On Fri, 05 Nov 2004 10:45:57 -0800, Jim Kelley
wrote:

I have a question. Can you express the mathematical and/or physical
relationship between Rr and antenna gain? It would sure help to clarify
the point you were trying to make.

Hi Jim,

I would have thought someone else could, given the bandwidth of
discussion in making the current taper shorter and the constant
current section longer. Testing does not bear their facile
relationship out however, and for the topic of a short antenna
(otherwise, why are we talking about loading coils?) it would seem
that antenna gain is immutable over several octaves below a
quarterwave length.

Of course, I coulda done something wrong. I did use a commonly
available design. I did use a commonly available modeler. I even may
have done the wrong thing in choosing a design that could be evaluated
for free. Perhaps I erred in providing the cogent details of
construction. It took all of 20 minutes to accomplish (far less time
than that expended in theories of current-in/current-out). These
technical hurdles appear to have set the bar too high for my work's
refutation in kind. I appreciate that "it's hard work!" ;-)

To answer your question, if you just abandon the perfect load, then
you stand to achieve a higher gain. If you shorten the antenna, then
you stand to achieve a higher gain. There is no change in Rr with the
addition of Xl. Hence the mathematical relationship for an antenna
shorter than quarterwave would be suggested as:
gain ~ 1/Rr
gain ~ 1/Xl
Rr Z

Don't take this gain to the bank however.

73's
Richard Clark, KB7QHC