Question

Filter1 is: 2nd Order - High-Pass filter - Butterworth filter

a.) Design Filter1 with a corner/center frequency of about Freq: 1.2 kHz and a load resistance of about R_L: 50 ohms.
b.) Draw the circuit diagram.

Answer 1

The circuit diagram for 2^nd order butterworth filter is given below

Considering design parameters for the circuit,

for a simple design,we can choose R₂ = R₃ = R and C₂ = C₃ = C

The lower cut off frequency of the filter is f_L = 1/(2 R_2*R_3*C₂*C₃) = 1/( 2R*C)

Now that this is a NON-inverting op-Amp,the feedback gain A_F = 1+ R_f/R₁

the voltage gain magnitude equation of the filter is given below

1)Here fL is given as 1.2KHz 1/( 2R*C) = 1200 Hz

R*C = 1/( 2* 1200) = 1.326 * 10^-4.

So we have to choose R and C values such that R*C is 1.326 * 10^-4

Let us take C₂ = C₃ = C 1F   R₂ = R₃ = R =132 ohm

2) Now, A_F = 1+ R_f/R₁ = 1.586

R_f/R₁ = 0.586   R_f = 0.586 * R​​​​​​​₁

Now choose R₁ 100 k    R_f = 0.586 * 100   60 k