Second-Order Circuits [相容模式]

2012/10/241 Second-Order Circuits Introduction Finding Initial and Final Values The Source-Free SeriesRLCC ircuit The Source-Free ParallelRLCC ircuit Step Response of a SeriesRLCC ircuit Step Response of a ParallelRLCC ircuit General Second-Order Circuits Duality ApplicationsIntroduction A Second-Order circuit is characterized by asecond- order differential equation. It consists of resistors and the equivalent oftwo energy storage Initial and Final Values v(0),i(0),dv(0)/dt,di(0)/dt,v( ), andi( ) Two key points: vandiare defined according to thepassive signconvention. Continuity properties: Capacitor voltage:(VS-like) Inductor current:(IS-like))0()0()0()0( LLCC iivvvi+_Example).(,)((c),)0(,)0((b)),0(, )0((a)Find:Q vidtdvdtdivi V4)0()0(A2)0()0(V4)0(2)0(A22412)0( tanalysisdcApply(a):Solvviiivi2012/10/24 3 Cont dV12)(A0)(.0foranalysisdcApply(c):Sol vitCont :0findTo(b):Sol CidtdviiCidtdvidtdvCdtdvCCCC)()()()()( t= 0+2 A2012/10/244 Cont dt= 0+A/s0250000haveweThus0481200000412gives KVLapplying, (b):Sol.

2012/10/24 1 Second-Order Circuits •Introduction •Finding Initial and Final Values •The Source-Free Series RLC Circuit •The Source-Free Parallel RLC Circuit •Step Response of a Series RLC Circuit •Step Response of a Parallel RLC Circuit •General Second-Order Circuits

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