# How to calculate multiple pole active filter manually?

For example I want to make a 6-pole multiple feedback topology active bandpass filter that have the specifications of 0.25 db chebychev , that the range of the filter is 2000 hz to 3000 hz.

I already know how to calculate a single 2-pole filter if I wanted to , but I don't understand how to calculate the filters for each section to make a 6-pole filter.

I know a 6-pole active filter is usually made up of 3 2-pole filter sections connected together.

So How would a person calculate each section required for a filter? I have always used online filter calculators and have never learned how to calculate each section required manually.

• Use the tables for 0.25dB n=6 and normalized f and Q . The poles follow an ellipical curve. Aug 16, 2021 at 17:42
• 6-pole Chebyshev requires fairly tight component value tolerance. I'd suggest you do a simulation that varies component values to get a feel for what's required to keep within your 0.25 dB spec...every added pole tightens tolerance. tools.analog.com/en/filterwizard does suggest each component tolerance in their design applet. Don't forget to add parasitic capacitances Aug 16, 2021 at 17:45
• Math en.m.wikipedia.org/wiki/Chebyshev_filter. But higher the Q, the tighter the tolerances which increase with f at each stage Aug 16, 2021 at 17:46
• e.g. {fn,q}= 0.444fo Q=0.637, 0.794 fo Q= 1.556, 1.0311fo Q=5.52 for 3 stages Aug 16, 2021 at 18:13
• @TonyStewartEE75 Where do I find the information you just gave? I tried looking for formulas online , but really having a issue on finding the correct stuff for multi-pole filters. Obviously there are different things that I have found online, just not sure what to use. Aug 16, 2021 at 18:52

First find the transfer function for the chebyshev (the tool I usually use is matlab) once you find this you can find a physical realization (sallen-key, state-variable among others) for opamps (or you could just use LC or RC filter components which are more lossy than an active filter). To find the sallen key realization I usually decompose the transfer function into second order sections and then match it up with an opamp second order section.

But you don't have to use a second order section to physically realize a filter, you can use any filter topology as long as the transfer function of the opamps sufficiently approximates the transfer function of the elliptic filter design.

If you want to find the Chebyshev transfer function directly it is part of elliptic filter design, which is more information than could fit in an answer, but this is worth a read: Lecture Notes on Elliptic Filter Design
I usually leave this to the tools to find as I don't want to rewrite code that is already on my computer.