Question

In the circuit given below, C= C1 = C2. The gain of the multiple-feedback band-pass filter is ___________

(a) A0 = \(\frac{R_2}{R_1}\)

(b) A0 = \(\frac{R_1}{R_2}\)

(c) A0 = \(\frac{R_2}{2R_1}\)

(d) A0 = \(\frac{R_1}{2R_2}\)

I got this question during an internship interview.

This is a very interesting question from Advanced Problems on Filters in section Filters and Attenuators of Network Theory

Answer 1

Right choice is (c) A0 = \(\frac{R_2}{2R_1}\)

Explanation: The total output C = CINPUT + COUTPUT that is the gain capacitor.

∴ The total Resistance is equal to the Resistance input and Resistance output.

Again, the total resistance gain = \(\frac{R_1 R_2}{R_1 + R_2}\)

Hence, the gain = A0 = \(\frac{R_2}{2R_1}\).