If you pay me, I'll put it into laymans terms. $200/hr.
Should take 10-12 hours, to get you the basics so you can build on that foundation.
What you're asking is so broad and vast that quite literally I have offerred you a bargain.
Crossovers are about division thus math is necessary to explain what is happening with any kind of precision.
So what I recommend as "cliff notes" to get you started is get a DIY book like the Loudspeaker Cookbook by vance Dickason or I think martin Collums book touches on the subject too. The fact is very few speakers have text book crossovers in them despite what they claim since most drivers do not not exhibit text book responses and with phenomena like the baffle step etc. this will alter a crossover from stock too.
I'm afraid it takes some time and initiative to get to where even "layman's explanation" can be understood otherwise you will be in a world of mostly false generalizations...worse off than you are now.
Thus I look to your own vision statement and say you will need some DIY experience and some math. Without understanding the basic elements you will be lost on the concepts. You have to meet it atleast half way, learn the math and the relevent vocabulary and the concepts will make more sense. Otherwise you'll just be kidding yourself.
The orders are the degree of turn over at the knee, the point where the cross over rolls your drivers off. The 1st order is 6db/octave, and the 2nd is 12, and 3rd is 18, and 4th order is 24db/octave. The higher the order the sharper the cut-off. The type of filter, Bessel, LinkR, Butterworth, etc describe the circuit apporach to the design. All are quite similiar and different type have different plus and minus's to them. The LinkwitzR, type is often used in D'Appolitto type designs for it's advantage if phase projection.
So without getting into math, that's about as clean as I can tell it.
In simple terms, first order is the simplest and things become more complex as you the order number increases.
You can say roughly that the order number relates to the number of major components in line (series) with each driver. A first order has one part in line with each driver - a cap with the tweeter, and an inductor with the woofer.
Not to get too technical, but a second order crossover adds an inductor in parallel to the tweeter, and a cap in parallel to the woofer. Third order adds another cap in series with the tweeter, and inductor in series with the woofer. Fourth order does the same thing the second order did to the first order on a third order network.
Despite most trying to make this stuff rocket science, it's nowhere near as complicated as we are led to believe. But, watch how many disagree with me here in this thread...
It's not quite as complex as the first post states.
Let's say you have a two way system and you want the crossover point to be 1000 Hz. The crossover separates the frequencies so each driver gets the appropriate ones, below 1000 to the woofer, above 1000 to the tweeter. However, there is no such thing as a perfect crossover so it can't just stop at 1000, (termed a brick wall filter) which in the case of the woofer would be 999 getting through at full strength, but 1001 being completely blocked.
The order tells you how fast the response drops off beyond the cutoff frequency like loontoon says and this is determined by the complexity of the crossover as Trejla points out. The higher the order the faster the signal drops off beyond the cutoff frequency, i.e. the more it acts like a perfect brick wall type filter. So it seems that higher order would be better, but all filters introduce phases shifts, and the higher the order the more complex these phase shifts become, and depending on the design it can also start to have amplitude peaks and dips in it's response that extend into the frequency range it is designed to pass.
The fourth order Linkwitz-Riley that you asked about is a design that some feel has a roll off rate and phase response that is the best compromise between a higher rolloff and flatter phase response. Others feel that anything beyond a simple first order filter introduces too much phase shift to be acceptable.
A full understanding does require a lot of study and a lot of math but the basics are just that, pretty basic.
Okay, well that was all pretty helpful. In any case, it helped answer my underlying question. It seems that many people feel that lower order xovers are the "purest" method, in that due to their simplicity, they "color" the sound the least. Less components = more direct reproduction. I've seen it argued that higher order xovers can introduce more problems than they solve. So, my underlying question was, are higher order/more complicated xovers "bad"? It appears that the answer, like most things audio is, "it depends."
If I've misinterpreted anything here, please let me know. Also, is it logical to assume that as you add more drivers, the crossover necessarily becomes more complicated? (I.e., a 4-way system is going to be more complicated than a two-way)
Indeed, it depends...on LOTS of things. BUT...I believe you should not obsess about crossover networks or even make the simplicity/complexity of the crossover a 2nd or 3rd priority. LISTEN to them and go for the best-sounding speaker system you can afford.
You certainly have some overall considerations. Perhaps you're like my friend, a 'worn-out diddeebopper', who values grace under (high sound) pressure above all. He simply walks away from systems, no matter HOW else they sound, if they don't sound at ease while driven VERY LOUDLY*. Or perhaps you value razor-sharp imaging? Or perhaps you value overall soundstaging...ie the mimicking of the concert hall...above all else.
AFTER you buy a speaker, live with it for a while. If you still love it after 6 months or a year, consider improving the crossover components. But first, fall in love with a speaker.
* When he was evaluating speakers this summer, I couldn't be in the same room!
Actually, I would have no intentions of altering a speaker's crossover, or even basing speaker choice on the crossover type. Ultimately, I'm asking more out of general curiosity, given that there's so many different setups out there.
In the end, I'm going to buy whatever sounds the best to me. But, I like to have SOME understanding of how things work.
Generally, high-order filters are used to increase power handling at the expense of phase coherency.
Another thing I like to relay in layman's terms is that the order of the crossover more or less correlates to how much power one will need to drive the speaker.
Think of them as hurdles on a runner's track. The more obstacles one has to hurdle, the more difficult it is to get to the finish line. All things being equal, first order crossovers are the easiest to drive, and things become progressively more difficult as one moves upward.
The fly in the ointment are brands like Theil (first order) and Dynaudio (second order) who throw all sorts of networks in the crossover to flatten this or that, and end up with first order crossovers with 71 parts and loads that are just as difficult for an amplifier to drive as a higher order crossover.
So again, "it depends," right? At least now I have a little better understand of what's going on, which is really all that I wanted. I guess no one's going to come down definitively on one side or the order? It seems as if the complication of the crossover doesn't really translate into a speaker sounding "better or "worse," and what's really important is the execution.
1. For the same SPL excursion quadruples for each octave you drop in frequency.
2. IM distortion is a function of excursion.
3. The cross-over type determines the axis along which peak output occurs.
4. Steeper cross-over slopes reduce the effects of changing driver response beyond the pass-bind.
5. Higher order cross-overs have more ringing in the impulse response.
From 1+2 you need at least a third order slope so that excursion is decreasing below the cross-over point resulting in low IM distortion.
Adding 3 you need a 4th order Linkwitz-Riley XO that has its peak on-axis because this leads to the most natural sound.
4 means that the higher-order cross-over is an enabling technology that allows using stiff materials (magnesium) that are very pistonic in their passband (for low distortion) but ring like bells at higher frequencies.
5 means that you don't want to go beyond LR4.
Phase coherence doesn't matter. Time alignment at the cross-over frequency does as a tool to aim the peak response at the listening axis.
Other people have different opinions and subjectively excellent sounding speakers have been produced with all sorts of technologies.
Of course, the most important thing is what you find pleasing. If it floats your boat buy it or build it.
If you want a definitive opinion from me as to crossovers, I will tell you that first order are my favorite. Like most things in life, simple things, using the best ingredients often produce the best result.
Further, series, as opposed to parralel networks, are also more to my liking. You didn't want us to get technical, and so I will try not to...
First order networks are the easiest to drive, and sound the most natural to me. They are phase, and presuming the speaker allows, time coherent. Of course, the tradeoff is that the slow rolloff means that a superior driver (the finest ingredients) become more critical, as does the crossover components themselves. Otherwise, you get hit in the face with components operating out of their areas of comfort, and some drivers sound worse than others when this happens.
I don't want to get into dogma here, as just as many people exist who can tout the benefits or second, third, and fourth order networks.
I also feel series networks(99.999+% speakers use parallel networks) sound better to me, as I don't get a sense that I am listening to individual drivers. They also present a resistive, as opposed to reactive load to the amplifier - ooh sorry, don't get technical (but let me sneak in that the rolloff can be tailored via Zeta - balanced by the ratio of the cap to the coil, making even sharp rolloffs with a first order network easy). Let's just say they are a more friendly load to an amp!
If I remember correctly there is a 90 degree phase shift (between woofer and tweeter) for each 6 dB filter section. So, 6 dB is 90 degrees, 12 dB is 180 degrees, 18 dB is 270 degrees, and 24 dB is 360 degrees. Note that the 24 dB filter restores inphase signals for woofer and tweeter. Note also that with a 12 dB filter the same result can be obtained by hooking one driver up with wires reversed. There is no way to make a 6dB filter electrically "right", but perhaps the 90 degree phase shift is tolerable, and the benefits of a simple crossover offset the disadvantages. Also, the driver has its own natural roll off, perhaps 6 dB with a 90 degree phase shift, so that the net acoustical slope is 12 dB, with a 180 degree phase shift. Consistent with this, with 6 dB crossovers, the tweeter is often hooked up backwards.
The 24 dB design is not practical for passive crossovers because too many components are required. However, it is easily accomplished in a line level electronic crossover, and most of the electronic crossovers sold today are made this way.