Roy, David:

[snip]
It could also be accomplished numerically on a computer by using a
program [like the NEC programs] based on solving Maxwell's partial
differential equations iteratively.

As far as I know no one has ever attempted to do this... and
notwithstanding the possibility for "invention" or "discovery" I might
ask, why would one want to do this?

Hey it might make a good Ph.D. or M.Sc. thesis... but what is the
practical application?

It would be one of the easiest degrees ever attained. NEC-4 allows setting
the primary medium to any (reasonable) value of conductivity and
permittivity, so you can have the answer in seconds with a free space
analysis. Alternatively, you can bury the antenna deep in NEC-4's ground
medium and define the ground characteristics for your test.

I did a short consulting job a while back for some people interested in
transmitting RF for short distances under water. Immersing the antenna
eliminates the substantial signal loss incurred by reflection at the
air-water interface when the antenna is out of the water. And antenna
system design requires knowledge of the antenna feedpoint Z. I've seen
numerous papers in the IEEE publications about antennas immersed in other
media such as a plasma, and know that antennas buried in the ground are
used. So it's of considerable practical interest.

Roy Lewallen, W7EL
[snip]

Well thanks for that input Roy, that's very interesting and of course a
useful application.

But for the "thesis" idea I was thinking of something a little more
"challenging", e.g.

Clearly the antenna "driving point impedance" Z = R +jX is a complex
function f (Zo) of the "characteristic impedance" Zo, where in general Zo =
Ro +j Xo = sqrt[u/e] of the medium in which the antenna is immersed.

Clearly this function f(Zo) is the "transducer" function that David [The OP]
was seeking.

It's clear of course that f(zo) will also be a function of complex frequency
p = s + jw.

Now expressing this functionality as:

Z(p, Zo) = f (p, Zo)

One might ask [the thesis candidate, (grin)] to derive/discover and tell
us...

What. precisely, is the functional form of this complex "transducer"
function f that takes Zo to Z [377 Ohms to 73 Ohms! (grin)]

Is f(Zo) a simple linear function? [e.g. like a transformer turns ratio as
the OP David had asked] or perhaps... A non-linear function? or maybe... A
differential or integral relationship?

What?

Except for a few isolated niche applications, such as those you mentioned
having consulted on, I can't really think of any practical applications that
demand knowledge of the functional form of "f".

Which is likely why this subject is not mentioned in antenna textbooks or
widely discussed. i.e. No one ever needed to know it and so no one worked
out this relationship or even investigated it... Simply a matter of supply
and demand (grin)! We have Ohm's Law and other such well known
relationships such as V = IR because there was a demand by "scienticulists"
(grin) to know these relationships to do real Engineering, i.e. build stuff
they needed out of stuff they could get.

The discovery of the functional form "f" of this relationship might perhaps
be at least suitably hard for a Master's Thesis, a good challenge, and I
believe that it is suitably "academic", since there is very little use for
it (grin).

What exactly is "f (Zo)"?

Thoughts, comments.

--
Pete k1po
Indialantic By-the-Sea, FL