Old Fart at Play wrote:
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.

Remember that it's the acoustical 4th order Linkwitz-Riley that has the
so-called zero phase difference, not some speaker implemented with 4th order
crossovers. The acoustical 4th order is implemented with second-order
crossovers. The other second-order filters are the roll-offs of the speakers
themselves.