电路原理课件讲义英文版 Chapter_3.ppt

1、Scientistsstudytheworldasitis,engineercreatetheworldthatneverhasbeen.-TheodorevonKarman,Chapter3MethodsofAnalysis,3.1Introduction3.2NodalAnalysis3.3NodalAnalysiswithVoltageSources3.4MeshAnalysis3.5MeshAnalysiswithCurrentSources3.6NodalandMeshAnalysisbyInspection3.7NodalVersusMeshAnalysis3.10Summary,

2、3.1Introduction,Twopowerfultechniquesforcircuitanalysis:Nodalanalysis(basedonasystematicapplicationofKCL)Meshanalysis(basedonasystematicapplicationofKVL),3.2NodalAnalysis,Methods:ChoosingnodevoltagesinsteadofelementvoltagesFindingthenodevoltagesMerits:ConvenientThenumberofequationsisreduced,StepstoD

3、etermineNodeVoltages:Selectanodeasthereferencenode.Assignvoltagesv1,v2,vn-1totheremainingn-1nodes.Thevoltagesarereferencedwithrespecttothereferencenode.ApplyKCLtoeachofthen-1nonreferencenodes.UseOhmslawtoexpressthebranchcurrentsintermsofnodevoltages.Solvetheresultingsimultaneousequationstoobtaintheu

4、nknownnodevoltages.,TheFirstStep:Selectinganodeasthereferenceordatumnode(calledthegroundwithzeropotential),Typicalcircuitfornodalanalysis:,TheSecondStep:ApplyingKCLtoeachnonreferencenodeinthecircuit,Atnode1:,Atnode2:,Notice:Currentflowsfromahigherpotentialtoalowerpotentialinaresistor.,Then:,Intermso

5、ftheconductance,thereare,Soweobtain:,TheThirdStep:Tosolveforthenodevoltages,StandardMethods:SubstitutionmethodEliminationmethodCramersruleMatrixinversion,Thelasttwoequationscanbecastinmatrixformas,whichcanbesolvedtogetv1andv2.,Example1,Simplifyingtheequations,thereis,Atnode1:,Atnode2:,Example2,Simpl

6、ifyingtheequations,thereis,Atnode1:,Atnode2:,Atnode3:,3.3NodalAnalysiswithVoltageSources,Avoltagesourceisconnectedbetweenthereferencenodeandanonreferencenode,Case1,Case2,Avoltagesource(dependentorindependent)isconnectedbetweentwononreferencenodes,Asupernode(orgeneralizednode)isformedbyenclosinga(dep

7、endentorindependent)voltagebetweentwononreferencenodesandanyelementsconnectedinparallelwithit,Atsupernode:,Selectingaloopwithsupernode,ByKVL,thereis,Thevoltagesourceinsidethesupernodeprovidesaconstraintequationneededtosolveforthenodevoltages.Asupernodehasnovoltageofitsown.Asupernoderequirestheapplic

8、ationofbothKCLandKVL.,Notice:,Example3,FromEqs.(1)and(2),weobtain:,Atsupernode:,Aroundtheloopwithsupernode:,Expressingv1andv2intermsofthenodevoltages,thereis,Example4,Atsupernode1-2:,Atsupernode3-4:,Forloop1:,Inaddition:,Forloop2:,Forloop3:,FromEqs.(1),(2),(3)and(4),weobtain:,Assignment,Solvetheprob

9、lems3.3and3.7inpage109,3.4MeshAnalysis,APlanarCircuitisonethatcanbedrawninaplanewithnobranchescrossingoneanother;otherwiseitisNonplanar.,AMeshisaloopwhichdoesnotcontainanyotherloopswithinit.,Questions:,Howmanymeshesintherightfigure?Whatarethey?Ispath12301amesh?Why?,StepstoDetermineMeshCurrents:Assig

10、nmeshcurrentsi1,i2,in-1tothenmeshes.ApplyKVLtoeachofthenmeshes.UseOhmslawtoexpressthevoltagesintermsofthemeshcurrents.Solvetheresultingnsimultaneousequationstogetthemeshcurrents.,Methods:ChoosingmeshcurrentinsteadofelementcurrentsandthenfindingthemeshcurrentsMerits:Onlyapplicabletoacircuitthatisplan

11、ar,TheFirstStep:Assignmeshcurrentsi1,i2,intothenmeshes,TheSecondStep:ApplyingKVLtoeachmeshes,Formesh1:,Formesh2:,TheThirdStep:Solvingsimultaneousequationsforthemeshcurrents,Formesh3:,Notice:Thebranchcurrentsaredifferentfromthemeshcurrentsunlessthemeshisisolated.,Example5,Usemeshanalysistofindthecurr

12、enti0inthefollowingcircuit.,Solution:,Formesh1:,Formesh2:,Formesh3:,Inaddition,i0=i1-i2,so,Solvingsimultaneousequations(1),(2)and(3),weobtain:,3.5MeshAnalysiswithCurrentSources,Whenacurrentsourceexistsonlyinonemesh:,Case1,Formesh1:,Formesh2:,Formesh3:,Whenacurrentsourceexistsbetweentwomeshes:,Case2,

13、Forsupermesh:,Atnodea:,ASupermeshresultswhentwomesheshavea(dependentorindependent)currentsourceincommon,Thecurrentsourceinthesupermeshisnotcompletelyignored;itprovidestheconstraintequationnecessarytosolveforthemeshcurrents.Asupermeshhasnocurrentofitsown.AsupermeshrequirestheapplicationofbothKCLandKV

14、L.,Notice:,Example6,Usemeshanalysistofindthecurrenti1toi4inthefollowingcircuit.,Solution:,Forthelargesupermesh:,Atnodea:,Atnodeb:,Buti0=-im4,hence,Formesh4:,Fromthelastequations,weobtain:,Assignment,Solvetheproblems3.19inpage111Translatetheparagraphsof3.7inpage99,3.6NodalandMeshAnalysisbyInspection,

15、NodalAnalysis,Atnode1:,Atnode2:,Ingeneral,Gkk:SumoftheconductancesconnectedtonodekGkj=Gjk:Negativeofthesumoftheconductancesdirectlyconnectingnodeskandj,kjvnk:Unknownvoltageatnodekisnk:Sumofallindependentcurrentsourcesdirectlyconnectedtonodek,withcurrentsenteringthenodetreatedaspositive.,MeshAnalysis

16、,Formesh1:,Formesh2:,Formesh3:,Ingeneral,Rkk:SumoftheresistancesinmeshkRkj=Rjk:Negativeofthesumoftheresistancesincommonwithmesheskandj,kjimk:Unknownmeshcurrentformeshkintheclockwisedirectionvsk:Sumtakenclockwiseofallindependentvoltagesourcesinmeshk,withvoltagerisetreatedaspositive.,Assignment,Solvetheproblems3.53and3.56inpage115,3.9Applications:DCTransistorCircuits,Semiconductor半导体:Silicon(Si)硅orGermanium(Ge)锗N-typesemiconductorN型半导体SiorGe+P/Phosphorus磷MajorityCarrier多数载流子:FreeElectron自由电子MinorityCarrier少数载流子:Hole空穴P-typesemiconductorN型半导体SiorGe+B/Boron硼MajorityCarrier多数载流子:Hole空穴Minori