EMRFD Message Archive 1477

1477 2008-02-28 07:04:05 rickard.john Ultraspherical filters Message Date From Subject Hi EMRFD group, I was interested to come across the article describing Ultraspherical low pass filters in emrfd and would like to explore their properties both in simulation and experimentally. My problem is that there does not appear to be any accessable design literature in any of the standard filter design texts. There is information on various maths sites regarding Ultraspherical polynomials but unfortunately my maths is not up to the task of completing the involved step of converting the raw function into component values. As an aside I have found that cascading a pair of (HF) 3 pole chebychev LP filters designed for ripple of about 1 to 3 dB and coupling the 3 pole sections in series with a capacitor in the range .001 to .01 uF produces a very flat low loss band pass of 10 to 20% of the cut off freq followed by a very steep chebyshev like cut off on the high side. The unimportant band lower than the BP area has an increasing loss meandering down to DC. I doubt this cobbled together 5 pole filter is optimised but it appears to have the major charactoristics of an ultra spherical filter. Any comments would be appreciated. John. rickard.john wrote: > Hi EMRFD group, > > I was interested to come across the article describing Ultraspherical > low pass filters in emrfd and would like to explore their properties > both in simulation and experimentally. > > My problem is that there does not appear to be any accessable design > literature in any of the standard filter design texts. > There is information on various maths sites regarding Ultraspherical > polynomials but unfortunately my maths is not up to the task of > completing the involved step of converting the raw function into > component values. > > As an aside I have found that cascading a pair of (HF) 3 pole > chebychev LP filters designed for ripple of about 1 to 3 dB and > coupling the 3 pole sections in series with a capacitor in the > range .001 to .01 uF produces a very flat low loss band pass of 10 to > 20% of the cut off freq followed by a very steep chebyshev like cut > off on the high side. > The unimportant band lower than the BP area has an increasing loss > meandering down to DC. > > I doubt this cobbled together 5 pole filter is optimised but it > appears to have the major charactoristics of an ultra spherical > filter. > Any comments would be appreciated. Connecting the LP filters directly means their input and output impedances will interact, giving an overall transfer function that doesn't match any classic filter response. If you know the component topology of the ultraspherical you want, the component values can be determined using a filter optimization program that adjusts all the component values to give the desired transfer function that matches the goals you set. An easier way is to use a predetermined table of component values, but i don't know of any for ultraspherical filters. If you know the polynomial form of the transfer function, you can determine the component values using polynomial divisions.