As you point out, the resonance of a conductor is determined by length
(inductance) and diameter (distributed capacitance to itself). I don't
know the formula for that either, but I'm pretty sure that whatever you
get by reply to your question will be for a straight conductor. A bent
conductor like your halo will have somewhat more capacitance to itself
than a straight one.
Also, proximity has more effect at high voltage positions than at low
voltage positions ... which is how top hats work.
All that is why I usually just generate an EZNEC+ model, which at least
tries to geometrically take into account distributed capacitance. As a
general rule, almost every model I've ever done says that as I increase
the width (as long as it's an appreciable percent of a wavelength) the
resonant frequency goes down and the bandwidth increases ... but
configuration has a large effect.
73,
Dave AB7E
On 1/28/2020 11:19 AM, Larry Banks via TowerTalk wrote:
Hi TTers,
A friend of mine asked me what first appeared to be a simple question.
Paraphrasing:
“How do I calculate the length of my HB 2M halo, based on
the diameter of the aluminum rod. Is it like propagation
velocity with coax?”
My quick answer was: “No, propagation velocity only relates to transmission lines.
Use the graph in the literature for your design to start. Modeling will help. But let me do
some research.”
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
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