Consider a four-pole feedback system with a loop gain given by [T(f)=frac{betaleft(10^{3} ight)}{left(1+j frac{f}{10^{3}} ight)left(1+j frac{f}{10^{4}} ight)left(1+j

Consider a four-pole feedback system with a loop gain given by

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

Determine the value of \(\beta\) that produces a phase margin of 45 degrees.