The loop gain function of a feedback system is described by [T(f)=frac{betaleft(10^{3} ight)}{left(1+j frac{f}{10^{4}} ight)left(1+j frac{f}{10^{5}} ight)left(1+j frac{f}{10^{6}} ight)}] (a) Determine the frequency (f_{180}) at

The loop gain function of a feedback system is described by

\[T(f)=\frac{\beta\left(10^{3}\right)}{\left(1+j \frac{f}{10^{4}}\right)\left(1+j \frac{f}{10^{5}}\right)\left(1+j \frac{f}{10^{6}}\right)}\]

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

(b) For \(\beta=0.019\), (i) find \(\left|T\left(f_{180}\right)\right|\) and (ii) find the phase at which \(|T|=1\).

(c) Using the results of part (b), determine the low-frequency closed-loop gain \(A_{f}(0)\).