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


-> 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:



I only know some basic equations:




Low-pass 2nd order


simulate this circuit


High-pass 2nd order


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?

  • \$\begingroup\$ Good question, this will help many users:) \$\endgroup\$
    – Deepak
    Oct 5, 2020 at 19:27
  • \$\begingroup\$ Falstad filter designer makes this trivial. Define source and input impedances 1st. \$\endgroup\$ Oct 5, 2020 at 19:42
  • \$\begingroup\$ 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). \$\endgroup\$
    – TimWescott
    Oct 5, 2020 at 20:17
  • \$\begingroup\$ 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). \$\endgroup\$ Oct 6, 2020 at 16:17

2 Answers 2


Because both transfer functions are given already in the so called "normal" form with a denominator D(s)=1+As+bs², you can compare the corresponding denominator factors with the general form


As a result, you get two equations for the two unknown quantities wp (pole frequency) and Qp (pole quality factor). The quantity Qp is chosen according to the required Chebyshev approximation (ripple) and wp defines the passband.

Note that during this calculation you first have to choose two parts values because you have only two equations for 4 parts. On the other hand, design formulas are readily available from the literature.


Others may give the formulae, I will give an easy solution with an arbitrary input impedance.

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