# Feedback amplifier problem

1. Apr 5, 2015

### asdf12312

1. The problem statement, all variables and given/known data
Consider a feedback amplifier for which the open loop gain A(s) is given by:
A(s) = X/ [(1+s/Y)*(1+s/Z)2] |s=jω
Where X = 7500, Y = 90000, and Z = 800000

a) If the feedback factor is independent of frequency, find the frequency at which the phase shift is 180°.
b) Find the critical value of at which oscillation will commence.

2. Relevant equations

Af(s) = A(s)/ 1+A(s)B(s) (gain with feedback)

3. The attempt at a solution
I'm not sure how to start this problem. If is constant value then I get -tan-1(ω/90,000) - 2*tan-1(ω/800,000) = tan(180) or (ω/90,000) + (ω/800,000) = tan(60) and when I try to solve I get ω=140,000 rad/s, but maybe i'm doing it wrong.

2. Apr 6, 2015

### milesyoung

If you want to convert -180° to radians, then that's not the way to do it. The rest is fine.

3. Apr 6, 2015

### rude man

This equation equates arc tangents to a tangent, which is incorrect. Change the rhs of your 1st equation to + or - π and it's OK then.
EDIT:
I don't see how you got this 2nd equation. Would like to see your derivation thereof.
Solving your 1st equation, which is transcendental, I got ω = 885,438 rad/s or f = 140,922 Hz.

This may be irrelevant, but
if arc tan a + arc tan b = θ
then it does not follow that
a + b = tan θ.
Try it with a = 0.25 and b = 0.35: tan θ = 0.25 + 0.35 = 0.60, so θ = arc tan 0.60 = 30.96°
whereas 14.04° + 19.29° = 33.33°
It's close but not right. I'm not saying you did this but in case you did ...

Last edited: Apr 6, 2015