wrote:

If you plot the feedpoint Z over frequency as R and X on a
rectangular scale (not a Smith chart), you get a spiral. thin
antennas have a big spiral crossing the R axis at X=0 very steeply
(implying narrow match bandwidth), while fat antennas have a smaller
diameter spiral.

As someone else has pointed out, the spiral eventually converges to
something like R=377 when frequency is very high.
. . .

377 ohms is the impedance of free space, which is the ratio of E to H
fields of a planar TEM wave. People keep looking for this value when
dealing with antenna impedances, apparently due to the common
misconception that antennas are "transformers" of some sort to "match"
the impedance of free space (an E/H ratio) to a transmitter impedance (a
V/I ratio).

Quite a few people have tackled the problem of the impedance of an
infinitely long dipole. In _Antennas and Waves_, King & Harrison
conclude (p. 234) that the impedance is approximately 214 - j189 ohms.
However, this requires extrapolation from calculated and measured
results, since convergence is extremely slow. In _Antennas_, Kraus's
analysis doesn't show convergence, but it's based on a simpler theory
which I don't believe is as complete. Because it's not of much practical
interest, most of the analyses appear in academic papers rather than
antenna textbooks. It's not at all a trivial problem.

Roy Lewallen, W7EL

Roy Lewallen wrote:

...
377 ohms is the impedance of free space, which is the ratio of E to H
fields of a planar TEM wave. People keep looking for this value when
dealing with antenna impedances, apparently due to the common
misconception that antennas are "transformers" of some sort to "match"
the impedance of free space (an E/H ratio) to a transmitter impedance (a
V/I ratio).
...
Roy Lewallen, W7EL

I believe the "misconception" is that the E/H fields induced by the
injection of an electromagnetic signal into the media (ether) ARE the
properties of the ether; I don't believe they are.

Rather, these fields are only the effect of the affect ...

Regards,
JS