"If you look at HOW an inductor works, the current flowing in one
terminal ALWAYS equals the current flowing out the other terminal."
I think that is true. If you define current as electron flow, then the fields
and radiation that a large coil may be subjected to, will not increase or
decrease the number of electrons that the coil contains. As such, the amount
of electrons entering the base of the coil, will equal the same number exiting
the coil, with time displacement.
I think you've just proven that all antennas must have a constant
current distribution on their driven element... the same argument can
probably be made about a piece of straight wire!
More generally: I'd like to propose a thought experiment, which I
think may cause you to reconsider your conclusions.
The experiment: start with a straight length of wire 1/4 wavelength
long (minus a bit) at a frequency of interest. Install it over an
infinite ground plane and feed it at the base. You've got a resonant
"1/4 wavelength" monopole.
I think most people will agree that the net-current distribution in
said monopole is tolerably close to being a cosine function - highest
at the feedpoint, and lowest near the tip.
Mark two positions on the wire, 1/3 and 2/3 of the way along its
length. Consider the three sections of wire to be the "base", "mid",
and "tip" sections.
I think most people will agree that the net currents at the two ends
of the "mid" section are not equal. We haven't changed the
cosine-like current distribution by simply marking the third-of-the-
way points.
Now... take the "2/3" point, and pull it back (or down) towards the
base of the antenna, by some small amount... say, 1% of the length of
the "mid" section. Leave the "1/3" point right where it was. There's
now a small amount of slack in the "mid" wire. Shape the "mid"
section into a small-diameter helix, with uniform spacing between the
turns, so that the helixing of the wire just takes up the slack.
The antenna has now been shortened slightly, and some inductance has
been added to the "mid" section. Add or subtract wire at the end of
the "tip" to bring the antenna back into resonance.
Now... are the net currents at the "1/3" and "2/3" points suddenly
equal? Or, are they still unequal (but perhaps different from what
they were when the mid section was straight)? If unequal, by how much?
Now, continue repeating this process... pull the "2/3" point back
towards the base by the same amount you did before (1% of the original
length of the "mid" section), re-coil the "mid" section into a helix
to take up the slack, adjust the length of the "tip" to re-resonate
the antenna, and re-evaluate the net currents at the "1/3" and "2/3"
points. You can do this "shorten and re-resonate" step a total of 100
times, at which point the "mid" section has no physical length and is
a "pure" inductance. [Let me know what page you find it on in the
Digi-Key catalog, please!]
You may use any strategy you wish for deciding how many turns are in
the helix at each step, and what its diameter is at each step, as long
as you're consistent and as long as all of the slack is used up each
time.
So... we now have a total of 101 sets of measurements... all the way
from "mid is a straight length of wire" to "mid is a pure inductance
having no physical length". We could graph "difference in net current
between points 1/3 and 2/3" on the Y axis, and "number of shortening
steps taken" along the X axis.
Question: exactly how many shorten/re-coil/re-trim steps must we go
through, before the net currents at the two ends of the mid-section /
helix / coil become the same (mathematically identical, assuming zero
resistance in the wire)?
--
Dave Platt AE6EO
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http://www.radagast.org/jade-warrior
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