How can we compare different capacitance sensors?

Andrey (your name?) you have a clean pair of eyes when it comes to this stuff, you raise some interesting points, and it's certainly not my intention to dampen your enthusiasm.

The thing with RC is it doesn't oscillate on its own, some circuitry is needed to precisely sense at least one voltage threshold and do something about it at least once per cycle, so you have per-cycle systematic error that can add up, rather than average out.  If you think about it, there really is no such thing as a high precision RC oscillator, the 555 with a voltage regulator is about as good as it gets.  And when the bulk of the C in the RC is exposed to the environment, the thresholding issue becomes even more problematic.

Whereas you can ping an LC and it will oscillate on its own for many cycles with no intervention until it runs down due to parasitic R losses in the coil and the environment.  The circuitry to keep an LC oscillating can be as simple as a single transistor, and it can be easily arranged so as to not influence the resonant frequency much.  If the periodic LC stimulus is timed OK it doesn't have to be all that precise nor abrupt. 

On top of mains hum, there is RF from AM radio, and also the voltage gradient in the air that could cause problems.  Unless you average it too much for Theremin use, an RC running a 3V will get swamped when the hand isn't very far away from the antenna.  That said, there are low voltage Theremins out there, the Burns is RC, the Open.Theremin and the Theremini are LC, and their fields tend to be small.  The Theremini is filtered down to ~2Hz, which makes it noticeably quite sluggish feeling, with vibrato getting lost and such.

I do wish there were a more tractable and straightforward RC approach, as it would allow variable measurement periods, thus averaging out environmental noise via spread spectrum.  With high Q (and thus high voltage) LC you can't vary the stimulus much without hurting the oscillation amplitude.

So one big thing to think about is how interference influences the fundamental operation of the oscillator.  The C is just hanging out there in a fairly polluted electrical environment, so the solutions need to be inherently robust.

I want to measure capacitance measuring its discharge time.
-- Andrey

I think you can use astable multivibrator, e.g. on IC like 555 timer (symmetrical charge/discharge between 1/3 and 2/3 of VCC).
You can try MIC1555 (or other 555 modern analog).
Interesting article about fastest 555.

Assuming antenna C is changed by 20% when hand is moved.
In this case, RC gives 20% change, while LC frequency is changed by 10% (sqrt(C) vs C).

So, at first sight, RC gives one bit more than LC sensor.

Why RC approach is not used in theremins?

Voltage swing on antenna for LC oscillators is usually 30..300V.
For simple RC oscillator, voltage swing will be less than 3.3V.
With 10..100 times bigger voltage on antenna, signal/noise ratio is being increased by 10..100 times for LC.
As well, LC tank naturally filters out noise outside its resonance peak.

Can we improve signal/noise ratio for RC?
We can try to figure out some way to feed RC with higher voltage.

Is there any way to increase square wave voltage (except bigger power supply)?

I've tried to use fixed frequency LC oscillator with high voltage swing, and drive RC from it (in LTSpice simulation).
But once RC (antenna via resistor) is connected to LC tank, voltage swing drops down (but is still high - 30..60V for big enough R).
Shift between RC input and RC output may be measured. R or C divider is required in to bring signal voltage to measureable range (0..3.3V).

Of course, you can experimentally check if RC sensor is good enough for theremin.

Here's a paper where they use RC 555 and fancy filtering to locate bodies in a room:

https://iris.polito.it/retrieve/handle/11583/2648228/402694/sensors-16-01448.pdf

But had they used LC (separated in frequency) many of their filtering issues would have been greatly eased (garbage in, garbage out).

One of their findings is that larger plate area gives better SNR, which isn't surprising.  I know it's not "traditional" but using plate antennas on a digital Theremin can give you at least one more bit of SNR (and they are easier to play in the near field IMO).  Ideally, plate area should be on the order of the thing you are sensing, for the human hand something around a car license plate, but square.

And Vadim (Buggins) is exactly right, you can easily experiment with these things to see what might and what might not work for you.  Though I guess you're here wondering where to start! :-)

Has anyone tried the fancy capacitance to digital ICs such as AD7746, FDC1004, PCAP04?

Would you like to join this project? - Buggins

Thank you for the offer, check your private messages ))

Andrey (your name?) - dewster

Yes, this is my name )))

So one big thing to think about is how interference influences the fundamental operation of the oscillator.  The C is just hanging out there in a fairly polluted electrical environment, so the solutions need to be inherently robust. - dewster

I think the main problem will be with RF from radio. My estimation of thermal noise was only 1.8mV while radio waves can increase it dramatically. I don't know how to estimate antenna responce to radio waves in wide frequency range, so I have to just measure it.

Of course, you can experimentally check if RC sensor is good enough for theremin. - Buggins

Yes, I definitely will check it ))) I chose this board to do my experiments on. Running at 216 MHz, it has timer resolution of 4.6ns which is enough for me. 

I know it's not "traditional" but using plate antennas on a digital Theremin can give you at least one more bit of SNR (and they are easier to play in the near field IMO) - dewster

Did you try ring antennas (like on this photo)? For analog theremins it is a good way to "stretch" the neck (is it called neck for theremins?) near antenna.

Has anyone tried the fancy capacitance to digital ICs such as AD7746, FDC1004, PCAP04? - edavid

I started this post to figure out how I can compare these ICs to my design. As you can see, the only common parameter on this forum is resolution in bits. If I am correct, PCAP04 has only 15 bit effective resolution at 100Hz sample rate (assuming 2pF span and 10pF base). It seems to me that I can achieve such resolution without any specialized IC.

[EDIT] Fonts changed, thanks to Buggins

This forum engine has a lot of issues.
To avoid strange big fonts in copypasted text, in message edit mode press button and clean font/color tags manually

Did you try ring antennas..."  - andreyrogatkin

No, and thanks, but I'm not really interested in trying them as they have insufficient surface area.  There's not a lot of point in trying to linearize things geometrically when you can do so almost perfectly in software.  Rods and rings leave whole bits of SNR on the floor, and in this biz that's just asking for trouble.  You will likely encounter interference situations where 3dB or so could make the difference between playable and unplayable.

"I started this post to figure out how I can compare these ICs to my design. As you can see, the only common parameter on this forum is resolution in bits. If I am correct, PCAP04 has only 15 bit effective resolution at 100Hz sample rate (assuming 2pF span and 10pF base). It seems to me that I can achieve such resolution without any specialized IC."

You find out pretty quickly that exceedingly few off-the-shelf items are a good fit for building a Theremin, unfortunately.  They don't even make the RF chokes used in the Etherwave anymore.  Capacitance sensing ICs are not designed for long range and fast response.  I would submit that one can immediately rule out any solution that employs very low voltages at the antenna (if you're trying to design a pro level instrument).

Speaking of coils, you'll find that LC Q at resonance is limited to around 100 or so, no matter what you do.  A single layer air core solenoid should give sky high Q, so I think this upper limit is due to environmental R losses.  In other words, there is an intrinsic R coupled to the intrinsic C, and the high Q energy is dissipated as heat.  This is something quite basic that I didn't anticipate, and in practice it gives you more leeway when designing coils, as there are diminishing returns to lowering DCR.