Wide-Band 40-Meter Yagis
Part 3: A 3-Element Wire Design

L. B. Cebik, W4RNL (SK)


At the end of Part 2 in this series, we introduced a 3-element Yagi beam that used phased drivers and a single director to provide reasonably good performance on 40 meters. Fig. 1 shows the general outline.

The phased-driver and director system offers a number of advantages over other designs.

Fig. 2 graphically summarizes the beam's performance, with selected numerical data in Table 1.

Table 1.  Dimensions of the 3-Element Wide-Band Yagi with Phased Drivers

Note: All dimensions are in inches. Multiply by 2.54 for centimeters,
0.0254 for meters.

Antenna Element Spacing Half-Length Tip Length
3-Element Rear Driver 0 432 46
Forward Driver 98 401 15
Director 275 393 7
Performance

Frequency Free-Space Front-Back Feedpoint Z 50-Ohm
MHz Gain dBi Ratio dB R +/- jX Ohms SWR
7.0 6.13 13.56 38.2 + j 5.5 1.35
7.15 6.57 15.30 48.4 + j 1.8 1.05
7.3 7.05 13.49 45.2 - j 15.2 1.40

Like all Yagis with directors, the beam shows a rising gain curve with increased operating frequency. The front-to-back ratio peaks near the band center with roughly equal values at the band edges. The phased drivers require no matching system for compatibility with a standard 50-Ohm coaxial cable feedline (although a common-mode attenuation device is always in order).

The dimensions for the beam presume a very husky aluminum tubing taper schedule. The two driver elements require insulation and isolation from the boom for the feedline and phase line connections. Hence, the gap insulation structure and the mechanical boom connections demand special attention to ensure strength. Even within the genre of tubing-based 40-meter full size beams, the addition of a third element represents major increases in beam weight and wind loading. Still, the boom stress and the wind loading are not as high as would be the case for a wide-band standard 3-element design with its much longer boom.

Full-size heavy Yagis with all of the required supporting mechanisms and structures lie beyond the capabilities of a very large number of amateurs. Many members of the excluded group would be happy with a fixed position beam composed of wire. However, obtaining very wide-band performance requires considerable real estate, especially since single-wire element designs cannot match the performance of fat-element tubular designs. Hence, wire-beam designers often add elements or use very wide element spacing to obtain good results across the entire 40-meter band (as defined for the U.S., that is, from 7.0 to 7.3 MHz).

So we have an unanswered question: can the 3-element phased-driver design undergo adaptation to the needs of the fixed-position wire-beam user? The answer is affirmative, if we are willing to make only a small set of concessions.

The 3-Element Phased-Driver-Director Yagi in Wire Form

Adapting a Yagi design intended for use with aluminum tubing in a complex taper schedule to a uniform wire size requires multiple steps. There is no absolute order to them, but a good first effort is to find the uniform-diameter length and diameter for the elements in the original design. One may use either the facility within a modeling program or an external calculator (program or spreadsheet) to arrive at the values. For the 3-element beam described above, we find the following equivalent uniform-diameter elements:

When we use an invariant set of diameter sets for all elements and vary only the length of the outer tip, the diameter value progression is not unusual. The longer rear element tip results in a smaller equivalent uniform diameter than we find for the director with its shorter tip section. Nevertheless, the variation in diameters is less significant in this case than the fact that all three diameters are nearly 1.5".

The most commonly used antenna wire size is AWG #12. With a diameter of 0.0808", this wire is only about 0.05 of the tubular element diameter. Such a small-diameter wire has two consequences of special import in this context. One is the fact that the mutual coupling between adjacent elements is much less than for the tubular elements. The phased drivers are just as dependent upon mutual coupling (in conjunctions with the phase line between them) as are the director and the drivers in a conventional parasitic arrangement. Therefore, a single-wire element set would require very significant compression of the element spacing, as well as adjustments to the element lengths to arrive at a working beam of the current design.

The second consequence is that the small diameter wire will result in a shrinking operating bandwidth that includes gain and front-to-back ratio as well as SWR. One of the goals of the adaptation is to see how much of the large-element performance we can preserve using wire elements. The single-wire route is not promising.

We can simulate larger diameter wires by using multiple wires in each element. We need not resort to cages, since we can approximate the full tubular element diameter with a 2-wire pair using a spacing of about 3" or so. While 3" spacing is feasible, we might also try closer spacing and see how a commonly available material might work. For example, we can purchase open-wire transmission line (ladder line) composed of AWG #12 conductors and about a 1" spacing. The rough equivalent single-wire diameter would be about 1/2". Fig. 3 provides an outline of how we would use the line for the elements in the beam.

The two drivers require a center insulator to provide a gap between element halves. The 50-Ohm cable connects to the forward driver. The 250-Ohm phase line with a single half twist runs between the forward and the rear drivers. For a wire beam, one should use home-built line. Table 2 provides dimensions for 250-Ohm lines using various wire diameters.

Table 2. 250-Ohm open-wire transmission line dimensions
AWG Wire Size Wire Diameter Center-to-Center Spacing
#14 0.0641" 0.262"
#12 0.0808" 0.330"
#10 0.1019" 0.416"
#8 0.1285" 0.525"

You will need spacers about every 3" to maintain the wire spacing accurately. The best way to make spacers is to drill the wire holes in a long strip of polycarbonate, Plexiglas, or similar plastic. Cut the spacers to size after you complete the drilling. Do not make the holes too large; you want a tight fit. A drop of one of the superglues at each hole will lock the spacers in place. The velocity factor of this phase-line will be very close to 1.0. You will need just under 8' of the phase line.

You can construct the ladder-line elements in a similar manner, or you can purchase commercial ladder line if the conductors are hard-drawn copper. Using this type of material, the required dimensions with both length and spacing adjustments appear in Table 3. Both drivers are slightly longer than the uniform-diameter equivalent lengths, as fits the smaller equivalent diameter of the ladder-line elements. To compensate for the reduced mutual coupling, the spacing between the drivers shrinks by 5". The director is considerably longer than the uniform-diameter equivalent and about 10" closer to the driver set. The resulting "boom" length is a total of 260", about 15" shorter than the boom length of the tubular version of the beam.

The selected data in Table 3 and the graphs in Fig. 4 show that some compromises are at work in preserving as much performance as possible. The resistance, reactance, and SWR data show that the minimum SWR is not quite as ideal as in the tubular version, although the maximum SWR remains below 1.5:1 across the band. It is possible to tweak the dimensions further. For example, reducing the director spacing from the drivers will increase the gain and front-to-back slightly, but at the cost of the broad SWR curve.

Table 3.  Dimensions of the 3-Element Wide-Band Wire Yagi with Phased Drivers

Note: All dimensions are in inches. Multiply by 2.54 for centimeters,
0.0254 for meters.

Antenna Element Spacing Half-Length Full Length
3-Element Rear Driver 0 403 806
Forward Driver 93 379 758
Director 260 377 754
Performance

Frequency Free-Space Front-Back Feedpoint Z 50-Ohm
MHz Gain dBi Ratio dB R +/- jX Ohms SWR
7.0 5.92 12.89 35.8 + j 4.0 1.42
7.15 6.42 15.48 50.9 + j 5.2 1.11
7.3 6.97 13.22 54.5 - j 20.0 1.48

The average gain across 40 meters for the wire version of the antenna is about 0.15 dB less than for the very heavy tubular array. The band-edge front-to-back ratio declines by about a half-dB. One could not detect these amounts in operations for beams at the same height. A comparison of the E-plane pattern shapes at the bottom of Fig. 2 and of Fig. 4 shows that the ladder-line version of the antenna preserves the beam width of the forward lobe and the rear lobe shape across the band.

On this basis, one may judge the ladder-line elements to be a successful adaptation of the original design. Of course, there are no rules against constructing one's own wider 2-wire elements. Every increase in wire spacing will improve the operating bandwidth of the array. However, the task is somewhat daunting, since the elements require a total of about 2400" (200') of 2-wire element line. As well, widening the spacing between wires in the elements will require adjustments to the element lengths and spacing values. In most cases, the adjusted values will fall between the values for the tubular beam and those for the ladder-line version.

Installation and Expectations

Installing a wire Yagi or other flattop array of any sort involves establishing 4 corner vertical supports and then developing a perimeter rope assembly to hold the elements both at the desired height and also in relationship to each other. Fig. 5 sketches the barest outline of such a system. Actual systems will be as varied as the installation sites.

The vertical posts can be anything that is tall and sturdy. In some areas, trees are plentiful. The distance from the tree to the array corner may vary at each corner so long as the installer adjusts overall tension to hold the wires in the correct position. One may also use existing towers for upper-HF beams. Other arrangements are possible. Stresses in the direction of the beam are generally less critical within the limits of strength of the non-conductive ropes used. However, the stress along each element should be sufficient to prevent undue catenary sag without pressing the limits of the wire strength.

The feedpoint at the forward driver deserves extra thought for support. The coaxial cable feedline and any common-mode attenuator tend to be heavy compared to other portions of the beam. Adding a vertical post beneath the feedpoint to minimize the unsupported cable run is one way to minimize the stress.

Most 40-meter beams will serve at lower heights--as measured in fractions of a wavelength--than upper HF beams. This fact will be true regardless of the beam construction. The rule of height ("the higher, the better") remains in effect at 40 meters. Fig. 6 overlays the elevation patterns for the 40-meter 3-element Yagi at 35', 70', 105', and 140'. The last height is about 1/2 wavelength. The patterns show the lowering of the lowest lobe as the height increases, thus improving low-angle long-distance skip transmission and reception.

The use of phased drivers does not wholly eliminate the effects of ground on the feedpoint impedance. However, it does minimize them to a generally acceptable degree. Fig. 7 provides the 50-Ohm SWR sweeps for all four heights. The SWR remains well below 2:1 at all heights. With some element adjustment, one may be able to hold the value at less than 1.5:1 at the band edges at any of the heights with the 2-wire construction.

Generally, when adjusting the phased driver lengths, the following rules of thumb will apply. To lower the frequency of minimum SWR either lengthen the rear driver or shorten the forward driver--or both. To raise the frequency of minimum SWR, do the opposite. Be prepared also to adjust the length of the director to center the SWR curve within the passband for roughly equal band-edge SWR values. In most cases, these adjustments will be so minor as not to affect the general beam performance across the band. These rules are not absolute, since they do not take into account possible interactions with other objects at the installation site.

Conclusion

These notes do not add anything new to the general ideas on wide-band 40-meter beams covered in Parts 1 and 2. They do show that it is possible to adapt such designs to wire construction. In general, single wire elements tend not to provide the desired wire operating bandwidth when we include gain and front-to-back ratio to the usual SWR conception of operating bandwidth. However, even the relatively narrow spacing of ladder line is sufficient to preserve the performance of fat tubular element designs to a degree that makes a wire beam in a fixed position worthwhile.

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