A three-pole feedback amplifier has a loop gain given by [T(f)=frac{betaleft(5 times 10^{4} ight)}{left(1+j frac{f}{10^{3}} ight)left(1+j frac{f}{5 times 10^{4}} ight)^{2}}] (a) Determine the frequency (f_{180})

A three-pole feedback amplifier has a loop gain given by

\[T(f)=\frac{\beta\left(5 \times 10^{4}\right)}{\left(1+j \frac{f}{10^{3}}\right)\left(1+j \frac{f}{5 \times 10^{4}}\right)^{2}}\]

(a) Determine the frequency \(f_{180}\) at which the phase is -180 degrees.

(b) At the frequency \(f_{180}\), determine the value of \(\beta\) such that \(\left|T\left(f_{180}\right)\right|=0.25\).