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

[Tom Wiltshire]

On 19 Dec 2015, at 02:14, Magnus Danielson <magnus at rubidium.dyndns.org> wrote:
>> 
>> The circuit, identical-stages filter above, typical 4-pole butter worth below:
>> 
>> http://www.tomwiltshire.co.uk/Butterworth.png
>> 
>> And the responses:
>> 
>> http://www.tomwiltshire.co.uk/ButterworthResponse.png
>> 
>> Now, my question is "What am I missing?" or "Why is my simulation lying to me again?" since I find it difficult to believe that people have been building unnecessarily complicated filters since 1930 without spotting that they could make life much simpler.
>> Is it that the identical-stages version would be very sensitive, or does it have some other flaw?
> 
> Say hello to your Linkwitz Riley filter:
> https://en.wikipedia.org/wiki/Linkwitz%E2%80%93Riley_filter
> 
> Don is correct in his description of the Butterworth filter:
> https://en.wikipedia.org/wiki/Butterworth_filter

Ok, so what I did is a Linkwitz-Riley filter, and whilst it ought to have a roll-off of 24dB/oct like I wanted, it should also have an attenuation of -6dB at the cutoff point, -3dB worse than the standard 4-pole Butterworth. I'd have thought that'd be visible on the LTSpice frequency response graph, but if anything, the Linkwitz filter looks like it has a bit of a peak there. Any ideas what might be going on there? I'll have to have a look more zoomed in and see if I can't see the difference.

Thanks Magnus

Tom