Multi-way cardioid principle like Kii Three?

Hello!

I'm wondering how Kii Three actually works.
As far as I know, the basics of cardioid are that drivers with the same response are separated by a desired distance, inverted in phase, and given a delay corresponding to that distance. This allows the sound waves emitted by the front driver to be effectively absorbed by the rear driver, resulting in a cardioid radiation pattern.

But when this becomes a 3-way like the KII THREE, things seem to get complicated. My understanding from listening to bruno putzey's youtube explanation is that the midrange driver of the kii three plays from 250hz to 2khz(crossover to tweeter at 2khz), the rear LF woofers are responsible for the extreme low end to 250hz (i.e. it's like a crossover with the midrange driver), and the side LF woofer works in reverse phase and cancels out 100hz to 750hz, which is the starting point of the cardioid pattern.

However, it appears that whatever delay you give the rear LF woofer will be canceled by the side LF woofer, and it will not be able to crossover with the midrange driver. I've done quite a lot of simulations with Vituixcad but couldn't find out how its filters should be. Perhaps I'm misunderstanding something, so if anyone has a specific understanding of what the filter behavior should be, I'd so appreciate some advice.
 
The lateral drivers don't cover the same frequency range as the subs at the back of the speaker, that's all. Crossover frequency is the key.

As the D&D 8c and the Kii Seven show, you can also ditch the lateral drivers. This comes at the price of the low frequency cardioid behavior getting somewhat compromised, as the subs need to be crossed higher in comparison to a 4-way active cardioid, to counteract positive summation in the mid frequencies. Given this trade-off, it's possible and can be realized with a three way Hypex plate amp for example. If SPL levels should not be a limitation, you might need to get the higher power versions to supply enough power to the rear mounted subs on a single channel. Still, much more affordable than the industrial product.

To learn more about this, start simulating a cardioid speaker in VituixCAD until you end up with the desired cardioid pattern. Then check for SPL levels with a given driver at the available amplifier power and listening distance in WinISD, factor in headroom for peaks and compare it with your actual listening levels with an SPL meter at home. On an apple device, DecibelX is considered okay, but simple SPL meters are also affordable. Then you can decide what amplifier to use.
 
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Thanks for your explanation @sheeple !

Apparently if the side woofers and rear woofers have the same polarity(reversed) the problem gets quite simple.
For example, like midrange : 80 - 2khz. side woofer(reversed) : 250 - 700hz, rear woofer(reversed) : 80 - 250hz
But the problem is that midrage driver than should cover the sub-bass frequency as well.

If you watch this video, Bruno kindly explains how the it works.

All trade secrets are in the fine details of the implementation but the basic idea is quite simple

6 drivers are individually driven by their own amplifier. What allows me to do is over the range frequency to 50hz to roughly 250hz. I'm actually runing the side woofers and the rear woofers out of phase, in opposite polarity but with a short extra time delay so that the sound comes radiating of the side woofers and moves along toward the back get cancelled exactly by the output of the rear woofers.

And the same trick is repeated with the side woofers and the midrange again. The sound radiated by the midrange will try to work its way around the cabinet but then a delayed and inverted signal is applied to the side woofers again so that in the same range from 250 to about 700hz. The midrage output is attenuated behind the speaker and then above 700hz the front baffle itself will roughly produce the same dispersion so that's why we get a very even response as you go around the speaker.

So I thought in terms of polarity, the midrange should be +, side woofers -, and rear woofers +.
And also side woofers seem to have to work through entire frequnecy, from 50hz to 700hz.
What I was wondering is how the specific delayes and crossovers should be.
I'm familiar with VituixCAD but I wasn't sure I'm going in the right direction.

Kii Three Nearfield Components (~23mm from baffle).png

And I think this nearfield component measurement isn't helpful to see how the drivers work.