Regarding ground level or slightly below ground radials under a vertical
They don't work like a ground plane or counterpoise, in which dimensions
are essential to resonance of the antenna system.
Think of the radials as being one plate of a capacitor. The other plate
is earth. The purpose of the radials, when on or in the ground, is to
couple the feedline to ground, which serves as one element of a dipole
antenna (The vertical is the other element.). They reduce the
resistance losses associated with antenna current in the earth, by
spreading that current over a large area of the ground rather than
letting it be concentrated into a small volume of earth surrounding a
They do not act as resonant antenna elements. Their length is not a
critical part of antenna tuning. Under a 1/4 wave vertical, they are in
the area of highest current density, the area nearest the vertical
element. That is the reason that a limited amount of wire is applied
most effectively in making a large number of short radials, even if they
don't reach very far from the antenna.
The ground currents from multiple vertical antenna elements add, at any
point on the ground, in accordance with the rules for adding currents of
multiple phases, where the phases are referenced to common axes. Those
ground currents are divided between the radial wires and the ground, in
accordance with rules concerning parallel conductors (and accounting for
The ideal ground element under a vertical antenna element would be a
large metal sheet covering the ground for a considerable distance from
the antenna. Under multiple vertical elements, cover all the ground
between and extending beyond the elements. Next best for a single
vertical element is conductive radials, since all the ground currents
flow along radial paths from the antenna. The radial wires offer less
resistive loss than the ground does. If a radial is forked at a
distance from the antenna, the current at the fork will divide between
the two fork elements and the ground, with the net current from the
intersection equaling the current into the intersection. Kirchoff's law
applies, I believe.
In any case, there is a small gain from continuing the radials across
the radial field of another antenna, associated with providing a low
resistance path for the radially directed current, unless the currents
at the intersection happen to sum to zero. There may be another small
gain from connecting them, depending on the net current. If you don't
connect them, they will, nevertheless, be connected via capacitive
coupling between radials and between radials and earth, with some loss
associated with current in earth.
The lifetime of the radials will depend upon the pH of the soil and on
any corrosive environmental effects. In many cases, electric fence
wire, much less expensive than copper and still very effective as ground
radials, is an inexpensive way to put down more than enough radials.
The primary advantage of larger guage radial wire is reduced
susceptibility to mechanical damage and a longer lifetime before
corrosion consumes them.
I'll await more rigorous analysis, perhaps even some calculations, from
those so inclined.
73 de WOØW
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