Antenna length and sound frequency of a theremin.

"Capacitance is not between the antennas, but between the antennas and ground (earth) - your hand affects that value." - rupertchappelle

I've actually investigated this pretty thoroughly.  There is some modulation of the antenna intrinsic C due to the hand, and there is some actual mutual C between the hand and the antenna.  I agree that the mutual return path is ground.

""Antenna" is a marking term since radios were very popular with the Theremin were introduced. It does not transmit and if it receives, you get radio coming through your music, so it really is not purposed as a radio antenna."

Yes, I think most here understand this, but it doesn't hurt to point it out now and then.

"The choice of a rod for the plate has made theremins very difficult to master."

The choice for a rod-shaped pitch antenna was probably made mainly to linearize the near-field, which actually makes them easier to master.

Dewster, Since I bought the Model 302 Theremin with plate antennas, I have not played the Etherwave at all. The model 302 is the easiest theremin to play - one without pitch correction. I am one of the few thereminists who do not have to use vibrato, because the rod antenna is like walking a tightrope and the plate antenna is like walking down the sidewalk. Once you hit a note, you can hold it steady.

Plate antennas linearity can be easily adjusted by aiming at the corner of the plate rather than the center. Using a curving motion from the elbow creates an arc that gives you more space between the higher notes . Aiming for the center of the plate gives you the highest note range few wish to play or listen to. Ask my cats.

Since the theremin I use is unknown by most of you, especially those considered "expert" here is a link to a youtube video showing the opening of the box, the set up of the theremin and my playing technique:

Opening the Harrison Instruments Model 302 Theremin

https://youtu.be/ZtWvNXJA26Q

Thank you for all your replies!!!!!

I have another question regarding my investigation.

I need to find the capacitance of my theremin with the varying lengths of the antennas. The formula of the capacitance I am using is:

C = εr * εo * (A/d)

C being the capacitance in Farads;

A being the area of the plates in m²;

εr being the dielectric constant of the insulator between the plates (in Farad per meter: F·m⁻¹);

εo being the electric constant = 8.854×10⁻¹² F⋅m⁻¹;

                             d being the distance between the two plates in  m.

Now my question is, when it says the Area of the two plates, is it the area of the antenna + the area of the hand (in my case I am using a metal plate)? How can I calculate that area?

Thank you :)

"Now my question is, when it says the Area of the two plates, is it the area of the antenna + the area of the hand (in my case I am using a metal plate)? How can I calculate that area?"

The answer you are looking for, unfortunately, is: "it's complicated".  So complicated that unless you are talking about certain specific really simple and highly symmetric geometries in toy environments, you have to collect actual data or simulate via FEA (finite element analysis, where the capacitor plates, and even the walls and floor, are divided into hundreds or thousands of smaller plates with constant voltage) to get any meaningful answer.  Once you have the data for a certain geometry of antenna and hand you can generalize to some degree for that case via curve fitting.

In “Physics of the Theremin”, by Kenneth D. Skeldon et al., American Journal of
Physics, Volume 66, Issue 11, pp. 945-955 (1998), formulas are given including both the capacitance of an isolated cylindrical antenna in a certain high about ground without human influence and the additional capacitance by hand in dependence on distance. Does anyone here know this article in whole? We could test these formulas.

Here is the Reference
Physics of the Theremin" by Kenneth D. Skeldon, Lindsay M. Reid, Viviene McInally, Brendan Dougan, and Craig Fulton, 1998:

Capacitance due to hand

Chand = pi*epsilon0*L / (10*ln(4*x/D))

where: L = length of antenna in meters
D = diameter of antenna in meters
x = distance from hand to antenna in meters
epsilon0 = permittivity of free space = 8.85 pF m^-1

But unfortunately the article is not for free but in several citations. So the assumptions are not available for me. Many authors. I think the formula is not right. Hand capacitance cannot be linear to the length of the pitch antenna.

JPascal, the formula for antenna capacitance above ground in that paper isn't too bad, but the capacitance due to the hand is wayyyy off.  I used it for years before I had anything better (real data) and before I realized how wrong it was.  A wild guess would be better than that hand C formula.

Hi, Dewster,

many thanks for your analog excel sheet data. It was certainly so much time consuming but is really very, very helpful.

I want to fit your data with my simple theoretical approach and have two questions: Is the measured frequency in 0.1 Hz (instead of 1 Hz from your collected_data sheet)? I suppose that 9 kHz is more likely the range for audio signal between 0,5 and 0,05 meter hand distance.

During the measurements: Was the thumb of your fist leftside or upwards?

Thanks a lot for answer.

"Is the measured frequency in 0.1 Hz (instead of 1 Hz from your collected_data sheet)? I suppose that 9 kHz is more likely the range for audio signal between 0,5 and 0,05 meter hand distance." - JPascal

The frequency is measured in Hz.  The difference (or heterodyned) range is large because the nominal frequency is fairly high (2.3MHz, most Theremins use anywhere from 200kHz to maybe 1MHz here) and there is no additional capacitive padding on the antenna.  You probably need to pad the antenna if you intend on using higher nominal frequencies.  But using higher frequencies with padding means the intrinsic stability of the oscillators becomes more of an issue.

Doing this digitally means I don't really care what the nominal frequency is, so I pick something low enough to easily generate in an FPGA, but high enough to make the air-core inductors physically small.

"During the measurements: Was the thumb of your fist leftside or upwards?"

Upwards, though my hand was in a fist with my thumb pretty much pulled in to it.  I was using my thumbnail to index the distance notches in the "ruler" running from the antenna to my shoulder.