Alan Peake wrote:

If one were to find lossless material (superconductors?) for the short
antenna and it's corresponding matching network, what would happen as
the antenna became shorter and shorter compared with the half-wave
dipole? Would it simply approach an isotropic radiator?
Alan

No. The answer can be found in any antenna textbook, because the
lossless short dipole is a very good platform to illustrate a number of
principles without the confounding additional consequences of loss.

Briefly,

-- The pattern of an infinitesimally short dipole is very similar to
that of a half wave dipole. The difference is due to the triangular
current distribution of the short dipole as opposed to the sinusoidal
current distribution of the half wave dipole. Because the patterns are
very similar and both antennas radiate all the applied power, the gain
of the two antennas is nearly the same. The short dipole's pattern is a
little fatter so it has slightly -- about a half dB -- less gain. But
the pattern of even an infinitesimally short dipole retains the basic
two-lobed dipole shape with around 1.7 dB gain over isotropic in its
favored directions.

-- The input resistance of the very short lossless dipole is very low
and the capacitive reactance very high. The resistance approaches zero
and the reactance negative infinity as the length approaches zero.
There's no comparison to an isotropic radiator, since the latter is a
purely fictional source with no even theoretical physical realization
and therefore no definable input characteristics.

-- The Q of the short dipole is very high, so the reactance varies very
rapidly with frequency. A matched short antenna would have an extremely
narrow bandwidth.

Most of these properties of the dipoles can easily be observed with the
free EZNEC demo program from http://eznec.com, and much more information
about the properties of the short lossless dipole can be found in any
antenna text.

Roy Lewallen, W7EL