Crossover definition

Could someone please explain the difference between Bessel, Butterworth, Linkwitz-Riley(sp?). I bought an active crossover with the ability to switch between these at various slopes. I know which slopes to use but not the type.
I'm not too technically knowledgeable but I'll go out on a limb here a little bit.

I don't think that Butterworth is a crossover. Rather it's a filter used in the crossover. It prevents the frequency response from getting too wavy around the crossover point. Since almost all crossovers use Butterworth filters, they are often called Butterworth crossovers.

Perhaps someone more knowledgeable might be able to add to (or contradict) this.
I don't think that Butterworth is a crossover. Rather it's a filter
A crossover IS a filter. As you know, the xover is there to divide frequencies between drivers through attenuation (dependng upon how strong -- the slope or order -- that attenuation is one speaks one 1st order, 2nd, etc). To expand on the original question would be outside the scope of a post IMO. Suffice to say that each "type" of xover, Bessel, Butterworth, L/R, etc has electrical characteristics other than the order. One place to visit is here. There is alot of info on the net. Cheers
All topologies do ABOUT the same trick, but depending up a number of variable a designer will chose one over a another. Hence, there is no BEST way. Usually the decision is based upon the drivers measured characteristics.

The biggest difference between the types of X/O topologies is the knee portion of the cross over.

The intent is to provide a seamless match, but due to the nature of the filter unless one opts for eliptic's a or derivative there-of (aka Joseph Audio, or Infinite Slope's)
there is substantial overlap or "blending" of the two drivers. The slope function of the different types are more similiar than different so what's left is the knew or the amount of accoustic loss or gain at the exact cross over point. For some you want absolutely flat, which is usually where the LR 4th orders are employed, again only an example. Butte Worths, Bessels ect, all have slightly different knee functions and can be used to offset notches or peaks at the X/O point.

One cans use LEAP or many other software programs to get on close, but the key to using simulators is they can only model what their told, they can't select topologies or types.

Thge skill of the designer, the choices in type, the choices in components and drivers is what allows two similiar products to sound remarkably different.

Without getting into graphs and charts, and math, thats about as close to a non technical explination as I can get.

Like Gregm said: a speaker xover IS a filter! Hence people say "butterworth xover", linkwitz -riley xover", etc, etc.

A butterworth filter/xover is a maximally flat amplitude response filter. IOW, the filter pays more attention to the amplitude characteristic of the signal @ the expense of the phase. It is usually used in places where the screwing up the phase is not much of an issue. The roll-off of this filter is very smooth thereby yielding very little perturbation to the amplitude characteristic of the music signal. This is achieved by placing all the poles of the filter on a unit circle - there is no in-band ripple. (Roll-off of is area of the filter where the signal starts to get attenuated - it's the commencement of the what is called the transition region of the filter. In the pass-band of the filter, the filter response is such that the music signal passes thru largely unhindered).

A bessel filter is a maximally flat phase response filter. It pays more attention to the phase of the music signal rather than the amplitude. If I remember correctly, the Bessel response rollds off/attenuates the music signal even more gradually compared to a Butterworth. The Butterworth has a shallow roll-off. Well, the Bessel filter is even shallower! That is why you do not see Bessel filters used much - you need a higher order Bessel filter vs. a Butterworth. However, the Bessel is better @ preserving phase than the Butterworth.

A Linkwitz-Riley filter is an active filter (the Butterworth & Bessel xover used in the industry as 80-90% passive i.e. simply using R, L & C) i.e. it uses op amps to do its job. Thus, most speakers made by Linkwitz Lab use external active xovers. It seems that the Linkwitz-Riley xover is a modified Salen-Key filter. It is then followed by an active all-pass filter to smooth out the radiation patterns of the drivers. This all-pass network, as its name suggests, passes all frequencies un-hindered but provides a delay. You might know that the acoustical plane of a tweeter, a midrange & woofer are staggered in that the acoustical center of a tweeter is the most in front of the driver plane while the woofer's is at the plane. That is why you see the baffle of a speaker is sloped (like a Thiel or Meadowlark). This active all-pass network provides an active delay so that the drivers can be put on a non-sloped baffle.

ANyway, I hope that this helps. FWIW.
I came across this link while trying to educate myself on this topic, keeping in mind that I'm not too technically knowledgeable. It contains other links to basic information on crossovers. Perhaps. along with other posts, it will help in getting you down along the road to the information which you seek
Without getting into the theory, these are some generalizations without knowing anything about the room, the speaker type, the number of drivers, the driver's parameters or the listening postition:

Use the Bessel setting for a better transient response. If you like the snap of a snare drum or the pluck of guitar strings to be emphasized (poor word, just as a reference), then a better transient response may be obtained with the Bessel. If the drivers exhibit poor behaviour (distortion) at frequency extremes, this setting may not be the best choice.

Use the Butterworth if you want to increase the size of the off-axis response (sweet spot); or if you have a large room and need to tame the lower frequency room modes.

Use the L-R if you want to give a slight boost to the bass response of a speaker or if you are using a turntable and need to minimize low or subsonic frequencies such as rumble and flutter. If you find that the Butterworth sounds good in your setup, then the L-R will probably slightly improve on it without any trade-offs and may be the better choice. But the L-R may not work as well as the Butterworth in a larger room.

Again, these are just generalizations, YMMV.
So Pierre at Mapleshade endorses the pure maple syrup Master Cleanser Fast?