EMRFD Message Archive 1477

Message Date From Subject
1477 2008-02-28 07:04:05 rickard.john Ultraspherical filters
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.
1482 2008-02-29 06:52:45 Russell Shaw Re: Ultraspherical filters
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.