Hi Tim -- just for fun, I modeled a square full-wave 80m loop at < 1/4 wl
high -- 15m up at 80m. It's true that the peak radiation from such an
antenna on its fundamental is straight up, but the radiation at 23 degrees
elevation, which is a good approximation of the takeoff angle of a high
dipole or 4-square, is only 8 db down from that straight-up peak.
Even more to the point, the signal is 5 dB better at that angle than a
somewhat idealized 1/4 wave ground-mounted vertical over real ground. With
the usual sort of radial system, one might regain 3-4 dB of that, which
still makes the loop look like a pretty decent performer. This situation
even pertains at least down to 10m in height.
On the higher bands, the antenna has a fair amount of gain at useful DX
angles (at least on 20m and above) even at the lower height. The trouble
is that it also develops some pretty deep nulls. With modeling, you might
be able to place them usefully just by moving the feedpoint around the loop.
So my conclusion would be that, particularly in a case where you have
adjoining power lines or some other constraint on a high antenna, the
horizontal loop has something to recommend it.
There is another interesting variation on the theme, called the N4PC Loop.
It is 51 feet on a side, fed in phase at opposite corners, and at 50 feet
height it produces a better pattern by a few DB on 80, and has fewer nulls
on the high bands as well. The added feed complexity might be worth it.
73, Pete N4ZR
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