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

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

(a) $A_0 = \frac{R_2}{R_1}$

(b) $A_0 = \frac{R_1}{R_2}$

(c) $A_0 = \frac{R_2}{2R_1}$

(d) $A_0 = \frac{R_1}{2R_2}$

I got this question in class test.

I'm obligated to ask this question of Ideal LPF, HPF, BPF and BSF Characteristics topic in section Signal Transmission Through Linear Systems of Signals and Systems

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The correct answer is (c) $A_0 = \frac{R_2}{2R_1}$

For 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 = $A_0 = \frac{R_2}{2R_1}$.

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