From: Dave Dal Farra <gpz750@bnr.ca>
Subject: Re: Active Crossovers
X-Xxdate: Tue, 5 Jan 93 15:58:18 GMT
Organization: BNR Ltd.
X-Useragent: Nuntius v1.1.1d9
Date: Tue, 5 Jan 1993 15:50:01 GMT

In article <1993Jan4.033157.26862@magnus.acs.ohio-state.edu> Carleton Wu, 
carlwu@magnus.acs.ohio-state.edu writes:

>BTW, what's the difference between Butterworth and Linkwitz-Riley 
>types?  Is one better?

The answer to this question isn't so simple.  A loudspeaker system is a
very 
complex entity.   The final objective and subjective performance of the
beast is determined by not only the performance of the individual drivers
and the individual crossover choice, but how well the choice of crossover
integrates with the individual drivers AND the combined response of the
drivers at crossover.  Things like driver acoustic phase, directivity,
roll-off rate and relative positioning around cross-over will dictate the 
x-over design choice.

In short, there is no one "best" crossover but only the "best" crossover
for a given compliment of drivers within a cabinet.

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).

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.

On the other hand, odd order Butts show flat power response while L-R
types have a small power (not frequency response!) dip at x-over .
In my opinion, after designing many systems, I've found that the trade
off in power response is worth the better lobing performance for equal
order filters.

Other points:

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.

My favorite choice for x-overs as a starting point in design is the fourth
order Linkwitz-Riley.   It is has a flat response on axis, and will not
show
floor reflection problem.  It is a real nice sounding topology and I
prefer it to the 4th order Butt as it exhibits a better final polar
response.
The extra filter order over a 3rd Butt will also help futher  protect your
tweeter from an early death if you happen to like to crank the volume
once 
in a while.

By the sounds of it, the Sledge-hammer model sounds like it was properly
designed.  If the power supply in it looks well filtered and of hefty
enough proportions, it would probably be worth the extra bucks.

As an aside, I just built a 4-th order active L-R with 1% metal-films and
polyprope/teflon caps and am real happy with it.

Ciao,

Dave
Newsgroups: rec.audio