Crossover and Phase.
 

It's well known that a 1st order crossover has constant phase shift of pi/2 radians over all frequencies. How do you figure out which crossovers have which kind of phase shift? Even with any given order of crossover, there are many ways to achieve it. A first order crossover for example, is not necessarily a capacitor and inductor, it can be far more complex.

I assume you mean constant phase shift between the two sections. Each section has a non constant phase shift relative to its input.

If a crossover is truly 1st or 2nd or 3rd, it would have the phase shift of that order no matter how it was created. If you are using more components than the minimum you are typically compensating for a non flat impedance, other wise the minimum number of components would suffice.

The phase shift comes along inseperably with the response (see Hilbert Transform). A better way to think of it is that each order adds another 90 degrees of phase shift in the stop band, with only half that value (N x 90) at the corner frequency. There is little or no phase shift in the pass band.

David

Yes I mean constant phase shift between woofer and tweeter if its a two way. Are there any other crossover types that can do that? I believe this is what gives such designs the coherence that I hear.

well, Im no expert on these matters
but I take it the phase shift is slower and more gradual on low order filters
and I suppose, less gradual and faster turning with steeper filters

and each driver in different 'direction', so to speak
I suppose the trick to get the coherence we all want you must get this turning phase in the stopbands to follow a mutual patter common, in unity, somehow

I may have achieved it, so I do think its possible, some of the way at least
I just dont know excactly how or why it works

I think you might be referring to constant group delay? Only a first-order crossover can achieve that...in the analog world.

Anyways, try using one of the many utilities or speaker-design programs to allow visualization of the phase response of various crossover schemes. Here's one:

Transfer Function Designer - Crossover Response Target Generator

Dave.

Actually thst is not the case. There are an infinite umber of analog crossovers that can result in constant GD.

like?

Like constant voltage crossovers and symmetric 2nd order transient perfect crossovers.

Constant voltage crossovers don't necessarily sum with constant group-delay. Most don't.
Unless you're redefining "constant voltage" crossovers for us.

Cheers,

Dave.

I'm referring to CV crossovers as defined by Small. By construction they are flat, zero GD.

[Edit] Smalls work came before the LR crossovers were developed. I guess you could include LR crossover as a subset of CV crossover that do not have constant GD.