SECOND ORDER CIRCUIT Second order circuit Forced Response

SECOND ORDER CIRCUIT

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

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

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

Second order circuit Forced Response of Parallel RLC Circuit (Step response Parallel RLC Circuit) i(t) = Itran + iss These apply to voltage as well: v(t) = vtran + vss

Second order circuit Forced Response of Parallel RLC Circuit (Step response Parallel RLC Circuit) where, If is the final value of i(t) If = i( ) Vf is the final value of v(t) Vf = v( )

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

Second order circuit Forced Response of Series RLC Circuit (Step response Series RLC Circuit) t=0 Vs R L i We solve vc(t) by finding i(t): By KVL, + vc C

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

Second order circuit Forced Response of Series RLC Circuit (Step response Series RLC Circuit) where, Vf is the final value of v(t) Vf = v( ) If is the final value of i(t) If = i( )