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

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.

Have the laws of physics changed since my LDC4 was published?

Section 7.21:Combined response of two-way crossovers
"....exhibit a high-pass and low-pass phase relationship which
is in-phase."

Graphs 7.58 and 7.59 show what I mean.


Ok, I can see where your confusion is coming from. No, the laws of
physics haven't changed, but the LS cookbook doesn't make things clear.
If you read on in the same section, you'll see that it says "the two
sections sum together flat when the level of both filters is down 6dB at
the crossover frequency".

This is the crux of the issue. To get a flat amplitude response from an
even order filter, the crossover frequency should be at the -6dB point,
but to get the two outputs to be in-phase (actually 180 out of phase,
but this is cured by turning the connections round on either the tweeter
or the bass unit), the crossover frequency needs to be at the -3dB
point.

Here's an example. It's for a second order Butterworth. (And remember
that a 4th order L_R is simply two identical 2nd order Butterworths in
series)

If the crossover is at the -3dB point, the phase is at 90 degrees at
that point, and the HP and LP will be consistently 180 degrees out of
phase, BUT the magnitude will sum to have a 3dB hump.

If the crossover is at the 6dB point, the magnitude will sum to be flat,
but as the phase shift at the -6dB point is 110 degrees (rather than 90)
the phase shifts of the two outputs will not track.

In reality a passive crossover is tweaked to give a compromise (and to
allow for the amplitude/phase characteristics of the drivers...if you've
got a competent design team that is.

An active crossover can be made to have perfect phase tracking between
the HP and LP outputs by judicious use of all-pass networks. (Though as
Jim says, that may not be what you want for best fidelity)
--
Chris Morriss