The only radials on which resonance is truly effective, whether they be
coil-loaded or not, are the elevated variety. ie., those which are roughly
1/10 wavelengths or more above ground level. At lower levels the loss
induced in the ground or in the loading coils, although perhaps not
immediately apparent, can be undesirably high.

Radial proximity to the ground has two effects - first is the obvious loss
induced in the ground due to soil resistivity. Second is the more insidious
reduction in propagation velocity along the radials due to soil permittivity
which makes a mess of the resonant frequency.

For low-height radials it is incorrect to use calculated lengths from the
usual formulae. Depending on soil constants (and radial angles) it is
necessary to shorten radials by careful pruning aided by readily available
antenna impedance analysers.

When radials are lying on the ground, with ordinary soils, the propagation
velocity is roughy half of the free-space velocity. Consequently, the
physical resonant length is only half of the value when radials are well
elevated.

But because of the higher loss in radials lying on the ground the pruning to
obtain resonance is much less critical. The resonant Q may be down to 2 or
3.

When radials are buried to a depth of fractions of an inch or more the
velocity factor can fall very fast to as low as 0.1 at the lower HF
frequencies. It depends on moisture content of the soil. Pure water has a
very high dielectric constant (permittivity) of 80.

Incidentally, soil relative magnetic permeabilty, which also affects
velocity factor to the same extent, always remains in the neighbourhood of
unity simply because the pure iron and similar magnetic materials content of
ordinary soil is quite small by volume.

So at HF a buried radial wire (unless in dry Sahara sand) is a high-loss
transmission line with a low velocity factor. Resonance effects are
practically non-existent. For usual length radials line input impedance is
Zo of the line. The lossy effects are due only to the resistive conponent
of Zo. The reactive component is of no consequence because it is tuned out
simultaneously with a vertical antenna reactance.

The resistive component of input impedance of a set of buried radials is a
complicated function of frequency which does not bear a very close
relationship with soil conductivity. So the actual value of soil
conductivity at VLF, even if it is known, and it seldom is, entered in
modelling programs is of little use.

Only at HF, say at 30 MHz and above, in very high resistance soils, do small
resonant effects re-appear. And not surprisingly ground losses decrease
down to values experienced in soils of very low resistivities.

When the soil is an insulator ground losses are zero. Does maximum ground
loss occur when ground resistivity is 377 ohm-metres at which no reflections
occur.

For an approximate analysis of the performance of a set of buried radials,
download program RADIALS2 from website below. Download in a few seconds and
run immediately. You may be pleasantly relieved at the short lengths and
nunber of radials required to acheive a reasonable performance. It won't be
the oft-advertised, magazine magic number of 120 which is divisible by 60,
30, 20, 15, 12, 10, 8, 6, 5, 4, 3 and 2.
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Reg, G4FGQ

Obtain program RADIALS2 from website below.
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Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
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