From: Rik Strobbe <Rik.Strobbe@fys.kuleuven.be>
To: "rsgb_lf_group@blacksheep.org" <rsgb_lf_group@blacksheep.org>
Date: Fri, 18 Mar 2011 19:17:16 +0100
Thread-Topic: Re: Loop TX antennas at VLF?
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Hello Jim, Roger,

skin depth at 9kHz is about 0.8mm (http://www.calculatoredge.com/electroni=
cs/skin%20effect.htm).
For a 3mm wire the AC resistance (@ 9kHz) will be 28% larger than the DC=
 resistance.
Some 1.5mm wires in parallel might be better.=20
Coax cable (shielding and inner wire in parallel) could be a good alternat=
ive to keep losses low.=20

73, Rik  ON7YD - OR7T


________________________________________
Van: owner-rsgb_lf_group@blacksheep.org [owner-rsgb_lf_group@blacksheep.or=
g] namens James Moritz [james.moritz@btopenworld.com]
Verzonden: vrijdag 18 maart 2011 16:26
Aan: rsgb_lf_group@blacksheep.org
Onderwerp: LF: Re: Loop TX antennas at VLF?

Dear Roger, LF Group,

> Just wondering if anyone has done the maths to work out what sort of ERP
> could be expected at 8.97kHz with, say, 100W to a smallish loop antenna=
 in
> the garden?

A 10m x 10m, 100m^2 loop of  "thickish" 3mm dia solid wire would have a
resistance at 9kHz of roughly 0.1ohm. With 100W available, 32A antenna
current should be possible, assuming negligible tuning capacitor losses.
Inductance would be of the order of 40uH. A tuning capacitor of roughly 8u=
F
would be needed.

The radiation resistance of an electrically small loop is:

320 * pi^4 * A^2 / (lambda)^4, where A =3D area, lambda =3D wavelength

for 100m^2 at 9kHz, Rrad is about 250 pico-ohms (!)

The ERP is then 1.8 * I^2 * Rrad, about 0.45uW

So pretty low, but with a bit bigger loop and a bit more power, it would
seem to be competitive with small verticals of a similar size. This is
perhaps mainly because of the serious losses present in loading coils that
people have been able to make for verticals, combined with high voltage
limitations of fairly short wire antennas, and high environmental losses=
 of
various types also due to high electric fields. The voltage in this exampl=
e
would only be about 70V. So might be worth trying for "back garden"
experiments (assuming your antenna masts can support thick enought wire!),
although I think it would not be competitive for bigger balloon/kite
supported vertical antennas.

Cheers, Jim Moritz
73 de M0BMU