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1、4/17/2006WilkinsonDividerEvenandOddModeAnalysis1/14Even/OddModeAnalysisoftheWilkinsonDividerConsideramatchedWilkinsonpowerdivider,withasourceatport2:Port2Z0+λ4Vs-Port12Z02ZZ002ZPort30λZ04Toosimplifythisschematic,weremovethegroundplane,whichincludesthebottomconductorofthetransmi
2、ssionlines:Port2λ4Z0+V-sPort12Z02Z0Z02Z0λ4Port3Z0JimStilesTheUniv.ofKansasDept.ofEECS4/17/2006WilkinsonDividerEvenandOddModeAnalysis2/14Q:Howdoweanalyzethiscircuit?A:UseEven-Oddmodeanalysis!Remember,even-oddmodeanalysisusestwoimportantprinciples:a)superpositionb)circuitsymmetry
3、Toseehowweapplytheseprinciples,let’sfirstrewritethecircuitwithfourvoltagesources:VVssV222λ4Z0V2Z102Z0Z02Z0λ−VsVs4V223Z0Turningoffonepositivesourceateachport,weareleftwithVsanoddmodecircuit:Vo22λ4Z0oV2Z102Z0Z02Z0λo−Vs4V23OddModeCircuitZ0JimStilesTheUniv.ofKansasDept.ofEECS4/17/2
4、006WilkinsonDividerEvenandOddModeAnalysis3/14Notethecircuithasoddsymmetry,andthustheplaneofsymmetrybecomesavirtualshort,andinthiscase,avirtualground!VsVo22λ4Z0Zo02Z0V12Z0V=0o2Z0V12ZZ00λo−Vs4V23Z0Dividingthecircuitintotwohalf-circuits,weget:λZ04++2ZVo2ZZo+Vs0100V-22−−λZ04++2ZVo2
5、ZZo+Vs0100V-−23−−Notewehaveagaindrawnthebottomconductorofthetransmissionline(agroundplane)toenhanceclarity(Ihope!).JimStilesTheUniv.ofKansasDept.ofEECS4/17/2006WilkinsonDividerEvenandOddModeAnalysis4/14Analyzingthetopcircuit,wefindthatthetransmissionlineisterminatedinashortcirc
6、uitinparallelwitharesistorofvalue2Z0.Thus,thetransmissionlineisterminatedinashortcircuit!λZ04++oZo+VV=02Z0Vs102-2−−ooThisofcoursemakesdeterminingVtrivial(hint:V=0).11Now,sincethetransmissionlineisaquarterwavelength,thisshortcircuitattheendofthetransmissionlinetransformstoanopen
7、circuitatthebeginning!Z0oAsaresult,determiningvoltageV2+isnearlyastrivialasdeterminingo+VoZsvoltageV.Hint:0V2-21−VZVVo=s0=s22ZZ+400Andfromtheoddsymmetryofthecircuit,welikewiseknow:ooVsV=−V=−324Now,let’sturnofftheoddmodesources,andturnbackontheevenmodesources.JimStilesTheUniv.of
8、KansasDept.ofEECS4/17/2006WilkinsonDividerEvenandOddMo
