LF: Re: Loop TX antennas at VLF?

["James Moritz" <james.moritz@btopenworld.com>]

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 8uF 
would be needed.
The radiation resistance of an electrically small loop is:

320 * pi^4 * A^2 / (lambda)^4, where A = area, lambda = 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 example 
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