# How can I calculate the parameters of an inverse Chebyshev active filter?

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?

• 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. Commented Nov 16, 2023 at 14:08
• Aren't the equations that follow this figure in your linked document adequate?? Where are you getting stuck?? Commented Nov 16, 2023 at 14:25
• thanks! It's the first time I heard about sensitivity analysis. I'll try
– PAT
Commented Nov 16, 2023 at 14:32
• What now is your problem (because you have shown a 5th-order filter)?
– LvW
Commented Nov 16, 2023 at 14:35
• @ScottSeidman This circuit is at page140. It doesn't have any equation.
– PAT
Commented Nov 16, 2023 at 14:37

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).

• 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.
– PAT
Commented Nov 16, 2023 at 15:10
• Yes - I know. What about using an alternative topology (my formulas)? Or you can try to find details about the Boctor-Filter.
– LvW
Commented Nov 16, 2023 at 15:14
• Understood. I'll go look for information on the Boctor filter first.thanks!
– PAT
Commented Nov 16, 2023 at 15:25
• 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.
– LvW
Commented Nov 16, 2023 at 15:57