<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><br class=""><blockquote type="cite" class="">On Dec 19, 2015, at 2:26 AM, Tom Wiltshire <<a href="mailto:tom@electricdruid.net" class="">tom@electricdruid.net</a>> wrote:<br class=""><br class="">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?</blockquote><div class=""><br class=""></div><div class="">A L-R filter would require two Butterworth stages, each with a Q of .707. Your cascaded filters have a Q of 0.842, so it's not exactly a L-R.</div><div class=""><br class=""></div><div class="">Let's plot the math:</div><div class=""><br class=""></div><div class=""><img apple-inline="yes" id="5834059B-9DDA-4F6A-8C48-0EFC6CD70CA5" height="310" width="640" apple-width="yes" apple-height="yes" src="cid:86A6B234-9ABB-4FB1-BEE4-A9621453813D@sonic.net" class=""></div><div class="">(I did these in a couple minutes with the Grapher program that comes with the Mac. Highly recommended for this sort of thing.)</div><div class=""><br class=""></div><div class="">The green curve is a Butterworth: Q's of .54, 1.31.</div><div class="">The blue curve is your cascaded pair: Q's of 0.842, 0.842.</div><div class="">The red curve is an L-R: Q's of 0.707, 0.707.</div><div class=""><br class=""></div><div class="">So your fake Butterworth filter is remarkably close. </div><div class=""><br class=""></div><div class="">Your simulation curves seem off. The Butterworth curve shouldn't peak and I have no idea what the deal is with the other curve, it doesn't look remotely right. Do your opamp models introduce any poles?</div><br class=""> -- Don<div class=""><br class=""><div class="">--<br class="">Don Tillman<br class="">Palo Alto, California<br class=""><a href="mailto:don@till.com" class="">don@till.com</a><br class="">http://www.till.com<br class=""><br class=""></div></div></body></html>