Step Response of Series RLC

Given: iL(0) = Io, vC(0) = VoFind: v(t)

Two Parts:

a) Homogeneous:

b) Steady State:

Example 4.Given: R = 2 Ω , L = 1H, F = 1/5 FVS = 12V

Find: v(t) and i(t), t>0

Step Response of Parallel RLC

Given: iL(0) = Io, vC(0) = VoFind: i(t)

Find i(t) and iR(t).

General Second-Order Circuit

1. Find transient response by removing sources.a) Apply KVL, KCL, etc 2nd order ODEb) Solve characteristic equation s1, s2

i. Overdamped

ii. Underdamped

iii. Critically damped

2. Find steady-state value: L s.c.; C o.c.

3. X(t) = Xs-s + Xtransient

4. Find IC’s: from no jump conditions

Example. Find v(t) and i(t) for >0.

a. Transient response