This topic is a hot one in ham literature. The most common information is a tabulation of gain relative to number of radials. This is used to point out the benefit of relatively few elevated radials compared with the relatively large numbers used for ground plane vertical antennas. Tuning is ordinarily dealt with by angling radials downward at 45°.
Yet we see commercial vertical antennas that do not angle radials.
Hy-Gain Super-Penetrator, MFJ Pulsar TM, MFJ-1756 6-meter vertical. We see verticals with only 3 very short, slightly sloped radials like the Diamond X-series. Or with 8-radials at extreme angle like the their Discone Base Antennas. Or the MFJ-1790 10-meter vertical with only 2- radials at 90°.
What do they know that we don't?
Perhaps one of the reasons for the lack of in-depth public information is the relative difficulty involved in conventional antenna modeling. To overcome this, a special type of antenna model was developed using spherical geometry. This allows one or many radials to be modeled...
For these studies, the 4NEC2 antenna model first establishes the length of a resonant vertical half-wave dipole as a reference. As radials are added or angled, the resonant length changes. Accordingly, the results of each run is based on the computer model finding the % change in length that gives the best SWR and impedance in a particular configuration.
4NEC2 Antenna Models: 1-Radial 2-Radials 3-Radials 4-Radials 6-Radials 8-Radials
From these models it is now possible to find out-
What happens if...
we start with a standard vertical monopole
and systematically add 1, 2, 3, 4, 6 and 8 radials.
The standard conditions are: #14 wire for the antenna and a feed-point at 1/2 wavelength over ground.
We begin with 1-Radial at 90° A 50-50 ratio, bent dipole commonly called an "L-Antenna".
Table 1 gives the downward radial Angle° that produces an impedance of 50 Ohms.
Looking at the tabulated antenna characteristics note that:
Low impedance can also be adjusting by the vertical/radial Ratio. This off -center feed approach makes the vertical taller and gives a good match for coaxial cable.
Table 2 gives the off-center feedpoint Ratio (OCF) to produce an impedance of 50 Ohms.
Comparing the resulting antenna characteristics of Table 2 with Table 1, note that:
There is an interesting interplay between the total length of the vertical+radial and the number of radials. Take a close look in Figure 1 below.
Notice that the 8-Radial configuration has the shortest radials, about a tenth of the resonant length, but the vertical is only about 7/10ths, not 9/10ths as one might expect. The apparent discrepancy is because the % Length at resonance is only 80.31% of the 100% Reference Dipole length. All of the Vertical-Radial bars below represent the % Length listed in Table 2.
Up to this point, tuning has been studied by angling radials or lengthening the vertical. There remains the question of what happens when both methods are combined?
The answer appears to be a cone-like antenna.
Modeling a vertical/radial Ratio of 0.6, the angle for 3,4,6,and 8-radials all converged on 20° down-angle. Gain was 1.69, 1.87, 1.97 and 2.06 dBi respectively... the highest so far. The SWR match for coaxial cable was 1.01 for 3- radials, 1.07 for 4-radials, 1.13 for 6-radials and 1.16 for 8-radials.
This suggests that a perfect match to coax can be found for
any number of radials by adjusting the vertical/radial Ratio.
A confirmatory study for 8-Radials at 20° found a 50 ohm match at a vertical/radial Ratio of 0.522. Resonant Length: 93.3% of a dipole. A wide band-width: 5.6% under 2 SWR. Omni-directional beam-width: 20° centered at 15° elevation above horizon. Gain: 2.19 dBi. (65% greater than a vertical dipole).
Radials that are physically identical may not be RF identical. If anything interacts with any part of the radials, that radial or radials will no longer be resonant. The tuning will change and the balance in RF current will shift - often to concentrate in the most resonant radial. The radiation will no longer be omni-directional. The far field radiation pattern will be skewed in the direction of the concentrated RF.
Dick Reid, KK4OBI at qsl.net