Microstrip Antennas

85 Pages·2012·3.54 MB·English

International Journal of Antennas and Propagation
Microstrip Antennas
Microstrip Antennas
International Journal of Antennas and Propagation
Microstrip Antennas
Copyright©2012HindawiPublishingCorporation.Allrightsreserved.
Thisisafocusissuepublishedin“InternationalJournalofAntennasandPropagation.”Allarticlesareopenaccessarticlesdistributed
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videdtheoriginalworkisproperlycited.
Editorial Board
M.Ali,USA Se-YunKim,RepublicofKorea SadasivaM.Rao,USA
CharlesBunting,USA AhmedA.Kishk,Canada SembiamR.Rengarajan,USA
FelipeCa´tedra,Spain TribikramKundu,USA AhmadSafaai-Jazi,USA
Dau-ChyrhChang,Taiwan ByungjeLee,RepublicofKorea SafieddinSafavi-Naeini,Canada
DebChatterjee,USA Ju-HongLee,Taiwan MagdalenaSalazar-Palma,Spain
Z.N.Chen,Singapore L.Li,Singapore StefanoSelleri,Italy
MichaelYanWahChia,Singapore YilongLu,Singapore KrishnasamyT.Selvan,India
ChristosChristodoulou,USA AtsushiMase,Japan ZhongxiangQ.Shen,Singapore
Shyh-JongChung,Taiwan AndreaMassa,Italy JohnJ.Shynk,USA
LorenzoCrocco,Italy GiuseppeMazzarella,Italy M.SinghJitSingh,Malaysia
TayebA.Denidni,Canada DerekMcNamara,Canada Seong-YoupSuh,USA
AntonijeR.Djordjevic,Serbia C.F.Mecklenbra¨uker,Austria ParveenWahid,USA
KaruP.Esselle,Australia MicheleMidrio,Italy YuanxunEthanWang,USA
FranciscoFalcone,Spain MarkMirotznik,USA DanielS.Weile,USA
MiguelFerrando,Spain AnandaS.Mohan,Australia QuanXue,HongKong
VincenzoGaldi,Italy P.Mohanan,India TatSoonYeo,Singapore
WeiHong,China PavelNikitin,USA YoungJoongYoon,Korea
HonTatHui,Singapore A.D.Panagopoulos,Greece WenhuaYu,USA
TamerS.Ibrahim,USA MatteoPastorino,Italy JongWonYu,RepublicofKorea
NemaiKarmakar,Australia MassimilianoPieraccini,Italy AnpingZhao,China
Contents
ModalResonantFrequenciesandRadiationQualityFactorsofMicrostripAntennas,JanEichler,
PavelHazdra,MiloslavCapek,andMilosMazanek
Volume2012,ArticleID490327,9pages
TunableCompactUHFRFIDMetalTagBasedonCPWOpenStubFeedPIFAAntenna,LingfeiMoand
ChunfangQin
Volume2012,ArticleID167658,8pages
SomeRecentDevelopmentsofMicrostripAntenna,YongLiu,Li-MingSi,MengWei,PixianYan,
PengfeiYang,HongdaLu,ChaoZheng,YongYuan,JinchaoMou,XinLv,andHousjunSun
Volume2012,ArticleID428284,10pages
NewConfigurationsofLow-CostDual-PolarizedPrintedAntennasforUWBArrays,GuidoValerio,
SimonaMazzocchi,AlessandroGalli,MatteoCiattaglia,andMarcoZucca
Volume2012,ArticleID786791,10pages
DesignandAnalysisofWidebandNonuniformBranchLineCouplerandItsApplicationinaWideband
ButlerMatrix,YuliK.Ningsih,M.Asvial,andE.T.Rahardjo
Volume2012,ArticleID853651,7pages
IsolationImprovementofaMicrostripPatchArrayAntennaforWCDMAIndoorRepeaterApplications,
HongminLeeandJinwonPark
Volume2012,ArticleID264618,8pages
Series-FedMicrostripArrayAntennawithCircularPolarization,Tuan-YungHan
Volume2012,ArticleID681431,5pages
VerticalMeanderingApproachforAntennaSizeReduction,LiDeng,Shu-FangLi,Ka-LeungLau,
andQuanXue
Volume2012,ArticleID980252,5pages
MicrostripPatchAntennaBandwidthEnhancementUsingAMC/EBGStructures,R.C.Hadarig,
M.E.deCos,andF.Las-Heras
Volume2012,ArticleID843754,6pages
High-PerformanceComputationalElectromagneticMethodsAppliedtotheDesignofPatchAntenna
withEBGStructure,R.C.Hadarig,M.E.deCos,andF.Las-Heras
Volume2012,ArticleID435890,5pages
AWidebandHigh-GainDual-PolarizedSlotArrayPatchAntennaforWiMAXApplicationsin5.8GHz,
AmirRezaDastkhoshandHamidRezaDaliliOskouei
Volume2012,ArticleID595290,6pages
HindawiPublishingCorporation
InternationalJournalofAntennasandPropagation
Volume2012,ArticleID490327,9pages
doi:10.1155/2012/490327
Research Article
Modal Resonant Frequencies and Radiation Quality Factors of
Microstrip Antennas
JanEichler,PavelHazdra,MiloslavCapek,andMilosMazanek
DepartmentofElectromagneticField,FacultyofElectricalEngineering,CzechTechnicalUniversityinPrague,Technicka´2,
16627,Prague,CzechRepublic
CorrespondenceshouldbeaddressedtoPavelHazdra,[email protected]
Received9August2011;Revised10January2012;Accepted13January2012
AcademicEditor:CharlesBunting
Copyright©2012JanEichleretal.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,
whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
The chosen rectangular and fractal microstrip patch antennas above an infinite ground plane are analyzed by the theory of
characteristic modes. The resonant frequencies and radiation Q are evaluated. A novel method by Vandenbosch for rigorous
evaluation of the radiation Q is employed for modal currents on a Rao-Wilton-Glisson (RWG) mesh. It is found that the
resonantfrequencyofarectangularpatchantennawithadominantmodepresentsquitecomplicatedbehaviourincludinghaving
aminimumataspecificheight.Similarly,aspredictedfromthesimplewiremodel,theradiationQexhibitsaminimumtoo.Itis
observedthatthepresenceofout-of-phasecurrentsflowingalongthepatchantennaleadstoasignificantincreaseoftheQfactor.
1.Introduction Equation (1) is usually treated within the method of
moments(MoMs)[8]frameworkand,duetothestructure
Evaluation of the basic properties of microstrip patch discretization, the L operator is known as the “complex
antennas(MPA)hasbeennumerouslydiscussedinliterature, impedancematrix”[Z]=[R]+ j[X].
see, for example, [1–3]. The two main MPA attributes are ThentheassociatedEuler’sequationtobesolvedis
resonant frequency (or frequencies but we will deal mostly
withthedominantmode)andtheradiationQfactor.Sofar, XJn=λnRJn. (2)
only approximate results and semianalytic equations have
been published. To our knowledge, this is the first time
Equation (2) is a standard weighted eigenvalue equation
that these important characteristics have been studied in a
leading to a set of real characteristic eigencurrents Jn and
rigorous way. The antennas are treated by using a modal
associated eigenvalues λn. Properties of eigenvalues are
approach (hence we do not a priori consider any feeding
described in [9], at this moment it is important to note
to be connected), namely, by the theory of characteristic
modes (TCM), [4, 5]. Evaluation of the radiation Q is that λn reflects the amount of net reactive power (thus λn =
0 means resonance). Instead of eigenvalues, the so-called
performedbothbytheTCMfromtheeigenvaluesslopeand
characteristicanglesαn areintroducedtoshowmorevisible
bynovelrigorousequationsderivedbyVandenbosch[6]and
behaviorwithfrequency[9].Characteristiccurrentsforma
VandenboschandVolski[7].
complete orthogonal set, and hence the total current on a
conducting body may be expressed as a linear combination
2.TheTheoryofCharacteristicModes
ofthesemodecurrents[10].
Forcompleteness,letusformulatethebasicsofthecharac-
teristicmodesforperfectlyconductingbodiesofareaS.The 2.1. Implementation of the Characteristic Modes Theory.
scatteredfieldEsisrelatedtotheelectricsurfacecurrentsJby Implementation of the modal decomposition process has
theelectricfieldintegralequation(EFIE)[8] beendoneintheMATLAB[11]environmentusingMakarov
(cid:2) (cid:3)
EFIE codes [12] with the RWG basis functions [13]. This
L(J)−Ei =0. (1)
tan usage is restricted to arbitrary 3D PEC structures with air
2 InternationalJournalofAntennasandPropagation
dielectrics.OurdevelopedTCMtool[14]hasthefollowing
T (x,y,z)
mainadvantages: 1
(i)ComsolMultiphysics[15]/MATLAB’sPDETooLbox J
1
meshimport, r21=| r 2 − r 1 |
Ω
(ii) Optional Green’s function for infinite ground plane
simulations, J
2
(iii) Single solver/multicore solver/distributed solver y r2 r1
(within a computer network with installed
MATLAB). (0,0) T (x,y,z)
x 2
3.TheRadiationQFactor Figure1:Distancebetweennonoverlappingcurrentelements[23].
In [6] a novel theory able to rigorously calculate radiated
power and stored energies directly from currents flowing In [18], (10) is supposed to be an approximation of the
alongtheantennahasbeenpresented.TheradiationQfactor radiationQ,butinresonanceitisactuallyexact.
isthenreadilyevaluatedbythedefinition[16]: Sincecharacteristicmodesarenormalizedtoradiateunit
Q=2ωmax(cid:4)W(cid:5)m,W(cid:5)e(cid:6). (3) powerPr =1[4],(3)reducesto(cid:4) (cid:6)
Pr Q=2ωmax W(cid:5)e,W(cid:5)m . (11)
TheequationsforradiatedpowerPr andstoredelectricand
ForparallelorseriesRLCcircuit(hence,foronemode),the
magneticenergiesW(cid:5)e,W(cid:5)mare “impedanceQZ”equalstheexact“currentQ”[6]:
(cid:7) (cid:8)(cid:9) (cid:9)
1 (cid:10) (cid:11) (cid:12) (cid:12) (cid:12) (cid:12)
Pr = 8πωε0 Ω1 Ω2 k2J(r1)J(r2)−∇·J(r1)∇·J(r2) Q=QZ = ω20(cid:12)(cid:12)(cid:12)∂∂ωZ(cid:12)(cid:12)(cid:12)= ω20(cid:12)(cid:12)(cid:12)∂∂ωR + ∂∂Xω(cid:12)(cid:12)(cid:12). (12)
sin(kr )
× 21 dΩ1dΩ2,
r Inserting
21
(4) (cid:2) (cid:4) (cid:6)(cid:3)
1
Z =R+ jX = |I2| Pr+ j2ω W(cid:5)m−W(cid:5)e (13)
1
W(cid:5)e = 16πω2ε0(Ie−IR), (5) validforlosslessantennas[19]andusingthefactthatPr =1,
(12)resultsin
1
W(cid:5)m= 16πω2ε0(Im−IR), (6) Q=QX = ω20(cid:12)(cid:12)(cid:12)(cid:12)∂∂Xω(cid:12)(cid:12)(cid:12)(cid:12)= ω20∂∂ω(cid:2)2ω(cid:4)W(cid:5)m−W(cid:5)e(cid:6)(cid:3)
where (14)
(cid:9) (cid:9) ω ∂λ
k (cid:10) (cid:11) = 0 =Q ,
IR= 2 Ω1 Ω2 k2J(r1)J(r2)−∇·J(r1)∇·J(r2) (7) 2 ∂ω eig
×sin(kr )dΩ1dΩ2, providingthat
21
(cid:4) (cid:6)
(cid:9) (cid:9) λ=2ω W(cid:5)m−W(cid:5)e . (15)
cos(kr )
Ie = Ω1 Ω2∇·J(r1)∇·J(r2) r2121 dΩ1dΩ2, (8) ItisthereforeconcludedthatthemodalQeigequalstheQXby
(cid:9) (cid:9)
cos(kr ) definition,anditcanbeproven(usingthereactancetheorem
Im=k2 J(r1)J(r2) r 21 dΩ1dΩ2, (9) [20, 21]) that in resonance it also equals the radiation Q
Ω1 Ω2 21 definedfromenergiesby(11).
wherek isafree-spacewavenumber,Jisthesurfacecurrent
density, and r21 is the distance between interacting current 3.2. Software Implementation. The above equations were
elements.ThetildedenotesthattheradiationcontributionIR implemented in MATLAB for the RWG triangular mesh
hasbeensubtractedfromthestoredenergiesateverypoint wheretwodifferentinteractionsituationsoccur:
inspace[17].Itisassumedthatthecurrentsareflowingina
vacuum.
(a)DistantElements. Whenthetriangularelementsarenot
overlapping, current density on triangles may be simply
3.1.TheModalRadiationQ Factor. ThemodalradiationQ
approximated as point sources located at the centre of
factormaybeevaluatedfromtheslopeofmodaleigenvalues
triangles [22], see Figure1. No actual integration is then
[18]:
needed.Thiscentroidapproachisveryfastwithsatisfactory
ω dλ accuracy as will be shown later (however it may fail for
Q = 0 . (10)
eig 2 dω patcheslocatedveryclosetothegroundplane).
InternationalJournalofAntennasandPropagation 3
P3(x3,y3) β z
h13 (0,1)
P1(x1,y1) A P0 T1(x,y,z) P T1(α,β,γ) 0.01
0
h23 α 0.005
r
y 2 h12 (0,0) (1,0)
r P2(x2,y2) 0 2H
1
(0,0) x
−0.005
y
(a) (b)
Figure2:Self-termevaluation.(a)Originalproblem,(b)simplex −0.01 x
coordinatestransformation[23].
0.015
0.01
(b)Overlapping(Self)Elements. Asknownfromthemethod 0.005
of moments, the so-called “self” contributions are of great 0
importance when dealing with calculations on discrete −0.005
elements(meshes). −0.01 0.01 0.02
Here, the self-interaction occurs when two triangles are −0.015 −0.02 −0.01 0
overlapping each other. Due to the behavior of integral −0.03
kernels, only rapidly varying term cos(kr )/r has to be
21 21
carefullytreated.Sincek R → 0(R beingthelongestside Figure 3: Model of MPA above infinite ground plane for H =
0 21 21
ofthetriangleT)issatisfied,oneneedsonlytousethefirst 10mm,dominantmodeTM shown.
01
termintheTaylorseriesexpansion.Thedominantsingular
staticpartis1/r andtheintegraltobeworkedoutis
21 4.5
(cid:9) (cid:9)
1
I = (cid:13) (cid:14) (cid:15) dxdydx(cid:4)dy(cid:4), (16) 4
T T(cid:4) (x−x(cid:4))2+ y−y(cid:4) 2 Regular
3.5
behaviour
whereT =T(cid:4)isatriangulararea.Usingsimplexcoordinates Hz) 3
transforma(cid:16)tion(Figure2),theresultis[23,24] (cid:17) f (Gres 2.5 Min. fres
I=−4A2 ln(1−2h12/L)+ln(1−2h13/L)+ln(1−2h23/L) , 2 Min. Q
3 h h h
12 13 23 1.5
(17)
1
where A is the triangle area, hij are the edge lengths (see 0 5 10 15 20 25 30 35 40 45 50 55 60
Figure2),andListheperimeterofthetriangle. H (mm)
fr (TCM)
4.Applications:RectangularPatchAntenna fr (analytic equation)
Let us first concentrate on a rectangular patch antenna of Figure 4: R50 × 30 resonant frequency of the dominant TM01
dimensionsL = 50mmandW = 30mm(furthernotedas mode.Thedashedredcurveisaquasianalyticalequationfrom[1].
R50×30)placedinairataheightHaboveaninfiniteground
plane. Only the dominant TM mode will be studied. The
01
reasonforchoosingapatchwithL/W=/ 1isthatwedonot H/λ < 0.08),theresonantfrequencydecreases“regularly,”
res
havetodealwithdegeneratedmodes. and quasianalytical formulas (see, e.g., [1, 3]) based on
Using the image theory, the radiator in the XY plane the fringing field concept are valid below this range. For
at height z = H above an infinite electric ground plane is H ∼= 25mm (H/λ ∼= 0.188) there is absolute minimum
res
modelledastwopatchesseparatedby2H.Thetotalnumber of the TM resonant frequency. Further on, the resonant
01
oftriangularelementsis676.IntheTCManalyser,aproper frequency rises to reach its maximum for H ∼= 40mm
out-of-phasemodeisselected(Figure3). (H/λ ∼= 0.51). Around this specific height the patch also
res
Theresonantfrequencyofthedominantmodeisshown showstheminimumoftheradiationQ.Theabovedescribed
asafunctionofheightH,seeFigure4.Ithasbeenevaluated process repeats periodically. It is yet unclear to the authors
from a modal resonant condition for eigenvalues λ = aswhatisthephysicalbackgroundtotheresonantfrequency
2ω(W(cid:5)m − W(cid:5)e) = 0 employing an adaptive frequency discontinuityaroundH/λres∼=0.5.
sweep for each height. The behaviour is quite peculiar, The terms 2ωW(cid:5)m,2ωW(cid:5)e, and 2ω(W(cid:5)m − W(cid:5)e) obtained
especiallyforgreaterheights.Forlowheights(H <10mmor from (5)–(9) and eigenvalues λ are plotted at Figure5 for
4 InternationalJournalofAntennasandPropagation
20 anapproximateanalyticalsolutionisavailableandin[25]we
showedthattheQisledbythefunction
15
es 10 fQ(H)∼= k2H−2sHin(k2H). (18)
gi
ner fres Afterderiving(18),theconditionisworked-out
ctive e 5 tan(k2H)=k2H, (19)
a
e 0
R and the first nontrivial root of (19) could be approximated
as[25]
−5 (cid:7) (cid:8)
H =∼ 3 − 1 =0.358. (20)
−10 λ 8 6π2
1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 min
f (GHz) Forsinusoidalcurrentsondipolestheminimum(evaluated
numerically)occursforH =0.36λ.
λ 2ω(We)
The minimum of the patch under study is obtained at
2ω(Wm) 2ω(Wm-We) H ∼= 0.4λ, a value that is remarkably close to the simple
Figure5:ReactiveenergiesandtheirdifferencesforanR50×30 dipolemodel.
patchatheightof25mm.
4.1. Algorithm Convergence. Since no other methods for
calculatingmodalQareavailable,Q istakenasareference,
eig
50
andtherelativeerrorpercentageisdefinedas:
45 (cid:12) (cid:12)
(cid:12) (cid:12)
40 (cid:12)QJ −Qeig(cid:12)
relativeerror= ·100, (21)
35 Q
eig
30
–) where QJ is calculated from the currents using (11). Four
Q ( 25 different heights H were chosen, H = 1mm (0.01λ), H =
20 2mm (0.0185λ), H = 10mm (0.0803λ), and H = 20mm
15 (0.151λ),andtherelativeerrorwasevaluatedasafunctionof
10 totaltriangularelements(includingthemirror),seeFigure7.
5 Allqualityfactorswereevaluatedattheresonantfrequency
0 ofthedominantmodefortheR50×30patch.Asdiscussed
0 5 10 15 20 25 30 35 40 45 50 55 60
earlier,thecentroidapproximationbecamemoreinaccurate
H(mm)
with low heights H. However, even for the lowest analyzed
Q value H = 0.01λ, the relative error is in the order of
eig
Q a few percent for reasonable mesh density (hundreds of
J
elements).Furtherimprovementstotheintegrationroutine
Figure6:TheradiationQfordominantmodeofanR50×30patch areconsideredforthefuture.
asafunctionofheightH.
4.2.FractionalBandwidthoftheR50×30PatchAntenna. It
is known that the fractional bandwidth (FBW) is related to
H = 25mm as a function of frequency. There is excellent theunloadedQfactorandthedesiredmatchingVSWRlevel.
agreementbetweenthedifferenceinstoredenergiesandthe ForVSWR<swehave[26]
eigeTnvhaelrueeiss,balostohvoebrytaginoeoddiangareceommepnltetbeelytwdeieffnertehnetemxaanctnQerJ. FBW∼= sQ−√1s [%]. (22)
and Q confirming the validity of the proposed algorithm
eig
via(14),seeFigure6.NotethatQ in(10)doesnotrequire Using a full-wave simulator CST-MWS [27], an R50 × 30
eig
the currents to be calculated on the structure while QJ is patchhasbeensimulatedandtheFBWCSTforVSWR<2was
evaluatedinarigorouswayfrommodalcurrents(11). calculatedas:
From Figure6 it is seen that the radiation Q has a f − f
minimumforaspecificheight.Itisdeducedthatthereason FBWCST= 2 f 1, (23)
liesinthecancellingoftheradiatedpowerbetweenthetwo 0
out-of-phasecurrents.Similarbehaviourhasbeenobserved where f and f are margins for VSWR < 2 and f is
2 1 0
inthecaseoftwohalf-wavethin-wiredipoleswithopposite the centre frequency. Only very low heights were studied
sinusoidalcurrents,separatedbyd=2H,see[25]fordetails. since we used a simple probe feed which introduces an
Actuallythesetwoout-of-phasedipolesmayserveasavery inductance component to the total input impedance. The
simple model for a patch antenna with a dominant mode. comparison in Figure8 shows good agreement of both
Whenthedipolesarereducedtoelementary(Hertzian)ones, fractionalbandwidths.