(a) Design a three-pole low-pass Butterworth active filter with a cutoff frequency at \(f_{3 \mathrm{~dB}}=20 \mathrm{kHz}\) and a unity gain magnitude at low frequency.

(b) Determine the magnitude (in \(\mathrm{dB}\) ) of the gain at (i) \(f=10 \mathrm{kHz}\), (ii) \(f=15 \mathrm{kHz}\), (iii) \(f=20 \mathrm{kHz}\), (iv) \(f=25 \mathrm{kHz}\), and (v) \(f=30 \mathrm{kHz}\).