A little addition to multiway crossovers a la Linkwitz: multi-cascading

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... here we go.
2.5-Way target with 100% coherent phases. Shown is
- synthesis circuit
- SPL responses (with total phase)
- Phase responses (which are all the same and identical to the total phase)

System highpass is Bu5@40Hz, Butterworth 5th order (equivalent of ported bass with 1st order protection).
Woofer roll-off is LR2@500Hz, Linkwitz-Riley 2nd order.
Mid-to-tweeter XO is LR4@2000Hz, Linkwitz-Riley 4th order.

This would be a usable target for a small 2.5-Way with 4"...5"-midwoofers and a nice, low-Fs 1" dome.

The key point is that the woofer low-pass (WfLP) phase contribution is mimicked in the allpass cell (WfLP-comp) in the midrange and tweeter paths. The total phase contribution of the XO is that of a 3-way with LR2@500Hz and LR4@2000Hz, so this is where the (small) penalty is. But excess phase can always easily be removed with FIR-phase-unrolling applied to the source signal.

Of lesser importance here (because the Mid-Tweeter XO is high) is that the system highpass is applied to all ways.
 

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In SL's pictures - why for both bandpass driver networks (W) and (M) - is W lower in amplitude vs. M when both are direct from source (not cascaded)? Why is W automatically lower? Shouldn't M suffer the same fate being a bandpass also? or is SL's argument the longer wavelengths provide more opportunity for destructive phase lowering output between SW - W - M?
 
The drop in level is going with the inverse of the distance of surroung XO point freqs because phase mismatch is larger and the sum (which is a vector sum, then) drops. With 90° phase mismatch, for example, the sum of two equal sound pressure magnitudes is only sqrt(2)=1.41 times the magnitude.
 
Probably I am misunderstanding something here, but if we go back to Robbin’s original VituixCad picture in post 1, we have a (sub) woofer, crossing over at 120hz with 24 dB octave. Now this driver is further rolled off at 1000 Hz and 10000 Hz.
At 1000 Hz this (sub)woofer is already 62 dB down, then rolled again with 24 dB/octave. Then, again, when this (sub)woofer is below -100 dB relative to its passband, it is rolled off again with 24 db. So final steepness above 10000 Hz is 62 dB/octave
If I understand it all correctly, the idea is that that introduction of further phase shift in the stopband, way past any reasonable level ( past -40dB!) would contribute to better system integration.
To be honest, I do not see that immediately. In a twoway-system, yes, its is relevant.
But here, in a 4 way? Would not the passband phase characteristic of the “active” driver in question determine system phase behavior only, whereas the drivers in their stopbands do not contribute anything to system behavior below minus 40dB?
It also raises the interesting question as to how much attenuation in the stopband of a driver would still affect any system contribution. In other words: are driver anomalies below, say, -40 dB, irrelevant?
Maybe Robbin and KSTR can shed some light on this.
 
I think that's a good question Boden, and it has relevance to other aspects of speaker design as well. For instance, 3rd order harmonic distortion of drivers is often in the -50 to -70 dB range at 2.83 V. Does a -65 dB driver sound better, all else being equal, than a -55 dB driver? Does the THD of your electronics that run your speakers actually matter below .1% or so?

These questions have been debated long and hard on this and other forums :)
 
ILikeFoods has understood the point of the theory. In practice, Boden has a valid point. How many layers of cascading you are willing to add depends on the listener, and the setup.
A friend of mine has now implemented multi-cascading in his three-way consisting of SB WO-24, SB MW16, DXT tweeter. Stereo-imaging improved greatly, driver integration improved. He does not ever want to switch back to non-cascaded. His friends in turn commented on the stereo image and are asking about how it was achieved.

I would really like it if people try it. You can always revert to the old situation if you don't like it.

An analogy I can compare it with is making a picture. If you zoom in, you can see what's there in the distance. If you then focus, the image suddenly becomes clear.
 
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Hi!
I asked Kimmosto (author of VituixCAD) to comment your thread, he kindly replied in his thread about VituixCAD, but I will copy/paste his answer.
This is OT, but

Phase matching: Elliptical slopes could enable better phase matching, but that is realized in a quite small listening/design spot at high frequencies because distance difference from each driver to spot varies when listening/design spot moves to any direction - also closer and further.
Better phase match could improve power response with dipole speakers, but could make it worse with unidirectional (boxed speakers). This is related to separate sources (multi-way), generic directivity features of radiating area and dimensions of baffle and radiator.

Steeper slopes: Elliptical slopes reduce signal much above LP and below LP frequency. This could make sound more clean (assuming that drivers are used on their optimal/linear range).
Less overlapping i.e. steeper slopes could improve power response with dipole speakers, but could make it worse with unidirectional (boxed speakers). This is related to vertical off-axis lobes which makes power response more straight/flat especially if directivity of driver does not reduce at HP frequency or increases at LP frequency.
In the other hand, drivers can work together with shallow slopes assuming that they are capable to help neighbors.

Cone break-up and other non-minimum phase features destroy this kind of fancy theories and dreams in practice. SL used cascaded filter stages (also) to reduce amount of all-pass stages, but that method is usually not directly available or needed with DSP. Many DSP applications do not allow multiple 2nd order biquads or any other elliptical than standard Bessel.

Modern application for the same goals is linear-phase FIR, which also enables steep slopes without phase distortion. Of course, that also includes possibly negative features of steep slopes such as lower directivity and worse (more curvy) power response and DI. Also advantages such as narrower lobing bands at crossover frequencies when user stands up from listening couch.

Generally, advantages and disadvantages are not absolute. They depend on listening environment (acoustics, dimensions, materials, speaker/listener locations) and preferences of the listener.
 
Hi!
I asked Kimmosto (author of VituixCAD) to comment your thread, he kindly replied in his thread about VituixCAD, but I will copy/paste his answer.

Well said.

Even if you succeed in bringing all drives to the same phase on every frequency, which is not a trivial task, even with a DSP solution and requires exceptional drivers too, this will only apply to a very minimal listening area.
Would that be enough for salvation?

The measurements would be welcomed, and we haven't seen anything yet.
 
Still, direct sound is the king and horizontally most modern speakers retain phase summation quite well at least to 30¤. Even further off-axis, sound only makes reflections and then everything gets messed with thousands of other reflection paths anyway, until reaching two human ears that are 20cm apart laterally. For wide off-axis, spl smoothness is much more important than phase coherence.

Vertical off-axis is challenging for normal multi-ways, usually problems can be seen +/- 10¤ or more only above 2kHz xo and coaxials pass even that. I agree with kimmosto, that vertical problems are not very important, except some extreme cases.

I don't have terribly much experience, but after playing with dps-active projects and testing different xo types and frequencies, I have learned to value pedantic on-axis phase match. It sounds good.

This is just my personal experience and opinion, feel free to disagree!
 
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