The following circuit schematic presents a two-pole Sallen-Key low pass filter.

Question

Determine the value of resistor R1 to achieve the Butterworth frequency response.
Calculate the cut-off frequency of the filter.
RA = 10 kΩ
Rb = 10 kΩ
Ca = 100nF
Cb = 100nF
R2 = 10 kΩ
VCC = 12V
VEE = -12V

Answer 1

To achieve the Butterworth frequency response, we need to use the formula:

R1 = R2 / (√(2) - 1)

R1 = 10 kΩ / (√(2) - 1) ≈ 2.61 kΩ

To calculate the cut-off frequency, we use the formula:

fC = 1 / (2π√(R1R2C1C2))

fC = 1 / (2π√(2.61 kΩ × 10 kΩ × 100 nF × 100 nF))

fC ≈ 159.2 Hz

Therefore, the cut-off frequency of the filter is approximately 159.2 Hz.