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Loops and radiation.

Stu,

Any size loop can be used for any frequency. The rub is the radiation resistance. In other words if a loop is very small with respect to the wavelength of the signal it won't couple for beans to the ether. I touched on this in some earlier postings with Geoff when I was at the coast. Since I'm home now and have access to my library I can put some numbers to it.

The radiation resistance of a small loop per Kraus, Antennas, 1950 is:
Rr=31,200[n(A/lambda^2)]. Where n=turns,A=loop area,lambda=wavelength.

Running the numbers for F=8.3Hz gives a Rr=5.6E-12ohms. Free space is around 377ohms so there is huge mismatch. That just means that there will be almost no far-field radiation. Near-field, which in this case is about anywhere in the same hemisphere, the field will be predominantly magnetic and as I suggested can be readily calculated using the Biot-Savart law or modeled with FEMM. Easier yet, we've all seen the "lines of force" in iron filings from a bar magnet, imagine one of those sticking vertically through the axis of the loop and you will have a good mental picture of the relative field strength and vectors produced by the loop.

By the way, I used 10 turns in the numeric example above. The inner turns on a PCB loop do essentially nothing because their area is small so I figured that was a reasonable estimate.

So forget the wavelength, it's just a red-herring in this case. All that matters is the magnetic field and the sensitivity of the listener or equipment or whatever to it. As you get further away, it just gets weaker if you stay on the same angle. It will be much stronger on axis than off to the side and drop more quickly as you get away from it. If you really want a dose, put it on top of your head. But I don't recommend that on general principles. I'm with Thurber: "Leave your mind alone."

Rick


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