Armstrong, Hartley, Colpitts, Clapp, Wallin...

Very interesting topic.  I would have viewed it sooner but it sounded like a law firm with a lot of partners......

Ahahahah.
I thought these names look familiar for everyone who is looking for LC oscillator.
Unfortunately I cannot rename the topic to make it less confusing.
BTW, is current sensing based oscillator - a new kind of oscillators, and a real invention made by Eric? I still did not get an answer...

Vadim, thank you for posting your fascinating findings and sims!  I'm a bit underwater at the moment but plan to play with your designs shortly.  Your inverter version is the one to beat, truly an outstanding oscillator!

Eric, I hope you will check some of them on breadboard
I like playing with LTSpice, but don't have a breadboard, components, scope anymore after moving to Porto.
I tried to play with inverters and opamps as drive buffer, and found that it's hard to get them working stable.
So now I think having your 4-bjt buffer on emitter followers is probably the best option.

I've combined two recent schematics I've posted here. 10 BJTs. (LTSpice model link to play with)

Diff amplifier uses current mirror load, and its current output is converted to voltage on a resistor divider.
I've tried to tune this oscillator to minimize phase error and maximize antenna voltage swing.
I've managed to get nice smooth symmetric sine-like drive signal with 6-7ns phase error.
BTW, delay from 4-BJT output cascade is only ~400ps...

The price for now delay is high power consumption (~35mA).

Drive swing is 1.7V. It feeds LC tank with 5mA, giving ~200V voltage swing on antenna.

Main concern is still a behavior of oscillator when hand touches the antenna.

Very interesting topic.  I would have viewed it sooner but it sounded like a law firm with a lot of partners......Ahahahah.I thought these names look familiar for everyone who is looking for LC oscillator.Unfortunately I cannot rename the topic to make it less confusing.

Just kidding around.  It really is a pleasure and honor to read you and Dewster go back and forth and The knowledge gained is appreciated.  To be exposed to open dialogue between top experts of a field developing theories and practical applications ,
“D-LEV”, 
is inspirational...

Thanks to all at Theremin World, especially Jason.

"I would have viewed it sooner but it sounded like a law firm with a lot of partners......"  - Yngvox Moogsteen

Dewster, Cheatem & Howe ;-)

Yet another attempt to design a good current sensing based ("wallin") oscillator.
Good oscillator should have small phase error, high voltage swing, nice smooth drive waveform.
Current sensing approach looks as a best one for me. I think it should have low noise level (noise from antenna is filtered out by LC tank) and high sensitivity - the only C of LC tank is antenna + hand.

Found interesting differential cascade based voltage follower cirquit, as a good current sensing output cascade.
It's in "precise voltage follower" section on "Differential cascade" wiki page, but it does not have English version.

But I believe it can be google-translated.

It's fast (<< 0.1ns) and precise. Keeps output voltage matching to input while inputs and outputs are in working range (0.5..VCC-0.9) and current of output cascade is big enough.
Differential cascade compares voltages on input and output and control emitter follower to keep output voltage equal to input.
Easy to add gain - by adding voltage divider in output voltage sensing part.
Easy to measure output current - e.g. by putting shunt resistor to output cascade emitter follower transistor power rail.
Although this cascade can easy amplify input, and voltage on sensing resistor can be amplified by this cascade itself, I have not figured out how to implement smooth limiter on it.
So, if you try to make an oscillator working only on this buffer, drive signal becomes distorted after output voltage starts exceeding the working range, and delay grows.

Voltage follower on diff amp as output stage of current sensing theremin oscillator.
LTSpice model link to play with.

Max working range: 1.9Vpp with 1.55V center point (0.7V .. 2.4V)

With 4.25 mA 1.9Vpp sine drive, it gives 165Vpp on antenna.

Buffer latency depends on differential cascade current - the bigger current is, the faster buffer you get.
Diff cascade 1mA  - 1.2ns delay
Diff cascade 2.6mA - 0.55ns delay
Diff cascade 5.5mA - 0.275ns delay

Sensing shunt resistor eats part of working range - about 0.25V in this configuration.

Making oscillator based on this buffer.

Ok, let's add one more differential cascade, as limiting amplifier for current sensing.
This schematic looks a bit overcomplicated, has 17 BJTs.
According to simulation it should work fine.
Github link to LTSpice model.

Drive is 1.6Vpp symmetric sine-like 4.7mA.

Small 4ns phase error.

180Vpp on antenna.

Voltage on shunt resistor, currents in sensing amplifier diff cascade, voltage on sensing amplifier output and drive signal:
(Just a nice tech porn)

Still trying to find a better schematic.
This one has acceptable low phase error and nice shaped drive.
But its drive signal range (and hence the voltage swing on antenna) is limited, and the design is a bit complicated.

The best possible output buffer should have common emitter transistor drive on both of rails to get output range close to power rails.
Probably, current mirror like drive on both rails should resolve it.
Differential cascade should be used to control output voltage waveform.
Some good and natural way is needed for output current measurement. Is it possible to get it in some natural way avoiding shunt resistor which reduces drive range?
Will continue to play with LTSpice.