Measuring Antenna Capacitance

Aluminum foil + Cardboard = l'uminum Peter

There is a cutout in body to pass the "hand" through it. The "player" is mounted on a plywood base which can move on the table (providing different positions relative to antenna):

I thought for a long time about trajectory to move the player, because there are lot of possible options. Finally, I chose the same trajectory that the hand is moving along:

It is useful on following reasons:
- when the hand is reaching the "body" the surfaces lies in the same plane (model is more ideal),
- this moment is easily captured,
- position of player can be aligned by hand position, plus coordinate of player (S) can be accurately determined by the step number.

Of course, the position "hand in the stomach" (or behind the body) has no physical meaning, and all the extra data should be discarded. But it's still interesting what happens in this case too.

I couldn't get the distance less 13 cm (due to short length of plywood base) and more than 70 cm (intersection with the parts of setup).

Of course, "Peter" is grounded.

Antenna capacitance curves are shown below (antenna has 8.3 mm diameter and 50 cm length). Note that this representation informs us about a COMMON (hand+body) introduced capacitance. This corresponds to case when  player set the pitch control once ("hand and body are away") and doesn't touch it anymore.

Antenna behavior is quite predictable. The closer the player to antenna the narrower the capacitance variation range. The slope of curves dramatically decreases near the player, which means too much stretched pitch scale there.

Thanks for sharing that ILYA!  Very nice presentation!

1. Your arm / body arrangement makes a lot of sense and is fairly similar to the way many players actually play.
2. The body raises the intrinsic C of the antenna, which the hand then "steals away" as it approaches.  It's not a simple C in parallel type thing, and it actually lowers absolute sensitivity, something I wasn't aware of until I examined the results of FEA, which separated the two.
3. Your vertical axis is log10(C) - how well do you think this reflects actual heterodyned pitch field linearity?

"It's not a simple C in parallel type thing"  - dewster

Agree.

I have met the statement "the equivalent of body is a capacitor in parallel to antenna" (value depends on position).

Well...
To prevent overload, I left only three of curves (for positions 13, 36 and 69 cm):

These curves tend to values 0.98, 0.32 and 0.14 pF respectively, which are the induced capacitances from "body". Summing the capacitance of "hand without body"  (black curve) with these values, we get the curves (thick lines) that should coincide with the curves from experimentation (thin ones). But we dont see a coincidence!

This reflects one of  electrostatic field law: "the capacitance of a whole conductor is always less than the sum of capacitances of his parts taken separately".

Even if we'll try adjusting the values to get matchings for end points of hand movement (limited by "body" position), we will not get a full match:

Conclusion: the capacitance induced from body is not a constant value, but depends on position of hand.

The following figure shows an another representation of data, the pure "hand capacitance" i.e. the full antenna capacitance minus capacitance in position "hand is pressed to body". This corresponds to case when the player adjust the "pitch" control whenever he changes position of body.

As you can see, the closer the body to antenna, the steeper the curve (which means a compressed pitch scale). Experienced thereminists are well aware of this fact: to make the scale compressed and not worsen in linearity, you need moving the body closer to antenna, but also do adjust "Pitch" control. This fact just is confirmed here.

"how well do you think this reflects actual heterodyned pitch field linearity?" - dewster

Pretty well while two conditions are true:
- Ch (induced capacitance) << Ca (static capacitance of antenna),
- frequency of FPO is set equal to frequency of VPO when "the hand is far away".

I checked it numerically (in Excel) but sure there is a mathematical basis ("in fairly small region, the curve can be replaced by a straight line" and so on).

- frequency of FPO is set equal to frequency of VPO when "the hand is far away".

BTW this condition is used in Theremin Explorer to autocalculate the frequency of fixed pitch oscillator.

New (1.19) version is avalible using old download page.

Most excellent work ILYA!  Thank you for boiling down so much technical theory, grounding it in real measurements, and ensconcing it highly useful software!

I haven't researched this at all, but I wonder what would happen if one stimulated a series EQ inductor with an RC oscillator rather than an LC oscillator?  I think there is an eternal tradeoff between oscillator pullability and stability, and it is this ratio that is the main quality factor when choosing an oscillator for  Theremin use.  High frequency noise / instability can be LP filtered / averaged away to some degree, but we're usually stuck with low frequency noise (though mains hum fundamental and harmonics can be notch filtered down in some scenarios).

"I wonder what would happen if one stimulated a series EQ inductor with an RC oscillator rather than an LC oscillator" - dewster

Using a RC oscillator to stimulate antenna resonance circuit (in coupling manner) is a novel idea. I think that no one has worked out the theoretical background of this subject yet.
Possible that is a doctoral thesis!