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Resonant and Nonresonant Radials
The only radials on which resonance is truly effective, whether they be coilloaded 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 lowheight 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 freespace 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 highloss transmission line with a low velocity factor. Resonance effects are practically nonexistent. 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 reappear. 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 ohmmetres 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 oftadvertised, magazine magic number of 120 which is divisible by 60, 30, 20, 15, 12, 10, 8, 6, 5, 4, 3 and 2.  Reg, G4FGQ 
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Obtain program RADIALS2 from website below.
 .................................................. .......... Regards from Reg, G4FGQ For Free Radio Design Software go to http://www.btinternet.com/~g4fgq.regp .................................................. .......... 
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