Hi Thierry..
Yeah - Even I am (despite having worked with them before) getting too old to keep up with FPGA's etc.
What puzzles me is why people are so 'afraid' of coils! - One simple adjustable inductor which can be bought for about $1 from Mouser (use one winding of the 42IF106 IF transformer), allows a simple LC oscillator to be constructed.. This simple oscillator will kick the s**t out of any RC oscillator costing twice the price!
Still need to build my compensated 555 osc.. This may be something which could interest you, Jo.. If one keeps the supply voltage stable, and use NPO capacitors, the TS555C is quite stable over +/- 10C..
http://www.thereminworld.com/Forums/T/28556/new-theremin-circuits
"If you want to build something without coils, follow the digital ideas which FredM and dewster are developing here. " - Thierry
Actually, even "digital" theremins often have an analogue front end (AFE) which incorporates coils..
Lots of good reasons for using inductors - one which sometimes gets missed is that with RC oscillators, the voltage of the waveform at the antenna is limited to the supply voltage - and any local RF signal source has a strong chance of messing up this signal - Using an inductor one can have voltages on the antenna anywhere up to several hundred volts - a lot less susceptable to influence from local low voltage interfering signals!
I should also say that this is Dewster's project exclusively - I am quite out of my depth, and am not persuing digital theremin design myself - Analogue and mixed signal are the theremins in my 'comfort zone' - LOL.