I'm game if you are. Be gentle.
I'm interested too! I must confess I looked at this and couldn't make sense of it. I thought it sounded a lot like a passive radiator but then what do I know.
The following is my understanding of the Brane “Repel Attract Driver” with “Magnetic Negative Spring”. I do not claim to have a solid technical grasp of the details of the design, but will attempt a ballpark description.
Let's suppose we want to manufacture a portable battery-powered wireless speaker that has good bass. We need to keep the efficiency fairly high for the sake of battery life. To illustrate the tradeoffs involved, let's say we build a prototype that's 86 dB efficient and goes down to 80 Hz in a 5 liter sealed box. Not bad, but not enough bass. Suppose we want the bass to extend one octave deeper (down to 40 Hz). We can either increase the box size to 40 liters (an eight-fold increase), or we can reduce the efficiency down to 77 dB (shortening battery life or requiring much heavier batteries). Or some combination thereof. My point is this: The penalty in box size and/or efficiency for extending the bass significantly deeper is huge. Realistically, we'd probably design for a peak in the bass region and hand it off to our marketing department to make the best of it.
The culprit is the air trapped inside the sealed box. It acts as a spring, resisting the motion of the woofer cone. The smaller the box, the stiffer the spring. And it's a non-linear spring: The futher inwards the woofer cone moves, the harder the air inside the box pushes on it. And the further outwards the woofer cone moves, the harder the now-partial-vacuum inside the box pulls on it. To make matters a little bit worse, in general the farther the voice coil moves from its rest position when doing long excursions, the weaker the force that the motor generates.
Wouldn't it be nice if we could make the force that the woofer's motor generates actually INCREASE as the voice coil moves farther from its rest position? Wouldn't it be even nicer if this increase in force exactly offsets the air-spring behavior of the enclosure? IF we could do this, then the internal air volume of the enclosure would no longer be the limiting factor that it once was! There would still be some practical limitations, but it might actually be feasible to get something in the ballpark of 40 Hz from our little 5 liter sealed box without having to massively trade off efficiency to get it.
This is what the Brane woofer is intended to accomplish (though I have no idea whether the arbitrary numbers I've been using correspond with Brane's targets). Their voice coil has small magnets attached which pull it AWAY from its center position once the voice coil starts moving. The farther the voice coil is displaced from its neutral rest position, the stronger the additional pull. In fact, the amount of this pull is calculated to offset the air-spring effect of the air inside the box. So in effect we have a magnetic “spring” that behaves inversely to the air-spring of the enclosure... a “magnetic negative spring”.
(My understanding is that much of the invention is devoted to properly modulating the force that the small magnets apply to correctly offset the air-spring, and to keeping the voice coil properly centered while subject to these multiple magnetic forces. I am under the impression that a position-sensing device and multiple electromagnets are involved. I'm not going to explore those details here, as I don't fully understand them, but my assumption is that the devils are mostly in those details.)
In my opinion this seems to be an extraordinary development in subwoofer driver design, at least for its particular size-and-weight-constrained application. I'm not in a position to evaluate the claims of their marketing department, but the concept and the technology make sense to me to the extent that I understand them.