电路基础chapter11

1FundamentalsofElectricCircuits2007.9Chapter11Two-PortNetworks2Chapter11TwoPortNetworks11.1Introduction11.2Impedanceparametersz11.3Admittanceparametersy11.4Hybridparametersh11.5Inversehybridparameters11.6TransmissionparametersT11.7InverseTransmissionparameters11.8InterconnectionofNetworks3Whatisaport?Itisapairofterminalsthroughwhichacurrentmayenterorleaveanetwork.11.1Introduction4OneportortwoterminalcircuitTwoportorfourterminalcircuit•Itisanelectricalnetworkwithtwoseparateportsforinputandoutput.•Noindependentsources.511.2Impedanceparameters(1)Assumenoindependentsourceinthenetwork22212122121111IzIzVIzIzV21212221121121IIzIIzzzzVVwheretheztermsarecalledtheimpedanceparameters,orsimplyzparameters,andhaveunitsofohms.611.2Impedanceparameters(2a)z11=Open-circuitinputimpedancez21=Open-circuittransferimpedancefromport1toport2z12=Open-circuittransferimpedancefromport2toport1z22=Open-circuitoutputimpedance0I12210I111122IVzandIVz0I22220I211211IVzandIVz711.2Impedanceparameters(2b)0I12210I111122IVzandIVz0I22220I211211IVzandIVz•Whenz11=z22,thetwo-portnetworkissaidtobesymmetrical.•Whenthetwo-portnetworkislinearandhasnodependentsources,thetransferimpedancesareequal(z12=z21),andthetwo-portissaidtobereciprocal.8V1V2I2I1Example1DeterminetheZ-parametersofthefollowingcircuit.11.2Impedanceparameters(3)0I12210I111122IVzandIVz0I22220I211211IVzandIVzAnswer:70404060z22211211zzzzz91011.3Admittanceparameters(1)Assumenoindependentsourceinthenetwork22212122121111VyVyIVyVyI21212221121121VVyVVyyyyIIwheretheytermsarecalledtheadmittanceparameters,orsimplyyparameters,andtheyhaveunitsofSiemens.110V22220V211211VIyandVIy11.3Admittanceparameters(2)y11=Short-circuitinputadmittancey21=Short-circuittransferadmittancefromport1toport2y12=Short-circuittransferadmittancefromport2toport1y22=Short-circuitoutputadmittance0V12210V111122VIyandVIy12V1V2I1I2Example2Determinethey-parametersofthefollowingcircuit.0V12210V111122VIyandVIyS0.6250.50.50.75yAnswer:0V22220V211211VIyandVIySyyyyy2221121113V1V2I2I1=iExample3Determinethey-parametersofthefollowingcircuit.22212122121111VyVyIVyVyIS0.250.250.050.15yAnswer:2122110.25V0.25VI0.05V0.15VI)I2(I)I4(2iV)I2(I8IV21222111ApplyKVL141511.4Hybridparameters(1)Assumenoindependentsourceinthenetwork22212122121111VhIhIVhIhV21212221121121VIhVIhhhhIVwherethehtermsarecalledthehybridparameters,orsimplyhparameters,andeachparameterhasdifferentunits,referabove.1611.4Hybridparameters(2)0V12210V111122IIhIVh0I22220I211211VIhVVhh11=short-circuitinputimpedance()H2=short-circuitforwardcurrentgainH12=open-circuitreversevoltage-gainH22=open-circuitoutputadmittance(S)Assumenoindependentsourceinthenetwork17V1V2I1I2Example4Determinetheh-parametersofthefollowingcircuit.0V12210V111122IIhandIVhS4Ωh913232Answer:0I22220I211211VIhandVVhShhhΩhh2221121118Example5DeterminetheTheveninequivalentattheoutputportofthecircuitshowninthefollowingFig.22212122121111VhIhIVhIhV1911.5Inversehybridparameters11111222211222IVgIVgVgIg11111122122222IVVgggggVII221111I02211I0VVhVIg111122022220gIVgIVVIg11=open-circuitinputadmittance(S)g21=open-circuitforwardvoltagegaing12=Short-circuitreversecurrent-gaing22=short-circuitoutputimpedance(Ω)2011.6Transmissionparameters(1)Assumenoindependentsourceinthenetwork221221DICVIBIAVV222211IVTIVDCBAIVwheretheTtermsarecalledthetransmissionparameters,orsimplyTorABCDparameters,andeachparameterhasdifferentunits.2111.6Transmissionparameters(2)0I210I2122VICVVA0V210V2122IIDIVBA=open-circuitvoltageratioC=open-circuittransferadmittance(S)B=negativeshort-circuittransferimpedance()D=negativeshort-circuitcurrentratio22V1V2Example6DeterminetheT-parametersofthefollowingcircuit.1.1760.059S15.294Ω1.765TAnswer:221221DICVIBIAVV221221I1720V171II17260V1730V)I20(I3IV)I20(I10IV21122111ApplyKVL23V1V2I1I2Theoutputportisconnectedtoavariableloadformaximumpowertransfer.FindRLandthemaximumpowertransferred.Example7TheABCDparametersofthetwo-portnetworkbelowareT=20.1S20Ω424Answer:VTH=10VV;RL=8;Pm=3.125W.Example8TheABCDparametersofthetwo-portnetworkinfollowingFig.are4200.12STheoutputportisconnectedtoavariableloadformaximumpowertransfer.FindRLandthemaximumpowertransferred2511.7InverseTransmissionparametersInversetransmissionparametersaredefinedbyexpressingthevariablesattheoutputportintermsofthevariablesattheinputport.211211VaVbIIcVdI211211VVVabtIcdII1121I021I0VaVIcV1121V021V0VbIIdIa=open-circuitvoltagegianc=open-circuittransferadmittance(S)b=negativeshort-circuittransferimpedance()d=negativeshort-circuitcurrentgainIntermsofthetransmissionorinversetransmissionparameters,anetworkisreciprocalifAD-BC=1ad-bc=12611.8InterconnectionofNetworks(1)1a11a1a12a2a2a21a1a22a2aVzIzIVzIzI1a11a1a12a