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

I think you'd better use an oscillator such as ours, square it immediately and do everything else in the firmware (or FPG-irmware or whatever is called, programming inside an FPGA)

I'm telling this because, in addition to ensuring the resolution, it is important to keep the noise down and to obtain this, there's nothing better than a Colpitts circuit with a low noise FET. The BF862 is designed for VFO circuits, and the best VFOs, after nearly 100 years of tests, turned out to be the Colpitts. (Note 1)

(Note 1) VFOs (Variable Frequency Oscillator) have been used throughout the last century by amateur radio operators and are the spearhead of the ultra-stable, but at the same time variable, oscillators. A VFO to decode the USB, must be stable to some Hz, while oscillating at several MHz and must have a very low phase noise. These are pretty hard performances to obtain.

I understand that a digital oscillator based on a quartz, could be more stable and with virtually zero noise. But this reasoning forgets that a perfect oscillator, which nothing can detune, would not work for a Theremin. For this application, it must be stable but at the same time, also be very sensitive to the movements of the hand.

The stability alone is not important, what you need to maximize is the result of the following formula:

(sensitivity to the hand) / (thermal shifts + noise + harmonics uptake of digital circuits)

To obtain this, the oscillator components should be well away from any source of noise (ideally in an absolute vacuum and isolated as much as possible by any other component).

All digital components (including FPGAs) generate all kinds of harmonics, because of their square waves with fast fronts. For this reason, the oscillating circuit must be physically away from the CPU and separate by an isolation preamp. The tracks of the PCB, should be very far from each other and the PCB must be single-sided (without ground layer, to reduce stray capacitance)

In practice the left part of our CapSensor. They are just four components and it is the minimum possible hardware.

We have been doing tests on capacitive sensors, for the last ten years. We too started, with digital oscillators. First we used the 4069 (which the OpenThereminUNO uses), then the 40106, then the same components but in HC version. We then tested various digital configurations with PICs, with the series 16 before and then the 24. Finally, at the beginning of 2001, we moved decisively to FET. First we used the BF245A , then the BF246A and in recent years the BF862 (specific for low noise VFOs). Same story for the inductors, in the first trials we used coils on ceramic with pre-tensioned, silver plated wire. Instead now, we use microscopic 330uH TDK impedances, with much better results.

I am sure that no digital oscillator can compete in sensitivity/noise ratio with the BF862 + TDK 330uH couple. Those who don't believe can make a test, using the left side from one of our CapSensor.

Who writes is a digital fundamentalist, I would have preferred an all-digital solution, but unfortunately at the critical points, where the noise is measured in fractions of a micro-volts, you need FETs.

A few examples:
- condenser microphones
- electret microphones
- Distance capacitive sensors, for scientific applications, with sub-micrometer precision
- MEMS accelerometers
- Charge amplifiers for PIN diodes (gamma spectrometry)
- Ion chambers for radon measurement

Almost all modern communications rely on frequency synthesis, which is to say NCOs and PLLs.  My early Theremin prototype worked just fine with a modified digital phase locked loop (DPLL) driving an LC tank.  The LC delayed the voltage drive by 90 degrees at resonance, the DPLL worked to lock this 90 degree phase offset with the drive.  Even the RF spatter from the multiplexed LED display didn't seem to bother it too much. 

The beauty of an NCO is you get extremely wide variable frequency with the precision of a crystal.  Dithering the output gives good enough spectral purity (SFDR or spur free dynamic range) for most applications.  The beauty of NCO + LC + digital phase detector + digital loop filter is that any temperature dependence will be due to the LC and nothing else.  Doing this in an FPGA makes the LC oscillator quite malleable, with the opportunity to tap directly into the operating point.

I haven't studied them extensively, but Colpitts oscillator drive seems directly bound to the tank, which could make large voltage swings and ESD protection difficult, and they seem to have no phase shift between drive and sense so they could stall.

I may at some point switch over to an analog oscillator, but only after I've exhausted the digital route.  FPGA NCOs are easy in the 100s of kHz, but get somewhat harder in the low MHz.

Your strategy is correct and I really hope that it can work well. (because I am a digital fundamentalist)

What do you think about an oscillator without the inductor?
This solution seems to me very interesting because of the direct (not square rooted) dependence of the deltaF from deltaC.

"What do you think about an oscillator without the inductor?"  - livio

It seems doomed to failure for long distance capacitance sensing.  It's been tried with the Open.Theremin project and rejected.  FredM tried it as well.  I've tried modulating a resistor with digital pseudo-random noise and looking at the capacitive delay on the other side, but this solution seems plagued by the inductive effects of any antenna you hang off of it.  Though it might work OK for short ranges.

The consensus here is that you need the high Q (selectivity) and large voltage swing that LC provides in order to overcome environmental interference.

To overcome enviromental interferences the antenna must be short and large (large area in square centimeters) And absolutely not tuned with a inductor! 

We need to measure a capacity, not to send and receive electromagnetic fields. So more the antenna is similar to a capacitor and less is similar to a antenna and less it will be influenced by electromagnetic fields.

Large voltages and tuned antennas are OK for radio communications, not for Theremins.

(Sorry for my bad english. I might sound polemical but it is not my intention. I just want to design good circuits together))

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When you say "long distance" what do you mean? What are the distances that are considered good for a Theremin?

"To overcome enviromental interferences the antenna must be short and large (large area in square centimeters)..."  - livio

Short length in relation to the wavelengths involved, yes, I agree.  The area is a trade-off because a larger area means higher static capacitance, though it can also form a larger capacitance with the hand (a question of ratios and the resulting sensitivity).  A square or round flat plate probably makes the best "antenna" but people like to play rods, and the rod shape likely linearizes analog Theremins to some degree.

"And absolutely not tuned with a inductor!"

Any LC has an L somewhere, like the tank.  And many Theremins use a second inductor in series with the antenna.  My latest design is a single series inductor with no additional capacitance other than the antenna C for resonance.

"Large voltages and tuned antennas are OK for radio communications, not for Theremins."

I'm not talking about tuning the antenna in a quarter wave sense, but tuning the resonant frequency of the antenna C and the inductor L that the antenna is connected to.  Higher voltage swings on the antenna (maybe 30V to 100V) help because they are so much larger than any environmental noise that might be influencing the antenna.

"When you say "long distance" what do you mean? What are the distances that are considered good for a Theremin?"

I think it's pretty impressive when Theremins are played with 1/2 meter or more between the hand and the pitch antenna.

"A larger area means higher static capacitance"

True, but only if the area is really too much. The best area is about 2 or 3 times the area of the hand (so approx 200 cmq, not 26 cmq as a 26x1cm rod). 

To minimize the static capacitance, the large section must be far from any metallic object and far from the Theremin body. Our petal antennas are shaped to do this.

We tested this and the results are incontrovertable. With a 26 cmq rod antenna it is difficult to work at 40 cm. Instead, with a 500 cmq antenna it is very easy to work at 1 meter, with 8 octaves. When the hand is steady, the notes are absolutely steady in every position of this incredibly large 8 octaves range. I am preparing some videos about. 

 "A single series inductor with no additional capacitance other than the antenna C for resonance."

A series inductor tunes the antenna to resonance, also if the antenna is very short! If the inductor is about 40 mH and the antenna 8 pF (as the Etherwave) the system inductor-antenna is resonating. The voltage on the antenna is increased to about 200 Volt peak to peak. The antenna impedance becomes purely resistive and very low. As the antenna+inductor is optimal coupled to the oscillator, the efficiency as transmitter and receiver of electromagnetical felds is greatly increased.

The increased antenna-oscillator coupling produces also a limited increased sensitivity to the hand movements, but there are better methods to do this (without transforming the Theremin into a radio receiver and transmitter)

The Etherwave increases the oscillator sensitivity from 0.03% (without 40 mH inductor) to about 2% (with inductor) (oscillator sensitivity is the percentual of change in frequency from hand at 100 cm to hand at 1 cm)

But increasing the area and using 3MHz oscillators we push the oscillator sensitivity to 22% (180 cmq) and also more then 30% increasing the area to more than 300 cmq.

In addition a large area capacitor plate is only bi-directional (not omni-directional as a rod capacitor) and this, plus the not-resonating antenna, minimizes the cross-interferences when Theremins are only some meters one to each other.   

"I'm not talking about tuning the antenna in a quarter wave sense, but tuning the resonant frequency of the antenna C and the inductor L that the antenna is connected to."

The result is the same.
The antenna impedance becomes purely resistive and with a low value. The antenna-oscillator coupling becomes optimal and about all the oscillator power is transformed in electromagnetical energy. And the Theremin becomes also a good radio-receiver.

"Higher voltage swings on the antenna (maybe 30V to 100V) help because they are so much larger than any environmental noise that might be influencing the antenna."

This sounds to me as a power-war. This not helps with the FCC and not helps to minimize cross-interferences for Theremins working in the same room.

Theremins working with not resonating, short and large area antennas, can:
 - work side by side (some meters)
 - change easely the operation frequency and the antenna area (without a 40mH inductor impossible-tuning)
 - permit to change the antenna "at the fly" from 1 cmq to some square meters - without tuning nothing
 - emit only some microwatt (instead than 100 mW - Etherwave)

"I think it's pretty impressive when Theremins are played with 1/2 meter or more between the hand and the pitch antenna."

Many, many thanks for this!!!  

This is a very good news for us, we are working at this 0.5 meter distance with 8 octaves perfectly playable and with perfectly staedy notes.

With large area antennas it is easy to do the same also at 1, 1.5 and 2 meters, I have tested a 1 square meter antenna playing from more than 3 meters, not with the hand but walking... And always with perfectly steady notes - no noises - no interferences.

"The rod shape likely linearizes analog Theremins to some degree."

Yes, it is true. We are obtaining this with a little capacitor in series to the large area antenna.

When the hand is far the series capacitor is not influent but when the hand is near, the little capacitor limits the max capacitance and linearizes the response.

In addition this little capacitors isolates galvanically the oscillator from the outside world. A so little capacitor about 10pF, can be easely a 10kV component and helps to protect from ESD events. 

"People like to play rods"

People will love our fantastic petal-shaped antennas and also the new spectacular stage-antennas as the Cobrantenna (a antenna with a large head and a long horizzontal tail to linearize the play range up to some meters)

Our new line of antennas are constituted by two external shells, with two internal Kapton layers and finally a thin copper layer, impossible to ESD them.

The Cobrantenna is very scenographic but too large for use at home, but it can be easely substituted with a smaller one.

Our new antennas are detachable with a small connector 3 x 30 mm and 20 mm deep, with the contact at the bottom. So, FredM will not be able to insert his fingers, to reach the contacts, trying to burn our CapSensors.

:)

"The Etherwave increases the oscillator sensitivity from 0.03% (without 40 mH inductor) to about 2% (with inductor) (oscillator sensitivity is the percentual of change in frequency with hand at 100 cm to hand at 1 cm)"

Yes, that's what I've found too.  The way I look at the EW is a series L (40mH) driving a C to ground (antenna) and stimulated by a secondary parallel LC tank.  The dual resonance is troublesome to tune correctly and the parallel tank can draw very high currents if slightly mistuned.

"But increasing the area and using 3MHz oscillators we push the oscillator sensitivity to 22% (180 cmq) and also more then 30% increasing the area to 200 and 500 cmq."

To be clear, the increase in the operating frequency to 3MHz isn't increasing the sensitivity (unless you are heterodyning).

"In addition a large area capacitor plate is only bi-directional (not omni-directional as a rod capacitor) and this, plus the not-resonating antenna, minimizes the cross-interferences when Theremins are only some meters one to each other."

Good point.

"The antenna impedance becomes purely resistive and with a low value."

I don't understand what you mean here.  The only time an antenna becomes resistive is when it is tuned to emit RF, and Theremin antennas are way to short for that.  When the tank L and antenna C are brought to the natural resonance point of the LC it forms, and if it is high Q, will require little power to to keep it resonating.  Is that what you mean?

"We are obtaining this with a little capacitor in series to the large area antenna."

FredM actually came up with this a while ago and used it on his Theremins.

"- emit only some microwatt (instead than 100 mW - Etherwave)"

I haven't done the math, but it's hard for me to believe an EW produces 100 mW of RF.  And if your design is operating at 1/3 the voltage but 10x higher in frequency I'd think it could actually produce more RF than the EW due to real antenna effects.

"we are working at this 0.5 meter distance with 8 octaves perfectly playable"

Too many octaves can be a negative thing.  Peter Pringle noted that the most playable Theremin he owns has the least amount of octaves spread over a fairly large playing field.  In my designs I'm going to leave this adjustment up to the player so they can set it as they like.  Lots of octaves for special effects, few octaves for precision playing.

"To be clear, the increase in the operating frequency to 3MHz isn't increasing the sensitivity (unless you are heterodyning)"

We are pushing the sensitivity to 22% without heterodyning. This is a net gain of about 20 dB, (while heterodyning can push the gain only 4 to 8 dB as your graphics yellow blue clearly shows)

Our high sensitivity is obtained because using 3 Mhz the parallel capacitance is not the usual 150 pF (OpenThereminUNO and also your 120 KHz test oscillator are all 150 pF)

Instead our parallel capacitance is only 8 pF with little antennas (50 cmq) to 15 pF with very large antennas (500 cmq) 

The low parallel capacitance and the high area of the antenna pushes our oscillator sensitivity to 22% - without heterodyning!

This is true oscillator sensitivity! Not a deaf oscillator, artificially amplified by etherodining that amplifies also defects and noise. 

"The only time an antenna becomes resistive is when it is tuned to emit RF, and Theremin antennas are way to short for that"

You are in error, I can produce simulations that demonstrates that a short antenna tuned with a inductor at the base is really tuned and (at the resonant frequency) becomes a pure resistor of low value.

In this condition the oscillator is well coupled to the antenna and sends main part of the power to the antenna.

The Etherwave oscillator drains 120 to 150 mW from the power supply and sends about 100 mW of power to the antenna!

I am sure of this. 

"it's hard for me to believe an EW produces 100 mW of RF.  And if your design is operating at 1/3 the voltage but 10x higher in frequency I'd think it could actually produce more RF than the EW due to real antenna effects."

Please test yourself with LTSpice or some other simulator. I have done all the simulations and I am sure of this. Maybe it can produce a little less power for some effect not well simulated, but surely more than 50 mW.

In contrast, because we do not tune the antenna our said "antenna" is only a side of a variable capacitor. The impedence is very very high and the power very very low. Only some tenth of microwatt are emitted as an electromagnetic field.

"Too many octaves can be a negative thing.  Peter Pringle noted that the most playable Theremin he owns has the least amount of octaves spread over a fairly large playing field.  In my designs I'm going to leave this adjustment up to the player so they can set it as they like.  Lots of octaves for special effects, few octaves for precision playing."

Yes, the player must be free to select any range, we do exactly what you say and more...

Our ThereminSynth range is stored in the named "Voices", the voices are stored in named "Banks" and all is stored in named "Configurations"

The user can select the range from 2 semitones to 8 octaves and recall this (and other 80 params) as needed for each single performance.

"...and also your 120 KHz test oscillator are all 150 pF"  - livio

No, my early test oscillator was 10-20 pF, my newer oscillators have no explicit capacitance other than the antenna capacitance.

"The low parallel capacitance and the high area of the antenna pushes our oscillator sensitivity to 22% - without heterodyning!"

Yes, so the increase in sensitivity you describe is not due to the higher operating frequency.  If you are not heterodyning then decreasing the static capacitance and increasing the dynamic capacitance will increase sensitivity the same and regardless of the operating frequency.

"while heterodyning can push the gain only 4 to 8 dB as your graphics yellow blue clearly shows"

The vertical axis of that graph is bits/interval.  Each bit is 6dB.  Heterodyning can dramatically increase resolution (though likely at the expense of SNR).

"In contrast, because we do not tune the antenna our said "antenna" is only a side of a variable capacitor. The impedence is very very high and the power very very low. Only some tenth of microwatt are emitted as an electromagnetic field."

I think you've got something fundamentally wrong in your thinking.  Both the EW and your designs have a capacitive antenna as part of a resonant LC circuit.  One can't be emitting 50-100 mW and the other a tenth of a uW.  That's a factor of ~1,000,000 which on it's face seems not credible.