Dear Jim, Stefan, LF Group,
One obviously cannot make a precise prediction of ERP without
experimentally-derived data, so you will just have to find out what can
actually be achieved. But one can make a realistic estimate of the upper
limit of ERP - here's mine:
Assume 200W max TX power, frequency 10kHz (highest frequency = highest
antenna efficiency)
The effective height of the antenna depends somewhat on the exact geometry
of the wires making up the antenna, and also on shielding effects of objects
in the environment close to the antenna. Assume no shielding effect (best
case for ERP). The effective height will always be less than the physical
height of the antenna; for a heavily top-loaded inverted-L like this, maybe
80% of the physical height. Again let's assume a "best possible case"
effective height of 10m. The radiation resistance would then be Rrad =
160*pi^2*heff^2 / lambda^2, i.e. 175micro-ohm. You could get a more specific
figure for heff / Rrad using the text-book formulae (see ON7YD's antennas
site), or by doing a NEC simulation using the actual wire geometry, with
perfect ground and perfect conductors.
You could also estimate the antenna reactance using a NEC simulation; but a
good-enough estimate is to assume 6pF/m for a total of 50m of wire, i.e.
300pF capacitance, Xc = 53kohm at 10kHz. This reactance is much higher than
any likely value of antenna loss resistance, so effectively defines the
antenna voltage for a given antenna current. If there is no limit on
transmitter power, antenna breakdown voltage will be the limiting factor on
antenna current and ERP. In my experience, antenna voltages of 20kV can be
achieved with care on "back garden" antennas, maybe more on a dry day...
This limits maximum antenna current Iant to 20kV/53kohm = 0.38A.
The loss resistance defines required TX power to achieve a given antenna
current. Rloss varies widely depending on environment and possibly earthing.
I have measured figures at VLF between several tens of ohms and several
hundred ohms, usually more the latter. To this you have to add the loss of
the loading coil, probably also hundreds of ohms. If we assume total Rloss
of 1kohm, the TX pwr for 0.38A antenna current is P = I^2R = 144W, so in
your case antenna voltage will probably be a limiting factor rather than TX
power. If Rloss turns out to be very high for your antenna, the maximum
200W TX power would limit Iant to <0.38A.
The effective radiated power is Iant^2 * Rrad * D, where D is the
directivity of the antenna relative to a free-space dipole. For an
electrically short vertical, D = 1.8. So the maximum ERP you can achieve
with Iant = 0.38A, Rrad = 175uohm, is 45uW. In practice, this is very much a
"best case", and ERP will certainly be reduced by various adverse factors
(lower Heff, non-zero enviromental loss and so on could easily knock off
10dB or more). So 45uW is very much an upper boundary on the achievable ERP
from your system. A few uW is probably realistic, not as bad as you thought!
Good luck with the application,
Cheers, Jim Moritz
73 de M0BMU
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