Richard Clark wrote:

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.

Point being that antenna gain has spatial implications which Rr by
itself could not provide in the solutions.

One should conclude from your results (very nice work, by the way) that
the modeler apparently doesn't figure Xl as contributing to the
radiation resistance. But isn't that basically the crux of the argument
here - whether or not that is in fact the case? If not, then we would
have to conclude that loading coil has zero physical and electrical
length, and that the impedance is constant from one end to the other.
Obviously I could be wrong, but I think those are the assumptions made
in your modeling software. On the other hand, if the impedance of the
coil is not constant from one end to the other, and it in fact does have
some real physical and/or electrical length, then I think the radiation
resistance of the antenna would have to be effected by its presence in
the circuit. That is, if indeed Ro is the integral of disributed r
along the entire physical and/or electrical length of the antenna
(credit for that formula going to an esteemed contributor to this
newsgroup earlier today). Or perhaps more concisely put, if the loading
coil itself contributes to the field radiating from the antenna, then it
should likewise have a Rr associated with it. The converse would of
course still be true.

73, Jim AC6XG