8.4 The Natural Response of a Series/Parallel RLC Circuit

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8.5 The Step Response of a Series/Parallel RLCCircuit(a) Step response of a seriesRLC circuitStep 1. Mesh analysis (i=i L )di 1L + Ri+ idt = Vs, t > 0dt C∫Case(i) take derivatived 2i + Rdi + i = 02Ldt dt CC.T. PanSame as natural response but with i(0 + )=I 0+ Vs−IR 0−V0( 0 ) =39d idtL8.5 The Step Response of a Series/Parallel RLCCircuitCase(ii) use v as unknowndvi = C dt2dv Rdv v V+ + = s2dt Ldt LC LCStep 2. Complete solution = v h +v pph( )v t = VsSt 1 St 2⎧ Ae1+ Ae2overdamped⎪v t A At e critically damped−αt() = ⎨( 1+2 )⎪ −αt( cos + sin )⎩e A1 wtdA2wtdunderdampedC.T. Pan 40
8.5 The Step Response of a Series/Parallel RLCCircuitStep 3. Initial conditions+ −( 0 ) ( 0 )v = v = Vd vdtdvC+( )0 = ?= idtC0+( 0 ) I0d iCv+∴ ( 0 ) = =dt C CThen the unique solution can be determinedC.T. Pan 418.5 The Step Response of a Series/Parallel RLCCircuit(b) Step response of a parallel RLC circuitI 0 , V 0 GivenStep 1.Nodal equationv 1 t dv+ vdt C Is, t 0R L∫+ = >dtCase (i) Take derivativeC2dv 1 dv 12dt Rdt L+ + v=0Same as natural responseC.T. Pan 42
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
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Page 28 and 29: 8.6 State EquationStep1. Pick a tre
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Page 32 and 33: • Example 3 : Find v R48.6 State
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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