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Message-ID: <5.1.0.14.0.20021114103946.00a93000@gemini.herts.ac.uk>
Date: Thu, 14 Nov 2002 17:08:08 +0000
To: rsgb_lf_group@blacksheep.org
From: "James Moritz" <j.r.moritz@herts.ac.uk>
In-reply-to: <DDC408CAE72CD511827A0002A5131CD6D9F82B@exc_wil08>
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Subject: Re: LF: RE: Loop vs Marconi
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Dear Bill, LF Group

At 23:50 13/11/2002 -0500, you wrote:
>. My data and mathematical
>studies indicate that a simple 50'x50' loop with a .37" conductor is ~6db
>inferior to a 50' tall vertical, having a 50' diameter top hat and with a
>elaborate ground system located in an open field.

One point worth making - US Lowfer activity centres around 185k, while in 
Europe we are concerned with 137k. Since the radiation resistance of a 
vertical varies with the square of frequency, while that of a loop varies 
with the 4th power, the difference in frequency swings things in favour of 
the loop for lowfers by roughly (185/137)^2, about 2.6dB, if everything 
else is equal. Alternatively, you could scale the size of antennas with the 
wavelength, so to get the same result as Bill is talking about on 136k, we 
would be looking at a basic dimension of 68 feet (21m) instead of 50 feet - 
unrealistically big for most of us, unfortunately.

My back-of envelope-reckoning goes like this:- A 10m high, 40m long antenna 
is the biggest I can put up. As a vertical, it has a radiation resistance 
of around 26milliohms. Using the same space, and with a bit of clearance 
for obstacles on the ground, a loop would be about 320m^2. This has a 
radiation resistance of 140 micro-ohms. If we are lucky, and the loop acts 
as if it is over a perfect ground plane, this might increase to 280 
micro-ohms. To get the same radiated power, the current would have to be 
sqrt(26m/280u) times bigger, about 48A instead of 5A. The loss resistance 
of the vertical is about 40 ohms, so efficiency is about 0.00065. To get 
the same efficiency from the loop, the loss resistance would have to be 
kept down to (280u/0.00065) = 0.43 ohms. But there is also the problem of 
directionality of the loop. Due to the shape of my garden, it must run due 
E-W. But the USA, for example, is in a NW direction. This results in about 
3dB "loss" in field strength in the desired direction. So to produce the 
same field strength as the vertical in the USA, the current would have to 
go up by 3dB to 68A. For the same transmitter power, this would require 
loss resistance to be kept below 0.22ohms.

I am not sure how feasible it is to reach these figures, but I am sure it 
is easier to make a vertical with 40 ohm loss resistance capable of 5A 
antenna current than it is to make a loop with 0.22ohms and 68A antenna 
current. At the least, getting a sufficient amount of metal into the air 
would require stronger antenna supports than I currnetly have. There are 
plenty of unknown variables which might shift the result either way by 
several dB, but these can only be found by experiment. I do plan to try 
back-to-back comparison experiments between a loop and vertical antennas 
when time permits, probably next summer - but I will be surprised if a 
practical loop antenna proves to be more efficient than a vertical.

Cheers, Jim Moritz
73 de M0BMU