Message-ID: <4B09D502.8030200@toya.net.pl>
Date: Mon, 23 Nov 2009 01:19:14 +0100
From: =?UTF-8?B?UGlvdHIgTcWCeW5hcnNraQ==?= <sq7mpj@toya.net.pl>
User-Agent: Mozilla/5.0 (Windows; U; Win98; en-US; rv:1.7.2) Gecko/20040804 Netscape/7.2 (ax)
MIME-Version: 1.0
To:  rsgb_lf_group@blacksheep.org
Subject: LF: N-turn TX Loop
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Sender: owner-rsgb_lf_group@blacksheep.org
Precedence: bulk
Reply-To: rsgb_lf_group@blacksheep.org


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/