I'm currently designing an inverse Chebyshev 7th order low-pass filter with three 2nd-order low-pass notches and an RC low-pass filter.

I've already used Simulink to obtain the s-domain transfer function and the positions of poles and zeros, but the circuit's transfer function is too complex to determine the values of R and C.

How can this 5th-order Chebyshev low-pass filter be designed?

enter image description here

Image from www.ice77.net/electronics/Active%20filters.pdf

  • \$\begingroup\$ Building this with accurate component values will likely be difficult. In your simulation, do a sensitivity analysis so as to get a feel for component tolerance. \$\endgroup\$
    – glen_geek
    Commented Nov 16, 2023 at 14:08
  • \$\begingroup\$ Aren't the equations that follow this figure in your linked document adequate?? Where are you getting stuck?? \$\endgroup\$ Commented Nov 16, 2023 at 14:25
  • \$\begingroup\$ thanks! It's the first time I heard about sensitivity analysis. I'll try \$\endgroup\$
    – PAT
    Commented Nov 16, 2023 at 14:32
  • \$\begingroup\$ What now is your problem (because you have shown a 5th-order filter)? \$\endgroup\$
    – LvW
    Commented Nov 16, 2023 at 14:35
  • \$\begingroup\$ @ScottSeidman This circuit is at page140. It doesn't have any equation. \$\endgroup\$
    – PAT
    Commented Nov 16, 2023 at 14:37

1 Answer 1


Quote: "LvW I don't know how the values of these resistors and capacitors are determined"

Well - you must apply the classical method which is to be used for all second-order stages:

  • Select a suitable 2nd-oder topology (with zeros)
  • Find/determine the transfer function of this stage in "normal" form ("s"-polynom in the denominator)
  • Compare this transfer function with the general function which explicitely shows pole/zero frequencies (wp, wz) and quality figures Qz and Qp for zeroes and poles.
  • Find the correct values for wp, wz, Qp and Qz with the help of filter tables according to your damping requirements.
  • From this comparison you can derive the formulas for all components (and realize that you have the chance to select some componenet values from the beginning).

Final comment: I could give you a set of expressions where the mentioned four filter parameters are related to R- and C-values - however, not for the topology you have selected. My values are for a very similar topology ("Boctor"-Filter: 2 capacitors: C1 as a first series element and C2 between opamp output and inv. input).

  • \$\begingroup\$ thx, i know this is the acuurate way to get parameters, but the transfer function of this sencond-order low pass notch is extremely complex. \$\endgroup\$
    – PAT
    Commented Nov 16, 2023 at 15:10
  • \$\begingroup\$ Yes - I know. What about using an alternative topology (my formulas)? Or you can try to find details about the Boctor-Filter. \$\endgroup\$
    – LvW
    Commented Nov 16, 2023 at 15:14
  • \$\begingroup\$ Understood. I'll go look for information on the Boctor filter first.thanks! \$\endgroup\$
    – PAT
    Commented Nov 16, 2023 at 15:25
  • \$\begingroup\$ By the way: I think, the topology as shown by you can also be called "Boctor"-Filter because it is based on the classical multi-feedback lowpass with an additional input at the non-inv. opamp node. \$\endgroup\$
    – LvW
    Commented Nov 16, 2023 at 15:57

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