotion(RIM). thattheconductivityofthematerialcanbeconsideredasapart
The authors are with the Department of Electrical and Computer Engi- of .Withthisassumption,thecurrentisnonzeroonlyoverthe
neering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail:
regionoccupiedbytheantenna,whichisenclosedbythevirtual
[email protected];[email protected]).
DigitalObjectIdentifier10.1109/TAP.2011.2167934 sphere.Outsideofthissphere,fieldsaresolutiontosourcefree
0018-926X/$26.00©2011IEEE
ARBABIANDSAFAVI-NAEINI:MAXIMUMGAINOFALOSSYANTENNA 3
Maxwell’sequationsandcanbeexpandedintermsofvectorial notedthatalthough and constituteasetofmutually
sphericalharmonics[11] orthogonalvectorialfunctions,theydonotformacompleteset
asshownin(8a)and(8b)atthebottomofthepage.
Thetotalradiated power bythe antennacanbe foundusing
(3a)and(3b)withintegrationofthePoynting’svector
(9)
(3a)
because of the orthogonality of the modes, the total radiated
poweristhe superpositionofthepowerradiatedbyeachindi-
vidualmode.Maximumradiationintensity,aswasassumedat
(3b) thebeginning,isinthe 0directionandcanbefoundfrom
(3a)inthefar-fieldregionas
where is the spherical Hankel function of the second
order, arethesphericalharmonics
(4)
and isadifferentialoperatordefinedas (10)
(5)
Nowthemateriallosswillbeconsidered.Thedissipativeloss
oftheantennaresultsfromtheantennamateriallossandisgiven
The and in (3a) and (3b) are coefficients of the
by
and modes,respectively.Thesecoefficientscanbefoundby
projectingthevolumecurrentdensityonanorthogonalvectorial
set.If representsthespherevolume,then(seeAppendixA)
(11)
(6a)
Itwillbeshownthatforagivenantennasize,theantennagain
(6b)
onlydependsonadimensionlessparameterdefinedas
where and are given in (41a) and (41b) in Ap-
(12)
pendixA.Itcanbeverifiedthat and aremutually
orthogonal
which is referred to as “loss merit factor.” Using this new pa-
(7a)
rameter,materiallossbecomes
(7b) (13)
(7c) is an “effective loss merit factor” for the antenna and is
defined according to (13). This parameter is equal to the loss
where isKronecker’sdeltafunctionwhichisnonzeroonly merit factor of the antenna material if the antenna is made of
when and, in this case, it is equal to , and onlyonetypeofmaterial.Foraninhomogeneousantenna,the
arenormsof and ,respectively.Thesenorms effectivelossmeritfactorissmallerthanthelargestmeritfactor
aregivenin(8a)and(8b)andareindependentof .Itshouldbe ofitsdifferentconstituents.
(8a)
(8b)
4 IEEETRANSACTIONSONANTENNASANDPROPAGATION,VOL.60,NO.1,JANUARY2012
Thevolumecurrentdensity canbewrittenasthesummation andbydefining
of two parts: Its projection on the space spanned by and
andapartwhichisorthogonaltothisspace,thatis (20a)
(14) (20b)
where isorthogonalto and Equation(19)canberewrittenas
(15)
and and areprojectionsof onnormalized and
andaregivenby
(21)
(16a)
it can be seen from (21) that and are efficiencies of
eachindividual and modes.Finally,theantenna
(16b) gaincanbefoundtobegivenby(22),shownatthebottomof
the page.
isthenonradiatingpartoftheequivalentcurrentdensity.The
III. OPTIMIZATIONOFTHEGAIN
fields generated by vanish identically at any point outside
thespherevolume .Thenonradiatingcurrentdensity nei- In(22),thetermsinthenumeratorandthedenominatorareall
therexcites nor modesoutsidethesphere.Furtherdis- positiveand isonlypresentinthedenominator.Tomaximize
cussiononnonradiatingcurrentdensitiescanbefoundin[12]. thefraction,thedenominatorcanbeminimizedindependently
From(14)and(15),thenormof canbewrittenas by setting the nonradiating current density to zero. As was
mentioned in Section II, does not radiate and according to
(18), it adds to the dissipated power; therefore, the optimum
antennashouldhave .Similarreasoningleadsto
(17) (23)
pluggingtheleft-handsideof(17)in(13)gives Bydefining
(24a)
(24b)
(24c)
(18)
(24d)
Theantennatotalinputpoweristhesummationoftheradi-
atedanddissipatedpower Equation(22)canberewrittenas
(25)
Becauseofthesymmetryof(25)withrespectto and and
(19) with respect to and , equating partial derivatives of the
(22)
ARBABIANDSAFAVI-NAEINI:MAXIMUMGAINOFALOSSYANTENNA 5
tozerowillresultinsimilarequationsandidenticaloptimal
valuesforthesecoefficients
(26a)
(26b)
Furthermore,thenumeratorismaximizedbyrequiring
(27)
using(26)and(27),(25)issimplifiedas
(28)
Fig.1. Modeefficienciesfor(cid:0)(cid:2)((cid:0) )and(cid:0)(cid:3)((cid:0) )modesasafunction
of(cid:2)for(cid:3)(cid:4) (cid:4)10and(cid:5) (cid:4)(cid:5)(cid:6) .
Finally, and give
(29)
and
(30a)
(30b)
IV. RESULTSANDDISCUSSION
Plugginginnormsof and from(8)into(20),the
modeefficienciesarefoundas
Fig.2. Maximumantennagainasafunctionof(cid:3)(cid:4)fordifferentvaluesof(cid:5)
(31a) for(cid:3)(cid:4)between0.05and0.5.ThedashedlinecurveshowsHarrington’snormal
gain(cid:6) (cid:4)(cid:7)(cid:3)(cid:4)(cid:8) (cid:9)(cid:10)(cid:3)(cid:4).
(31b)
with are propagating modes and other modes are in
cutoff. Our results show that the efficiency of each individual
Theseequationsshowthatthemodeefficienciesand,therefore, sphericalmodeisindependentof .Thestep-likedependency
themaximumgainareonlyafunctionof andtheantenna of efficiencies on can be regarded as a cutoff, but the cutoff
size. For copper, silver, and gold, the loss merit factor ( ) at edgeisnotonlyafunctionoftheantennasizebutalsoantenna
microwavefrequenciesisontheorderof andforadielectric material(“effectivelossmeritfactor”).Forexample,inFig.1,
material with a permittivity of 10 and a loss tangent of modeswith canbeassumedtobepropagatingmodes,
isabout5 .Fig.1showsthemodeefficiencies andothermodeshavesmallefficiencyandcanbeignored.
asafunctionof for 10and .Ascanbeseen Figs.2and 3showthe maximum antennagain for different
fromthisfigure, and showstep-likebehaviorandare values of . The dashed line curve shows Harrington’s
almostequaltoeachotherforthesamevalueof .Thisstep-like “normal”gaindefinedas .Itisclear
behavior is reminiscent of the assumptions made by Chu and thatforalargeandmoderatevalueof ,themaximumgain
Harringtonforomn-directionalanddirectionalantennas[1],[2]. is larger than what Harrington found using only modes with
For a directional antenna, based on the mode impedance for .Thislargergaincomeswithhigherqualityfactorand
eachofsphericalmodes,Harringtonassumedthatonlymodes smallerinputimpedancebandwidth.
6 IEEETRANSACTIONSONANTENNASANDPROPAGATION,VOL.60,NO.1,JANUARY2012
Fig.3. Maximumantennagainasafunctionof(cid:0)(cid:2)fordifferentvaluesof(cid:3) Fig.5. Efficiencyoftheantennawithmaximumgainasafunctionof(cid:0)(cid:2)for
for(cid:0)(cid:2)between0.5and5.ThedashedlinecurveshowsHarrington’snormal differentvaluesoftheantennaeffectivelossmeritfactor((cid:3) ).
gain(cid:4) (cid:0)(cid:2)(cid:0)(cid:2)(cid:3) (cid:4)(cid:5)(cid:0)(cid:2).
V. CONCLUSION
In this paper, a new fundamental limit on antenna gain was
introduced. It was shown that although a lossless antenna re-
gardless of its size can have arbitrarily high gain, the antenna
dissipativelosslimitsthegainforarealantenna.Themaximum
gainisafunctionoftheantennasizeanditsmateriallossmerit
factor. General plots for maximum gain for different antenna
sizeandlossmeritfactorwereprovided.
APPENDIX
SPHERICALHARMONICSCOEFFICIENTSOFTHEFIELDOFA
VOLUMECURRENTDENSITY
Coefficientsoffieldexpansionintermsofvectorialspherical
harmonicscanbefoundfromvolumecurrentandchargedensity
as [11]
Fig.4. Radiationpatternoftheantennawithmaximumgainwith(cid:5)(cid:2) (cid:0) (cid:5)
and(cid:3) (cid:0) (cid:6)(cid:7) .
(33a)
Using(14),(16),and(30),theequivalentcurrentdistribution
(33b)
insidethesphereforanantennawithmaximumgainisgivenby
where is the speed of light in vacuum and is the volume
chargedensityrelatedtocurrentdensitybythecontinuityequa-
tion
(32)
(34)
Fig.4showstheradiationpatternofanantennawiththemax-
after substituting from (34) into (33a), the first term in the
imumgainfor and .Since and
right-handsidecanbewrittenas
are almost the same, the radiation patterns in different cutting
planes containing the axis are similar. As can be seen from
thisfigure,thesidelobelevelisabout20dB.Fig.5showsthe
efficiency of the antenna with maximum gain as a function of
itssizefordifferentvaluesoftheeffectivelossmeritfactor.
ARBABIANDSAFAVI-NAEINI:MAXIMUMGAINOFALOSSYANTENNA 7
(42b)
(35)
REFERENCES
thesurfaceintegraliszerobecause isassumedtobeenclosed
[1] R.F.Harrington,TimeHarmonicElectromagneticFields. NewYork:
inthevolume .Theright-handsideof(33b)canbesimplified McGraw-Hill,1961.
as [2] L.J.Chu,“Physicallimitationsofomni-directionalantennas,”J.Appl.
Phys.,vol.19,pp.1163–1175,Dec.1948.
[3] H.A.Wheeler,“Smallantennas,”IEEETrans.AntennasPropag.,vol.
AP-23,no.4,pp.462–469,Jul.1975.
[4] R.C.Hansen,“Fundamentallimitationsinantennas,”Proc.IEEE,vol.
69,no.2,pp.170–182,Feb.1981.
[5] R.L.Fante,“Maximumpossiblegainforanarbitraryidealantenna
with specified quality factor,” IEEE Trans. Antennas Propag., vol.
AP-40,no.12,pp.1586–1588,Dec.1992.
[6] W. Geyi, “Physical limitations of antenna,” IEEE Trans. Antennas
Propag.,vol.51,no.8,pp.2116–2123,Aug.2003.
(36) [7] S.R.Best,“TheFosterreactancetheoremandqualityfactorforan-
tennas,”IEEEAntennasWirelessPropag.Lett.,vol.3,pp.306–309,
2004.
and with similar reasoning, the surface integral has vanished. [8] R.W.ZiolkowskiandA.Erentok,“Metamaterial-basedefficientelec-
Using(35)and(36),(33a)and(33b)canberewrittenas tricallysmallantennas,”IEEETrans.AntennasPropag.,vol.54,no.7,
pp.2113–2130,Jul.2006.
[9] A. Karlsson, “Physical limitations of antennas in a lossy medium,”
IEEETrans.AntennasPropag.,vol.52,no.8,pp.2027–2033,Aug.
2004.
[10] D.A.B.Miller,“Fundamentallimitforopticalcomponenets,”J.Opt.
Soc.Amer.B,vol.24,no.10,Oct.2007.
[11] J.D.Jackson,ClassicalElectrodynamics,3rded. NewYork:Wiley,
1999.
(37a) [12] A.J.DevaneyandE.Wolf,“Radiatingandnonradiatingclassicalcur-
rentdistributionsandthefieldstheygenerate,”Phys.Rev.D,vol.8,no.
4,pp.1044–1047,1973.
(37b)
AmirArbabi(S’06)wasborninMalayer,Iran,in
1984.HereceivedtheB.Sc.degreeinelectricalengi-
Usingthefollowingidentities:
neeringfromtheUniversityofTehran,Tehran,Iran,
in2006,theM.Sc.degreeinelectricalengineering
(38) from the University of Waterloo, Waterloo, ON,
Canada,in2009,andiscurrentlypursuingthePh.D.
degreeinelectricalengineeringattheUniversityof
and Illinois,Urbana-Champaign.
HehasbeenaResearchAssistantwiththePho-
(39) tonicSystemsLaboratory,UniversityofIllinois,Ur-
bana-Champaign,since2009.Hisresearchinterests
includeplasmonicandnanophotonicdevices,fastnumericalmethodsforsimu-
Equations(37a)and(37b)arefurthersimplifiedas
lationanddesignofnovelphotonicdevices,andfundamentalfeaturesandlimits
inopticsandelectromagnetics.
Mr.ArbabiwasarecipientoftheOntarioGraduateScholarshipandthePres-
ident’sGraduateScholarshipwhileattheUniversityofWaterloo.Heisastu-
dentmemberoftheOpticalSocietyofAmericaandareviewerfortheIEEE
PHOTONICSJOURNAL.
(40a)
(40b) SafieddinSafavi-Naeini(M’00)wasborninGach-
saran,Iran,in1951.HereceivedtheB.Sc.degreein
electricalengineeringfromtheUniversityofTehran,
andbydefining Tehran, Iran, in 1974 and the M.Sc. and Ph.D.
degreesinelectricalengineeringfromtheUniversity
of Illinois, Urbana-Champaign, in 1975 and 1979,
respectively.
HejoinedtheDepartmentofElectricalandCom-
puterEngineering,UniversityofTehran,asanAs-
(41a) sistantProfessorin1980andbecameanAssociate
Professor in 1988. Since 2002, he has been a Full
ProfessorintheDepartmentofElectricalandComputerEngineering,Univer-
(41b) sityofWaterloo,Waterloo,ON,Canada.Hisresearchinterestsandactivities
includenumericalelectromagneticsappliedtoradio-frequency/microwave/mil-
limeter-wavesystemsandcircuits,antennasandpropagation,wirelesscommu-
equations(40a)and(40b)become nicationsystems,very-high-speeddigitalcircuits,andopticalcommunication
systems.Hehasbeenascientificandtechnicalconsultanttoanumberofna-
(42a) tional and international telecommunication industrial and research organiza-
tionssince1980.
8 IEEETRANSACTIONSONANTENNASANDPROPAGATION,VOL.60,NO.1,JANUARY2012
Experimental Validation of Performance Limits and
Design Guidelines for Small Antennas
DanielF. Sievenpiper,Fellow,IEEE, DavidC. Dawson,Member,IEEE, MinuM. Jacob,StudentMember,IEEE,
Tumay Kanar,StudentMember,IEEE, SanghoonKim, Jiang Long,and RyanG.Quarfoth,StudentMember,IEEE
Abstract—Thetheoreticallimitforsmallantennaperformance papersaswellasothersthatfollowedhaveprovidedtheoretical
thatwasderiveddecadesagobyWheelerandChugovernsdesign guidelinesforotheraspectsofsmallantennadesign.Ingeneral,
tradeoffsforsize,bandwidth,andefficiency.Theoreticalguidelines
thebestperformancewillbeachievedifthedielectricconstant
have also been derived for other details of small antenna design
isaslowaspossible,iftheaspectratioisclosetounity,andif
such as permittivity, aspect ratio, and even the nature of the in-
ternalstructureoftheantenna.Inthispaper,weextractandan- the internal structure of the antenna is such that the fields fill
alyze experimental performance data from a large body of pub- the minimum size enclosing sphere with the greatest possible
lished designs to establish several facts that have not previously uniformity.
beendemonstrated:(1)Thetheoreticalperformancelimitforsize,
Alongwiththeworkthathasbeendonetodeveloptheoretical
bandwidth, and efficiency are validated by all available experi-
limits,alargeamountofefforthasbeenputintodevelopingspe-
mental evidence. (2) Although derived for electrically small an-
tennas, the same theoretical limit is also generally a good design cificantennadesignsinanattempttooptimizetherelationship
ruleforantennasthatarenotelectricallysmall.(3)Thetheoretical between size and bandwidth. In the 64 years since Wheeler’s
predictionsfortheperformanceduetodesignfactorssuchasper- first paper, thousands of new antenna designs have been pub-
mittivity,aspectratio,andtheinternalstructureoftheantennaare
lished, and each year we continue to see new publications ex-
alsosupportedbytheexperimentalevidence.Thedesignsthathave
ploringeveryconceivablearrangementofmetalshapesanddi-
thehighestperformancearethosethatinvolvethelowestpermit-
tivity,haveanaspectratioclosetounity,andforwhichthefields electricregions.However,manyofthesedesignshavesub-op-
filltheminimumsizeenclosingspherewiththegreatestuniformity. timumperformance,andcouldhavebeenpredictedtoperform
Thisworkthusvalidatestheestablishedtheoreticaldesignguide- poorly if the theoretical design guidelines were more clearly
lines.
understood from the start. In addition, many antenna designs
Index Terms—Bandwidth, dielectric resonator antenna, effi- are proposed for which performance is overestimated, such as
ciency, fractal, metamaterial, planar antenna, quality factor, slot by ignoring losses or incorrectly calculating the true electrical
antenna,smallantenna.
sizeoftheantenna.Thischallengesnotonlyantennaengineers,
whomustaddresstheseunphysicalperformanceclaims,butalso
system engineers,whoenduprelyingonperformancemetrics
I. INTRODUCTION
that are ultimately unachievable. These issues may be caused
inpartbecausethetheoreticaldesignguidelinesarenotwidely
S MALLantennashavebeenanimportanttopicofresearch understood, and in fact have never been rigorously validated
for many decades, and interest in the field is increasing experimentally.
with the development of new systems that require broadband Unfortunately, it is impossible to experimentally “prove” a
antennas with a small form factor. The analysis of small an- physicaltheory—itcanonlybedisprovenbycontradictoryex-
tennasisgenerallyconsideredtohavebegunwith theworkof perimentalevidence.Nonetheless,atheorythathasbeentested
Wheeler[1]andChu[2],whoestablishedthetheoreticallimits extensivelyandfoundtobetrueinalltestsisgenerallyaccepted
thatshowhowelectricalsizeandbandwidtharerelated.Since ascorrect,atleastuntilcontradictoryevidenceisfound.Inthe
thisearlywork,numerousauthorshaverevisitedthesetheories, fieldofsmallantennas,therehavebeenmanyattemptstoopti-
andhavesuggestedfurtherrefinements.Althoughslightlymore mizeantennadesignstogetascloseaspossibletothetheoretical
accurate,allofthesenewtheoriessharethesamebasicconclu- limits. However, each of these antennas represents a local op-
sionsestablishedinthe1940s—thatsizecanonlybereducedat timization,andineachcaseitispossiblethattheauthorshave
theexpenseofbandwidthorefficiency.Furthermore,theearly simplynotchosenthebestdesign,andperhapsanotheronemay
befoundthatcouldexceedthetheoreticallimit.Thepurposeof
thispaperistosystematicallyextractexperimentalresultsfrom
a sufficiently large sample of existing designs to demonstrate
Manuscript received February 10, 2011; revised May 17, 2011; accepted
July12,2011.DateofpublicationSeptember15,2011;dateofcurrentversion that the Wheeler-Chu limit is valid and correct across a broad
January 05, 2012. This work was supported by SPAWAR under Contract rangeofelectricalsizesandbandwidths.Wefurthermoreshow
N66001-03-2-8938.
thatthedesignguidelinesthathavebeenestablishedforpermit-
D.F.Sievenpiper,M.M.Jacob,T.Kanar,S.Kim,J.Long,andR.G.Quarfoth
areallwiththeUniversityofCaliforniaSanDiego,LaJolla,CA92093USA tivity,aspectratio,andtheinternalstructureoftheantennaare
(e-mail:[email protected]). alsosupportedbytheexperimentalevidence.
D. C. Dawson is with SPAWAR Systems Center Pacific, San Diego, CA
Thispaperestablishesseveralimportantfacts:(1)Whenthe
92152USA(e-mail:[email protected]).
DigitalObjectIdentifier10.1109/TAP.2011.2167938 sizeandefficiencyarecorrectlycalculated,themeasuredband-
0018-926X/$26.00©2011IEEE