Engineering High Pass Filter RL circuit: Time/Frequency Response

[aznkid310]

Homework Statement

For circuit B on page 2, find:

a) the time domain response v0 for a unit step input
b) input/output transfer function T(s) = v0/v_in
c) plot v0 vs. time
d) plot sinusoidal steady state vs. frequency: the magnitude in dB and phase in degrees of T(s)

Homework Equations

I'm getting stuck am an not sure how to proceed. Can someone check my work and also guide me along?

The Attempt at a Solution

a)R_thev = (2.2k)(1k)/(2.2k + 1K) = 687.5 ohms

V = 2.2k*v_in/(1k + 2.2k) [voltage divider]

tau = time constant = L/R_thv = 1.45454e-5

Then vo = .6875(1-e^(-t/tau)) = .6875(1-e^(-68750t)) assuming v_in = 1

T(s) = v0/v_in, where v0 = Z_eq/(Z_eq + 1K), Z_eq = (jwL)(2.2k)/(jwl + 2.2k)

My problem is converting this into a usable form to graph.

 

[DaveE]

Sorry, I didn't follow your use of Thevenin's theorem. You are on the right track treating the inductor as an impedance of $Z_L = j \omega L$. Your transfer function is correct as far as you have taken it, but it can be further simplified. The transfer function is just a complex number that depends on $\omega$. You will just use the magnitude and phase formulas for a complex number to generate your graph (bode plot) for different values of $\omega$. Maybe this website will help explain it.