SECOND ORDER CIRCUIT. Forced Response of Parallel RLC Circuit (Step response Parallel RLC Circuit) Second order circuit When switch is open, a STEP current.

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Presentation transcript:

SECOND ORDER CIRCUIT

Forced Response of Parallel RLC Circuit (Step response Parallel RLC Circuit) Second order circuit When switch is open, a STEP current is applied to the circuit We want to find i L (t) for t >0 By KCL, +v+v iCiC iRiR iLiL R L C IsIs t = 0 We will solve i L (t) by finding v(t) and substitute this value into

Forced Response of Parallel RLC Circuit (Step response Parallel RLC Circuit) Second order circuit +v+v iCiC iRiR iLiL R L C IsIs What is v(t) ? By KCL, t = 0 Differentiate once, This is similar to what we have seen in source-free circuit  solutions have similar forms

Forced Response of Parallel RLC Circuit (Step response Parallel RLC Circuit) Second order circuit Overdamped Critically damped Underdamped If we substitute v(t) intowe will get: Overdamped Critically damped Underdamped

Forced Response of Parallel RLC Circuit (Step response Parallel RLC Circuit) Second order circuit i(t) = I tran + i ss These apply to voltage as well: v(t) = v tran + v ss

Forced Response of Parallel RLC Circuit (Step response Parallel RLC Circuit) Second order circuit I f is the final value of i(t)  I f = i(  ) V f is the final value of v(t)  V f = v(  ) where,

Forced Response of Parallel RLC Circuit (Step response Parallel RLC Circuit) Second order circuit In general, x(t) = x tran + x ss Transient response - similar to natural response : Steady state response - response as t  Capacitor  open circuit Inductor  short circuit

Forced Response of Series RLC Circuit (Step response Series RLC Circuit) Second order circuit RL C i +vc+vc t = 0 VsVs By KVL, We solve v c (t) by finding i(t):

Forced Response of Series RLC Circuit (Step response Series RLC Circuit) Second order circuit Substituting these into gives: Overdamped Critically damped Underdamped Which has the general form as: v(t) = v tran + v ss

Second order circuit I f is the final value of i(t)  I f = i(  ) V f is the final value of v(t)  V f = v(  ) where, Forced Response of Series RLC Circuit (Step response Series RLC Circuit)