Unit2TechniquesofCircuitAnalysis

Unit2TechniquesofCircuitAnalysisKeyWordsandTerms1.algebraicadj.代数的,关于代数学的2.interconnectionn.互相关联3.Kirchhoff’scurrentlaw基尔霍夫电流定律4.Kirchhoff’svoltagelaw基尔霍夫电压定律5.noden.节点6.converselyadv.相反地7.yieldv.产生8.closedpath闭环路径9.loopn.回路,环路,圈10.voltagedrop电压降11.ammetern.安培表，电流表12.resemblevt.相似,类似13.clockwiseadj.顺时针方向的14.meshn.网孔15.consistencyn.一致性，连贯性16.perimetern.周长，边缘17.substitutionn.替换，代替18.determinantn.行列式19.redundantadj.冗余的、多余的20.junctionn.汇合点NotationsandTranslationKirchhoff’sLawAcircuitissaidtobesolvedwhenthevoltageacrossandthecurrentineveryelementhavebeendetermined.Ohm’slawisanimportantequationforderivingsuchsolutions.Insimplecircuitstructures,Ohm’slawissufficientforsolvingforthevoltagesacrossandthecurrentsineveryelement.However,formorecomplexinterconnectionsweneedtousetwomoreimportantalgebraicrelationships,knownasKirchhoff’slaws,afterGustavKirchhoff,whofirststatedtheminapaperpublishedin1848.ThetwolawsthatstatetheconstraintsinmathematicalformareknownasKirchhoff’scurrentlawandKirchhoff’svoltagelaw.ItisnecessarytoidentifynodesinordertouseKirchhoff’scurrentlaw,anodeisapointwheretwoormorecircuitelementmeet.AndKirchhoff’scurrentlawcanbestatedasfollows:Thealgebraicsumofallthecurrentatanynodeinacircuitequalszero.abcd+-UsR1R2R3IsI3I1I2U3+++---U2U1Figure2.1Circuitdiagram然而，对于更为复杂的连接方式的求解，需要两个重要的代数关系，即基尔霍夫定律。该定律以古斯塔夫·基尔霍夫的名字命名，他于1848年发表了相关的论文。InFigure2.1,thenodesarelabeleda,b,c,d.TouseKirchhoff’scurrentlaw,analgebraicsigncorrespondingtoareferencedirectionmustbeassignedtoeverycurrentatthenodes.Assigningapositivesigntoacurrentleavinganoderequiresassigninganegativesigntoacurrententeringanode.Conversely,givinganegativesigntoacurrentleavinganoderequiresgivingapositivesigntoacurrententeringanode.①ApplyingKirchhoff’scurrentlawtothefournodesinFigure1,usingtheconventionthatcurrentsleavinganodeareconsideredpositive,yieldsfourequations:Nodea30sIINodeb320IINodec210IINoded10sIIBeforewecanstateKirchhoff’svoltagelaw,wemustdefineaclosedpathorloop.Startingatanarbitrarilyselectednode,wetraceaclosedpathinacircuitthroughselectedbasiccircuitelementsandreturntotheoriginalnodewithoutpassingthroughanyintermediatenodemorethanonce.②ThecircuitshownintheFigure1hasonlyoneclosedpathorloop.Forexample,choosingnodeaasstartpointandtracingthecircuitclockwise.Weformtheclosedpathbymovingthroughnodesd,c,b,andbacktonodea.WecannowstateKirchhoff’svoltagelaw:Thealgebraicsumofallthevoltagesaroundanyclosedpathinacircuitequalszero.WenowapplyKirchhoff’svoltagelawtothecircuitshowninFigure2.1.Weselecttotracetheclosedpathclockwise,assigningapositivesigntovoltagedrops.Startingatnodedleadstotheexpression3210sUUUUMesh-CurrentMethodInthemeshcurrentmethod,youwillworkwithloopcurrentsinsteadofbranchcurrents.Abranchcurrentistheactualcurrentthroughabranch.Anammeterplacedinagivenbranchwillmeasurethebranchcurrent.Loopcurrentsaredifferentbecausetheyaremathematicalquantitiesthatareusedtomakecircuitanalysissomewhateasierthanwiththebranchcurrentmethod.Thetermmeshcomesfromthefactthatamultiple-loopcircuit,whendrawn,canbeimaginedtoresembleawiremesh.③Themethodofmeshanalysisisgiveninthefollowingsteps:Step1.Althoughdirectionofanassignedloopcurrentisarbitrary,wewillassignacurrentintheclockwisedirectionaroundeachnonredundantclosedloop,forconsistency.Thismaynotbetheactualcurrentdirection,butitdoesnotmatter.Thenumberofloop-currentassignmentsmustbesufficienttoincludecurrentthroughallcomponentsinthecircuit.Step2.Indicatethevoltagedroppolaritiesineachloopbasedontheassignedcurrentdirections.Step3ApplyKirchhoff’svoltagelawaroundeachclosedloop.Whenmorethanoneloopcurrentpassesthroughacomponent,includeitsvoltagedrop.Thisresultsinoneequationforeachloop.Step4.Usingsubstitutionordeterminantssolvetheresultingequationfortheloopcurrents.Figure2.2Exampleofcircuitdiagramformeshanalysismethod支路电流是通过一支路的真实电流。将一电流表接在支路中可以测量出支路电流。而回路电流则不同，它们只是一个数学量，使得电路的分析在某种程度上比支路电流法要简单。AsshowninFigure2.2,first,theloopcurrentsI1andI2areassignedintheclockwisedirection.Aloopcurrentcouldbeassignedaroundtheouterperimeterofthecircuit,butthiswouldberedundantsinceI1andI2already+-Us1R1R2R3I1I2+-Us2passthroughallofthecomponents.Second,thepolaritiesofthevoltagedropsacrossR1,R2andR3areshownbasedontheloop-currentdirections.NoticethatI1andI2areinoppositedirectionsthroughR2becauseR2iscommontobothloops.Therefore,twovoltagepolaritiesareindicated.Inreality,theR2currentcannotbeseparatedintotwoparts,butrememberthattheloopcurrentsarebasicallymathematicalquantitiesusedforanalysispurposes.Thepolaritiesofthevoltagesourcesarefixedandarenotaffectedbythecurrentassignments.Third,Kirchhoff’svoltagelawappliedtothetwoloopsresultsinthefollowingtwoequations:forloop1112121()sRIRIIUforloop2322212()sRIRIIU沿着电路的周边指定回路电流，由于I1和I2流经所有的元件，将产生冗余。第二，R1,R2和R3两端的电压降极性按回路电流的方向给出。请注意，由于R2同时属于两个回路，I1和I2流经R2的方向相反，将有两个不同的电压极性。在实际中流经R2的电流是不会分为两个部分的，不过别忘了，回路电流只不过是用于分析目的的数学量。NoticethatI1ispositiveinloop1andI2ispositiveinloop2.Fourth,theliketermsintheequationsarecombinedandrearrangedintoaformforconvenientsolutionsothattheyhavethesamepositionineachequation,thatis,