电路理论-华科电气-7-First-Order-Circuits-2.pptxVIP

7.5TheZero-StateResponseIfalloftheinitialconditionshavezerovalue,thenthecircuitissaidtobeinthezero-state,andthesolutiontononzeroinputsforthecircuitisknownasthezero-stateresponse.(零状态响应)Zero-StateResponseOfAnRCCircuitt=0－：uC(0－)=0

Theparticularsolution：Itisusuallycalledtheforcedresponseorthesteady-stateresponse.uC(∞)=US，uCp=uC(∞)=USThehomogeneoussolution：Thecharacteristicequation：RCS+1=0Thecharacteristicvalue：Thehomogeneoussolutionisusuallycalledthenaturalortransientresponse.

uC(0+)=uC(0?)=0=US+A

?A=?USThegeneralformofthestepresponseofRCcircuits：

US-USUSRiuC0tuC=US(1-e)-RCt（t?0）i=-RCtUSRe（t?0）1zero-stateresponseofDCinput:uC=US–USe-RCt（t?0）特解齐次解稳态分量暂态分量+-uC+-CRiUS（2）Discussion

7.6StepResponseCircuitWhenthedcsourceissuddenlyapplied,thesignalofthesourcecanbemodeledasastepfunction,theresponseisknownasastepresponse.Thestepresponseofacircuitisitsbehaviorwhentheexcitationisthestepfunction,whichmaybeavoltageoracurrentsource.

7.6.1StepResponseofRCCircuitsUs1(t)t=0－：uC(0－)=U0Itssolutionincludestwoparts:theparticularsolutionandthehomogeneoussolution.Completeresponse:externalsourceandinitialconditionofthestorageelement

Theparticularsolution：Itisusuallycalledtheforcedresponseorthesteady-stateresponse.uC(∞)=US，uCp=uC(∞)=USThehomogeneoussolution：Thecharacteristicequation：RCS+1=0Thecharacteristicvalue：Thehomogeneoussolutionisusuallycalledthenaturalortransientresponse.

uC(0+)=uC(0?)=U0=US+A

?A=U0?USThegeneralformofthestepresponseofRCcircuits：

CompleteResponse例ucUsC12R+-U0US?U0uc(0+)=U0RC=USduCdt+（t?0）uCUSuC=(U0US)e-RCt+Therearetwowaystoexcitethecircuit:Byinitialconditionsofthestorageelementsinthecircuits.Byindependentsources.

1、Twowaystodeterminecompleteresponse:（1）tolinearcircuit:Completeresp