Table Of ContentGeneralized
Transmission Line Method
to Study the Far-zone Radiation
of Antennas under a
Multilayer Structure
Synthesis Lectures on
Antennas
Editor
ConstantineA.Balanis,ArizonaStateUniversity
Generalized Transmission Line Method to Study the Far-zone Radiation of Antennas
underaMultilayerStructure
XuanHuiWu,AhmedA.Kishk,andAllenW.Glisson
2008
NarrowbandDirectionofArrivalEstimationforAntennaArrays
JeffreyFoutz,AndreasSpanias,andMaheshK.Banavar
2008
MultiantennaSystemsforMIMOCommunications
FrancoDeFlaviis,LluisJofre,JordiRomeu,andAlfredGrau
2008
ReconfigurableAntennas
JenniferT.Bernhard
2007
ElectronicallyScannedArrays
RobertJ.Mailloux
2007
IntroductiontoSmartAntennas
ConstantineA.BalanisandPanayiotisI.Ioannides
2007
AntennaswithNon-FosterMatchingNetworks
JamesT.AberleandRobertLoepsinger-Romak
2007
ImplantedAntennasinMedicalWirelessCommunications
YahyaRahmat-SamiiandJaehoonKim
2006
Copyright© 2008byMorgan&Claypool
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GeneralizedTransmissionLineMethodtoStudytheFar-zoneRadiationofAntennasundera
MultilayerStructure
XuanHuiWu,AhmedA.Kishk,andAllenW.Glisson
www.morganclaypool.com
ISBN:9781598298130 paperback
ISBN:9781598298147 ebook
DOI10.2200/S00156ED1V01Y200810ANT009
APublicationintheMorgan&ClaypoolPublishersseries
SYNTHESISLECTURESONANTENNAS
Lecture#9
SeriesEditor:ConstantineA.Balanis,ArizonaStateUniversity
SeriesISSN
SynthesisLecturesonAntennas
ISSNpending. Print1930-0328 Electronic1930-0336
Generalized
Transmission Line Method
to Study the Far-zone Radiation
of Antennas under a
Multilayer Structure
Xuan HuiWu,Ahmed A.Kishk,and AllenW.Glisson
DepartmentofElectricalEngineering
UniversityofMississippi
SYNTHESISLECTURESONANTENNAS#9
M
&C Morgan &cLaypool publishers
ABSTRACT
Thisbookgivesastep-by-steppresentationofageneralizedtransmissionlinemethodtostudythe
far-zoneradiationofantennasunderamultilayerstructure.Normally,aradiationproblemrequires
afullwaveanalysiswhichmaybetimeconsuming.Thebeautyofthegeneralizedtransmissionline
methodisthatittransformstheradiationproblemforaspecifictypeofstructure,saythemultilayer
structure excited by an antenna,into a circuit problem that can be efficiently analyzed.Using the
ReciprocityTheoremandfar-fieldapproximation,themethodcomputesthefar-zoneradiationdue
toaHertziandipolewithinamultilayerstructurebysolvinganequivalenttransmissionlinecircuit.
SinceanantennacanbemodeledasasetofHertziandipoles,themethodcouldbeusedtopredict
thefar-zoneradiationofanantennaunderamultilayerstructure.Theanalyticalexpressionforthe
far-zonefieldisderivedforastructurewithorwithoutapolarizer.Theprocedureofobtainingthe
Hertziandipolemodelthatisrequiredbythegeneralizedtransmissionlinemethodisalsodescribed.
Severalexamplesaregiventodemonstratethecapabilities,accuracy,andefficiencyofthismethod.
KEYWORDS
Transmission Line, Antenna, High Directivity, Multilayer Structure, Optimization,
EBG,HertzianDipole,Reciprocity,AsymptoticBoundaryConditions,Far-fieldRa-
diation,Polarizer.
vii
Contents
SynthesisLecturesonAntennas...................................................iii
Contents .......................................................................vii
1 Introduction .....................................................................1
2 AntennasUnderaMultilayerDielectricSlab........................................3
2.1 Introduction...............................................................3
2.2 Radiationduetoanelectricdipole...........................................3
2.2.1 Evaluationofthehorizontalcomponentusingchainmatrix ..............5
2.2.2 Evaluationoftheverticalcomponent..................................7
2.2.3 Fieldprojection .....................................................8
2.2.4 EvaluationofthehorizontalcomponentusingSchainmatrix............9
2.3 Radiationduetoamagneticdipole.........................................12
2.3.1 Evaluationofthehorizontalcomponentusingchainmatrix.............13
2.3.2 Evaluationoftheverticalcomponent.................................13
2.3.3 Fieldprojection....................................................14
2.3.4 EvaluationofthehorizontalcomponentusingSchainmatrix...........14
2.4 Resultsverification........................................................15
2.5 Applications..............................................................21
2.5.1 Thinwiremonopoleantennainatwo-layerstructure .................. 23
2.5.2 DRAinafour-layerstructure........................................24
2.6 Conclusions..............................................................27
3 AntennasUnderaPolarizedMultilayerStructure...................................31
3.1 Introduction..............................................................31
3.2 Radiationduetoanelectricdipole..........................................31
3.3 Radiationduetoamagneticdipole.........................................35
viii CONTENTS
3.4 Asymptoticboundaryconditions ...........................................36
3.4.1 PEC-typeasymptoticboundaryconditions ........................... 36
3.4.2 PMC-typeasymptoticboundaryconditions...........................39
3.5 Applications..............................................................40
3.5.1 Crosspolarizationreduction.........................................40
3.5.2 Polarizer...........................................................42
3.6 Discussion ...............................................................45
3.7 Conclusions..............................................................46
4 HertzianDipoleModelforanAntenna............................................51
4.1 Introduction..............................................................51
4.2 NarrowbandHertziandipolemodel.........................................52
4.2.1 Particleswarmoptimizationmethod .................................52
4.2.2 PSOmodelforgettinganarrowbanddipolemodel ....................53
4.3 Limitationsofthenarrowbandmodel.......................................54
4.4 WidebandHertziandipolemodel ..........................................59
4.4.1 PSOmodelforgettingawidebanddipolemodel ......................59
4.4.2 Modelingofawidebandantenna.....................................61
4.4.3 Application........................................................63
4.4.4 RejectionofGaussiannoise .........................................68
4.4.5 Frequencyscalability................................................71
4.5 Conclusions..............................................................72
A DerivationofEquationsinChapter2 .............................................73
A.1 DerivationofEquation(2.24)..............................................73
A.2 DerivationofEquation(2.29)..............................................74
A.3 DerivationofEquation(2.30)..............................................75
B MaximaSourceCode............................................................77
B.1 MaximasourcecodeforaPEC-SI..........................................77
B.2 MaximasourcecodeforaPMC-SI.........................................80
CONTENTS ix
Bibliography....................................................................83
Biography ......................................................................85
