# Triangulating Bobtail Curtains

### L. B. Cebik, W4RNL

The bobtail curtain is a vertically polarized array used by many operators on the lowest amateur bands. Essentially a wire antenna, the array requires only 1/4 wavelength for the vertical portion of its elements plus safety clearance from the ground. Hence, it is shorter than most vertical antennas, but provides a very good bi-directional pattern at low elevation angles. This collection of notes has featured the bobtail curtain in several places. In the basic SCV series, see "Part 5: Shorties, Double-Wides, and Twins." As well, see "Voltage Feeding SCV Loop". You may also wish to explore "The 40-Meter Bobtail Curtain as An All-Band Wire Antenna.".

Recently, Ed Boutwell, W4ZSB, tried a promising arrangement on 20 meters: a triangle of bobtails. I translated the idea to 40 meters, where bobtails are more common and explored its properties in some details. These notes provide the results of that expedition into geometry. However, to provide enough background for those notes in this location, let's begin by reviewing some basic bobtail properties.

The Single Bobtail Curtain

The bobtail curtain is actually a set of 3 1/4 wavelength vertical elements that we top-feed in phase. Although developed earlier, the bobtail is an electrical outgrowth of the smaller half-square, a set of 2 vertical 1/4 wavelength elements that we also top-feed and phase-feed. Ideally, a half-square works best when the tops of each element have the same current magnitude and phase angle. A 1/2 wavelength horizontal wire between the two verticals provides the necessary phasing while the radiation from that connecting wire largely cancels itself, leaving only a bi-directional (mostly) vertically polarized radiation pattern broadside to the plane of the wires.

The bobtail curtain extends the half-square by adding a further half wavelength horizontal wire and a third vertical 1/4 wavelength wire. However, that change produces some interesting changes in the antenna's operation. Fig. 1 shows the outline of a bobtail curtain and indicates one of the major changes.

The total horizontal length of a bobtail is about 1 wavelength. We can call the antenna an SCV (self-contained vertical array) because its entire structure is above ground and it requires no ground-plane radial system to complete the antenna. As the diagram indicates, we feed the center vertical, and the horizontal phasing wires supply energy to the outer verticals. (The green dots in the diagram simply indicate the segmentation used for this particular model of a bobtail.) As a consequence of the feedpoint, the center vertical requires twice the current of each outer vertical. The relative current magnitude curves show the difference in current between the center and outer vertical in the binomial current distribution.

The diagram shows the feedpoint at the top of the center vertical. Actually, we may feed the element anywhere along its length. The top-most point may show an impedance that is under 50 Ohms, so we may wish to bring the feedpoint lower to match common coaxial cables. Alternatively, we may feed the vertical at its end using standard voltage-feeding techniques. We may even extend the center element to near ground level (but leave the outer verticals alone) to place the usual high-Z tank tuner more conveniently. In all cases, the current will be highest at the top of the center vertical element.

The current distribution curves also show the relative phase angle of the currents. The horizontal wires show the reversal of current phase that largely, but not completely, cancels the horizontal radiation component from the antenna. The curves on the end vs. center elements sometimes trouble viewers, who think that the elements may therefore be out of phase. However, the diagram does not show the voltage magnitude and phase along the wires. The simplest way to demonstrate that the bobtail elements are in phase with each other with respect to radiation is to compare what happens when we purposely reverse the phase of the outer verticals with respect to the center vertical.

The left side of Fig. 2 shows a typical bobtail patterns. It is the same pattern that we get when feeding 3 1/4 wavelength verticals in phase, with the center vertical fed twice the current of each outer vertical. If we phase the outer elements 180 degrees relative to the center vertical, then we obtain the pattern on the right, and the elements become an end-fire array. This is not the pattern that we derive from the bobtail with its single feedpoint.

I noted that the bobtail curtain horizontal wires largely but incompletely cancel the horizontal radiation component from the array. An array of 3 1/4 wavelength vertical would shows almost no horizontal radiation component--just enough to indicate the effects of the radiation being composed of both direct and ground-reflected components. If the bobtail could cancel all of the horizontal radiation, it would produce a similar set of components to its total field. However, see Fig. 3, which shows the components of the bobtail.

The brown vertical-component lines show a beamwidth that is somewhat narrower than the total field beamwidth. The difference emerges from the remnant horizontal component, shown in blue. The peak strength of the horizontal component is about 10 dB below the maximum gain level. Because the horizontal lobes are not broadside to the plane of the wires, they do not affect the maximum signal strength--only the beamwidth. In the broadside direction relative to the wire plane, the signal is virtually only vertically polarized.

One of the reasons why low-band operators favor the bobtail is its radiation pattern. The elevation pattern is the key. Let's place a dipole at 50' above ground for 40 meters. Let's also build a bobtail with the same top height. Fig. 4 overlays the elevation patterns of the two antennas in the specified places.

Admittedly, the dipole shows the higher maximum gain level. Indeed, a full wavelength wire (the same horizontal length as the bobtail) would show about 1.5-dB higher gain yet. However, note the elevation angle at which the dipole and its longer kin achieve maximum gain: well above 30 degrees. In contrast, the bobtail obtains maximum gain at considerable lower angles, usually below 20 degrees elevation. Since most long-distance ionospherically refracted signals are at angles below 20 degrees, the bobtail has an advantage. In addition, much (but not all) of the atmospheric noise comes from closer sources arriving at higher elevation angles. The dipole is far more sensitive to higher-angle radiation than the bobtail. As a consequence, bobtail users who have properly aimed their antennas to broadside target regions usually report better DX communications, not only with stronger signals, but as well with a better signal-to-noise ratio, especially on the lower HF bands.

Fig. 1 indicated a set of dimensions applicable to the bobtail. The dimensions include an overall horizontal (h) value, with half of h devoted to each side of the center vertical. The diagram also indicates a vertical dimension (v) for the length of the main radiators. Finally, the dimensions include a base height of the vertical bottoms above the terrain (ht). Let's see how these dimensions play out using the universal AWG #12 copper wire at the center of 40 meters (7.15 MHz).

In fact, there are two rough forms of the bobtail, one based on conventional general ideas and one based on optimizing the array for maximum gain. Table 1 provides the dimensions and the modeled performance of the bobtails over average ground (conductivity 0.005 S/m, permittivity 13).

```Table 1. Bobtail array dimensions and modeled performance
Version        h feet   v feet   ht feet   h wl     v wl     Gain dBi   TO angle    Beamwidth   Impedance
Conventional   124.8    38.0     12.0      0.907    0.276     4.90      18 deg      54 deg      42.8 + j3.4 Ohms
Maximum Gain   149.0    33.5     12.5      1.083    0.244     5.05      19 deg      50 deg      29.1 + j0.0 Ohms
```

The conventional version rests on using 1 wavelength as the measure of the total length and of each side of the array (center-vertical + horizontal-wire + end-vertical). Of course, the total length of each section rests in part on bringing the verticals to resonance. Hence, the length of each section is 1.006 wavelengths. Since each design has its own optimum height above ground, the conventional design shown has a top height of 50'. Actually, the base height is not too sensitive and +/- a foot or so will not affect performance. However, the feedpoint resistance does go down as the antenna height decreases. For the top-fed version shown, the impedance is adequate for a direct connection to common coaxial cables.

The maximum-gain versions rests on the empirical work of SM4CAN, which models have confirmed. We can slightly increase the bobtail maximum gain value by extending the value of h and shortening the values of v. The total section length does not significantly increase (1.030 wavelengths). However, for maximum gain, the base height goes down slightly and the shorter vertical sections leave the array top height at 46'. Due to the slight reduction in base height, the improved gain costs us about 1 degree in the elevation angle of maximum radiation. In most circumstances, the ordinary operator might not notice either change.

The maximum-gain design imposes one noticeable penalty: a significant reduction in the feedpoint resistance when using a top-feed method. In fact, most users of the SM4CAN-type bobtail use a high-voltage feed system, with the tank circuit close to ground. Since differences of impedance become a simple process of selecting the correct tapping points on the parallel tank circuit, the actual impedance at the junction of the center vertical with the horizontal wires becomes a matter of no concern.

There are slight differences in the patterns produced by the two bobtail versions, although once more, they are not likely to be significant in normal operation. Fig. 5 shows the differences.

The conventional design elevation pattern shows very slightly less sensitivity to very high-angle signals than does the maximum-gain version. As well, the conventional version shows a very deep null in line with the wires. In contrast, the longer maximum-gain design shows the beginnings of side lobes. These lobes are 25 dB below the level of the main lobes, and they are consistent with what happens when we set up independent in-phase-fed verticals. Perfect 1/2 wavelength spacing produces the cleanest pattern. However, we can squeeze a bit more gain from the set by widening the spacing slightly. The cost is the emergence of those same sidelobes. Eventually, as we further increase the spacing, the sidelobes grow to levels at which they steal significant energy from the main lobes, which become weaker. However, for small increases in length beyond exact 1/2 wavelength spacing, the lobes can emerge only at the expense of the beamwidth of the main lobes. Note that the beamwidth of the conventional design is almost 5 degrees wider than for the maximum-gain design.

It is now time to look at the idea of triangulating bobtail curtains. I would have had to provide most of the graphics and tabular information to use for comparison with the triangles. So the review of basic bobtail properties has seemed like a productive way to frame the data.

Bobtail Triangles

A bobtail feeds the center vertical, allowing the horizontal wire to act as a phase lines relative to the outer verticals. Suppose one wished to work in several directions and not just the pair created by a single bobtail curtain. The most compact installation might be a triangle in which the corner verticals performance multiple duties, depending on which of 3 center verticals would be active at any given moment.

In principle, by mental visualization only, the verticals at the center of the other two sides and the vertial at the far end across from the actively fed vertical would receive low current levels. As well, they are farther way from the fed vertical and at angles outside the plane formed by the basic bobtail. Would their presence be fatal to the scheme? Or would they somehow enhance the broadside patterns?

We can easily model the concept of a triangle of bobtails, using the same materials (AWG #12 copper wire) and frequency (7.15 MHz) that we used for the single bobtails. However, we have multiple possibilities that form a small matrix. In one direction, we have two slightly different bobtail designs. We should see if that difference is significant or not when we triangulate the system. In the other direction, we have two ways to handle the unused feedpoints. One way is to leave them open, and the other is to place a short across the unused feedpoint gaps. We obtain a shorted unused feedpoint in a model simply by removing the source from that wire. To create a genuine open circuit at the unused feedpoint, we need to add a very high resistance load. A resistance of 1e10 Ohms is satisfactory to achieve this goal.

Let's begin with the conventional bobtail design that uses the shorter horizontal lines and longer verticals. Table 2 shows the data for the system with the unused feedpoints both shorted and open. Note that the table gives two gain values, one for the direction toward the triangle apex ("apex") and one toward the flat side ("side") of the triangle. The difference of these values creates a small front-to-back ratio that is also listed in the table. In addition to the two value sets, I have included the data for a single bobtail of the same design dimensions.

```Table 2. Bobtail triangle modeled performance: convention design
Version             Apex Gain   Side Gain   TO angle   Front-Back Ratio    Beamwidth   Impedance
Single              4.90 dBi    4.90 dBi    18 deg     0.0 dB              54 deg      42.8 + j3.4 Ohms
Shorted Feedpoints  5.08        3.81        18         1.27                59          43.1 + j12.6
Open Feedpoints     5.19        4.52        17         0.67                58          46.5 + j1.0
```

The data show only slight variations between the properties of a single bobtail and the triangle. In both cases, the gain of the two lobes of the single bobtail falls about midway between the gain values for the triangles in each direction. The remaining differences show up better in the radiation patterns that appear in Fig. 6.

Both elevation patterns (representing shorted and open unused feedpoints) show a significant increase of the higher-angle sensitivity in the direction from the feedpoint to the opposite apex of the triangle. Compare these patterns to the elevation pattern in Fig. 5, which shows plots both bobtail designs. For the triangle, the azimuth patterns show greater balance between the two broadside lobes when the unused feedpoints are open relative to when they are closed. Regardless of how we handle the unused feedpoints, the triangular array shows increased radiation off the ends, compared to the deep side nulls of the conventional design azimuth pattern in Fig. 5.

Before we reach any conclusions about the performance of the bobtail in a triangle, let's perform the same set of modeling tests on the maximum-gain design. Table 3 provides the data.

```Table 3. Bobtail triangle modeled performance: maximum-gain design
Version             Apex Gain   Side Gain   TO angle   Front-Back Ratio    Beamwidth   Impedance
Single              5.05 dBi    5.05 dBi    19 deg     0.0 dB              50 deg      29.2 + j0.0 Ohms
Shorted Feedpoints  4.41        5.19        20         0.78                49          29.1 - j3.0
Open Feedpoints     4.59        5.39        19         0.80                48          28.5 - j0.7
```

As shown in the patterns in Fig. 7, the higher gain occurs away from the apex and toward the fed side of the triangle. Relative to the conventional design, the maximum-gain version shows less performance difference relative to the handling of the unused feedpoints. However, the azimuth patterns shows some differences that the simple numbers cannot reveal. With the feedpoints shorted, the maximum-gain design shows a much higher level of radiation in the plane of the active bobtail than with open unused feedpoints. In both cases, the small sidelobes that we saw in Fig. 5 for this type of bobtail curtain are clearly evident and not as insigificant.

The sensitivity to higher angle radiation occurs in the direction of the triangle apex. However, since this direction in the maximum-gain design is slightly weaker, the increase is less pronounced than in the conventional design.

We may account for many of the differences in performance among the various antennas by looking at the relative current magnitude distribution for each of the triangles. Fig. 8 provides some simple representations.

Although matters of scale do not permit magnifying the current along the horizontal wires, we can see indications of it on the wires beyond the active bobtail. This current level decreases with distance from the plane of the active bobtail, but is still sufficient to produce higher-angle radiation toward the apex of all of the models.

For each design type, the two current charts clearly show the difference between shorting and opening the unused feedpoints. With open feedpoints, the side center verticals are relatively inert. Hence, with open unused feedpoints, only the apex vertical contributes to the overall pattern formation. The exact magnitude and phase angle of the current on that vertical element is enough to tilt the pattern in one or the other direction. Remember that the apex vertical is closer to the active bobtail in the conventional design than it is in the maximum gain design. When the mid-side verticals are active, that is, when we short the unused feedpoints, we obtain somewhat different results in the two designs. In the conventional design, the active mid-side verticals contribute to a wide beamwidth in the apex direction, relative to the lobe in the opposite direction. In the maximum-gain design, the active mid-side verticals increase the radiation off the ends of the active bobtail plane.

Conclusion

If we wish to operate in many directions with a bobtail curtain, setting up a triangle is one way to proceed. We save the construction of 3 verticals relative to having 3 independent bobtails. As well, the performance differences relative to independent bobtails are functionally rather small and may well be acceptable. In fact, unless we had unlimited space, it is dubious whether we could avoid interaction among the elements of independent bobtails oriented in different directions.

Perhaps the key limitation of the bobtail curtain triangle is that we cannot cover the entire horizon. The beamwidth is simply too narrow (50-55 degrees) for 3 bi-directional arrays to achieve this goal. However, we may come close enough to satisfy our needs--at least until we need only a few more countries, all of which fall in the crevices between adjacent azimuth patterns.

My own interest in the array is neither to recommend nor to discommend its use. Rather, the interesting activity for me is to have seen what happens when we triangulate bobtail curtains.

Updated 03-24-2006. © 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.