From: Dave Dal Farra <gpz750@bnr.ca>
Subject: Re: Active Crossovers
X-Xxdate: Tue, 5 Jan 93 00:31:46 GMT
Organization: BNR Ltd.
X-Useragent: Nuntius v1.1.1d9
Date: Wed, 6 Jan 1993 00:23:27 GMT

Dick, Carleton, a few points;

I deliberately over-generalized my discussion on x-overs and made 
reference to that in the opening paragraph where I discuss the 
complications involved.  I understand the complications and intricasies
involved MUCH MUCH MUCH better than Dick seems to assume.  Dick 
accurately points out that I did not mention explicitely the problems 
of driver acoustic phase, acoustic center seperation and frequency 
response non-linearity in x-over design.  I appologize for any confusion
this may have caused.

But, let me correct/clarify a few of Dicks points:

>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.

This is an over simplification;  All pass x-overs may be derived using
original alignments of any Q (Bessel, etc.) while still maintaining
the all pass characteristic (I know! I know! Not with real drivers!!).
Each different "all-pass" topology derived will impart quite different 
properties to the final system. (See the Lipshitz-Vanderkooy AES papers
for details)

>>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).

I don't agree.  At all.  Saying this is "completely wrong", is very
misleading.

The amount of lobing error present also depends upon the 
relative distances between driver acoustic centers.  If the acoustic
centers are properly aligned in terms of depth and if the driver 
acoustic centers are close enogh together in terms of height on
the baffle so as to be appreciably small compared to the wavelength at 
x-over, lobing will not be problematic with an L-R x-over.   This of
course assumes that the driver acoustic phase responses are properly
behaved and that the frequency responses are also flat.   R. Chapula
shows in his AES paper that the response only need be flat within
1/3 octave of x-over to maintain response within 1 dB on axis with
a 4th order L-R.  Some typical design criteria are to chosse drivers
flat within +/- 30 deg horizontal and vertical windows over at least 
an octave above and below the crossover point and with resonance 
points at least 3 octaves away from x-over (to avoid phase probs). 
Finding such drivers is a bitch, but they exist.

>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. 

I thought this was too obvious too even mention. It is an obvious fact 
that loudspeaker drivers can not be treated as resistors (or anything
even close) in the acoustic (or electrical) domain.  Jeez!

>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.

Good point: most designers ignore this.  I don't.

>>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!

Yes, real world drivers are equidistant only in one 2-D plane in space
and 
are never perfect BUT THE GENERAL TRENDS IN MY POST STILL HOLD.

A 2nd order Butt will still create a hump or a suck-out at x-over 
unless the x-over point is so close to tweeter resonance or the drivers 
are so far apart that acoustic phase plays a part. In that case, the
x-over
will generally SUUUUUUUCCK (in Corey Greenberg-speak) for other reasons
and you might as well put an egg on the tweeter 'cause it will FRY!!

The third order will still hold the general properties I discussed, again 
assuming a properly designed x-over (tweeter phase controlled and driver
acoustic centers close enough together).

A proper discussion of the elements affecting speaker design will make the
King James version read like the Sunday funnies.  It is even MUCH more
complicated than Dick and myself have alluded to here.

Don't sweat it Carleton.  My original advice holds.  An off the shelf
4th order L-R active crossover is probably your best choice given the 
fact that you can't custom make one yourself.

Happy listening!!

Dave