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

[Tom Wiltshire]

I've had a closer look at the freq response plot:

http://www.tomwiltshire.co.uk/ButterworthResponse.png
http://www.tomwiltshire.co.uk/Butterworth.png

The Linkwitz-Riley / identical-stages filter has a slight peak of resonance around the cutoff, less than 1dB. It shouldn't if the two filters are "proper" butter worth filters. However, it seems that this slight extra resonance (Q=0.842 instead of the required Q=0.841) cancels out the extra -3dB drop you get at the cutoff with a Linkwitz-Riley filter. The shift in resonance was caused by my rounding to E6/E24 values.

For my purposes (BBD filtering), I think this not-quite-a-Linkwitz-Riley filter will do fine. It's simple to build, uses few component values, and gives a 24dB/oct response. The minor bump can go down as "character".

Thanks for the help,
Tom



On 19 Dec 2015, at 10:26, Tom Wiltshire <tom at electricdruid.net> wrote:

> 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
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