The loop gain of an amplifier is given by [T(f)=frac{betaleft(5 times 10^{5} ight)}{left(1+j frac{f}{10^{4}} ight)left(1+j frac{f}{5 times

The loop gain of an amplifier is given by

\[T(f)=\frac{\beta\left(5 \times 10^{5}\right)}{\left(1+j \frac{f}{10^{4}}\right)\left(1+j \frac{f}{5 \times 10^{5}}\right)\left(1+j \frac{f}{10^{7}}\right)}\]

The pole at \(f_{P 1}=10^{4}\) is to be moved such that the feedback amplifier with a closed-loop low-frequency gain of 40 has a phase margin of 60 degrees.

(a) Find the value of \(\beta\).

(b) Determine the new pole frequency.