The supposed 600-ohm Zo of a random length of wire has very little to
do with it.
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Depending on length, height and wire diameter, Zo can vary between 450 and
650 ohms or thereabouts. What's yours?

Then what balun ratio would the guru's and old wives recommend? And to
confuse even further, receivers can have an input impedance anywhere between
50 and 1000 ohms.

Some tuned receivers have an indeterminate input impedance. Who needs a
balun?
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Reg , G4FGQ