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« on: November 01, 2015, 1923 UTC »
A normal loop at resonance at half-wave off the ground is supposed to be 100 ohms or so impedance. Because of the low or very low height of this thing, it may well be only 50 ohms or perhaps even quite a bit less at resonance, or 100 ohms or less at the second harmonic. Using a 4:1 in this case would probably put it further from a match between feed and antenna than just plain coax. A dual-coax balanced line (using only the 2 center conductors) would be about 100 ohms, a near perfect match to the 2nd harmonic (pirate band) of this particular "antenna", and have no need for a balun... speaking roughly and theorectically, as I haven't actually measured the exact length of the thing.
On the transmitting side, I never worried about trying to match impedances between my 300 ohm feeds and antennas, because the calculations were only correct for a narrow range of frequencies, and I tended to move around so much-- and using the balanced line eliminated the need for any balun, and reduced line losses vs. coax from the use of non-resonant frequencies. Any signal loss from mismatch was probably more or less cancelled out by the lower loss of the balanced lines vs. coax. (I actually researched those at length at one time via your 'RF Toolbox' !)
Just out of curiosity, and leaving impedance matching out of the question-- is there any other particular reason to use a balun on a receive-only loop, even if fed with coax? I mean, you aren't worried about feedline radiation... or is that a question I should not ask? ;-)