Yes, "resistance" is traditionally used to mean the real part of an
impedance, which in turn is expressed as a complex number. An equivalent
circuit for an impedance is then a series R - X, with the R and X
corresponding to the real and imaginary parts of the impedance
respectively. Parallel equivalents are of course also used, but usually
explicitly described as a parallel equivalent, or given as a complex
admittance (G + jB, with G and B representing the shunt conductance and
susceptance).

As an antenna gets smaller, the impedance does rise, causing a
requirement for more voltage for a given power. The rise, however, is
due to increasing (series) reactance, not radiation resistance. If you
make the antenna long enough to reach resonance, then continue making it
longer, the impedance again rises until you hit "anti-resonance"
(parallel resonance). In that region it's due to both an increasing
reactance and an increasing radiation resistance.

A real consequence of the low radiation resistance of a small antenna is
that the conductor current is very high for a given applied power. This
results in increased I^2 * R loss in the conductors. The loss can be
very substantial in small antennas.

Roy Lewallen, W7EL

John Larkin wrote:
On Wed, 17 Sep 2003 15:41:33 -0700, Roy Lewallen
wrote:


Well, actually, no. The radiation resistance generally decreases as an
antenna gets smaller, assuming it's small compared to a wavelength.

Roy Lewallen, W7EL



At any given frequency, you can analyze the impedance of a small
antanna as a series R-C or a shunt R-C. Viewed as a shunt resistance,
Rr increases as the antenna gets smaller, and as a series network, it
gets smaller.

I guess the standard convention must be to treat Rr as a series
element, so it gets smaller as the antenna gets smaller.

Either way, it takes more volts (or, if you prefer, more amps) to
force a small antenna to radiate as much as a larger one.

John