Thanks, and please keep us informed, maybe you can contact some radio amateurs in your region, also via email.
Frequency shifts and "birds " produced by radio interferences
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I can add another useful info: no one of our 3MHz theremins, has never experienced noises (altough unfortunately, we have very little statistics about this, and just limited to Europe)
Instead, much of the literature, discusses interferences suffered by Theremins working at 300 kHz (and even worse those who work at 600 KHz, in full medium wave)
The thereminists call them "birds" and are a sure sign of heterodyning with a third frequency, coming from the ether.
Where are broadcast transmitters (500 Kw and up) ?
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In 1995, the FCC again extended the Standard Broadcast Band from 540-1600 kHz to 540-1700 kHz (but with a 10 Kw max power)
The 500 Kw trasmitters are all below 1500 KHz
Which distance should you keep, from broadcast center frequency transmission?
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If you live close to broadcast transmitters, you might be disturbed, even if the frequency is not exactly the same as the transmitter. The power of some transmitters is such that, even 100 or 200 KHz of distance is not safe, some examples:
Vatican Radio transmitters = 3 * 500 kW each
French radio transmitters = 12 * 500 kW each + one 1 Mega Watt trasmitter
Luxembourg Radio = 1.3 Mega Watt in Medium Waves (it reached 2 Mega Watt in Long Waves, before possibly closing, in 2002)
The sidebands of these transmitters (and electromechanical defects of their antennas) emit hundreds of watts, even many hundreds of KHz away from their central frequency.
Therefore, it is a good idea to stay as far as possible from them and given that the transmitters of this power, just reach 1.5 MHz, remaining still 900 KHz, before the 2.4 MHz, which is the lowest frequency that we normally use.
FCC rules
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The FCC rules establish an "Unlicensed operation" for the "Extreme low power" transmitters. It is not given the highest power, but the distance in meters of their "effective service" (200 feet = 61 meters *)
(*) According to 47 CFR (Code of Federal Regulations) Sections 15.207, 15.209, 15.219, and 15.221, these devices must accept any interference caused by any other operation, which may further limit the effective service range.
The maximum power for QRP transmitters is 150mW, being 10mW for experimental transmitters (according to some regulations, it is not certain that it is so, all over the world).
In the absence of a specific rule regarding "low power", I'd recommend using the lowest possible amount. In any case, in order to avoid problems, is safe to ensure that from the outside of the room in which it operates, the signal is so low that it cannot be measured.
Our oscillators consume about 2 milli watts, but only a small fraction of this power is actually emitted from the antennas. I did a quick simulation and the output power was about 4 micro watts. (note that Theremin antennas are not tuned, so their impedance is very high, and the consequent emitted power very low)
I believe nobody get worried for a 4 micro-watt output, but you can definitely feel more confident, with 2 mW oscillators (Theremino System), then with 100 mW oscillators (Etherwave)