电工电子技术第3章电路的暂态分析[ENG].ppt

Ch3TransientAnalysisofCircuits 电路的暂态分析 transientstate暂态steadystate稳态transientprocess暂态过程lawofswitch换路定理first ordercircuit一阶电路three factormethod三要素法timeconstant时间常数integralcircuit积分电路differentialcircuit微分电路 Terms 2Grasplawofswitchandcomputeinitialvalue 3ConceptsofZero inputResponse Zero stateResponse CompleteResponse 1Understandtheconceptsoftransientstate steadystateandphysicalsignificanceoftimeconstant Outline 4Applicationofthree factormethod Forthedirectcurrentcase Lisshort circuited Forthedirectcurrentcase Cisopen circuited BeforethemovementofK i 0 uC 0 i 0 uC Us Transitionprocessofcircuit LongafterKisclosed Transitionprocess theprocessbeundergonebythecircuittransientingfromonesteadystatetoanothersteadystate Switching thecircuit structureorparameter changes Kisclosed 2 thestructureorparametersofthecircuitarechanged Differencesbetweensteady stateanalysisandtransientanalysis SteadystateTransient 1 Longafterswitching 1 Justafterswitching 2 iL uCtime varying 3 Circuitdescribedwithalgebraicequations 3 Circuitdescribedwithdifferentialequations 2 IL UCkeepunchanged Reasonsfortransitionprocess 1 Thecircuitcontainsenergy storageelementsL C 3 1lawofSwitchandInitialValues RCcircuit Note lawofswitchisjustusedtodeterminetheinitialvalueuC iLatthemomentofswitching RLcircuit LawofSwitch capacitorvoltageandinductorcurrentcannotchangeabrubtlyattheinstantofswitching Determinationofinitialvalue Outlineofsolution Initialvalue thevalueofeachu iatt 0 inthecircuit 1 FinduC 0 oriL 0 withtheaidofthecircuit steadystate beforeswitching 2 DetermineuC 0 oriL 0 withlawofswitch 3 Drawequivalentcircuitdiagramatt 0 1 ifuC 0 0 Replacecapacitorbyshortcircuit iL 0 0 Replaceinductorbyopencircuit 3 Drawequivalentcircuitdiagramatt 0 2 ifuC 0 0 Replacecapacitorbyvoltagesource iL 0 0 Replaceinductorbycurrentsource Getthevalueatt 0 thedirectionisidenticaltoassumeddirectionofcapacitorvoltageandinductorcurrent 4 Findthevalueofdesiredvariablesatt 0 within0 circuitdiagrambyknownmethods Ohm slawetal Example1 Accordingtotheconditions Bylawofswitch ForthecircuitinFig a letusdeterminetheinitialvaluesofeachvoltagesandcurrents Supposethatthecircuitisinsteadystatebeforecircuitswitching andUC 0 IL 0 iC uLchangedabruptly 2 Accordingtot 0 circuit solveforinitialvaluesofothervoltagesandcurrents Example2 DeterminetheinitialvaluesofcurrentsandvoltagesincircuitshowninFig Supposethatthecircuitisinsteadystatebeforecircuitswitching Continued Accordingtolawofswitch Continued 2 Accordingtot 0 circuit findiC 0 uL 0 uc 0 Substitute iL 0 Weget Results Electricquantity canchangeabruptly Summary 1 换路瞬间 uC iL不能跃变 但其它电量均可以跃变 3 换路前 若uC 0 0 换路瞬间 t 0 等效电路中 电容元件可用一理想电压源替代 其电压为uc 0 换路前 若iL 0 0 在t 0 等效电路中 电感元件可用一理想电流源替代 其电流为iL 0 2 换路前 若储能元件没有储能 换路瞬间 t 0 的等效电路中 可视电容元件短路 电感元件开路 3 2ResponseofRCCircuit Solvingmethodofone ordertransientcircuit 1 Classicmethod accordingtoexcitation source findtheresponseofcircuitthroughsolvingdifferentialequation 2 Three factormethod containingonlyoneenergy storageelement describedbyone orderdifferentialequation iscalledone orderlinearcircuit One ordercircuit substituting Given 1 ApplyingKVL 1 CapacitorvoltageuC t 0 Zero inputresponse excitationisswitchedoff theresponseiscausedonlybyinitialenergy storageofcapacitor Essence DischargingofRCcircuit 3 2 1Zero inputResponseofRCCircuit 2 Solvingequation eigenequation hence uCwoulddecayexponentiallyfrominitialvalue 3 CapacitorvoltageuC Initialvalue Weobtain resistorvoltage dischargingcurrent capacitorvoltage 2 Capacitorcurrentandresistorvoltage 3 variationcurve 4 Timeconstant 2 Physicalsignificance Let unit S 1 dimension when Thevalueoftimeconstantreflectsthelengthoftimespentontransientprocess thelenghthoftimethatisspentbycapacitorvoltageondecayingto36 8 oftheoriginalvoltage whent 5 transientprocessisnearlyover uCreachestosteady statevalue 3 Transienttime Theoretically circuitreachestosteadystate Inengineeringperspective atransientlasts3 5 3 2 2Zero stateresponseofRCcircuit Zero stateresponse Theresponsecausedbytheexcitationofenergy storagecomponentwithoutinitialenergy Essence chargingprocessofRCcircuit Given uC 0 0 Caculate capacitorvoltageuC t andcurrenti t Completesolution paticularsolution complementarysolutionofhomogeneousequations 1 CapacitorvoltageuC 1 ApplyingKVL 2 Particularsolution Weget Forcedresponse steady stateresponse 强制分量 稳态分量 3 Complementarysolution Homogeneousequation Complementarysolution Completesolution 4 Completesolution FrominitialvalueuC 0 0 SoA U freeresponse transientresponse Transientresponse Steady stateresponse Steady statevoltage OnlyexitsinTransientprocess 3 variationcurve whent describesthelengthoftimespentonthevalueofuCrisingfrominitialvalueto63 2 ofsteady statevalue 2 CurrentiC 4 Timeconstant 3 2 3CompleteResponseofRCCircuit Completeresponse energy storagecomponentshaveinitialenergyattheinstantofswitching andthecurcuitcontainsexcitationafterswitchingoperation AccordingtoSuperposition Completeresponse Zero inputresponse Zero stateresponse Steady stateresponse Zero inputresponse Zero stateresponse Transientresponse Conclusion2 Completeresponse Steady stateresponse Transientresponse Conclusion1 Completeresponse Zero inputresponse Zero stateresponse Steady statevalue Initialvalue SolutionofFirst orderCircuits Classicmethod 1 Determinetheinitialvalueoftheenergystorageelement 2 Writethedifferentialequationforthecircuitfort 0 3 Determinethetimeconstantofthecircuitfort 0 4 Writethecompletesolutionasthesumofthenaturalandforcedresponse 5 Applytheinitialvaluetothecompletesolution todeterminetheconstanK Finalvalue Initialvalue 3 3Three factorMethodforOne orderCircuit AccordingtoresultsofClassicmethod Completeresponse representsvoltage currentfunctionsofone ordercircuit where WhencircuitdrivenbyDC thesolutionofone orderlinearcircuitdifferentialequationisgenerallyexpressed Allone ordercircuitcanbesolvedbythree factormethod Keypointsofthree factormethod 1 Findinitialvalue steady statevalue andtimeconstant 3 Drawvoltage currentvariationcurve 2 Substitutethesevaluesintogeneralexpression Findcurrentsandvoltagesafterswitching wherecapacitorCbehavesasopencircuit inductorLbehavesasshortcircuit 1 Caculate DeterminationofThreeFactors 1 Findatt 0 inthecircuit 3 Findthevalueofdesiredvariablesatt 0 within0 circuitdiagrambyknownmethods Ohm slawetal Inequivalentcircuitatt 0 Note 2 Caculate 1 Forsimpleone ordercircuits R0 R 2 Forcomplexone ordercircuits R0equalsequivalentresistancebetweenterminalsofenergy storageelementbyzeroingthesourcesandenergy storageelement 3 Caculate Forone orderRCcircuit Forone orderRLcircuit Note ThecaculationofR0issimilartothatofTheveninresistence bylookingbackintothetwoterminal