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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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Elevated Radials

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.

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".
  • 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°.
  • % Length gets longer than the vertical arm with 1-radial, then gets gradually shorter as identical radials are added.
  • 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.
  • % Length gets even shorter as identical radials are added.
  • Gain decreases with added numbers of radials except for 8-Radials
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.

1,2,3,4,6,8 Elevated Radials Graph
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.
8-Radials 20 dgree cone
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). 

Reminder
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