Notes on Wide-Band Multi-Wire "Folded Dipoles"
Part 2: Some More Real Potentials

L. B. Cebik, W4RNL (SK)


In Part 1 of this exercise, I developed idealized models of multi-wire terminated wide-band antennas as a pathway to understanding better their performance. I replicated 2-, 3-, and 5-wire terminated arrays using idealized techniques of feeding the antennas and examining the free-space patterns taken broadside to the plane of the wires. The patterns were all tidy, and the data seemed to show improved performance as a. we increased the number of wires and b. we increased the spacing between the wires.

In this follow-up episode, we shall try to rectify some of the shortcomings of the initial models. For the 3- and 5-wire antennas, we shall reform the models into all-wire versions for comparison with the idealized models. We shall also explore both the broadside and edge-wise patterns to see if we can find any differences of note. One of our goals is to improve upon the partial and sometimes faulty understanding offered by Part 1. Another goal is to stress the need for a full exploration of alternative ways of forming models and of the complete data set offered by modeling programs before declaring the work complete.

One major departure from the models in Part 1 rests upon some of the data that we acquired. Although terminated wide-band antennas offer a good match when we use them at frequencies below the knee frequency, rapidly increasing losses to the terminating resistor render such operations marginal to useless. Therefore, I increased the antenna length to 250', the length needed to ensure that the antenna was electrically at least 1/2-wavelength at the lowest test frequency: 2 MHz. A simple doublet of this length shows considerable inductive reactance at a center feedpoint. Hence, we can be assured that the new models operate completely above the knee frequency. I also increased the wire size to AWG #10 on the premise that this size is a relatively wise selection for a 250' span of wire.

2-Wire Terminated Wide-Band Antennas

The traditional 2-wire terminated wide-band antenna is a good starting point for our work. It does not require special treatment for the feedpoint, since we may place the modeling source at the center of the unterminated wire. Hence, we shall have only 2 major concerns, both of which apply to the models in Part 1. First, we shall look at the effects of taking patterns edgewise to the wire plane instead of taking them broadside to the 2 wires. See Fig. 1 for an outline sketch of the two orientations.

Second, we shall review the effects of spacing the wires. We must increase the basic spacing in proportion to the scaling of the antenna that moved the knee from about 5.5 MHz down below 2 MHz. I shall employ a simple set of spacing values that will apply to all models in this part.

    Spacing Standards for This Exercise Set
Category Spacing Between Parallel Wires (Feet)
Narrow 1
Medium 5
Wide 15

Most wide-band terminated antennas use a spacing between wires that is 1' or less. I chose 1' because it allows a reasonable narrow space for versions of the models scaled for higher frequencies and shorter lengths. At the other end of the line, 15' is a little under 5 meters, the scaled value that emerges from the wide versions of the antennas in Part 1. (Compare 250:15 and 27.2:1.5) Of course, I rounded the new numbers for bookkeeping simplicity.

For the new antennas, I also selected a single value for the terminating resistors in all versions: 900 Ohms. This value is especially useful, since one might create it from a parallel combination of 3 2700-Ohm non-inductive resistors. As noted in Part 1, there are other techniques for creating the terminating resistor.

Regardless of spacing, the 250' 2-wire antenna shows a very usable 900-Ohm SWR curves from 2 to 30 MHz. Fig. 2 overlays the curves for the 3 spacing values. The SWR spikes occur at intervals a little under 4 MHz, since the antenna passes integral full-wavelengths (electrically) at those points. The narrow version shows a few peaks just above 2:1 in the upper part of the overall passband. However, both wider versions manage to remain below the standard limit. In fact, the widest version shows a declining curve with increasing frequency.

Note that the SWR reference impedance is the same as the value of the terminating resistor. This fact will become more interesting as we later look at the 3-wire and 5-wire antennas using the same 900-Ohm terminating resistor. For the moment, we may classify the SWR behavior of the 2-wire antenna--in any width--as quite well behaved.

The remaining question is whether the patterns are as well behaved as the SWR curve. In Part 1, we could not fairly evaluate this facet of performance because we took the patterns broadside to the plane of the two wires. In practice, at least the narrow versions of the antenna twist and turn in the wind and weather and hence may wash out any difference that we might find between edgewise and broadside behavior. However, the wider versions of the antenna would likely have a fixed non-twisting installation set-up. Most likely, that set-up would place all of the wires parallel to the ground. Hence, it will be useful to look at the edgewise performance.

The following brief table samples both the edgewise and broadside free-space gain values of the narrow, medium, and wide versions of the 250' 2-wire terminated antenna.

Free-Space Maximum Gain Values for 3 Versions of the 250' 2-Wire Wide-Band Antenna
Frequency 2 3 4 5 15
Maximum Gain (dBi) E/W B/S E/W B/S E/W B/S E/W B/S E/W B/S
Antenna
Narrow (1') -3.37 -3.45 -2.67 -2.74 -2.87 -2.88 -2.20 -2.32 1.61 1.47
F/B Ratio dB 0.16 0.13 0.01 0.23 0.29
Medium (5') -3.00 -3.30 -1.71 -1.94 -2.02 -2.08 -1.47 -1.96 2.12 1.98
F/B Ratio dB 0.61 0.49 0.16 1.08 0.48
Wide (15') -2.38 -3.03 -1.07 -1.47 -1.17 -1.53 -0.56 -1.97 3.28 2.20
F/B Ratio dB 1.45 1.01 1.07 3.65 4.50
Reference Doublet 2.08 2.77 3.93 4.99 5.39
Note: E/W = Edgewise; B/S = Broadside; F/B = Front-to-Back

Despite its brevity and incompleteness, the chart generally confirms the trend noted in Part 1: as we increase the spacing between the conductors of a 2-wire terminated antenna, the gain generally rises. The rise does not occur for all frequencies at every widening, as shown by the move from 5' to 15' at 5 MHz, if we look at the broadside gain value. Nevertheless, the general gain trend is upward with wider element spacing.

At the same time, sampling the edgewise gain values introduces a new dimension to 2-wire performance: a gain differential between the heading of maximum gain and a heading 180 degrees opposite. The chart calls this difference a front-to-back ratio. For narrow spacing, the differential is minuscule and operationally insignificant. Even at medium spacing (5' for a 250' antenna or 2%), only one of the listed values is potentially problematical. However, when the spacing reaches 15' (6%), the differential grows to troublesome proportions. At 15 MHz, the maximum gain in the favored direction is 3.28 dBi, but in the opposite direction the gain drops to -1.22 dBi. For modest front-to-back values, the front-to-back ratio is roughly twice the differential between the edgewise and the broadside gain. However, as we increase frequency and encounter higher differentials, the front-to-back ratio climbs at a faster rate. This phenomenon suggests that the pattern may undergo some serious distortion relative to the nearly perfect bi-directional patterns we expect from the narrow version of the antenna.

Fig. 3 provides a small demonstration by providing edgewise patterns for all three spacing values at 2, 5, and 15 MHz. In all cases, view the antenna as running up and down the page or graph. The right side of the pattern is the direction toward the feedpoint and away from the terminating resistor. The left side of the pattern is the direction toward the resistor and away from the source. The 2-MHz patterns show a classical figure-8 pattern with a growing lobe toward the feedpoint side as we increase spacing. In contrast, the 5-MHz patterns show their growth toward the terminating-resistor side of the antenna. In addition, note that the widest spacing yields a difference in pattern shape. What we would call the main lobe on the higher-gain side becomes weaker on the opposite side, and the side lobes grow in strength to equal it.

The 15-MHz plots show major distortions of the pattern established by the narrow version of the antenna. If you closely examine the medium-version pattern, you can see a very slight displacement of the lobes toward the higher-gain side of the antenna. When we reach the limits of our spacing exercise, the pattern is very seriously distorted relative to the narrow-spacing version. Moreover, we find extra lobes. Of course, the overall loop circumference at the widest spacing is about 5.5% longer than at the narrowest spacing. As well, the 15' end wires are 0.2 wavelength. At that spacing, the mutual coupling between wires does not form a single element, but acts somewhat like a distended loop antenna that is about 530' in total circumference--about 8 wavelengths overall.

The 2-wire terminated wide-band antenna is notorious for its low gain relative to a simple doublet. The table lists maximum gain values for the listed frequencies. The doublet's patterns as virtually identical in shape to those of the narrow version of the antenna, but the gain differentials for just the listed values range from about 4 dB to over 7 dB. Hence, the temptation to widen the spacing to obtain higher gain is strong. As shown in Fig. 2, the wider versions of the antenna sustain the SWR curves. However, before embarking upon the widening process, one must closely examine all patterns to determine if they will satisfy the needs of the application for the revised antenna. For general skip communications, the medium (5') version might fulfill the need, although the gain increment is marginal relative to the increased complexity of construction.

3-Wire Terminated Wide-Band Antennas

The 3-wire terminated wide-band antenna is especially interesting by virtue of its symmetry. Two outer wires, equally spaced from the center wire that contains the terminating resistor, are fed in parallel. The balanced layout results in a symmetrical edgewise pattern. From this perspective, the 3-wire array eliminates the front-to-back problem that appears in wider versions of the 2-wire antenna. However, effectively modeling the 3-wire version of the wide-band antenna presents challenges. Fig. 4 outlines 2 ways to proceed with the modeling.

The modeling scheme on the left uses the NEC transmission-line (TL) facility to create near-zero-length lossless leads to a remote source wire. I used this method of modeling in Part 1 as an initial assessment of the potentials for the antenna. For this exercise, I replicated the system with the 250' long 3-wire antenna, creating 3 variations. The narrow version uses a spacing of 1' between wires for an overall antenna width of 2'. The medium version uses 5' spacing for a total width of 10'. The wide version uses 15' spacing and results in a 30' maximum antenna width. Nevertheless, the leads from the wires to the combined parallel source remain very short electrically. Fig. 5 overlays the SWR curves for the 3 versions of the 3-wire antenna.

The idealized model provides very well-behaved SWR curves for all 3 versions of the antenna. Note that the reference impedance is 450 Ohms, half the value used for the 2-wire antenna and half the value of the 900-Ohm terminating resistor. We obtained similar SWR curves in Part 1 with the shorter 27.2-m (89') 3-wire antenna.

Although useful as a preliminary modeling venture, the idealized model does not represent structural reality for any of the 3 versions of the 3-wire antenna. For parallel feeding of the antenna, we must use wires that reach from the outer element center to a common feedpoint. Therefore, I remodeled the antenna according to the right-hand sketch. The limitation of this modeling method is the need for the center or source wire to equal in length a segment on the outer wire and for the segments on the connecting wires to be as equal in length as feasible to the other segment lengths. These requirements are not always well met, but the resulting models are adequate enough to detect general departures from the idealized model.

Fig. 6 shows the overlaid 450-Ohm SWR curves for the revised model. The all-wire model suggests that the narrow version of the array is usable above 28 MHz before the SWR seriously exceeds 2:1. (We shall not consider impedance transformation losses and cable losses that might show a lower SWR at the operating position.) The medium version begins to show serious SWR excursions from about 22 MHz upward. The widest version starts to exceed the 2:1 SWR standard at about 15 MHz. These curves are based on a feedpoint 1' below the terminating resistor and may vary in detail with different positions. As well, the exact structure of the feed segment and the connecting wires may further alter the curves. Nevertheless, we can see that the idealized model gives us too optimistic a portrait of the SWR behavior of the 3-wire wide-band array.

The picture is not necessarily bleak, however. Many applications for a antenna of this sort do not require full spectrum coverage. As well, numerous receiving applications may use relaxed SWR standards, perhaps up to 3:1 relative to the reference impedance. So the 3-wire antenna remains a viable alternative to the 2-wire wide-band antenna, while offering freedom from the front-to-back differential that besets wider versions of the 2-wire array. The questions is whether the promise of higher gain will justify the more complex 3-wire array. As a sampling, I have set up a table similar to the one used for the 2-wire array.

Free-Space Maximum Gain Values for 3 Versions of the 250' 3-Wire Wide-Band Antenna
Frequency 2 3 4 5 15 30
Maximum Gain (dBi) E/W B/S E/W B/S E/W B/S E/W B/S E/W B/S E/W B/S
Antenna
Narrow (1') -0.26 -0.26 -0.96 -0.96 -1.35 -1.34 0.00 0.01 2.85 2.92 6.46 6.53
Medium (5') -0.92 -0.91 -0.65 -0.65 -0.81 -0.76 -0.07 0.03 2.66 2.98 4.93 5.50
Wide (15') -0.80 -0.67 -0.24 0.02 -0.23 0.24 -0.68 0.15 1.49 4.14 2.69 6.76
Reference Doublet 2.08 2.77 3.93 4.99 5.39 8.11
Note: E/W = Edgewise; B/S = Broadside

In virtually every sampled case, the 3-wire gain exceeds the 2-wire gain, and often by a significant margin. The rough average of the gain differential between the 3-wire narrow antenna and the doublet is about 3 dB, just over half the deficit shown by the 2-wire array. From a raw gain perspective, the 3-wire array is attractive for applications committed to a wide-band terminated antenna.

However, the 3-wire array is not immune to pattern distortion. One form is evident from the tabulated data. As we widen the spacing between wires and increase frequency, the broadside gain shows ever-larger values relative to the edgewise gain. The differential likely makes no great difference up through medium spacing. However, the wide-space version shows well over a 1-dB differential from the frequency mid-range upward. Note that the differential shows itself most vividly in the frequency region in which the wide-space version shows the largest SWR excursions. As well, the tabulated data does not show a clear gain advantage over medium and narrow spacing.

A second form of pattern distortion appears in the wide version of the array within the upper frequency edgewise patterns themselves. Fig. 7 shows the 15-MHz patterns for both the broadside and edgewise planes of the wide version of the antenna. For the edgewise pattern, visualize the antenna as extending vertically within the plot. For the broadside pattern, orient the antenna horizontally with respect to the graph. On the right side of the figure are the patterns for the narrow version of the antenna. These plots follow the form of a single-wire doublet, but at lesser strength. The broadside pattern for the wide version of the antenna almost replicates the pattern for the narrow 3-wire antenna. However, the edgewise pattern for the wide version is significantly different. As well, the tabulated data shows this pattern to be not only weaker than the broadside pattern, but also weaker than the edgewise pattern for the medium and narrow versions of the array.

To establish that the 15-MHz pattern is not an isolated instance of more severe pattern distortion, Fig. 8 shows the patterns for 30 MHz, using the same format. Once more, the patterns for the narrow antenna show little, if any, difference between broadside and edgewise views. However, the wide antenna shows changes to both patterns. The broadside patterns shows a widening and shrinking of the peak values of the minor lobes. The edgewise pattern shows the opposite development, although some careful observation is necessary to see it. In the narrow edgewise pattern, careful scrutiny will show some very tiny minor lobes between the larger minor lobes--almost invisible without either a table of radiation pattern values or a gross enlargement of the pattern. In the edgewise pattern for the wide antenna, those lobes have grown to equal size with the other minor lobes to form a large and complex set of lobes.

Unlike the 2-wire wide-band terminated antenna, which showed a significant improvement of gain as we widened the space between wires, the 3-wire array does not show the same gain development when we model it using an all-wire configuration. Rather, we find the relative gain values of the 3 widths simply to vary across the spectrum. In some cases, the narrow version yields the highest gain; in others, it does not. When we add to this gain variability the fact that only the narrow version promises a stable SWR curve across the entire operating spectrum, we begin to approach a conclusion. Add in the absence of significant pattern distortion and a relative simplicity of construction and the conclusion becomes more solid. In a 3-wire wide-band array, the narrow version has perhaps the most potential of the 3 widths for actual use.

The narrow 3-wire array holds the promise of higher gain by a significant margin over the 2-wire array, although the actual gain margin will change from one frequency to the next. However, even the 3-wire array falls significantly short of the gain offered by a single wire doublet that uses no termination. In amateur radio service, where the use of parallel transmission line and a wide-range antenna tuner in the shack may serve very well to handle frequency changes, the single-wire doublet is still the antenna of choice. For short-wave reception--especially in Europe, where overloading signals are common--the 2-wire terminated system may be the antenna of choice, since the overall signal reduction may prevent or at least ease receiver overload and resultant spurious products. Only where a system needs both to transmit as well as receive and to be able to change frequencies without any equipment retuning does the 3-wire system come into its own--so long as there is excess receiving gain to compensate for the loss of sensitivity and there is excess power available to make up for the losses within the terminating resistor.

5-Wire Terminated Wide-Band Antennas

The 5-wire terminated wide-band antenna showed great promise of better approaching the level of gain performance achieved by the simple single-wire doublet while providing a possibly usable SWR curve. Of course, like all of the antennas in our survey, the initial models checked only the broadside free-space patterns and used the idealized model for initial checks. The leftmost part of Fig. 9 shows the end view of that modeling scheme.

Converted to the scale used in this exercise, the antenna is now 250' long and has a total width of 4' for the narrow version, 20' for the medium type, and 60' for the widest version, using parallel wire spacing of 1', 5', and 15', respectively. In addition, we shall orient the antenna so that the edgewise view is parallel to the ground, although we shall take interest in the differential between the edgewise and broadside patterns in free space.

The antenna uses a 900-Ohm terminating resistor, the same value as used in all of the other wide-band antennas in this exercise. The required SWR reference impedance turns out to be 300 Ohms for all variations on the 5-wire antenna. We may note in passing that the decrease in the required SWR reference impedance undergoes a regular progression in its descent as we add wires to the array.

Fig. 10 reviews the 2-30-MHz SWR curves for the narrow, medium, and wide versions of the 5-wire array. Even under the idealized feed conditions with near-zero-length leads for the parallel-connected wires, the SWR curve is somewhat limited. The narrow antenna provides the best curve, although the SWR is somewhat high at the low end of the operating spectrum. As we increase spacing, the curve improves at the lowest frequencies, but the wide version appears to be usable only up to the middle of the spectrum (about 16 MHz).

We may proceed in two general ways to create all-wire models with more realistic feed systems. The center sketch in Fig. 9 shows a 2-lead version (A). Wires extend from the inner fed element to the central feedpoint 1' below the terminating resistor. The outer elements simply connect to the inner elements to complete the overall feed system. In effect, the outer elements acquire extra length compared to the inner wires, with another increment of length added at the far end of the wires. Fig. 11 shows the resulting SWR curves for the 3 antenna widths.

Note that the SWR curves begin to gyrate widely, and somewhat wildly for the widest version. In common, the curves show increasingly high peak SWR values as we raise the operating frequency. The narrow version of the array is the only one usable for most of the operating spectrum, but only if we relax the 2:1 SWR limit standard.

As an alternative, I modeled the arrays with separate leads from each fed wire to the common feedpoint. The right-most sketch in Fig. 9 shows the general outline of the 4-lead model (B). The question was whether this feed system would alter the SWR curves relative to the 2-lead model. Fig. 12 shows the results of the trials.

Clearly, we do not gain anything by using the alternative feed method. Although the details differ in terms of the exact frequencies and values for SWR peaks, only the narrow version of the 5-wire antenna shows potential for extended frequency use. The medium-width version of the antenna is again usable up to about the middle of the spectrum, and the wide version shows a rapid decay of good SWR performance above about 7 MHz. Varying the reference impedance does not alter the performance significantly. The key problem in all versions of the 5-wire array is the presence of very significant reactance levels at most frequencies.

Despite the initial optimism offered by the idealized model in terms of developing a 5-wire wide-band antenna, remodeling the array more realistically with wire leads to the center feedpoint presents serious obstacles to further development. Only the narrow version of the antenna has a bandwidth potential resembling the curves that we obtained for the 2-wire and 3-wire antennas--and then only if we relax the SWR standard. However, one feature that gave the basic idea of a 5-wire array its allure was the potential for significantly higher gain than either of the smaller antennas. Despite the SWR problems, we should explore this facet of the antenna. The following table of sample values parallels the one for the 3-wire antenna to provide for direct comparisons. As we did when checking maximum gain for the 3-wire antenna, we shall provide gain values for both the edgewise and broadside planes relative to the antenna. In addition, we shall examine values for both the 2-lead and the 4-lead versions of the array.

Free-Space Maximum Gain Values for 3 Versions of the 250' 5-Wire Wide-Band Antenna
Frequency 2 3 4 5 15 30
Maximum Gain (dBi) E/W B/S E/W B/S E/W B/S E/W B/S E/W B/S E/W B/S
2-Lead Antenna
Narrow (1') 1.59 1.59 0.28 0.28 -0.16 -0.14 1.72 1.74 3.74 3.83 7.14 7.29
Medium (5') 0.93 0.97 0.73 0.82 0.73 0.90 1.56 1.85 3.33 4.19 5.46 6.56
Wide (15') 0.84 1.19 0.92 1.71 1.07 2.60 -0.42 2.50 0.79 6.92 4.93 -0.22
4-Lead Antenna
Narrow (1') 1.44 1.44 0.36 0.37 0.03 0.04 1.74 1.76 3.81 3.91 7.02 7.16
Medium (5') 0.81 0.85 0.53 0.62 0.56 0.73 1.46 1.75 2.54 3.36 4.17 0.78
Wide (15') 0.76 1.11 0.71 1.50 0.94 2.47 -0.42 2.55 1.54 8.82 5.11 -0.71
Reference Doublet 2.08 2.77 3.93 4.99 5.39 8.11
Note: E/W = Edgewise; B/S = Broadside

As expected, the wider the array and the higher the operating frequency, the greater differential that we find between edgewise and broadside maximum free-space gain values. In general, there is no significant difference between the gain behavior of the 2-lead and 4-lead versions of the 5-wire antenna. Both narrow versions show a good coincidence between the edgewise and broadside gain values. However, as we widen the antenna, the upper spectrum values actually show a decline relative to the narrow version of the antenna. As well, the differentials grow to considerable proportions, with one value set showing a 7-dB differential. Initially, then, the first order conclusion might be that only the narrow version of the array holds potential for wide frequency use. Interestingly, this conclusion from free-space gain data coincides with the conclusion suggested by the SWR data.

The sampled gain values reveal another interesting pattern to antenna performance. Let's overlay a few patterns for the single-wire reference doublet and the 5-wire narrow antenna, using the 2-lead version. However, let's examine both the free-space values and the values 75' above average ground (conductivity 0.005 S/M, permittivity 13). Additionally, we shall restrict the frequency range to extend from 2 to 6 MHz. This last measure operates on the premise that not all applications of wide-band antennas require coverage of the entire HF spectrum. Instead, some operational needs require no-tune operation of some part of the spectrum. Fig. 13 provides the SWR curves for the 5-wire array using the 300-Ohm standard and for the single-wire doublet using a 75-Ohm standard.

The antenna height (75') is only a small fraction of a wavelength at the lower end of the spectrum. Hence, we find deterioration of the SWR curve for both antennas relative to the free-space model. The doublet curves clearly show that the antenna is longer than 1/2 wavelength at the lowest operating frequency. As well, the doublet curves show the need for extesive impedance matching efforts as we change frequency. Although the 5-wire SWR curves are not perfect, they present far less of a matching challenge to 300 Ohms (and from that value down to a coaxial cable value via a wide-band impedance transformer).

Now let's compare the maximum gain values, letting ground-reflection phenomena settle any remnant differential between edgewise and broadside gain values that we encountered in free space. The following table tracks doublet and 5-wire narrow values every half-MHz for our reduced operating spectrum.

Maximum Gain values for a Single-Wire Doublet and a 5-Wire 2-Lead Narrow Array 75' above Average Ground
Single Wire Doublet
Frequency 2 2.5 3 3.5 4 4.5 5 5.5 6
Maximum Gain (dBi) 6.84 7.07 7.09 7.30 7.87 8.73 9.42 8.09 7.64
Elevation Angle 90 90 71 55 48 41 36 33 28
5-Wire 2-Lead Wide-Band Antenna
Frequency 2 2.5 3 3.5 4 4.5 5 5.5 6
Maximum Gain (dBi) 6.22 5.77 4.53 3.95 4.19 5.20 6.51 6.11 7.53
Elevation Angle 90 90 72 56 47 41 36 33 29

The table shows that at the low and high ends of the restricted operating range, the gain values for the 5-wire array virtually match those of the single-wire doublet. At the center of the range, from 3.5 to 4.5 MHz, we find the greatest difference in values, with a 3.5-dB deficit. Fig. 14 provides a few sample patterns for both antennas, overlaid to show the degree of coincidence or difference.

Once the antenna passes the 1.25-wavelength mark in electrical length, it of course results in a pattern where the main lobes are no longer broadside to the wire, as shown by the 6-MHz pattern. However, we may also view a more fundamental correlation by jointly examining Fig. 13 and Fig. 14 (or the table). The doublet 75-Ohm SWR values--and hence, the general level of the feedpoint impedance--are lowest at or near those frequencies for which the 5-wire array shows a gain level that most closely matches the doublet's gain. When the parallel combination of fed wires in the wide-band antenna would present a very low impedance, the terminating resistor absorbs (and dissipates) the least energy, resulting in the highest gain. When the resistor value is low relative to the feedpoint impedance without it, the resistor handles a proportionately higher percentage of the power, leaving less for radiation. This theory of operation applies to all multi-wire wide-band antennas using a terminating resistor. The 5-wire version of the antenna simply makes the process more graphically apparent.

With a restricted operating range, the antenna models make apparent the danger of simply taking an average value of gain deficit of a wide-band antenna relative to a doublet. The more pressing question facing a design engineer is whether the worst-case deficit falls above or below the level of acceptability relative to the intended application.

Since we have explored the difference between the SWR curves for the 5-wire, 2-lead antenna over a limited range, we might also explore whether the differences apply to other parts of the overall operating spectrum. Fig. 15 shows the comparative plots for the narrow 2-wire wide-band antenna. The antenna is 75' above average ground for all comparisons. As the plots show, the SWR curves diverge until about 9 MHz. At that frequency, the antenna is about 0.7 wavelength above ground. Below that frequency, we find small differences in the curves that likely would not create any operational problems.

In Fig. 16, the graph compares SWR curves for free-space and over-ground versions of the narrow 3-wire wide-band antenna. The curves overlay each other very well down to just below 10 MHz. Again, the 0.7-wavelength (or perhaps the 0.75-wavelength) height marks the beginning of SWR curve divergence. Note that in this case, the modeled over-ground value for the all-wire antenna just exceeds 2:1 at 2 MHz. The actual test measurement for the antenna under these conditions would depend upon impedance transformation and line losses, as well as construction variables relative to the model.

Fig. 17 expands the narrow 5-wire, 2-lead SWR curves shown in Fig. 13 to encompass the entire potential operating spectrum. Once more, the free-space and over-ground curves track each other very well from about 9.5- to 10-MHz and upward. Below the transition frequency area, the curves diverge, with the over-ground curve showing a higher SWR value at the lowest frequency in the spectrum covered. Lengthening the antenna might well move the SWR from 2 to 6 MHz below 2:1, but at the same time, it would reduce the frequency span over which we can obtain bi-directional patterns. The relative importance of each factor is an application-specific determination.

Construction Variables

The sensitivity of the multi-wire terminated antenna arrays to changes in width relative to various performance characteristics suggests that these notes inevitably fall far short of covering all possible design variations. However, length and width are not the only variables available for alteration. One significant variable may escape attention. The all-wire models place the common feedpoint 1' below the terminating resistor and its element wire. We may vary that placement and see what might happen. To test the matter, I created a very narrow version of the 3-wire (all-wire) antenna using a spacing of 0.5' between wires. Then I set the feedpoint 1, 2, and 3 feet below the antenna, using a free-space model. The key question in this exercise focused on the effects of the 3 placements on the SWR curve. Fig. 18 shows the results.

The very narrow version of the 3-wire array shows the most acceptable SWR curve with the common feedpoint 3' below the terminating resistor wire, the limit of this particular exercise. The 450-Ohm SWR does not exceed 2:1 until the operating frequency reaches 29 MHz, and then not by much. To see whether the phenomenon is unique to the very narrow spacing or more general, I repeated the test using the standard narrow 3-wire spacing (1'). The results appear in Fig. 19.

The results for the standard narrow spaced 3-wire array are less dramatic. The closest feedpoint spacing shows the widest excursions of SWR--both high and low--for most of the operating range. The widest feedpoint spacing appears to improve SWR performance in the upper range, but not to the degree possible with very narrow spacing.

Wide-band terminating-resistor arrays are subject to many construction variables, and these simple exercises provide only a sample. However, they do show that we cannot assume that any particular variable is either significant or insignificant until we examine it in detail.

Conclusion

At the end of Part 1, based on a limited exploration of terminated antenna properties, I reached a set of conclusions. We may now assess how well each holds up and what qualifiers we may have to place on some of them.

1. All terminated wide-band "folded dipoles" have knee frequencies, below which the gain drops very rapidly. The recommended operating range for any of the antennas is from an electrical length of about 1/2 wavelength upward in frequency.

The first conclusion remains correct, although we by-passed testing it in this exercise by using an antenna that was longer than the critical minimum length at the lowest test frequency.

2. As we add more fed wires to a terminated antenna, we increase its average gain over the operating spectrum. The gain increase never quite reaches the level of a single-wire doublet.

We must heavily qualify this statement. Although the average gain of the 3-wire array exceeds the average gain of the 2-wire version, and the 5-wire average gain is higher still, average gain may not be the key factor in making design decisions. The gain will be highest wherever the equivalent doublet length shows the lowest impedance. However, we must keep a sharp eye out for the lowest gain levels within a proposed operating span to determine if the gain at critical frequencies is high enough for the proposed communications application. We may examine that gain as an intrinsic value or as a deficit relative to the single-wire doublet, depending on the frame of reference.

3. As we add more wires to a terminated wide-band antenna, the center or reference SWR impedance decreases both intrinsically and with respect to the value of the terminating resistor.

Our extended exercises actually provided a bit more precision to this statement by standardizing the terminating resistor at 900 Ohms and watching the required SWR reference impedance. The criteria for setting the SWR reference impedance are not precise, since the setting requires a judgment call as to what counts as the smoothest obtainable SWR curve over a given operating region. Nevertheless, the 2-wire array showed its best curves when the SWR reference impedance matched the value of the terminating resistor. The 3-wire array gave the best results when the SWR reference impedance was 1/2 the value of the terminating resistor. With the 5-wire arrays, the best reference impedance was 1/3 the value of the terminating resistor.

4. 2- and 3-wire terminated wide-band arrays show stable SWR curves through their operating ranges. However, adding further wires tends to produces curves with greater SWR excursions relative to the reference impedance.

Once we modified the 3-wire and 5-wire antennas to provide all-wire model construction, the stability of even the 3-wire curves began to slip badly as we widened the array. The SWR performance for the 3-wire array showed wide SWR swings in the wide version. The 5-wire all-wire model strongly suggested that it was useful only over restricted frequency ranges, and then only in the narrow version.

5. Terminated wide-band antennas show increased gain by widening the distance between wires. Spacing adjustments may require revision of the optimal terminating resistor value and the reference SWR impedance.

The final conclusion in the series requires the greatest modification. The initial models registered gain as a function of free-space patterns broadside to the plane of the wires. Hence, they could not show the growing differential of edgewise and broadside gain as we increased the spacing between wires. Our exploration of the 5-wire models in this extended exercise shows that the net gain of a wide model may not always exceed that of a narrow model. Moreover, the existence of any differential at all makes a strong recommendation for modeling a proposed design over ground at the anticipated height of actual use. At the low end of the operating range, we may fairly gauge the effects of the mounting height and soil type on the SWR performance. As we move up the spectrum, the gain differentials increase, and modeling over ground allows us to arrive at a single gain value, whether we handle it independently or in comparison to the single-wire doublet that the wide-band antenna ostensibly replaces.

To the list of conclusion derived from Part 1 and modified here, we may add a new one.

6. Due to the many construction variations possible with a multi-wire wide-band terminated antenna, range testing at the anticipated use height and over the anticipated ground quality is an essential ingredient in the development of a successful antenna.

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