From: DPierce@world.std.com (Richard D Pierce)
Subject: Re: Active Crossovers
Organization: The World Public Access UNIX, Brookline, MA
Date: Tue, 5 Jan 1993 22:32:19 GMT

In article <1993Jan5.155001.9098@bnr.ca> Dave Dal Farra writes:
>
>>BTW, what's the difference between Butterworth and Linkwitz-Riley 
>>types?  Is one better?

Dave gives an interesting discussion of crossover issues in general, which
I have deleted for brevity, but then posts a couple of misconceptions as
well as an overly complicated description of a Linkwitz-Riley crossover:

>
>A Linkwitz-Riley is also called a "squared Butterworth" filter because
>it is mathematically derived by squaring an n-th order Butterworth 
>transfer unction to arrive at a "2n-th" order linkwitz-Riley ("L-R").  
>Obviously, L-R x-overs can only be obtained in even orders (i.e. 2nd,
>4th, 6th, etc.) while Butterworth x-overs are found in any order.
>Realize too that the squaring is mathematical!!  Putting two active
>n-th order Butts in series will give an 2n-th order L-R, but
>this will not work with passives (obviously).

Another, simpler way to look at it is that a Linkwitz-Riley network is one
which has all-pass characteristics. This, among other things, means that
the phase response and frequency response characteristics are not minimum
phase.

>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). The difference is that a
configuration using a mirror-symmetric arrangement of three drivers (for
example, two woofers/midranges and one tweeter arranged in a vertical
linear array) will show no lobing, PRESUMING THE DRIVERS THEMSELVES HAVE
NO LOBING AND EFFECTIVELY NO RESPONSE ERRORS THROUGH THE CROSSOVER REGION. 

Because of this last caveat, which most choose to ignore, the benefits of
a true M-T-M Linkwitz-Riley (as first proposed and documented by Joe
D'Appolito) seldom if ever achieve their theoretical capabilities.

>
>Be wary of using Butterworth x-overs unless you are very carefull.
>Second order Butt's are disastrous in that they invert the phase
>of the tweeter relative to the woofer.  The result is a 2 dB hump at
>x-over.
>If the tweeter were in phase, there would be a suck-out of Grand Canyon
>proportions. This x-over is not recommended!!!!
>
>Second order L-R's also invert tweeter phase and are not recommended.
>
>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!


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