HW5 Prob 2 Value Check

Hey everyone, just wanted to do a value check on HW5 prob2:
b) when I compute the steady state V expression @ fso= 110k, I get Vout = 23.9-j48.2
I'll skip small signal since it can't be evaluated without 's' as well as 2c's expression
d) I get Genv(0) = 27.5 this seems wrong to me.

For part d I did the following:
Genv(s) = v_hat / d_hat (Kpwm term multiplies into this but doesn't change the value)
v_hat = ((V* x v_hat) + (V x v_hat*)) / (2 x ||V||)

Last question, the 's' in the small signal voltage AM expression 's+jwso' (part b of this problem) is the update rate of the duty-cycle modulation correct?

Ugly Algebra

Is anyone getting a manageable version of ||H(jwso)||? I am at the point where I can barely fit the equation on a single sheet of paper and it's not looking good about reducing the thing much more...

Here's what I got for ||H(jwso)||:

RCwso/(sqrt((RCwso)^2 + (1-LCwso^2)^2))

Just wondering if anyone got anything would would get rid of the radical and help to reduce the massive ugliness that ensues with Genv(s).

Thanks!

The principle of modulation frequency

Hey everyone, just want to make sure I am thinking of modulation frequency, fmod, correctly. fs is the switching frequency and basically fmod is how often I am adjusting the switching frequency, is that correct? So in a real system, fmod would be fixed value, a lower value for slower output regulation, and a higher value for faster output regulation, correct?

Also, the 's' in Genv(s) is the modulation freq (s = j*2*pi*fmod), correct?

Thanks for the clarification.