The input impedance of 26 radials is NOT equal to all 26 connected in
parallel. There is a non-linear relationship between the number N and
input impedance because they share the same volume of soil at least
when they are short.

For 26 radials the resonant effects have disappeared which I cannot
explain. Yet attenuation is the same, Zo converges on Zin at
approximately 8 or 10 metres as before.

You appear to have automated the results. Can you do a large number
of radials, say around 100, from 0.4 to 8.0 metres?

And can you do a small number of radials such as 6 or 8, from 0.4 to
8.0 metres?


Reg,

Here is the analysis of an 8 radial system. All other parameters
the same:

0.4 m -- Radial Z = 65.4 - j 58.1 -- Efficiency 11.2%
0.6 m -- Radial Z = 48.7 - j 55.4
0.8 m -- Radial Z = 39.8 - j 29.6
1.0 m -- Radial Z = 34.2 - j 23.5
1.2 m -- Radial Z = 30.2 - j 19.2
1.4 m -- Radial Z = 27.2 - j 16.1
1.6 m -- Radial Z = 24.9 - j 13.7
1.8 m -- Radial Z = 23.0 - j 11.7 -- Efficiency 19.4%
2.0 m -- Radial Z = 21.3 - j 10.0
2.2 m -- Radial Z = 19.9 - j 8.5
2.4 m -- Radial Z = 18.7 - j 7.1
2.6 m -- Radial Z = 17.7 - j 5.9
2.8 m -- Radial Z = 16.7 - j 4.6
3.0 m -- Radial Z = 15.9 - j 3.5
3.2 m -- Radial Z = 15.2 - j 2.3 -- Efficiency 22.4%
3.4 m -- Radial Z = 14.7 - j 1.1
3.6 m -- Radial Z = 14.3 + j 0
3.8 m -- Radial Z = 14.0 + j 1.1
4.0 m -- Radial Z = 13.9 + j 2.2 -- Efficiency 23.2%
4.2 m -- Radial Z = 13.9 + j 3.2
4.4 m -- Radial Z = 14.1 + j 4.2
4.6 m -- Radial Z = 14.4 + j 5.0
4.8 m -- Radial Z = 14.7 + j 5.7
5.0 m -- Radial Z = 15.2 + j 6.3 -- Efficiency 23.0%
5.2 m -- Radial Z = 15.6 + j 6.7
5.4 m -- Radial Z = 16.1 + j 7.1
5.6 m -- Radial Z = 16.5 + j 7.3
5.8 m -- Radial Z = 16.9 + j 7.4
6.0 m -- Radial Z = 17.2 + j 7.5
6.2 m -- Radial Z = 17.5 + j 7.5 -- Efficiency 22.5%
6.4 m -- Radial Z = 17.8 + j 7.5
6.6 m -- Radial Z = 18.0 + j 7.4
6.8 m -- Radial Z = 18.1 + j 7.4
7.0 m -- Radial Z = 18.3 + j 7.4
7.2 m -- Radial Z = 18.4 + j 7.3
7.4 m -- Radial Z = 18.4 + j 7.3
7.6 m -- Radial Z = 18.5 + j 7.2
7.8 m -- Radial Z = 18.6 + j 7.2
8.0 m -- Radial Z = 18.6 + j 7.2 -- Efficiency 22.4%

Note that after 4 m the antenna efficiency starts to drop,
which is not the case for large numbers of radials.

Now I have to figure out the best way to model a 100
radial system.

Frank