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<!DOCTYPE html>
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<title>The 5/8-Wavelength Mystique Part 1: 80-Meter Monopoles With Buried Radials</title>
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<h1><img src="../images/gpbut.gif" align="left" width="90" height="84" border="2" vspace="5" hspace="10"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">The 5/8-Wavelength Mystique<br>
Part 1: 80-Meter Monopoles With Buried Radials</h1>
</center>
<center>
<h3>L. B. Cebik, W4RNL</h3>
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<p>For the lower-HF portion of the study, I selected 3.75 MHz as a reasonable test frequency, even though it is unlikely that anyone would have the wherewithal to construct a 164' 5/8 wavelength monopole. I also used 0.1" diameter copper wire throughout the 80-meter portion of the study. First, the wire size is quite reasonable for a radial system. A large radial system of 128 wires creates a major junction, and the use of relatively thin wire ensures that the shortest wire length (0.5') will create no significant problems of segment inter-penetration at the junction of the radials. Second, the use of 0.1" diameter wire throughout ensures that there are no angular junctions of wires having dissimilar diameters in the model. Moreover the losses of 0.1" diameter wire at 80 meters a quite low, allowing the results to stand for those which might be obtained with the much larger-diameter elements used in actual 80-meter monopoles.</p>
<p>Modeling a buried radial system requires attention to several constraints of NEC-4. First, the vertical elements must pass through the ground surface at a segment junction. This requirement is most easily met by using a 1-segment wire from the ground level to the radial junction, which is 0.5' below the ground surface. As well, the source segment should be of the same length as the segment immediately adjacent to it for maximum accuracy. Therefore, I used a 0.5', 1-segment wire for the source wire, the lower end of which is at ground level. Above the source segment, the vertical radiator was developed using segment length-tapering, a convenient facility on EZNEC software. The 1-segment wire above the feedpoint is 0.5' long, the one above that is 1.0' long, and so on until a maximum segment length of 8' was reached. <b>Fig. 3</b> provides a partial sketch of the technique.</p>
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<p>Angular wire junctions are most accurate if the segments that meet are the same length. Therefore, the radials were also created using segment length-tapering techniques, with the inner-most segment 0.5' long, as shown in <b>Fig. 3</b>. Model creation was speeded by another convenience of EZNEC, the ability to select the group of wires composing an initial radial and then simply specifying the total number of radials required by the model. For comparative purposes, I explored models using a MININEC ground with no radials as well as buried radial systems using 32, 64, and 128 radials per model. <b>Fig. 4</b> shows an outline sketch of the 32- radial model. For a discussion of the history and mathematics of classical ground calculations, see Rudy Severns, N6LF, "Verticals, Ground Systems, and Some History, " <i>QST</i> (July, 2000), 38-44. For a discussion of the techniques used in NEC-4 for the evaluation of the Sommerfeld/Asymptotic model, see Gerald J. Burke, <i>Numerical Electromagnetics Code--Nec-4: Method of Moments; Part II: Program Description--Theory</i> (LLNL: 1992), pp. 32-56.</p>
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<p>To provide a cross section of the performance of the 1/4 wavelength and 5/8 wavelength monopoles, I used 4 different types of ground conditions, as shown in <b>Table 1</b>. As I demonstrated in Part 2 of the series, "Some Facts of Life About Modeling 160-Meter Vertical Arrays," in The National Contest Journal (2000 and 2001 in a 5-part sequence), the use of the traditional sequence of ground conditions called "very poor," "poor," "good," and "very good" provides a fair sampling of soil varieties for most lower HF purposes. As well, the modeling techniques for buried radial system using NEC-4 are described in more detail in that series. Also included are demonstrations of limitations in using the MININEC ground and the NEC-2 close-to-ground radial systems as substitutes for a fully modeled buried radial system.</p>
<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 1. Soil types used in the study.
Soil Type Conductivity Permittivity
Siemens/meter dielectric constant
Very Poor 0.001 5
Poor 0.002 13
Good (Average) 0.005 13
Very Good 0.0303 20
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p>Many antenna analysts use MININEC or a version of NEC with a MININEC ground in order to simplify the modeling of vertical monopoles. Since EZNEC provides the MININEC ground as a user option, I produced a set of reference materials for the 64' 1/4 wavelength and the 164' 5/8 wavelength monopoles. <b>Table 2</b> provides data for the two verticals for the various soils. There is a single feedpoint impedance value listed, since MININEC calculates the impedance over a perfect ground, regardless of the soil type specified for the far field pattern.</p>
<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 2. 1/4 and 5/8 wavelength vertical monopoles over MININEC ground.
1/4 WL Monopole 5/8 WL Monopole
Soil Type Gain TO Angle Feed Z Gain TO Angle Feed Z
dBi degrees R+/-jX dBi degrees R+/-jX
Very Poor -1.73 28 37.0+j2.2 1.07 19 83.7-j477
Poor -0.26 26 1.09 15
Good 0.46 25 0.47 13
Very Good 2.51 19 2.86 19
Note: Since use of a MININEC ground results in the calculation of the source impedance over
a perfect ground, the single value of feedpoint impedance applies to all cases.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p>The shorter monopole gain values follow what I shall term "naive" expectations: with improvements in soil quality, gain increases and the take-off (TO) angle (or elevation angle of maximum radiation) decreases. In contrast, the 5/8 wavelength radiator shows a decreasing gain value from very poor soil through good soil, with an increase only as we approach very good soil. This difference is explicable by reference to <b>Fig. 2</b>, which showed the difference in the position of maximum current along the radiator. (To be brief, the less conductive the soil, the higher the effective height of the 5/8 wavelength monopole current maximum above ground at the region of reflection that forms the far-field pattern. The 1/4 wavelength current maximum remains at ground level for any soil type.)</p>
<center>
<img src="58-2.gif" width="350" height="440" border="2" vspace="5" hspace="9">
</center>Most evident is the lower TO angle of the longer monopole for all soil qualities. <b>Fig. 5</b> places the patterns of the two monopoles over good ground, where the maximum gain is virtually the same. Evident is the lower TO angle for the longer antenna, along with the secondary high-angle lobe of radiation. For reception, it would appear that the quarter wavelength monopole would be somewhat quieter relative to high-angle QRN.
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<p>If general pattern shape were the only interesting factor in the comparison of 1/4 and 5/8 wavelength monopoles, the MININEC ground models might serve. However, The ability to model fully buried radial systems of various sizes leads to a number of questions concerning the effect of field size upon monopole performance. Therefore, I constructed models using 32, 64, and 128 radials for both monopoles, retaining the initial heights of 64' and 164', selected during the MININEC-ground modeling. The 64' height of the shorter antenna was nearly resonant under MININEC ground analysis. The 164' height is 5/8 wavelength at the test frequency of 3.75 MHz.</p>
<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 3. 1/4 wavelength vertical monopoles over Sommerfeld-Norton ground with a buried radial
system of various sizes (3.75 MHz).
Soil Type No. Radials Gain TO Angle Feedpoint Impedance
dBi degrees R +/- jX Ohms
Very Poor
32 -1.16 29 36.4 + j 8.8
64 -0.43 30 34.0 + j 9.9
128 -0.28 29 32.0 + j 8.0
Poor 32 -0.07 26 39.4 + j 10.4
64 0.53 27 36.6 + j 10.5
128 0.70 26 34.2 + j 8.9
Good 32 0.26 24 40.3 + j 10.0
64 0.71 25 37.6 + j 9.7
128 0.87 25 35.5 + j 8.4
Very Good 32 2.20 19 40.0 + j 9.7
64 2.39 19 38.6 + j 9.3
128 2.53 19 37.3 + j 8.6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p><b>Table 3</b> shows the results for the 1/4 wavelength monopole. For each soil quality, the addition of radials up to the tested limit, there is the expected gain increase. The increment of gain increase itself is most evident in the move from 32 to 64 radials and is most effective with the worst of the soil qualities used. The increment of improvement in the move from 64 to 128 radials is much smaller and is least over good soil.</p>
<p>The table shows a fluctuation in the TO angle, never more than one degree. This phenomenon is a function of rounding values to the nearest whole degree and is insignificant. More notable is the fact that modeling the buried radial system shows a set of progressions that a MININEC ground cannot show. For any given soil quality, the more numerous the radials, the lower the feedpoint impedance. (Due to the construction of the model, the feedpoint position is invariant throughout the sequence of models.) However, with one exception (32 radials over very good soil), the feedpoint impedance for any size radial field increases with improvements in soil quality.</p>
<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 4. 5/8 wavelength vertical monopoles over Sommerfeld-Norton ground with a buried radial
system of various sizes (3.75 MHz).
Soil Type No. Radials Gain TO Angle Feedpoint Impedance
dBi degrees R +/- jX Ohms
Very Poor
32 0.82 18 81.6 - j 445.5
64 0.87 19 81.0 - j 447.0
128 0.88 18 80.9 - j 447.6
Poor 32 0.99 15 80.9 - j 446.4
64 1.03 15 80.3 - j 447.9
128 1.04 15 80.2 - j 448.6
Good 32 0.47 13 80.4 - j 446.8
64 0.51 13 79.8 - j 448.2
128 0.53 13 79.6 - j 448.9
Very Good 32 2.98 10 80.2 - j 448.8
64 3.01 10 79.7 - j 449.8
128 3.02 10 79.6 - j 450.9
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p><b>Table 4</b> shows comparable information derived from the model of the 5/8 wavelength radiator over the same radial systems. Radials were held to 1/4 wavelength (65.6') for all 80-meter models. Once more, there is a gain increase for any soil type with increasing numbers of radials, but the increments are much smaller and would be operationally insignificant. The general gain pattern for the long vertical varies in accord with the MININEC ground values, but at a lower level except for the use of a good ground. A good ground yields the lowest gain of the test group owing to the particular composite ground conductivity-permittivity phase angle in the calculation of ground effects in the Sommerfeld-Norton (S-N) system, a factor first noted (to the best of my knowledge) by Jack Belrose. Good ground is not always best for a vertical radiator. In passing, one should note that the ground used in modeling is homogenous and cannot take into account affects of stratified changes in ground quality with depth. Since radiation penetration at MF and lower HF is considerable, real conditions for a vertical monopole for 80 meters might vary considerably from the conductivity measurements made near the surface. Although the radial system may respond according to the model, the far field may vary in strength and TO angle from the modeled result.</p>
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<p>The use of a buried radial system does not alter one major result of the study, despite considerable variance between MININEC-ground and S-N ground. As shown in <b>Fig. 6</b>, there is no significant variation of gain between a 1/4 wavelength and a 5/8 wavelength radiator over good ground. The chief edge for the longer radiator lies in the lower elevation angle of the main lobe of radiation, but with the drawback of having a fairly strong higher lobe of radiation. Any advantage in gain for the longer radiator shows up over worse quality soils. With the largest radial fields, the 5/8 wavelength radiator shows a 0.5 dB advantage over a 1/4 wavelength radiator when the soil approximates the poor level and a full dB advantage when the soil is very poor. Over very good soil, the longer radiator again shows a half-dB advantage.</p>
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<p>An interesting aspect of the 5/8 wavelength radiator is its pattern when we compare different soil qualities. For reference, <b>Fig. 7</b> shows the 1/4 wavelength patterns for very poor and very good soil using the 32-radial field. As we might expect, there is little to distinguish the pattern shapes. Essentially, only the signal strength and the TO angle have changed significantly. Making a similar comparison of 5/8 wavelength patterns yields a feature that has not been well-noted in amateur literature. In <b>Fig. 8</b>, we find the same decrease in signal strength and TO angle for the pattern taken over very poor soil. However, the angle and strength of the secondary lobe in the region of 50-55&oslash; elevation does not change over the range of soil qualities. Both conditions yield about the same susceptibility to high-angle QRN. Of course, if we speak in relative terms, the high-angle QRN over very poor soil will be stronger in comparison to the received signal strength from low-angle radiation.</p>
<center>
<img src="58-8.gif" width="640" height="255" border="2" vspace="5" hspace="9">
</center>For the purposes of comparison, I modeled a vertical dipole with the same top height s the 5/8 wavelength monopole. The model achieved resonance with the base 35.7' above ground. Although impractical to implement, the dipole was center-fed. The goal was to find out whether the 5/8 wavelength monopole showed any superiority over the dipole, since both antennas would show a current maximum at just about the same height. The dipole was modeled over a MININEC ground, over an S-N ground with no radials, and over an S-N ground having 32 radials. We can compare the results in <b>Table 5</b> with those for the long monopole in <b>Table 4</b>.
<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 5. 1/2 wavelength vertical dipole over MININEC and Sommerfeld-Norton ground (with and
without a 32-radial ground plane) (3.75 MHz).
Soil Type Ground Type/ Gain TO Angle Feedpoint Impedance
No. Radials dBi degrees R +/- jX Ohms
Very Poor
MININEC/0 -0.27 18 75.3 + j 0.2
S-N/0 -0.11 17 72.8 + j 3.5
S-N/32 0.02 18 73.8 + j 4.7
Poor MININEC/0 0.36 15 75.3 + j 0.2
S-N/0 0.47 15 73.5 + j 2.5
S-N/32 0.55 15 74.5 + j 3.0
Good MININEC/0 0.11 13 75.3 + j 0.2
S-N/0 0.22 14 73.5 + j 1.6
S-N/32 0.28 14 74.1 + j 2.1
Very Good MININEC/0 3.04 11 75.3 + j 0.2
S-N/0 3.09 11 74.4 + j 0.6
S-N/32 3.10 11 74.6 + j 0.7
Note: Dipole was set for the same top height (164') as the 5/8 wavelength monopole, resulting
in a bottom height of 35.7' for a near-resonant length of 0.1" diameter copper wire.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p>Over very good ground, there is no practical difference in performance between the elevated dipole and the 5/8 wavelength monopole, regardless of the presence or absence of radials beneath the dipole. However, with soil worse than very good, the monopole shows an increasing gain advantage over the dipole--nearly a full dB over very poor soil. As well, the presence of a buried radial system (using 1/4 wavelength radials) beneath the dipole shows a small but definite performance improvement over a no-radial condition, and the effect becomes greater with worsening soil conditions. Whether the performance improvement is significant enough for the investment of resources in putting the radial system in place would be a user judgment.</p>
<p>The upshot of these studies into the performance of a 5/8 wavelength monopole over and against a 1/4 wavelength monopole can be summarized this way,</p>
<ul>
<li>1. The 5/8 wavelength radiator shows significant gain advantage over a 1/4 wavelength monopole only over soils that are poor or worse, but in any event, the gain advantage is far less than the theoretical 3 dB that yielded the 5/8 wavelength mystique.</li>
<li>2. The 1/4 wavelength monopole, besides its considerable mechanical simplicity, has an advantage in the absence of a secondary high-angle lobe of considerable strength relative to the main lobe; hence, the quarter wavelength radiator may be quieter in most installations.</li>
<li>3. The chief advantage of the 5/8 wavelength monopole lies in the lower TO angle for the main lobe.</li>
</ul>
<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 6. Ground wave strength of 1/4 wavelength and 5/8 wavelength monopoles at 10
wavelengths from the antenna at ground level with 1000 watts (3.75 MHz).
Soil Type 1/4 WL Gnd Wave 5/8 WL Gnd Wave Difference
milliVolts/meter milliVolts/meter percent
Very Poor 54.04 84.81 57%
Poor 99.61 147.49 48%
Good 161.60 222.92 38%
Very Good 319.33 437.77 37%
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p>The last point in part explains the preference--when feasible--for a 5/8 wavelength radiator in MF applications where ground wave strength is a design goal. <b>Table 6</b> provides ground wave values in mV/m at a distance of 2623' (10 wavelengths at 3.75 MHz) from the two types of monopoles, taken at ground level. The 5/8 wavelength radiator shows a significantly higher field strength. The percentage of increase in the field strength over that produced by the 1/4 wavelength radiator increases with decreasing soil quality.</p>
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<p>I must add one final note before turning to VHF applications of these radiators. Although there is no magic to using a precise 5/8 wavelength radiator relative to imprecisely approximating that height, there is a danger in letting the radiator become too long. As is the case with the related extended-double Zepp (the EDZ, a 1.25 wavelength center-fed radiator), further increases in radiator length reduce field strength perpendicular to the radiator and increase the strength of lobes at oblique angles to the radiator. The EDZ pattern in horizontal use devolves into 6 lobes of approximately equal strength when the radiator reaches 1.5 wavelengths. <b>Fig. 9</b> shows what happens when we let the monopole grow to a corresponding 3/4 wavelength height. The low-angle radiation disappears, and the strongest radiation is in the vicinity of a 45&oslash; elevation angle. This note is perhaps unnecessary for experienced antenna designers planning to use a monopole at its fundamental frequency. However, such antennas are often pressed into service on higher frequencies, where they are correspondingly longer in terms of wavelengths. Users often wonder at the absence of low-angle radiation without considering the effects of vertical length on the radiation pattern.</p>
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<p><i>Updated 04-17-2001. &COPY; 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.</i></p>
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<p><a href="58-2.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Part 2: 2-Meter Elevated Ground-Plane Antennas</a></p>
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<!DOCTYPE html>
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<head>
<meta charset="UTF-8">
<meta name="keywords" content="Vertical, VHF / UHF">
<title>The 5/8-Wavelength Mystique Part 2: 2-Meter Elevated Ground-Plane Antennas</title>
<link rel="stylesheet" href="../styles.css">
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<center>
<h1><img src="../images/gpbut.gif" align="left" width="90" height="84" border="2" vspace="5" hspace="10"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">The 5/8-Wavelength Mystique<br>
Part 2: 2-Meter Elevated Ground-Plane Antennas</h1>
</center>
<center>
<h3>L. B. Cebik, W4RNL</h3>
</center>
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<p>At VHF, both the 1/4 wavelength monopole and the 5/8 wavelength monopole are widely used, but in circumstances quite different from those applicable to an 80-meter monopole. Some 15 years ago, Don Reynolds, K7DBA, looked at "The 5/8-Wavelength Antenna Mystique" (in <i>The ARRL Antenna Compendium</i>, Vol. 1 [Newington: 1985], pp. 101-106). I knew my title had to have a source other than pure creativity. In any event, although the article must be read in the context of affiliations with AEA, which began back then marketing an effective telescoping 1/2 wavelength antenna for handhelds, the measurements used as the basis of the article will interest those who read further into this modeling study.</p>
<p>The VHF monopole is designed for elevated use, normally with 4 symmetrical 1/4 wavelength radials. We shall not here deal with monopoles of any length without radials, although radial-less dipoles will be noted. To understand the relative performance potential of these antennas, it was necessary to construct a number of models to account for the variety of configurations. <b>Fig. 10</b> shows the span of models considered, where all models used 0.25" diameter aluminum for every element.</p>
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<ul>
<li>1. A 1/4 wavelength (20.15") radiator and 4 19" radials at right angles to the vertical.</li>
<li>2. A 1/4 wavelength (18.7") radiator with 4 18.5" radials sloping downward 45&deg;.</li>
<li>3. A 1/2 wavelength (38.14") vertical dipole.</li>
<li>4. A 5/8 wavelength (50.5") radiator and 4 19" radials at right angles to the vertical.</li>
<li>5. A 5/8 wavelength (50.5") radiator with 4 18.5" radials sloping downward 45&deg;.</li>
</ul>
<p>The test frequency was 146 MHz, where a wave is 80.84" long, making the selection of the length of the longer monopole obvious. The 1/4 wavelength monopoles were adjusted for resonance, with adjustment also to the sloping radial length to bring the radiator and radial lengths into rough alignment.</p>
<p>Each model was run over the standard soil varieties. Given that VHF antennas are used under varying circumstances, I approximated two major ones. For roof and tower mounting, I used a height of 25' (300") at the base of the monopoles and the center of the dipole. Further height increases would not have altered the results significantly in terms of operational trends. Vertical monopoles are also used in mobile and temporary installations. For that case, I used a base height of 5' (60").</p>
<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 7. 146 MHz 1/4 wavelength vertical monopole with 4 90&deg; radials at 5' and 25' base height.
5' Base Height 25' Base Height
Soil Type Gain TO Angle Feed Z Gain TO Angle Feed Z
dBi degrees R+/-jX dBi degrees R+/-jX
Very Poor 2.76 12.2 26 - j 1 5.83 3.4 26 - j 0
Poor 2.32 34.3 26 - j 1 5.28 3.4 26 - j 0
Good 2.32 33.9 26 - j 1 5.28 3.4 26 - j 0
Very Good 2.90 33.5 26 - j 1 4.90 3.3 26 - j 0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p><b>Table 7</b> summarizes the results for the 1/4 wavelength monopole with 4 radials at right angles to the radiator. At a height of 60", the radiated field strength of the antenna is best over very poor and very good soils. However, note that the TO angle for all but the worst soil is not the expected very low angle. The low angle corresponding to the strongest lobe over very poor soil has a reduced signal strength, although not down by more than about 1 dB or so from the higher-angle lobe. <b>Fig. 11</b> shows the changing balance between the lower and higher lobes of the array as we change the soil quality beneath it at a base height of 5'.</p>
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<p>At a height of 300", the expected low radiation angle for the major lobe is present. However, note the decreasing gain with increasing soil quality. Although the amount is not operationally significant, the trend is interesting.</p>
<p>A further factor to note is the lower-than-expected feedpoint impedance for the 1/4 wavelength monopoles. Received wisdom anticipates a feedpoint impedance of about 35-36 Ohms, based on ground mounted monopoles over perfect ground. An elevated monopole does not easily answer to this conception. The monopoles constructed for this model began with a free-space 1/2 wavelength dipole. One half of the dipole was replaced with 4 radials, with lengths adjusted until two conditions were achieved. First, the maximum current level is at the feedpoint, and the sum of the currents on the first radial segment of each of the four radials was close to the source segment current value. Second, the lengths of the radiator and the radials were adjusted to achieve resonance and to retain the current maximum position.</p>
<p>A useful technique for establishing a reasonable equality between the current level on the source segment of the monopole and the sum of the current levels on the first segment of the four radials is to use a maximum of segments consistent with maintaining a reasonable segment-length-to-radius ratio. As well, a close equality should be maintained between the segment lengths on the monopole and on the radials, since the source segment will be immediately adjacent to the first segments on the radials. For the 90&deg; and sloping radial 1/4 wavelength monopoles, 31 segments per element provides a very usable figure while still maintaining a small enough model that does not require segment length-tapering to run on basic NEC-2 software. Small deviations from the goal of equal currents did not produce significant changes in the feedpoint impedance, which is about 38% lower than image-based conceptions of a monopole would dictate. Changing the number of radials does not materially affect the impedance or the vertical radiator length, if the radial lengths are adjusted to bring the assembly back to resonance.</p>
<p>The 1/4 wavelength monopole with sloping radials was constructed in the same manner. The length of the radiator and the lengths of the 45&deg;-sloping radials were adjusted to place the maximum current at the feedpoint and to have a division of current among the radials so that sum of the currents in the 4 radials at their junction equaled the current level at the feedpoint, with the assembly as close to resonance as feasible. Consequently, both the radiator and the radial lengths are different from those used in the 90&deg; radial model.</p>
<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 8. 146 MHz 1/4 wavelength vertical monopole with 4 45&deg; radials at 5' and 25' base height.
5' Base Height 25' Base Height
Soil Type Gain TO Angle Feed Z Gain TO Angle Feed Z
dBi degrees R+/-jX dBi degrees R+/-jX
Very Poor 3.24 13.0 51 - j 0 6.74 3.5 50 + j 0
Poor 2.47 37.5 51 - j 0 6.18 3.4 51 + j 0
Good 2.48 37.5 51 - j 0 6.18 3.5 51 + j 0
Very Good 3.03 36.7 51 - j 0 5.79 3.4 51 + j 0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p><b>Table 8</b> collects the results of running the model at both high and low levels. At 5', the sloping-radial monopole shows the same pattern of high-angle main lobes except over very poor soil. At 25', the pattern of decreasing gain with increasing soil quality also reappears. The chief difference in performance is a noticeable increase in gain at all levels and soils relative to the 90&deg; radial monopole. At 25', the difference amounts to nearly 1 dB.</p>
<p>The reason for the gain increase is simple: the sloping radials have both a horizontal and a vertical component to their radiated fields. The horizontal components cancels (if the radials are identical in length and symmetrically distributed). However, the vertical component--non-existent in the 90&deg; monopole--contributes to the overall radiation of the antenna, yielding a small gain increase.</p>
<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 9. 146 MHz 1/2 wavelength vertical dipole at 5' and 25' (feedpoint height).
5' Base Height 25' Base Height
Soil Type Gain TO Angle Feed Z Gain TO Angle Feed Z
dBi degrees R+/-jX dBi degrees R+/-jX
Very Poor 3.08 13.2 72 - j 0 6.79 3.6 72 - j 0
Poor 2.19 11.0 73 - j 0 6.22 3.5 72 - j 0
Good 2.14 11.1 73 - j 0 6.22 3.5 72 - j 0
Very Good 2.42 38.0 73 - j 0 5.83 3.4 72 - j 0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p>If the sloping radials increase gain, then a true vertical dipole should show additional increases in antenna gain. Therefore, I modeled a reference dipole for the test frequency--with the dipole center at the test heights so that the maximum current position would be consistent among the models. <b>Table 9</b> reports the modeling results. At 25'. the dipole shows a minor (and operationally insignificant) increase in gain over all soils relative to the 45&deg;-radial monopole. At the lower height, the dipole shows a reduction in gain--largely as a function of the closer proximity of the lower antenna end to the ground. However, except over very good soil, the TO angle of the strongest lobe is now at the expected low angle. Hence, for poor and good soils, the gain comparison is not especially valid, since the radiation is headed in different directions. Nonetheless, the dipole can be considered to have a slightly weaker signal, but one more likely to be directed at a favorable elevation angle. <b>Fig. 12</b> compares elevation patterns of the three antennas so far considered at a height of 25' above good ground. In practical terms, the low- angle lobes of the dipole and the 45&deg; sloping-radial monopole overlap, with the 90&deg;-radial monopole slightly weaker.</p>
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<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 10. 146 MHz 5/8 wavelength vertical monopole with 4 90&deg; radials at 5' and 25' base
height.
5' Base Height 25' Base Height
Soil Type Gain TO Angle Feed Z Gain TO Angle Feed Z
dBi degrees R+/-jX dBi degrees R+/-jX
Very Poor 3.74 9.9 65 - j 227 5.78 3.2 65 - j 227
Poor 2.87 25.2 65 - j 227 5.28 3.2 65 - j 227
Good 2.87 25.2 65 - j 227 5.28 3.2 65 - j 227
Very Good 3.36 24.5 65 - j 227 4.94 3.2 65 - j 227
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p>The key question is whether a 5/8 wavelength radiator will have any advantage over the array of monopoles and dipoles we have so far explored. <b>Table 10</b> tells the story for a 50.5" radiator over quarter wavelength radials set at 90&deg; to the radiator. At a base height of 5' above ground, the 5/8 wavelength monopole shows the same progression of gain values and the same relatively high-angle main lobes as the 45&deg; sloping-radial monopole, the better of the two 1/4 wavelength monopole arrays. <b>Fig. 13</b> reveals, as do the tabular numbers, that the 5/8 wavelength monopole has a slightly lower-angle lowest lobe and slightly greater strength, with the elevation pattern taken over good ground.</p>
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<p>Notable in the comparison of patterns is the fact that the elevation pattern of the longer monopole has one more lobe than the pattern for the 1/4 wavelength antenna. Hence, while the lowest lobe is stronger than that of the shorter antenna, the longer monopole also has stronger radiation at considerably higher angles than the 1/4 wavelength monopole. The consequence of the third lobe is to increase the complexity of the lobe structure variations as we change the soil type over which we operate the antenna at a height of 5'. <b>Fig. 14</b> shows the elevation patterns for the 5/8 wavelength monopole for very poor, good, and very good soils in order to demonstrate the changing balance among lobes. (Poor soil is omitted since its pattern overlaps the pattern for good soil.)</p>
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<p>Although the 5/8 wavelength monopole shows a very slight advantage over the 1/4- wavelength monopole with sloping radials, the advantage disappears when we raise the longer antenna to 25' at its base. Comparing the numbers in <b>Table 8</b> and <b>Table 10</b> sets the stage for examining <b>Fig. 15</b>. With both antennas over good soil, the 1/4 wavelength monopole with sloping radials shows nearly a full dB additional gain over the 5/8 wavelength model.</p>
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<p>In the end, it is dubious whether a 5/8 wavelength monopole has any significant operating benefit over a 1/4 wavelength monopole, each with 4 radials. Perhaps the higher top height of the longer antenna will yield some benefit when its base is very close to the ground. However, the 5/8 wavelength monopole always requires some form of matching system for use with a 50- Ohm coaxial cable, and matching systems at VHF are not without loss. At rooftop and higher levels, the sloping radial monopole with a 1/4 wavelength radiator or a half wavelength dipole will do as well--or better.</p>
<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 11. 146 MHz 5/8 wavelength vertical monopole with 4 45&deg; radials at 5' and 25' base
height.
5' Base Height 25' Base Height
Soil Type Gain TO Angle Feed Z Gain TO Angle Feed Z
dBi degrees R+/-jX dBi degrees R+/-jX
Very Poor 3.02 50.2 65 - j 191 3.95 36.2 65 - j 191
Poor 3.83 51.1 65 - j 191 4.90 36.1 65 - j 191
Good 3.84 51.0 65 - j 191 4.90 36.1 65 - j 191
Very Good 4.21 51.1 65 - j 191 5.30 36.1 65 - j 191
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p>One tendency of those who home brew VHF monopoles is to attempt to replicate the advantages of the sloping radial system that adds to the performance of a 1/4 wavelength monopole. Hence, they slope the radials of a 5/8 wavelength monopole. In principle, the radiation resistance goes down, requiring only a series inductance as a means of compensating for the capacitive reactance at the feedpoint. Unfortunately, the maneuver results in a major change in the elevation pattern of the antenna over all qualities of soil, as revealed in <b>Table 11</b>. Radiation from the lowest lobe is over 2 dB down from the flat-radial system. <b>Fig. 16</b> shows the situation graphically over good soil at a height of 25'. The number of lobes in the pattern does not change with the change in radial angle, but the power distribution changes very significantly. In general, a 5/8 wavelength monopole with sloping radials cannot be recommended for general communications.</p>
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<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 12. 146 MHz 1.25 wavelength vertical EDZ at 5' and 25' (feedpoint height).
5' Base Height 25' Base Height
Soil Type Gain TO Angle Feed Z Gain TO Angle Feed Z
dBi degrees R+/-jX dBi degrees R+/-jX
Very Poor 4.31 10.5 115 - j 389 9.49 3.5 108 - j 385
Poor 3.70 9.3 118 - j 390 8.93 3.4 108 - j 385
Good 3.65 9.4 118 - j 390 8.93 3.5 108 - j 385
Very Good 3.22 8.7 120 - j 391 8.54 3.4 108 - j 385
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p>There is one more antenna that deserves passing recognition before we summarize the results of the VHF use of monopole. Although completely impractical at 80 meters, a vertical EDZ can be effectively used at VHF in many circumstances. <b>Table 12</b> summarizes the results of modeling a 111" center-fed EDZ at the center heights used for the dipole: 60" and 300". At the lower height, the antenna is only 10" above the ground, but it outperforms any of the monopoles and the dipole. It shows a consistent low angle for the main lobe, a fact illustrated in the 5' outline of the elevation pattern in <b>Fig. 17</b>. As well, the antenna shows the decreasing gain with improvements in soil quality so that with very good soil, the gain drops just below the level achieved by the 5/8 wavelength monopole with its base at 60" above ground.</p>
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<p>With the antenna center at 25' above ground, the EDZ provides just under 3 dB additional gain relative to the best of the other antennas in the collection examined here. The elevation pattern is also shown in <b>Fig. 17</b>. The feedpoint impedance of the vertical EDZ will be a challenge to transform to what a 50-Ohm cable requires, but there are both network and linear transmission line methods of achieving the match. Even allowing for the losses in such systems, the vertical EDZ may be worth considering for some applications. See, for example, Rick Littlefield, "The 2-Meter PVC-EDZ Antenna, <i>Communications Quarterly</i> (Summer, 1997), pp. 104-106. As well, see <a href="../edz/edzfeed.html"><b>"Feeding the EDZ"</b></a> at this site for additional notes on this general technique, sometimes called using "delay lines."</p>
<p>Whatever the advantages of using a straight vertical radiator, the question that formed the basis for this VHF study was whether there is any profit in using a 5/8 wavelength monopole in preference to a 1/4 wavelength monopole when each is equipped with 4 radials. The results of our investigation might be summarized as follows.</p>
<ul>
<li>1. At heights well above 1 wavelength, the 5/8 wavelength monopole is no better than a 1/4 wavelength monopole--and the shorter antenna may have a slight advantage when its radials are sloped 45&deg;. In addition, the sloping-radial short monopole may offer matching benefits.</li>
<li>2. At low heights, the longer monopole offers very slight gain advantages, but like the 1/4 wavelength monopole, the elevation of maximum radiation over most soil types tends to be quite high.</li>
<li>3. For lower operating heights, a vertical dipole or EDZ offer more consistent low angle performance over most soil types, although the mounting and matching questions may present the builder with considerable challenges.</li>
</ul>
<p>The modeling application to house-top mounted monopoles is--except for nearby metallic structures--applicable to reality without much adjustment. However, the results for lower mounting heights would need adjustment for the effects of the antenna surroundings. Hand-held antennas are almost impossible to predict relative to surrounding influences on radiated signals. However, Dan Richardson, K6MHE, is performing some studies of typical monopoles and other antennas mounted on various types of vehicles, as simulated by a series of detailed wire-grid structures. I shall await the results of his work to see if the greater height of the current maximum for a 5/8 wavelength monopole mounted on the trunk of a car makes a significant difference relative to the lower current maximum of a 1/4 wavelength monopole mounted in the same position. In short, a final decision on which type of antenna may be best (including both vertical dipoles and EDZs) must rest on a full analysis of the operating circumstances. At best, these general notes are indicators, but they are not final or universal judgments.</p>
<p>Before we can complete the overall picture of 5/8 wavelength monopole performance relative to the more familiar 1/4 wavelength monopole, we must look at one more frequency region: the upper HF bands.</p>
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<p><i>Updated 04-17-2001. &COPY; 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.</i></p>
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<p><a href="58-3.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Part 3: Upper HF Monopoles</a></p>
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<title>The 5/8-Wavelength Mystique Part 3: Upper HF Monopoles and a "Poorly Grounded" Speculation</title>
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<h1><img src="../images/gpbut.gif" align="left" width="90" height="84" border="2" vspace="5" hspace="10"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">The 5/8-Wavelength Mystique<br>
Part 3: Upper HF Monopoles and<br>
a "Poorly Grounded" Speculation</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>From various sources, the idea persists that it is possible to create a "gain" vertical monopole for the upper HF bands by using a 5/8 wl radiator instead of the more usual 1/4 wl radiator. From various books, the idea tends to migrate on occasion into magazine articles, where new generations of amateurs accept the premise as gospel. The purpose of this final section of our investigation is to see what truth, if any, lies in this persistent notion.</p>
<p>To accomplish the investigation, I modeled monopoles with 4 1/4-wl radials at 20 and 10 meters--specifically, at 14.15 MHz and 28.5 MHz. The 20-meter monopoles used 1" diameter radiators, while the 10-meter models used 0.5" vertical elements. All radials were #12 AWG wire.</p>
<p>The 20-meter radials were 199.4" long, with a 211" 1/4-wl vertical and, alternatively, a 41.5' 5/8-wl vertical. For the 1/4-wl monopoles, I used the same standard as with the VHF monopoles: the sum of the currents on the first segments of each radial added up to the value of the source current on the main radiator. The one exception to these dimensions is the last section of <b>Table 13</b>, where I revised the dimensions of the 1/4-wl monopole with radials that sloped at a 45-degree angle to bring the system to resonance and to effect the "equal current" standard. In this revised monopole, the radiator is 200" long, with 191" radials. No such revision was made to the non-resonant 5/8-wl radiator.</p>
<p>Similarly, at 10 meters, I used a 104.75" radiator with 99" radials for the 1/4-wl monopole system. Since there was no significant change in any parameter except the feedpoint impedance when revising the 20-meter sloping-radial model, I did not perform the same operation on the 10-meter antenna. The 5/8-wl monopole used the same radials, but with a 255" vertical radiator.</p>
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<p><b>Fig. 18</b> shows the 4 types of models for each band. Both the 1/4-wl and 5/8-wl monopoles were modeled with radials at 90 degrees to the radiator and with radials sloping 45 degrees downward. Each 90-degree monopole was modeled at heights of 1, 5, and 25 feet to simulate ground, low, and roof-top positioning of the antenna base. Only the 25' high monopole was adapted to sloping radials. Since the fixed physical heights for test modeling represent different heights in terms of wavelengths for each of the two bands, I modeled each band separately.</p>
<p>As with all other antennas--and subject to some speculative discussion at the end of this section--the antennas were modeled over the standard spectrum of soil quality samples: very poor, poor, good, and very good. See part 1 of these notes for full details on the conductivity and permittivity of each soil grade.</p>
<h3>20 Meters</h3>In a partial way, <b>Table 13</b> and <b>Table 14</b> sum up the results for 1/4-wl and 5/8-wl monopoles. However, there is a cursory and misleading way to read the tables and a more accurate method of digesting them.
<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 13. 20-Meter 1/4-wl monopoles over various soils.
Soil Type Gain TO Angle Lobe Feedpoint Impedance
dBi degrees No. R +/- jX Ohms
1/4-wl Monopole, 90-degree radials, 1' above ground
Very Poor -1.03 28 1 35.8 + j 6.7
Poor 0.00 26 1 38.5 + j 10.2
Good -0.24 25 1 37.6 + j 9.9
Very Good 0.76 22 1 42.8 + j 12.1
1/4-wl Monopole, 90-degree radials, 5' above ground
Very Poor -0.39 25 1 29.2 + j 0.4
Poor 0.43 22 1 31.3 + j 0.7
Good 0.16 22 1 31.3 + j 0.2
Very Good 1.05 19 1 33.6 + j 0.3
1/4-wl Monopole, 90-degree radials, 25' above ground
Very Poor 1.37 17 1 23.2 + j 4.2
Poor 1.11 14 1 22.8 + j 4.1
Good 0.55 14 1 22.8 + j 4.2
Very Good 1.00 33 2 22.4 + j 4.3
1/4-wl Monopole, 45-degree radials, 25' above ground
Very Poor 1.43 18 1 55.3 + j 35.8
Poor 1.54 15 1 54.9 + j 34.7
Good 1.05 15 1 54.6 + j 34.7
Very Good 1.17 12 1 53.8 + j 33.6
1/4-wl Monopole, 45-degree radials, 25' above ground (revised dimensions)
Very Poor 1.40 18 1 47.5 + j 0.8
Poor 1.54 15 1 47.2 - j 0.2
Good 1.05 15 1 46.9 - j 0.3
Very Good 1.19 12 1 46.3 - j 1.2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 14. 20-Meter 5/8-wl monopoles over various soils.
Soil Type Gain TO Angle Lobe Feedpoint Impedance
dBi degrees No. R +/- jX Ohms
5/8-wl Monopole, 90-degree radials, 1' above ground
Very Poor 1.70 19 1 107 - j 366
Poor 1.74 16 1 107 - j 366
Good 1.29 16 1 107 - j 366
Very Good 1.26 14 1 107 - j 366
5/8-wl Monopole, 90-degree radials, 5' above ground
Very Poor 1.98 18 1 106 - j 370
Poor 1.81 15 1 106 - j 369
Good 1.33 15 1 106 - j 369
Very Good 0.96 12 1 105 - j 369
5/8-wl Monopole, 90-degree radials, 25' above ground
Very Poor 3.00 14 1 108 - j 369
Poor 2.67 38 2 109 - j 369
Good 2.87 37 2 109 - j 369
Very Good 3.95 37 2 109 - j 369
5/8-wl Monopole, 45-degree radials, 25' above ground
Very Poor 3.29 36 2 104 - j 351
Poor 4.18 37 2 105 - j 351
Good 4.31 36 2 106 - j 352
Very Good 5.27 35 2 107 - j 352
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p>According to the modeling analysis, at 1' above ground, the 5/8-wl antenna shows a 1.37 dB average gain advantage over the 1/4-wl monopole. As we raise the base height to 5', the advantage on average remains about 1.31 dB--very consistent with the advantage at the lower height. However, when we place that antenna atop a 25' roof, the 5/8-wl vertical outstrips the 1/4-wl assembly by 2.11 dB with 90-degree radials and by 2.96 dB with sloping radials. From this quick readout, it would appear that the 5/8-wl vertical has finally achieved the 3 dB advantage so many claim for it relative to the shorter vertical.</p>
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<p>However, for the elevated 5/8-wl monopole, we must pay special attention to the "Lobe Number" column in the tables. For the 1/4-wl antenna, as partially illustrated by <b>Fig. 19</b>, the elevation patterns show their strongest radiation from the lowest lobe--if there is more than one. The 1' high antenna (1-90 in the figure) and the 5' high antenna (5-90 in the figure) have only a single lobe in their elevation patterns due to the very low mounting heights. The higher versions with 90-degree or 45-degree radials (25-90 and 25-45 in the figure) show the emergence of a second lobe at a higher angle. Only for the 90-degree radial 25' high monopole over very good ground does the second lobe grow stronger than the lower lobe. In all other cases, the lower lobe dominates the pattern. Hence, the recorded signal strength of maximum gain is almost always for the lowest lobe (#1) for the 1/4-wl monopole at all heights.</p>
<p>When we turn to the 5/8-wl monopole, partially illustrated in Fig. 20, we discover that the situation is not at all the same. For almost all cases where the antenna is mounted at 25', the strongest lobe is not the lowest one, but instead is the higher-angle second lobe. The only exception among angles tested is the 90-degree-radial 5/8-wl monopole when placed over very poor soil. This particular case is the basis for some speculations on ground quality at the end of this study.</p>
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<p>As <b>Fig. 20</b> reveals, there is something curious about the patterns for 5/8-wl monopole. The lowest lobe remains at a relatively constant angle and strength. Lowest-lobe signal strength varies between 1.29 and 1.51 dBi over good soil as we change the base height, and the lobe TO angle is between 12 and 16 degrees above the horizon. The higher maximum gains reported by the models when the antenna has a base height of 25' are wholly a function of the upper lobe, the TO angle of which ranges above 35 degrees. If we use the lower lobe of the 5/8-wl pattern as a guide (instead of the stronger upper lobe), then the 5/8-wl monopole advantage over the 1/4-wl monopole at the same base height drops to the 0.5 to 1.0 dB range--far below the desired 3-dB advantage.</p>
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<p><b>Fig. 21</b> shows what the gain advantage amounts to, using the 90-degree radial versions of the two monopoles, each with a base height of 25' above good ground. In operation, there would be little to choose between the two antennas. The very slight gain advantage of the longer monopole is offset by its greater sensitivity to high-angle QRN. Whether a 41.5' rooftop radiator is sufficiently easy to maintain relative to the standard 17.6' 1/4-wl radiator to go for the extra partial dB is a user judgment.</p>
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<p>As shown in <b>Fig. 22</b>, a set of elevation plots for the 5/8-wl monopole with 90-degree radials at a base height of 25', the vertical antenna exhibits some of the same properties as the VHF verticals. As we improve the soil quality both beneath the antenna and in the ground-reflection region, the lower lobe shrinks and the upper lobe increases in strength. Contrary to the expectations of many, the strongest lowest lobe occurs over very poor soil.</p>
<p>The 20-meter monopoles at a 25' base height are only about 1/3 wavelength above ground. That same physical base height is above 2/3 wavelengths on 10 meters. Therefore, the 10-meter versions of our monopole sets deserves independent attention.</p>
<h3>10 Meters</h3>The 10-meter monopoles used the same range of physical base heights as those for 20: 1, 5, and 25' up, with the highest versions using both a 90-degree radial set and a sloping 45-degree set. <b>Table 15</b> and <b>Table 16</b> summarize the results of the modeling.
<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 15. 10-Meter 1/4-wl monopoles over various soils.
Soil Type Gain TO Angle Lobe Feedpoint Impedance
dBi degrees No. R +/- jX Ohms
1/4-wl Monopole, 90-degree radials, 1' above ground
Very Poor -0.66 27 1 33.4 + j 4.2
Poor 0.23 25 1 36.1 + j 6.1
Good 0.07 25 1 36.4 + j 5.8
Very Good 0.43 23 1 38.8 + j 6.2
1/4-wl Monopole, 90-degree radials, 5' above ground
Very Poor 0.43 22 1 25.2 + j 1.3
Poor 0.95 19 1 26.1 + j 0.5
Good 0.75 20 1 26.0 + j 0.3
Very Good 0.81 17 1 26.5 - j 0.5
1/4-wl Monopole, 90-degree radials, 25' above ground
Very Poor 2.99 13 1 24.1 + j 4.0
Poor 2.67 35 2 24.2 + j 3.9
Good 2.73 34 2 24.2 + j 3.9
Very Good 3.78 33 2 24.1 + j 3.8
1/4-wl Monopole, 45-degree radials, 25' above ground
Very Poor 3.11 13 1 59.3 + j 38.3
Poor 2.42 38 2 59.6 + j 38.2
Good 2.51 37 2 59.6 + j 38.1
Very Good 3.52 36 2 59.8 + j 38.0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 16. 10-Meter 5/8-wl monopoles over various soils.
Soil Type Gain TO Angle Lobe Feedpoint Impedance
dBi degrees No. R +/- jX Ohms
5/8-wl Monopole, 90-degree radials, 1' above ground
Very Poor 2.13 19 1 82 - j 307
Poor 1.97 16 1 82 - j 307
Good 1.72 16 1 82 - j 307
Very Good 1.05 13 1 82 - j 308
5/8-wl Monopole, 90-degree radials, 5' above ground
Very Poor 2.43 17 1 83 - j 307
Poor 1.88 14 1 83 - j 307
Good 1.63 14 1 83 - j 307
Very Good 2.21 46 2 83 - j 307
5/8-wl Monopole, 90-degree radials, 25' above ground
Very Poor 4.13 10 1 84 - j 308
Poor 3.16 26 2 84 - j 308
Good 3.19 25 2 84 - j 308
Very Good 4.19 24 2 84 - j 308
5/8-wl Monopole, 45-degree radials, 25' above ground
Very Poor 3.02 10 1 83 - j 283
Poor 3.57 25 2 84 - j 283
Good 3.54 25 2 84 - j 283
Very Good 4.26 23 2 84 - j 282
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p>If we again begin with a casual reading of the tabular data, we find that the 5/8-wl monopole has an advantage over the 1/4-wl antenna at every height. At the 25' level, the advantage is about 0.6 to 0.7 dB. The reason for this low figure, compared to what we initially encountered on 20 meters at the same height, is that both the 1/4-wl and the 5/8-wl antennas show maximum strength in the second, higher lobe. The common exception is once again when the antenna is over very poor soil, where the lower lobe dominates.</p>
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<p>On 10 meters, even the 1/4-wl monopole shows a strong development of the second elevation lobe when the base of the antenna is 25' up. As shown in <b>Fig. 23</b>, over good ground, the differences between the flat-radial and sloping radial systems are minimal. Similarly, the there are no highly significant differences in the patterns for 90-degree and sloping 45-degree radial systems when we turn to the 5/8-wl monopole. With respect to the two lower lobes, as shown in <b>Fig. 24</b>, the structures are similar. However, note that the 5/8-wl monopole has developed a third elevation lobe near the 50-degree elevation angle. With sloping radials, this lobe is stronger than the lowest lobe. With the 90-degree radial set, the situation is reversed, even though the second lobe remains the strongest in both cases.</p>
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<img src="58-24.gif" width="640" height="280" border="2" vspace="5" hspace="9">
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<p>At a 25' height, the lowest lobe for either version of the 5/8-wl monopole is between 1.7 and 1.8 dBi. The lowest lobe of the 1/4-wl vertical with the same base height is about 1.5 dB whether the radials are straight or sloping. Hence, at the most desired angles of radiation, the 5/8-wl monopole advantage drops to a small fraction of a dB--hardly worth the extra 12' feet of vertical radiator in most cases.</p>
<p>We have tended to focus on the performance of the antennas at roof-top height. However, the two types of monopoles are also worth comparing at lower base heights. Here the 5/8 wl gain advantage is in the 1.3 to 1.7 dB range on 10 meters. Perhaps of equal importance is the fact that elevation angle of maximum radiation is 6 to 8 degrees lower than for the 1/4-wl monopole--indeed, it sits squarely in the most desire elevation-angle region for effective DX operation. Note as well that the 1/4-wl monopole shows its highest gain over poor soil, while the 5/8-wl version has its highest gain over very poor soil. That phenomenon accompanies another: the 5/8-wl monopole at a 5' base height already has sufficient second lobe development over very good ground to place the maximum gain at a high angle.</p>
<h3>Summary--So Far</h3>The results of the analysis of upper HF monopoles may well be summarized in two statements:
<blockquote>
<p>1. At roof-top heights, the advantage of the of an upper HF 5/8-wl monopole over a 1/4-wl version is well under 1 dB, while the added radiator length above the roof-top may create significant mechanical challenges to offset the small gain in signal strength.</p>
<p>2. At base heights near the ground, the 5/8-wl monopole advantage may sometimes exceed 1 dB at lower angles of radiation, but does not reach 2 dB, even on 10 meters. The lower TO angle of the 5/8-wl monopole may prove to be of some advantage in such situations. Although each advantage of the longer monopole may be individually somewhat marginal, together, the advantages may add up to a noticeable improvement in performance over a 1/4-wl vertical.</p>
</blockquote>
<p>Although I have used good ground for most of the illustrative patterns in this study, we should take note of the performance of all of the monopoles over very poor soil. On 10 meters, we can show the effects by comparing 25' high 5/8-wl monopoles with 90-degree and 45-degree radial sets. See <b>Fig. 25</b>.</p>
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<p>The 10-meter patterns show once more that the use of sloping radials is marginal or detrimental, just as it was in the VHF region when the antenna was several wavelengths above ground. The flat-radial monopole has the greater signal strength at the lowest elevation angles. However, what may be more important is the fact that for either case, the poorer the ground, the better the antenna performance, both in terms of gain and in terms of pattern shape.</p>
<p>Now, if we only knew how good or bad the ground was beneath and around our antenna. . .</p>
<h3>Some Poorly Grounded Speculations</h3>
<p>This section of the investigation is somewhat speculative and based on inadequate evidence. However, it may have some use in fostering further investigations that might better resolve the questions we shall raise.</p>
<p>In some 7 MHz investigations of vertical antenna performance in concert with Dave Bowker, W1FK, he measured the soil conductivity of his Maine antenna site at 0.0002 to 0.00025 S/m. The readings were not only repeatable with good equipment, but as well showed the proper trends for rainy and dry spells. Using these values and some careful measurements of a 7-MHz vertical with a number of different elevated radial fields, we developed a permittivity value of about 7 for the area. First, this value of dielectric constant turned out to be assigned to shale, which is not unlike the constitution of the antenna site sub-soil. Second, using the value permitted careful models of the antenna and radial system to track all variations such that the modeled resonant impedance and the measured resonant impedance were always within 1 Ohm of each other--or less.</p>
<p>This anecdote--and that is all it can be at this stage--is coincident with reports that soil conductivity decreases with increases in frequency. (This claim is not the same as saying that for a given conductivity, ground losses increase with increasing frequencies. This other principle is already accounted for in the Sommerfeld-Norton ground calculation algorithms used by NEC. The new claim is not, since the user enters values--presumably measured or accurately estimated--of conductivity and permittivity (relative dielectric constant) into the S-N ground calculation system.) The measured value of the Maine antenna site is well below any value listed in standard soil quality charts--most of which were generated for AM broadcast antenna use. Indeed, a conductivity value of less than 1 mS/m is no where in such charts associated with a dielectric constant as high as 7.</p>
<p>The sum of these considerations is a question: just how poor is the soil beneath our upper HF vertical antennas? Although I cannot answer that question directly, I can look at some models using very low values of conductivity and permittivity. In fact, we can look together at the results of some speculative modeling. I used an initial value of 0.0002 S/m for conductivity and reduced the value to 0.0001 S/m. For a constant dielectric constant of 7, there was no significant change in the modeled performance of the subject antennas for the 2:1 change in soil conductivity. However, at low values of conductivity, changes in permittivity have a stronger influence on performance. See <a href="../160/160v2.html"><b>Part 2 of Some Facts of Like About Modeling 160-Meter Vertical Arrays: Part 2: Appreciating Conductivity and Permittivity</b></a>. Therefore, using the 0.0001 S/m value of conductivity, I reduced the permittivity in steps from 7 to 1.</p>
<p>The modeled antennas were the 20-meter and 10-meter 1/4-wl and 5/8 wl monopoles at 25' above ground using 90-degree radial sets. The results of the modeling tests appear in <b>Table 17</b>.</p>
<pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 17. 20-Meter and 10-Meter 1/4-wl and 5/8-wl monopoles over low-quality
soils.
Soil Cond. Gain TO Angle Lobe Feedpoint Impedance
& diel. const. dBi degrees No. R +/- jX Ohms
1/4-wl 20-Meter Monopole, 90-degree radials, 25' above ground
.0002/7 1.54 16 1 23.1 + j 4.1
.0001/7 1.57 16 1 23.1 + j 4.1
.0001/5 1.72 17 1 23.2 + j 4.0
.0001/3 1.98 18 1 23.5 + j 4.0
.0001/1 3.01 14 1 24.0 + j 3.8
5/8-wl 20-Meter Monopole, 90-degree radials, 25' above ground
.0002/7 2.86 13 1 109 - j 369
.0001/7 2.88 13 1 108 - j 369
.0001/5 3.19 14 1 108 - j 369
.0001/3 3.61 15 1 108 - j 369
.0001/1 4.30 11 1 108 - j 370
1/4-wl 10-Meter Monopole, 90-degree radials, 25' above ground
.0002/7 2.71 12 1 24.2 + j 4.0
.0001/7 2.72 12 1 24.2 + j 4.0
.0001/5 3.06 12 1 24.2 + j 4.0
.0001/3 3.52 13 1 24.2 + j 4.1
.0001/1 3.72 9 1 24.2 + j 4.3
5/8-wl 10-Meter Monopole, 90-degree radials, 25' above ground
.0002/7 3.86 10 1 84 - j 308
.0001/7 3.87 10 1 84 - j 308
.0001/5 4.18 10 1 84 - j 308
.0001/3 4.56 11 1 84 - j 308
.0001/1 4.50 8 1 84 - j 308
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
<p>For all of the models, there is a significant increase in gain as we decrease the dielectric constant, using a very low value of conductivity. To gain a sense of what the table shows, we can turn to some illustrations.</p>
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<img src="58-26.gif" width="640" height="280" border="2" vspace="5" hspace="9">
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<p>F<b>ig. 26</b> shows the tabular extremes for the 20-meter antennas. Note that the lower lobe of the best 1/4-wl monopole performance coincides closely with the lowest lobe of the 5/8-wl monopole using the starting values of the progression. The improvement on 20 as we decrease the dielectric constant is about 1.5 dB total.</p>
<center>
<img src="58-27.gif" width="640" height="280" border="2" vspace="5" hspace="9">
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<p>In <b>Fig. 27</b>, we see the same data in pattern form for 10 meters. The increment on this band is only about 1 dB, possibly due to the more complex lobe structure that results from the antenna being higher in terms of wavelengths than the 20-meter models.</p>
<p>The upshot of the speculative modeling is simply this: the worse the soil, the better that most verticals perform. This statement has some assumptions built into it. The most important is that we are not located near a large body of salt water and that the soils with which we are making comparisons are not any better than that which we classified as very good. However, the pattern continues to repeat itself: lowest lobes dominate over the poorest soils, while with better soils (poor to very good), higher lobes often take over, to the detriment of low-angle radiation.</p>
<p>It would be glib to jump to conclusions. However, I do not know the answer to the question of how well our upper HF vertical perform, since I do not have decent data at hand for the conductivity and permittivity of the usual soils at the upper HF frequency range. All that I can do is draw from these notes a conditional conclusion: if any of this speculative material has relevance to real antenna performance, then we may one day have to re-evaluate our judgments of the performance of vertical antennas in the upper HF range.</p>
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<p><i>Updated 04-17-2001. &COPY; 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.</i></p>
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<title>The 5/8-Wavelength Mystique Index</title>
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<h1><img src="../images/gpbut.gif" align="left" width="90" height="84" border="2" vspace="5" hspace="10"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10"> The 5/8-Wavelength Mystique</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>The 5/8 wavelength vertical monopole has long held the reputation of providing about a 3-dB gain advantage over the 1/4 wavelength vertical monopole. The foundation of that reputation rests upon theoretical calculations that show the longer monopole to have the derived gain increase when both monopoles are set over a perfect ground. <b>Fig. 1</b> shows the modeled elevation patterns of the two subject antennas under the prescribed conditions. Both antennas are set up as 0.1" diameter copper elements, which have negligible losses. At the 3.75 MHz test frequency, the 1/4 wavelength monopole showed a gain of 5.08 dBi, compared to the 8.01 dBi figure for the 5/8 wavelength monopole.</p>
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<p>For an example of the claim or illustrations of the theoretical gain of the 5/8 wavelength monopole over the 1/4 wavelength monopole, see Terman's <i>Radio Engineers' Handbook</i> (McGraw-Hill, 1943), pp. 793-795. Recent college antenna texts fold vertical monopole concepts into more general considerations, although many antenna texts through at least 1970 present the theoretical relationship of a 1/4 wavelength radiator to a 5/8 wavelength radiator in the classic terms of Fig. 1. This idea persists in amateur radio literature. For examples, see Orr and Cowan, <i>Vertical Antennas</i> (RAC, 1986), p. 162, and by the same authors, <i>Simple and Low-Cost Wire Antennas</i> (RAC, 1990), p. 115.</p>
<p>A second factor contributing to the reputation of the longer monopole for higher gain is the current distribution along the element. <b>Fig. 2</b> shows the distribution for both the long and short monopoles, with the ground plane elements omitted for clarity. The 1/4 wavelength antenna presents its "half-dipole" current distribution curve, while the 5/8 wavelength antenna provides a "half-EDZ" distribution curve. The peak current at a position well above the top of the short antenna is said to give the longer monopole a lower-angle of radiation and additional gain.</p>
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<p>Although the claim of "3 dB more gain" for a 5/8 wavelength vertical radiator has considerably quieted in recent years, little by way of systematic exploration of the claim has appeared in amateur literature. Therefore, a little study seemed in order. However, the examination is complicated by the fact that the 1/4-vs.-5/8 question arises in two ot three different contexts. In the lower HF region of the spectrum, vertical monopoles are implemented with their bases normally at ground level, with a buried set of ground-plane radials. In the VHF region, vertical monopoles and their radials are elevated at least 1 wavelength above ground and often up to several wavelengths. The third main but lesser used region for monopoles are the upper HF bands from 20 through 10 meters, where they are sometimes employed by space-restricted hams. Consequently, our look into the 5/8 wavelength monopole question will require three related but relatively independent investigations, one for each frequency region and antenna assembly.</p>
<p>The three-part investigation appears in the following items:</p>
<ul>
<li>
<a href="58-1.html"><b>Part 1: 80-Meter Monopoles With Buried Radials</b></a>
</li>
<li>
<a href="58-2.html"><b>Part 2: 2-Meter Elevated Ground-Plane Antennas</b></a>
</li>
<li>
<a href="58-3.html"><b>Part 3: Upper HF Monopoles</b></a>
</li>
</ul>
<p>The exploration proceeded using NEC-4 as a suitable modeling vehicle for examining the question of relative gain. The VHF and upper HF portions of the study might well have been undertaken with NEC-2 in any of its basic commercial implementations, since the number of elements are few and the antenna geometry does not challenge any of the software limitations. However, NEC-2 cannot directly model a buried radial system, and many basic NEC software packages are limited in the total number of segments a modeler can use. Therefore, professional software using NEC-4.1 becomes the necessary tool for buried ground-plane systems involving up to 128 radials.</p>
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<p><i>Updated 04-17-2001. &COPY; 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.</i></p>
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<h1><br>
1 MHz Ground-Wave Analysis<br>
<br>
A Comparison Among MININEC and NEC Modeling Implementations</h1>
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L. B. Cebik<br>
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<p>Ground-wave analysis in the frequency region of 0.5 to 1.5 MHz is crucial within the AM broadcast industry. Recent recommendations to the FCC would permit the use of antenna modeling calculations to replace some (but not all) field measurements. To provide an inter-program basis for comparing ground-wave calculations, a comparative data gathering exercise was undertaken using various implementations of MININEC 3.13, "Expert" MININEC (EM Sci), NEC-2, and NEC-4. This report provides the results of the work.</p>
<p><em>1. Ground-wave analysis for vertical antennas and arrays.</em> The basic unit of measure for ground-wave analysis is the Volt/meter (V/m), although many common applications call for figures in milli-Volts/meter (mV/m). The parameter measured is the vertical component of the radiation field (sometimes designated E-theta), using a specified power and distance. The most common power used is 1,000 W (1 kW). The most common distances are 1 mile (1609 m) and 1 km (1,000 m or 0.6214 mi). Often, readings are rechecked at further distances. For this study, distances of 1, 3, and 5 km are used for modeled calculations.</p>
<p>To make the comparisons, a single near-resonant 1/4 monopole was modeled. Ground selection was dependent on the program used, since not all cores or all implementations of modeling cores permit access to the same types of ground system calculations. For example, in MININEC and NEC, the monopole was modeled with a direct connection to ground and no buried radials, since such radials are not available in most versions of these programs. However, NEC-4 permits a model using a buried radial system, and one such model was developed for this study.</p>
<p>Ground-wave analysis in all forms of MININEC is limited to the use of a perfect ground, since there is no provision for a ground-wave analysis other than the determination of far-field values at 0 elevation angle (90 theta or zenith angle) and a specified distance. NEC-2 and NEC-4 have provisions for a separate ground-wave output via request by the RP1 card. The results may be specified as a radial distance and an observation height. The provision of a ground-wave analysis output permits the specification of soil qualities in terms of conductivity and permittivity for the model, in addition to the use of a perfect ground.</p>
<p>One implementation of both NEC-2 and NEC-4 (EZNEC Pro) provides a MININEC ground calculation system for use in conjunction with the specified NEC core. By employing a MININEC ground and specifying soil quality values, the modeler obtains the ability to make ground-wave calculations that cannot be done within MININEC itself. As well, the use of the MININEC ground is said to overcome the inaccuracies inherent in the use of either the reflection-coefficient or Sommerfeld-Norton ground calculations with simple "no-radial" models. Whether this assertion is validated by comparison among models will become part of the data from this study.</p>
<p>A third method of ground-wave analysis involves the use of a buried ground radial system, a possibility within NEC-4. The ground-wave output from this modeling structure may use any permissible soil quality values. However, the model may not use a perfect ground, since part of its structure is below the ground surface.</p>
<p><em>2. Models used in this study.</em> The basic vertical monopole antenna used in this study consists of a single wire 0.0254 m (1.0") in diameter. The reason for this selection involves the ease of modeling this thin diameter using a buried radial system in NEC-4, to be explained shortly. The resistivity of the wire was 1.72E-08, the approximate value for copper.</p>
<p>The length of the monopole for NEC-2, NEC-4, and Expert MININEC is 72.771 m (2865") to yield an antenna that is resonant within +/-j1 reactance over perfect ground. For versions of MININEC 3.13, the requisite length was 72.898 m (2870"). One version of MININEC 3.13 (NEC4WIN95) contains a "NEC-correction" feature, which returned the monopole length to the shorter value for resonance as here defined.</p>
<p>Models connected directly to ground and using no radials initially employed 21 segments, a value that places all critical dimensions well within the convergence and other boundaries of modeling. MININEC models place the source at the junction of the ground and the wire segment adjacent to ground. NEC models place the source within the segment adjacent to ground. No deleterious effects were noted from the differential in source placement between the two types of cores.</p>
<p>The NEC-4 model calls for special comment, due to the requirements for establishing a buried radial system. Such models must meet two major requirements. First, there must be a wire segment junction at the point where the wire enters ground. This requirement is usually met by specifying a wire end at Z=0. Second, wire segments adjacent to the segment on which the source is placed should be the same length as the source segment for greatest accuracy.</p>
<center>
<img src="comp1-1.gif" width="603" height="423" border="2" vspace="5" hspace="9">
</center>
<p><strong>Fig. 1</strong> provides a simplified sketch of the rudiments of the model used in this study. The radial system was placed 0.152 m (6") below ground. Other studies have shown that there is very little difference in the outcome of models with identical radial systems buried from about 3" to about 24" below ground.<sup>1</sup> The radial placement yields a single segment wire between the radial junction and the ground surface. A second single-segment wire of the same length extends above the surface and becomes the source wire. Above the source wire, a series of length-tapered wires extends, the shortest being the same length as the source segment. The height above ground was set at 72.771 m (2865"), the same as the other NEC monopole models that use no radials. All monopole wires have a diameter of 0.0254 m.</p>
<p>The radial system consists of 120 2mm (0.0787") diameter, 74.948 m (2950.7") long copper wires, with equal angular spacing between them. Each of these wires is also length tapered, with the shortest wire being equal to the monopole wire forming the junction. No problems of accuracy have been encountered in the use of large radial systems in NEC-4 if all radials are thin and have the same length, despite the angular junction of wires having dissimilar diameters.</p>
<p>The model just described meets all requirements, however conservative, for length-to-diameter ratios for even the shortest wires in any element. One reason for the selection of the thin monopole (relative to what is commonly found in AM broadcast antenna installations) is that the modeling is greatly simplified. However, there are usable techniques for modeling thicker monopoles and/or shallower radial fields.<sup>2</sup></p>
<p>A significant question is whether the length-tapered monopole is equivalent within relevant limits to the 21-segment monopoles with which it is being compared. That comparison proves to be more than 1-dimensional and is part of the data gathered in the course of the study.</p>
<p><em>3. Modeling cores and programs used in this comparison.</em> The cores and programs compared in this study are the following.</p>
<ul>
<li><em>MININEC 3.13</em> ELNEC (Lewallen)<br>
NEC4WIN 95 (Orion)<br>
AO 6.5 (Beezley)</li>
<li><em>Expert MININEC</em> (EM Sci, Inc.)<br>
Expert MININEC Broadcast Professional</li>
<li><em>NEC-2</em><br>
EZNEC Professional (Lewallen)<br>
NEC-Win Pro (Nittany-Scientific)</li>
<li><em>NEC-4</em><br>
EZNEC Professional (Lewallen)<br>
GNEC (Nittany-Scientific)</li>
</ul>
<p>Except for the unique ability of EZNEC Professional to provide ground-wave analysis over a MININEC ground using either NEC-2 or NEC-4, there was no difference in the values provided using the NEC cores with either Nittany-Scientific or Lewallen implementations.</p>
<p><em>4. MININEC 3.13 results.</em> The <strong>Table 1</strong> lists the results of ground-wave analysis obtained--insofar as was possible--from implementations of MININEC 3.13. The models are single-wire monopoles with no modeled radial system. All ground-wave calculations have been expressed in mV/m, even if program outputs registered V/m. The ground-wave calculation, where available, is based on a distance of 1,000 m and a power level of 1,000 W.</p>
<center>
<table width="100%"></table>
<table border="5" cellpadding="5" cellspacing="5">
<tr valign="top">
<td><strong>Program</strong></td>
<td><strong>ELNEC</strong></td>
<td><strong>AO</strong></td>
<td><strong>NEC4WIN unc.</strong></td>
<td><strong>NEC4WIN cor.</strong></td>
</tr>
<tr valign="top">
<td>Height (m)</td>
<td>72.898</td>
<td>72.898</td>
<td>72.898</td>
<td>72.771</td>
</tr>
<tr valign="top">
<td>Impedance (Ohms)</td>
<td>36.15 - j0.17</td>
<td>36.0 - 0.4</td>
<td>38.08 + j0.18</td>
<td>36.17 - j0.83</td>
</tr>
<tr valign="top">
<td>Gain (dBi)</td>
<td>5.14</td>
<td>5.12</td>
<td>5.14</td>
<td>5.14</td>
</tr>
<tr valign="top">
<td>Field Strength (mV/m)</td>
<td>312.85</td>
<td>312*</td>
<td>not available</td>
<td>not available</td>
</tr>
</table>
</center>
<center>
Table 1. A comparison of MININEC 3.13 results
</center>
<p>Only values for 1 km are available from EZNEC, while AO allows the specification of a distance. However, AO provides somewhat truncated values, since it rounds extensively. For example, it rounded the conversion of 1,000 m into 0.6 miles. I found no way to extract field strength data from NEC4WIN. These values are in themselves of academic interest, although they may be useful in comparisons with other values enumerated in later tables. Internally, perhaps the most interesting aspect of the numbers is the consistency of calculated source impedance for all uncorrected models.</p>
<p><em>5. Expert MININEC Broadcast Professional and NEC-2/-4 results over perfect ground.</em> Expert MININEC provides the user with the ability to specify virtually any power level and any distance when taking field strength readings, within the limitations of using the far field computation at 0 elevation over perfect ground. Therefore, it is possible to arrive at field strength values for 1, 3, and 5 km.</p>
<p>In addition, one can obtain comparable results from both NEC-2 and NEC-4 using virtually any implementation of these cores. Therefore, one may combine the results into a single table, since all three employ a 21-segment 72.771 m monopole, and none of the models uses a radial system.</p>
<center>
<table width="100%"></table>
<table border="5" cellpadding="5" cellspacing="5">
<tr valign="top">
<td><strong>Perfect Ground Values</strong></td>
<td><strong>Expert MIN.</strong></td>
<td><strong>NEC-4</strong></td>
<td><strong>NEC-2</strong></td>
</tr>
<tr valign="top">
<td>Source Impedance (R +/- jX Ohms)</td>
<td>36.09 - j0.27</td>
<td>36.22 + j0.26</td>
<td>36.22 + j0.26</td>
</tr>
<tr valign="top">
<td>Ground Wave @ 1 km (mV/m rms)</td>
<td>312.78</td>
<td>312.75</td>
<td>312.74</td>
</tr>
<tr valign="top">
<td>Ground Wave @ 3 km (mV/m rms)</td>
<td>104.26</td>
<td>104.25</td>
<td>104.25</td>
</tr>
<tr valign="top">
<td>Ground Wave @ 5 km (mV/m rms)</td>
<td>62.56</td>
<td>62.55</td>
<td>62.55</td>
</tr>
</table>
</center>
<p align="center">Table 2. A comparison of ground-wave field strength values for Expert MININEC Broadcast (EMB), NEC-4, and NEC-2 (Nittany-Scientific or Lewallen).</p>
<p>The results shown in <strong>Table 2</strong> are remarkably clear. For the test model, there is no significant difference in calculated performance within any entry on the table. Expert Mininec Broadcast and NEC-2/-4 calibrate coincidentally for the class of cases involved in this study using exactly vertical wires when the calculations are made over perfect ground. As well, comparison with <strong>Table 1</strong> shows that there is no significant difference in the available field strength readings between MININEC 3.13 and the cores recorded in <strong>Table 2</strong>.</p>
<p><em>6. NEC-4 results using buried radials over various soils.</em> Evaluating the results of a modeled vertical monopole of the type used in this study must eventually involve a comparison with a version that modeled a buried radial system to complete the monopole antenna. The 120-radial system of 0.025 radials (74.948 m or 2950.7") using 2 mm diameter copper wire was chosen because it replicates common practice in the frequency range (1.0 MHz) and allows relatively accurate modeling results.</p>
<p>However, comparing the results of such a model in NEC-4 to other models over perfect ground is not without some issues, since there are limitations to the comparison. The NEC-4 model with buried radials cannot be modeled with a perfect ground, since part of the essential structure is below ground level. The question that will arise is whether one can reasonably extrapolate from the buried-radial model to those over perfect ground with attention to the ground-wave field strength values. The question will require some attention to differences in ground-wave calculations produced by NEC-4 and NEC-4D (single and double precision versions of the core).</p>
<center>
<table width="100%"></table>
<table border="5" cellpadding="5" cellspacing="5">
<tr valign="top">
<td><strong>NEC-4 with 120 Buried Radials</strong></td>
<td><strong>NEC-4</strong></td>
<td><strong>NEC-4D</strong></td>
</tr>
<tr valign="top">
<td><strong>Very Poor (0.001 S/m; 5)</strong></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>-0.80 / 25</td>
<td>-0.80 / 25</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>41.46 - j 2.92</td>
<td>41.46 - j 2.92</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>189.49</td>
<td>189.50</td>
</tr>
<tr valign="top">
<td>GW: 3 km</td>
<td>36.33</td>
<td>36.33</td>
</tr>
<tr valign="top">
<td>GW: 5 km</td>
<td>14.20</td>
<td>14.20</td>
</tr>
<tr valign="top">
<td><strong>Poor (0.002 S/m; 13)</strong></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>0.67 / 23</td>
<td>0.67 / 23</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>38.75 - j 0.63</td>
<td>38.75 - j 0.63</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>229.68</td>
<td>229.68</td>
</tr>
<tr valign="top">
<td>GW: 3 km</td>
<td>54.76</td>
<td>54.76</td>
</tr>
<tr valign="top">
<td>GW: 5 km</td>
<td>25.22</td>
<td>25.22</td>
</tr>
<tr valign="top">
<td><strong>Good (0.005 S/m; 13)</strong></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>1.86 / 21</td>
<td>1.86 / 21</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>37.87 + j 0.98</td>
<td>37.87 + j 1.00</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>276.10</td>
<td>276.08</td>
</tr>
<tr valign="top">
<td>GW: 3 km</td>
<td>79.78</td>
<td>79.78</td>
</tr>
<tr valign="top">
<td>GW: 5 km</td>
<td>42.46</td>
<td>42.46</td>
</tr>
<tr valign="top">
<td><strong>Very Good (0.0303 S/m; 20)</strong></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>3.44 / 15</td>
<td>3.44 / 15</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>36.90 + j 1.57</td>
<td>36.90 + j 1.58</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>304.79</td>
<td>304.80</td>
</tr>
<tr valign="top">
<td>GW: 3 km</td>
<td>99.01</td>
<td>99.00</td>
</tr>
<tr valign="top">
<td>GW: 5 km</td>
<td>58.18</td>
<td>58.18</td>
</tr>
</table>
</center>
<center>
Table 3. Ground wave and other values deriving from NEC-4 and NEC-4D models.
</center>
<p>Therefore, <strong>Table 3</strong> provides data for both core outputs, using the same 1, 3, and 5 km standard distances at a power of 1 kW. In addition, the model has been placed over a variety of soils, according to the widely used standard listing in Terman's <em>Radio Engineer's Handbook</em> (p. 709), which derives from "Standards of Good Engineering Practice Concerning Standard Broadcast Stations," <em>Federal Register</em> (July 8, 1939), p. 2862. In other studies, the use of the chosen categories of soil quality constants for Sommerfeld-Norton ground calculations has been found to be a fair, if not perfect, sampling of the range of possible soil conditions.<sup>3</sup> The first listed value in each portion of the table is conductivity in S/m, while the second value is the permittivity or relative dielectric constant.</p>
<p>Of first notice in the table is the spread of values of ground-wave field strength for any given distance at the set power as we change the soil quality. Although the ground-wave field strength values over very good soil approach those from models placed without radials over perfect ground, over very poor soil the values are only about 60% of the perfect ground values. In addition, there is a progression of decreasing source impedance as soil quality improves which cannot show up when calculations are made solely over perfect ground.</p>
<center>
<img src="comp1-2.gif" width="648" height="506" border="2" vspace="5" hspace="9">
</center>
<p>Of second notice is the tendency to extrapolate from the values for very good soil to the values for perfect ground calculations on the basis of the general tendencies shown in the output results. Although such an extrapolation is probably satisfactory for many applications, a more precise version of the process is beset with problems relating to the complexity of the calculations involved.</p>
<p>One problem involves the fact that a 120-radial system may approach the performance of a solid surface, but it does not reach that level. <strong>Fig. 2</strong> shows graphically the increase in ground-wave field strength at 1 km with 1 kW of power over poor soil (0.002 S/m; 13) as we increase the number of radials in a NEC-4 model. As is readily apparent, the curve has not reached a final plateau.</p>
<p>A second problems involves the extension of the soil quality into higher values. Perhaps the standard of quality is salt water, with a conductivity of 5 S/m and a dielectric constant of 81. <strong>Table 4</strong> provides values for NEC-4 and NEC-4D models of the system in use over salt water.</p>
<center>
<table width="100%"></table>
<table border="5" cellpadding="5" cellspacing="5">
<tr valign="top">
<td><strong>NEC-4 with 120 Buried Radials</strong></td>
<td><strong>NEC-4</strong></td>
<td><strong>NEC-4D</strong></td>
</tr>
<tr valign="top">
<td><strong>Salt Water (5.0 S/m; 81)</strong></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>5.29 / 07</td>
<td>5.28 / 06</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>32.72 - j 2.58</td>
<td>32.72 - j 2.57</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>400.48</td>
<td>328.14</td>
</tr>
<tr valign="top">
<td>GW: 3 km</td>
<td>135.89</td>
<td>109.36</td>
</tr>
<tr valign="top">
<td>GW: 5 km</td>
<td>123.33</td>
<td>65.60</td>
</tr>
</table>
</center>
<center>
Table 4. Ground wave values deriving from NEC-4 and NEC-4D models over salt water.
</center>
<p>The NEC-4 values are wholly unreliable and stem from unreliable calculation behavior that actually begins as the soil quality approaches the level listed as very good. At these values of conductivity and permittivity, calculated ground-wave field strength values show variability when listed in 1 increments. Although the differential between maximum and minimum values is small (about 0.02 mV/m rms), it varies from the anticipated uniform value at all compass points. NEC-4D provides uniform values. As conductivity reaches a value of about 0.5 S/m, the maximum-minimum spread in NEC-4 output values grows to over 4 mV/m, and for each doubling of conductivity above that level, the spread nearly triples. Increasing the dielectric constant over this range from 20 to 50 does not change the spread from maximum to minimum very much, but it does change the maximum and minimum values themselves. Therefore, above a conductivity of about 0.1 S/m and a dielectric constant of about 20, NEC-4 values of ground-wave field strength for the type of model used here become quite unreliable.</p>
<p>In contrast, the ground-wave field strength values produced by NEC-4D always provide a uniform value at every azimuth bearing for a vertical monopole of the type used in this study. For several echelons of increase beyond the soil quality called very good, the results are generally reliable. However, the reliability is not perfect. The results for the subject model with "salt-water" ground constants exceed the result of every model surveyed, when the monopole is placed over perfect ground without radials. The 1-km ground-wave value is over 4% greater than any of the perfect ground values.</p>
<p>Whether or not the differentials have any practical significance, it remains the case that one cannot numerically extrapolate with any degree of precision from the radial model to the perfect ground model or vice versa. Moreover, more deeply burying the radial system will not resolve the issue. In a series of models using 60 radials, it was found that increasing the depth to 12" increased the 1 km field strength by 6 mV/m rms. The values remained constant within 1 mV/m thereafter until at least a depth of 24".</p>
<p>The NEC-4 and NEC-4D results for soil qualities that are very good or worse are too close for repetition in further tables in this study. However, whatever the ground type, with or without a radial system, as soil quality approaches very good, the NEC-4D ground-wave field strength readings will begin to decrease relative to those produced by NEC-4.</p>
<p><em>7. NEC-2/-4 results over a MININEC ground.</em> One implementation of NEC-2 and NEC-4 (EZNEC Professional from Lewallen) provides the user with the option of employing a MININEC ground calculation while using one or the other of the NEC cores. This option enables the user to employ the RP1 option to develop ground-wave field strength readings. As well, it permits the user to select any set of soil quality constants. The limitation of this option is that the source impedance is calculated as it would be in MININEC 3.13, that is, only over perfect ground. Consequently, although the ground wave values will vary with the soil constants selected, the source impedance will remain the same for all cases.</p>
<p>The assumption underlying the use of MININEC ground with NEC calculations on a monopole with no radials is that the MININEC ground calibrates well to a full NEC-4 model with radials. Other studies have shown that this assumption is not adequate for systems with few radials, but for purely vertical antenna structures, it may hold well enough to simplify some orders of modeling.<sup>4</sup> Models that employ any horizontal or sloping elements, whether directly fed or parasitic, may encounter erroneous results if any portion of a sloping or horizontal wire is below about 0.2 above ground.</p>
<p><strong>Table 5</strong> provides a listing of results using NEC-2 and NEC-4 with a MININEC ground within EZNEC Pro. The entries parallel those in <strong>Table 3</strong>, which records the outputs for the full 120-buried radial model. In addition, the table provides for each core 2 listings, one of which corresponds to the standard 21-segment models used over perfect ground, and the other of which corresponds to the length-tapered element used in the 120-radial model. The length-tapering for these new models is identical to that portion of the 120-radial model that is above the surface of the ground. For both models, the source is on the wire segment that joins the ground.</p>
<p><strong>Table 5</strong>, then, provides the data necessary to perform two tasks: a. to discover if the length-tapered model is a reasonable correlate of the 21-segment standard model monopole, and b. to determine if the use of NEC with a MININEC ground provides, with a simplified model, usable results with respect to treating a 120-radial model as a standard.</p>
<center>
<table width="100%"></table>
<table border="5" cellpadding="5" cellspacing="5">
<tr valign="top">
<td><strong>NEC Core, MIN Gnd, No Radials</strong></td>
<td><strong>NEC-4; 21 Segs.</strong></td>
<td><strong>NEC-4; L-Tapered</strong></td>
<td><strong>NEC-2; 21 Segs.</strong></td>
<td><strong>NEC-2; L-Tapered</strong></td>
</tr>
<tr valign="top">
<td><strong>Very Poor (0.001 S/m; 5)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>-0.80 / 26</td>
<td>0.00 / 26</td>
<td>-0.08 / 26</td>
<td>0.00 / 26</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>36.22 + j 0.26</td>
<td>35.48 - j 0.24</td>
<td>36.22 + j 0.26</td>
<td>35.47 - j 0.26</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>206.41</td>
<td>208.14</td>
<td>206.25</td>
<td>208.04</td>
</tr>
<tr valign="top">
<td>GW: 3 km</td>
<td>39.52</td>
<td>39.85</td>
<td>39.80</td>
<td>40.14</td>
</tr>
<tr valign="top">
<td>GW: 5 km</td>
<td>15.44</td>
<td>15.57</td>
<td>15.60</td>
<td>15.74</td>
</tr>
<tr valign="top">
<td><strong>Poor (0.002 S/m; 13)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>1.01 / 23</td>
<td>1.09 / 23</td>
<td>1.01 / 24</td>
<td>1.09 / 24</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>36.22 + j 0.26</td>
<td>35.48 - j 0.24</td>
<td>36.22 + j 0.26</td>
<td>35.47 - j 0.26</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>239.39</td>
<td>241.43</td>
<td>238.52</td>
<td>240.60</td>
</tr>
<tr valign="top">
<td>GW: 3 km</td>
<td>57.02</td>
<td>57.51</td>
<td>57.17</td>
<td>57.67</td>
</tr>
<tr valign="top">
<td>GW: 5 km</td>
<td>26.26</td>
<td>26.48</td>
<td>26.36</td>
<td>26.59</td>
</tr>
<tr valign="top">
<td><strong>Good (0.005 S/m; 13)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>2.11 / 21</td>
<td>2.18 / 20</td>
<td>2.11 / 21</td>
<td>2.18 / 21</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>36.22 + j 0.26</td>
<td>35.48 - j 0.24</td>
<td>36.22 + j 0.26</td>
<td>35.47 - j 0.26</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>284.46</td>
<td>286.89</td>
<td>282.60</td>
<td>285.07</td>
</tr>
<tr valign="top">
<td>GW: 3 km</td>
<td>82.16</td>
<td>82.86</td>
<td>81.99</td>
<td>82.71</td>
</tr>
<tr valign="top">
<td>GW: 5 km</td>
<td>43.73</td>
<td>44.10</td>
<td>43.67</td>
<td>44.05</td>
</tr>
<tr valign="top">
<td><strong>Very Good (0.0303 S/m; 20)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>3.53 / 15</td>
<td>3.61 / 15</td>
<td>3.54 / 16</td>
<td>3.61 / 16</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>36.22 + j 0.26</td>
<td>35.48 - j 0.24</td>
<td>36.22 + j 0.26</td>
<td>35.47 - j 0.26</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>308.37</td>
<td>310.96</td>
<td>306.82</td>
<td>309.53</td>
</tr>
<tr valign="top">
<td>GW: 3 km</td>
<td>100.13</td>
<td>101.00</td>
<td>99.99</td>
<td>100.87</td>
</tr>
<tr valign="top">
<td>GW: 5 km</td>
<td>58.85</td>
<td>59.34</td>
<td>58.79</td>
<td>59.31</td>
</tr>
</table>
</center>
<center>
Table 5. NEC-2 and NEC-4 with MININEC ground.
</center>
<p>Within the table, the maximum variation among ground-wave field strength calculations is about 1.3%. The lower source resistance values for the length-tapered models in both NEC-2 and NEC-4 is partly attributable to the closer proximity of the source to the actual ground. For most purposes, the data from either the standard 21-segment model or the length-tapered model would be interchangeable.</p>
<p>Relative to the 120-radial NEC-4 model, these models show higher values for ground-wave field strength calculations, ranging from under 2% for very good ground to nearly 10% for very poor ground. The differentials have sufficient pattern to them to suggest that the variations may be systematic. The range of values in mV/m (rms) runs from a little over 5 for very good ground to well above 18 for very poor ground. Therefore, it is unlikely the setting the buried radial system to a lower level would increase the field strength calculation outputs sufficiently to reach the levels resulting from the use of a MININEC ground.</p>
<p>The precise differential that represents a threshold between a usable and an unusable correlation of values between the two ways of modeling monopoles is, in the end, a task driven judgment. The task will contain, implicitly or explicitly, the appropriate criteria for determining the adequacy of a no-radial substitute model for a fully-modeled buried radial system.</p>
<p><em>8. NEC-2/-4 results over reflection coefficient and Sommerfeld-Norton grounds with no radials.</em> Every implementation of NEC-2 and NEC-4 cautions against using the output values from a model that places a monopole in direct connection with ground with no radial system when employing either the Sommerfeld-Norton or the reflection coefficient approximation ground calculation methods. However, little exemplary evidence for the dangers of this procedure appear in software or other literature. Within the present context, it might be useful in developing an appreciation of the sound advice to present ground-wave field strength values and related data as they emerge from the standard and the length-tapered models misplaced on the ground with no radials.</p>
<center>
<table width="100%"></table>
<table border="5" cellpadding="5" cellspacing="5">
<tr valign="top">
<td><strong>NEC Core, RCA Gnd, No Radials</strong></td>
<td><strong>NEC-4; 21 Segs.</strong></td>
<td><strong>NEC-4; L-Tapered</strong></td>
<td><strong>NEC-2; 21 Segs.</strong></td>
<td><strong>NEC-2; L-Tapered</strong></td>
</tr>
<tr valign="top">
<td><strong>Very Poor (0.001 S/m; 5)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>-11.1 / 26</td>
<td>-25.4 / 26</td>
<td>0.83 / 26</td>
<td>1.53 / 26</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>420.0 - j 673</td>
<td>8620 - j 14810</td>
<td>29.42 - j 0.49</td>
<td>24.96 - j 2.79</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>57.90</td>
<td>11.23</td>
<td>229.14</td>
<td>248.25</td>
</tr>
<tr valign="top">
<td><strong>Poor (0.002 S/m; 13)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>-8.69 / 24</td>
<td>-22.5 / 24</td>
<td>1.67 / 23</td>
<td>2.20 / 23</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>317.2 - j 494</td>
<td>6342 - j 10900</td>
<td>31.17 - j 0.30</td>
<td>27.51 - j 2.27</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>77.97</td>
<td>15.84</td>
<td>258.15</td>
<td>274.38</td>
</tr>
<tr valign="top">
<td><strong>Good (0.005 S/m; 13)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>-6.75 / 21</td>
<td>-20.1 / 21</td>
<td>2.54 / 21</td>
<td>2.90 / 20</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>267.0 - j 312</td>
<td>5211 - j 6875</td>
<td>32.81 - j 0.54</td>
<td>30.07 - j 2.38</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>101.89</td>
<td>21.70</td>
<td>298.89</td>
<td>311.60</td>
</tr>
<tr valign="top">
<td><strong>Very Good (0.0303 S/m; 20)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>-2.61 / 16</td>
<td>-15.2 / 16</td>
<td>3.71 / 15</td>
<td>3.90 / 15</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>146.6 - j 124</td>
<td>2514 - j 2740</td>
<td>34.78 - j 0.23</td>
<td>33.19 - j 1.43</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>151.20</td>
<td>35.59</td>
<td>314.67</td>
<td>321.48</td>
</tr>
</table>
</center>
<center>
Table 6. NEC-2 and NEC-4 with a reflection coefficient approximation ground.
</center>
<p>In <strong>Table 6</strong> and <strong>Table 7</strong>, field strength values for 3 and 5 km are omitted, since the 1 km figure provides adequate evidence that the values are not usable. In <strong>Table 6</strong>, the NEC-2 figures are obviously far off the mark. However, it is interesting to note that the length-tapered model--which was stable in relationship to the standard model over a MININEC ground--has become highly unstable with results that little resemble those of the standard model.</p>
<p>At first sight, the results from NEC-4 appear to be more reasonable. Had one taken only a single model over a single set of soil quality values, one might have been tempted to accept the results. However, both sets of values result in 1 km field strength values that are higher than those from placing the monopole on a perfect ground. In addition, the progression of source impedance values proceeds in the wrong direction, showing the appearance of higher ground losses as the soil quality improves.</p>
<center>
<table width="100%"></table>
<table border="5" cellpadding="5" cellspacing="5">
<tr valign="top">
<td><strong>NEC Core, S-N Gnd, No Radials</strong></td>
<td><strong>NEC-4; 21 Segs.</strong></td>
<td><strong>NEC-4; L-Tapered</strong></td>
<td><strong>NEC-2; 21 Segs.</strong></td>
<td><strong>NEC-2; L-Tapered</strong></td>
</tr>
<tr valign="top">
<td><strong>Very Poor (0.001 S/m; 5)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>-8.52 / 26</td>
<td>-21.2 / 26</td>
<td>-1.40 / 25</td>
<td>-1.28 / 25</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>249.9 - j 63.71</td>
<td>4499 - j 1502</td>
<td>48.92 + j 4.75</td>
<td>47.48 + j 2.59</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>78.03</td>
<td>18.13</td>
<td>177.37</td>
<td>179.77</td>
</tr>
<tr valign="top">
<td><strong>Poor (0.002 S/m; 13)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>-5.02 / 24</td>
<td>-16.9 / 24</td>
<td>-0.16 / 24</td>
<td>-0.06 / 23</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>144.5 - j 32.70</td>
<td>2197 - j 838.0</td>
<td>47.40 + j 5.65</td>
<td>46.23 + j 4.55</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>119.02</td>
<td>30.27</td>
<td>209.14</td>
<td>211.51</td>
</tr>
<tr valign="top">
<td><strong>Good (0.005 S/m; 13)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>-1.80 / 21</td>
<td>-12.3 / 21</td>
<td>1.14 / 20</td>
<td>1.22 / 21</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>89.0 - j 1.11</td>
<td>1013 - j 146.7</td>
<td>45.26 + j 5.76</td>
<td>44.37 + j 5.24</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>180.16</td>
<td>53.29</td>
<td>254.47</td>
<td>256.69</td>
</tr>
<tr valign="top">
<td><strong>Very Good (0.0303 S/m; 20)</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr valign="top">
<td>Gain (dBi)/TO Angle (degrees)</td>
<td>2.26 / 16</td>
<td>-3.98 / 16</td>
<td>2.98 / 15</td>
<td>3.05 / 15</td>
</tr>
<tr valign="top">
<td>Source Impedance (Ohms)</td>
<td>48.7 + j 3.78</td>
<td>203.9 - j 2.40</td>
<td>41.19 + j 3.69</td>
<td>40.40 + j 3.60</td>
</tr>
<tr valign="top">
<td>GW: 1 km</td>
<td>264.81</td>
<td>129.18</td>
<td>298.19</td>
<td>291.58</td>
</tr>
</table>
</center>
<center>
Table 7. NEC-2 and NEC-4 with a Sommerfeld-Norton ground.
</center>
<p>As <strong>Table 7</strong> shows well, the NEC-2 values are beyond the pale of credibility, and the instability between the standard and length-tapered models shows itself, although perhaps not to the extremes revealed by the use of a reflection coefficient ground. In contrast, the NEC-4 results more closely approach credibility with a reasonably close coincidence between the standard and the length-tapered models. Nevertheless, for most purposes, the values throughout the table are too distant from either the models over perfect ground or the 120-radial model for practical use.</p>
<p>The purpose of this last exercise was not to simply state the obvious, namely, that values derived from monopole models connected directly to a reflection coefficient or Sommerfeld-Norton ground are not generally reliable. The tables focus attention on the degree of departure from reliable figures and the ways in which the modeling results go astray under the specified conditions.</p>
<p><em>9. Conclusions.</em> The data presented in this study provides an inter-program comparison of the expected results from modeling 0.25 vertical monopoles over a number of ground systems ranging from perfect ground to a full 120-radial buried system. The data are relevant to evaluating various modeling schemes that might be employed in the calculation of ground-wave field strength values applicable to MF (AM broadcast) antennas and arrays.</p>
<p>MININEC 3.13, Expert MININEC, and NEC (-2/-4) produce well-correlated output values of ground-wave field strength when the models are simple monopoles connected to a perfect ground.</p>
<p>The NEC-4 120-radial buried system model correlates reasonably closely to both MININEC and NEC models that are simple monopole connected directly to perfect ground--so long as the NEC-4 model soil quality is very good or better. Lesser soil quality leads to greater disparity between the model outputs. Wherever soil quality is a significant consideration and the quality may be less than very good, a model over perfect ground may not prove fully adequate.</p>
<p>Over the span of soil qualities usually encountered, the use of a MININEC ground with a simple monopole model correlates to a fair degree with the outputs from the NEC-4 120-radial buried system model. However, the two types of models increasingly diverge in output values as soil quality becomes worse.</p>
<p>In all cases, the acceptability of a model depends upon the criteria of evaluation employed. since these criteria are determined by the project goals and specifications, no conclusion can be drawn generally about the acceptability of using one model in preference to another. The exceptions to this conclusion are models connecting a monopole directly to a reflection coefficient or Sommerfeld-Norton ground: for most purposes, the outputs of such models are wholly unreliable.</p>
<center>
<strong>Notes</strong>
</center>
<p>1 See Part 4 ("A Potpourri of 160-Meter Vertical Antennas and Modeling Issues") of "Some Facts of Life About Modeling 160-Meter Vertical Arrays," forthcoming in <em>The National Contest Journal</em>.</p>
<p>2 See Part 3 ("Complex Radial Systems and Limitations of the MININEC (No-Radial) Ground") of "Some Facts of Life About Modeling 160-Meter Vertical Arrays."</p>
<p>3 See Part 2 ("Appreciating Conductivity and Permittivity") of "Some Facts of Life About Modeling 160-Meter Vertical Arrays."</p>
<p>4 See Part 1 ("Some Baseline Data") of "Some Facts of Life About Modeling 160-Meter Vertical Arrays."</p>
<p>This four part series can be found on the <b><a href="../160/160v.html">Some Facts of Life About Modeling 160-Meter Vertical Arrays</a></b> page.</p>
<p>Also see the <a href="../model/nec.html">Antenna Modeling Programs</a> page for more information about modeling software.</p><br>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
</center>
<p><i>Updated 02-23-01. &COPY; 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.</i></p>
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<title>Counterpoises, Capacity Hats, and A Standard for Suspected of Feedline Radiation</title>
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<body>
<center>
<h1>Counterpoises, Capacity Hats, and A Standard<br>
for Comparing Antennas Suspected of Radiation from the Feedline</h1>
</center>
<center>
<h3>L. B. Cebik, W4RNL</h3>
</center><br>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
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<br>
<p>Investigators have suspected that a number of very small antennas do not themselves have significant radiation. Instead, the so-called antenna structures form non-radiating or very low-level radiating structures, and the main radiation from the antenna assembly as a whole occurs from the outer surface of the braid of the coaxial cable feedline.</p>
<p>Most of the tests so far performed lack one essential ingredient to an unambiguous test result: one or more standards against which to compare the system under study. These notes are designed to suggest a standard against which to compare subject antennas.</p>
<p>At the outset, I shall suggest that 50 MHz may be a good test frequency. It is within an amateur band, allowing the use of legal transmitters. The structures are large enough not to require ultra-finicky adjustments either for tune-up or for measurement. As well, upper-HF construction techniques work well. At the same time, they are small enough to be inexpensive and physically manageable. For example, the suggested mounting height will be 1/2 wavelength. At 50 MHz, a half wavelength is 2.998 meters, 9.836', or 118.03". A ten-foot mast of non-conductive material--such as PVC--serves well with a home-made tripod mount. Careful backyard testing becomes very feasible.</p>
<p>The immediate problem is that many subject antennas are designed for other frequencies. Therefore, the subject antenna will normally require that the tester construct a 50-MHz version for tests. However, since it is the antenna principles that are under test--and not a specific antenna device--the substitution presents no theoretical problems.</p>
<p>Before setting up the suggested standard, let's examine some candidates for the task. In the process, we can perhaps get rid of a few common terminological problems that may inhibit either good testing or good reader understanding of the test results.</p>
<p><b>Vertical Dipoles and Ground-Plane Radial Monopoles</b></p>
<p>Essentially, our basic choice for a test antenna standard will be a vertically polarized antenna. If, as the test suspicion indicates, it is the feedline that is radiating, that line normally proceeds downward from the antenna structure under test. This situation provides another reason for using 50 MHz as a test frequency. With a 1/2 wavelength non-conductive mast, the feedline will be able to drop vertically from the antenna assembly. At low HF frequencies, the feedline may have to bend, twist, coil, or crawl along the ground for most of the first quarter wavelength from the antenna. A definitive test requires that we use a single orientation for the suspected actual radiator.</p>
<center>
<img src="cp-th-1.gif" width="775" height="500" border="2" vspace="5" hspace="9">
</center>
<p><b>Fig. 1</b> shows 3 antenna configurations. The vertical dipole is electrically the simplest structure. However, because we need to feed the antenna at its center, the feedline should run horizontally for a considerable distance from the antenna. In practice, we use such antennas along with as many decoupling devices as a given situation needs to prevent pattern distortion due to unwanted coupling to the feedline.</p>
<p>The center vertical monopole uses 4 radials to form a nearly non-radiating ground plane for the antenna. Largely because the radiation from the horizontal radials is nearly zero, early texts on these antennas introduced two expressions into the antenna lexicon, one more dangerous than the other. The expression "ground-plane" radial system is itself not always accurate, because the horizontal radials do not necessarily form a ground plane, where we take the term "ground" seriously. Common practice is to connect the coaxial feedline braid to the radials and the center conductor to the vertical element. Hence, we have the illusion of the radials somehow being connected to ground. However, those radials function even when the antenna is many wavelengths from the energy source and form a ground conductor only for static build-up on the elements. In this context, we sometimes connect an RF choke between the vertical element base and the radial system in order to bleed static build-up from the vertical element as well. However, the antenna radial system may make no connection to the earth and still perform its function within the antenna perfectly well.</p>
<p>A second term is even more insidious: "counterpoise." This term entered antenna work from the world of mechanics in which some machinery required well-balanced counterweights in order to perform its function. Early thought about antennas led to underground wires paralleling horizontal antennas, buried and elevated radial systems, etc., and all received--for want of an understanding of their actual function--the vague label "counterpoise." Today, we find uses for the term that range from highly refined and defined applications to vague and ambiguous uses. Unfortunately, a large number of readers may not be tuned into the more rigorous uses within an article and carry away the idea that whatever constitutes the counterpoise requires less stringent standards of construction or analysis than the so-called antenna proper. I have read an advertisement for an antenna that uses a very long piece of wire as a "counterpoise," with the advice to kick it around until the antenna achieves resonance. In an article within a respected journal, I read about a portable monopole for use on balconies, and the author advised the reader simply to drop a counterpoise downward, with no concern for where it went or in what environment it operated. I have even seen the term used to characterize the coaxial cable feedline of antennas in which the tester suspected that the cable or counterpoise did the radiating.</p>
<p>In fact, in antenna work, there is no such thing as a counterpoise. Every part of the antenna system performs a function that we may directly analyze and calculate--and measure as well. The carelessly dropped "counterpoise" wire was actually the lower half of a vertical dipole. It exhibits a current distribution comparable to the distribution on the upper section, the so-called antenna proper. Radiating coaxial cables are susceptible to measurement and adjustment either to maximize or minimize the radiation. Finally, the radial system of the monopoles in <b>Fig. 1</b> also show appropriate current distributions along their lengths, and they do radiate. They just happen to be horizontal and their far-field radiation is mostly self-canceling.</p>
<p>Let's compare the 3 configurations as physical NEC-4 models and see what we obtain in free space. Free space has no other object in its universe other than the antenna structure modeled. Hence, there is no ground. We shall note something else that is lacking shortly.</p>
<pre>
Dimensions of Free-Space Models of Vertical Dipoles and 4-Radial Vertical Monopoles
Vertical Dipole
Element Length WL Inches Millimeters Diameter WL Inches Millimeters
0.474 111.891 2842.04 2.118e-3 0.5 12.7
4-Radial Vertical Monopole (both versions)
Element Length WL Inches Millimeters Diameter WL Inches Millimeters
0.245 57.834 1468.98 2.118e-3 0.5 12.7
Radial Length WL Inches Millimeters Diameter WL Inches Millimeters
0.255 60.195 1528.94 1.059e-3 0.25 6.35
</pre>
<p>There is a reason for the element diameters used in the model. Ultimately, we want a standard that will reasonably replicate a main element composed of large diameter (low-loss) coaxial cable, that is, a cable whose braid approaches 1/2" in diameter. Also note that the monopole length is slightly greater than 1/2 the length of the vertical dipole. That maneuver results from the fact that the virtual position of a source is in the center of a model segment. The vertical dipole uses 31 segments with the source assigned to segment 16 at the center of the wire. The vertical element in the monopoles uses 16 segments, with the source assigned to the segment nearest the junction with the radials. By lengthening the vertical element about half the length of a segment, the monopole has a source position that is about the same distance from the vertical element tip as in the dipole.</p>
<p>We recognize that the right-most portion of <b>Fig. 1</b> is simply the center antenna turned upside down. In free space, the orientation makes no difference, so long as we select the correct polar plot to show the resulting pattern. In all cases, I selected E-plane plots, which in modeling terminology means azimuth plots. The results appear in <b>Fig. 2</b>.</p>
<center>
<img src="cp-th-2.gif" width="600" height="275" border="2" vspace="5" hspace="9">
</center>
<p>The gain of the dipole is 2.13 dBi (using aluminum elements throughout, although that hardly matters, given the large diameter of the elements). Both of the monopoles show a gain of 1.35 dBi. Note that the horizontal structure of each monopole creates no difference in the elevation angle of maximum radiation. It remain perpendicular to the vertical element.</p>
<p>If you explore the current distribution on the antennas, you will easily discover that that vertical dipole current decreases slowly at first as we move away from the source. A similar distribution occurs on the vertical section of the monopoles and is identical for both versions. The radials also participate in the current distribution. However, the current divides into 4 equal components at the junction, with each radial's first segment showing about 1/4th the source current. The radials are active parts of the antenna and critical to its proper operation.</p>
<p>In fact, the radial length was selected to bring the monopoles to near resonance, defined as a remnant source reactance of less than +/-j1 Ohm. Hence, they are slightly longer than the vertical element. Radial length is a function in part of the few radials used. I have elsewhere shown on a number of occasions that the higher the number of radials, the shorter the radial length needed to achieve system resonance. Somewhere in the region of 60 to 70 radials in free space, the radial length closely approaches the radius of a thin solid surface.</p>
<p>The modeled source impedance of the vertical dipole is, as we would anticipate, 72.04 + j0.35 Ohms. A persistent error in much literature would have the monopole impedance be 1/2 half that value, since the vertical element of the monopole is half the length of the dipole. Unfortunately, this easy derivation holds true only if we use a perfect ground, that is, if we mathematically recreate the missing half of the dipole with no radials in the model. When we place the monopoles in free space, we obtain a source impedance of 23.19 - j0.24 Ohms. To arrive at 36 Ohms, we must lengthen the vertical element considerably with a consequential shortening of the radials to return to near resonance. The result is an off-center-fed vertical element with its maximum current well above the feedpoint on the segment that joins with the radials.</p>
<p>We are now in a position to look more closely at the upside-down monopole. Suppose that we had inserted 2 or 3 segments of vertical wire between the present source segment and the radials. To achieve resonance, we would have shortened the radials to compensate for the added vertical length. As well, we would have dubbed the radial structure a "capacity hat." As long ago as the 1950s, Laport's classic text clearly notes that the name is based not on solid electronic theory, but on an analogy that is useful for approximate calculations of the required hat size based on the capacitive reactance of short vertical monopoles at ground level used in the low frequency region of the spectrum. Nevertheless, the name and idea persisted in amateur circles due to an article in <i>QST</i> in the 1970s, and the article was reprinted often in various antenna books. I have elsewhere shown that the calculations are seriously off in the HF region and above. As well, there is a complex relationship between the vertical element diameter and the diameter of the radials (or spokes, when speaking of hats).</p>
<p>In the end, the so-called capacity hat has nothing to do with capacity. We do not have one plate of a capacitor, the other plate of which is presumed to be the universe itself. Our free-space universe for the model has nothing in it to form the other plate of the so-called capacitor. Rather, the spokes of a top-hat structure provide the element length necessary for a normal current distribution such that the source impedance is whatever the designer needs it to be, normally, near to resonance. Because the hat spokes are at right angles to the main radiator and are symmetrically arranged, they contribute nearly nothing to the overall element radiation. The element end is actually 4 ends: the tips of the radials, not the flat plane created by the right-angle structure.</p>
<p>In point of fact, our upside-down monopole is simply an extreme form of top-hat. If we place the virtual source at the center of the source segment, then the radials are already displaced slightly from the source and constitute a top-hat. However, we have already seen that the free-space operation of the antenna is identical to the right-side up version, for which we are not in the least inclined to apply the term capacity-hat to the radials. In fact, the radials complete the antenna structure--relative to dipole current distribution--and do not form either a ground or a capacitor. Hence, it is likely that calling the structure a "top-hat" (or "end-hat" on horizontal elements) may be preferable to continuing the use of the label "capacity hat."</p>
<p>We can illustrate the relative identity of the ground-plane radials and the top hat by bringing the monopoles closer to earth--dragging the vertical dipole along for the ride. As a first step. let's use the so-called average ground for our earth (conductivity = 0.005 S/m; relative permittivity = 13). Next, let's set the source at 1/2 wavelength above ground. This is not yet a fair test, because the right-side-up monopole extends from 1/2 wavelength upward, while the upside-down monopole extends from 1/2 wavelength downward. If we take elevation plots of the three antennas in their new positions, we obtain the patterns shown in <b>Fig. 3</b>. The figure also shows the maximum gain and take-off angle for each configuration.</p>
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<p>The first thing to notice about vertical antennas is that their source impedances do not change much until we bring them very close to the ground. The antennas in <b>Fig. 3</b> are at the border of this region. The vertical dipole remains within a half-Ohm of its free-space value with an impedance of 69.45 + j0.72 Ohms. The right-side-up monopole shows a modeled impedance of 23.63 + 0.44 Ohms, again within a half-Ohm of its free-space value. Only the up-side-down monopole, with its tip about 1/4 wavelength from ground shows a slightly larger deviation: 22.02 - j2.09 Ohms.</p>
<p>The right-side-up monopole shows a very high TO angle, largely due to the fact that all of its radiating structure is above 1/2 wavelength. If we drop the antenna to a base height of 0.25 wavelength, the gain is 1.16 dBi at a TO angle of 16.2 degrees. The source impedance also changes to 21.59 - j1.77 Ohms. These values closely parallel those of the upside-down monopole, which has very similar top and bottom height values relative to the revised position of the right-side-up version. In short, the two monopoles remain the same antenna, even when we bring the earth into the picture.</p>
<p>I have noted that the radiation from the radials is nearly zero. However, it does not go completely to zero. We may observe remnant radiation from the radials by taking azimuth plots of the vertical dipole and either of the monopoles--and we may use the models in free space or over ground. For each type of antenna, there will be no difference due to the presence or absence of a ground surface. As <b>Fig. 4</b> shows, the vertical dipole has no detectable horizontal component to the overall radiation pattern. The monopoles, however, have an 8-lobe pattern that shows up at the -40 dB level. For all practical purposes, we can ignore this small horizontal component. Nevertheless, the horizontally polarized component does establish that the radials--whether at the top or bottom of the monopole structure--do radiate. Most of that radiation is self-canceling, taking the symmetrical arrangement into account. But some radiation does emerge.</p>
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<p><b>Transforming the Upside-Down Monopole into a Testing Standard</b></p>
<p>The upside-down monopole represents an example of an antenna wherein the top structure radiates as little as possible, and for practical measurements, not at all (unless the measuring equipment is capable of detecting -40 dB radiation relative to the main field). Hence, it is suitable as a standard of comparison with antennas suspected of feedline radiation as the main source of far fields. However, the radials are 5' long and may sag a good bit in their top position. Therefore, we should try to shrink the assembly without changing its basic operation.</p>
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<p>One way to shrink the top hat assembly is to add more radials. However, we may use a more efficient means. We can add a perimeter wire from radial tip to radial tip. <b>Fig. 5</b> shows the general outline. Note the lines that indicate the path of current distribution. Now they extend from the radial hub to the center of each perimeter wire. For the 50 MHz monopole using 0.25" radial assembly wires, the total path length is about 0.253 wavelength, in contrast to the radial-only length of 0.255 wavelength. The slight shortening of the path is due to the sharp corner at the radial tips.</p>
<p><b>Fig. 6</b> compares the relative current magnitudes in the standard 4-radial top-hat and the version that uses a perimeter wire in an EZNEC graphic that overlays the current curves on the outline of the models. If you place a ruler on the graphic, you will see on both outlines that the distance between the radial hub and the current line is about 1/4 the distance between the vertical monopole and its current maximum. In the version using the perimeter wire, the current at the tip of each radial is about twice the current in the connecting perimeter wires. Of cources, we have at those points a second splitting of the current paths. The decrease of the current to zero at the exact centers of the perimeter side shows clearly.</p>
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<p>The radials themselves have decreased to a length of 0.148 wavelength (34.93" or 887.39 mm). The overall hat assembly is only 58% as large as the radial-only version. The modeled free-space performance data shows a gain of 1.59 dBi, with a source impedance of 21.47 - j0.49 Ohms. With the top-hat 1/2 wavelength above average ground, the gain is 1.20 dBi at a TO angle of 15.5 degrees, with a source impedance of 20.43 - j1.83 Ohms. The horizontal component has shrunk to the -50 dB level relative to the main elevation lobe of the antenna.</p>
<p>It is likely that any version of the standard top hat antenna using a perimeter-wire top-hat will employ a perimeter wire that is considerably thinner than the radials: perhaps AWG #12 or #14 or 2-mm wire. Because NEC (even NEC-4) becomes less accurate when we have non-symmetrical junctions of wires having different diameters, it is not possible to provide a precise design. However, modeling suggests that for AWG #12 perimeter wire, the radials should be about 0.156 wavelength (36.82" or 935.35 mm).</p>
<p>The entire purpose of setting up a standard is to measure it on the test site using all available test equipment. The measurements include--besides the obligatory source impedance record--near-field and ground-wave measurements at distances clearly marked for replication. Do not use hand-held instruments, but devise mounting brackets so that each measurement uses an identical position. You may also generate current probes using a multi-turn winding around a toroidal core and letting the antenna element form the other 1-turn winding of the resulting transformer. By rectifying and filtering the induced voltage or current, you may derive relative current readings along the length of any portion of the array. All of these readings together form the base-line of data for further comparisons. In this set-up, the feedline should operate only as a feedline. If necessary (due to the odd angle of departure from the assembly top), add a choke-balun (common-mode choke) at the feedpoint.</p>
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<p><b>Fig. 6</b> shows the basic top-hat monopole along side an adaptation to determine the radiating properties of coaxial cable. The cable serves as both the feedline and the main vertical radiator. It is similar in principle to feeding the cable through the center of the driven element tube, except that the role of the tube is played by the outer surface of the coaxial braid. The cable should be at least 1/2 wavelength long, that is, long enough to reach from the top of the 1/2 wavelength non-conductive mast to the ground.</p>
<p>The diagram shows two possible ways to connect the cable: with the center conductor to the hat or with the braid to the hat. In theory, with a perfectly balanced line, there should be no difference in any measurements applied to the system, since any imbalance created by the hat on one side of the line will couple through to the outer surface of the braid. However, practice may show otherwise. The diagram also shows the presence of a ferrite bead choke. At 50 MHz, you may use about a dozen FT-43 toroid cores that have an inner diameter just large enough slide over the coax jacket. Because toroids are available in different lengths, about 6-8 inches of cores is about right for 6 meters. The so-called bead-balun choke is most useful in this application because you can move its position to one in which a. you obtain the maximum radiation and b. you obtain the minimum radiation from the cable. The diagram shows various positions for the coax line on the source side of the bead-balun. Varying the line position below the vertical length needed for maximum radiation is a good way to find out if other forms of coupling to the line may occur.</p>
<p>Measure the same set of parameters as for the basic antenna. Include relative current readings from both the main vertical length of coax that forms the prime radiator and from positions beyond the choke-balun to determine if there is coupling to the line by direct radiation. In theory, it should be possible to obtain just about the same performance from the coax + hat assembly as from the basic antenna in which the feedline operates solely as a feedline. Not shown in either case is the matching network that you may need to raise the low impedance of the assembly (20-25 Ohms) to the 50-Ohm level required by the coax. A quarter wavelength section of parallel 70-75-Ohm cable (taking the line's velocity factor into account) is a simple way to match the top-hat monopole to the line, although a simple L-circuit will also work well.</p>
<p>Now you may take the third step and replace the hat assembly with any desired test antenna assembly that you suspect may rely on the feedline for radiation. Since many of these top assemblies may not allow easy measurement of their radiation or their current levels due to the shape of their parts. you may estimate better the degree to which they radiate and to which the feedline radiates by comparing measurements with the two base-line antennas. As well, you may compare near-field and ground-wave readings with the choke in various positions on the coax, after ensuring that there is no significant coupling by direct radiation to the coax beyond the choke.</p>
<p>The hat assembly is an example of a half dipole that radiates only about 40-50 dB below the level of the vertical radiator--plus whatever radiation may occur from the feedpoint connection mechanical components. Its very low level of radiation is partly a function of the symmetry of its construction and its size, where the "right" size is determined by resonance when using a vertical main element that is 1/2 the length of a resonant dipole. It is part of the antenna assembly--as determined by the current distribution along its radials and perimeter wire--but unlike some other assemblies that call themselves antennas, the hat is not supposed to radiate significantly.</p>
<p>If the current distribution along the coax feedline substitute for the main vertical element matches the current distribution with a test antenna and if the near-field and ground-wave measurements also match up, then we have strong evidence that the test antenna is little more than a "hat-substitute" and has about the same radiation properties. If the current distribution along the coax outer surface is different for the test antenna, but the near-field and ground-wave readings are the same, then it is likely--subject to more detailed analysis--that the test antenna presents the feedpoint with a different set of impedance conditions, but does not contribute significantly to radiation. If the radiation levels increase with the subject antenna, then it is likely that the antenna assembly is radiating to some degree. (For further comparisons, you may wish to make reference near-field and ground-wave readings with a vertical dipole.) If the overall near-field and ground-wave readings are lower with the subject antenna in place, it is likely that the subject antenna is creating a resistive load that is converting some supplied energy into heat rather than radiation. The comparative measurements do not provide definitive final answers, but they do provide both probable answers and pointers toward the system elements that may need further analysis.</p>
<p><b>Conclusion</b></p>
<p>I have dwelt at a bit of length establishing that the top-hat monopole as simply a different but highly usable standard for comparing test results with antennas suspected of relying on feedline radiation for their far fields. It seemed necessary to clear the field of potential misconceptions attaching to notions like "ground plane," "counterpoise," and "capacity hat." The top-hat monopole and its smaller cousin that uses a perimeter wire to shrink the top-hat spread are simply inverted ground-plane monopoles and operate in exactly the same manner.</p>
<p>As a test standard, the top-hat monopole is useful because the hat structure--whether only radials or radials plus a perimeter wire--is designed to minimize radiation. Hence, it provides a standard of comparison by which one can obtain data to determine if a subject antenna radiates better or worse. I have suggested a battery of tests that include ground-wave, near-field, and relative current readings to provide a sufficiently complete portrait of antenna operation by which to reach conclusions supported by evidence with a minimum of assumptions. Refined test equipment is desirable, but rudimentary test instruments based on handbook designs are likely satisfactory if well constructed and if the test set-up is carefully handled to provide consistent results. Moreover, the test set-up requires very little more than a roomy backyard at 50 MHz.</p>
<p>Although a calibrated test range or chamber is superior, the test set-up described that includes standards of comparison as well as a reasonable compliment of measurements should go a long way to determining whether some of the suspected antennas in fact rely wholly, partially, or not at all on feedline radiation as their main mode of operation. If the reliance on the feedline is sufficiently strong, then we can save much effort and money by simply creating a hat to replace the complex and often expensive non-radiating antenna.</p>
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<p><i>Updated 11-01-2004. &COPY; L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for October, 2004. 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.</i></p>
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<h1>Counterpoise?<br>
On the Use and Abuse of a Word</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>The term <i>counterpoise</i> has a long history in antenna engineering and amateur practice. Today, it may be among the most misused terms in amateur circles. Indeed, if we examine both the history of the term, its meaning, and its misuses, we might reach an interesting conclusion: there is no such thing as a counterpoise in antenna analysis, even though the term has a long and somewhat respectable use in antenna engineering.</p>
<p>Although my bookshelf has many gaps and covers antenna history in fits and spurts, we can detect some trends in the use of the terms, along with the seeds of misuse. Therefore, let's begin with a small informal history of the term counterpoise.</p>
<p><b>The Rise and Fall of the Counterpoise</b></p>
<p>I have several texts and popular books on radio and on antennas dating to the 1920s. In none of them do I find the term counterpoise. However, I do find references to a venerable antenna type that shall prove significant in these notes: the inverted-L. Fed at its base and strung between the equipment building and a far-end support, the antenna was once the most popular home antenna for those experimenting with radio receivers in the early 1920s. In Chapter 3 of <i>Practical Radio</i> by Henry Smith Williams (1922), we find the antenna name along with diagrams and instructions on how to arrange it. Part of the discussion involves grounding. However, the concern is for lightning protection to meet the requirements of the Board of Fire Underwriters. Hence, we meet such new ideas as the lightning arrestor (a gap mechanism) and old ideas such as the knife switch to short the antenna terminals to a ground connected either (ideally) to a ground rod or (practically) to a water piper. (My local cable system still--for convenience--uses a water-pipe ground connection out of doors.)</p>
<p>My earliest ARRL book is <i>The Radio Amateur's Handbook</i> for 1930. Chapter 11 covers antennas. This chapter makes no reference to a counterpoise. However, it does divide antennas into two categories. "Those in which the ground is an essential part are known as Marconi antennas." "The second type of antenna is the Hertz antenna, in the operation of which the ground does not play an essential part." (Page 159) Although few people still refer to a Hertz antenna in general categorical ways, the term "Marconi antenna" still makes its appearance, some times referring generically to a vertical monopole system (with or without a top hat structure) and sometimes referring to a specific design. The referent to the term requires a scorecard.</p>
<p>The idea of a counterpoise worked its way into amateur radio literature largely from AM broadcast practice, although references to the counterpoise rarely reveal the term's source. Instead, we have to follow indirect clues. For example, many references to the term appear in descriptions of antennas for 160 meters. Indeed, many earlier (pre-1960) uses of the term do not include references to 80- and 40-meter antennas, strongly suggesting that early writers took the 1.8- to 2-MHz band to be an extension of the AM broadcast band. However, not all references are quite so specific.</p>
<p>In the <i>Frank C. Jones Radio Handbook</i> for 1937 (p. 39), we find the critical distinction derived from AM broadcast practice.</p>
<blockquote>
A counterpoise which consists of one or more wires in a network insulated from the ground wil often reduce loss resistances which might occur when the quarter wave antenna is connected to poorly conducting earth. The counterpoise in the case of a network of several wires acts as a condenser plate with high capacity to earth, with the result of lower loss in the antenna system; for this reason the counterpoise should be fairly close to the ground. [See <b>Fig. 1.]</b>
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<p><b>Fig. 2</b> shows a vertical antenna with an elaborate ground wire system buried under the surface of the earth for the purpose of obtaining low loss resistance connection to the ground. This system is more generally used than the counterpoise.</p>
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<p>The Jones handbook of course eventually became the famous Editors and Engineers <i>Radio Handbook</i> so ably edited for decades by Bill Orr, W6SAI. However, the last edition (the 23rd) contains no mention of the counterpoise. Nevertheless, Jones captures the critical distinction that gave the term counterpoise its good sense. It distinguished the buried radial system from a system of radials very slightly elevated from the ground. The entire radial system is insulated from the ground so that the only electrical connection occurs by virtue of the capacitance between the radials and the earth.</p>
<p>The sketch of the counterpoise system in <b>Fig. 1</b>, which is adapted from figure 6 in Jones' handbook and contains the essential features, also contains the seeds of some later misuses of the term. The antenna is the inverted-L, a necessity for most amateurs with limited yard space. More relevant is the drawing of the counterpoise wires. We find a few wires that do not form a full radial structure, and they all go in the direction of the horizontal portion on the inverted-L. An uncritical reader might well get some odd ideas. For example, perhaps we do not need a full set of radials in a counterpoise. In addition, perhaps it is important that the wires appear beneath the horizontal leg of the inverted-L. Finally, perhaps a counterpoise wire or set of wires is important to horizontal antennas. Following Windom's 1929 <i>QST</i> article, we might treat the vertical portion of the inverted-L as simply a one-wire feedline to the true element, the horizontal portion of the antenna.</p>
<p>Following the end of World War II, the amateur market once more received a spate of books on all facets of radio practice including antennas. <i>Antenna Manual</i> by Woodrow Smith, appeared in 1948. Unfortunately, it did not result in the periodic updates that marked the other Editors and Engineers offering by Orr. However, it remains a classic in amateur literature. On p. 154, Smith repeats the Jones statement about the counterpoise, in contrast to the buried radials ground system.</p>
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In the case of very rocky or poorly conducting soil a <i>counterpoise</i> often is substituted for a buried network of wires. A counterpoise is a network of wires place <i>above</i> the earth a slight distance and insulated from it, so arranged to produce a very high capacity to the earth.
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<p>In the same post-war era, ARRL developed a continuing series that has become as well-known as its Handbook. The earliest <i>The ARRL Antenna Book</i> on my shelf is the 5th edition from 1949. On page 62 we find a discussion of elevated vertical monopole radials, followed by this statement:</p>
<blockquote>
The lengths of wires and the configuration used are not especially critical. . ., particularly when the ground plane is close (in terms of wavelengths) to the actual ground. The ground plane is usually called a <b>counterpoise</b> when so used.
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<p>The first and seemingly casual statement about counterpoises actually marks the beginning (or close to it) of another misuse of the term as it folds together all forms of elevated radial systems. As we shall see, there may be good reason to separate the elevated radials from a counterpoise system as understood by AM broadcast engineers of the period.</p>
<p>On pages 220 and 221 of the same volume, in a discussion of antennas for 160 meters (Chapter 10), we find a more extended discussion of "The Counterpoise."</p>
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The counterpoise is a form of capacity ground which is often quite effective. Its use is particularly beneficial when a extensive buried system is not practicable, or when an ordinary pipe ground cannot be made to have sufficiently low resistance, as in rocky or sandy soils.
<p>The shape of the counterpoise may be made anything convenient; square or oblong arrangements are usually easy to construct and will work satisfactorily.</p>
<p>To work properly, a counterpoise must be large enough to have considerable capacity to ground, which means that it should cover as much ground area as the location will permit. . . .The capacity of the counterpoise will be approximately equal to that of a condenser consisting of two plates, each of the same area as that of the counterpoise, with spacing equal to the height of the counterpoise above ground.</p>
<p>The height of the counterpoise is not particularly critical. . .from 6 to 10 feet [0.01 wavelength to 0.02 wavelength] above ground.</p>
<p>[T]he best performance will be secured as a general rule, when the counterpoise is insulated from ground.</p>
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<p>The discussion contains further details on the construction of a 160-meter counterpoise system. Indeed, it is one of the most extensive discussions in amateur radio literature. Interestingly, <i>The Radio Amateur's Handbook</i> for 1952, especially in connection with 160-meter antennas, in Chapter 14, on p. 342, under the heading of 160-meter monopoles that are usually inverted-Ls, repeats the kernel of the <i>Antenna Book</i> account.</p>
<blockquote>
The use of a counterpoise is recommended where a buried system is not practicable or where a pipe ground cannot be made to have low resistance because of poor soil conditions. A counterpoise consists of a number of wires supported from 6 to 10 feet above the surface of the ground. Generally, the wires are spaced 10 to 15 feet apart and located to form a square or polygonal configuration under the vertical portion of the antenna.
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<p>The 1952 <i>Handbook</i> reason for using a counterpoise does not jibe completely with engineering practice in the same year. In fact, we may turn to an engineering classic, <i>Radio Antenna Engineering</i> by Edmund A. Laport, which appeared in 1952. The full discussion of radial system alternatives is too long to quote extensively, but Laport describes the basic idea succinctly on p. 52.</p>
<blockquote>
The counterpoise is an insulated net of radial wires assembled above the ground to form a large capacitance with the ground. From the earliest days of radio, the merits of the counterpoise as a low-loss ground system have been recognized because of the way in which the current densities in the ground are more or less uniformly distributed over the area of the counterpoise. Any tendency toward nonuniformity of current distribution in the ground will increase the portion of the ground current toward the edge of the counterpoise. It is inconvenient structurally to use very extensive counterpoise systems, and this is the principle reason that has limited their application. The size of the counterpoise depends upon the frequency. It should have sufficient capacitance to have a relatively low reactance at the working frequency so as to minimize counterpoise potentials with respect to ground.
<p>There should not be any connection to actual ground in the antenna circuit when a counterpoise is used.</p>
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<p>See <b>Fig. 3</b> for a sketch adapted from Laport's volume. My version is simplified in omitting the antenna control box ("tuning house" below the wires) and, more significantly, in only showing a few of the wires that make up the counterpoise system. As Laport notes, the counterpoise system is preferable to a buried radial system in terms of loss reduction in the AM broadcast band. However, for ground-mounted installations, it is usually impractical. Hence buried wires in AM broadcast antenna systems are more common. However, the counterpoise system remains necessary in urban situations, when such antenna must be mounted atop buildings with somewhat dubious conductive structures below the ground-plane system.</p>
<p>However, the extensive references to the details of a counterpoise system begin to dwindle after Laport's work. (In many ways, Laport's volume is a compendium of engineering practices in antennas for the 2 decades prior to the release of his text in the early 1950s.) For example, in <i>Wave Propagation and Antennas</i> by George B. Welch, 1958, we find on p. 183 only a small reference to the counterpoise in connection with increasing the efficiency of short vertical monopoles.</p>
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A ground system mounted in insulated supports a short distance above the earth is called a <i>counterpoise</i>.
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<p>By 1974 and the 13th edition of <i>The ARRL Antenna Book</i>, the extended account of the counterpoise system has disappeared from the discussion of 160-meter antennas. Instead, we have a somewhat vague mention of raising the antenna and radials off the ground, although some reference to the capacitances involved still occur.</p>
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Such a system is sometimes called a counterpoise.
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<p>The absence of detail on the counterpoise, as understood in the 1949 to 1952 period, was bound to result in some potential confusions. Just when they begin is dim, but by 1991 and the 16th edition of <i>The ARRL Antenna Book</i>, they are in relatively full force. On pages 2-36 to 2-37, we find a detailed account of the work of Doty, Frey, and Mills, who used a 64-radial system 5' above ground at 27-30 MHz to test the effectiveness of a vertical monopole. Despite that fact that the large radial system is 0.12 to 0.15 wavelength above ground, a relatively great height for such systems, the text still calls the assembly a counterpoise system. In addition, on page 3-11, we find an additional statement.</p>
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The effect of a perfectly conducting ground (for radiation resistance purposes) can be simulated under an antenna by installing a metal screen or mesh such as poultry netting (chicken wire) or hardware cloth on or near the surface of the ground. The screen or counterpoise system should extend at least a half wavelength in every direction from the antenna.
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<p>The use of a densely packed ground screen has been common practice in AM broadcast work for many decades, although it often shows up in the form of short radials placed between the longer radials on the standard 120-radial broadcast buried ground plane. However, texts like Laport's do not call this a counterpoise. It lacks the required elevation above the ground.</p>
<p>By the appearance of the 20th edition of <i>The ARRL Antenna Book</i> in 2003, the departure from engineering practice in the use of the term counterpoise is relatively complete. For example, on page 2-16, we find the following statement.</p>
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The term <i>ground plane</i>is also used to describe a vertical antenna employing a 1/4 wavelength vertical radiator working against a <i>counterpoise</i> system, another name for the ground plane that supplies the missing half of the antenna. The counterpoise for a ground-plane antenna usually consists of four 1/4 wavelength radials elevated well above the earth.
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<p>Of course, this use of the term flies in the face of the history of the term to refer to radial systems that are close enough to the ground to exhibit a relatively high capacitance between the radials and the ground. As well such systems would contain many radials or other wires to simulate to the degree possible a solid plate for maximum capacitance. To further the confusion on the use of the term counterpoise, we find on page 3-2 a repetition of the statement quoted from page 3-11 of the 16th edition, referring to the ground screen on or in the ground at the antenna base. Finally, on pages 6-8 to 6-9, we find reference to the work of Al Christman, KB8I (now K3LC), who has perhaps done the most research with monopoles using elevated radial systems. Christman is clear in noting that the height of the radials that allows the use of only a few radials (compared to the large radial systems needed in buried systems) introduces a change in the way in which we view the radials. Whereas the counterpoises of Laport and others contained many wires of somewhat indefinite length (up to perhaps 1/2 wavelength), the elevated radials in his study required attention to the combined lengths of the radials and the vertical section to obtain resonance. <b>Fig. 4</b> outlines the differences.</p>
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<p>Nevertheless, on page 6-8, we find the following statement.</p>
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A counterpoise is most commonly a system of elevated radials, where the radial wires are interconnected with jumpers. . ..
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<p>With respect to systems using vertical monopoles, the confusion or conflation is now complete. At one time, the notion of a counterpoise distinguished a certain kind of ground system from the typical system of buried radials. The counterpoise consisted of radials (ideally) or other shapes (practically in restricted spaces) insulated from the ground and placed relatively close to ground as measured in terms of wavelengths. The theory of the counterpoise involved creating sufficient capacity between the ground radial system and the ground itself to increase the efficiency of the monopole system, and as reported by Laport and others, it yielded higher efficiencies in some cases than buried radials.</p>
<p>One consequence of the engineering use of the term counterpoise was a 3-part distinction. Below the ground, we have <i>buried radial systems</i> with the wire in direct (or nearly direct, if the wires are insulated) contact with the ground. Next, we have <i>the counterpoise</i> alternative to buried radials. The counterpoise size and wire density equaled that of the buried radial system for maximum efficiency. Third, we have <i>elevated radials</i>, where the capacitance between the radials and the ground is too small to be effective in the determination of antenna efficiency. Rather, the radials become part of the antenna structure sufficiently independent of the ground that antenna resonance is a function of the overall antenna size at the operating frequency. Under these conditions, of course, the required element and radial lengths will change according not only to antenna height, but as well with the number of radials used and whether we leave the tips open like spokes or connect them together with a perimeter wire. The general properties of elevated radials apply regardless of the height of the antenna above ground once we pass through the frontier between the counterpoise and genuinely elevated radials.</p>
<p>Unfortunately, current literature available to radio amateurs blurs the distinction among these three relatively distinct cases, only one of which corresponded to the traditional engineering use of the term. If the term now covers every type of antenna with radials, then we may completely drop the term and simply say that an antenna needs radials to work. Or we might even resurrect the term "Marconi" antenna, although that option might itself create more confusions than it resolves.</p>
<p><b>Practical Consequences and Recent Aberrations</b></p>
<p>As "they" say in television advertisements, "But wait. There's more."</p>
<p>The conflation of the traditional engineering use of the term counterpoise with monopole radial systems in general leaves the would-be antenna builder with massive decisions and no way to answer them. The counterpoise itself, as described in the literature, requires complete insulation from the ground. A buried radial system is already in direct contact with the ground. An elevated radial system may use without harm a single safety lead connected to the hub of the radials and a ground rod. For static discharge and lightning safety, the counterpoise requires different safety switching and discharge methods relative to the other systems.</p>
<p>More intriguing is the question of at what height to place, respectively, the counterpoise and the elevated radials. For convenience and safety of individuals using the ground-plane space, most literature recommends a height of 6 to 10 feet for a 160-meter counterpoise. However, that height may in fact be greater than optimal for maximum capacitance between the counterpoise and the ground. Heights closer to perhaps 1 to 1.5 meters (3.3 to 4.9 feet) may be more satisfactory, with proportional reductions when using a counterpoise on either 80 or 40 meters.</p>
<p>In contrast, the minimum height at which elevated radials become very effective is between 2 and 3 meters (6.5 and 9.8 feet), almost regardless of which band one uses in the lower HF spectrum. In this region, 6 to 8 radials generally suffice for an elevated system, but the length of the radials requires adjustment in concert with the length of the vertical section to obtain resonance and a stable feedpoint reactance over small changes in system height above ground. The physical distances represent heights that average about 0.15 wavelength at 160 meters, 0.3 wavelength on 80, and 0.6 wavelength on 40 meters. As well, these are only heights where the performance and the feedpoint impedance stabilize. Some additional height is possible before the far-field radiation pattern begins to show signs of deterioration. For further information on lower-HF elevated radial systems, see any of Al Christman's articles or see Chapter 6 of <i>Ground Plane Notes</i>, available from <i>antenneX</i>.</p>
<p>In its engineering form, the counterpoise emerged as an alternative to buried radials systems for AM broadcast use. We may model both systems using equivalent monopoles and radials systems. Let's use a test frequency of 1 MHz, in the middle of the AM broadcast band. For a buried radials system, let's lay down 128 radials, each 0.003-m in diameter (about the same diameter as AWG #10 wire). The radials will be 1/2 wavelength long, since that is one of the recommended values for a counterpoise system, and buried radials are not extremely sensitive to length. The radials will be 0.1-m (about 4") below the surface of average ground (conductivity 0.005 S/m, relative permittivity 13).</p>
<p>We may use the same set of radials for a counterpoise by raising them to a height of 2-m (6.56' or 0.0067 wavelength) above the same ground, with no connection between the radials and ground. Otherwise, the radials are identical to the buried set. Let us assume for at least a moment that 128 radials composed of wires with the specified diameter form a very reasonable approximation of a solid surface. We may calculate a capacitance value for the virtual capacitor of which the counterpoise is one plate. The calculated capacitance is about 3.5e-7 Farads, which yields a capacitive reactance at the design frequency of about -j4.5e-1 Ohms. The reactance is under 1/2 Ohm, although the initial assumption may be shaky. The actual reactance is likely some higher figure due to the open-end structure of the modeled counterpoise radial system. Nevertheless, the calculation shows the general range of values toward which counterpoise designers aimed.</p>
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<p><b>Fig. 5</b> overlays elevation patterns for the two monopole installations. Both patterns have a TO elevation angle of 21 degrees. The buried-radial system yields a maximum gai of 2.24 dBi, while the counterpoise system shows a maximum gain of 1.93 dBi, about a 0.3-dB difference. One might change the counterpoise system gain by solidifying the radial structure, perhaps with cross wires linking the radials, especially in the outer regions in which the radials show maximum separation.</p>
<p>Despite the similarity of antenna performance, the current distribution along buried radials is not the same as along the slightly elevated counterpoise wires. <b>Fig. 6</b> shows graphs of the current magnitude along the radial wires. Both parts of the figure use the same maximum current value (red) in order show the variations. The monopole current will appear wholly red, since the currents in the individual radials begin in the feedpoint segments at 1/128 the source current.</p>
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<p>The currents in the buried radials begin at a relatively low level and continually decrease along the length of the radials. Because buried radials are in a medium of limited conductivity and significant relative permittivity, the current distribution is not the same as in wires in air. The level of segmentation in the model does not permit us to view small fluctuations in the radial currents, but the overall progression is typical of radials systems of all sizes.</p>
<p>In contrast, the counterpoise radials show an interesting pattern with a current peak roughly 1/4 wavelength from the monopole and then a relatively smooth current magnitude decrease toward the radial ends. Although the current progression is smooth along the radial wires of the counterpoise system, it is not symmetrical on each side of the peak (red) values. An adequately sized counterpoise system is one in which the radials or other structures are large enough to allow the current distribution its full progression. Nevertheless, the monopole alone plays the dominant role in setting system resonance, just as it does with a buried radial system.</p>
<p>Counterpoises, as understood in mid-20th century engineering literature and some amateur literature of the same period, then, are far different electronic devices than true elevated radials that are part of the antenna's resonant length. Elevated radials, ranging from Christman's research subjects to VHF ground-plane radials, are intrinsically more similar to each other than elevated lower-HF radials are to counterpoises.</p>
<p>Unfortunately, radio amateurs, even those who write about their successful antennas, are subject to impressions and truncated sound bites. Let's combine elements of less adequate treatments of the counterpoise that have occurred in the last quarter of the 20th century. We may begin with one enduring picture, sketched in <b>Fig. 1</b>. The antenna shown is an inverted-L, with a truncated 3-wire counterpoise extending under the horizontal portion of the antenna wire. Let's add the sound bite that virtually any wire extending from the base of a monopole is a so-called counterpoise wire. In this combination we have the makings of some serious misuses of the idea of a counterpoise.</p>
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<p><b>Fig. 7</b> outlines 3 antennas that I have encountered in amateur radio magazines over the lest decade or so. I am purposely omitting the identities of the antenna builders. What the antennas share is a common claim that at least one wire in the system is a counterpoise. The first case involves a field antenna, either in the form of an inverted-L or in the form of a sloping wire. Since the antenna is end fed, we normally require an antenna tuner to match the impedance at the wire's end to the transceiver in use. Normal practice would show as direct a connection between the tuner's ground terminal and the earth. What the innovator adds is a somewhat long wire that he terms a counterpoise, and this wire leads to the earth connection.</p>
<p>The second antenna comes from a number of sources. In one article, the innovator creates a monopole and then uses a so-called counterpoise wires to dangle off the edge of his apartment balcony or deck. Having heard that the counterpoise wire length is not critical, he cuts it casually. The third case involves a horizontal wire antenna end fed with parallel transmission line. Adhering to the apparent picture in <b>Fig. 1</b>, he adds a wire underneath the horizontal aerial wire and claims that this counterpoise improves performance.</p>
<p>All three claimed antenna parts called counterpoises emerge from the murkiness that has come to surround the term. The term "counterpoise" comes from mechanical systems contexts. It means a counter-balancing force, ordinarily a weight on the other side of a fulcrum. This name, as it has been conflated in amateur literature to suggest anything with radials, has acquired the additional meaning of an antenna part that does not itself radiate but permits the radiating parts to radiate better than they would without it. There is nothing in the world of antennas that corresponds to the dead weight facet of this misshapen version of the concept of a counterpoise. Every part of an antenna contributes to the antenna far-field pattern (except those parts that we specifically design to have self-canceling radiation). Hence, there is no such thing as a mere counterpoise.</p>
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<p><b>Fig. 8</b> shows both the claimed and the actual antenna on the left in <b>Fig. 5</b>. The actual antenna runs from the earth connection through the tuner to the far end of the wire, whether it is sloping or bent. Since the tuner is effectively in series with the wire, it forms an off-center feedpoint for the antenna. Of course, the current in the wire running close to or one the ground contributes little if anything to the antenna's far-field pattern. At most, it may present the terminals of the ATU with an impedance that more easily fits within the tuning range of the components.</p>
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<p>The claimed version of the antenna in <b>Fig. 9</b> is among the most insidious because of the market for commercially made mini-monopoles. One such antenna comes with a bale of wire that the user is supposed to unroll. He then tunes his antenna and kicks around the wire bale until he achieves a satisfactory match. What the user does not realize (since he has already purchased the antenna) is that most of his antenna is lying at his feet. In the less problematical version shown in the figure, the entire antenna constitutes a vertical dipole. The length of the upper and lower ends together contribute to the overall resonant length, and the lower portion of the antenna--if we mount it from an elevated support--does as much of the radiating as the upper portion. In most circumstances, it will not matter whether the actual feedpoint position is slightly off-center with respect to the peak current position on the overall antenna. Since the current level changes very slowly in the vicinity of its peak value on a dipole element, the feedpoint impedance will also change very slowly.</p>
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<p>The third case (C) is a modern adaptation of a very old scheme of running a second wire at or near the ground under a horizontal wire, ostensibly to improve some mysterious relationship between the upper wire and the earth. Actually, the horizontal antenna performance remains unchanged, and the wire becomes a trip for anyone careless enough to walk through it. At best, it serves as a parasitic reflector, possibly converting a general-purpose antenna into an NVIS (Near Vertical Incidence Skywave) special, as suggested by <b>Fig. 10</b>. However, single wires close to the ground do virtually nothing to improve even the performance of NVIS antennas. A ground screen that exceeds the elevated antenna's dimension by about a half wavelength in every direction is necessary to create an effective planar reflector.</p>
<p>In every case, the so-called counterpoise can be analyzed (and modeled) as a part of the antenna.</p>
<p><b>Where Does All of the Discussion Leave Us?</b></p>
<p>On the one hand, we have the information left to us by the history of radio antennas before the concept of a counterpoise lost its meaning. On the other hand, we have the collection of misunderstandings (a collection larger than the samples shown here) that have resulted from the conversion of the term counterpoise into a general-purpose word having little import. The fuzzy, blurry current use has been the source of many an egregious error by casual writers about antennas that they have built. Indeed, the present use is only a malevolent ghost of the original.</p>
<p>One major option is to restore the term to its traditional meaning alone to indicate a large radial or screen insulated from the ground but close to it to serve as a capacitively coupled ground for monopoles. That option would force upon writers of articles and handbooks several responsibilities.</p>
<p>1. The treatment of the counterpoise would need restoration to the length at least of the version found in the 1949 edition of <i>The ARRL Antenna Book</i> or in sources like Laport's <i>Radio Antenna Engineering</i> in order to give the term clear sense.</p>
<p>2. Such writers would also have to clearly distinguish between a true counterpoise and monopole radials elevated far enough off the ground to lose enough of their capacitive coupling to ground to act as the simple completion of a dipole, with one end composed of a symmetrical set of elements whose radiation is largely self-canceling.</p>
<p>3. The same writers would have to overcome the temptation to refer to any set of monopole radials as a counterpoise. Indeed, they would have to overcome the temptation to call anything other than the traditional counterpoise by that name.</p>
<p>Now let us suppose that we find fault in either the correctness of the theory that underlay the traditional antenna engineering concept of a counterpoise or that we determine it no longer has relevance in that meaning to current antenna practice. Because confused and conflated alternative meanings for the terms tend to create greater misunderstandings than they resolve, this option leads to only one action: that we drop the term altogether from the antenna lexicon.</p>
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<p><i>Updated 01-01-2007. &COPY; L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for Dec., 2006. 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.</i></p>
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<title>Building a QRP Field Vertical</title>
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<h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Some Techniques for Building a QRP Field Vertical</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>The requirements for a QRP field vertical--usually base-loaded--are few but critical. It must be sturdy and easy to handle in the field. The field may be anything from a hotel room to an actual meadow. The parts must be easy to hold but hard to lose. The entire structure should breakdown into a set of pieces that fit within a small bag or case.</p>
<p>Over the years, I have seen a wide variety of parts used for such antennas, some better than others. These notes simply add to the collection of techniques available to the QRP field operator, as he or she designs a personal field vertical.</p>
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Fig. 1. Basic elements of a vertical with base loading.
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<p><b>Fig. 1</b> shows the basic elements of a field vertical intended for base loading. We must have a main radiator. The height of this radiator is caught between two demands. On the short end, it should be usable within the 8' high ceiling of a hotel or motel room. On the long end, it should be as tall as we can manage for the sake of efficiency. The shorter the radiator, the greater the size of the loading coil and, hence, the lower the radiated power for a given amount of power fed to the system.</p>
<p>The antenna requires a support system that will keep it vertical and stable (even in a modest breeze). The larger the support spread, the sturdier the mount. However, once more we encounter conflicting needs. The support system should break down or collapse into manageably short pieces for transport and not be unreasonably heavy. The support system may also form the hub of the radials that we use to complete what is essentially a shortened vertical monopole. The better the radial system, the better the performance.</p>
<p>Finally, we need a way to feed the antenna. For this type of antenna, feeding also includes loading and matching. A shortened vertical has a low resonant impedance: the shorter the antenna, the lower the resonant impedance and the higher the inductive reactance required to offset a high capacitive reactance. We need a small assembly-- consistent in size with the pieces of the system--and a means of connecting it to the antenna and the radials.</p>
<p>With these essentials in mind, let's look at a few of my personal preferences for the pieces of the system.</p>
<p><i><b>The Main Radiator.</b></i> <b>Fig. 2</b> shows how I prefer to make up the main radiator for a field vertical. T6063-832 aluminum tubing is light and readily available from sources such as Texas Towers (http://www.texastowers.com). It comes in 6' lengths to avoid UPS excess shipping charges, but we shall use shorter sections than this length. The figure shows the largest diameter as 0.75". This specification depends on two major factors. First is the question of weight. The larger the tubing, the higher the weight. For a home ground- mounted vertical, I might start with 1.25" diameter tubing, but this antenna is for the field.</p>
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Fig. 2. A radiator made up of nested aluminum sections.
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<p>I use certified 6063-T832 aluminum with a wall thickness of about 0.05" for a reason: the interior will be smooth, allowing me to nest the tubing easily. Hardware depot tubing sometimes has a seam that roughens the interior. (At the end of these notes, I shall make some maintenance suggestions, including keeping the tubing interiors clean.) All of the sections shown in the figure collapse into a single unit that is still light, not to mention compact.</p>
<p>The section lengths are all equal, and we have a choice for that length. Ignoring the top rod, 4 sections of 2' tubing will make a 7' 3" radiator, which fits nicely under a room ceiling, if we overlap the section by 3" for strength. 5 sections of 3' pieces, including the top rod, make a 14' vertical, which is significantly more efficient as a ground-plane antenna. The choice depends on your intended operations and the length of your carry-bag.</p>
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Fig. 3. Key hardware items for the portable vertical.
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<p>For field use--but not for permanent installations--we may simplify the junctions. The figure shows small holes about 7/64" to 1/8". These holes are for hitch pins, shown in <b>Fig. 3</b>. The figure also shows the source: page 2971 of the McMasters-Carr on-line catalog (http://www.mcmasters.com). Hitch pin clips, also called hairpin cotter pins, come in a variety of sizes and materials. Stainless steel is best, but cheaper plated pins are adequate if never subjected to rain. The main radiator uses a pin size intended to hold 1/2" to 3/4" diameter rods or other similar fixtures. They also have large round ends for easy gripping. However, I hot-glue ribbons through the round ends so that the pins cannot hide in the grass.</p>
<p>Now we can return to the optional top rod of the main radiator. A pin of the size specified is a bit large for the 3/8" tube to 1/4" rod junction, adding a different hitch pin size to our hardware. As well, the weight per unit length of the rod is higher than that of the 3/8" tube. The difference will not make the rod unusable, but only a bit troublesome relative to our otherwise simple structure.</p>
<p>Drill the hitch pin holes through both pieces to be joined in one operation to assure alignment. Be sure to deburr the holes so that the drilled aluminum tubes still nest smoothly for storage. Since it is likely that the holes will be only close to perfectly centered, make a pencil line from one section to the next for easy field alignment. Renew the line after every few uses of the antenna. The hitch pin clips are easy to use and mechanically sound for this application. However, the antenna relies on the metal-to-metal contact between tube sections for electrical continuity in the antenna. The practice is satisfactory for short-term field use, but not for long-term permanent home installation. The condition of using this system is guaranteeing clean aluminum for the junctions.</p>
<p><i><b>The Support Stand.</b></i> A 4-legged stand provides good stability for the field vertical under indoor or gentle weather conditions. The stand that I built from scrap PVC appears in <b>Fig. 4</b>. It consists of 5 separate parts. 4 of the parts are 2' long legs of Schedule 40 1/2" nominal diameter PVC (Part A in the figure). Each leg has an in-line junction cemented on the outer end (Part B). This junction allows you to insert additional lengths of tubing for longer legs and added stability. As well, you can drill the junction to accept aluminum tent pegs to hold the legs firmly to the soil in the field. Alternatively, you can bend stiff steel wire into Us that fit over the legs near the outer ends: press these Us into the soil.</p>
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Fig. 4. Details of the 5-piece PVC support stand
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<p>The hub of the legs is a 4-way junction of the same PVC material (Part C). However, I modified the hub by drilling a 5/8" hole through the center. Into this hole, I cemented an 18" length of 1/2" nominal CPVC tubing, which has a 5/8" outside diameter (Part D). Because CPVC has a thinner wall than Schedule 40 material, I inserted a 3/8" wood dowel and then filled the interior of the tube with fiberglass resin used in auto repairs (Bondo). This addition stiffens the vertical section against stresses created by the main radiator.</p>
<p>At the base of the CPVC is a 1.5" length of 1" diameter aluminum tubing (Part E). On opposing sides of the short tube, I installed 1/2" long #10 stainless steel bolts, with the heads inside the tube. A little filing flatted the round heads so that the tub fit over the CPVC. The figure shows one of the bolts aligned with one leg of the stand, but that is a function of my limited drawing skills. The bolt actually is aligned between the legs on opposite sides of the tube. To center the tube and provide an insulated separation between the 1" tube and the main radiator, I added a very short section of 3/4" nominal diameters CPVC (Part F). The 3/4" CPVC fits inside the 1" aluminum tube and over the 1/2" CPVC. I cemented the CPVC separator in place, thus locking the short base aluminum tube in place as well. The main radiator simply slips over the CPVC and slides down to the separator.</p>
<p>The small base aluminum tube serves two purposes. With a wing nut on each bolt, the tube forms the hub of any radials used with the antenna, as well as for any special ground rod connection. I recommend a full set of radials for each band. You can construct these from flat 4-wire TV rotator cable, cutting each strand to a quarter wavelength for 10, 15, 20, and 40 meters. The exact length is less important than the presence of as many radials as possible, with a field minimum of 4 recommended for adequate efficiency. Connect the 4 strands together at the inner end and use a ring connector under the wing nut and over the hub bolt. Above the hub bolts, we may connect the match/load/feed system base, with its top end going to the main radiator.</p>
<p><i><b>The Match/Load/Connector System.</b></i> <b>Fig. 3</b> showed not only a sketch of the hitch pin clip, but also the outline of a handy tool clip. The clip is also available from McMaster-Carr (page 2726) and comes in numerous sizes in both plated and stainless types. Once more, stainless steel is best for durability, but plated clips will last well if not subjected to rain. The size shown (1/2" to 3/4") will work, even with the 1" base tube, but a larger size is also dandy for a base coil and feed system.</p>
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Fig. 5. Mounting plate for the loading and matching components.
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<p><b>Fig. 5</b> shows the outlines of a plate that holds the loading and matching components. I recommend 3/16" thick (or thicker) Plexiglas or polycarbonate. The part of the clips with a mounting hole (which uses #6 hardware) comes arched. As you tighten the hardware, the section flattens against the plate, forcing the spring section to close very tightly. When fully tightened, the arch exerts considerable force on the plate and can deform 1/8" thick material over the span of a few hours. The stiffness of the tool clips makes excellent electrical contact with the tubing.</p>
<p>The plate shows a sketch of a simple loading system using two coils. The high-band coil covers 10-20 meters with an 8-10-foot vertical. An added plug-in 10 micro-Henry coil allows loading on 40 meters. A lead from the coax center pin to coil taps does the tuning for the simplest version of this base-loaded vertical.</p>
<p>However, finding a tap that gives a low SWR is often difficult with higher levels of loading. The resonant impedance gets lower and lower, and by the time we find a tap near 50 Ohms, the reactance is considerable. To overcome this problem, you may add a capacitor across the coax terminals. A receiving variable with about 1200 pF total capacity should work with all but the shortest verticals on 40 meters. (Higher bands are less problematical.) The physical size of the capacitor depends on the desired power handling capabilities. For an old-fashioned multi-section receiver capacitor, you can offset the tool clips toward the coax connector side of the plate. There will be about 1/2" of space between the plate and the main radiator, due to the shape of the tool clips.</p>
<p>Adding the capacitor converts the simple base loading system into an L-network for matching low load resistances to 50 Ohms while compensating for the capacitive reactance of the short vertical. Jumpers can use banana plugs and chassis jacks to simplify the overall set-up. How much of the assembly consists of plug-in components and how much you permanently mount to the plate depends on your operating needs and the sizes that you choose for the main radiator sections.</p>
<p>I have not given any specific values on a band-by band basis for some components, especially for the loading coils and the L-network capacitor. My reasons are many. First, the required values will vary with your selection of the main vertical length. Second, they will vary with the height of the antenna base above the real ground. Third, they will also vary with the number and length of the radials that you use--and somewhat with variations in how you arrange them. Two 10 microHenry coils--one for the upper bands and tap-able, the other a fixed coil added in series for 30 meters and below--should handle most cases, along with a 1200 pF shunt capacitor on the coax side of the coils, if you choose the L-network option. (You may parallel a 100 pF capacitor with the big one to provide a fine-tuning control.) Nevertheless, there are too many variables involved in the personalized versions of this system to guarantee a good match in every circumstance.</p>
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Fig. 6. Other ways to use the tool clips.
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<p>The tool clips are handy in a variety of circumstances that range from field antennas to prototype experimental designs. <b>Fig. 6</b> illustrates a couple of situations where they work well. The simple plate and its coax connector are useful for feeding a dipole center, illustrated by the left side of the vertical sketch in the figure. By using a fiberglass rod inside two sections of tubing--fixed in place with hitch pins--the center connector simply snaps into place. For mid-element loading coils in field or trial use, the plate and tool clip system, along with a fiberglass separator, allows one to develop the exact loading coil or trap needed for a given design, all without having to remove and replace screws in the element.</p>
<p><i><b>Maintenance.</b></i> The system just described requires no tools in the field. The tool clip hardware is shop-tightened and requires no further field work. Everything simply snaps into place, whether a hitch pin or a tool clip. This feature allows for quicker assembly and disassembly, leaving more operating time. The entire collection of parts (nested main radiator, 5-part support, and matching/loading/connector plate) fits into a bag as short as 24" long. (Extras, such as additional field braces, SWR meters, etc., are the user's responsibility.)</p>
<p>However, the system will only work well if you give it the required pre- and post-use maintenance.</p>
<p><i>1. Before use</i>: Test assemble the antenna to ensure that all parts fit together as prescribed. Perform any adjustment necessary (such as burr removal). If the aluminum has become cloudy during storage due to oxidation, clean the surfaces with a plastic scouring pad. (Do not use steel wool or course sandpaper.) Check all coils for electrical and structural soundness. Count parts to ensure that everything is available.</p>
<p><i>2. After Use</i>: Clean all parts of the antenna thoroughly. Remove any dirt from the stand, using any good cleaner or detergent. Check for use damage to the vertical section of the stand to ensure a smooth fit with the lower aluminum tubing at the next use. Clean the outer surface of the aluminum tubes with a mild cleanser to remove field dirt and stains. Clean the inner surfaces of the tubes with a stiff long-handled bottlebrush. Recheck the coils for any damage--and repair immediately. Re-wrap components together to restore a factory-like presentation. Count components to ensure nothing is missing. Replace any missing component immediately.</p>
<p>With these measures, the antenna should provide many years of satisfactory service. However, I fully suspect that long before the antenna wears out, you will be experimenting with other improved field antennas.</p>
<p>The ubiquitous base-loaded vertical is far from the most efficient antenna that you can use. However, it is cheap, compact, and reliable, even if the gain goes down with the frequency and the amount of loading required. The system shown here uses a longer main radiator than most whip-based systems for a modicum of higher efficiency. The L-network can provide a somewhat better match for the rig. Even with these improvements, the system remains light for easy field transport. It requires no tools for assembly and disassembly. Allowing for leftover aluminum tubing and hardware bought in excess quantities (all useful for other projects), the net cost is about $25 to $35, depending on the sources used and the size of your junk box. (If you purchase components for the matching/loading system, the cost may go up accordingly.)</p>
<p>Even if you do not build your own field vertical, perhaps the use of hitch pin clips and tool clips will give you some ideas for other projects.</p>
<p><i>Updated 05-25-2002. &COPY; L. B. Cebik, W4RNL. This item originally appeared in</i> QRP Quarterly<i>, April, 2002, pp. 17-20. 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.</i></p>
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<h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">A Modeling Perspective on "Ground" Planes</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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Most of what we have learned about ground planes beneath vertical antennas arose from LF and MF practice. There is another perspective from which we can approach the subject: modeling in programs like NEC and MININEC. Moreover, there is an alternative point of departure for investigations to the normal survey of landscape and subsoil properties. The alternative is free space. The combination of the two underlies the notes in this collection.
<p>My aim is not to replace classic vertical antenna theory. Instead, it is to see what antenna modeling might add to the array of considerations we give to vertical monopole antennas and their ground planes. To that end, I have let the modeling lead where it may. At most, the notes may guide some of our expectations, but they are not likely to alter our explanations.</p>
<p>This is all background. There are no practical antennas in these notes, although there may be a practical idea or two. For one of the best arrays of practical applications combined with recent insights into vertical antenna pattern analysis and elevated radials, see ON4UN's <i>Low-Band DXing</i>. This book is still the current standard, as are the continuing investigations of Jack Belrose, VE2CV. But if I list every classic and worthy study, this index will be longer than the notes. ON4UN has an excellent bibliography.</p>
<p>Since there have been numerous recent developments in the understanding of elevated ground planes, the following references are suggested:</p>
<p>Arch Doty, K8CFU, John Frey, W3ESU, and Harry Mills, K4HU, "Efficient Ground Systems for Vertical Antennas," <i>QST</i> (February, 1983), 20-25</p>
<p>Al Chrisman, KB8I, "Elevated Vertical Antenna systems," <i>QST</i> (August, 1988), 35-42</p>
<p>Al Chrisman, KB8I, "Elevated Vertical Antennas for the Low Bands," <i>ARRL Antenna Compendium</i>, Vol. 5 (1966), 11-18</p>
<p>KB8I and professional colleagues have also published a numbers of studies on this subject in the <i>IEEE Transactions on Broadcasting</i>.</p>
<p>L. A. Moxon, G6XN, "Ground Planes, Radial Systems and Asymmetric Dipoles," <i>ARRL Antenna Compendium,</i> Vol. 3, (1992), 19-27</p>
<p>Dick Weber, K5IU, "Optimal Elevated Radial Vertical Antennas," <i>Communications Quarterly</i> (Spring, 1997), 9-27</p>
<p>Rudy Severns, N6LF, "The Lazy-H Vertical," <i>Communications Quarterly</i> (Spring, 1997), 31-40</p>
<p>Rick Littlefield, K1BQT, "Build a 20-Meter DX Pole," <i>Communications Quarterly</i> (Spring, 1997), 98-102</p>
<p>Note: By the conclusion of this series of notes, you should understand fully why the last three articles are essentially about the same antenna.</p>
<blockquote>
<p><b>1. <a href="gp1.html">Part 1: Some Preliminary Notes on the Ground</a></b></p>
<p><b>2. <a href="gp2.html">Part 2: "Capacity" Hats</a></b></p>
<p><b>3. <a href="gp3.html">Part 3: Planes in Space</a></b></p>
<p><b>4. <a href="gp4.html">Part 4: Down to Earth Verticals</a></b></p>
<p><b>5. <a href="gp5.html">Part 5: Regional Differences</a></b></p>
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<p><i>Updated 6-6-97. &COPY; 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.</i></p>
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<h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Part 1:<br>
Some Preliminary Notes on the Ground</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<p>We are very careless with the ground. We tend to treat it as a single homogenous entity. In simplest terms, that means that we think about the ground in the same way, no matter in what radio context it appears.</p>
<p>We are not as careless as we used to be. When forced by circumstance, we do sort out the following grounds.</p>
<p>G1. The DC and static discharge ground: This is the ground of long ground rods by which we ensure that DC, small static charge build-ups, and power line AC are shunted to ground. Our station ground strap gets into the act here, because we make a common ground for all cases, keeping them at the same potential, hopefully ground potential if our distance from the rod into the earth is not too long.</p>
<p>G2. Circuitry common bus (ground): We have also learned that there is a difference between a circuitry common and an earth ground. Sometimes we have learned this the hard way with shocks and tingles.</p>
<p>G3. Lightning ground: We have also learned that lightning strokes and other sudden high voltage and high current impulses require more attention than G1-type grounds. The details of a satisfactory, equipment-protecting grounding system for lightning are more complex than those required for simply preventing the wind from building a static charge on our dipoles.</p>
<p>G4. RF ground: Effective RF ground also requires attention to many details. Deep rods, while useful, may be less effective as RF grounds than we previously thought, and the U.S. Army developed a system of perimeter straps and a sequence of shorter rods to effect a satisfactory overall station RF ground. RF paths to and from ground via transmission lines, circuitry-to-case connections, common mode paths, and numerous other sources are receiving increased attention both by those who build equipment and by those who assemble operating stations.</p>
<p>We might extend this list--not to mention subdivide it. But let's turn to a couple of new categories created out of one old one. Both have to do with antennas.</p>
<p>We tend to think of the ground relative to an antenna as a single ground. Hence, we tend to lump together the ground from which signals reflect to contribute to antenna far field patterns and the ground directly under a monopole antenna. The "only" difference is their relative distance from the antenna itself. However, let's see where separating the two ideas leads.</p>
<p>G5. Far field reflective ground: The ground quality is usually specified in terms of conductivity (given in Siemens or milli-Siemens per meter) and a dielectric constant (permittivity). ON4UN did some modeling with some vertical radiators that suggests the ground kicks in as a reflective medium somewhere around 2 and a half wavelengths from the antenna--possibly more for highly elevated antennas. Although the ground immediately under the antenna has some effect on antenna effectiveness relative to far field patterns, the effect is small (unless the ground is needed to complete the antenna). Dipoles, for example, exhibit only small gain changes as the quality of soil is ranged from very poor through very good.</p>
<p>Do not confuse ground quality with terrain considerations. The quality of ground at varying distances from an antenna is only one factor among many with which terrain evaluation is concerned. Slope and interfering objects are samples of other factors that go into terrain evaluation for determining the ultimate elevation pattern for a given antenna and site.</p>
<p>Self-contained vertically polarized antennas, running from the vertical dipole to complex arrays like the bobtail curtain, exhibit the same far field radiation properties with respect to ground as do dipoles and other horizontally polarized antennas at HF. The surface wave of an HF antenna is small, relative to the sky wave. Losses may be slightly higher than with a high horizontal antenna, but generally are not significant.</p>
<p>G6. Antenna-completion ground: Monopole antennas are generally analyzed as having their missing pole (relative to a dipole) within the ground. This is often pictorially presented as an "image" antenna sticking straight into the earth. While this portrayal allows the solution to certain basic equations, it is actually a very poor picture of what is going on.</p>
<p>It is the surface volume of the ground that provides the completion of the antenna. Signals penetrate the ground to depths that vary directly with wavelength and inversely with frequency. However, even with a monopole, the penetration does not act like a spear into the ground.</p>
<p>A more correct picture is a surface area (with some depth) around the monopole. The conventional radius of this surface is about 1/4 wl. Since even the best soil is lossy compared to conductors, we lay screens and radials under the soil to improve its conductivity. Somewhere between 60 and 120 radials approaches the conductor saturation point of most soils. This is the most traditional ground plane.</p>
<p>Of course, we can also elevate the ground plane. A number of investigators (nicely referenced by ON4UN) have discovered that even a few feet of elevation can improve the performance of a monopole over that obtainable with buried radials.</p>
<p>Another interesting phenomenon is that rooftop monopole vertical antennas do not seem to benefit from littering the roof with 60 to 120 radials. 4 to 8 seems to be enough to achieve all the performance of which the antenna design is capable.</p>
<p>Let's add one more phenomenon: Experimenters have discovered that the best length for radials is slightly less than 1/4 wl. Of course, these were elevated radials.</p>
<p>And one more: If we model a monopole with radials in free space, it does not care what its orientation is.</p>
<p>If we construct a monopole with the feedpoint high, and then if we add another monopole atop the first, we have a vertical dipole. Now let us shorten the upper monopole and compensate with a hat. A hat is a symmetrical array of wires ranging from 2 to very many, with or without a perimeter ring or inner rings. Its function is to complete the current path necessary to achieve some specified state at the feedpoint, usually resonance. We used to call this a "capacity" hat based on the way we calculated its size at LF and VLF, but those methods go to pot at HF. (I know this from having written a very convoluted program to calculate them from 3 to 30 MHz for antenna length reduction only down to 70% full size.) So let's just call our structure a hat. Because it is at right angles to the antenna, and because it is symmetrical, it ideally does not radiate. All the field from one leg is cancelled by a field equal in magnitude but opposite in phase from an opposing leg.</p>
<p>Now continue to shorten the upper monopole until it is very short, perhaps even insignificantly short. The hat has to grow in order to provide an ever longer current path to maintain resonance (or some other specified condition) at the feedpoint. In fact the hat grows to nearly 1/4 wl in radius. Since it is a very fat wire indeed, it does not grow to a full 1/4 wl.</p>
<p>What we have is an upside down conventional monopole. Turn it right side up at many wl above the ground, and the far field pattern is indistinguishable from the upside down version. Tilt the legs making up the hat, and they are no longer at right angles to the single-wire monopole end: hence, they partially radiate and partially cancel--as every maker of simple 2-meter sloping GP antennas knows. Upside down, we called the structure a hat; rightside up, we call it a ground plane. The antenna does not care because an antenna-completing structure by any other name performs just as sweetly.</p>
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<p>Now bring the antenna closer to the dirt ground. The fields from the hat-plane begin intersecting the ground in earnest, and those intersections yield interactions that may alter the required size of the hat-plane. But the basic function of the hat-plane is to complete the antenna. In short, the antenna-completing ground is not a ground at all.</p>
<p>Instead, we sometimes use the ground to do the work of the hat-plane. More precisely, we have used the conductivity of dirt ground materials to do the work of the hat plane. Everyone who has ground-mounted a vertical in the middle of a septic tank drain field has gotten decent performance without radials.</p>
<p>So, what about that class of self-contained vertically polarized wire antennas (SCVs)? This group includes a number of 1 wl loop and open antennas, such as the delta, the square, the rectangle, and the half- square. All these antennas produce vertically polarized radiation independently of the dirt ground by virtue of the fact that part of the antenna structure acts as a phasing line in which horizontal structure radiation is cancelled, while radiation from the vertical elements is phased for additive field production.</p>
<p>SLVs model nicely in free space with properties that carry over into models and real antennas mounted several wavelengths above ground. Up and down make no difference to these antennas under the given conditions. Such antennas depend only on the far field reflective ground with respect to their patterns.</p>
<p>Brought closer to the dirt ground--which is inevitable when we use SCVs on the lower HF bands--the antenna fields intersect with the "semi-conductive" ground materials--just as they might if we sandwiched one of the antennas between two sheets of metal. The results are modifications to antenna performance. But, the antenna does not depend upon the ground for its basic performance as an antenna--that is, the ground does not complete the antenna. The ground is not a ground plane.</p>
<p>In fact, the so-called ground plane is never a GROUND plane, but always a hat-plane. Hence, the so-called antenna-completing ground is not a ground at all--even though we sometimes use the ground to do the work of the plane. This is not the first time we have misnamed something in radio. It took a long time to weed out the term "condenser." It will likely take even longer to drop the term "ground" from ground plane.</p>
<p>But do we not always connect the braid of the coax to the plane and the center to the monopole? Most of us do, but it is not required if we separate our DC and RF grounds from the antenna end of the transmission line. We can feed a monopole through an inductively coupled balanced ATU and then connect either side of the line to either antenna terminal. Once again, we collect a number of functions into a single configuration, like connecting the case to the coax braid and the braid to the monopole ground rod as our station ground: then we forget to sort out the functions, and the configuration makes it hard to separate them. Nonetheless, the antenna, as an antenna alone, does not need a ground for its ground plane. (But add one anyway for lightning, static discharge, RF, and DC grounding.)</p>
<p>By sorting out our grounds--and further sorting real grounds from planes we only call grounds--we can achieve a better understanding of a. how monopoles work and b. why some vertically polarized antennas do not need a ground plane. But I doubt if the term "hat-plane" will ever gain currency.</p>
<p>Eventually, we shall add pictures and quantifications to these initial notes. Nonetheless, I hope they prove useful as a start in sorting out the many grounds of radio work, especially if you, like Karl Mannheim, ever say, "Ich habe meine Grunde vergessen." ("I forgot where I started.")<br>
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<p><i>Updated 5-20-97. &COPY; 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.</i></p>
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<h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Part 2:<br>
"Capacity" Hats</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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If we are to succeed in looking at ground planes in a different way, as suggested in Part 1, then we must first understand some things about so- called capacity hats. While this discussion may seem initially to be a digression, we shall see in later parts that almost all of what can be said about hats can also be said about so-called ground planes--except this: hats go on top, planes go on the bottom.
<p>A true hat is a symmetrical conductive structure that we place on the end of an antenna element, and at right angles to it, so that two effects occur. First, the net radiation from the hat is zero, due to the cancellation of radiation from one part of the structure by that from another part. Second, by using the hat as a path for antenna currents, we may shorten the main element length and still achieve resonance or some other specified condition.</p>
<p>We may also use slightly non-symmetrical structures to achieve, what is usually called top-loading. So long as the structure does not radiate a field more than about -30 dB relative to the field from the main element, the radiation from the field will not materially affect the overall pattern or the feedpoint impedance of the antenna. Non-symmetrical top loading may, however, have an affect on the operating bandwidth and gain of the antenna element.</p>
<p>Although we refer to these methods as top-loading, they are quite distinct from base or mid-element loading. All the two forms of loading have in common is that they allow us to use a shorter main element in our antenna. Base-loading and mid-element loading normally use either solenoid inductors or shorted transmission line stubs to introduce into the antenna an inductive reactance that compensates for the capacitive reactance that emerges as the element is shortened. Inductive reactance comes at the cost of resistance that transforms some of the energy reaching the antenna into heat. Every mode of inductive loading, including the use of inductive transmission line stubs, has a finite Q, and that means a source of gain loss in addition to the loss of gain which is natural to the shortening of an antenna element.</p>
<p>A hat is simply a form of antenna length completion so that the current has a path of a correct length to achieve resonance, despite the use of a shortened main element. The only losses are those associated with the shortening of the element and the materials used to construct the hat.</p>
<p>From the perspective of modeling, we may drop the word "capacitive" when referring to hats. That term arose from a method of calculating the size of hats for LF and VLF and rests on using an open transmission line analogy for antennas. From the beginning, the technique was considered only an approximation, and it breaks down severely at HF, where the diameter and relatively uniform diameter of antenna elements violates the fundamental terms of the analogy. Hence, from this point forward, I shall simply refer to hats or top hats.</p>
<p>We may construct hat structures in many forms. The most common form is a series of radials extending from the end of the main element outward. The radials are spaced at equal angles to each other. Hats require a minimum of 2 opposing radials, but may have any large number until they form a solid disk. Along the way, we shall examine an alternative to this structure that has some interesting properties.</p>
<p>The length of a hat radial (or "spoke," as it is sometimes informally called) depends on many variables: the length of the main element relative to the frequency of interest, the diameter of the main element, the diameter of the radial wire, and the number of radials. Let's freeze the element and radial diameters for a moment at 2" and 0.25" respectively, and let's make them aluminum. That will simplify some modeling exercises by not varying everything at the same time. Let's also make our frequency of interest 7.05 MHz.</p>
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<p>We shall start with the arrangement shown in Figure 1. Here we have a vertical monopole atop perfect ground. We shall use a top hat consisting of 4 spokes, and then shorten the antenna 10% at a time and see what length the spokes must be to reresonate the antenna. Gain and feedpoint impedance figures are included to see what shortening the element does to them.</p>
<pre>
Length (%) Length (ft) Radial Gain (dBi) Feedpoint Z
Length (ft) (R +/- jX ohms)
100% 33.25 --- 5.14 35.97 - 0.63
90% 29.925 2.060 5.13 35.19 + 0.70
80% 26.6 3.800 5.08 32.76 - 0.66
70% 23.275 5.570 5.02 29.08 - 0.71
60% 19.95 7.600 4.96 24.34 + 0.13
50% 16.625 9.900 4.88 18.81 - 0.66
40% 13.3 12.700 4.80 13.07 + 0.19
30% 9.975 16.100 4.71 7.83 - 0.42
20% 6.65 20.700 4.59 3.67 - 0.62
10% 3.325 27.100 4.29 1.00 - 0.42
</pre>
<p>Although the shortening progresses linearly, the rate of decrease in gain and feedpoint impedance increases more rapidly past the 70% mark. Historically, commercial antenna engineers have used 2/3 full size as a bench mark for minimum efficient antenna operation. However, the gain over a perfect ground decreases by less than a full dB down to the 10% mark, making very short amateur antennas feasible, if the feedpoint impedance can be overcome.</p>
<p>The use of hats is not restricted to vertical monopoles. We may employ them on dipoles with equal results. NEC programs model vertical monopoles over perfect ground by the use of the antenna image, essentially a copy of the antenna below the ground level. If we move each of these resonant antennas along with its image into free space, we obtain a resonant dipole whose feedpoint impedance is simple twice the figure for the monopole. Gain reductions will parallel those for the vertical monopole (although starting in the vicinity of about 2.13 dBi in free space for the dipole). In the end, a short dipole with a hat on either end will still have very usable gain. A 2-element Yagi with hatted elements about 70% full-size will rival its full-size cousin in both gain and front-to-back ratio, although the feedpoint impedance will be lower. Indeed, the failure of the hatted 2-element Yagi to achieve the kinds of front-to-back ratio that are achieved by linear and coil loaded Yagis is further evidence of the difference between the two routes to shorter elements.</p>
<p>Hat spoke length decreases as we add more radials to the structure. If we double to number of radials to 8 with the same main antenna, here is what we get.</p>
<pre>Length (%) Length (ft) Radial Gain (dBi) Feedpoint Z
Length (ft) (R +/- jX ohms)
100% 33.25 --- 5.14 35.97 - 0.63
90% 29.925 1.505 5.13 35.18 - 0.06
80% 26.6 2.730 5.08 32.84 - 0.40
70% 23.275 4.000 5.03 29.27 + 0.23
60% 19.95 5.400 4.97 24.49 + 0.73
50% 16.625 7.000 4.90 18.87 - 0.02
40% 13.3 9.000 4.83 13.10 - 0.45
30% 9.975 11.650 4.77 7.81 - 0.61
20% 6.65 15.500 4.69 3.62 - 0.03
10% 3.325 22.000 4.52 0.95 - 0.20</pre>
<p>There are several things to notice about this table. First, radial lengths range from about 75% to 80% of those required for a 4-radial hat. Second, there is no significant change in gain between the two hat sizes until the antenna length is less than 70% full-size. At shorter lengths, hats with more radials yield slightly higher gains, but that advantage quickly diminishes to the level of the unnoticeable. Third, the feedpoint impedance does not change as the number of radials in a hat increase; it is a function of the main antenna element length.</p>
<p>We can plot the decrease in radial length with the increasing number of radials more readily by spot checking antenna. The following three tables use antenna elements of 90, 70, and 50 percent full size (2" diameter aluminum) with 0.25" hat radials that double with each step.</p>
<pre>Length Number Radial Gain (dBi) Feedpoint Z
(% and ft) of Radials Length (ft) (R +/- jX ohms)
90% 29.925 4 2.060 5.13 35.18 - 0.06
8 1.505 5.13 35.18 - 0.06
16 1.235 5.13 35.21 + 0.10
32 1.090 5.13 35.19 - 0.19
64 1.022 5.13 35.19 - 0.07
Length Number Radial Gain (dBi) Feedpoint Z
(% and ft) of Radials Length (ft) (R +/- jX ohms)
70% 23.275 4 5.620 5.02 29.24 + 0.57
8 4.000 5.03 29.35 + 0.82
16 3.150 5.03 29.35 + 0.48
32 2.720 5.03 29.32 + 0.12
64 2.500 5.03 29.25 - 0.52
Length Number Radial Gain (dBi) Feedpoint Z
(% and ft) of Radials Length (ft) (R +/- jX ohms)
50% 16.625 4 9.900 4.88 18.81 + 0.66
8 6.950 4.90 18.86 - 0.31
16 5.450 4.91 18.98 + 0.66
32 4.650 4.91 18.99 + 0.29
64 4.250 4.91 19.00 + 0.12</pre>
<p>I would have carried the exercise out to 128 radials, except for three factors. First, even with the shortest antenna element, the gain and feedpoint impedance values had stabilized well before the 64-radial mark. Second, a well-converged model for the 50% full size 64-radial antenna had already exceeded 1,000 segments. And third (the reason I did not have to run the big model more than once), the radial lengths for larger arrays are completely predictable.</p>
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<p>Figure 2 is a graph of the values charted above. If you examine the data by taking the decrease in length for each doubling of the number of radials, you will discover that for each doubling, the length decrease halves. The 50% model with 128 radials will therefore have radials just about 4.05' long. (Moreover, we already know the antenna gain and feedpoint impedance.) The exact increment to be halved with each step will, of course, vary as we change the diameters of the main element and of the radials.</p>
<p>There is a second popular way to construct top hats. Instead of using radials alone, we may use radials and connect them together with a perimeter wire. Figure 3 illustrates the difference. With a perimeter wire, the required length of the radials decreases significantly. In the table below are figures for a 4-radial assembly with a perimeter wire. Compare the radial lengths with those required by the radial-only structure.</p>
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<pre>Length (%) Length (ft) Radial Gain (dBi) Feedpoint Z
Length (ft) (R +/- jX ohms)
100% 33.25 --- 5.14 35.97 - 0.63
90% 29.925 1.320 5.13 35.17 - 0.11
80% 26.6 2.380 5.05 33.02 + 0.62
70% 23.275 3.400 5.03 29.29 + 0.19
60% 19.95 4.500 4.96 24.38 - 0.91
50% 16.625 5.800 4.90 18.89 - 0.15
40% 13.3 7.350 4.83 13.15 + 0.28
30% 9.975 9.200 4.76 7.83 + 0.05
20% 6.65 11.400 4.68 3.62 - 0.94
10% 3.325 14.400 4.45 0.96 + 0.43</pre>
<p>Compared to the spoke-only version of the 4-radial top hat, the radial + perimeter model creates no changes in feedpoint impedance. The slightly elevated gains of the perimeter model suggest that adding the outer wire allows the hat to perform with an equivalence to a hat with twice the number of radials. Finally, required spoke length of the hat decreases more rapidly as the antenna is shortened. The degree of shortening decreases as the basic number of radials is increased, but never diminishes to zero.</p>
<p>The use of a perimeter wire permits more compact hat structures than are possible with the open radial structure. However, no weight savings are gathered this way. In very approximate terms, the current path for a perimeter model is equal to the length of the radial plus one-half the length of the perimeter segment to the next radial. Hence, one will use more wire in the perimeter version, but will be able to place it more securely closer to the main element.</p>
<p>Understanding the behavior of top hats is important in itself, since hatted vertical monopoles are growing more common as hams use ingenuity in finding ways to support such structures and as they learn of the reduced losses and wider operating bandwidth possible with such antennas in comparison to base-loaded verticals. Moreover, since we have finally learned that hats are simply antenna current pathways and not capacitor plates, we may be in a position to use them wisely in dipole assemblies (both vertical and horizontal).</p>
<p>However, for our purposes, a short study of hats is a preliminary to inverting them to form planes--which we are ready to do, if you will join me in free space.<br>
<br></p>
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<p><i>Updated 5-20-97. &COPY; 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.</i></p>
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<title>NEC-2 and NEC-4: Reading Trends with Caution 7 MHz Vertical + Ground Plane</title>
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<h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">NEC-2 and NEC-4: Reading Trends with Caution<br>
A Case Study with a 7 MHz Vertical + Ground Plane</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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<br>
When doing some systematic modeling, it is often useful to read trends in values, even if the actual differences would make no operational difference for a given antenna design. However, one must use great care when interpreting results as a trend: the progression of differences may not in fact represent a trend of antenna performance so much as a trend in the manner in which the modeling program calculates various values.
<p>A case in point came to light while doing some work with NEC-2 on some simple 1/4 wl vertical monopoles with ground planes of various sizes--both as free space models and as highly elevated antennas. The test frequency was 7.05 MHz, and all antenna elements were specified as aluminum (6061- T6). The 1/4 wl vertical section remained constant: 10.1346 m long with a diameter of 50 mm. The test radials systems included 4, 8, 16, and 32 radials, all of 6.35 mm diameter. 32 radials is at the limit of wires to a single junction recommended for NEC-2.</p>
<p>As an interesting side note, the length of the radials, when uniformly adjusted to achieve resonance without changing the length of the vertical element, underwent changes as the table below shows.</p>
<pre>Number of Radials Length of Radials in meters
4 11.796
8 12.314
16 12.588
32 12.863</pre>
<p>Both NEC-2 and NEC-4 showed resonance (within the limits of +/- j 1 Ohm) with these lengths both in free space models and with models whose base was 40 m high (with a vertical top height of 50.1346 m). In this regard, the two programs are well-calibrated to each other.</p>
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<p><b>Figure 1</b> shows one version of the model used, this one with 16 radials. Since the object of the exercise was not extreme precision relative to an actual antenna, simplified modeling procedures were used. Each element has 10 segments (resulting in a 330-segment model with 32 radials). The source is placed on the lowest segment of the vertical element. (Somewhat greater accuracy might be obtained by length tapering all wires toward the junction, although it is advisable to create a separate wire for the source and length taper the vertical wire above it so that the source segment and all adjacent segments are as close to the same length as feasible.)</p>
<p>For the examination of trends, the simple model sufficed. It had been run in two implementations of NEC-4 (EZNEC Pro from W7EL and GNEC from Nittany Scientific) with no differences of either gain or source impedance that amounted to anything more than rounding conventions unique to each implementation. The maximum difference in reported source resistance was 0.02 Ohms, and the maximum reported difference in source reactance was 0.03 Ohms (with this last difference occurring only once). Gain figures coincided exactly to 2 decimal places, and TO values were exact to 2 significant figures, the limits checked.</p>
<p>NEC-2 is another matter. The NEC-2 core has been around for many years and has been updated and customized by those offering full implementations. The are 16-bit and 32-bit versions as well. The same models were run on the version of NEC-2 included with EZNEC Pro and with the 32-bit version provided with NECWin Pro. As one might expect, output data from NEC-2 does not replicate that from NEC-4. However, for a given model and situation, all source values among the 2 versions of NEC-2 and the NEC-4 versions were within 0.3 Ohms resistance and 0.5 Ohms reactance. Gain values were within 0.07 dB.</p>
<p>These differences are all operationally insignificant. However, the object of the test was to study the trends in values, especially gain, for the increasing number of radials in the models, both in free space and 1 wl over various types of ground. The types of ground used were those classified as "very good" (cond.=0.0303 S/m; D.C=20), average (cond.=0.005 S/m; D.C=13), and very poor (cond.=0.001 S/m; D.C=5).</p>
<p>The charts below compare the gain output for both versions of NEC-2 (NWP=NECWin Pro; EZ-2=EZNEC Pro) with the gain output for NEC-4 (the same in both implementations).</p>
<p>Also see the <a href="../model/nec.html">Antenna Modeling Programs</a> page for more information.</p>
<h4>1. Free space values</h4>
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<p>Note that, in <b>Figure 2</b>, the NEC-4 decrease in gain is nearly linear for a geometric increase in the number of radials. The curves for NEC-2 for each program show the same trends and are nearly parallel to the NEC-4 curve. These are the curves which might set up some anticipations of values in other contexts for all NEC programs.</p>
<h4>2. Very good ground values</h4>
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<p>The NEC-4 curve in <b>Figure 3</b> shows the same type of decreasing gain pattern as it did in free space. However, the EZNEC-2 values are flat--or nearly so, since the hump in the curve represent a gain change of 0.01 dB, which might be an artifact of rounding. The NWP curve, however, shows a distinct and almost linear increase in value, although the values themselves are closer to those yielded by NEC-4. (Elevation angle of maximum radiation is 24 degrees. for all curves.)</p>
<h4>3. Average soil values</h4>
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<p>Although the NEC-4 curve in <b>Figure 4</b> is not visually linear, the degree off linear is only 0.01 dB, again, possibly due to rounding. The NWP curve is again closer in value to the NEC-4 curve, but it ascends. The EZNEC-2 figures are flat within a 0.01 dB range. The elevation angle of maximum radiation moved from 26 degrees to 25 degrees as the number of radials increased.</p>
<h4>4. Very poor soil values</h4>
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<p>The curves in Figure 5 all show descending tendencies, with the NEC-4 curve being the most linear. The elevation angle of maximum radiation was 11 degrees for all cases. (Those who insist that good soil is a necessity in the territory of a highly elevated vertical monopoles should study the effects of soil more thoroughly. Although the gain values for average soil and for very poor soil are quite close, with the 1 wl base height of the antenna, the very poor soil allows the gain to appear in the lowest lobe, while with average soil, the highest gain appears in the next lobe upward.)</p>
<p>If one asks the question, "What are the trends in values as we add more radials to a free space or highly elevated ground plane antenna system model?" no single answer emerges that is wholly reliable. The NEC-2 curves show sufficient variation from one implementation to another and from one soil type to another, that it would be untenable to insist upon any trend from the data. What one implementation gives, the other takes away, whether in terms of curve shape or coincidence of values with NEC-4.</p>
<p>Even the NEC-4 curves must be treated with caution. The curves are internally consistent from one case to the next, which increases the confidence that they exhibit a general trend. However, nothing in the models identifies the trend as being either an accurate reflection of reality or simply a calculational trend of the computational core.</p>
<p>Since this exercise was performed without access to the codings of either the core or the specific implementations of the input and output systems used, one is left without means of settling the disjunction. This situation is the one most common to users of NEC-2 and NEC-4. Hence, reading trends from small variations in program outputs must be done with extreme caution, whether those variations are regular or irregular.</p>
<p>It is easy to read too much into visually apparent numerical differences below the level of operational significance. Hopefully this exercise may provide a sufficient cautionary note in the opposite direction. If the question of whether or not a trend is simply an artifact of the computational system cannot be settled, the claim of a trend may be dubious at best. Moreover, it pays to cross check one implementation of a computational system with another before before deciding that one has a trend in the first place.<br></p>
<p>For reference, here are descriptions of 2 of the models used, given in EZNEC form for compactness.</p>
<pre>1/4 wl w/GP: 7.05 MHz 09-12-1998 06:34:16
Frequency = 7.05 MHz.
Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
--------------- WIRES ---------------
Wire Conn. --- End 1 (x,y,z : m ) Conn. --- End 2 (x,y,z : m ) Dia(mm) Segs
1 0.000, 0.000, 10.135 W2E1 0.000, 0.000, 0.000 5.00E+01 10
2 W3E1 0.000, 0.000, 0.000 11.796, 0.000, 0.000 6.35E+00 10
3 W4E1 0.000, 0.000, 0.000 0.000, 11.796, 0.000 6.35E+00 10
4 W5E1 0.000, 0.000, 0.000 -11.796, 0.000, 0.000 6.35E+00 10
5 W1E2 0.000, 0.000, 0.000 0.000,-11.796, 0.000 6.35E+00 10
-------------- SOURCES --------------
Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type
Seg. Actual (Specified)
1 10 1 / 95.00 ( 1 /100.00) 1.000 0.000 V
Ground type is Free Space</pre><br>
<br>
<pre>1/4 wl w/GP: 7.05 MHz 09-12-1998 06:35:05
Frequency = 7.05 MHz.
Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
--------------- WIRES ---------------
Wire Conn. --- End 1 (x,y,z : m ) Conn. --- End 2 (x,y,z : m ) Dia(mm) Segs
1 0.000, 0.000, 50.135 W2E1 0.000, 0.000, 40.000 5.00E+01 10
2 W3E1 0.000, 0.000, 40.000 12.588, 0.000, 40.000 6.35E+00 10
3 W4E1 0.000, 0.000, 40.000 11.630, 4.817, 40.000 6.35E+00 10
4 W5E1 0.000, 0.000, 40.000 8.901, 8.901, 40.000 6.35E+00 10
5 W6E1 0.000, 0.000, 40.000 4.817, 11.630, 40.000 6.35E+00 10
6 W7E1 0.000, 0.000, 40.000 0.000, 12.588, 40.000 6.35E+00 10
7 W8E1 0.000, 0.000, 40.000 -4.817, 11.630, 40.000 6.35E+00 10
8 W9E1 0.000, 0.000, 40.000 -8.901, 8.901, 40.000 6.35E+00 10
9 W10E1 0.000, 0.000, 40.000 -11.630, 4.817, 40.000 6.35E+00 10
10 W11E1 0.000, 0.000, 40.000 -12.588, 0.000, 40.000 6.35E+00 10
11 W12E1 0.000, 0.000, 40.000 -11.630, -4.817, 40.000 6.35E+00 10
12 W13E1 0.000, 0.000, 40.000 -8.901, -8.901, 40.000 6.35E+00 10
13 W14E1 0.000, 0.000, 40.000 -4.817,-11.630, 40.000 6.35E+00 10
14 W15E1 0.000, 0.000, 40.000 0.000,-12.588, 40.000 6.35E+00 10
15 W16E1 0.000, 0.000, 40.000 4.817,-11.630, 40.000 6.35E+00 10
16 W17E1 0.000, 0.000, 40.000 8.901, -8.901, 40.000 6.35E+00 10
17 W1E2 0.000, 0.000, 40.000 11.630, -4.817, 40.000 6.35E+00 10
-------------- SOURCES --------------
Source Wire Wire #/Pct From End 1 Ampl.(V, A) Phase(Deg.) Type
Seg. Actual (Specified)
1 10 1 / 95.00 ( 1 /100.00) 1.000 0.000 V
Ground type is Real, high-accuracy analysis
Conductivity = .005 S/m Diel. Const. = 13
--------------- MEDIA ---------------
Medium Conductivity(S/m) Dielectric Const. Ht(m ) R Coord(m )
1 5.000E-03 13.00 0 (def) 0 (def)</pre><br>
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<p><i>Updated 9-12-98. &COPY; 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.</i><br>
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<title>Modeling Perspective on Ground Planes Part 3: Planes in Space</title>
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<h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Part 3:<br>
Planes in Space</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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We are very comfortable modeling dipoles in free space. We use such models as the starting point for many a disquisition on dipole properties. So let us begin our journey just here.
<p>We should note that in free space, we may model a dipole along any of the three Cartesian coordinates (or even traversing them at an angle). Free space has nothing in any direction and in every direction. Wherever the dipole broadside is, off that broadside will be maximum gain.</p>
<p>This reminder of free space properties is to remove any initial anxiety about modeling our dipole along the Z axis--which would be height, if we had a ground below. Since we are interested in vertical antennas relative to ground, this strategy will be handy for modeling over ground.</p>
<p>Let's not be too hasty in getting close to the ground. For present purposes, we shall stay 2 wavelengths above ground. At this height and above, antennas show virtually the same feedpoint impedance they show in free space, and some basic gain comparisons will be instructive as we move from full size dipoles toward monopoles with planes.</p>
<p>We shall retain our 2" diameter aluminum main element. If we add a plane or a hat, it will be composed of 0.25" aluminum radials. This procedure will preserve consistency throughout the exercise. Moreover, we shall continue to list gain and feedpoint values to 2 decimal places. Although this level of reporting the modeling program output has little if any practical antenna building significance, it occasionally reveals some numerical trends that might be obscured by rounding the numbers to a construction level.</p>
<p>Building a full size dipole in free space means nothing more than doubling the full size monopole over perfect ground. NEC does the same thing for us with the monopole as it constructs an image during calculations. The only difference shows up in the feedpoint impedance: values will be twice those reported for the monopole. Let's compare the monopole and the dipole. Gain figures list the monopole over perfect ground and the dipole in free space. They are not significant here, but will become so later.</p>
<pre>Antenna Length Feed Z Gain
(ft) (R +/- jX ohms) (dBi)
Monopole 33.25 35.97 - 0.06 5.14
Dipole 66.50 71.92 - 0.27 2.13</pre>
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<p>As shown in Figure 1, we may place hats at the ends of a dipole in a manner identical to placing one at the top of a vertical monopole. Moreover, we may construct a hatted dipole in the same way we constructed the dipole: simply by joining two monopoles with hats in the center and keeping the main elements in a line. Once more, we may expect the dipole feedpoint impedance to be twice that of the monopole. "Gain loss" is referenced to the gain of the corresponding full size antenna above. The hats on each end of dipoles consist of 4 wires of the same lengths used for the monopoles: 70%: 5.57' each; 50%: 9.90' each; and 20%: 20.7' each.</p>
<pre>Antenna Length Feed Z Gain Gain loss
(ft) (R +/- jX ohms) (dBi) (dB)
70% Full-size
Monopole 23.275 29.08 - 0.71 5.02 -0.12
Dipole 46.550 58.15 - 1.50 2.01 -0.12
50% Full-size
Monopole 16.625 18.81 + 0.66 4.88 -0.26
Dipole 33.250 37.63 + 1.39 1.87 -0.26
20% Full-size
Monopole 6.650 3.67 - 0.61 4.59 -0.55
Dipole 13.300 7.34 - 1.41 1.58 -0.55</pre>
<p>The relatively precise feedpoint impedance doubling is obvious. Now here is where the gain figures acquire some importance. The differences in gain of each shortened monopole relative to the full size monopole are exactly reflected in the differences in gain of each shortened dipole relative to the full size dipole. A hatted dipole (or monopole) 20% of full size, relative to a full size dipole, loses only 0.55 dB of gain--or about 1/10 of an S-unit as such measures are loosely reckoned.</p>
<p>Similar results accrue over ground. Since we are limiting ourselves to approaching only 2 wavelengths from ground, let's set the feedpoints of the vertical dipoles at 280' up and see what happens.</p>
<pre>
Antenna Length Feed Z Gain Gain loss
(ft) (R +/- jX ohms) (dBi) (dB)
Full-size
Dipole 66.50 71.83 - 0.79 4.44
70% Full-size
Dipole 46.550 58.02 - 1.43 4.34 -0.10
50% Full-size
Dipole 33.250 37.53 + 1.45 4.21 -0.23
20% Full-size
Dipole 13.300 7.32 - 1.13 3.94 -0.50
</pre>
<p>Again, the dipole only 20% of full size loses only a half dB relative to a full size dipole, as do equivalently shrunken monopoles. If we can handle the low feedpoint impedances involved, these antennas can be useful.</p>
<p>The shortest of the hatted antennas has hat radials far longer than the main element itself. However, the radiation from these hats fully cancels so that all radiation in the far field pattern is vertically polarized. Moreover, the hats do not interact, as evidenced by the fact that the shortest dipole reflects the same feedpoint impedance doubling and gain reduction amount as the monopole over perfect ground. Each hat is the antenna current completion path for each of the monopoles forming the dipole.</p>
<p>The symmetrical hat at right angles to the main element does not radiate. However, if the radials of the hat are angled, significant radiation does occur. In general, if the antenna is vertical, and we construct a so- called sloping ground plane of wires, horizontally polarized radiation from the plane wires does cancel while vertically polarized radiation adds to the radiation of the antenna. In essence, as we split one monopole into 4 wires, leaving the other as a single element, we can bend the wires through the arc of 90 degrees and end up with a monopole and plane, as shown in Figure 2</p>
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<p>Modeling this progression requires a caution: The wires resulting from splitting the main element yield a fatter wire than the former end of the one-wire dipole. This fatter 4-part wire carries slightly higher currents closer to the feedpoint, which raises the overall gain of the antenna in a near-dipole configuration. This shows up as a shorter length for the 4- part wire than for the 1-wire upper end. With this in mind, we can construct some models of the transition using angles of 5, 45, and 90 degrees, in order to look at both the gain and the pattern of the antenna. In all case, the upper end is 33.25' of 2" aluminum, while the lower part is 4 0.25" wires of the length given in the table.</p>
<pre>
Antenna Radial Length Feedpoint Z Gain
(feet) (R +/- jX ohms) (dBi)
Simulated dipole: 5-deg from vertical
Free space 27.5 57.27 - 0.79 2.58
2 wl up 57.16 - 0.71 4.91/7 deg
Sloping plane: 45-deg from vertical
Free space 29.5 48.33 + 0.51 2.08
2 wl up 48.26 + 0.62 4.47/7 deg
"Ground" plane: 90-deg from vertical
Free space 38.7 21.38 - 0.66 1.32
2 wl up 21.42 - 0.59 3.85/6 deg
</pre>
<p>We can look at the gain figures in two ways. First, we can view the sloping plane antenna as reduced in gain by about 0.5 dB from a true vertical dipole of similar materials. Second, we can view the sloping plane antenna as providing about 2/3 dB gain over a similarly situated monopole with a level plane. Although the gain may not be much, it is real. However, we often throw it away by being careless with the placement of sloping radials or by not attending to the matter of resonating the entire antenna, including the sloping radials. We shall discuss the importance of resonance in a later episode. By way of preview, the importance lies not in any special property of resonance itself, but instead by what it indicates with respect to the high current position on the entire antenna, where antenna includes both the main element and the radials.</p>
<p>In free space, we cannot accurately model only half the antenna. The model consists of both the main element and the radials, whether those radials are pointed straight down, sloped at an angle, or placed at right angles to the main element to form a plane. Adding the term "ground" to the expression "plane" adds nothing to the model. With respect to free space modeling, the plane is simply the other half of the dipole so constructed as not to add to the overall radiation. In fact the plane does not even bend or distort the free space radiation pattern of the antenna in any way, as the elevation pattern in Figure 3 indicates. The plane acts just like a hat--or a hat acts just like a plane. In free space, the only distinction seems to be this: we use the term "hat" when the structure replaces some of the main element length, and we use the term "plane" when the structure replaces all or virtually all of the main element length, where "length" is referred to each monopole making up a dipole. electrically, there is no difference: hat and plane differences are functions of the variables we discussed in the last episode: main element diameter, main element length, radial diameter, and number of radials.</p>
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<p>Moreover, as indicated in Figure 4, there is no rule that prevents the construction of asymmetrical hatted/planed antennas. Indeed, many short verticals for the lowest HF bands are precisely such constructions: hatted, planed vertical antennas.</p>
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<p>Before we return to earth to muddy up the situation a bit, let's look at a problem attached to modeling dipoles that consist of one linear monopole and a plane. NEC has a limitation in that it will not permit placement of a split feedpoint at a multiple wire junction. The standard view of a vertical antenna and its plane seems to require precisely this move. One temptation is to move the feedpoint to the wire segment immediately adjacent to the junction with the radials. This can lead to problematical results, as shown in the next table. All main elements are 33.25' long.</p>
<pre>Antenna Radial length Gain Feedpoint Z
(feet) (dBi) (R +/- jX ohms)
4-radials
Free space 38.7 1.32 21.38 - 0.66
2 wl up 3.85/6 deg 21.42 - 0.59
8-radials
Free space 40.4 1.24 21.90 - 0.22
2 wl up 3.79/6 deg 21.95 - 0.30
16-radials
Free space 41.3 1.18 22.30 - 0.50
2 wl up 3.74/6 deg 22.36 - 0.43
32-radials
Free space 42.2 1.11 22.73 - 0.26
2 wl up 3.69/6 deg 22.80 - 0.19</pre>
<p>The descending gain and increasing feedpoint impedance indicate that the antenna is being feed increasingly off center. With a dipole whose halves are identical, the physical center is also the electrical center. With an antenna whose two halves are of different construction, the electrical center may well be elsewhere. The electrical center of the antenna (dipole) is the point of highest current. As we add more radials, we increase the working diameter of the monopole we call the plane. The point of highest current moves further out away from the junction, calling for more wire on the other side of the electrical center, namely, in the radials, to return the system to resonance.</p>
<p>Moving the region of highest current further into the plane moves it also into the region of cancelled radiation. Although the loss may not be very large, it is definite, as the progressively lower gains of the models demonstrates.</p>
<p>To overcome this modeling problem and permit the exercise to continue, I have adopted a convention for further models of planes. To the base of the upper 33.35' main element, I have added a single wire 1' long. The plane radials join at the base of this section. The feedpoint is a split feed at the junction of the in-line wires. The procedure does not end the slight movement of the electrical center of the antenna toward the radials, but it effectively limits the movement to within the 1' wire. The sum of currents on the radials never exceeds the current on the added wire.</p>
<p>In addition, the revised model reflects at least one of the more common construction practices on the lower HF bands. Many builders join their radials in a single "wad" that rises out of the ground to meet a slightly elevated upper main element. Whatever the practice, a table of models built along the revised pattern yields the following data.</p>
<pre>
Antenna Radial length Gain Feedpoint Z
(feet) (dBi) (R +/- jX ohms)
4-radials
Free space 35.6 1.38 22.88 - 0.18
2 wl up 3.88/6 deg 22.91 - 0.22
8-radials
Free space 34.5 1.34 23.03 - 0.06
2 wl up 3.85/6 deg 23.06 - 0.02
16-radials
Free space 32.5 1.38 22.81 + 0.06
2 wl up 3.88/6 deg 22.82 + 0.13
32-radials
Free space 30.0 1.45 22.39 - 0.37
2 wl up 3.94/6 deg 22.42 - 0.31
</pre>
<p>The gain of the models has largely stabilized, as has the feedpoint impedance. Radial lengths decrease as the number of radials increases. Although the models do not precisely locate the electrical centers of each antenna, they are perhaps accurate enough for us to bring the vertical antenna with a plane down to earth. Two wavelengths is a long way, and we shall want to pay attention to our landing patterns.<br>
<br></p>
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<p><i>Updated 5-20-97. &COPY; 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.</i></p>
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<title>Modeling Perspective on Ground Planes Part 4: Down to Earth Verticals</title>
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<h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Part 4:<br>
Down to Earth Verticals</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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Most accounts of elevated ground planes begin with wires under the ground and proceed to elevate them. Since we started in free space and skimmed the atmosphere at a height of 2 wavelengths, let's continue our top-down progression. In figures and tables, and with a minimum of words, we can find some very interesting phenomena.
<p>For example: many hams are familiar with the elevation patterns of horizontal antenna and can speak with assurance of take-off angles, secondary lobes, etc. But few are familiar with the patterns created by elevated vertical antennas. Therefore, as a small compendium, here are a few patterns taken with a model of an 8-radial 1/4 wl vertical. All patterns are over medium earth. Exact gain numbers are omitted (they will appear in tables later) because it is pattern shape that is our focal interest.</p>
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<p>Figure 1 gives a representative high-altitude elevation pattern--280' on 40 meters. Patterns for antennas above and somewhat below this height are similar.</p>
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<p>At 1 wavelength up, in Figure 2, the vertical begins to show the domination of a higher angle lobe. This pattern appears from grounds as good as salt water to poor earth.</p>
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<p>In Figure 3, at a half wavelength up, high angle radiation dominates, although over salt water, there is a strong lower lobe.</p>
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<p>As is evident if Figure 4, when the base of the plane reaches about 0.25 wl, the lower lobe again dominates, although high angle radiation is readily apparent. A similar pattern appears as self-contained vertical 1 wl wire antennas are raised "too high."</p>
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<p>At about 0.15 wl between the ground and the base of the plane, as shown if figure 5, secondary lobes are virtually absent, with radiation concentrated in a single main lobe whose angle increases as soil conditions worsen.</p>
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<p>Below 0.1 wl, the pattern simply grows more bulbous, with lower gain and a higher elevation angle of maximum radiation. This pattern holds good as the plane is brought to ground and even below ground.</p>
<p>The patterns are typical of any ground plane antenna. A vertical dipole, however, presents some interesting variations--or perhaps compressions may be a better description. The vertical dipole has a widely separate feedpoint and element end. For feedpoint heights down to about 0.5 wl, the corresponding figures apply. Pattern changes compress below about 3.8 wl feedpoint height. At this height, the element end is about 20' off the ground at 40 meters, and the pattern resembles that if Figure 4 (ground plane at 0.25 wl). With the antenna end only 5' off the ground and the feed point nearly 40' up, the pattern is like Figure 4-5. Lowering the antenna just another 3' yields a pattern similar to Figure 4-6. Without bends or end hats, the true vertical dipole is just about at its lower limit.</p>
<p>We have already seen that the natural free space feedpoint impedance in ohms) of a quarter wavelength vertical with a plane is in the lower 20s, a value that also holds good at a 2-wl height. This feedpoint impedance value is at odds with experience when verticals are placed on or just above the ground. Additionally, ground and near-ground verticals do not exhibit the gain shown by the models at 2 wl up.</p>
<p>How do we account for the discrepancy? To see the answer to this, we need to look at models of ground plane verticals gradually lowered from their lofty heights to the earth. Fortunately, NEC-4 makes it possible not only to bring the plane close to earth, but--with the Sommerfeld-Norton ground system--to take the plane below ground.</p>
<p>It is important in looking at various planed-vertical models to seek out both differential and parallel alterations of fields and of feedpoint impedances as the models are lowered. Therefore, I have run several models through successive steps over four kinds of earth: perfect (which does not permit penetration), salt water with a conductivity of 5 S/m and a dielectric constant of 81 (for which height values within about 0.2' above the surface return faulty results, but for which sub-surface values of height are functional), very good earth with a conductivity of 0.0303 and a dielectric constant of 20, and medium/average earth with a conductivity of 0.005 and a dielectric constant of 13.</p>
<p>The tables list for each level both feedpoint impedance and elevation pattern values (maximum gain and take-off angle for that gain). It is important to remember that these are separate data. Feedpoint impedance is a function of the earth conditions just below the antenna and in its most immediate vicinity. Far field data are functions of earth conditions beginning at some distance (something at least over a wavelength, if not farther) from the antenna. If the conditions under the antenna have been improved, then the feedpoint impedance of "very good ground" might apply, but the far field might still be no better than that shown for "medium" earth. Conversely, island operations might show "medium" earth impedances while giving salt water far field results.</p>
<p>Table heights are listed in feet, and are given for the feedpoint. The tables must be read with two understandings. First, a wavelength at the target frequency of 7.05 MHz is about 140' long, so that the table begin at 2 wl, with check point at 1.5, 1.0, 0.5, 0.375, 0.25, 0.15 wl and lower. Second, in accord with the model construction technique described in the last episode, the plane will be 1' below the feedpoint. At upper heights, this difference makes no difference, but becomes increasingly important at the lowest heights, e.g., 20 10, 5, 1.5, 1.2, 1.1, and 0 feet up. There are two zero feet feedpoint values, one with a modified model for plane wires buried 0.5' down; the other unmodified with plane wires 1.0' below the surface. The modified model appears not to have introduced unreasonable numbers for the plane 0.5' below surface.</p>
<p>Commentary on the tables will appear afterwards.</p>
<pre>Vertical Dipole (for reference): 2" dia. al. element, 66.5' long
Free space: Gain: 2.13 dBi; Feed Z: 71.98 - 0.85 ohms
Perfect Earth Salt Water
Height Feed Z Gain/TO angle Feed Z Gain/TO angle
(feet) (R +/- jX) (dBi/degrees) (R +/- jX) (dBi/degrees)
280-2wl 71.75 - 0.82 8.16 / -- 71.75 - 0.82 7.54 / 14
210-1.5 71.56 - 0.81 8.17 / -- 71.57 - 0.81 7.31 / 19
140-1wl 71.02 - 0.81 8.21 / -- 71.03 - 0.80 6.45 / 28
70-0.5 67.82 - 1.10 8.40 / -- 67.85 - 1.07 7.22 / 5
52.5 73.02 - 8.99 8.05 / -- 72.97 - 8.95 7.06 / 5
43.25 83.92 - 8.03 7.46 / -- 83.81 - 8.06 6.59 / 6
38.25 93.00 - 1.17 7.07 / -- 92.90 - 1.28 6.25 / 6
35-.25 101.3 + 11.0 6.80 / -- 101.8 + 10.7 6.02 / 7
Very Good Earth Medium Earth
Height Feed Z Gain/TO angle Feed Z Gain/TO angle
(feet) (R +/- jX) (dBi/degrees) (R +/- jX) (dBi/degrees)
280-2wl 71.78 - 0.79 5.18 / 13 71.83 - 0.79 4.44 / 7
210-1.5 71.62 - 0.76 5.45 / 18 71.71 - 0.75 3.43 / 9
140-1wl 71.14 - 0.68 5.21 / 27 71.34 - 0.63 3.52 / 27
70-0.5 66.21 - 0.48 1.25 / 14 68.99 - 0.15 0.20 / 13
52.5 71.79 - 8.39 2.09 / 12 71.00 - 7.05 0.35 / 15
43.25 82.01 - 9.07 2.15 / 13 79.21 - 8.90 0.23 / 16
38.25 91.25 - 3.82 2.07 / 14 87.86 - 5.76 0.07 / 17
35-.25 101.0 + 6.95 1.98 / 15 97.89 + 3.14 0.11 / 18</pre>
<p>Notes: The pattern of feedpoint impedance does not change significantly as one changes the soil type beneath the antenna. The greatest change occurs close to the ground with the transition from very good to medium earth, and a similar change will likely be noted in the transition from medium to poor earth.</p>
<p>Variable in antenna gain and take-off angle are noticeable with changing far field earth conditions. However, most notable is the sudden decrease in gain over very good and medium earth between 1 wl and 0.5 wl heights. Low-mounted vertical dipoles with salt-water paths are capable of approximately 6 dB better performance than the same antenna with medium earth paths.</p>
<pre>1/4 wl Vertical (2" dia. al. element, 33.25' long), with 4 0.25" radials
each 35.6' long, set 1' below the feedpoint
Free space: Gain: 1.38 dBi; Feed Z: 22.88 - 0.18 ohms
Perfect Earth Salt Water
Height Feed Z Gain/TO angle Feed Z Gain/TO angle
(feet) (R +/- jX) (dBi/degrees) (R +/- jX) (dBi/degrees)
280-2wl 22.90 - 0.18 7.39 / -- 22.90 - 0.18 6.94 / 13
210-1.5 22.92 - 0.94 7.39 / -- 22.92 - 0.10 6.87 / 18
140-1wl 22.96 + 0.12 7.38 / -- 22.97 + 0.11 6.53 / 26
70-0.5 23.30 + 1.01 7.33 / -- 23.30 + 0.99 5.98 / 4
52.5 20.90 + 0.49 7.80 / -- 20.93 + 0.50 6.63 / 5
35-.25 21.14 - 3.55 7.71 / -- 21.12 - 3.49 6.75 / 6
20-.15 27.08 - 5.53 6.62 / -- 26.95 - 5.51 5.86 / 7
10 33.72 - 2.05 5.71 / -- 33.53 - 2.19 5.08 / 8
5 37.46 + 3.37 5.31 / -- 37.30 + 3.09 4.73 / 9
1.5 40.03 + 12.9 5.09 / -- 41.21 + 14.2 4.40 / 9
1.2 39.94 + 14.8 5.10 / --
1.1 39.82 + 15.4 5.12 / --
0-.5 37.23 + 1.09 4.45 / 9
0-1.0 38.31 + 1.96 4.33 / 9
Very Good Earth Medium Earth
Height Feed Z Gain/TO angle Feed Z Gain/TO angle
(feet) (R +/- jX) (dBi/degrees) (R +/- jX) (dBi/degrees)
280-2wl 22.91 - 0.20 5.07 / 27 22.91 - 0.22 3.88 / 6
210-1.5 22.94 - 0.13 4.85 / 17 22.94 - 0.17 3.21 / 36
140-1wl 23.01 + 0.05 5.09 / 25 23.01 - 0.04 3.24 / 24
70-0.5 23.42 + 0.79 3.49 / 44 23.42 + 0.51 2.33 / 44
52.5 21.26 + 0.68 1.71 / 52 21.68 + 0.66 0.73 / 52
35-.25 20.84 - 2.90 1.86 / 12 20.91 - 2.16 0.14 / 15
20-.15 25.73 - 5.69 2.02 / 15 24.49 - 5.13 0.19 / 18
10 32.40 - 3.87 1.81 / 18 30.36 - 4.48 0.02 / 22
5 37.14 + 1.01 1.64 / 19 34.82 - 0.44 -.13 / 24
1.5 43.72 + 22.6 1.24 / 21 40.64 + 21.1 -.46 / 25
1.2 45.84 + 37.3 1.04 / 20 42.94 + 35.5 -.65 / 25
1.1 49.03 + 52.1 0.75 / 21 46.61 + 49.0 -.94 / 25
0-.5 52.63 + 12.9 0.33 / 21 67.38 + 13.7 -2.6 / 26
0-1.0 54.11 + 17.4 0.21 / 21 68.62 + 18.6 -2.6 / 26</pre>
<p>Notes: There are numerous things to notice about this table set. With respect to feedpoint impedance, note the slight rise at 70' (1/2 wl), just where the vertical dipole impedance dipped. Although NEC-4 does not return sensible values for planes set at distances of 0.2' and 0.1' above the surface, the values for the plane set below ground provide an indication of the standard monopole feedpoint impedance values when the antenna is mounted without a plane but in contact with perfect earth. However, these values increase rapidly with a degradation in earth quality immediately under the antenna. Moreover, the resonance of the system is also disturbed--with a further shortening of the radials as the indicated need. Shortening the radials will also slightly lower the value of the resistive component of the feedpoint impedance. The progression of increase in feedpoint impedance begins as the antenna is lowered below the 0.25 wl point, whatever the ground type.</p>
<p>The far field pattern displays a variability in the angle of the lowest lobe, depending on the type of far field ground. In the region from 0.375 wl through 1 wl over very good and worse earth, high angle radiation dominates the pattern. Over these same earths, the gain takes a sudden nose-dive below the 0.5 wl antenna height, but progresses more smoothly down over slat water and better. At a certain height which varies with the level of earth quality, the take-off angle of low-mounted antennas reaches a minimum and then rises as the antenna is brought lower, including with the plane below the surface. The differential in gain between the value for a 2 wl height and for the lowest height modeled increases as the earth condition values decrease.</p>
<pre>1/4 wl Vertical (2" dia. al. element, 33.25' long), with 8 0.25" radials
each 34.5' long, set 1' below the feedpoint
Free space: Gain: 1.34 dBi; Feed Z: 23.03 - 0.06 ohms
Perfect Earth Salt Water
Height Feed Z Gain/TO angle Feed Z Gain/TO angle
(feet) (R +/- jX) (dBi/degrees) (R +/- jX) (dBi/degrees)
280-2wl 23.05 - 0.06 7.36 / -- 23.05 + 0.06 6.91 / 13
210-1.5 23.06 - 0.14 7.36 / -- 23.06 + 0.14 6.84 / 18
140-1wl 23.11 + 0.36 7.35 / -- 23.11 + 0.35 6.49 / 26
70-0.5 23.42 + 1.25 7.30 / -- 23.43 + 1.23 5.95 / 4
52.5 21.03 + 0.69 7.77 / -- 21.06 + 0.70 6.60 / 5
35-.25 21.34 - 3.35 7.66 / -- 21.33 - 3.30 6.71 / 6
20-.15 27.38 - 5.26 6.56 / -- 27.26 - 5.24 5.80 / 7
10 34.08 - 1.84 5.66 / -- 33.89 - 1.99 5.02 / 8
5 37.81 + 2.76 5.26 / -- 37.59 + 2.40 4.69 / 9
1.5 40.45 + 9.97 5.04 / -- 40.38 + 9.71 4.48 / 9
1.2 40.25 + 11.8 5.07 / --
1.1 39.95 + 13.1 5.10 / --
0-.5 37.23 + 1.09 4.45 / 9
0-1.0 38.32 + 1.95 4.33 / 9
Very Good Earth Medium Earth
Height Feed Z Gain/TO angle Feed Z Gain/TO angle
(feet) (R +/- jX) (dBi/degrees) (R +/- jX) (dBi/degrees)
280-2wl 23.06 + 0.04 5.04 / 27 23.06 + 0.02 3.85 / 6
210-1.5 23.08 + 0.11 4.82 / 17 23.08 + 0.07 3.17 / 36
140-1wl 23.15 + 0.29 5.06 / 25 23.15 + 0.21 3.21 / 24
70-0.5 23.55 + 1.03 3.44 / 45 23.56 + 0.76 2.27 / 44
52.5 21.39 + 0.89 1.63 / 52 21.81 + 0.88 0.65 / 52
35-.25 21.02 - 2.71 1.82 / 12 21.08 - 1.96 0.11 / 15
20-.15 26.03 - 5.47 1.96 / 15 24.76 - 4.93 0.15 / 19
10 32.74 - 3.84 1.76 / 18 30.65 - 4.60 0.03 / 22
5 37.17 - 0.44 1.64 / 20 34.80 - 2.36 -.14 / 24
1.5 40.66 + 10.3 1.55 / 21 37.87 + 7.47 -.19 / 25
1.2 40.93 + 19.5 1.53 / 20 38.54 + 16.0 -.23 / 26
1.1 41.84 + 28.0 1.43 / 21 39.84 + 22.9 -.34 / 26
0-.5 47.37 + 11.1 0.81 / 21 54.61 + 12.6 -1.5 / 26
0-1.0 49.19 + 16.3 0.66 / 21 56.33 + 18.5 -1.6 / 26</pre>
<p>Notes: For all values over perfect earth and salt water, and for all values down to a low antenna height, the differences in numerical values between the 4-radial and 8-radial models parallel those between the respective free space models.</p>
<p>At heights below 5' (plane at 4' or less), the 8-radial model shows significant improvements. with the plane above the earth, the impedance does not rise as fast as that of the 4-radial model. The seeming anomaly of a lesser increase at low heights for the model over medium earth relative to the model over very good earth is more apparent than real. With smaller increases in reactance at those levels, the overall non-resonant condition is less radical than that of the model over very good earth. Bringing the model over very good earth back to resonance will lower the resistive component and make the values more comparable.</p>
<p>With the plane below the surface, feedpoint reactances are similar to those for the 4-radial model, but the resistive component values are significantly less.</p>
<p>With the plane below 5' (0.035 wl), the 8-radial model begins to exhibit significant improvements in gain over the 4-radial model over very good or worse earth. With the planes below the surface, the improvement is greater than 1 dB. With the planes higher than 5' above ground, gain differences are insignificant.</p>
<pre>1/4 wl Vertical (2" dia. al. element, 33.25' long), with 16 0.25" radials
each 32.5' long, set 1' below the feedpoint
Free space: Gain: 1.38 dBi; Feed Z: 22.80 + 0.06 ohms
Perfect Earth Salt Water
Height Feed Z Gain/TO angle Feed Z Gain/TO angle
(feet) (R +/- jX) (dBi/degrees) (R +/- jX) (dBi/degrees)
280-2wl 22.81 + 0.17 7.40 / -- 22.81 + 0.17 6.94 / 13
210-1.5 22.82 + 0.25 7.40 / -- 22.82 + 0.25 6.87 / 18
140-1wl 22.86 + 0.47 7.40 / -- 22.86 + 0.46 6.51 / 26
70-0.5 23.12 + 1.35 7.36 / -- 23.13 + 1.33 6.01 / 4
52.5 20.82 + 0.69 7.81 / -- 20.84 + 0.70 6.64 / 5
35-.25 21.33 - 3.28 7.66 / -- 21.31 - 3.22 6.71 / 6
20-.15 27.48 - 4.82 6.54 / -- 27.36 - 4.82 5.79 / 7
10 34.15 - 0.92 5.64 / -- 33.97 - 1.08 5.01 / 8
5 37.84 + 3.92 5.25 / -- 37.64 + 3.46 4.68 / 9
1.5 40.59 + 9.50 5.02 / -- 39.93 + 8.42 4.53 / 9
1.2 40.60 + 10.0 5.03 / --
1.1 40.23 + 11.1 5.07 / --
0-.5 37.25 + 1.08 4.45 / 9
0-1.0 38.34 + 2.49 4.33 / 9
Very Good Earth Medium Earth
Height Feed Z Gain/TO angle Feed Z Gain/TO angle
(feet) (R +/- jX) (dBi/degrees) (R +/- jX) (dBi/degrees)
280-2wl 23.82 + 0.15 5.05 / 27 22.82 + 0.13 3.88 / 6
210-1.5 22.84 + 0.22 4.86 / 17 22.84 + 0.18 3.16 / 36
140-1wl 22.90 + 0.40 5.08 / 25 22.91 + 0.32 3.24 / 24
70-0.5 23.25 + 1.14 3.40 / 45 23.27 + 0.88 2.24 / 44
52.5 21.15 + 0.90 1.53 / 52 21.56 + 0.91 0.57 / 52
35-.25 20.98 - 2.67 1.84 / 12 20.99 - 1.93 0.13 / 15
20-.15 26.16 - 5.13 1.96 / 15 24.86 - 4.70 0.14 / 19
10 32.99 - 3.04 1.75 / 18 30.96 - 4.01 -.06 / 22
5 37.52 + 0.52 1.61 / 20 35.32 - 1.73 -.20 / 24
1.5 40.61 + 5.86 1.57 / 21 38.15 + 2.87 -.24 / 25
1.2 39.38 + 9.51 1.71 / 20 37.55 + 7.21 -.15 / 26
1.1 39.17 + 15.0 1.73 / 21 38.21 + 11.3 -.21 / 26
0-.5 43.41 + 9.01 1.20 / 21 44.90 + 10.3 -.63 / 26
0-1.0 45.41 + 15.2 1.04 / 21 46.88 + 16.9 -.74 / 26</pre>
<p>Notes: Once more, most differences in numerical values parallel the differences in free space models. The most notable differences occur over very good or worse earth at antenna height below 5' (plane below 4'). Doubling the number of radials to 16 drops the very good earth impedance by about 5 ohms and the medium earth impedance by 10 ohms, the same rate of change as between 4 and 8 radials. Reactance at low levels also decreases further, except as the plane goes below the surface.</p>
<p>Above ground gain, even at very low heights, increases only marginally. However, there is nearly a 0.9 dB increase in gain for the models with the plane below the surface--a 1.9 dB increase over the 4-radial models.</p>
<pre>1/4 wl Vertical (2" dia. al. element, 33.25' long), with 32 0.25" radials
each 30.0' long, set 1' below the feedpoint
Free space: Gain: 1.45 dBi; Feed Z: 22.39 - 0.37 ohms
Perfect Earth Salt Water
Height Feed Z Gain/TO angle Feed Z Gain/TO angle
(feet) (R +/- jX) (dBi/degrees) (R +/- jX) (dBi/degrees)
280-2wl 22.40 - 0.28 7.47 / -- 22.40 - 0.28 6.99 / 13
210-1.5 22.41 - 0.21 7.47 / -- 22.41 - 0.21 6.93 / 18
140-1wl 22.43 + 0.01 7.47 / -- 22.43 + 0.01 6.55 / 26
70-0.5 22.63 + 0.88 7.44 / -- 22.64 + 0.87 6.10 / 4
52.5 20.44 + 0.11 7.87 / -- 20.47 + 0.12 6.72 / 5
35-.25 21.19 - 3.73 7.68 / -- 21.17 - 3.68 6.73 / 6
20-.15 27.41 - 4.86 6.54 / -- 27.30 - 4.87 5.79 / 7
10 34.00 - 0.42 5.66 / -- 33.84 - 0.58 5.03 / 8
5 37.63 + 4.99 5.27 / -- 37.46 + 4.62 4.70 / 9
1.5 40.39 + 11.0 5.04 / -- 39.63 + 9.68 4.56 / 9
1.2 40.60 + 11.0 5.02 / --
1.1 40.42 + 10.9 5.05 / --
0-.5 37.25 + 1.07 4.45 / 9
0-1.0 38.35 + 1.92 4.33 / 9
Very Good Earth Medium Earth
Height Feed Z Gain/TO angle Feed Z Gain/TO angle
(feet) (R +/- jX) (dBi/degrees) (R +/- jX) (dBi/degrees)
280-2wl 22.41 - 0.29 5.09 / 27 22.42 - 0.31 3.94 / 6
210-1.5 22.43 - 0.23 4.92 / 17 22.44 - 0.27 3.18 / 37
140-1wl 22.48 - 0.04 5.12 / 25 22.49 - 0.12 3.29 / 24
70-0.5 22.77 + 0.69 3.38 / 45 22.81 + 0.44 2.22 / 44
52.5 20.74 + 0.33 1.44 / 53 21.15 + 0.38 0.48 / 51
35-.25 20.81 - 3.17 1.90 / 12 20.76 - 2.45 0.17 / 15
20-.15 26.15 - 5.28 1.98 / 15 24.83 - 4.96 0.15 / 19
10 33.05 - 2.63 1.75 / 18 31.11 - 3.83 -.07 / 22
5 37.70 + 1.53 1.60 / 20 35.70 - 1.07 -.24 / 24
1.5 41.47 + 6.44 1.49 / 21 39.32 + 2.54 -.39 / 25
1.2 40.09 + 7.45 1.65 / 21 38.59 + 4.60 -.30 / 26
1.1 38.41 + 10.1 1.82 / 21 38.49 + 6.85 -.28 / 25
0-.5 40.54 + 7.19 1.48 / 21 38.83 + 6.15 -.17 / 26
0-1.0 42.51 + 14.1 1.33 / 21 40.34 + 13.4 -.24 / 26</pre>
<p>Notes: Above ground mounting of the antenna and plane yields performance that improves slightly in only one area: the degree of reactance induced at the feedpoint by close mounting to the ground. Performance actually degrades in other categories, but by amounts that are either insignificant or not especially reliable. Indeed, the improvement in gain between the 4- radial model and the 32-radial model at plane heights of 4 to 9 feet is only about 0.1 dB</p>
<p>When the plane is below the surface, the feedpoint reactance continues to drop, but by lesser amounts than with other radial doublings. Gain improvements amount to less than 0.3 dB over very good ground and by less than 0.5 over medium earth. Doubling the number of radials once more may be dubious if the far field earth is very good, but may bring about further gain improvements (in the neighborhood of 0.25 dB) if the path ground is medium or worse. Because of time constraints, 64-radial plane modeling has not been more than sampled.</p>
<p>All of these antennas constitute tuned systems (in the sense noted in passing by Moxon): they are resonant (or at very low heights, near resonant) antennas. Planes have been modeled just as would any open-spoke hat system for shortening the length of an antenna elements.</p>
<p>Since hats can be modeled with spokes plus a perimeter wire, I decided to model a 1/4 wavelength vertical with a plane of this design. A 4-spoke + perimeter model was constructed and run through the same exercise as all of the open-spoke models.</p>
<pre>1/4 wl Vertical (2" dia. al. element, 33.25' long), with 4 0.25" radials
each 19.4' long, with a perimeter wire forming a square, all set 1' below
the feedpoint
Free space: Gain: 1.70 dBi; Feed Z: 20.76 - 0.60 ohms
Perfect Earth Salt Water
Height Feed Z Gain/TO angle Feed Z Gain/TO angle
(feet) (R +/- jX) (dBi/degrees) (R +/- jX) (dBi/degrees)
280-2wl 20.75 - 0.51 7.72 / -- 20.75 - 0.51 7.20 / 14
210-1.5 20.74 - 0.45 7.72 / -- 20.74 - 0.45 7.11 / 18
140-1wl 20.71 - 0.27 7.73 / -- 20.72 - 0.28 6.65 / 26
70-0.5 20.65 + 0.51 7.75 / -- 20.66 + 0.50 6.43 / 4
52.5 18.99 - 0.72 8.11 / -- 19.00 - 0.70 6.98 / 5
35-.25 20.76 - 3.89 7.68 / -- 20.74 - 3.87 6.76 / 6
20-.15 27.25 - 3.00 6.51 / -- 27.17 - 3.03 5.77 / 7
10 33.54 + 4.46 5.69 / -- 33.47 + 4.29 5.06 / 8
5 37.04 + 13.7 5.34 / -- 37.02 + 13.4 4.76 / 8
1.5 39.54 + 25.4 5.14 / -- 40.73 + 26.5 4.46 / 9
1.2 39.74 + 28.6 5.13 / --
1.1 39.76 + 29.5 5.13 / --
0-.5 37.34 + 0.95 4.44 / 9
0-1.0 38.38 + 1.85 4.32 / 9
Very Good Earth Medium Earth
Height Feed Z Gain/TO angle Feed Z Gain/TO angle
(feet) (R +/- jX) (dBi/degrees) (R +/- jX) (dBi/degrees)
280-2wl 20.76 - 0.52 5.15 / 27 20.77 - 0.53 4.16 / 7
210-1.5 20.76 - 0.46 5.13 / 17 20.77 - 0.49 3.27 / 9
140-1wl 20.76 - 0.31 5.25 / 25 20.79 - 0.37 3.43 / 25
70-0.5 20.82 + 0.39 3.11 / 45 20.91 + 0.19 1.97 / 45
52.5 19.17 - 0.45 1.20 / 10 19.50 - 0.30 -.01 / 13
35-.25 20.27 - 3.56 2.07 / 13 19.99 - 2.96 0.30 / 16
20-.15 26.32 - 3.82 2.02 / 16 25.01 - 4.06 0.15 / 19
10 33.57 + 2.00 1.76 / 18 32.22 - 0.09 -.16 / 23
5 38.67 + 10.5 1.58 / 20 37.83 + 6.84 -.40 / 24
1.5 44.55 + 32.0 1.27 / 21 43.86 + 26.2 -.71 / 25
1.2 46.65 + 49.4 1.08 / 20 46.14 + 41.7 -.90 / 25
1.1 49.88 + 68.4 0.79 / 21 49.66 + 56.6 -1.2 / 25
0-.5 52.13 + 12.7 0.35 / 21 63.87 + 8.36 -2.5 / 26
0-1.0 53.53 + 17.0 0.25 / 21 64.35 + 14.8 -2.5 / 26</pre>
<p>At high mounting points, the perimeter plane offers slightly improved performance over a corresponding open radial system of 4 wires--up to about 0.25 dB over medium earth. This technique offers little advantage to HF operators, but could make a VHF plane vertical more compact. Why this technique is not used (besides a general failure to be aware of it) is subject to speculation. One might cite the feedpoint impedance. But that would lead us to suggest that the array of plane verticals available to the amateur community are being fed somewhat distant from their electrical centers in order to achieve a 50-ohm feedpoint impedance. since the plane is started at this point, the electrical center of the antenna may well lie in the plane, where radiation is self-cancelling.</p>
<p>At low mounting heights (less than 5 feet, but above ground), differences between the perimeter and the open-spoke 4-radial models are marginal, being in the main 0.2 dB or less. However, the feedpoint impedance-- especially the reactive component--of the perimeter model is subject to much greater increases as the antenna approaches the earth than open-spoke models.</p>
<p>With the plane below ground, the perimeter model equals or exceeds the open-spoke 4-radial model with respect to both the increases in reactance and the antenna's gain. Those who have limited property on which to place a radial system with 64 to 128 spokes may wish to investigate further the possibilities of a simple perimeter ground plane with spokes under 0.14 wavelength. Systems with 8, 16, 32, or any number of radials can be designed. However, the larger the number of spokes, the less the shortening factor for adding a perimeter wire.</p>
<p>Despite the potential for reader boredom, I have reproduced the entirety of the modeling result tables, rather than making spot comparisons. I have not noted every interesting feature of the emergent patterns. Nor have I made specific recommendations other than for further investigation into certain possibilities. Hence, you may find your own interesting results in them, including a decision to buy a Caribbean island as a mounting station for your next vertical antenna.</p>
<p>However, there is a distinct difference between the dimensions of the modeled radial systems and those in general use. Moreover, we have some remnant questions about the electrical centers of these antennas and their potential feed points. All of these matters suggest that at least one more exercise is in order.<br>
<br></p>
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<p><i>Updated 5-22-97. &COPY; 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.</i></p>
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<title>Modeling Perspective on Ground Planes Part 5: Regional Differences</title>
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<h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Part 5:<br>
Regional Differences</h1>
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<h3>L. B. Cebik, W4RNL</h3>
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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.
<p><b>1. Subsurface plane</b>: 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.</p>
<p><b>2. Close to earth</b>: 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.</p>
<p><b>3. Transition</b>: 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.</p>
<p><b>4. Free Space</b>: 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.</p>
<p>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.</p>
<center>
<h4>Subsurface Plane</h4>
</center>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.
<p>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 suggesting 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).</p>
<p>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.</p>
<p>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)</p>
<pre>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</pre>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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 non-resonant antenna.</p>
<center>
<h4>Close to Earth</h4>
</center>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.
<p>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.</p>
<p>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:</p>
<pre>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</pre>
<p>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.</p>
<center>
<h4>Transition</h4>
</center>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.
<p>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.</p>
<pre>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</pre>
<p>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.</p>
<p>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.</p>
<center>
<img src="gp5-1.gif" width="609" height="270" border="2" vspace="5" hspace="9">
</center>
<p>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.</p>
<center>
<h4>Free Space</h4>
</center>
<p>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.</p>
<p>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 re-resonate the antenna. For our hatted, this may be done either to the main element or to the radials/hat spokes.</p>
<center>
<img src="gp5-2.gif" width="458" height="331" border="2" vspace="5" hspace="9">
</center>
<p>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.</p>
<p>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.</p>
<pre>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</pre>
<p>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.</p>
<pre>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
feed
Free Space 45.00 7.80 2.08 --- 66.19 - 0.61
1 wl up 3.61 24 66.33 - 0.09</pre>
<p>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.</p>
<p>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.</p>
<center>
<img src="gp5-3.gif" width="619" height="276" border="2" vspace="5" hspace="9">
</center>
<p>As one last comparison, let's throw in the vertical dipole:</p>
<pre>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</pre>
<p>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.</p>
<p>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:</p>
<pre>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</pre>
<p>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.</p>
<p>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.)</p>
<p>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 discrepancy between these 7.05 MHz models, all done on NEC-4, and models done with MININEC--about 2.5%. At that size of discrepancy, 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 discrepancy is dimensional only and does not affect the progressions of data drawn from the models.</p>
<center>
<h4>Conclusion</h4>
</center>
<p>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).<br>
<br></p>
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<p><i>Updated 5-26-97. &COPY; 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.</i></p>
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