On Thu, 04 Nov 2004 20:38:35 -0700, Wes Stewart
wrote:

Or, model a short lossless monopole over perfect ground and determine
the feedpoint R. In this case, R is totally due to radiation loss,
i.e. "radiation resistance." Add a lossless loading inductance
somewhere in the middle and see what happens to R.

Hi Wes,

The difference between the two (perfect/real) insofar as Z is hardly
remarkable.

First I will start with a conventionally sized quarterwave and by
iteration approach the short antenna and observe effects. I am using
the model VERT1.EZ that is in the EZNEC distribution and modifying it
by turns. For instance, I immediately turn on the wire loss.

40mm thick radiator 10.3 meters tall:
Impedance = 36.68 + J 2.999 ohms
which lends every appearance to expectation of Rr that could be
expected from a lossless perfect grounded world.
Best gain is
-0.03dBi

next iteration:

cut that sucker in half:
Impedance = 6.867 - J 301 ohms
which, again, conforms to most authorities on the basis of Rr.
best gain
0.16dBi
How about that! More gain than for the quarterwave (but hardly
remarkable). This makes me wonder why any futzing is required except
for the tender requirements of the SWR fearing transmitter (which, by
the way, could be as easily taken care of with a tuner).

next iteration:

load that sucker for grins and giggles:
load = 605 Ohms Xl up 55%
Impedance = 13.43 + J 0.1587 ohms
Did I double Rr? (Only my hairdresser knows.)
best gain
0.13dBi
Hmm, losing ground for our effort, it makes a pretty picture of
current distribution that conforms to all the descriptions here (sans
the balderdash of curve fitting to a sine wave). I am sure someone
will rescue this situation from my ineptitude by a better load
placement, so I will leave that unfinished work to the adept
practitioners.

next iteration:

cut that sucker down half again (and remove the load):
Impedance = 1.59 - J 624.6 ohms
Something tells me that this isn't off the scale of the perfect
comparison.
best gain:
0.25dBi
Hmm, the trend seems to go counter to intuition.

next iteration:

-sigh- what charms could loading bring us?
load = 1220 Ohms Xl up 55%
Impedance = 3.791 + J 1.232 ohms
more than doubled the Rr?
best gain:
0.23dBi

Now, all of this is for a source that is a constant current generator;
we've monkeyed with the current distribution and put more resistance
(Rr?) into the equation with loading; and each time loading craps in
the punch bowl.

So much for theories of Rr being modified by loading. I would
appreciate other effort in kind to correct any oversights I've made
(not just the usual palaver of tedious "explanations" - especially
those sophmoric studies of current-in/current-out).

73's
Richard Clark, KB7QHC