Part 5:
Regional Differences

L. B. Cebik, W4RNL

From the tables in the last episode, it should be clear that when talking about vertical antennas, it is misleading to think that they are everywhere the same and that one account for all verticals leads to a clear set of expectations of them. The tables lead me to want to distinguish several regions of interest for vertical antenna investigators. There is nothing absolute about these distinctions, especially the lower ones, since antenna interaction with the lossy but conductive medium called earth changes with frequency. With that reservation in mind, let's tentatively distinguish the following regions.

1. Subsurface plane: As the name implies, this region includes antennas with their planes below the surface of the earth--and, needless to say, their main elements above the surface.

2. Close to earth: We may loosely define this region as including about heights greater than zero up to about 0.07 to 0.1 wavelength. In this region, we find that antenna-earth interaction creates the greatest detuning of a free-space designed vertical antenna with a plane. The upper boundary is more a frontier than a line, just as "greatest" detuning cannot be defined as a distinct line.

3. Transition: 0.1 to 0.5 wavelength forms a region in which the gain of a vertical antenna drops precipitously with height decreases over lossier mediums, but descends in an orderly fashion over highly conductive media like salt water. Regardless of the medium in this region, the feedpoint impedance tends to meander.

4. Free Space: From 0.5 wavelengths upward, the properties of a vertical antenna with a plane (and vertical dipoles as well) most closely adhere to the properties of models in free space.

Let's see if we can summarize some of the features of each region, with attention to some distinctive phenomena that occur in each region.

Subsurface Plane

When the plane of a 1/4 wl vertical is below the surface, the feedpoint of the antenna begins to approach its "half-dipole" value of about 35 ohms. The more subsurface radials we add up to about 32 or so, the closer the approximation. (With salt water, we can achieve an even closer approximation with as few as 4 radials.) This situation most clearly approaches the perfect-earth and image-antenna picture that is fundamental to classic vertical antenna theory.

Gain, which involves the quality of earth at a distance from the antenna, is another matter. To a considerable degree, it also depends on the size of the subsurface ground plane in terms of the number of radials. Literature which suggests that 64 to 128 radials yields the best gain coincides with the progression of models (which was arbitrarily cut off at 32 radials except for spot checks at 64 radials).

When the plane in question uses an open-spoke assembly of radials, unless the number of radials is very great, there will be only slight differences in gain between systems using standard 1/4 wl radials and those using lengths to create a "tuned" system. In fact. models suggest that especially with perimeter-wire systems, trimming the main element for resonance is not only physically easier, but electrically sound as well. The following table of antennas and their gain tells the story.

All antennas us a plane 0.5' under the surface and adhere to the models used previously: Main element = 2" dia. al.; radials = 0.25" dia. al.; Frequency = 7.05 MHz; medium earth (C=0.005 S/m; DC=13)

Gain      TO angle       Feed R         Feed X
dBi       degrees        ohms           ohms

4 Radials:
free space design:  Main = 33.25'; radials = 35.6'
-2.56     26             67.38          + 13.67
radials resonated:  Main = 33.25'; radials = 10.8'
-2.25     26             59.86          - 0.12
main el resonated:  Main = 32.30'; radials = 35.6'
-2.68     26             63.73          + 0.01

8 Radials:
free space design:  Main = 33.25'; radials = 34.5'
-1.50     26             54.61          + 12.62
radials resonated:  Main = 33.25'; radials = 12.6'
-1.68     26             51.66          + 0.10
main el resonated:  Main = 32.40'; radials = 35.6'
-1.57     26             51.44          + 0.20

16 Radials:
free space design:  Main = 33.25'; radials = 34.5'
-0.63     26             44.90          + 10.32
radials resonated:  Main = 33.25'; radials = 15.0'
-1.23     26             46.44          - 0.37
main el resonated:  Main = 32.50'; radials = 35.6'
-0.66     26             42.30          - 0.76

4 Radials + perimeter wire:
free space design:  Main = 33.25'; radials = 19.4'
-2.48     26             63.87          +  8.36
radials resonated:
Note:  no resonant point shorter than 19.4' found
main el resonated:  Main = 32.50'; radials = 35.6'
-2.55     26             61.78          + 0.52

The 4-radial plus perimeter plane proved interesting because shortening the radials dropped the reactance to about 7.0 from which point it rose again with further shortening of the radials.

For all cases except the 4-radial open-spoke plane, resonating the antenna decreased the gain relative to the designs generated to resonate in free space. Shortening the radials to achieve resonance created a larger decrease in gain than shortening the main element. The decreases in gain occasioned by shortening the main element are largely academic and of no practical import.

For the 4-radial open-spoke design, shortening the radials actually produced a 0.43 dB increase in gain relative to the free space design. Whether this is achievable in practice with the radically shortened radials (-24.8') is unknown.

It is interesting to note that, even as an idle impracticality, the free space design yielded the highest gain of the variant models tested. It is tempting to suggest that the 1/4 wl subsurface plane vertical is essentially a nonresonant antenna.

Close to Earth

In the region below 10 feet at 7 MHz, but still above ground, we discovered that using more than 4 radials added little if anything to planed verticals. In the 5-10' region, where most amateur place their elevated radials, the feedpoint impedance was in the mid 30s with little reactance when a free space model was used as the basis for design. Although performance improves with the condition of the medium, mounting elevated radials over salt water for the low HF bands is normally impractical except on the largest ships.

For this region of use, the perimeter plane is especially significant, since it shortens the wire structure needing elevation, adding to a relative freedom from safety and maintenance concerns. Initial and later adjustment is also eased relative to buried radials.

Although a full-size vertical dipole cannot be operated in this region, hatted dipoles certainly can. Below is a comparison among the standard open-spoke 4 radial vertical, the perimeter 4 radials vertical, and a vertical using hats on each end. The comparison is interesting:

Antenna             Main el   Radials   Gain TO angle  Feedpoint Z
                    L (ft)    L (ft)    dBi  degrees   R +/- jX ohms
Bottom 10' off the ground
4 radial vertical   33.25     35.6      0.02   22      30.36 - 4.48
4 radials + per.    33.25     19.4      -.16   23      25.01 - 4.06
30% dipole/hats     19.95     16.1      -.37   24      27.72 + 4.88

Bottom 5' off the ground
4 radial vertical   33.25     35.6      -.13   24      34.82 - 0.44
4 radials + per.    33.25     19.4      -.40   24      32.22 + 6.84
30% dipole/hats     19.95     16.1      -.75   26      33.42 + 17.1

Although the hatted vertical dipole needs a bit of design perfection, it is only down by about 0.6 dB from the better of the two competitors in this medium earth comparison. The hats, of course, may be replaced with perimeter hats with under 7.8' spokes. (See the section on "Free Space" below for reference to a commercial antenna using a similar technique.) All in all, we have not appreciated the place of hatted dipoles in the near-earth-mount vertical antenna category.


The region from 0.1 to .05 wl up is a transitional region in which antenna gain drops rapidly as the feedpoint height is decreased. It is also the lowest region in which one can mount a full-size vertical dipole.

For the test frequency of 7.05 MHz, this region also host most verticals with drooping radials. Let us therefore compare briefly the vertical dipole, the drooping radial vertical, and the flat plane vertical. As usual, all antennas are 2" dia. aluminum main elements, with 0.25" dia aluminum radials. As a test, we shall compare the antennas over medium earth at heights of 35' (1/4 wl) and 52.5' (3/8 wl) up at the feedpoints. The sloping-radial models will use a 45-degree angle for the 4 radials.

Antenna             Main el   Radials   Gain TO angle  Feedpoint Z
                    L (ft)    L (ft)    dBi  degrees   R +/- jX ohms
3/8 wl up
Dipole              66.5'     ---       0.35   15      71.00 - 7.05
Sloping radials     33.25     30.0      0.41   14      46.60 + 0.91
Flat plane          33.25     35.6      0.73   52*     21.68 + 0.66

1/4 wl up
Dipole              66.5'     ---       0.11   18      97.89 + 3.14
Sloping radials     33.25     31.0      0.39   17      56.16 + 0.60
Flat plane          33.25     35.6      0.14   15      20.91 - 2.16

The vertical with the sloping radials (or the dipole with the split and spread lower end) shows a superiority to both the flat plane vertical and the vertical dipole in varying degrees ranging from small to very significant. At 3/8 wl up, the gain of the flat plane vertical is at a very high elevation angle, which is suppressed to a considerable measure in the dipole and sloping radial antenna. However, a significant secondary lobe remains at the higher angle.

When 1/4 wl up, the sloping radial vertical is superior to either of the alternatives, if for no other reason than the closer match to 50-ohm coaxial cable. Moreover, the elevation pattern, even though 3 degrees higher at maximum than its corresponding 3/8 wl antenna, is devoid of the high secondary lobe. Figure 5-1 overlays both patterns so that the reader can determine whether the secondary lobe is a help or a hindrance to intended operation.

It should be noted in passing that this transitional region is also the natural home to many forms of self-contained vertically polarized 1-wl wire loop antennas (including the half-square), all of which have bi-directional gain greater than any of the half-wavelength antennas discussed here.

Free Space

From a half wavelength upward, plane verticals retain their free space characteristics at the feedpoint and show gain levels commensurate with their height above ground, regardless of the nature of the medium. Although gain over medium earth is less than that over salt water, the progression of gain figures is orderly, and the level of gain is in all cases useful. Moreover, the gain level of the antenna does not vary significantly with the number of radials.

As viewed from the perspective of free space modeling, the planed vertical is simply a hatted dipole. With a feedpoint impedance ranging from 20-23 ohms at resonance, the hatted dipole does not present the most favorable match to 50-ohm coaxial cable. However, this problem is easily solved is we remember that a dipole can be fed virtually anywhere along its length. As the feedpoint is moved well away from center, a slight adjustment may be necessary to reresonate the antenna. For our hatted, this may be done either to the main element or to the radials/hat spokes.

In general, we have three options for feeding the hatted dipole: at the electrical center, usually called the base of the vertical; up the main element to a point where the feedpoint impedance at resonance is near 50 ohms; and off-center in the opposite direction. Figure 2 illustrates the options. Since we cannot easily feed all 4 radials (or 8, 16, 32, etc.) at the same time, we may simply lengthen the main element and shrink the radials until the desired point appears at the "base of the vertical." As we shall see, off-center feed yields a modicum of gain as a tiny bonus. Since we have seen that drooping radials add to the antennas vertical radiation, we shall also include versions of the 3/8 wl vertical with radials dropping at a 45-degree angle.

The following table provides a comparison among the three types of feed for free space and at a height of 1 wl (140' for 7.05 MHz). As always, we retain the 2" dia. al. main element and the 0.25" al. radials.

Antenna             Main El   Radial    Gain      TO Angle  Feedpoint Z
                    L (ft)    L (ft)    dBi       degrees   R +/- jX ohms

4 Radial:  standard base feed:
Free Space          33.25     35.6      1.38      ---       22.88 - 0.29
1 wl up                                 3.24      24        23.01 - 0.04
4 Radial:  feedpoint 55% from center
Free Space          33.25     35.6      1.53      ---       49.24 - 0.25
1 wl up                                 3.39      24        49.53 + 0.31

4 Radial:  3/8 wl with base feed
Free Space          45.00     13.6      1.88      ---       53.51 + 0.46
1 wl up                                 3.45      24        53.75 + 0.86

4 Radial:  3/8 wl with 45-degree drooping radials and base feed
Free Space          45.00     12.1      2.06      ---       68.85 - 0.17
1 wl up                                 3.59      24        68.99 + 0.37

Either of the off-center feed systems improves the design of the antenna. Since the basic 4-radial system may be shrunken by the use of a perimeter wire, I ran the same exercise on the basic antenna model.

Antenna             Main El   Radial    Gain      TO Angle  Feedpoint Z
                    L (ft)    L (ft)    dBi       degrees   R +/- jX ohms

4 Radials with perimeter:  standard base feed
Free Space          33.25     19.4      1.70      ---       20.76 - 0.60
1 wl up                                 3.43      25        20.79 - 0.37
4 Radials with perimeter:  feedpoint 55% from center
Free Space          33.25     19.5      1.74      ---       47.50 + 0.35
1 wl up                                 3.47      25        47.57 + 0.87

4 Radials with perimeter:  3/8 wl with base feed
Free Space          45.00     7.75      1.91      ---       51.30 + 0.30
1 wl up                                 3.48      24        51.49 + 0.68

4 Radials with perimeter:  3/8 wl with 45-degree drooping radials and base
Free Space          45.00      7.80     2.08      ---       66.19 - 0.61
1 wl up                                 3.61      24        66.33 - 0.09

Gains might well be greater over real ground at a different antenna height. With little effort, the feedpoint impedances of the drooping radial models can be altered to 50 ohms.

The antenna elevation pattern, which is the same for all the antennas excepting maximum gain, appears in Figure 3. Note the higher lobe and its ability to obscure gain at lower elevations. It is likely the at 2 wl the main lobe would show the free space gain improvement of over 1.2 dB.

As one last comparison, let's throw in the vertical dipole:

Antenna             Main El   Radial    Gain      TO Angle  Feedpoint Z
                    L (ft)    L (ft)    dBi       degrees   R +/- jX ohms

Vertical dipole:  center feed
Free Space          66.50     ----      2.13      ---       71.92 - 0.24
1 wl up                                 3.53      27        71.34 - 0.63

Perhaps it is time to view the half-wavelength dipole rather than the quarter wave vertical as the basic vertical antenna, especially at VHF, where inattention to dipole possibilities has limited antenna design. Since VHF antennas are used almost exclusively from 1 wl upward, application of these principles should be a natural development.

In addition, at any HF or VHF frequency, we may hat both ends of a dipole with little gain loss. The limiting factor tends to be the feedpoint impedance. As an example, here is a dipole 30% of full length with hats at either end and vertically oriented:

Antenna             Main El   Radial    Gain      TO Angle  Feedpoint Z
                    L (ft)    L (ft)    dBi       degrees   R +/- jX ohms

Vertical hatted dipole:  30% of full-length and center feed
Free Space          19.95     16.1      1.70      ---       15.65 - 0.99
1 wl up                                 3.56      28        15.46 - 0.91

The 4-wire open-spoke hat may be replaced with either a many-spoked version or a perimeter model to shrink the end arrays considerably. Versions for HF and VHF using a different end loading system are already commercially available (The ZR family from Force 12), with one model having been adjusted for near ground use.

Since the 3/8 wl antenna with the small drooping radials is both compact and quite superior to the quarter wavelength model, I suspect VHF designers may eventually discover it. In the interim, for VHF, take two quarter wavelength pieces of hardware store tubing, find some PVC for a center insulator and a mount for one end. Shove coax up the lower tube and attach to each side of the insulator-tube junction. Presto: instant vertical dipole (even if the older literature misnames it something else--which I won't repeat, since I try to avoid reinforcing misconceptions even by naming them). With 1" tubing at 2 meter, the feedpoint impedance will be closer to 50 ohms than to 70. Thanks to N6BT for reminding me that I forgot something here: the need to decouple with beads the feedpoint and a choke at the point where the coax emerges from the lower half of the dipole. Alternatively, you can use a PVC Tee and bring the coax out to the side for side-mounting to a pole or tower. (Schedule 40 and related PVC, although not UV rated, is quite durable, cheap, and easily worked--almost Tinker Toys for adults.)

Of course, there is nothing to prevent you from adapting one of the designs above to VHF use. Experimentation will be necessary, since there is a small but distinct discrepency between these 7.05 MHz models, all done on NEC-4, and models done with MININEC--about 2.5%. At that size of discrepency, and with limitations within both programs, it is not possible with home workshop building techniques to say definitively which is closer to the mark. However, the discrepency is dimensional only and does not affect the progressions of data drawn from the models.


Free space design of flat plane verticals as hatted dipoles has proven its relevance from the very highest mounting altitudes to the very lowest. Perhaps the exercise has also given us some appreciation of the different characteristics of verticals as we move them up and down through the regions we have marked out for purely pragmatic reasons. Whichever may be our main interest, the exercise has been useful (at least to the writer).

Updated 5-26-97. L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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