# 79. Developing Antenna Expectations Using Modeling Software

### L. B. Cebik, W4RNL

Last month, we examined the vertical dipole. This month, we shall explore its half-brother, the vertical monopole. Actually, we shall divide our work in two, examining fraternal twins: the elevated vertical monopole with an attached ground plane and the ground-mounted vertical monopole with a ground plane on or under the soil. By starting with the elevated monopole, we can begin the sampling as we did for every other episode in this series: in free space.

As always, we shall look systematically at a number of antenna properties that modeling software can unfold for us.

A. Elevated vertical monopole
1. Monopole development

2. Height above ground

3. Ground quality

B. Ground-mounted monopole
1. Perfect vs. lossy ground

5. Vertical length

Coverage will be incomplete, but by combining our explorations with those you have acquired from past episodes, you can produce your own complete survey.

A. Elevated Vertical Monopoles

Elevated vertical monopoles generally consist of a vertical element approximately 1/4 wavelength long. To the base of this element goes the center conductor of a coaxial feedline cable. The braid of the cable connects to a symmetrical set of radials extending usually at right angles to the vertical element. Because we think of the coaxial cable braid as being grounded and serving as a shield, we often think of the antenna as consisting of a vertical radiating element and a relatively inert "counterpoise." Nothing could be farther from the truth. Every part of the antenna structure radiates and is active in yielding the performance that emerges from a vertical monopole.

1. Monopole Development

To understand the elevated vertical monopole, we may begin where we left off last month: with a vertical dipole. Then we can proceed to develop the vertical monopole out of that antenna, as suggested by Fig. 1.

Let's begin our work on 2-meters, 146 MHz, to be more precise. Verticals are used at all frequencies, from LF through UHF, so a VHF example is suitable for our work. We shall use 0.25" (6.35-mm) aluminum as our material for both the vertical element and, eventually, for ground plane radials. Since we wish to have a baseline against which to compare our development, let's use the vertical dipole. In free space, a resonant 1/2 wavelength vertical dipole will have the properties shown in the following brief table.

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Vertical Dipole:  146 MHz

Diameter:                    0.25"         6.35 mm
Length:                      38.1"         967.74 mm
Free-space gain              2.13 dBi
Source impedance
R +/- jX:                  72.11 + j 0.35 Ohms
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .```

For all of our work on 2 meters, we shall expressed dimensions in inches and millimeters. My tables emerge from NEC-4 models, so the exact figures produced by your model may differ slightly. But as always, the trends will remain good for any version of NEC-2 or MININEC. The patterns for the free-space vertical dipole are identical to those we discussed in the preceding column.

We may view a vertical monopole with a ground plane attached as simply an adapted vertical dipole. We retain the upper portion of the dipole--about 1/4 wavelength long--and revise the lower half of the vertical element. Instead of a single wire, we construct a symmetrical set of spokes or radial elements, connected together at the source and extending at right angles to the upper portion of the element. We may use any number of radial elements, but 4 has proven sufficient for highly predictable performance.

In constructing our initial vertical monopole, we shall use a fixed vertical length that is 1/2 the length of the vertical dipole. Then we shall add 4 radials. The radial lengths will be equal and set to achieve 2 goals. First, we wish to achieve resonance. Second, we wish the current to divide equally, not only among the radials, but also between the two halves of the assembly. The current at the base of the vertical element, where we place the modeling source, should equal the sum of the currents on the innermost segments of the radials. The result of our work will resemble the following model in both dimension and performance.

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First Model: Vertical Monopole with 4 Radials:  146 MHz

Diameter:                            0.25"         6.35 mm
Vertical Length:                     19.05"        483.87 mm
Free-space gain                      1.01 dBi
Source impedance
R +/- jX:                          23.17 + j 0.12 Ohms
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .```

The table should raise many questions. The first concerns a mythology attaching to vertical monopoles that lists their resonant source impedance as about 35-36 Ohms. That value holds true of 1/4 wavelength vertical radiators over and connected to perfect ground. However, the elevated vertical monopole with ground plane has a much lower impedance. What we build, we can rebuild as soon as we examine a second question: Why is the gain so low?

A conventional and wrong answer to this question is that only the vertical portion of the antenna is radiating. In fact, all parts of the antenna radiate. However, the symmetrical portion of the assembly radiates in such a way, due to the symmetry of the radials, that the radiation almost cancels. See Fig. 2.

The "azimuth" or H-plane pattern shows the total far field along with its horizontal and vertical components. The vertical component is invisible behind the black line showing the total field. The horizontal component appears in blue at the center of the pattern in the form of 8 very small lobes. It is the remnant calculable radiation after cancellation among the fields produced by each of the 4 radials. Over ground, the horizontal component of the total field will be slightly stronger, but never strong enough to alter the dominantly vertical polarization of the antenna.

Our initial model of the vertical monopole actually has radials that are longer than the vertical element. We can approach more conventional dimensions by lengthening the vertical element a bit and shortening the radials. The work would result in the following model--and its performance.

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Second Model: Vertical Monopole with 4 Radials:  146 MHz

Diameter:                            0.25"         6.35 mm
Vertical Length:                     20.15"        511.81 mm
Free-space gain                      1.34 dBi
Source impedance
R +/- jX:                          24.66 - j 0.30 Ohms
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .```

The model achieves an almost perfect current equality between the upper and lower halves of the assembly. It also yields a vertical element a bit longer than the radials. However, the source impedance remains under 25 Ohms at resonance.

We did increase the gain by about a third of a dB, a function of lengthening the vertical portion and shortening the radials. Perhaps we can further lengthen the vertical element and achieve the "ideal" 35-Ohm vertical monopole. The results appears in the following table.

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Third Model: Vertical Monopole with 4 Radials:  146 MHz

Diameter:                            0.25"         6.35 mm
Vertical Length:                     23.45"        595.63 mm
Free-space gain                      1.68 dBi
Source impedance
R +/- jX:                          34.94 + j 0.51 Ohms
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .```

The vertical element is longer and achieves a higher gain than the preceding vertical monopole models. However, the vertical portion of the assembly is not a resonant 1/4 wavelength element. Rather, it is longer than 1/4 wavelength, as indicated by the fact that the current peaks above the feedpoint segment in the model. Note that to do this analysis, we are examining data that we have not checked with other models in this series of exercises: the element current. There is no intrinsic harm or fault attached to this situation--only a name change. Rather than being the analog of a vertical dipole, the new monopole is an analog of an off-center-fed 1/2 wavelength element.

Since we have a procedure for producing a 35-Ohm monopole assembly, we may as well go all the way to a 50-Ohm assembly. The results should resemble those in the following table, as we continue to extend the vertical element and shrink the length of the radials.

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Fourth Model: Vertical Monopole with 4 Radials:  146 MHz

Diameter:                            0.25"         6.35 mm
Vertical Length:                     26.30"        668.02 mm
Free-space gain                      1.83 dBi
Source impedance
R +/- jX:                          50.55 - j 0.09 Ohms
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .```

The antenna is highly off-center-fed, since the current reaches its peak value about 20% of the way up the vertical element. We achieved a 50-Ohm source impedance. However, you may find that the dimensions are a bit more finicky to pick out as we shorten the radials to about a third of the length of those used in the initial model.

The exercise is designed to remove some common misconceptions about elevated vertical monopoles. The vertical monopole can be derived from the vertical dipole without reference to ground, either real or perfect. The H-plane pattern establishes that all parts of the assembly are active radiators, although the radiation from the radials almost cancels completely. We can make the monopole--within the initial 1/2 wavelength total size--any length we wish in order to effect a desired source impedance, and the resulting increase in vertical element length tends to increase the overall gain of the assembly.

Before we leave free space for an environment closer to the ground, let's examine an intermediate step between the vertical dipole and the vertical monopole with radials extending at right angle from the vertical element. We may slope the radials at any angle downward from the right-angle plane, as suggested by the middle portion of Fig. 3. If we select an angle of about 45 degrees, we can obtain a vertical monopole that takes up less radial room while using a shorter vertical element. As well, the array will have a 50-Ohm resonant impedance, equal current division between upper and lower parts, and a slightly higher gain than we have so far obtained. The following table summarizes the design.
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Vertical Monopole with 4 Sloping Radials:  146 MHz

Diameter:                            0.25"         6.35 mm
Vertical Length:                     18.70"        474.98 mm
Radial length (see text):            18.50"        469.90 mm
Free-space gain                      1.98 dBi
Source impedance
R +/- jX:                          51.24 + j 0.48 Ohms
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .```

Although the radials are 18.5" (469.9 mm) long, they use only 13.08" (332.23 mm) distance from the vertical centerline of the assembly. Of course, they also extend downward by the same distance, since we set them at a 45-degree downward angle. Sloping radials are a standard technique in vertical monopole construction to obtain a system that shows a good match to common 50-Ohm coaxial cables.

Even though the vertical element is shorter than the other 50-Ohm model, we obtain slightly higher gain. Actually, the vertical element in this model does not end at the feedpoint or base of the exactly vertical element. It extends downward to the lower tips of the sloping radials.

As Fig. 4 shows, the horizontal component of radiation from the radials remains well-canceled. However, the radials also have a vertical dimension, and the radiation in that plane does not cancel. Rather, it contributes to the overall vertically polarized radiation of the entire assembly from top to bottom. Not only are the radials not an inert counterpoise, they are an essential active ingredient in the vertical monopole and necessary to make it function in the desired manner.

2. Height Above Ground

We shall omit from these notes certain exercises that you should perform for yourself. For example, check the performance of the vertical monopole in free space using various materials, as we did for the vertical dipole. In addition, perform frequency sweeps across the 4 MHz of the 2-meter band for each model to determine the operating bandwidth, not only relative to SWR, but also with respect to other performance parameters. To save a bit of column space for ground-mounted vertical monopoles, we shall leap to an examination of the vertical monopole at various heights above ground.

For the exercise, we shall use the version of the monopole with a 20.15" (511.81-mm) vertical element. From that model, we obtained a free-space gain of 1.34 dBi and a source impedance of 24.66 - j 0.30 Ohms. Our first test will cover a broad swath: from 0.5 to 5 wavelengths in height in 0.5 wavelength increments. This coverage reflects the fact that VHF vertical monopoles are used at many heights, depending upon operating circumstances. For reference, 1 wavelength at 146 MHz is 6.737' or 2.053 m. We shall use good ground (conductivity: 0.005 S/m; permittivity: 13). The antenna height will reflect the distance between ground and the base or feedpoint of the assembly. The results yield the following table.

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Vertical Monopole Performance vs. Height Above Ground:  146 MHz

Height Above Ground                 Gain           TO Angle      Source Impedance
WL     Feet           Meters        dBi            degrees       R +/- jX Ohms
0.5     3.368          1.027        1.42           45.3          25.04 + j 0.43
1.0     6.737          2.053        2.61            9.1          24.72 - j 0.08
1.5    10.105          3.080        3.65            7.0          24.69 - j 0.19
2.0    13.474          4.107        4.33            5.6          24.68 - j 0.23
2.5    16.842          5.133        4.81            4.7          24.67 - j 0.26
3.0    20.210          6.160        5.16            4.1          24.67 - j 0.27
3.5    23.579          7.187        5.42            3.6          24.67 - j 0.28
4.0    26.947          8.213        5.63            3.2          24.67 - j 0.28
4.5    30.316          9.240        5.79            2.8          24.67 - j 0.29
5.0    33.684         10.267        5.93            2.6          24.66 - j 0.29
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .```

The table of performance values vs. height uses an elevation angle increment of 0.1 degrees rather than the more usual 1.0-degree increment. As we raise an antenna above 1 wavelength, the rate of change of TO angle with each change of height decreases. If we want to know the maximum gain, using 1-degree angle intervals may not yield a reliable answer, since the width of the lobe may be narrow, and a few tenths of a degree difference in angle may show as much as a half-dB difference in gain. The higher the antenna, the more critical it becomes to use the finest elevation angle increment available on the software.

The vertical monopole shows nothing unexpected. The source impedance is virtually constant, regardless of height within the table's range. The lowest lobe is strongest for all but the 0.5 wavelength height, and the progressions of gain and TO angle are normal in every way.

We should investigate the performance of the same vertical monopole in the lower height region, using heights comparable to those used with the vertical monopole in the preceding column. The results appear in the following table, although the physical heights are listed in terms of inches and millimeters. For reference, at 146 MHz, a wavelength is 80.8415" or 2053.37 mm.

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Vertical Monopole Performance vs. Height Above Ground:  146 MHz

Height Above Ground                 Gain           TO Angle      Source Impedance
WL     Inches         mm            dBi            degrees       R +/- jX Ohms
0.25    20.21          513.3        1.25           16.0          23.19 - j 2.06
0.35    28.29          718.7        1.26           14.1          23.28 + j 0.08
0.45    36.38          924.0        1.19           13.2          24.55 + j 0.67
0.55    44.46         1129.4        1.79           42.4          25.28 - j 0.03
0.65    52.55         1334.7        2.29           37.6          25.06 - j 0.65
0.75    60.63         1540.0        2.57           33.7          24.51 - j 0.68
0.85    68.72         1745.4        2.63           35.9          24.33 - j 0.29
0.95    76.80         1950.7        2.53           27.7          24.58 - j 0.05
1.05    84.88         2156.0        2.71            8.7          24.83 - j 0.16
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .```

As we did in the first table, we used good ground beneath the vertical monopole for the test. The range of source resistance values is only 2.09 Ohms, and the range of source reactance is only 2.73 Ohms, despite the great range of heights. The antenna shows a high TO angle from a height of 0.55 wavelength through a height of 0.95 wavelength. You may wish to compare this table with the corresponding table for the vertical dipole in the last episode, understanding that the heights in the two tables mean two different things. The vertical dipole heights mark the height of the dipole center, while the monopole heights mark the base of the antenna. However, in both cases, the height represents the antenna feedpoint.

For both antennas, 0.55 wavelength marks the beginning of the high TO angle or the dominance of the second elevation lobe. However, the vertical dipole does not return to the dominance of the lowest lobe within the limit of the table, 1.25 wavelength. Still, the tables are not directly comparable in detail, since one antenna is for 7.15 MHz and the other is for 146 MHz. You may wish to create either a 146-MHz vertical dipole or a 7.15-MHz vertical monopole to produce a more exacting comparison.

3. Ground Quality

The are some correlations between the behavior of a vertical dipole and an elevated vertical monopole, but they are not universal. Hence, we cannot assume that the behavior of the vertical monopole over different ground qualities will replicate the work we did with the dipole. We need to give the monopole its own trials.

For this test, we shall alter the vertical monopole to one for which the trials might be more useful in guiding practical antenna work. We shall use a 10-meter (28.4-MHz) vertical monopole with a vertical element that is 8.75' (2.667 m) long with a 1" (25.4-mm) diameter. The radials will be 0.25" (6.35 mm) in diameter and 8.0' (2.438 m) long. The material is aluminum. At 28.4 MHz, a wavelength is 34.63' (10.56 m), and we find 10-meter verticals mounted at all heights from near the ground to a full wavelength above the ground (usually on rooftops). Therefore, we shall check our vertical monopole at base heights of 0.25, 0.5, 0.75, and 1.0 wavelength.

We shall use the same ground qualities as in the past, as shown in the following table.

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Some Useful Soil Types

Soil Type                    Conductivity                 Permittivity
S/m                          (Dielectric Constant)
Very Poor                    0.001                         5
Poor                         0.002                        13
Good                         0.005                        13
Very Good                    0.0303                       20
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .```

With these soil qualities, we obtained the following results for the 10-meter vertical monopole.

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Changes of Vertical Monopole Performance with Ground Quality

Base Height: 0.25-Wavelength
Soil Type             Gain          TO Angle              Source Impedance
dBi           degrees               R +/- jX Ohms
Very Poor             1.11          19                    23.24 - j 0.70
Poor                  1.29          16                    23.05 - j 1.34
Good                  1.04          16                    22.95 - j 1.34
Very Good             0.73          14                    22.63 - j 1.76

Base Height: 0.5-Wavelength
Soil Type             Gain          TO Angle              Source Impedance
dBi           degrees               R +/- jX Ohms
Very Poor             2.01          15                    24.72 + j 0.96
Poor                  1.54          46                    24.75 + j 1.21
Good                  1.64          45                    24.79 + j 1.21
Very Good             2.57          44                    24.89 + j 1.38

Base Height: 0.75-Wavelength
Soil Type             Gain          TO Angle              Source Impedance
dBi           degrees               R +/- jX Ohms
Very Poor             3.09          12                    24.29 + j 0.01
Poor                  2.70          34                    24.28 + j 0.10
Good                  2.76          33                    24.26 + j 0.10
Very Good             3.83          32                    24.21 + j 0.23

Base Height: 1.0-Wavelength
Soil Type             Gain          TO Angle              Source Impedance
dBi           degrees               R +/- jX Ohms
Very Poor             3.81          10                    24.46 + j 0.62
Poor                  2.71           9                    24.46 + j 0.69
Good                  2.64          26                    24.47 + j 0.69
Very Good             3.83          25                    24.50 + j 0.74

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .```

Although the source impedance is stable at every height over the range of soil types, it grows perceptibly more stable as we increase the height. The chief interesting elements in the table are the gain and corresponding TO angle values. At 0.25 wavelength, the lower lobe dominates for every soil types. However, above the height, only over very poor soil does the lower lobe dominate. As we move upward with the antenna base, we see a gradual return to lower lobe domination from worse to better soils, but the picture is only suggested by the table. You may wish to do further trials at 1.25 wavelength and above to discover at what point the lower lobe returns to domination for good and very good soils.

The gain values are also interesting, since they do not correlate directly with soil type. At heights from 0.5 wavelength to 1.0 wavelength, the antenna over very poor soil is superior to all but very good soil, and at the lowest height shown, poor soil takes gain honors. The differences are of only marginal operational interest--much less interest than the TO angle--but the trends will likely seem surprising relative to common assumptions about vertical monopoles.

To better gauge the importance of the tabular data, you may wish to overlay elevation patterns at each height for the 4 soil types. Fig. 5 shows the patterns at a height of 0.25 wavelength above ground. As in all of the overlays that you will obtain from these trials, the patterns for good and poor soil are virtual clones of each other. The pattern for very good soil shows the more distinct differentiation of the lower and the emerging second lobe. In contrast, the pattern for very poor soil does not show a distinct second lobe at all. In all cases, the vertical beamwidth is large enough that there is likely to be little detectable difference in the performance of the antenna with a change in soils.

As we move to a height of 0.5 wavelength above ground, Fig. 6 provides the relevant elevation patterns. Only over very poor soil is the development of the second lobe sufficiently retarded to allow the lower lobe to dominate in terms of maximum gain. As we improve soil quality, the upper lobe increasingly dominates over the lower lobe. Over poor and good soils, there is not a very great difference in the maximum gain for each lobe. However, over very good soil, the high-angle lobes has a considerable advantage over the lower lobe. As well, since all of the plots use the same gain scale, the lower lobe of the "very-good soil" pattern is weaker than for the other antenna environments.

In Fig. 7, we can find the first emergence of the third lobe, although it is not clearly identifiable in the pattern for very poor soil. In that pattern, the lowest lobe continues to have the maximum gain. In all of the patterns, the lower two lobes have begun to merge. Over poor and good soil, the two parts of the merged lobe have nearly the same strength. However, over very good soil, the lower component of the merged elevation lobe remains considerably weaker than the upper lobe. Hence, higher-angle radiation (and reception) dominates the antenna's performance.

In our final set of overlaid patterns--Fig. 8--at 1.0 wavelength above ground, we find that the third lobe has become very distinct in all of the patterns. Over good and poor soil, the merged lower lobes have very nearly equal strength--too near to make a difference. However, the pattern for very poor soil continues to show the clear dominance of the lowest lobe--virtually to the same degree that over very good soil, the upper lobe continues to dominate. Indeed, one must wonder how high one might have to raise the antenna over very good soil before the TO angle comes down to the level of the lower lobes of the patterns over other soil types.

These patterns should accomplish two goals. First, they should serve to question some of the assumptions that we may be inclined to bring to the study of vertical monopoles. With the proper systematic use of our modeling software, we may set aside assumptions and allow the data to develop as it will. Second, the patterns should prepare us for the highly complex sets of elevation lobes that we encounter when taking patterns of antennas set at considerable heights, when measured in terms of wavelengths.

We have spent considerable space looking at elevated vertical monopoles, and still many questions remain for you to explore on your own. What is the effect of using either fewer or more radials in the ground-plane system? What is the effect of the relative diameters of the vertical element and the radials on the required lengths of each for resonance? How would a vertical monopole with sloping radials perform at various heights and over different soils? Would it perform more like a vertical dipole or like the vertical monopoles that we have explored in this column? Are there differences of performance that are directly frequency related that we might detect by using directly scaled antennas? These are only a few of the questions unanswered by this small beginning in the systematic study of elevated vertical monopoles.

I had hoped to include in this episode a considered look at ground-mounted vertical monopoles. There are not only questions of performance expectations to develop, but as well a host of modeling questions to consider. Hence, to be fair to the ground-mounted vertical monopole, I shall have to wait until next time. Until then, you have time to work on the unanswered questions that I left behind for elevated vertical monopoles.

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