Topband: Modeling "Ground" and losses

[Bill N6MW]

As is touched on in a note found on the www with more detail than useful 
here ( http://n6mw.ehpes.com/AntennaGroundLoss3.pdf ) let me make a 
couple of points on ground losses without directly addressing the 
various and sometimes argumentative material posted on TB before.


First the role of "Displacement" currents. D-currents are not from the 
flow of charged particles, the C-currents, AND more importantly they do 
not contribute any losses. D-currents taken together with C-currents 
allows us to talk about continuous current loops for time dependent 
fields but the charm is deceptive. People, even experts, are sometimes 
none too careful in distinguishing D- and C-currents even though some do 
understand. For example, there is talk of the return current near a 
buried radial system flowing from the ground into the ends or sides of 
the radials. The current being referred to outside the wire (in the 
soil) is the sum of C-current and D-current. Here the current densities 
are JC = sigma*E and JD = epsilon*dE/dt. It turns out for the cases of 
interest to us (TB), that the amplitudes of the two currents (which are 
90 degrees out of phase) can be comparable, or not, making 
interpretation more difficult. To be exact, the current density ratio

|JC/JD| = sigma / (K*epsilon_zero*2*pi*freq) where K is the relative 
dielectric constant. So, for example, sigma=.002 S/m, relative 
dielectric K=10 soil gives |JC/JD| =1 at 3.6 MHz. Furthermore, these 
ground currents are pretty widely distributed and so can not necessarily 
be identified as the obvious part of any circuit.


Effects of Really "poor" soil. Consider a vertical monopole with, say, 
four typical horizontal radials in free space. There are essentially no 
ohmic losses. Now add a earth half space slightly below the radials and 
say the conductivity of this earth is vanishingly small ("very very poor 
earth") so the earth is a pure dielectric. There will be no C-currents 
in the earth. And if you bury the radial slightly below the surface (or 
more), still no C-currents in the earth and still no losses! And yet no 
one wants very poor soil?


Effects of a perfectly conducting ground surface: In place of radials, 
if the ground surface is a metal sheet (sea water not good enough) and 
still with a monopole with bottom just above the surface fed in the 
obvious way against the sheet, the soil below the metal sees no electric 
fields, so no C-currents (or D-) in the soil, and there are no ohmic 
losses. This, of course, differs from the Really poor soil case in the 
far field due to the low angle radiation benefits for low loss 
reflecting surfaces at and well away from the monopole. Also note that 
the Really poor soil case loses half of its radiated power down into the 
earth.


The real soil case with a finite number of elevated radials. Thanks to 
the effort of N6LF, it has become accepted (and from personal 
experiment) that (if done right) a small number of elevated radials for 
a vertical is similar in performance to a much larger number of surface 
(or buried) radials, perhaps especially for poor soils. In this case, 
there are E-fields in the ground and thus both D- and C-currents. 
However, these C-currents are not now able to flow into the radials. 
Nonetheless, the C-currents driven in the soil do suffer ohmic losses. 
Still it seems reasonable that since all the wire currents are now some 
distance from the soil, the soil E-fields generated by these currents 
are smaller than for surface or buried radials, giving lower losses. 
This seems to be the accepted reasonable explanation.


The real soil case with a finite number of round radials. The near field 
E-fields at antenna wires are generated by the currents in the wires. 
For non-elevated radials, these are in contact with the soil so at that 
point the E-fields are relative strong. The ohm's law local losses goes 
like sigma*E*E (JC dot E) so IF sigma is fixed (such as when lowering 
the radials to the ground) losses should increase, all else being equal. 
This is consistent with observations. The soil currents completing the 
antenna current loop are now both D- and C- types (depending on sigma) 
and not just from the induced fields of an elevated case - and this is 
also consistent with higher losses (although we are getting close to 
hand-waving now). Now you might guess that since losses go like 
sigma*E*E that larger sigma means larger losses -- this is of course not 
correct and the reason is that the E-fields in the soil are quickly 
reduced with increasing sigma in a non-obvious manner so this can be 
tricky business (Maxwell's equations). And that includes skin depth 
considerations when you to do it all right. Some of this is addressed in 
the note referenced above. As for surface vs buried radials and 
insulated vs non-insulated wire, I have not seen any convincing actual 
data (not models) and opinions are all over the map. However, it seems 
possible that if you have very good soil (high sigma) it might not be 
smart to bury radials a lot relative to the skin depth.


I don't think any of this is in contradiction of the quoted material 
from Brown, Terman and Laport although some of their phrasing might be 
quibbled with along with just what soil property parameter regime they 
are working in. Also, saying that the surface radials shields the ground 
loss seems consistent.


Finally most of our standard antenna models (up to and including NEC4) 
do not claim to provide excellent solutions to Maxwell's equations in 
all of space. Some near field approximations have been made to get, 
primarily, far field performance evaluation. And in this context, using 
loss estimates, based on changes of the peak in the pattern from the 
models, may be a red herring leading away from understanding.


Bill N6MW