130. Models vs. Prototypes: Why Field Adjustment Will Always be Necessary

L. B. Cebik, W4RNL (SK)




Within the limits of their guidelines, NEC and MININEC produce highly accurate models of round-wire antennas when the environment is a vacuum or dry air. Over the years, I have designed some antennas such that the models when translated into a physical reality required no post-assembly adjustment to operate in accord with the specifications predicted by the model. Although most of the antennas were for the HF range, some had design frequencies well into the VHF and UHF region. Not all of them used simple geometries, such as uniform-diameter linear elements. For example, many used stepped-diameter elements and a few (Moxon rectangles and quads, especially) used non-linear elements. Even some designs using phase lines, such as LPDAs or dual-driver Yagis, have tightly fit predicted operating curves immediately upon assembly. My experiences are not unique.

However, lest we begin to believe that there may be a "green-thumb" equivalent in antenna design work, my accumulated experience yields the conclusion that field adjustment of antenna prototypes is needed more often than not. Rarely are the adjustments gross. Rather, they fall into the range of fine-tuning. How finely we demand the tuning to be is always a matter of judgment. My first 10-meter stepped-diameter Moxon rectangle showed its SWR minimum 25 kHz below the model's prediction, well under 0.1% of the design frequency. Nevertheless, I dutifully shortened the elements enough to bring the array into alignment with the design model.

There are a number of reasons why field adjustment is always a necessary step in the transition from a design model to a working antenna. Some of the reasons relate to modeling, and other to antenna construction. It may be useful to catalog a few of the situations that are almost guaranteed to require adjustment. The exercise will alert us to the relationship between cautions that we accumulate in the design process and the need always to be prepared to make field adjustments.

1. Pressing NEC Limits and the AGT

One of the most common reasons for a model requiring from moderate to extreme levels of field adjustment in the prototype stage is using a model that presses one or more of the limitations of NEC. Many of the limitations have received treatment in past episodes, although others remain less formally listed. In many cases, the limits are not absolute. Instead, as the modeler approaches the limit, the numbers gradually become less accurate.

One of the most reliable general tests that a model is pressing limits, especially those for which NEC and its implementations issue no warnings, is the Average Gain Test (AGT). Too many modelers--both amateur and professional--fail to give the test due heed. Even though the AGT test is a necessary condition of model adequacy, it is not a sufficient condition, and there are configurations that achieve nearly ideal scores but still show aberrations. Despite this limitation, the AGT score is a relatively good guide that there is a potential need for prototype field adjustment.

As a sample, we may resort to a very common case: the stepped diameter HF element. Fig. 1 shows a highly sectioned center-fed dipole element for 14.175 MHz. The element contains 51 segments total so that all segments are approximately the same length. Fig. 2 shows the element structure in an EZNEC Wires table, along with the usual method of handling such elements, the Leeson substitute element formulation.

The total element length is set to provide a resonant feedpoint impedance when modeled in the substitute-element mode. The following table shows the results of modeling the element in that mode, plus modeling it with both NEC-2 and NEC-4 in uncorrected modes.

Modeled Results for a Stepped-Diameter Element at 14.175 MHz
Total Length Version Feedpoint Z (Ohms) FS Gain AGT AGT-dB
411.5" Leeson 71.16 + j 0.11 2.18 dBi 1.010 0.04
NEC-4 61.25 + j 3.05 3.07 1.235 0.92
NEC-2 43.54 + j11.51 4.68 1.786 2.52
410" NEC-4 60.50 - j 0.05 3.07 1.235 0.92
408" NEC-2 41.04 + j 0.74 4.66 1.784 2.51
398.68 x 0.6743" 71.89 - j 0.07 2.14 1.000 0.00

The NEC-2 results are the least accurate and also show the least ideal AGT score. Had we tried to model the element without the Leeson corrections, we would have ended up with a 408" element length and expectations of a 40-Ohm resonant feedpoint impedance, as shown lower down in the table. NEC-4 produces better results as a consequence of the current-calculation algorithm revision. However, it shows a significantly non-ideal AGT score, excessive gain, and an impedance about 10 Ohms lower than shown by the Leeson model. Had we used NEC-4 without correction and aimed the model for a resonant impedance, we would have ended up with a 410" element, but our impedance expectations would still be 10 Ohms low.

Perhaps surprising to some folks is that fact that the Leeson-corrected substitute element is not perfect as shown in the lower portion of Fig. 2. The element has a special feature used by many modelers to simulate elements that connect directly to a conductive boom. The center section is short and very fat. The step from the center section diameter to the actual element diameter is large. In addition, the center section length allows only a single segment. Therefore, the segments adjacent to the source segment have lengths that differ from the center section. The combination of ingredients is enough to yield a slightly non-ideal AGT value and a slightly high gain report. If we replace the sectioned Leeson element with a single wire having the same overall length and the Leeson-specified diameter with the same total number of segments, we obtain the results in the bottom line. The AGT score is ideal and the gain report is correct for the free-space environment. Fortunately, the impedance does not change enough to suggest that we might have a problem using a Leeson-corrected model.

The results of the test suggest several conclusions regarding the need for prototype field adjustment. Had we modeled the element using uncorrected NEC-2, the resulting dimension would need serious field revision to reach resonance at the design frequency. Had we used uncorrected NEC-4, we still would need significant field adjustment. Modeling the complexly structured elements using the Leeson substitute element (which yields identical results in both NEC-2 and NEC-4) would likely require the least adjustment, or perhaps none at all, depending on the designer's level of fussiness.

There are innumerable other ways to press NEC limitations. The AGT test will catch most of them. The greater the degree to which the AGT score is not ideal (above and below 1.000 in free space), the greater will be the degree of likely field adjustment involved in the prototype.

Unmodeled Wire Structures

To the degree that a model fails to include all geometric features within its structure, the model's reported performance will be off the mark and require field adjustment in any physical prototype. This generalization has greater or lesser application, depending upon what we omit from a model. For example, with a Yagi, if the elements are well insulated and isolated from any conductive boom, omitting the boom from the model will do not harm. If the elements physically connect to the boom, modeling it will not produce more accurate results, since NEC does not calculate transverse currents. This case falls within the preceding category of modeling within NEC limitations and guidelines. However, there are a myriad of different kinds of cases in which we habitually model elements and then construct them in a different manner, where that manner results in a structure that differs by at least a small amount from the model.

Perhaps one of the classic cases revolves around modeling quad loops. Fig. 3 shows four general ways in which builders physically connect the loop elements to the support arms of HF wire-loop quad antennas and arrays. In three of the four cases, we have conductive materials in proximity to each of 4 presumed corners for a square or diamond-shaped quad. Only the version with an RF-transparent support arm and an equally RF-transparent connector will reflect the structure that we normally model. Two of the remaining modes of construction employ conductive rings either in contact with or very closely coupled to the main loop. Each of these rings represents a closed 1-turn inductor that to one or another degree will detune the main loop relative to its modeled performance without the rings.

To demonstrate the degree of detuning that is possible, consider a model of a square quad loop that is resonant when modeled without accounting for the ring connectors. The subject model is for 28.5 MHz and uses AWG #14 wire for the element. Fig. 4 shows the general outline of the quad loop, along with two variations.

The top-right partial outline shows one corner of the basic loop as normally modeled. The lower sketch shows the same corner with a 1" square loop attached, simulating the ring connector often used in physical quads. Since the quad loop is about 109.5" per side exclusive of the loops, the small additions seem insignificant, even when we multiply the one shown by four. The following table tells another story.

A Quad Loop With and Without Corner Attachment Loops
Version Impedance (Ohms) Max. Gain (dBi) AGT AGT-dB
Without 125.4 - j 0.5 3.30 1.002 0.01
With 128.1 + j24.5 3.29 1.001 0.01

The sample will not exactly correspond to the loops and construction methods in any particular case, but it does show the degree to which the model may depart from reality in that reality contains loops the size of the ones included in the revised model. For every case of omitting details from models, the prototype will require adjustment to center the performance curves where the design model intended them to be. The problem becomes more acute with parasitic elements. One may use either a detailed or a shortcut procedure. The shortcut simply applies the percentage of change to the driver loop length to each of the parasitic elements. For greater precision, one would need to determine the resonant frequency of each parasitic element in the model and then adjust each corresponding physical element to self-resonance at the same frequency.

As we increase the operating frequency, "lumps" and "gobs" that make no difference in the HF range may begin to make considerable difference in the UHF range. An element wire made from common materials becomes a significant percentage of a wavelength at UHF. Hence, some common practices related to fastening loops to cable connectors may take on some detuning significance. We often create closed wire loops by overlapping, twisting, and then soldering wire ends, a generally invisible practice at HF. However, doubling the wire diameter, even for a small part of a UHF loop can detune it from its uniform diameter in the model. As well, closing a loop at a current maximum or a current minimum point can also make a difference.

Because we are wedded mentally to the arrangement of antenna features in horizontal beams, we often forget to make appropriate adjustments when rotating such beams for use with vertically polarized signals. A horizontal beam requires no attention to the mast, since the support is at right angles to the elements and the plane of the radiation pattern. Hence, we typically model horizontal beams without modeling the mast. When we turn the beam to orient it vertically, we cannot be so careless. Fig. 5 shows a vertically oriented beam with no boom modeled, along with two types of cases in which we model the support mast. One of the cases extended the conductive boom to a point 2" above the Yagi's boom at 240" (20') above average ground. The other case limits the conductive portion of the support mast to 180" (15') above ground, with a presumably RF-transparent mast section above that point.

The test frequency for the antenna is 52 MHz, which makes the two mast lengths close to even multiples of a half wavelength. The following table catalogs the modeled results for the three cases.

A Vertical 6-Meter Phase-Fed Yagi with Different Mast Situations
Version Impedance (Ohms) 50-Ohm SWR Max. Gain (dBi) To Angle (Deg.)
No Boom 43.6 + j 7.9 1.24 7.42 9
242" Boom 26.2 + j17.9 2.23 6.31 27
180" Boom 41.3 + j 5.8 1.26 7.24 9

Carelessly using a full-length conductive mast results not only in a detuning of the closely space driver, but also distorts the pattern to raise the elevation angle of greatest field strength to an unusably high level. Shortening the conductive portion of the mast returns to the beam to nearly full "no-mast" performance. Still, a builder might wish to do further modeling to ascertain just how long the conductive portion of the support mast can be and not affect performance at all.

Under certain circumstances, the close proximity of a mast can affect even a horizontal beam. Fig. 6 shows a 2-band Yagis with a common feedpoint. On the left is the typical mast-less model. The outline suggests that we are using a direct connection between the drivers for the two bands, a short section of exposed parallel transmission line.

On the right is an added dot representing the likely placement of the support mast in order to support the beam near its center of mass. The position is beside the transmission line connecting the two drivers. The combination of the mast and the plate-hardware combination used to join the mast and the boom may have a significant affect on the driver connection line, even if the metal mass leaves the elements themselves unaffected. For example, it may alter the effective characteristic impedance of the line, resulting in altered driver impedances on one or both bands. To forecast the potential effects of a closely spaced mast assembly, we may wish to model a short thick wire in the vicinity (but unconnected to the antenna elements) to see what may happen with a prototype. The exercise may also allow us to pre-plan for the adjustments that we may make to the prototype by indicating trends in effects and which modifications restore performance. It is easier to go through the head-scratching process in front of a computer than at the top of the prototype's support structure.

The are innumerable instances in which a model will be at variance with the prototype without any way of compensating within the model. The sketches in Fig. 7 shows the modeled and the actual situation that we often encounter with elements that necessarily change direction and yet have a significant element diameter. For example, we might encounter this situation in a Moxon rectangle in which the elements are relatively fat for the operating frequency and yet are metallically continuous. The physical antenna will require a bend on a radius that accommodates the element's diameter without weakening the structure. The bend radius "cuts" the corner, requiring an adjustment to both the left-right and the front-back dimensions to maintain the total element length. By using enough segments in the model's elements, we can often model an angular corner. However, we must ensure that we do not adversely affect the AGT score in the process so that we may correctly correlate the results of the corner simulation to the original model and to the physical prototype.

Although we have looked at a number of cases in which our models omit certain details of the physical prototype, we have not exhausted the list of possibilities. Nevertheless, perhaps this abbreviated catalog will suffice to alert modelers to the potentials for variation between the model and the physical.

Inductive Loading

All forms of R-L-C loading in NEC models present limitations, some of which can affect the model-to-prototype correlation. These types of loads, whether set up as series or parallel circuits, have no geometric dimension and therefore play no role in the initial matrix calculations. Instead, the program applies the load's equivalent resistance and reactance (real and imaginary components of the load impedance) to the assigned segment after initial calculations. The result is a modification of the current on the loaded and other segments, with further consequences for the calculation of overall antenna fields.

Inductive loads are susceptible to a growing inherent error as we move the inductance further from the high-current region of the antenna. In this connection, we might study the behavior of the current magnitude as we move loading inductances away from the center of a dipole, as shown in Fig. 8.

The top current distribution curve applies to an unloaded short dipole that shows a source impedance of 29.45 - j402.6 Ohms. To bring the dipole to resonance, we may add an inductive load on the center segment, which is also the source segment. The reactance of the load is j402 Ohms. The equivalent inductance at 28.4 MHz is 2.25 uH. If we omit a series resistance and assume an indefinitely large value for the inductor's Q, we obtain a gain of 1.88 dBi in free space (for either the loaded or the unloaded dipole). The center-loaded dipole reports a source impedance of 29.45 - j0.56 Ohms. Assuming a Q of 300 requires that we add a resistance of 1.34 Ohms, and the gain drops to 1.69 dBi. The resistive center load component adds to the unloaded resistive component, so the source impedance becomes 30.79 - j0.56 Ohms.

Center inductive loads are most accurate in NEC (equivalent to base-loading in a ground-mounted monopole) because the current at each end of the loaded segment is equal. This condition assures that the inductance reflects most closely a physical, that is, a virtually pure inductor. As we move the load outward from center, the situation changes, as shown in the lowest outline in Fig. 8. Assigning the two loading inductors positions that are midway from the source segment to the element tip, each inductive load requires a reactance of j402 Ohms to effect resonance. This value is equivalent to installing two 2.25-uH coils, one on each side of the center segment. With these inductors installed (without regard to inductor Q), the model reports a source impedance of 46.68 - j0.13 Ohms. If we add a series resistance to each inductance to equate with a Q of 300, we obtain a source impedance report of 48.69 - j0.23 Ohms. The gain with an infinite Q is 1.91 dBi and with a Q of 300 it is 1.73 dBi. (Note that there is no significant gain advantage to mid-element loading over center loading in dipoles.)

The current distribution curve for the mid-element loading example points to a significant facet of load behavior if we assume the use of solenoid inductors. The current at each end of the inductor is different. To the degree that the current levels differ, the wire within the inductor serves a second purpose in addition to creating an inductive reactance. The wire also serves as part of the length of the antenna, even if so oriented that it cannot contribute significantly to the antennas radiation. The wire in the uncentered inductor(s) will have an affect on the length of dipole necessary to achieve resonance. However, since the inductors in the model have no wire (in the sense that the segmented wires of the element do have wire), the model cannot show the contribution of the physical inductor wire to the antenna's length. As a result, a physical element that is highly loaded away from the high-current region of the antenna will not have the same length as modeled. The net consequence is a requirement for field adjusting the physical prototype.

Allied to the inherent inaccuracy (not severe but noticeable) of inductive loads away from the elements high-current region is a modeler oversight often encountered in models of trap elements. Consider an element designed for the amateur 12- and 17-meter bands, specifically 24.94 MHz and 18.118 MHz. A correctly modeled trap dipole would show source impedance values in the 71- to 73-Ohm range for each band using traps with a coil Q of 300. However, many modelers fail to achieve such results. We may understand why if we examine the trap situation shown in Fig. 9.

With respect to components, a trap consists of a parallel combination of an inductance and a capacitance. NEC offers only series and parallel load configurations, as shown at the center of the figure. The parallel combination is the most apt, but does not capture the equivalent circuit of a trap, such as shown at the right. Therefore, we must convert the series R-L leg of equivalent circuit into a parallel combination of resistance and inductance to obtain the required components for a parallel circuit.

Now we may add a further complication. We normally design traps for frequencies either at or just below the lower end of the band for which they operate as traps. The design frequency for the trap in the same antenna is 24.5 MHz. At the antenna's design frequency of 24.94 MHz, the trap serves as a slightly off-resonance parallel tuned circuit that presents a high impedance, thus terminating the antenna at the trap. At the lower frequency, many modelers simply presume that the capacitor disappears and that the remaining element loading is solely a function of the inductor value. Unfortunately, this assumption is incorrect. The loading reactance in each off-frequency trap (at 18.118 MHz) is a function of both components in a non-resonant parallel circuit. We cannot even preserve the parallel resistance that we used to set up the trap at the original frequency, since its value will also change. A model that uses only the value of the inductor (and its series resistance) to load the element for the lower band will be nearly 2' longer at resonance than one that re-calculates the net impedance of the entire trap.

Now we may add in the previously noted difficulty with inductive loads inserted well away from the antenna's high-current region. Although we may not need to make a significant adjustment to the inner length of the element on 12 meters, we can expect to require a fairly sizable adjustment to the overall length of the element when operating on 17 meters, even if we correctly calculate the loading of the trap on the lower band.

Conclusion

Catalogs must end somewhere, and this point is probably as good as any. Our fundamental theme has been the fact that there are many circumstances that will dictate a need for field adjustment to a physical prototype of any antenna designed via NEC software. Some of those circumstances involve pressing NEC limitations, whether those limitations relate to guidelines for adequate model geometry or to software techniques for loading and other non-geometric program functions. Other circumstances involve limitations on how precisely we may reflect reality within a model, with some limitations relating to the software and others to the habits and conventions we bring to the modeling process.

There are a large number of antennas that we can accurately model so that the model's specifications translate virtually exactly into a physical antenna that performs in according with model predictions. However, the number of cases that inherently call for field adjustment of the physical prototype is even larger. When converting a design model into a physical antenna, we should always be prepared to make such adjustments. If we use the software wisely, we can often know in advance the kinds of adjustment maneuvers that are most likely to bring the antenna into alignment with our design specifications.


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