CHAPTERS 5

CHAPTERS5&6NETWORKS1:0909201-018October2002–Lecture5bROWANUNIVERSITYCollegeofEngineeringProfessorPeterMarkJansson,PPPEDEPARTMENTOFELECTRICAL&COMPUTERENGINEERINGAutumnSemester2002networksIToday’slearningobjectives–applynewmethodsforreducingcomplexcircuitstoasimplerformequivalentcircuitssuperpositionThévenin’sequivalentNorton’sequivalentbuildunderstandingofmaximumpowerintroducetheoperationalamplifiernewconceptsfromch.5electricpowerforcities-donesourcetransformations-donesuperpositionprinciple-doneThévenin’stheorem-continueNorton’stheoremmaximumpowertransferhomework5Problems5.3-1,5.3-4,5.3-5,5.3-6,5.4-1review(ed)inlab,5.4-2,5.4-6,5.5-1,5.5-3,5.5-9,5.6-2,5.6-4,5.7-1,5.7-6Chapter6Pages244-245Problems6.4-1,6.4-2,6.4-6nextmonday’s-testtwocoversChapters3.4-6.4currentdivisionnodevoltagecircuitanalysismeshcurrentcircuitanalysiswhentousen-vvs.m-csourcetransformationssuperpositionprincipleThevenin’sequivalent-Norton’sequivalentmaximumpowertransferoperationalamplifiersThévenin’stheoremGOAL:reducesomecomplexpartofacircuittoanequivalentsourceandasingleelement(foranalysis)THEOREM:foranycircuitofresistiveelementsandenergysourceswithaterminalpair,thecircuitisreplaceablebyaseriescombinationofvtandRtThéveninequivalentcircuit+_vtorvocRtООabThéveninmethodIfcircuitcontainsresistorsandind.sourcesConnectopencircuitbetweenaandb.FindvocDeactivatesource(s),calc.RtbycircuitreductionIfcircuithasresistorsandind.&dep.sourcesConnectopencircuitbetweenaandb.FindvocConnectshortcircuitacrossaandb.FindiscConnect1-Acurrentsourcefrombtoa.FindvabNOTE:Rt=vab/1orRt=voc/iscIfcircuithasresistorsandonlydep.sourcesNotethatvoc=0Connect1-Acurrentsourcefrombtoa.FindvabNOTE:Rt=vab/1HWexampleseeHWproblem5.5-1Norton’stheoremGOAL:reducesomecomplexpartofacircuittoanequivalentsourceandasingleelement(foranalysis)THEOREM:foranycircuitofresistiveelementsandenergysourceswithaterminalpair,thecircuitisreplaceablebyaparallelcombinationofiscandRn(thisisasourcetransformationoftheThevenin)NortonequivalentcircuitiscООabRn=Rt••NortonmethodIfcircuitcontainsresistorsandind.sourcesConnectshortcircuitbetweenaandb.FindiscDeactivateind.source(s),calc.Rn=RtbycircuitreductionIfcircuithasresistorsandind.&dep.sourcesConnectopencircuitbetweenaandb.Findvoc=vabConnectshortcircuitacrossaandb.FindiscConnect1-Acurrentsourcefrombtoa.FindvabNOTE:Rn=Rt=vab/1orRn=Rt=voc/iscIfcircuithasresistorsandonlydep.sourcesNotethatisc=0Connect1-Acurrentsourcefrombtoa.FindvabNOTE:Rn=Rt=vab/1HWexampleseeHWproblem5.6-2maximumpowertransferwhatisit?oftenitisdesiredtogainmaximumpowertransferforanenergysourcetoaloadexamplesinclude:electricutilitygridsignaltransmission(FMradioreceiver)sourceloadmaximumpowertransferhowdoweachieveit?+_vtorvscООabRtRLOADmaximumpowertransferhowdowecalculateit?tLLLtLstLsLRRdRdpRRRvpRRviRip0)(22maximumpowertransfertheoremSo…maximumpowerdeliveredbyasourcerepresentedbyitsTheveninequivalentcircuitisattainedwhentheloadRLisequaltotheTheveninresistanceRtefficiencyofpowertransferhowdowecalculateitforacircuit?max%50/4)(2)(/22max2inoutLsLLsoutLstLsssininoutppRvRRvppRvRRvvivpppNortonequivalentcircuitsusingthecalculusonp=i2RinaNortonequivalentcircuitwefindthatit,too,hasamaximumwhentheloadRLisequaltotheNortonresistanceRn=RtHWexampleseeHWproblem5.7-6newconceptsfromch.6electronicsoperationalamplifiertheidealoperationalamplifiernodalanalysisofcircuitscontainingidealopampsdesignusingopampscharacteristicsofpracticalopampsdefinitionofanOP-AMPTheOp-Ampisan“active”elementwithahighgainthatisdesignedtobeusedwithothercircuitelementstoperformasignalprocessingoperation.Itrequirespowersupplies,sometimesasinglesupply,sometimespositiveandnegativesupplies.Ithastwoinputsandasingleoutput.OP-AMPsymbolandconnections_++–+–INVERTINGINPUTNODENON-INVERTINGINPUTNODEOUTPUTNODEi1i2iovov2v1NEGATIVEPOWERSUPPLYPOSITIVEPOWERSUPPLYTHEOP-AMPFUNDAMENTALCHARACTERISTICS_+INVERTINGINPUTNODENON-INVERTINGINPUTNODEOUTPUTNODEi1i2iovov2v1RoRiTHEIDEALOP-AMPFUNDAMENTALCHARACTERISTICS_+INVERTINGINPUTNODENON-INVERTINGINPUTNODEOUTPUTNODEi1i2iovov2v11221000vviiRRoiTHEINVERTINGOP-AMP_+i1i2iovov2v1RfRi+–vsNodea1.WriteIdealOpAmpequations.2.WriteKCLatNodea.3.Solveforvo/vsTHEINVERTINGOP-AMP_+i1i2iovov2v1RfRi+–vsNodea122100vvii0111foisRvviRvvifsofoisRRvv0RvRvAtnodea:THENON-INVERTINGOP-AMP_+i1i2iovov2v1RfRi+–vsNodea122100vvii00111foiRvviRvAtnodea:10ifsofosisRRvvRvvRvHWexampleseeHWproblem6.4-1TestTwonextMondayreviewneeded?ifso…select5-6problemsthatyouwouldlikepresenteddiscussed