Dear Roger, Jim, and others,
regarding the ongoing "VLF loop vs Marconi" discussion, I just can't
resist to add in my five cents...
In principle, both electric and magnetic antennas follow the same
scaling. The Chu-Wheeler bandwidth limit basically states that the maximum
possible efficiency of a small antenna is proportional to Q times an effective
volume of the antenna, divided by wavelength cubed. So if similar Q-factors
can be achieved, both antenna types should be equally effective.
In practice, the Q factor of an electric antenna is limited by
capacitively coupled losses from the environment. On the other hand, a
magnetic loop is a low impedance device and less affected, but you will have
to put much more copper up into the air.
For my small Maconi, I have measured an effective height of 9 m at LF,
and my estimate is that this is reduced to 7 m at VLF due to increased shunt
effects from nearby trees. Thus it would have a radiation resistance of 7
milliohms at 9 kHz. The total loss resistance is about 700 ohms, leading to an
efficiency of 1E-7 (-70dB). About half of the resistance is located in the 1.3
henry loading coil which has an unloaded Q of 220. It consists of 2.3 km of
0.4 mm copper wire, a mass of 2.6 kg.
For a loop above ground, the radiation resistance would actually be
doubled by the image current, giving 500 picoohms for the 10x10 m^2
example. To achieve the same -70 dB efficiency as the above Marconi, total
loss resistance would need to be less than 5 milliohms.
Eddy current losses in the ground will scale as frequency squared, so I
would expect little contribution from this effect at VLF. Capacitor ESR losses
can be kept low by using several in parallel. We could avoid skin effect by
multiple thin strands. Then efficiency ends up being proportional to loop area
times copper mass. In the example, we would need a cross section of about 140
mm^2, resulting in 50 kg of copper. Aluminium wire could be a lighter and
cheaper alternative.
Of course it is always possible to trade efficiency for transmit power.
For a Marconi, it is relatively easy to reach a voltage limit due to the onset
of corona discharges (about 22 kV for 60 W input to my antenna). For a loop,
current density and wire heating would impose a different, typically higher
limit.
As the antenna is likely to be built in an inhabited area, you may also
want to consider that magnetic fields are not shielded very well by most
housing construction materials. They will also penetrate our bodies, with an
(at least theoretical) possibility of nerve stimulation in the immediate
vicinity of very large AC currents.
Best regards,
Markus (DF6NM)
-----Ursprüngliche
Mitteilung-----
Von: James Moritz
<
[email protected]>
An:
[email protected]Verschickt: Fr., 18. Mrz. 2011,
16:26
Thema: 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 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
