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1、2012CrossStraitQuad-RegionalRadioScienceandWirelessTechnologyConferenceFarFieldofAnArbitrarilyOrientedHelicalAntennaovertheHalfSpaceCaoLe,WeiBing,GeDe-biao,XuHong-bing,GuoLi-xinDepartmentofPhysics,XidianUniversityXi’an,Chinabwei@xidian.edu.cn,sxin.cao@gmail.c
2、omAbstract—Basedonthereciprocitytheorem,thefarfieldformulationinthefrequencydomainofanarbitrarilyorientedelectricdipolelocatedabovetheinterfaceofthehalfspaceisdeduced.Thentheradiationpatternsofanarbitrarilyorientedhelicalantennaoverhalf-spacearegiven.Theresul
3、tsshowthatthisformulationcanbeappliedtofastcalculationthefarradiationfieldofanantennalocatedabovetheinterfaceofthehalfspace.Keywords-ElectricDipole,Helicalantenna,ReciprocityTheorem,FarField,HalfSpace(a)Thefiledofthesourcea(b)thefieldofthesourcebI.INTRODUCTIO
4、NFigure1.TwoEMproblemswiththesamemediaenvironmentoverthehalfTheradiationofthedipoleabovethehalfspaceisoneofspacethebasicquestionsinEM.Intheearly20thcentury,theanalyticalexpressionoftheverticalandhorizontaldipoleabovethehalfspaceisdeducedbySommerfeld[1].TheEMB
5、.Farradiationfieldofanarbitrarilyorientedelectricwavesradiatedbytheelectricdipoleabovethehalfspacedipoleoverthehalfspaceconsistoffourparts:(1)directedwave,(2)reflectedwave,(3)Supposeanarbitrarilyorientedelectricdipoleislocatedlateralwave,(4)surfacewave.Thestu
6、dyofWaitandKaiLietc.indicatedthatthemainradiationfarfieldoftheelectricabovethehalfspacewithaheightofhasitshowninFig.2.dipoleabovethelayeredhalfspaceisthedirectedwaveandTheobservedpointislocatedat()θ,ϕ,andtheelectricdipolereflectedwave[2-4].TheresultsofSommerf
7、eld,WaitandLiislocatedat()θϕ,.etc.aresuitfornearandfarfieldcases,buttheradiation00expressionoflayeredhalfspaceisverycomplicated.Inthispaper,Basedonthereciprocitytheorem,thefarfieldformulationinthefrequencydomainofanarbitrarilyorientedelectricdipolelocatedabov
8、etheinterfaceofthehalfspaceisdeduced.Thenthefarradiationfieldofhelicalantennalocatedabovethehalfspaceiscomputed.II.FARRADIATIONFIELDOFANARBITRARILYORIENTEDELECTRICDIPOLELOACATEDABOVEHALFS
