The loop gain of a three-pole amplifier is given by [T(f)=frac{10^{3}}{left(1+j frac{f}{10^{4}} ight)^{2}left(1+j frac{f}{10^{6}} ight)}] (a) Show

The loop gain of a three-pole amplifier is given by

\[T(f)=\frac{10^{3}}{\left(1+j \frac{f}{10^{4}}\right)^{2}\left(1+j \frac{f}{10^{6}}\right)}\]

(a) Show that this function will lead to an unstable feedback system.

(b) Insert a dominant pole such that the phase margin is 45 degrees. Assume the original poles remain fixed. What is the dominant pole frequency.