Monday, December 9, 2013

40 Meters Wire Yagi - First Models

DXing and contesting are made easier with antennas that are high and have gain. This implies the need for a tower or other substantial support structure. Further, since antennas with gain are (obviously) directional there is a desire to have a rotatable antenna so that the gain can be placed to best effect on every QSO. That definitely requires a tower.

Below 20 meters this is difficult, and often beyond the ability and budget of most of us. Even for serious operators wire antennas are the norm on low bands, or ground-mounted verticals for 80 and 160. Yet to be most competitive gain is required. Since anyone can purchase a kilowatt amplifier power is no panacea.

Rotatable antennas on the low bands are so large, heavy and expensive most efforts on gain typically focus on fixed yagis. These can be made with little more than wire and a tower.

I designed and built a 2-elements wire yagi for 40 meters around 1990 and had a lot of fun with it for a couple of years. It was switchable to "point" in either broadside direction. It outperformed the delta loop it replaced and cut down on QRM and QRN in other than the desired direction. If I ever erect a proper tower again I may very well upgrade to a wire yagi for 40. To this end I have been thinking about designs that suit my operating preferences.

With additional knowledge and maturity, and software tools, I can take a more methodical approach than I did back then. Although that yagi worked well its mechanical design was shoddy and the electrical design required a lot of tuning, tuning that meant a lot of work atop the tower plus a day or two of on-the-air tests between adjustments.

There are two elements of the methodical approach:
  • Theory: There are several performance criteria to be evaluated in yagi design, particularly gain, F/B and impedance. The contributing variables include element spacing, conductor material, matching system, height and element configuration (dipole or "bent" in some way). If there are other antennas nearby, in particular a rotatable high-bands yagi above it, the interactions must be managed.
  • Structure: The antenna must be survival and it should be easy to tune and maintain. Theory is great but since there will be tuning required it helps to make this as painless as possible. The mechanical design should aim for symmetry; symmetry is more critical to the performance of an antenna array than in any single-element antenna.
In this first post on wire yagis for 40 meters I'll design a 2-element antenna that exercises the theoretical aspects into a workable antenna. However this first design is not intended to be built. The reason, as you'll see, is that it would require multiple supports (i.e. non-optimal structure).

First to the theory. Every yagi is a compromise. Ideally we want an antenna that has high gain, high front-to-back (F/B) and low SWR, and to so across the spectrum of interest. This is not achievable. While this is readily apparent with modern tools such as EZNEC this has been rigourously researched decades ago.

One book I like to reference even though it is quite old and predates the common use of NEC, or even MiniNEC, is Yagi Antenna Design by the late Jim Lawson, W2PV. Although the computer modelling in there is awkward by modern standards the laws of physics have not changed, plus the quality of presentation and thoroughness are exemplary. Its results are are valid today as when the material was first written in the 1970s.

In free space the maximum gain of a 2-element yagi is ~7 dbi (4.9 dbd). For parallel elements the spacing to achieve this result is ~0.14λ, or 6 meters (20'). This is approximately the same whether the parasitic element is a director or reflector. What distinguishes the choice is the behaviour of gain and F/B with frequency. For a reflector the the gain and F/B degrade more quickly on the low side of resonance, whereas for a director the direction of degradation is reversed. Therefore for a 2-element yagi:
  • If your primary interest is CW or digital, make the parasitic element a reflector. Optimize it for the low-end of the band and you will get acceptable performance at the high end.
  • If your primary interest is SSB, make the parasitic element a director. Optimize it for the high-end of the band and you will get acceptable performance at the low end.
These frequency trends are starkly obvious in the frequency sweeps done by Jim Lawson. Although this was before we all had powerful NEC-based tools on our home computers his results are confirmed by these tools. I have done so with EZNEC. Since my interest is primarily CW the proper choice for parasitic element in a 2-element yagi is a reflector.

To test this figure I made a simple yagi model with EZNEC and indeed found that the maximum gain was around 6.9 dbi. This is for an antenna in free space with no conductor loss. Real antennas cannot do so well. Wires have real loss, a loss that is amplified in a yagi since the impedance is lower than in a single-element antenna. Lower impedance means higher currents, resulting in higher IR² losses.

Using EZNEC I modelled a reference wire dipole for 7.1 MHz that is made of 12 AWG wire 20 meters above ground. The gain is 7.67 dbi at 30° elevation and 1.97 dbi at 10°. (I will often quote the 10° gain value in this article since that is around the median of angles for DX paths on 40 meters.)

When copper losses are included in the model the respective gain drops to 7.61 and 1.92 dbi. For insulated wire the gain drops further (losses increase) to, respectively, 7.59 and 1.90 dbi. In every real sense losses of less than 0.1 db are inconsequential. As we'll discover further on, the losses for the same insulated copper wire in a yagi limits the gain to ~6.6 dbi, a loss of ~0.3 db. This is arguably inconsequential as well. However do keep this in mind since it reduces the gain a real wire yagi can achieve. HF yagis made from aluminum tubing typically have negligible conductor loss due to the large element diameter, despite aluminum being a poorer conductor than copper.

With the above reference dipole for comparison let's move on the simple wire yagi I promised earlier. It, too, will be placed 20 meters above the same real (medium) ground.

Configuration and Switching

The diagram at the right shows the configuration of the yagi (not to scale). The wire elements are identical, having the same length and conductor type (12 AWG, insulated), and are parallel to each other and the ground. They are connected to the central, tower-mounted switch box by a length of ladder line that is ½ the boom length. Deploying the switch box in this fashion eases tuning and maintenance.

The purpose of the switch box is to reverse the beam direction. It does this by attaching the coax feed line and the beta match stub to the element that will be the driven element, and the reflector tuning stub to the element that will be the reflector element. The stubs and lines to the elements are 300Ω ladder line, although other types can be used in the design. Both stubs are shorted at their ends.

The switch box consists of two DPDT relays. The common terminals of each connect to the components for each of the reflector and driven elements. The switchable terminals connect these components to the yagi elements. The relays can be powered by a separate cable or feeding the DC through the coax with couplers at both ends of the feed line. I recommend that the off position defaults to your favourite direction.

The beta match is desirable since the impedance over the band is as low as 25Ω. This is due to the close spacing and tuning for high forward gain. It isn't a perfect solution since the reactance has a wide range. Yagis are high-Q antenna and 40 meters is a wide band by percentage (4%). My design aims for best performance in the CW segment, and with good performance to at least 7.2 MHz.

Symmetry vs. Asymmetry

The antenna has a symmetric design apart from the stubs. This assures predictable and equal performance in both broadside directions. Do not take shortcuts! Asymmetries can reduce or erase the careful design for optimum gain, F/B and match. This includes using a current balun or coax (common mode) choke on the feed line near the switch box.

It is possible to design an effective asymmetric antenna as a design objective, not just due to carelessness. The wire yagi I built years ago was of this kind. That antenna had the same driven element for both directions, to which the coax was connected via a balun. Although there was no beta match my tube rig and amplifier could handle the SWR. The parasitic element had a tuning stub with a shorting bar for tuning. The switch box connected in a section of open-wire line to convert the element from a director to a reflector.

The design of that asymmetrical antenna was simple but was difficult to tune since the switch box was close to the end of the boom. Although the gain and F/B were similar in both directions the antenna resonance swung quite a bit, requiring fine tuning of the rig and amplifier. The parasitic element "pulls" the resonant frequency up (director) or down (reflector) due to the high mutual coupling. This is not so much a problem nowadays, since an automatic tuner is typically built into many transceivers.

In the present design I made symmetry a key objective.

Design Parameters

This antenna was iteratively adjusted using EZNEC to approach the performance objectives. The only fixed parameters were the boom (6 meters, non-conductive), ladder line impedance and velocity factor, and length of ladder line to each element (3 meters).

To give an idea of how the antenna was designed the process steps are approximately as described below. Note that the model does not contain a switch box. The two elements in the model have fixed roles as driven and reflector elements. It is sufficient to make the design symmetrical so that the switch box can work as intended.
  1. Design the first element of the yagi. Feed it through the section of ladder line and cut the element so that it resonates around 7.200 MHz. The influence of the reflector, when it is added, will pull it down to a lower frequency. The beta match design also requires the element to resonate at a higher frequency.
  2. The second element in the same way, but do it alone so that the elements don't interact. Cut it to the same length discovered above for the first element. Add a reflector stub that is somewhat longer than 3 meters and feed it at the end of the stub. Adjust the stub length so that the element resonates around 6.9 MHz.
  3. Combine both elements into one model. Remove the source from the reflector stub and short the end of the stub. Add a beta match stub to the driven element. My initial length was 1 meter. The stub is shorted at the end.
  4. For this step ignore the SWR. The tuning of the driven element has no effect on yagi gain and F/B. Change the frequency until you find where the gain is as high as possible but with only a modest degradation in F/B. The frequency is almost certainly not where we want it. Adjust the length of the reflector stub so that this frequency is shifted to 7.000 MHz.
  5. Plot the SWR. It will at first almost certainly look awful. The objective is to get the SWR to a minimum at a frequency such that the SWR is less than 2 at 7.000 MHz. I found that 7.050 MHz worked best. Shorten the driven element to raise the frequency of minimum SWR and lengthen it to lower the frequency of minimum SWR. Adjust the length of the beta match stub to get the SWR as low as possible. Iterate as necessary.
  6. Adjust the length of the reflector element to match the new length of the driven element.
  7. Adjust the length of the reflector stub so that the optimum performance is back at the frequency we previously selected.
  8. Go to step 5. Repeat steps 5 to 7 until all design objectives are met.
One of the nice things about 2-element yagis -- which Jim Lawson noted, and EZNEC confirms -- is that the parasitic and driven elements can be independently adjusted, both in models and in practice. The performance parameters of gain and F/B (with respect to fixed design frequency, element size and element separation) are set by the length of the parasitic element alone. That is, altering the driven element and matching network does not impact yagi performance parameters.

It is this independence that permits the use of the above step-by-step process to quickly achieve a useful result. The challenge is in achieving symmetry and match. Getting that match can be difficult because the R and X impedance components change quickly near the frequency of maximum gain. A simple beta match can tame the impedance of such an antenna but cannot perform magic. Even that requires careful adjustment. Yagis with more elements are, perhaps counter-intuitively, more managable in this respect.

Unlike most of my past antenna articles I am showing the exact EZNEC design parameters for this antenna. Once we get into arrays rather than single-element antennas the details matter. Arrays are finely-tuned creatures where accuracy in design, construction and tuning must be respected. Being cavalier may be in the "amateur spirit" but in this case it can lead to grief.

A screen shot of the wire and transmission line data was easiest so I pasted these above. Wire #3 is a short wire that is only in the model to serve as a terminal for the driven element ladder lines. The driven element is wires #1 and #2, with the reflector consisting of wires #4 and #5. I modelled each half of the elements so that I can later convert these into inverted vee elements.

The ladder line to the driven element is transmission line #1, and #3 is the beta match. The reflector stub is combined with the 3 meters long line to the switch box for ease in modeling. The actual stub is 1.12 meters long (4.12 - 3). The ladder line velocity factor is may be lower in commercial products so this would have to be adjusted for.

Notice that the element lengths are shorter than in a dipole (or inverted vee). They are only 17.7 meters long rather than the 20.2 meters of the reference dipole made from the same wire (see above). That is largely due to the insertion of the ladder line between the elements and the switch box. I modelled the transmission line loss as zero since in the real world the loss would be very small, though not quite zero. Loss in the insulated copper wire that comprise the elements is in the model, since the impact is noticable.

A final note on the antenna boom, assuming there is one, since it is not in the model. I assume a non-conductive boom, or at least one that is metal only in the centre section for strength. This is recommended since when mounted on a tower there is almost certainly a yagi for the high bands just above it and we want to minimize interaction. The impact is almost exclusively on the high bands yagi, not on the 40 meters yagi. There will be some degradation on the high bands the antennas are close when the booms are near alignment. From my experience with an inverted vee 40 meters wire yagi the interaction is noticable but not worrisome.


First we'll look at the SWR. The antenna has a high Q resulting in a narrow SWR bandwidth. The 2:1 SWR bandwidth is 200 kHz. Most transmitters should be happy with this antenna up to 7.175 MHz, and higher for those with a built-in tuner.

The -3 db beamwidth is 72° at an elevation of 10° (it's wider at the 30° elevation shown in the plot), so even without another antenna to cover the side nodes the high-gain azimuth coverage is very good (144° out of 360°). The elevation pattern at 7.050 MHz is representative of its DX capability.

Rather than show lots of EZNEC plots I have charted the gain and F/B across the band, including the gain of the reference dipole at the same height.

The gain and F/B bandwidth are narrow. The maximum gain of 4.52 dbd (compared to the reference dipole) is at 7.000 MHz while the maximum F/B of 16.3 db is at 7.080 MHz. In a 2-element yagi with element spacing optimized for gain it is impossible to make these fall on the same frequency. The equivalent maximum gain of 4.52 dbd is equivalent to ~6.63 dbi, or about -0.3 db below the theoretical maximum. That is primarily due to the wire loss, as discussed earlier.

At the bottom and top band edges the F/B is so low that in the reverse direction the net gain (gain - F/B) is not much lower than the reference dipole. So the attenuation of QRM may be poor even though the forward gain still accentuates the wanted DX. When you consider the relative attributes of the gain and F/B curves I think you will understand why I chose to tune this antenna for maximum gain at 7.000 MHz. I continued the plot below the band edge to illustrate what to expect if the point of maximum gain is moved to a higher frequency.

Notice that the gain of the reference dipole rises almost 1 db at the highest frequency. This is not an error. What you are seeing is the effect of increasing antenna height in wavelengths. Wavelength decreases as frequency increases so the antenna is effectively higher. The yagi is similarly affected, it just isn't obvious due to the larger effect of gain variation with frequency.

Aiming for Implementation

When I next visit this topic I will focus on changes to the antenna that make it more realizable in practice. This will include variations of turning the elements into inverted vees. My ultimate objective is to build one of these antennas if I decide to once again install a tower of suitable height. I also enjoy the learning process.

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