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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 quarter-wave 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 possible 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 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 feed point ratio can be raised 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:
  • At 76° down angle a 1-Radial antenna is 1.81% longer than a reference dipole.
  • The % Length compared to a dipole gets gradually shorter as radials are added.
  • A 45° downward angle works only for 2- or 3- radials, 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 high because of the stronger radiation towards the radial-side of the 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 90° angle  antenna characteristics of Table 2 with Table 1, note that:
  • 1-Radial plus Vertical now is longer, 2.38% longer than a dipole..
  • % Effic. and Gain for 1-radial is lower than in Table 1 but still high compared to multiple radials.
  • With more radials, the Radial + Vertical Length becomes considerabley shorter than a dipole.
  • As the Ratio gets larger, the Vertical is taller.
  • With added numbers of radials, gain decreases slightly... 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

To shorten 160, 80 and 40 meter antennas the Ratio can be reversed to make the vertical monopole the short element. The long element(s) become radials.



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

Reminder: All models are standardized to the ideal feedpoint elevation of one-half wave length.

What happens when elevated radials become close to ground?

In Figure 2 below, we look at the simplest case of two radials, in-line, set at 90-degrees to the vertical radiator.  Looking from right to left it is seen that from 0.5 wave length elevation, the normal Ratio of 0.71 (Table 2) falls slowly as the antenna is made lower.

It is obvious that large changes begin when the Feed point Elevation drops below 0.1 Wave Length (0.1 Lambda).  For example at 14.2 MHz:   0.1WL x 888/14.2 = 6.25 feet.  From the Red line, the Length Factor(F) ~ 448/14.2 = 31.5 feet.  From the Blue line, the Vertical/Length Ratio ~ 0.65 * 31.5 = 20.5 feet length of the Vertical radiator.  The Radials therefore are 31.5 - 20.5 = 11.0 feet each.

As the radials become close to ground, tuning changes greatly. To maintain the desired frequency the sum of Vertical + Radial  length increases substantially (Red line).  To adjust to the lowest SWR the Vertical/Length Ratio (Blue line) will be near 0.5. ie Radials are lengthened to approach the same length as the Vertical.


Figure 2

Tuning

It is advisable to tune a ground plane antenna at around a half wave length (0.5 Lambda) high or higher over ground (around 16 feet on 20 meters). This way the antenna can be mounted at any higher operating position without adjusting the tuning.
 
However, if the antenna is tuned at a height less than a quarter wave (0.25 Lambda is around 8 feet on 20 meters), raising the antenna can change the tuning as seen in Figure 2.
 
Tuning done at below 0.05 Lambda (around 4 feet on 20 meters) causes drastic changes when the antenna is raised to a operating position higher than a half wave length.

If tuning near ground must be done, the predicted values in Figure 2 can be used to make a reasonable guess as to vertical + radial Length (Red line) and the length of the vertical (Blue line ratio).



Up to this point antenna coax matching has been studied by angling radials or vertical-to-radial ratio..  There remains the question: 

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 70° 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 70° down angle found a 50 ohm match at a vertical/radial Ratio of 0.522.  Resonant Length: 93.3% of a dipole. A wide band-width of 5.6% under 2 SWR.  Omni-directional radiation 20° wide with a take-off angle of 15° above horizon. Gain: 2.19 dBi compared with 1.49 dBi for a typical 4-element ground plane.

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 to concentrate in the most resonant radials.  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