This is a discussion of the modeling results for a standard vertical monopole with 1,2,3,4,6 or 8 elevated radials.

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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...
1. On any compass setting
2. At any up-down angle
3. At any ratio of the length of a resonant antenna
This makes it easy to set one element as the vertical and one or more elements as radials.

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.

From these models it is now possible to find out-

What happens if...

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".
• The resonant length is 2.54% longer than a vertical dipole and the impedance is only around 42 ohms or 1.2 SWR at best
• The radiation pattern has 4.3 dBi gain on the side with the radial and -4.5 dBi quieting on the back
• % radiation efficiency is the highest of any radial configuration: 58.6%
• Compare this with 36% and 1.33 dBi gain for a vertical dipole
The 42 ohm impedance at the 0.5 ratio can be adjusted by angling the radial(s) downward to give a good match for coaxial cable.

Table 1 gives the downward radial Angle° that produces an impedance of 50 Ohms.
Looking at the tabulated antenna characteristics note that:
• 45° downward angle works only for 2- or 3- radials at this elevation, otherwise use 40°.
• Gain increases slightly as the number of radials increase from 2 to 6.  Not for 8-Radials.
• % Effic. and Gain for 1-Radial angled at 76.5° is still high because of the stronger radiation towards the radial-side half-circle.
 Table 1 Angle° Ratio % Length % Effic. Gain dBi Side dBi Pattern 1-Radial 76.5 0.5 101.81% 55.41 3.47 -2.8 half-circle 2-Radials 45 0.5 99.82% 41.06 1.32 1.04 oval 3-Radials 45 0.5 99.12% 41.82 1.33 1.27 circular 4-Radials 40 0.5 98.24% 42.27 1.49 1.49 circle 6-Radials 40 0.5 97.66% 43.21 1.72 1.72 circle 8-Radials 40 0.5 97.34% 43.64 1.66 1.66 circle

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:
• 1-Radial now has the longest % Length compared to the vertical arm.
• % Effic. and Gain for 1-radial is lower than in Table 1 but still high compared to multiple radials.
• As the Ratio gets larger, the vertical is taller and the radials are shorter.
 Table 2 Angle° Ratio % Length % Effic. Gain dBi Side dBi Pattern 1-Radial 90 0.60 102.38% 50.96 2.74 0.35 half-circle 2-Radials 90 0.71 93.33% 44.47 1.59 1.21 oval 3-Radials 90 0.75 87.68% 44.23 1.36 1.36 circle 4-Radials 90 0.798 83.95% 44.40 1.36 1.36 circle 6-Radials 90 0.803 80.06% 44.34 1.34 1.34 circle 8-Radials 90 0.856 80.31% 46.84 1.38 1.38 circle

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.

Figure 1

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