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From: "Alan Melia" <alan.melia@btinternet.com>
To: <rsgb_lf_group@blacksheep.org>
References: <4B09D502.8030200@toya.net.pl>
Date: Mon, 23 Nov 2009 01:09:24 -0000
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Subject: LF: Re: N-turn TX Loop
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Hi Piotr I think Laurence KL1X had 2 turns in Oklahoma.(about 100m
periphery)
I think there are other loss problems as you increase the turns. Jim M0BMU
is the expert on that.

Alan G3NYK

----- Original Message -----
From: "Piotr Młynarski" <sq7mpj@toya.net.pl>
To: <rsgb_lf_group@blacksheep.org>
Sent: Monday, November 23, 2009 12:19 AM
Subject: LF: N-turn TX Loop


> 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/
>