(This isn't a homework or anything like that. It's about an "universal filter" I'm trying to make.)
I'd like to know if there is a possibility to avoid elliptic functions. My direct and practical case involves trying to find the poles and zeroes of a Cauer (elliptic) filter with the aid of a spice simulator. There are some mathematical formulae to work with but, unfortunately, they are limited; I am talking about LTspice.
So, I was wondering if there isn't a possibility to use something like Taylor series that would permit me to use some spice directives with more "gentle" formulae and calculate the poles and zeroes "on the spot"?
Thank you in advance,
A simple yes or no will do, if all else, but I remember seing somewhere (and I keep looking for that, but luck isn't on my side) a series, something like:
where u was function of k, from here on there were some approximations, etc (Pade?).
For those interested, here are two of the answers:
Rapidly-convergent methods for evaluating elliptic integrals and theta and elliptic functions
Amazon.com: Analog and Digital Filter Design, Second Edition (EDN Series for Design Engineers) (9780750675475): Steve Winder: Books