I was daydreaming about building a miniature Tesla coil at some point as a weekend project. Like an 8-10" secondary with 500-700 turns of 28 gauge magnet wire, maybe.
I thought it also might be fun to make it a hybrid design, using lil power triodes or tetrodes for primary drive, driven from an xtal oscillator or SPI-controllable oscillator like the DS1077.
I'd imagine having a bifilar-wound center-tapped primary with B+ on the tap and each side going to an LC-tuned plate circuit tank would work, yeah? Could also drive the grids through a center-tapped transformer to have negative bias on the grids for class C, and match impedances from the generator to the grid circuit.
My question is that I don't know what kind of load the secondary would present to the plate circuits in that arrangement - would you have to do something different with the secondary as well to achieve balance?
Tuning could be difficult; I guess you could match the primary resonance to the secondary resonance by dynamically adjusting the clock frequency. Or a VCO/PLL to ensure that the primary voltage and current is always in phase. Bleh this is already getting complicated.