8.4 The Natural Response of a Series/Parallel RLC Circuit

8.6 State EquationStep2 Choose i L1 , i L2 , v C1 , v C2 as unknowns.Step3 Fundamental cutsets (KCL) for capacitors.dvC1C1= iL1dtdvC2C2= iL1+iL2dtStep4 Fundamental loops (KVL) for inductors.diL1L1= -vR1- vC1- vC2- vR5 + vR4dt= -R i - v - v - R ( i + i ) + v1L1 C1 C2 5 L1 L2 R4Note that v R4 should be expressed in terms of x and uC.T. Pan658.6 State EquationAbsorb voltages v R1and v C1 in currentsource i L1 ,and v R2 in i L2 .Absorb voltages v C2and v R5 in (i L1 + i L2 )current source.C.T. Pan66