I had realized that I really didn’t know the answer. I have looked in my two usual places:
the ARRL Antenna Book and Wikipedia and found lots of hand-waving and the usual references to the
“K-factor” graph, which appears to be derived experimentally. BUT NO THEORY, other
than vague references to the capacitance and inductance of the rod changing with dimensional changes
which, in fact, is similar to transmission lines.
Do any of you have a reference to some real theory and an equation that allows
me to calculate this based on length, diameter, and material characteristics?
(Ignoring environment effects of course. This would be for free space.)
73 -- Larry -- W1DYJ
The top expert on the K-factor that I know of is:
Steve Stearns, K6OIK
At the Pacificon antenna forum in 2019, he gave a talk
on dipole theory, including K-factor.
See:
https://www.fars.k6ya.org/docs/K6OIK-Dipole-Basics-ARRL-Pacificon-Oct_2019-r1.pdf
starting on page 40.
Basically, everything published on the topic was incorrect until
Steve recently did the correct calculations. Steve skillfully debunks
the vast array of folklore and nonsense about K-factor, and
then tells the "rest of the story."
Rick N6RK
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