Reg, thanks for the info. I see I was making an error with RADIALS2. Did
not realize that you had to add the radial impedance to the antenna
impedance; I thought it was computed in the final result. I figured
something was weird since the input impedance was similar to the antenna
modeled over a perfect ground. NEC2 does compute the input impedance of the
complete structure, but as mentioned before it is limited, in that all wires
must be = lambda/1000 above the ground (at 1.8 MHz about 6"). I am just
starting to delve into computational electromagnetics, so do not know that
much about NEC. It uses the "Method of moments" in its computations. The
theory of operation manual is available for download at several web sites.

Anyway, with RADIALS2, I now get an input impedance of 5.1 - j1303, and with
NEC2 2.9 - j1358. I did try entering a negative number for the depth of
the radials, but RADIALS2 did not like it.

Your comments about the effect on the radials of being buried are also very
interesting, and obviously indicate the reason for our slightly different
results. The very low VF of buried radials indicates that the length is
less important.

As for efficiency, NEC2 computes a normalized far E-field at 1 meter. For
phi independent structures it becomes trivial to integrate the power density
over a hemispherical region to arrive at the true total radiated power. 100
Watts into the antenna radiates 27 Watts, again, very close to RADIALS2'
computed efficiency of 23.5%. Come to think of it, I guess I could have
estimated the losses -- as you do -- by comparing the input impedance of an
antenna over a perfect ground with the same antenna over a lossy ground.
Still I think it was more fun playing with Excel spread sheets and coming up
with a similar answer.

Regard,

Frank

"Reg Edwards" wrote in message
...
Frank, as you say, the height of the radials in the NEC2 model is only 6
inches above ground.

The radials are shallow-buried in the RADIALS2 model. It can't do elevated
radials.

The ground loss resistance as height decreases, as seen by the antenna,
increases very fast percentage-wise as the radials get within a few inches
of the ground. It is due to very close magnetic and electric coupling to
ground. Radials are transmission lines, insulated from but running very
close to a resistive slab of soil.

This would account for the computed higher input resistance of the radials
( 3.5 - j*3.3 ohms ) ( for 29, 25-feet long radials. Rg=77, K=13 ) in
program RADIALS2.

The calculated antenna input impedance in RADIALS2 is that of the antenna
alone. For feedpoint impedance add the input impedance of the radial
system.
Presumably, NEC2 does not compute the input reactance of radials.

Efficiency is calculated in the usual way from the sum of antenna input
resistance and radials' input resistance.

If you contrive to change the radials input reactance without changing
frequency or the antenna, you will notice the loading coil tunes it out
along with antenna reactance.

Incidentally, when elevated radials are near the ground their velocity
factor decreases fast which makes a mess of the usual recommendation to
prune them to 1/4-wave free-space length.

When radials are actually lying on the ground surface the velocity factor
decreases to roughly 0.5 of the velocity of light. When buried the
underground VF can fall to as small as 0.15 depending on soil
permittivity.
(or moisture content.)
----
Reg, G4FGQ