> Why is the current into the antenna balanced?
Well, it isn't always. You are right to question that assumption.
Given a center fed dipole, which is physically a pretty good mirror
image (not a sloper, or one end running to a metal roof when the other
end has rope to a distant tree), the antenna currents ought to be
pretty well balanced if the feed is also balanced.
An OCF (off-center fed) dipole does not have balanced currents at the
feedpoint, and if you were to feed it with ladderline, you might want
a choke balun (bal-bal ?) at the feedpoint to keep it kosher. OCFs
tend to be designed to match coax, so I think that would be a rarity.
Ethernet uses baluns too. I think the usual Ethernet magnetics
contain a combination of isolation transformers in series with
common-mode chokes, in an effort to achieve a good wideband balance.
I think that a pair of wires (think bifilar), wound around a suitably
large ferrite, would provide the common-mode choking function while
handling the power. The odd-mode characteristic impedance of the
bifilar wires may not be that important if its discontinuity is only a
few feet on HF ... if it even matters at all, when using ladderline.
Antennas and feedlines work even when common mode currents aren't
choked off, and sometimes people get along quite well without even
thinking about baluns. Yes, it increase the chances for trouble, or a
non-textbook distorted pattern; but if you aren't having any trouble,
you might not care if it is technically "not right".
Andy
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