[sdiy] Designing 4-pole filters with identical 2-pole stages - why not?

[Tom Wiltshire]

What Don's plot shows is:

Green: Genuine Butterworth 4-pole filter. Stage1 Q = 0.541, Stage 2 Q=1.307
Blue: My "identical stages" filter. Q of both stages = 0.842 (I intended 0.841 by design)
Red: Linkwitz-Riley filter. Q of both stages = 0.707.

I think this shows that my attempt at an identical-stages Butterworth filter actually comes pretty close, within 1dB on the resonant peak. Perhaps with different component values to back the Q off to the design value of 0.841 (or maybe less) you could even get closer.

Tom

On 19 Dec 2015, at 19:48, Donald Tillman <don at till.com> wrote:

> 
>> On Dec 19, 2015, at 11:19 AM, Donald Tillman <don at till.com> wrote:
>> 
>> Let's plot the math:
> 
> Oh dear, no imbedded graphics?  (Paging Mr. Jansen...)
> 
> Here:
> 
>     http://till.com/random/butter.jpg
> 
>   -- Don
> 
> --
> Don Tillman
> Palo Alto, California
> don at till.com
> http://www.till.com
> 
> 
> 
>