# Chebyshev filter design (lowpass to highpass with specifications)

I have been trying to solve the following problem:

Design a band pass filter with 2nd order Chebyshev filters: Low-pass to high-pass (both 2nd order in cascade.) Find the component values (resistors and capacitors.) Use Matlab.

simulate this circuit – Schematic created using CircuitLab

Parameters:

-> Ripple[dB] = 3
-> flp = 10kHz
-> fhp = 3.2kHz


From the following code I have been able to find the transfer function for the low-pass:

n = 2;
ripple = 3;
[z,p,k] = cheb1ap(n,ripple)
H = zpk(z,p,k)
bode(H), grid on, shg


The output transfer function for the low pass filter:

$\frac{0.50119}{(s^2&space;+&space;0.6449s&space;+&space;0.7079)}$

I only know some basic equations:

$\frac{V_o(s)}{V_i(s)}=\frac{1}{s^2(R_1R_3C_2C_4)+sC_4(R_1+R_3)+1}$

$H(s)=\frac{1}{s^2+(\frac{2\xi\omega_n}{\omega_n^2})s+1}$

## Circuits:

Low-pass 2nd order

$\frac{V_o(s)}{V_i(s)}=\frac{1}{s^2(R_1R_3C_2C_4)+sC_4(R_1+R_3)+1}$

simulate this circuit

High-pass 2nd order

$\frac{V_o(s)}{V_i(s)}=\frac{s^2R_2R_4C_1C_3}{s^2(R_2R_4C_1C_3)+sR_2(C_1+C_3)+1}$

simulate this circuit

• My real trouble is knowing the equations I can use to find out the resistor and capacitor values to implement the circuit in a lab. What would you recommend?

• Are there Matlab functions I can use for the highpass?

• Good question, this will help many users:) Oct 5 '20 at 19:27
• Falstad filter designer makes this trivial. Define source and input impedances 1st. Oct 5 '20 at 19:42
• Homework? The general method of going from a transfer function to a circuit is to equate all the powers of $s$ in the numerator and the denominator. You end up with a system of equations that you then solve (often with at least one free component value that you pick to keep them all within a reasonable range). Oct 5 '20 at 20:17
• This site has all you need. Or search for "Opamps for everyone" (Ron Mancini), last time I checked it was freely available online and it has a chapter about active filer design. There are other books, but this one came to mind as free (as I knew it). Oct 6 '20 at 16:17