An open-loop amplifier can be described by [A_{v}=frac{10^{4}}{left(1+j frac{f}{10^{5}} ight)}] A dominant pole is to be inserted

An open-loop amplifier can be described by

\[A_{v}=\frac{10^{4}}{\left(1+j \frac{f}{10^{5}}\right)}\]

A dominant pole is to be inserted such that a closed-loop amplifier with a low-frequency gain of 50 has a phase margin of 45 degrees.

(a) Determine \(\beta\) and the required dominant pole frequency.

(b) The feedback transfer function is increased such that the closed-loop, low-frequency gain of the amplifier in part (a) is 20 . Determine the phase margin of this new amplifier.