In message , Old Fart at Play
writes
Chris Morriss wrote:

In message , Old Fart at Play
writes
You can keep the low-pass and high-pass outputs in phase
with a 4th-order filter.

Not without an additional all-pass filter you can't. And with an added
all-pass you can make a second order crossover have no phase difference
between the LP and HP sections if you want.

Perhaps you would like to refer to the Loudspeaker Design Cookbook
which has graphs of amplitude and phase for various filters
including the fourth order Linkwitz-Riley filter.


OK, I've looked at that, and it doesn't support what you say at all. I
think you are getting confused between a crossover that keeps the
outputs of all the sections in phase at all frequencies (which can only
be done with even-ordered networks, and then only in conjunction with
all-pass phase-correction networks) and the family of crossovers that
attempt to sum to a flat frequency and phase response, even though the
individual outputs have phase differences between them.

(By the way, you can't get a passive filter to have LP and HP outputs in
phase with each other at all frequencies, as it's not possible to
produce the right sort of all-pass network with passive components.)
You can of course make passive networks that have a summed flat
magnitude and phase response, but this is a different thing entirely.

Although all-pass phase corrected active crossovers can be made, they
are not universally liked, as the extra group-delay added by the
phase-compensating all-pass networks mean that the total variation in
phase across the whole audio band can be very considerable. (Whether or
not this is audible on music is debatable).

--
Chris Morriss