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Q & A: theremin principles

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Most recent answer: 02/07/2011
Q:
Hello, we are two French students working on our project of the year, which is the theremin We are actually having trouble finding on which principles interaction between the player’s hand and the antenna is based on. More precisely, we are working on the following problem : A capacitor is connected to an antenna (in series?) like in the schema. It is an oscillator (wien bridge) which frequency depends on the C value. As we read, the hand of the player is able to modify the C value by getting closer to the antenna. We’d be very glad if u could answer the few questions below, or give us your opinion about the subject. *How does the hand capacitance disrupt the electromagnetic field produced by the antenna? *How does the [capacitor + antenna] behave further to these disruptions? And to what extent can we considere the antenna as a capacitor connected to the other in parallel? (so we can add capacitance ?). Do you think of a ground capacitor? *If you had any idea about the relation between the shape of the antenna and its sensitivity and about the range of disruptions. *And if you could tell us about an experiment which could enlighten the phenomenon. Thank you very much for your answer.
- Michael Le Roux (age 19)
Paris, France
A:
I removed the link to the circuit diagram from your question because that site showed very bad internet etiquette. It's not that I'm objecting to the beautiful pictures on the ad that took over the screen, but to its refusal to allow simple navigation back to the site with the circuit. One would think that Ms. Rafaeli could get enough attention without resorting to such rudeness.

Here's a partial thought. Don't worry about "electromagnetic fields". The frequencies of this oscillator are low. Even at 20 kHz, the wavelength is 1.5 km, much bigger than any of the distances involved. So you need only consider simple electrostatics, ignoring magnetic fields. The basic idea is that your body provides a high-dielectric coefficient pathway to ground, with some conductance in parallel. Maybe you can simply treat the person as a near-short to ground and the person-antenna gap as a variable capacitor. The value of that variable capacitance (in cgs units) is roughly comparable to the area of the hand and antenna (say each is about 100 cm^2) divided by the hand to antenna gap (and by 4pi, to be faux-precise).
(1 cm cgs is about 1 pF SI.)


With only one op-amp and not very many circuit elements, it should then be possible to use techniques from standard electronics texts (e.g. Horowitz and Hill) to solve for the oscillation frequency.

For an experiment, you might see whether a hand behaved much differently from a metal plate of the same size connected by a wire to ground. That will give an idea of whether the approximation of treating the person as a short to ground is good at the relevant frequencies. (I'm not sure.)

Mike W.

(published on 02/07/2011)

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