In past episodes of this series, we examined the basic dimensions of axial-mode helical antennas and initially cataloged the properties of 5-turn helices with different wire diameters over perfect ground. We went on to explore longer helixes to identify how their characteristics vary from those of the initial set of 5-turn helices. Besides seeing the gain curves rise in peak value and generally slide to smaller circumferences, we also saw the increase in sidelobe development at smaller circumference levels. Finally, we made some comparisons, including a brief primer on how the NEC-2 and NEC-4 GH (helix) commands differ.
However, the entire study had a major limitation. Few amateur antennas have the opportunity to operate over indefinitely extended perfect grounds. Therefore, we need to explore, if only partially, how axial-mode helical antennas perform over self-contained ground planes that are elevated from the actual ground. That exercise will put us a position to do a rudimentary comparison between helices and other antennas amateurs might use the obtain high-gain circular polarization.
Elevated Self-Contained Ground Planes
The notes that we have examined so far present an idealized portrait of the axial-mode helix. Gain curves are smooth over the region that we have termed "stable." Within that region, the modeled values of source impedance have also varied within quite small limits. With the stepped increases in helix length, the patterns have shown a progressive development, especially with respect to sidelobe production.
However, the helical antennas that amateurs and others build do not have the benefit of a perfectly reflecting ground plane that is indefinitely large. Instead, in accord with the general outlines of Fig. 23, they appear on self-contained ground planes of finite size with the entire array placed above ground by an amount determined by operational needs and practical feasibility.
As noted near the beginning of these notes, a square ground plane is not the only possible helical antenna configuration. However, from the perspective of practical modeling, it is perhaps the most appropriate for initial modeling efforts. As shown in the graphic, we may terminate the helical portion of the model at the nearest intersection of wires making up the wire-grid ground plane. Hence, the source may remain on the very first segment of the helix itself. The technique holds the promise of allowing some comparisons between the models constructed over perfect ground and the new series of models.
The new models do not come without an associated cost. The models over perfect ground made use of the GH command that permitted very simple model structures. However, if we use the same circumference steps with the new series of models, we need to move the terminal point of the first helix segment from its natural location to the nearest junction of ground-plane wires. We cannot do that and still keep the models simple and uniform from one step to the next.
The workaround for this problem is to construct individual models for each helix-wire-grid combination. As note at the beginning of these notes, several programs are available to allow the construction of both parts of the antenna on a 1-wire-per-segment basis. For example, EZNEC Pro/4's current version has both facilities. The resulting models are not any more segment intensive than using the GH and GM commands to create and replicate wires under a single tag number. However, they do result in one-model-per-situation. Hence, instead of using 1 model for all 12° antennas, we have one model for each combination of helix pitch, circumference, and length, plus the selected size of wire-grid ground plane.
Fig. 24 shows the EZNEC helix-creation sub-screen. Essentially, it allows entering the same set of variables as the GH command in either NEC-2 or NEC-4. However, the output is a set of 200 wires, each a GW entry. The wire-grid structure for this exercise is 1.2WL by 1.2WL on a side, with the wires spaced at 0.1WL intervals. Wire 1 of the helix shifts from its position on the X-axis as created to the nearest intersection of wires, normally either X=0.1 or X=0.2.
The models are limited by the factors that go into their creation. For example, the misalignment of the first helix wire creates a very small error component. More serious is the fact that the helix wire approaches the wire-grid wires at a severe angle: 12°. The normal wire diameter for a wire-grid that simulates a solid surface is the segment length divided by pi. However, this fat a wire results in some larger-circumference models having a first wire that penetrates into the center section of the wire-grid wire that it meets at a junction. To overcome this problem, I reduced the wire-grid diameters to 0.015WL. Although not a perfect simulation of a solid plane, the resulting data was--for models that could handle both thin and thick wires--only a slight change in performance.
Due to these constraints, I created models only for the 12° versions of the helical antennas, using 5, 10, and 15 turns, with radii ranging from 0.75WL to 1.35WL. Each helix connects to a wire-grid that is 1WL above average ground (conductivity 0.005 S/m, permittivity 13). The goal is to determine to what degree these models may differ from the models created over a perfect ground. Table 6 provides the complete data on the modeling results. The AGT values tends to vary much more widely in these elevated ground-plane models than in the earlier set, but the values remain well within the range of what is usable to obtain suggestive (rather than definitive) trends.
The general utility of the models shows up in Fig. 25, which tracks of gain levels for both types of models. Over the region that we termed "stable" with the initial set of models, the new models show identical characteristics, with a gain minimum occurring very close to where it occurred over perfect ground. As well, once the models use circumferences that place them outside of effective axial-mode use, the curves overlap fairly precisely. At the small-circumference end of the scale, the new models show lower gain than their perfect-ground counterparts as the circumference reaches a value to Ohms small for axial-mode duty. Within the more central portions of the circumference rage, the two curves for each length of helix parallel each other. The two differences are 1. the elevated models have a higher average gain than the perfect-ground models, and 2. the elevated models show a less severe dip in gain at the minimum point.
Fig. 26 and Fig. 27 provide data for the elevated ground-plane models on the source resistance and reactance, respectively. The overlap in the curves for a good portion of their length suggests that--with one exception--they portray the source impedance trends quite well. The curves for circumferences above 0.90WL and those for 0.90WL and lower have slightly different slopes. 0.90WL is the last circumference using a 0.1WL grid-wire connection; from 0.95WL upward, the connection is to the 0.2WL grid wire junction.
The upper limit of source impedance stability is a circumference of about 1.15WL. At the lower end of the scale, the short (5-turn) helix deviates significantly below 0.8WL circumference. However, the other two sizes of helix appear to be stable to the limit of the survey. These results are consistent with the gain behaviors of the three sizes of helix.
The use of smaller circumferences for 12° helical antennas receives support from the evolution of patterns. Fig. 28 presents a set of three patterns for the 10-turn model at 0.85WL, 1.0WL, and 1.15WL circumferences. EZNEC provides circularly polarized patterns, although the present set has maximum values that do not differ materially from a total-field pattern. All antennas in the series use right-hand circular polarization. Because reverse orientation pattern lobes occur in null areas of the dominant orientation, the total field patterns would show more complex structures in the region of the secondary lobes.
For most cases, the elevated ground-plane models show slightly less severe sidelobe strength, down from 1 to 1.5 dB relative to patterns for models over a perfect ground. Nevertheless, the sidelobe structure of the 1.15WL circumference model is sizable and peaks only about 10 dB below the main lobe of the pattern. In contrast, the 0.85WL circumference model has scarcely any sidelobe structure at all. However, pattern cleanliness will cost about 1 dB in maximum gain.
The end result of our survey of 12° helices over elevated ground planes is a set of data that differs in detail but not in main lines from the data for helices over perfect ground. Pressing for maximum gain by using a larger circumference results in a pattern with a much higher sidelobe content. As well, the helix may approach a region of unstable operation where small physical changes may yield large and unexpected changes in the source impedance. Leaning toward smaller circumferences sacrifices some gain for the sake of cleaner patterns and more predictable source impedance behavior.
Is There a "Best" Ground Plane Size?
Within the context of square ground planes, the 1.2WL by 1.2WL wire grid used in the survey of 12° helices was both arbitrary and reasonable. I selected a size that I presumed was large enough to perform well in its function. However, without comparators, the ground plane that I used is not certifiably the best. To see if there might be a better size, I performed a final survey using 4 different square ground planes, with sides that are 0.8WL, 1.0WL, a.2WL, and 1.4WL long. Fig 29 shows their relative sizes with respect to a standard helix.
The ground planes all use 0.1WL wire spacing and 0.015WL wire diameters. This arrangement allows a standard relocation of the first wire in the helix. All first wires for 0.85WL circumference helices go to the 0.1WL position, while each of the two larger sizes (1.0WL and 1.15WL) move to the 0.2WL junction. A finer gradation of wire-grid sizes is desirable. However, such grids would create one or two problems. The use of standard 0.1WL wire spacing moves the first helix wire termination to a different position, creating deviations in the data and the AGT values. Creating a grid that places a wire at both the 0.1WL and 0.2WL position changes the performance of the grid for intermediate outside dimensions. Nevertheless, the 4 samples are enough to establish a basic trend.
Fig. 30 provides a view of the results of the sampling, while Table 7 gives the complete tabular results. Although nothing significant happens in the realm of source impedance, the 10-turn helices used in the survey show small but definite differences in gain as we change the size of the ground plane. The larger the circumference of the helix, the smaller is the ground-plane size that yields maximum gain. Each of the three sizes of helix--as measured by circumference--has its peak gain with a different size ground plane. What the survey cannot show is whether the overall length of the helix plays a role in the ground-plane size for peak gain, since the smaller circumference models also have a shorter total length.
The gain difference for the widest helix is not great across the span of ground-plane sizes. However, as we reduce the circumference of the helix, the curves grow steeper. Since the survey stops at a 1.4WL side length for the ground plane, it is not clear whether or not the 0.85WL circumference helix has reached its peak value. Still, ground-plane size is another of those factors that basic helix literature tends to overlook. The amateur who intends to build his own axial-mode helix should not ignore this factor. For the 0.85WL circumference helix, the gain difference between the smallest and largest ground planes in the series is over 1 dB.
Is the Helical Antenna the Best Choice for Amateur Radio Circularly Polarized Communications?
These notes have recorded some interesting limitations in the stability and the patterns of axial-mode helical antennas. Calculating the required helix dimensions turns out to be the simplest part of the planning process. Much more hangs upon the decisions we make with respect to selecting the circumference and ground plane sizes, as we weigh the contributing factors in a compromise between having the cleanest pattern, the most stable source impedance, and the maximum gain. A single set of dimensions may not satisfy all possible operating conditions.
Most engineering sources classify the axial-mode helical antenna as a broadband array. Within this classification, we expect limitations of the sort that we encountered. However, amateur communications calling for circular polarization generally require only narrow-band antennas. Before we close the notes, we should at least do a preliminary comparison of alternative antennas that an amateur might use in satellite communications.
Fig. 31 presents the outlines of three antennas. All are designed for the test frequency of 299.7925 MHz. The helix, selected from the cluster that we have studied, uses 10 turns, 2-mm wire, and a 12° pitch. The 1.15WL circumference results in a total length of 2.44WL. to make the model coincide with the other antennas, I elevated the terminal end of the helix and created a 1.2WL by 1.2WL wire grid as an elevated ground plane. Other ground plane structures are possible. I experimented with 32- and 64-radial ground planes. However, the need to terminate the first segment of the helix at the center of the radial system established quickly that the helix must be almost perfectly centered over its ground plane structure. Off-setting the radial planes by less than 0.2WL reduced main lobe gain by 3 dB and produced a major secondary lobe only 4-5 dB weaker than the main lobe.
The helix over the square wire grid was centered, with only the first segment moved slightly (about 0.017WL) to intersect a grid-wire end. The gain (corrected for an AGT-dB value of -0.66 dB) was 12.71 dBi with a beamwidth of 37°. The impedance (corrected for an AGT of 0.859) was about 245 Ohms, although the impedance at the actual junction will be somewhat lower still.
The other two antennas in the set are a 4-element quad with a turnstiled driver and an 8-element crossed Yagi with turnstiled drivers. The quad is only 1.87WL long from reflector to the forward-most director. Using 1-mm diameter wire for the elements, it has a gain of 10.35 dBi when placed 1WL above average ground. The beamwidth is 58°. Because a quad allows some flexibility in the placement of the driver without undue adverse effects on the array gain, we may arrive at a single-source impedance of about 95 Ohms resistive. Hence, a 1/4WL section of 93-Ohm cable forms a proper phase line run between successive corners of the driver. The result is a circularly polarized antenna. We may reverse the polarization simply by connecting the main feedline at one or the other end of the phase line. The result is a 50-Ohm impedance for the main feedline. The 4-element quad in the outline sketch has a 2:1 50-Ohm SWR bandwidth of more than 25 MHz, which eases the problems associated with construction variables. (Redesigning the antenna for fatter elements would yield a larger bandwidth.) Obviously, longer versions are possible for the quad if one desires more gain.
The 8-crossed-element Yagi is 2.42WL long, very close to the length of the sample helix. It uses half-inch (12.7-mm) elements. As the sketch shows, the parasitic elements meet at the center, although the drivers require a small separation to effect the turnstile feed. In this particular design, the single driver source impedance is 50 Ohms. Hence, the turnstile phase-line is also 50 Ohms. The resulting impedance presented to the main feedline is close to 25 Ohms. A length of 35-Ohm line (or a pair of 70-Ohm lines in parallel) provides the required match for a 50-Ohm main feedline. As with the quad, one may change polarization simply by swapping phase-line ends for the junction with the matching section and main feedline. To center the design frequency within the overall 2:1 50-Ohm SWR passband, the line lengths for both the phase line and the matching line are not true quarter wavelengths electrically. The electrical length of the phase-line is a bit over 0.22WL, while the matching line is close to 0.215WL. The 2:1 SWR passband runs between 270 and 330 MHz, a 60-MHz spread that should make home construction less critical.
The Yagi produces a modeled 12.58 dBi gain when the antenna reflectors are 1WL above average ground. The modeled beamwidth is 44°. Compare these values to the shorter quad values of 10.35 dBi and 58°. Anyone interested in either type of antenna can make the appropriate comparisons that weigh performance differences against construction complexity.
The Yagi and the helix are equivalent performers in terms of gain, while the shorter quad lags in performance while leading in simplicity. Regardless of the actual gain of each antenna in the field, we have another interest in the three antennas: the pattern shape and the sidelobe production.
The Yagi has a front-to-sidelobe ratio of about 16.6 dB. The corresponding ratio for the quad is about 14 dB. In contrast, the axial-mode helix has a front-to-sidelobe ratio of only 11.1 dB. Note the improvement of the sidelobe performance relative to the models over perfect ground. The elevated 10-turn helix shows a front-to-sidelobe ratio improvement of about 1.6 dB. Nevertheless, the helical antenna sidelobe structure bears watching. Equally important is the distribution of energy to the sides. For this purpose, I remodeled the helix (along with the quad and Yagi) in EZNEC Pro/4, since it provides pattern plots that distinguish the left-hand and right-hand circular polarization of any test antenna. Fig. 32 shows the plots for the three sample antennas.
Both the Yagi and quad show diminutive side lobes at low angles. The total energy in these sidelobes, as measured by the area they occupy, is quite small. In contrast, the higher-angle lobes of the helix occupy a broad front on each side of the main lobe. Hence, their sensitivity to signals and noise not associated with the communications target is considerably higher than the comparable sensitivity of the parasitic arrays.
In addition to having smaller sidelobes, both the quad and the Yagi show less reverse polarization energy as well. (Reciprocally, transmitted energy becomes receiving sensitivity.) Once past the 4-element stage, quads tend to require more boom length for a given gain, due to the increased coupling at the corners. Hence, the proper "rival" for the helix is the crossed-element Yagi, and its gain-to-boom-length ratio is virtually identical to that of the helix. If the Yagi's smaller sidelobes make a difference to communications quality, then it might make a better choice than the helix. If switching polarization is necessary, then the Yagi and the quad have an advantage over the helix, with its permanent spiral. With respect to gain, none of the models in this sample comparison squeeze the last fraction of a dB from the designs. Because the aim of this final section is only to show alternatives to the helix and their potential relative performance, I have omitted quad and Yagi dimensions.
Conclusion
I began this study because the available literature on axial-mode helical antennas seemed somewhat oblivious to matters other than the maximum potential gain. Pattern shape went largely ignored except in the context of a broadband antenna in the King and Wong treatment. Performance stability for the spot frequency applications that mark amateur use of these antennas also passed in relative silence. These notes have tried to focus on these aspects of helix performance by using a limited number of cases to establish some definite trends that apply to the home construction of axial-mode helices.
The net result has been to see that for most cases, it is unwise to try to derive the maximum gain of which a helix is capable by widening its base. Unstable source-impedance conditions and serious sidelobes develop before the antenna reaches the maximum gain size. In the end, a practical axial-mode helix has only the gain of a well-designed crossed-element Yagi of a similar boom length, and the Yagi tends to have smaller sidelobes and switchable polarization.
These results, of course, cannot contend with raw curiosity, which alone will lead many amateur antenna builders to construct helices. At most, these notes can temper enthusiasm with an appreciation of the limitations of the helix. It remains about the best high-gain broadband circularly polarized design available. However, to obtain the best from the design, one must attend to the costs and limits of the design as well as to its potentials.
Updated 10-20-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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