Let's Design and Build a (mostly) Digital Theremin!

This is the first time I've heard of a homopolar toroid.  Was that for a current sensor (e.g. Rogowski coil)?

In the electricity distribution domain, an homopolar toroid is a 20cm toroid ferrite with a secondary winding only, the tree phase wires pass through it and then you get an image of homopolar current at the secondary winding. In a lab, if current injection box has not enough power you need to manually wind a primary winding (e.g. 100 turns for 100 A injection). 

"https://patents.google.com/patent/US6414475" 

Yes, I would have loved to have such a machine, or only the same idea, at that time. I used a kind of weawing shuttle instead. Depending on whether the toroid can or cannot open, the experience is not the same...

Coiled Plates

So I've done a few rough experiments using three different coils as the Theremin antenna:

A CW (clockwise) solenoid, a CCW solenoid, and a spiral, all made of household solid copper wire.  Note that the spiral can be flipped over to make it CW or CCW.  I measured total Q while sitting on directly on top of a 10mH solenoid, and again with 30mm or so of spacing between the antenna and the 10mH solenoid.  As expected, total Q decreases a bit when the plate coil is counter wound to the 10mH and placed closer to it.  So nothing earth shattering or dramatic to report.

I also messed around in a spreadsheet, calculating the relative capacitance of a 2D rod type antenna to one's finger, where the finger is held a constant distance from the rod, but moved up and down the rod.  Playing with conductive weighting towards the ends of the rod, it seems one needs to massively weight the ends of the rod (vs the center) to make the up and down finger movement produce a constant response, and this response is only sorta linear when the finger is quite close, like 10mm or 20mm.  Moving closer you get a "hollowing out" of the middle, moving farther gives slightly better linearity over a solid conductive rod, but the returns are fairly marginal, and I have no idea how to very heavily weight conductivity to the rod ends like that.

The whole point of this investigation was to see if 
1. a nearfield plate could be better linearized over the area being addressed by the hand, and also 
2. if the plate could be made less of a Q damping "shorted turn" when placed very near the coil.  

The initial conclusion for (2) is that a spiral seems to allow closer placement to the coil.  For (1) the spiral turns could be concentrated more towards the outer edge.  But a spiral wouldn't have the full intrinsic C of a solid continuous plate.  What might work is a plate with a hole in the center, the diameter of which somewhat larger than diameter of the 10mH coil.  This and narrow radial slot cut in it to minimize the current loop might help to defray damping.  The hole, and extra plate material at the edges going 90 degrees backward might help to accentuate the edge response, improving linearity a bit.  The covering insulation might limit closeness and prevent hollowing out of the center response.  This is my next TODO experiment.

A square plate somewhere between 150mm to 200mm on a side feels to me like a comfortable playing surface size.