Dear LF group,
I would like to put for your consideration the issue of
multi-turn transmitting loops. Have you ever done such an experiment on
LF ?
This sunday evening i decided to do some simple math and it turns out
that such a N-turn TX loop should work ( at least on the paper)
The radiation resistance is proportional to the square of so called
"effective
height" and this last term can be easily derived for a loop i.e. it is
equal to
2*pi*A*N/lambda where A denotes area closed by a loop a N is the number
of turns
so the radiation resistance for a single turn loop reads as
320*pi^4*A^2/lambda^4
For the N-turns the radiation resistance obtained for a single turn is
multiplied
by N^2. Ok, the R (ac) is increased as we increase N but this is linear
with respect to N
and therefore we should have gain in the radiated power.
(there is an implicit assumption made: the loop is "small" i.e. the
current is constant)
i did some calculations: assumed TX power ( and later, perfect match to
the loop) 200 Watt
environmental loss: 1.5 Ohm, diameter of the wire d = 3 mm, rectangular
shape of the loop
i.e 10 meters by 20 meters ( less optimal than square or circle )
so A = 200 sq.m For N =1 (classical tx loop) we get R(AC) = 0.62 Ohm
( Rac formula taken from ARRL Antenna Handbook, f = 137.7kHz)
radiation resistance RRAD = 55.5 microOhm, total R loss = 2.12 Ohm,
efficiency is 0.0026% and radiated pwr 5.2 miliWatts, I = 9.7 Amp.
Next, I took N =3 so the wire length is changed from 60 meters to 180,
everything else was kept the same and now one gets: R(ac)= 1.85 Ohm so
R loss = 3.35 Ohm
RRAD = 499.5 microOhm, efficiency increased to 0.015% and radiated pwr
abt 30 miliWatt, I=7.7 Amp
I am sorry bothering you but i simply would like to learn
where is the 'catch' here - if there is one ...
I guess the assumed loop i.e. 10 by 20 mters is 'reasonable' as TX antenna
i took these values after reading the article about
WD2XES first TX loop: 40 feet by 65 feet - well , almost the same
dimensions.. :)
From practical reasons the N values will likely be small , say, 2 or 3
but as the above numbers show maybe it is worth doing it.
73 de Piotr, sq7mpj
qth: Lodz /jo91rs/
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