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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.

schematic

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:

 

 

I only know some basic equations:

 

Circuits:

 

Low-pass 2nd order

schematic

simulate this circuit

 

High-pass 2nd order

schematic

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?

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  • \$\begingroup\$ Good question, this will help many users:) \$\endgroup\$
    – Deepak
    Oct 5 '20 at 19:27
  • \$\begingroup\$ Falstad filter designer makes this trivial. Define source and input impedances 1st. \$\endgroup\$ Oct 5 '20 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 '20 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 '20 at 16:17
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Others may give the formulae, I will give an easy solution with an arbitrary input impedance.

enter image description here enter image description here

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  • \$\begingroup\$ Have you been on holiday Tony? \$\endgroup\$
    – Andy aka
    Oct 5 '20 at 21:13
  • \$\begingroup\$ Yes travelling all around the globe \$\endgroup\$ Oct 5 '20 at 21:18
  • \$\begingroup\$ On the web...ha...golfing having fun \$\endgroup\$ Oct 6 '20 at 2:20

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