Peter O. Brackett wrote:
Well, as we all "know" the current wave on a dipole antenna is exceedingly
close to sinusoidal, but not [exactly] sinusoidal, because if it were
exactly sinusoidal it wouldn't be radiating. That [small] difference
between the actual current distribution on an antenna and the actual current
distribution on a transmission line is the [tell-tale] residual that
separates us from an exact analytic expression for the driving point
impedance of a dipole.

Of course, but for conceptual purposes, both Balanis and
Kraus seem to give us permission to consider the current
distribution to be sinusoidal for "thin-wire" dipoles.
Kraus says: "... it is assumed that the current distribution
is sinusoidal. Current-distribution measurements indicate
that this is a good assumption provided that the antenna is
thin, i.e. when the conductor diameter is less than, say,
lambda/100." Balanis agrees: "If the diameter of each wire
is very small (d lambda), the ideal standing wave pattern
of the current along the arms of the dipole is sinusoidal
with a null at the end."

It would be interesting to compare how closely the input impedance of a 1/2
wave lossless feed line of appropriate Zo (Say 600 Ohms?) terminated in a 73
Ohm resistor would approximate that of a "real" dipole. At resonance it
would be 73 Ohms at least.

Of greater interest might be the construction of a stub using
resistance wire to simulate the "loss" to radiation plus all
the other losses. As one of gurus on r.r.a.a said, "One can
replace the resonant antenna with a dummy load without changing
anything." :-)
--
73, Cecil http://www.w5dxp.com