From: bill@verdix.com (William Spencer)
Subject: Re: Active Crossovers
Organization: Verdix Corp
Date: Fri, 8 Jan 1993 00:40:37 GMT

DPierce@world.std.com (Richard D Pierce) writes:
>In article <1993Jan5.155001.9098@bnr.ca> Dave Dal Farra writes:

>>The big design plus of the L-R type over the Butt is that the "lobing"
>>error at x-over is reduced to zero and the on axis response is flat
>>(assuming driver acoustic centers are in same plane and assuming flat 
>>drivers).  Lobing error, over-simplified, means that the sound energy is
>>not directed on axis at x-over.  Butt types show this error to a certain
>>degree.

>This is completely wrong. A Linkwitz-Riley network between two drivers
>will show as much lobing at the crossover as pretty much any other
>(although the lobing problems are different).

Yeah, like they're not near as much of a problem. You missed his big error
though -- a Butterworth x-over won't have lobing error either. It *will*
have a 3 dB on-axis peak however.

>[...]
>>Second order L-R's also invert tweeter phase and are not recommended.

Is this really grounds for non-recommendation? 3rd through 5th order normal
polarity connection crossovers have a full 360 degree phase shift through 
x-over, while 1st, 2nd & 3rd order reverse-polarity x-overs have only 180
degree shifts but reverse polarity in the passband of one driver. I (again)
ask the question -- which may be of only academic interest but could make
for a hell of an argument -- which is really better or worse?

>>Third order Butterworths have a flat power response, which is good, but
>>aim the sound around x-over 15 degress downward (assuming your tweeter is
>>obove the woofer on a flat baffle).   The result is a small notch in the 
>>response at x-over and a real bad floor reflection which can colour
>>the sound.   This filter can be made to work but certain design practices
>>inherent to the speaker must be present.  If your tweeter is located
>>BELOW your woofer, this x-over could work well.

>All of the above is true IF AND ONLY IF the driver phase response is
>perfect, the drivers' effective acoustical centers are equidistant from
>the listening/measuring position, etc. etc. In the real world of drivers,
>the answer to these issues is most definitaly: NOT!

It's also only true for a certain driver spacing relative to the wavelength
at crossover. Otherwise, the angle is other than 15 degrees.

There may also be some confusion about the merit and disadvantage of the 
tilted polar peak (yes, peak, just like the even-order Butterworth case).
The peak occurs at the angle at which the driver contributions come together 
in phase. At some other angle there will be some cancellation compared
to on-axis. Flat power response implies a constant total energy put into the 
room, therefore the same response in dry and reverberant environments
(assuming a LOT of that idealized world stuff). Since you know there will be
cancellation at some angle, and flat response on axis, you also know there
must be a peak at some other angle or the integral sum of energies at all 
angles can not be constant. The polar peak can be seen as good thing
if you want flat on-axis pressure response and a flat power response, because
otherwise you just can't do it!

Bill Spencer