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

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

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

(a) Sketch the Nyquist diagram for \(\beta=0.20\).

(b) Determine the value of \(\beta\) that produces a phase margin of 80 degrees.