A feedback amplifier with a compensation capacitor has a low-frequency loop gain of \(T(0)=100 \mathrm{~dB}\) and poles at \(f_{P 1}^{\prime}=10 \mathrm{~Hz}, f_{P 2}=5 \mathrm{MHz}\), and \(f_{P 3}=10 \mathrm{MHz}\).

(a) Find the frequency at which \(|T(f)|=1\), and determine the phase margin.

(b) If the frequency \(f_{P 1}^{\prime}\) is due to a compensation capacitor \(C_{F}=20 \mathrm{pF}\), determine the new dominant pole frequency \(f_{P 1}^{\prime}\) and phase margin if the compensation capacitor is increased to \(C_{F}=75 \mathrm{pF}\).