Topband: Modeling "Ground" and losses

[Richard Fry]

Comments to two earlier posts by separate posters (clips below):

> But if indeed a less lossy ground means that fewer radials are needed to 
> be placed in the field, then the coupling to the less lossy ground is 
> greater which I would expect to mean more loss in the radial field which 
> would then require more radials to reduce the effect.  I agree that 
> radials shield the field from the earth; however it seems that it is not 
> quite as simple as it first seems.

> I agree with Tom's analysis -- a good radial system SHIELDS the field from 
> the earth, returning the field and the IN PLACE OF the lossy earth. 
> Studying N6LF's excellent work lit up the light bulb for me in several 
> ways.  First, by noting that current in a radial inductively couples to 
> the lossy earth underneath it, which dissipates power.
_____________

The source of the r-f current flowing on buried radials is the r-f current 
flowing in the earth as a result of radiation from the vertical monopole. 
Current is not "lost" to the earth from the buried radials.  Instead, 
current _ enters_ the radials from the earth around them, because the radial 
wires provide a lower resistance path back to the 2nd terminal of the 
antenna system than does the earth.

The r-f resistance of a set of buried radials is a circuit element in series 
with the r-f current flowing on a monopole.  That is why it is important to 
system radiation efficiency for that r-f resistance to be as low as 
possible.

The concepts in my statements above are not original to me.  They are based 
on the publications of Dr. George H. Brown, Dr. Frederick E. Terman, Edmund 
Laport, and other authors of antenna engineering textbooks and papers.

Below are some supporting clips from the textbooks of G. Brown, F. Terman 
and E. Laport.

Please note that none of these authors writes that the function of buried 
radial wires is to act as a shield.

>From G. Brown et al, "Ground Systems as a Factor in Antenna Efficiency," 
Proceedings of the Institute of Radio Engineers, Volume 25, Number 6 -- June 
1937, page 757:

\\ The earth currents are set up in the following manner. Displacement 
currents leave the antenna, flow through space, and finally flow into the 
earth where they become conduction currents. If the earth is homogeneous, 
the skin effect phenomena keep the current concentrated near the surface of 
the earth as it flows back to the antenna along radial lines. Where there 
are radial ground wires present, the earth current consists of two 
components, part of which flows in the earth itself and the remainder of 
which flows in the buried wires. As the current flows in toward the antenna, 
it is continually added to by more displacement currents flowing into the 
earth. It is not necessarily true that the earth currents will increase 
because of this additional displacement current, since all the various 
components differ in phase. //

>From F. Terman, "Radio Engineers' Handbook,"  First Edition (1943), page 
842:

\\ Loss Resistance—Ground Systems ...   Ground losses arise from the fact 
that the current charging the capacity between the antenna and ground ?ows 
through the capacity from the antenna to the earth and then back through the 
earth to the grounding point at the transmitter. The earth is a relatively 
poor conductor, so special provision must be made for returning these 
currents to the grounding point on the transmitter with a minimum of loss. 
One way of accomplishing this is to bury wires near the surface of the earth 
for the purpose of providing a low resistance path through the ground back 
to the transmitter. In order to be effective, these buried wires must be so 
arranged that the charging currents entering the earth have only a small or 
moderate distance to travel through the earth to reach a wire. //

>From E. Laport, "Radio Antenna Engineering,"  McGraw-Hill (1952), pages 
115-118:

\\ 2.5. Ground Systems for Broadcast Antennas
Antenna performance is standardized with reference to the ground being a 
perfectly conducting flat plane. Such an assumption serves a very useful 
purpose in revealing the ultimate possibilities of a certain radiator in 
terms of its dimensions and longitudinal and sectional geometry at a given 
frequency. All practical deviations from this norm are due to a number of 
empirical circumstances, of which one is the earth itself.

A line of electric force (displacement current) extends from the top of the 
antenna through surrounding space to the earth. Upon entering a perfectly 
conducting earth it becomes a conduction current which returns to the base 
of the antenna and becomes a portion of the antenna current. The electric 
lines of force of the antenna field are thus seen to be the continuation 
current of a closed circuit through surrounding space.  With a perfectly 
conducting earth, the electric line of force is always normal to the 
surface. When the earth is imperfectly conducting, the line of force tilts 
forward in the direction of propagation. This means that the Poynting vector 
at the surface of the earth is tilted downward and has a component that 
points into the earth where it is dissipated. The component parallel to the 
earth represents the power propagated onward in the half space above the 
ground.

A vertical radiator above natural earth without any sort of ground system, 
energized by an electromotive force between the antenna and the earth, would 
require all earth currents to return to the antenna through a very imperfect 
conductor.  When a plane electromagnetic wave with its electric field normal 
to the direction of propagation impinges upon the surface of an imperfect 
dielectric, the power propagated into the dielectric sets up conduction 
currents and displacement currents, both in quadrature to each other.  The 
ratio of the two is dependent upon the frequency, the conductivity, and the 
inductivity. At the lowest radio frequencies, conduction currents are very 
large with respect to the displacement currents, permitting the latter to be 
neglected. With increasing frequency, displacement currents become more 
important relatively, and eventually a frequency is reached where 
displacement currents predominate over conduction currents.

The earth currents return to the base of a vertical antenna along radial 
lines. At the base of the antenna, all the ground currents add together to 
enter the antenna as the antenna current. The total ground loss is the 
integrated losses at all points due to all the returning ground currents. 
In ordinary soils this loss is considerable, and measures have to be taken 
to minimize ground loss by the use of systems of buried radial wires that 
conduct the returning ground currents to the base of the antenna through 
high-conductivity circuits.

The distance from the antenna at which returning ground currents are of such 
a low value as to be negligible is of the order of 0.5 wavelength.  Beyond 
about 0.4 wavelength, the gain in efficiency with increased length is seldom 
a good economic investment, when a sufficiently large number of radials is 
used.

Systematic measurements have shown that the effective length of a buried 
wire decreases as the number of radial wires is decreased. Ground resistance 
decreases as both the length and the number of buried radial wires are 
increased. However, when the number of radials exceeds 120 and their length 
exceeds 0.4 wavelength, one reaches the region of diminishing returns. With 
such a ground system, the circuital and radiational characteristics of a 
vertical radiator of the type used for broadcasting approach very nearly 
those computed from theory for a perfectly conducting earth. //

Sorry for the length of this post, but the information from these authors is 
worth reading and study (IMO).

R. Fry