40 Meters 3-element Wire Yagi

The most popular articles on this blog are a surprise to me. They are the articles I wrote over a year ago on small 40 meters single-element antennas that are effective for DXing. In retrospect I should not be so surprised. Commercially-available rotatable yagis are common on 20 meters and above, but once you drop down to 40 meters there are relatively few hams with the ability to erect a rotatable yagi.

There are indeed small (loaded) commercial yagis for 40 but they are relatively expensive, carry a large wind load penalty and need to be at least 20 meters above ground to compare favourably to a single-element vertically-polarized antenna.

This is not another article about small 40 meters antennas. Rather it is about a large antenna that should be within the reach of many hams. What you will need is 2 high supports, such as a pair of modestly-tall towers, enough space to string out a few wire elements, and the motivation to make the necessary effort. This antenna should prove of interest to those hams that want more than what a single-element can offer but are unable for whatever reason to install a rotatable yagi.

Motivation

Although I have no plans for an antenna of this size anytime soon it still serves a purpose. Yagis with 2 elements (wires or rotatable) have significant compromises. These relate to key performance metrics such as gain, gain bandwidth, F/B, SWR bandwidth and some complexity in making it switchable (between broadside directions). A 3-element yagi ameliorates much of these concerns.

A wire yagi is in many cases a favourable alternative to a rotatable yagi. A typical 3-element full-sized yagi on 40 meters weighs at least 100 kg (225 lb), 10 to 15 ft² of wind load, and costs upwards of US$2,500. There are few used yagis in this class since they frequently fall victim to wind and weather before they can be sold. They are not for the faint of heart.

A rotatable yagi is usually unnecessary. From my QTH a fixed, switchable wire yagi oriented 60°/240° true bearing addresses 80% of the important paths for DX and contesting. Toward the northeast its main lobe covers Europe, western Russia, the Middle East, south Indian Ocean and north Africa. When reversed it covers most of the continental US and the southern half of Oceania. Considering the low cost and high performance a wire yagi can be an ideal choice for 40 meters. It should be complemented by either a small rotatable yagi or other wire antennas to cover other paths and for contest flexibility.

Structure

By making the elements from inverted vee elements it is possible to build a yagi with any number of elements by tying a cable between two towers. A steel cable should be insulated from the towers, and even broken into smaller sections to minimize interactions with other antennas, including shunt-fed towers.

Of course the towers should be far enough apart and high enough to maintain some separation between yagis atop the towers and the wire yagi. Although trees can be used it is rare to have trees of suitable height and position, and they are difficult and dangerous to work with at these heights.

As you can imagine it is quite important that a line through the towers points in the most desirable direction since the main lobe's centre will fall on that line. If you ever do plan to put up a second tower you might want to consider placing it to allow for the possibility of low band wire yagis, and not just for 40 meters. With even taller towers (40+ meters) a similar yagi can be built for 80 meters. While simple, this clearly is not an antenna for a modest station! My present station included.

On 40 meters we should strive to achieve a minimum height of 20 meters (½λ). If the towers are 25 or more meters high and 25 or more meters apart we can achieve sufficient separation to minimize impact on high-bands yagis at the top of the towers.

It is important that the elements be placed so that they are parallel to each other and orthogonal to the support cable, and that the interior angles of the vees are identical. Carelessness will compromise performance so take care to get it right. Use high-quality insulators between the element ends and tie-down ropes to reduce detuning and losses to the environment, especially in the rain.

Don't over-tension the support cable, especially if the towers are self-supporting. You can compensate for sag to keep the elements at the same height by hanging the parasites lower below the cable than the driven element. The cable also serves as a messenger cable for the coax feed line and the relay power cables. Induction of antenna current on the coax exterior and the DC cables is small because they are at a right angle to the elements.

Design

I chose the same basic design as for the 3-element reference 20 meters yagi from my series on choosing a high-bands yagi. That antenna was adapted from a W2PV design that itself was a variation on an NBS yagi optimization process. I chose 1.04/0.96 for the respective lengths of the reflector and director. The centre frequency is 7.1 MHz. The "boom" length is 0.35λ, or 14.8 meters (48.5').

My intention with these choices was to ensure that the antenna would work well across the 40 meters band with respect to gain, F/B and, to the extent possible, SWR. The last is the most difficult since the yagi is a high-Q antenna and the band has a 4% frequency range.

I first created an inverted vee in free space that resonated at 7.1 MHz. In a 3-or-more element yagi the gain tends to peak high in the band while F/B peaks low in the band. Unlike the aforementioned 20 meters reference yagi it is necessary for the element separation to be equal (7.4 meters). The antenna will be switchable and therefore must be symmetrical with respect to both broadside directions.

The interior angle of the inverted vee is 120° so that it is most efficient and to keep the ends from getting too close to the ground. Ground proximity reduces low-angle radiation (bad for DX) and increases ground loss.

Once I had the driven element designed I made two copies of it, placing each in position as a parasite. I then adjusted their lengths to the calculated dimensions for the reflector and director. Each element has a 10 cm (4") horizontal segment at the centre to facilitate connection of transmission lines and loads.

I next confirmed in EZNEC that the antenna model worked as intended. There was some risk that it would not since the design parameters I chose were for horizontal elements, not inverted vees. It worked just as expected.

I then added copper wire loss and placed the antenna 20 meters above real (medium) ground. It continued to work as designed. Further adjustment should not be required at greater heights. The same is not true if the antenna apex height is moved more than a few meters lower (element ends lower than ¼λ above ground).

Switching

You can use this wire yagi as a unidirectional antenna by leaving the reflector at its full length. However it seems a shame to erect such a large antenna and not make it switchable. Depending on geography perhaps only one direction is needed in some cases. It's your choice. From the above azimuth plot (taken at 10° elevation and a height of 20 meters) the -3 db beamwidth is 67°. Making it switchable increases the total -3 db beamwidth coverage to 134°. That's so attractive that I am unwilling to lose half of that.

To make the antenna switchable I chose to use a coil to tune the parasites. This is quite simple to do. First, cut the length of the reflector to equal that of the director. Second, calculate the inductance of a coil that has ~70 Ω reactance at 7.1 MHz (the centre frequency). Finally, check the values of gain and F/B to ensure that the yagi performs as it did with the reflector at full length. As it turns out I had to increase the reactance to over 90 Ω to get the performance back to where it had been. This requires a coil inductance of 1.8 μH at 7.1 MHz.

To make the antenna switchable each parasite has this coil at its centre and an SPST or DPDT (shown) relay configured to short the coil. When the relays are not energized one coil is in series with the parasite (reflector) and the other coil is shorted (director).

When the relays are energized the action of the coils is reversed, and therefore the direction of the yagi. Since the antenna is symmetric its performance and SWR should be identical, unless there are asymmetric interactions with the environment between directions. It is recommended that when the relays are not powered that the yagi be configured to point in the direction most often used.

Unlike the 2-element yagis I previously designed there is no need for transmission lines between elements. It is only necessary to run a 2-wire low-voltage cable to the centres of the parasites to power the relays. A small plastic box hung from the cable at the centre of each parasite should be used to contain a relay and coil, and another at the driven element to terminate the coax feed line and split the DC relay power from the RF. A separate low-voltage DC cable can be run from the shack in parallel with the coax if preferred.

The final task is to match the feed point to 50 Ω. I chose a beta match. This involves shortening the driven element and placing a open-wire shorted stub across the feed point.

Dimensions

Final design dimensions:

• All elements made from insulated 12 AWG (2 mm) copper wire
• Director and reflector length: 19.66 meters
• Driven element length: 19.94 meters
• Parasite coil: 1.8 μH
• Beta matching stub: 2.3 meters of 150 Ω open wire line shorted at the end, or a coil having the equivalent inductive reactance

When constructing the antenna it is a good idea to first build a driven element and tune it to resonate at 7.1 MHz. Measure it and then cut both parasites to 0.96 of this measured length. Adjust the length of the driven element in proportion to any differential between the parasite length and the parasite design length of 19.66 meters. This last step should simplify tuning of the beta match.

The impedance of the beta match stub is somewhat critical so choose stiff wire (or rods) of a diameter and separation to achieve 150 Ω impedance. At other impedances the length of the stub must be adjusted and the SWR bandwidth may be a little worse. The stub should employ a shorting bar for adjustment. If a coil is used instead it, too, will need to be adjustable either with a movable tap or by spreading/compressing the coil.

Performance

At an apex height of 20 meters and 10° elevation (median of DX-friendly angles on 40 meters) this 3-element wire yagi outperforms a 2-element wire yagi (with inverted vee elements) by 2 db and one with dipole elements by 1 db. Better yet the gain is more consistent across the band than any 2-element yagi. F/B bandwidth and depth are also improved in comparison to 2-element yagis.

This performance differential is sustained as height is increased.

F/B peaks a little below the lower band edge. It can be moved higher but at the cost of lower gain in the CW segment. I consider this a poor trade-off though others may feel differently. As designed the 10° gain is 6.85 dbi at 7.0 MHz and gradually rises to a peak of 7.25 dbi near 7.2 MHz. Moving the antenna from free space to 20 meters over medium ground shifted the frequency of maximum gain by only 30 kHz.

At 7.180 MHz the main lobe peak is 12.04 dbi at an elevation angle of 27°.

The uncorrected radiation resistance of the antenna is ~24 Ω. A beta match was designed in EZNEC to match the antenna to 50 Ω coax. Dimensions were noted earlier in the article.

The 2:1 SWR bandwidth is 160 kHz. In practice the SWR bandwidth will be wider due to transmission line attenuation and environmental losses in the antenna's near field. An antenna tuner can be used to tame the modestly high SWR up to about 7.250 MHz, which would allow this antenna to pretty well cover the entire 40 meters band. Despite the high SWR, the gain remains good right up to 7.3 MHz.

It is a simple matter to shift the frequency of minimum SWR to better favour CW or SSB band segments by adjusting the beta match parameters. Gain and F/B will stay the same if the parasites are left as they are.

About wire loss and gain

It is possible to get more gain from this antenna. At least in theory. By spacing the resonance of the parasites closer together the free-space gain can be boosted from 8.7 dbi to 9.2 dbi. Unfortunately this requires a type of wire that is not currently available: zero loss.

The average I²R loss in this antenna built with 12 AWG insulated copper is -0.3 db. The quoted performance include this loss. When the gain is maximized by tightening the parasite tuning the average loss increases to around -0.8 db. In other words the increased gain is entirely erased by the increased wire loss!

This is one of the trade-offs of wire yagis we must learn to live with. Gain has an inverse relationship to radiation resistance in a yagi: the lower the radiation resistance the greater the I²R loss. Heavier gauge wire can be used, of course, but the expense (and weight) quickly rises.

I believe that 12 AWG wire is the largest that makes sense in antennas of this type. Smaller gauge wire should be avoided, not only for the increased loss but also tensile strength. Insulated copper-coated steel wire is available which both lowers cost (steel is cheaper than copper) and increases strength, so consider that choice if you decide to build a wire yagi.