On 1/28/20 12:19 PM, David Gilbert wrote:
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.
It's not exactly accurate to relate length to inductance and diameter to
capacitance for determining antenna resonant frequency. The dominant
factor is the length. Changes in diameter will change the impedance
bandwidth but not the resonant frequency (very much).
The K-factor graph can be derived semi-analytically - there are several
analytical expressions for the complex impedance of an antenna (and you
can solve for where X is zero) over a restricted range. Or, you can
numerically integrate the field equations - which is what people have
been doing since the late 1800s.
That whole "self capacitance end effect" is a hand-wavey thing that is a
conceptual explanation that isn't particularly accurate, but does seem
to work.
As Dave says - the way you solve this is to use a method of moments code
(like NEC and its ilk) which numerically integrates the electric field
equation.
EZNEC (and NEC) do not model "capacitance" per-se. What they model is
the current induced in a small piece of the antenna by the currents
flowing in all the other pieces of the antenna, subject to the
constraint that the voltages on the ends of connected pieces are the same.
It basically sets up a huge set of simultaneous equations (the
admittance matrix) and then solves it.
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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