S-parametersAnintroductionAuthor:JeanBurnikellPresented:MartynGaudionwww.polarinstruments.comS-parametersareausefulmethodforrepresentingacircuitasa“blackbox”S-parametersareausefulmethodforrepresentingacircuitasa“blackbox”Theexternalbehaviourofthisblackboxcanbepredictedwithoutanyregardforthecontentsoftheblackbox.Thisblackboxcouldcontainanything:aresistor,atransmissionlineoranintegratedcircuit.A“blackbox”ornetworkmayhaveanynumberofports.A“blackbox”ornetworkmayhaveanynumberofports.S-parametersaremeasuredbysendingasinglefrequencysignalintothenetworkor“blackbox”anddetectingwhatwavesexitfromeachport.Power,voltageandcurrentcanbeconsideredtobeintheformofwavestravellinginbothdirections.ForawaveincidentonPort1,somepartofthissignalreflectsbackoutofthatportandsomeportionofthesignalexitsotherports.IhaveseenS-parametersdescribedasS11,S21,etc.Canyouexplain?FirstletslookatS11.S11referstothesignalreflectedatPort1forthesignalincidentatPort1.ScatteringparameterS11istheratioofthetwowavesb1/a1.NowletslookatS21.S21referstothesignalexitingatPort2forthesignalincidentatPort1.ScatteringparameterS21istheratioofthetwowavesb2/a1.NowletslookatS21.S21referstothesignalexitingatPort2forthesignalincidentatPort1.ScatteringparameterS21istheratioofthetwowavesb2/a1.NowletslookatS21.S21referstothesignalexitingatPort2forthesignalincidentatPort1.ScatteringparameterS21istheratioofthetwowavesb2/a1.Alinearnetworkcanbecharacterisedbyasetofsimultaneousequationsdescribingtheexitingwavesfromeachportintermsofincidentwaves.S11=b1/a1S12=b1/a2S21=b2/a1S22=b2/a2Noteagainhowthesubscriptfollowstheparametersintheratio(S11=b1/a1,etc...)S-parametersarecomplex(i.e.theyhavemagnitudeandangle)becauseboththemagnitudeandphaseoftheinputsignalarechangedbythenetwork.(Thisiswhytheyaresometimesreferredtoascomplexscatteringparameters).ThesefourS-parametersactuallycontaineightseparatenumbers:therealandimaginaryparts(orthemodulusandthephaseangle)ofeachofthefourcomplexscatteringparameters.Quiteofte