Consider a feedback amplifier for which the open-loop gain is given by

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

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

(b) For \(\beta=0.0045\), determine the magnitude of the loop gain \(T(f)\) at the frequency \(f=f_{180}\) and determine the phase of \(A(f)\) when \(|T(f)|=1\). Determine the closed-loop, low-frequency gain. Is the system stable or unstable?

(c) Repeat part (b) for \(\beta=0.15\).