Re: LF: Re: Loop TX antennas at VLF?

[Markus Vester <markusvester@aol.com>]

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 <james.moritz@btopenworld.com>
An: rsgb_lf_group@blacksheep.org
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