On another website I posted the text below, and thought some readers here might be interested also.
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All monopoles need an electrical reference point to be "driven against."
Using a symmetrical arrangement of two or more 1/4-lambda-resonant, horizontal wires elevated sufficiently above the earth provides that by acting at their junction under the base of the monopole as a point with constant electrical characteristics with respect to the current flowing in the antenna system.
NEC shows the peak free-space gain of such a system using a 1/4-wave monopole to be the same as that of a 1/2-wave dipole in free space, e.g., 2.15 dBi. When that system is operating within a few electrical degrees above a perfect ground plane then the peak gain rises to 5.15 dBi, because all of the radiation is re-directed/confined to one hemisphere.
Horizontal wires lying on, or buried several inches below the surface of the earth do not have the same electrical characteristics or function as when they are elevated. Instead, they serve to collect the r-f currents generated by the displacement field radiation of the monopole -- which currents flow in the earth out to about 1/2 wavelength from the base of the monopole.
If the earth was a perfect conductor then those currents could travel through the earth without loss, and a single, short ground rod could serve as an electrical reference point for the r-f current flowing in the antenna system. The sum of those r-f currents flowing in the earth around the monopole, and collected by that ground rod will be equal to the base current in a 1/4-wave, series-fed monopole. The gain of this configuration is 5.15 dBi, the same as when using a few elevated, resonant wires as a counterpoise.
But the earth is not a perfect conductor. For that reason it is necessary, when using buried radials, to install enough of them in the surface area out to about 1/2 wavelength to collect those r-f currents before they have traveled through much of the lossy earth to reach those wires.
The benchmark 1937 I.R.E. paper of RCA's Brown, Lewis and Epstein showed that 113 x 0.412-lambda buried radial wires used with monopoles of about 45 to 90 degrees in height produced a radiated groundwave field when measured at 3/10 of a mile that was within several percent of the theoretical maximum for a perfect monopole radiator with a zero-ohm connection to a perfect ground plane -- and this despite the fact that earth conductivity at/near their test site was not better than 4 mS/m.
As an aside: NEC analyses for far-field conditions show an elevation gain of zero in the horizontal plane for a monopole over real earth, and peak relative field gain at some elevation angle above the horizontal plane. However the radiated, relative fields that exist at, and relatively close to the edge of the near-field boundary of the radiation hemisphere of all monopoles of 1/4 wavelength and less are very nearly equal to the cosine of the elevation angle -- which value is 1.0 at zero degrees (the horizon), and zero at the zenith. If they were not, then the fields measured by BL&E would be much different than they recorded in their 1937 paper (see clip at http://i62.photobucket.com/albums/h85/rfry-100/G.gif ).
It is only after those fields propagate a significant distance over a real earth path that they depart significantly, and progressively more significantly with distance, from the relative fields described by the cosine value of the elevation angle.
RF
________________
All monopoles need an electrical reference point to be "driven against."
Using a symmetrical arrangement of two or more 1/4-lambda-resonant, horizontal wires elevated sufficiently above the earth provides that by acting at their junction under the base of the monopole as a point with constant electrical characteristics with respect to the current flowing in the antenna system.
NEC shows the peak free-space gain of such a system using a 1/4-wave monopole to be the same as that of a 1/2-wave dipole in free space, e.g., 2.15 dBi. When that system is operating within a few electrical degrees above a perfect ground plane then the peak gain rises to 5.15 dBi, because all of the radiation is re-directed/confined to one hemisphere.
Horizontal wires lying on, or buried several inches below the surface of the earth do not have the same electrical characteristics or function as when they are elevated. Instead, they serve to collect the r-f currents generated by the displacement field radiation of the monopole -- which currents flow in the earth out to about 1/2 wavelength from the base of the monopole.
If the earth was a perfect conductor then those currents could travel through the earth without loss, and a single, short ground rod could serve as an electrical reference point for the r-f current flowing in the antenna system. The sum of those r-f currents flowing in the earth around the monopole, and collected by that ground rod will be equal to the base current in a 1/4-wave, series-fed monopole. The gain of this configuration is 5.15 dBi, the same as when using a few elevated, resonant wires as a counterpoise.
But the earth is not a perfect conductor. For that reason it is necessary, when using buried radials, to install enough of them in the surface area out to about 1/2 wavelength to collect those r-f currents before they have traveled through much of the lossy earth to reach those wires.
The benchmark 1937 I.R.E. paper of RCA's Brown, Lewis and Epstein showed that 113 x 0.412-lambda buried radial wires used with monopoles of about 45 to 90 degrees in height produced a radiated groundwave field when measured at 3/10 of a mile that was within several percent of the theoretical maximum for a perfect monopole radiator with a zero-ohm connection to a perfect ground plane -- and this despite the fact that earth conductivity at/near their test site was not better than 4 mS/m.
As an aside: NEC analyses for far-field conditions show an elevation gain of zero in the horizontal plane for a monopole over real earth, and peak relative field gain at some elevation angle above the horizontal plane. However the radiated, relative fields that exist at, and relatively close to the edge of the near-field boundary of the radiation hemisphere of all monopoles of 1/4 wavelength and less are very nearly equal to the cosine of the elevation angle -- which value is 1.0 at zero degrees (the horizon), and zero at the zenith. If they were not, then the fields measured by BL&E would be much different than they recorded in their 1937 paper (see clip at http://i62.photobucket.com/albums/h85/rfry-100/G.gif ).
It is only after those fields propagate a significant distance over a real earth path that they depart significantly, and progressively more significantly with distance, from the relative fields described by the cosine value of the elevation angle.
RF