Richard Fry wrote:

Could you please explain why, if the same fundamental equations given
in antenna engineering textbooks and I.R.E. papers are used by
modeling programs, the results of their use do not always support each
other very well?

I'm not aware of any cases where engineering textbooks and papers
disagree with modeling programs. NEC, for example, has been very
extensively tested against both theory and measurement. If there are
cases where the programs seem to disagree with theory, it's very likely
due to careless modeling resulting in a model which isn't the same as
the textbook model. Can you cite an example of disagreement between
computer model and textbook theory?

If it is accepted that the radiation resistance of a short monopole is
independent of the loss resistance in the loading coil and r-f ground
either alone or together, then what is the basis for the variation in
radiation resistance that you report?

It is indeed accepted that the radiation resistance of a monopole over a
perfect ground of infinite extent has the characteristics you ascribe,
and computer models show this independence as they should. (I haven't
yet received your model which you feel seems to show differently.) But
it's neither true nor "accepted" when the ground system is much less
than perfect. The variation is due to interaction between the vertical
and ground system, just as the radiation resistance of a VHF ground
plane antenna changes as you bend the radials downward. Altering the
number, length, depth, and orientation of radials has more of an effect
than simply adding loss.

BTW, the equations in the Carl Smith paper I referred to earlier in
this thread produce a radiation resistance of 0.113 ohms for a 1.65
MHz, 9.84' (3-m) x 0.25" OD, base driven monopole -- which is not
_hugely_ different than the values calculated by EZNEC.

EZNEC gives a result of 0.1095 ohm with 20 segments, converging to
around 0.103 ohms with many more segments. Keep in mind that the model
source position moves closer to the base as the number of segments
increases.

The author's result is good. If you examine the paper carefully, I'm
sure you'll find that the author had to make some assumptions and
approximations to arrive at his equations -- the most fundamental
equations can't be solved in closed form, and many, many papers and
several books were written describing various approximations to
calculate something as basic as the input impedance of an arbitrary
length dipole. If you do some research, you'll find that the many
different approximating methods all give slightly different results. The
small disagreement in the cited paper is really a measure of how good
his approximations were. Modeling programs have to use numerical methods
which are limited by quantization, but they have the advantage of not
needing the various approximation methods required for calculation by
other means.

Roy Lewallen, W7EL