8.4 The Natural Response of a Series/Parallel RLC Circuit

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• Example 3 : Find v R48.6 State Equationai 3Ri 43C 1L 1 L 2b hi L1 i L2g R 1e scR 2 R 4+- v C1d+C 2- v C2efR 5There are 8 nodes.C.T. Pan 638.6 State EquationStep1 Pick a tree as follows :ai L1i L2gbhC.T. Panc+ dv C1- +e -fv C2There are 7 tree branchesand 3 links.64
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
Page 2 and 3: 8.1 Linear Second Order Circuits•
Page 5: 8.3 Finding Initial ValuesUnder tra
Page 8 and 9: 8.3 Finding Initial Values• Examp
Page 14 and 15: 8.4 The Natural Response of a Serie
Page 20 and 21: 8.5 The Step Response of a Series/P
Page 28 and 29: 8.6 State EquationStep1. Pick a tre
Page 30 and 31: 8.6 State EquationStep2 choose i an
Page 34 and 35: 8.6 State EquationR∴v = e - ( i +
Page 36: Summary• Objective 1 : Be able to

8.4 The Natural Response of a Series/Parallel RLC Circuit

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