For various good reasons, programmers who implement either NEC-2 or NEC-4 provide warnings about vertical wires that meet the ground (Z=0) and end at that point. For example, EZNEC Pro warns that "If you connect a wire to ground when using the High Accuracy [Sommerfeld-Norton or S-N] real ground type, the program makes the connection with an unpredictable series resistance." EZNEC no longer makes the less-accurate reflection-coefficient approximation (RCA) ground calculation system available. It was designed for faster results in an era of much slower computer speeds. Today, there is no significant difference in model run times when using either ground calculation system, so EZNEC has omitted RCA. The system is widely available on other implementations of NEC-2 and NEC-4 (such as NEC-Win Pro, GNEC, 4NEC2, and NEC2GO). However, EZNEC does provide access to the MININEC ground calculation system from its implementations of NEC-2 and NEC-4. (4NEC2 also provides the MININEC ground system within a NEC package.) Nevertheless, for all general modeling purposes, the modeler should use the more accurate S-N ground calculation system. (Antenna Model, a version of MININEC, now includes the S-N ground system in its program.)
We have in past episodes explored the differences among the available ground calculation systems, listing the limits and the limitations of each one. In this episode, we shall focus on a slightly different way of looking at ground calculation systems by examining two different types of antennas that will test various ways of handling vertical wires that just reach the ground (Z = 0). The first case will extract data reports using a fairly standard test of wire-to-ground terminations. We shall look at differences among reports for a 1/4 wavelength monopole using the various ground systems when the monopole just reaches the ground and has no radials. We shall compare those reports with NEC-4 reports for the same monopole above ground, but with a buried radial system of 32 15' radials. We may call this the "normal" test situation for uncovering the problems that emerge when we fail to provide a proper termination for a wire that just touches the ground.
Then we shall look at a different type of antenna: a 10 wavelength terminated long wire. On common configuration for such antennas is to bring the ends of the wires vertically back to the ground. We place the source on one end and the terminating resistor on the other end, in both cases, right at ground level. (This is not the only possible configuration for a terminated long wire, but it is perhaps the most common configuration. Unlike some alternatives, it provides a very large operating bandwidth--several octaves--but with a changing pattern, since the antenna changes its length as we change the operating frequency.) We shall look at 4 different ways to model this antenna configuration, in each case placing the antenna's horizontal run 1 wavelength above ground.
As we shall discover, the matter of wires touching the ground with the S-N ground system (and others) are not quite so cut and dried as the simple modeling test might indicate.
The "Normal" Test Situation
Assessing the behavior of a vertical wire that just touches ground, with no other termination, when using the various ground systems in NEC-2 and NEC-4 usually involves setting up a 1/4 wavelength vertical monopole. So long as all models in the test sequence use the same monopole, frequency, and ground quality (wherever relevant), the selection of these parameters makes no significant difference to the test. Therefore, I shall begin with an aluminum monopole that is 33.25' tall with a 2" diameter. It will use 66 segments so that each segment is 0.5' long. This provision is not important for the tests that use the monopole alone. However, we shall also need a "properly" terminated monopole for comparison. For that set of runs, I shall extend the monopole 0.5' below ground and connect 32 aluminum radials, each 0.25" in diameter. Each radial will be 15' long. The length is short, but not so short as to invalidate the test comparisons. For adequate current distribution in a lossy medium, the radials are just about long enough, while allowing a very compact model. The ground quality--wherever relevant--will be average, that is, with a conductivity of 0.005 S/m and a relative permittivity of 13. Fig. 1 shows the outlines of the two models required for the test sequence.
The model with buried radials requires NEC-4 because the radial wires are below ground. It also requires the S-N ground system for the same reason. However, the simpler model sets up a more complex situation. We shall run the model in both NEC-2 and NEC-4 for all tests. Every implementation of both cores provides access to a perfect ground, that is, one using the simple image-reflection calculation system built into NEC. Likewise, every implementation of both cores allows access to the S-N ground system. However, we must turn to programs like NEC-Win Pro and GNEC, if we wish to see the results of using the NEC reflection coefficient approximation system (RCA). To access the MININEC ground from within wither NEC-2 or NEC-4, we must use EZNEC or 4NEC2. If we make all of the relevant model runs, we wind up with a table similar to Table 1.
Let's read the table from the bottom up. Both implementations of NEC-4 (EZNEC and GNEC) return virtually identical results for the monopole with buried radials. The tiny numerical variations between the reports are largely functions of using different compilers for the cores. Indeed, different CPUs may show further variations, depending upon their architecture. We should note that the gain and impedance values will also change as we alter both the number and the length of the radials beneath the monopole. Therefore, our reference buried-radial monopole array is simply one of many possible references that we might use.
The upper part of the table uses a single model with no permitted variation in its geometry (if we are to keep it consistent with the buried-radial antenna). Only the ground system changes among the model runs. Except for the use of a perfect lossless ground, we find one constant among all of the models: a take-off (TO) angle of 26 degrees. In fact, a single elevation plot, shown in Fig. 2 is applicable to all of the models using a lossy ground.
Regardless of the core or the program, the results over perfect ground coincide as completely as we could expect from separate compilations of the NEC-2 and NEC-4 cores. EZNEC gives us access to the MININEC ground, and the NEC-2 and NEC-4 results also coincide. As well, the feedpoint impedance values remind us that the MININEC ground always returns the impedance for perfect ground, not for the lossy average ground on which the far-field report is based.
In NEC-2, the two programs (EZNEC and NECWin Pro) provide identical results for the S-N ground. Since only NECWin Pro (of the two programs) provides an RCA output in NEC-2, we can only note its values that appear to be even more divergent from reality than the S-N unusable results.
In NEC-4, we find an additional divergence both among cores and among programs. The EZNEC and the GNEC results for the S-N ground do not agree. The RCA result for GNEC differs from the S-N value for the same program by almost the same gain difference as in the NEC-Win Pro S-N and RCA reports, but this is not in itself a suggestion that the GNEC/NECWin Pro results are superior to those of the EZNEC cores.
In fact, we have no way to estimate--short of setting up a physical experiment--which set of reported values may be the more nearly correct for a monopole with no radials placed in contact with average soil. Internal consistency of results would be only one measure of reasonableness. As well, it would constitute a necessary but not a sufficient condition of reliability of the reports. However, we do not have internal consistency. In addition, we cannot use the reports for the antenna that uses 32 15' radials, because--at best--these results apply to only one of many possible arrangements. Other radial lengths and other numbers of radials would each yield different results for both the far-field gain and the feedpoint impedance.
Buried-radial monopole systems that we model by using the S-N ground in NEC-4 do have a very reasonable track record of reliability relative to physical antennas--within the bounds of construction variables and the potential in any area for stratified soil. For example, the results coincide very well with the experimental results published in the classic Brown-Lewis-Epstein work on the 1930s. Since we do not have a similar record for the monopole without radials, the entire set of results over lossy ground using either the RCA or the S-N ground fall into the category of being simply unreliable. (We have examined the shortcomings of the MININEC ground system in other episodes.)
Our sample model only illustrates the problem of trying to model a monopole without providing it with a radial system. Nevertheless, it shows why program manuals tend to recommend against simply bringing a vertical wire to ground and using no other termination for it.
The Terminated Long Wire
A single wire that is many wavelengths long, fed at one end and terminated by a correct impedance at the other end, creates a directional beam. It is one of the earliest directional antennas used in HF point-to-point communications. With the use of a proper termination, the antenna is capable of wideband operation over frequency spans of more than 4:1. However, the beamwidth and the sidelobes tend to vary as the antenna changes its length when measured in wavelengths as a function of the operating frequency.
The terminated long wire has a number of possible configurations, but we are interested only in the most common of these ways of setting up the antenna. Let's consider a long wire that horizontally is 10 wavelengths. We shall set the antenna 1 wavelength above average soil. The most common way to feed the antenna is to bring a wire to ground and to place the source or feedpoint at the junction of the wire with the ground. Essentially, the ground forms the second terminal of the feedpoint. At the far end of the long wire, we shall also bring a wire from the end of the horizontal section down to ground. The ideal termination would be a complex impedance, the reactive part of which would vary with the operating frequency. However, for wideband use, we normally use a non-inductive resistor. Like the feedpoint, we place the resistor at the junction of the vertical wire and the ground. Ostensibly, the ground provides a return so that effectively the resistor and the feedpoint have a common terminal.
Ideally, we can find a load impedance that will provide the proper conditions for achieving full traveling-wave status for the terminated long wire. The calculation is based on treating the wire as a transmission line, and the load impedance must equal the characteristic impedance of the line. Balanis (Antenna Theory: Analysis and Design, p. 495) provides the following equation to approximate the proper value of the termination.
RL = 138 log10 (4h/d)
RL is the value of the impedance load in Ohms, h is the height of the wire, and d is the wire diameter, when both are in the same units. Note that the impedance of the line and hence the approximate load value is independent of frequency and dependent only upon a set of physical measurements that use the same units of measurement. The approximate recommended value of RL is 776 Ohms. For many installations, terminating resistors tend to range between 600 and 800 Ohms. The wire diameter is 4.745e-6 wavelength (or 0.16" wire at 3.5 MHz).
Equally important to the model is the configuration that we employ for simulating the termination of the antenna ends at the ground. Essentially, we have 4 options (A though D) as sketched in Fig. 3.
Option A brings the vertical elements of the antenna down to ground. The source or feedpoint is the first segment above ground of the left wire, while the terminating load appears on the last segment above ground at the far end of the antenna. Fig. 4 shows the general layout, along with elevation and azimuth patterns for the test model.
In the EZNEC Pro/4 implementation of NEC, we have at least 4 ways to model the structure: over perfect ground, with a Sommerfeld-Norton (S-N) average ground using NEC-4, with an S-N average ground using NEC-2, and with a MININEC ground. Use of a perfect ground provides a reference baseline for checking the sensibleness of other models. However, neither NEC-2 nor NEC-4 recommends simply bringing a source wire to ground, since at a minimum, the source impedance is likely to be off the mark. The MININEC ground does not provide accurate impedance reports for the ground quality selected, since it is restricted to using the impedance report for perfect ground.
Despite the limitations, we can tabulate the results. As a test case, I used a 10 wavelength terminated antenna alternately using termination resistors of 600, 800, and 1000 Ohms. For each option, Table 2 lists the maximum gain, the reported 180-degree front-to-back ratio, the elevation angle of maximum radiation, the beamwidth, the source impedance, and the 600-Ohm SWR at the test frequency.
Using the sequence over perfect ground as a background reference, the NEC-2 results for the S-N average ground and the MININEC average ground data appear to coincide fairly well. However, the NEC-4 runs for the S-N average ground appear to yield somewhat high gain values with more than anticipated inductive reactance in the source impedance. The gain values for NEC-4 and the S-N ground are only about 2.5-dB lower than the values over perfect ground.
Option B represents an adaptation of a NEC-2 technique for modeling vertical antennas with ground-plane radials. The return line between the load resistor and the source is 0.001 wavelength above ground, several times the diameter of the wire. See Fig. 5 for the layout and the associated elevation and azimuth patterns.
In principle, the model violates no constraints, but as Table 3 for both NEC-2 and NEC-4 shows, it yields a poor model of the terminated long-wire antenna.
Although NEC-2 and NEC-4 show a very close coincidence of data, the low gain, low front-to-back ratio, and high feedpoint impedance reports combine to suggest that this model is highly inadequate. The antenna amounts to a corner-fed terminated loop in which the low wire is an active part of the antenna rather than just a return line. However, the beamwidth and elevation-angle reports are consistent with the other models.
NEC-4 does allow the use of a subterranean return wire, shown in Option C in Fig. 6. To test this option, I placed a return wire 0.01 wavelength below ground level, connecting it to the above ground vertical wires with short segments. Both the source and the load for the antenna remain above ground. The layout and patterns appear together in Fig. 6.
Since this option is available only in NEC-4, the test-results in Table 4 are quite brief.
The results are modest, but coincide roughly with the NEC-2 results in Option A. The front-to-back reports are consistent with those for perfect ground. The difficulties with the model include the model size, since the return wire requires as many segments as its above-ground counterpart in Option B. As well, the return wire may actually yield slightly low gain reports by carrying more current than the ground itself. A real installation would not likely use a buried ground wire.
Therefore, I tried Option D, which replaces the below ground structure of option C with 2 simple ground rods. See Fig. 7 for the layout details and the patterns.
Each rod is a 1-segment wire about 0.05 wavelength, which is the length of the segments in the vertical wires above ground. Therefore, the source has equal length segments on each side of the feedpoint segment. 0.05 wavelength is about 4.3 meters or 14'. This length may be longer than the average ground rod, but substituting shorter segments did not change the reports by any significant amount. The results of the test appear in Table 5.
Except for the predicted very slight increase in maximum gain, all of the values correspond very well with those of the buried-return-wire model (option C), but with a 45% reduction in model size. For users of NEC-4, it is likely that this style of model is about as adequate as we may get for a terminated long-wire directional antenna. In fact, for users of NEC-2, the basic model (option A) coincides well enough for general guidance. In physical reality, there will be structural variables that will inevitably limit the precision attainable by any model. For example, the models presume a flat wire horizontal to the ground, which is not likely to appear with copper wire and real supports. Even if all supports provide the same height, catenary effects will vary the actual wire height above ground along the antenna pathway.
The net result of these preliminary tests suggest that option D is a very usable model capable of giving good guidance on the performance of the common-configuration single terminated long-wire antenna. We may largely dispense with the creation of complex radial systems under each end of the antenna, systems that would not likely be part of an amateur long-wire installation.
Almost incidentally, we may note two facts about these test long-wire antennas. First, we should expect some slight inductive reactance, since the wires are physically 10 wavelengths long. Hence, they are slightly long electrically, Second, the use of vertical wires at the ends of the main horizontal section modifies the performance relative to a configuration that uses only a horizontal wire. Fig. 8 compares the current distribution along two terminated long wires with equal-length horizontal sections. Since in long-wire technology, there is no perfect traveling-wave antenna, both versions show a standing wave superimposed on a certain constant traveling-wave current level. For the present context, the current distribution curves for the vertical sections of the lower sketch are most important. They limit both the gain and the front-to-back values for the antenna.
In addition, the vertical wires also modify the transmission-line analogy that resulted in the choice of the terminating resistor. Virtually all of the tables show that as we increase values of the terminating resistor, the feedpoint impedance grows, but at a slower rate. Apart from the small inductive reactance, the feedpoint impedance would more closely match the terminating resistor value when both values are somewhat lower.
Conclusion
With a simple monopole and no radials, the NEC-2 model showed results that seemed most to diverge from our expectations of a physical antenna. The NEC-4 results appeared--however ultimately unreliable--to be considerably closer to reality--as indicated by the reference model using radials.
In contrast, options C and D of the long-wire model with at least some buried elements provide a reference against which to measure the models without ground penetration. In this case, The NEC-2 model of option A more closely approximated the reference values on options C and D than did the corresponding option-A version using NEC-4. Although we cannot expect high precision (but only general planning guidance) from any of the models, the exercise does illustrate that we cannot draw singular universal conclusions. When wires just touch the ground, a model is suspect in the reliability of its reports. However, the level of reliability and the reasons for any given measure of distrust may vary with the type of antenna that we are modeling.
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