Monday, December 30, 2013

Construction Notes on Those Wire Yagis

In my preceding articles on the design of wire yagis for 40 meters -- dipole elements, inverted vee elements, inward-turning vee (diamond) elements -- I skipped over some important and useful construction details. That was deliberately done so that I could focus on the more important general design and performance aspects of these antennas.

To close out this series I will discuss these omitted topics. For the most parts they are presented as sets of options rather than one strong recommendation. Choose what works for you, provided that you do not take a lazy shortcut that can impact performance. Construction details, although not provided, should be straight-forward for most hams. You should just keep in mind that antenna arrays (2 or more elements) require attention to detail or all the painstaking effort can be for naught. It takes only one small mistake to erase the yagi's performance advantage.

I don't plan on reprising the design notes made in the yagi articles so you should review those (at the above links) as well as the list below.

Switch Box Placement

In the design articles the switch box used to reverse the antenna pattern is placed midway along the boom. That preserves array symmetry and, in most cases, places the switch box at the tower where the boom is likely to be side-mounted. This is an ideal location for robustness, tuning and maintenance.

The switch box itself can be metal or plastic. I've used both in the past. Plastic is probably best since modern plastics are very tough and easy to work with. They also do not interfere with electrical performance of coils and ladder lines.

Relays and Powering

The relays should be low-voltage DC, with internal construction and contacts suited to the power and frequencies. Internal switch box wiring (the schematic from an earlier article is copied at right) and relay construction will add effective length to the ladder lines and tuning stubs so keep that in mind when laying out components.

The relays can be powered via a thin gauge, 2-wire cable or the coax feed line itself. There are many simple designs and commercial products available for the latter choice. If you do use a separate power cable you should employ current chokes in the same manner and locations as the coax. At the very least use a section of cable wound into a choke coil that is effective at 7 MHz.


Use a plastic or fibreglass non-conductive boom to minimize disruption to the performance of a rotatable high-bands yagi above the 40 meters fixed yagi, and to the ladder line runs from the elements to the switch box. In the past I have used 1.5" (nominal) Schedule 40 ABS pipe for the 6 meters long boom, with a steel or aluminum centre section and a simple rope truss to counter the downward force applied by tension in the wire elements. Only the one truss is needed to stabilize the boom since, with the 2 half elements we have the equivalent of 3-point guying.

If the ladder line passes the metal section of the boom keep the line at least 10 cm away and parallel. It is better to run the ladder line underneath the boom to reduce rain and ice loading and to avoid inadvertent sagging onto the boom.

Reflector and Beta Match Stubs

All of these wire yagis designs employ transmission line stubs to tune the parasitic element (reflector) and drive impedance (beta match). I did this to keep the design and (theoretical) tuning process conceptually straight-forward. This is not necessarily nor always advisable in practice.

There are two significant concerns with using stubs: tuning and interactions. There is no way to tune these stubs except by cutting, adding or replacing. The potential for detrimental interactions comes from the need to put the stubs where they won't coupling to each other, the tower, the boom and anything else nearby.

One popular method (and one that I've used in wire yagis) is to construct a tunable stub as shown in the adjacent diagram. You need to use open wire line with bare inductors. For minimal interaction run these downward, perpendicular to the boom and parallel (but not too close) to the tower. Brace the stubs at the bottom so they don't move in the wind.

A sliding or movable shorting bar tunes the stub. Above the shorting bar the stub adds inductive reactance (shorted stub) and below the bar it adds capacitive reactance (open stub). Make the total stub length about 25% longer than called for in the design and slide the shorting bar during the tuning process to change the net reactance. The shorting bar can be as simple as a short length of wire with two alligator clips. Once tuned it is recommended that this be replaced with a soldered wire.

The stub length should be changed if the open wire line is other than 300Ω. The required length is, roughly, in inverse proportion to the design length, which was based on 300 lineΩ.

Alternatively you can use coils in the place of stubs. These can be put inside the switch box for weather protection. Make these air-core coils of rigid, bare copper with a inductance 25% to 50% greater than required by the design. The stubs in the preceding yagi designs have an inductive reactance of around 1.0 to 1.3 μH, so make the coils 1.5 to 2 μH. The coils should have one end open and have at least 10 turns. Tune the coils by moving the tap point. No matter where within the box you place the coils it is good practice to mount them at right angles to each other to minimize coupling.

Current Choke or Balun

The antenna design is deliberately made symmetric to equalize performance in both directions. Some asymmetries will inevitably creep into the antenna when built, and that can result in current imbalances. Use of a common mode choke -- balun or coax choke -- at or near the switch box limits the impact and also helps to eliminate conducted and induced current on the feed line from disturbing the antenna pattern. The main impact is F/B since it is highly sensitive to current phase and amplitude.

Additional chokes along the feed line can ensure that no resonant section of feed line appears anywhere along its length. With inverted vee elements especially it is likely that there will an opportunity for interactions.

Tuning the Antenna

Now comes the real test: you've built the antenna, raised it into the air and you put RF into it. No matter how careful the design and construction there will be real-world effects that will alter antenna performance. This includes everything from stray inductance within the switch box to ground conductance, metal (house wiring, gutters, etc.) in the vicinity and obstructions of all kinds. In other words, the antenna must be tuned.

Before you proceed to tune the antenna ensure that the wire elements are properly tensioned and in their correct positions. A little extra sage will, at the very least, shift resonance. Yagis and antennas for higher bands on the same tower are far more likely to be affected by the 40 meters yagi rather than the reverse. Therefore for the present objective we can ignore this particular interaction. But be sure to test the high-bands yagi for acceptable performance in all compass directions.

To begin, find the frequency where the SWR is minimum. Don't worry about the exact value for now, provided it isn't extremely high. If the found frequency is farther from the design frequency than you'd like you should calculate the percentage error and trim or add to all four element halves. For example, if an element half is 8.8 meters long and it resonates at 7.1 MHz rather than 7.05 MHz, the element halves should be lengthened by 100 x 50 / 7100 = 0.7%, or 6 cm. Typically you only have to do this trimming once, or twice at worst if you're careful. After trimming check that the SWR minimum is now at the correct frequency.

Next, we proceed to tune yagi gain and F/B. We do this by concentrating our effort on the F/B, not the gain. The gain curve is too flat to allow for accurate peak tuning. The F/B peak is relatively sharp.

Look at a local or great circle map to find the locales that are broadside to the antenna in both directions. If convenient you can use a local ham who is suitably located. Although not equivalent you can get close to correct tuning of the far-field sky wave by using ground wave or space wave. Back in the day (1990) I had a variety of short wave broadcasters to use as test signals. The best was the ideally (though illegally) placed Radio Tirana at 7.065 MHz. Today, alas, those antenna test beacons are gone.

Toggle the direction switch. You should see some difference in performance on test signals. That will confirm that it is (mostly) working as intended. Now take your friend up and down the band (or find other stations on other frequencies) and measure the F/B. Find the approximate frequency where it peaks. If this frequency is incorrect you will need to climb the tower and tune the reflector stub (or coil). Add or subtract inductive reactance to move the gain and F/B peaks down or up in frequency, respectively. Repeat this procedure until you get it right. You can use EZNEC or other software to determine how much to change the reactance to shift the frequency the desired amount.

When the F/B peak is at the correct frequency the peak gain will also be at the correct frequency. But test to be sure the gain and F/B performance are as they should be in both beam directions. If they are not you must have some asymmetry in the construction or with obstructions and conductors in the antenna's near field. Don't obsess over perfection but do address any serious shortcomings.

The last step is to adjust the beta match stub (or coil). You want to find the position where the SWR is 1.0 at the design frequency, which is where you trimmed the antenna for minimum SWR. If the frequency where the SWR is 1.0 has shifted too far you will need to go back and repeat the tuning procedure, starting with trimming the element halves.


That's all I have on 40 meters wire yagis for now. I have other design ideas for 40 meters antennas, both single elements and arrays, that intrigue me with their potential. More on those in 2014.

Happy New Year!

Thursday, December 26, 2013

40 Meters Wire Yagi - Diamond Vee Elements

If you are familiar with Spiderbeam and HexBeam commercial wire yagis for the high bands you will have noticed that they sweep the reflector and director elements inward at the ends. This allows a lightweight design through the use of wires rather than self-supporting tubular elements. The general principle is not new, having first run across it myself 30 years ago in the work by the late Les Moxon, G6XN, in his book HF Antennas for All Locations published in 1982 by the RSGB.

There is a price to be paid with such a design. First, the element interactions can prove problematic. Any metal placed near the end of a dipole will couple strongly and will certainly change element resonance. When that metal is another yagi element the impact is greater, including yagi performance characteristics.

Second, the centres of the parasitic elements must be moved outward to compensate for the folding since the point of average current is located inward. The same thing occurs with an inverted vee antennas and is the major reason why its low-elevation angle gain is less than a dipole whose centre is at the same height. This accounts for the average -1 to -1.5 db gain for the 40 meters yagi I modelled with inverted vee elements versus the one with dipole elements. The average height of the antenna currents in the inverted vee yagi is 1.5 meters lower than the one with dipole elements which at 0.6 db/meter accounts for much of the difference.

The 2-element wire yagi for 40 meters I had in 1990 was of the type with inward-folding inverted vee elements. Although I could not model the antenna back then to explore its performance I was intrigued with the general idea. I folded the elements inward and then tuned the elements to optimize its performance. I did not have someone else's design to work from.

For the present exercise I can use EZNEC to explore this class of wire yagis. My first step was to simply fold inward the inverted vee elements of the yagi described earlier. A new design parameter has also been added: the separation of the elements at their ends. There are a couple of things we should expect to see, even before we jump into the detailed design:
  • The gain and F/B will decline due to the lesser effective boom length. The effective length is approximately determined by the position of the average current; that is, the point on each element half where half the current is inward (and outward) from that point. The approximate value is 30% of the element half length from the element centre.
  • Increased coupling between elements will lower the antenna's resonant frequency. The elements will need to be shortened as the separation of the element ends is reduced.
  • Antenna Q is expected to increase due to stronger element coupling. This should at least impact the SWR bandwidth.
Unlike the previous two yagi designs there are more variables and calculations in the model. The most troublesome is finding the positions of the element ends as the boom, separation, vee angle and wire length are changed. EZNEC's scaling and rotation features are difficult to use, and usually more trouble than they're worth. You almost never get what you actually want. Instead I designed a spreadsheet which takes care of the trigonometry and algebra to get the X, Y and Z values to plug into the EZNEC wires table.

Above is an image of the spreadsheet for this model of the "diamond configuration" yagi. The variables to be entered are in gray/yellow and the wire ends are calculated in a form ready for EZNEC entry. The effective antenna height and boom length are also calculated. Notice that in this configuration the effective boom length has been shortened by more than 1 meter. This will impact yagi performance.

I followed the tuning procedure described in the first article in this series. The performance of the diamond configuration yagi is shown at right, and that of the previously-described inverted vee yagi for easy comparison.
  • Forward gain of 4.5 dbi is 0.7 db lower than at its maximum point in comparison to the inverted vee yagi with parallel elements. There is less gain degradation higher in the band.
  • F/B is degraded by 3 db, peaking at about -14 db. The frequency spread between maximum gain and maximum F/B is unchanged.
Each element half for this yagi is 8.77 meters long. The boom is 6 meters and the element-end separation is 2 meters. The beta match stub is 0.82 meters long and the reflector stub is 1.15 meters long. The direction switching system is as in the first article in this series.
Although the performance loss is small there is still the question of why do this at all? Unlike the case with a commercial rotatable antenna such as the Spiderbeam there would appear to be no good reason to fold in the elements of this fixed wire yagi. I will come back to this, but first let's look at the final performance parameter: SWR.

As expected the 2:1 SWR bandwidth has shrunk to under 100 kHz. To keep the SWR below 2 at 7.000 MHz I had to move the resonant frequency downward by about 20 kHz. As before the antenna is tuned for maximum gain at 7.000 MHz, since this continues to provide the best balance between performance and match for primarily CW operation.

The SWR impact is arguably the only deleterious impact of folding the elements into a diamond shape. Gain and F/B can be largely restored by increasing separation of the element ends, extending the boom, or some combination of both. However, while increasing the boom length can restore the effective boom length to what is was with parallel element the same gain cannot be achieved. In concert with the boom length the ladder line between elements and switch box must be lengthened, and the elements shortened. Shorter elements lower the achievable gain. Aside from matching considerations the gain of a λ/2 dipole is 2.13 dbi, which gradually declines to 0 dbi in the limit of zero length. The same applies to yagi elements.

On the other hand the diamond wire-yagi configuration does have advantages:
  • Fits into smaller lot sizes. By bringing the element ends together to a common tie point it is possible to orient the yagi to a wider ranges of directions. In a long (200') and narrow (50') property like mine I am restricted in the choice of directions which allow tie points for parallel elements. The range can be increased by reducing the inverted vee interior angle, at the cost of lower effective height and poorer performance. While modest, the shorter elements help to fit the antenna to the lot. For longer booms the elements can be even shorter (due to the loading of the longer runs of ladder line to the switch box).
  • There may not be suitable tie points (height and spacing) for all 4 ends of parallel elements that maintain antenna symmetry. Loss of symmetry negatively impacts yagi performance.
  • Symmetry is easy to achieve in this antenna. The diagram at right demonstrates the method of element tying that enforces symmetry for the element to boom angles, inward folding and element separation. Given the lengths of a half element, boom, interior angle and element-end separation the lengths of rope from element end to common junction can be calculated (see adjacent diagram). Grab the common tie rope and you will find there is only one radial line from the tower where the tension equal. Then you only need to tie the common rope at the height specified for the interior angle. The spreadsheet shown above calculates the lengths of the tie ropes and height of the junction per the model.
The design parameters I chose for the diamond configuration I described above are a reasonable compromise between performance and robust construction. I am not posting the EZNEC files and related spreadsheets, however I will happily supply them to anyone that asks. You can then play with them to come up with designs suitable to your individual circumstances.

In a future article, probably the next one, I'll say a little more about construction of the 40 meters wire yagis from this and previous articles.

Tuesday, December 17, 2013

40 Meters Wire Yagi - Inverted Vee Elements

A wire yagi made with dipole elements has the disadvantage of requiring multiple supports. The best arrangement in a two-element yagi is for 5 supports, all at the same height: one for the boom and four for the element ends. While that made the 40 meters yagi in my previous article essentially impractical to build it did serve as a good starting point, with the model allowing the inspection and optimization of performance, impedance matching and electronic direction switching.

The yagi modelled in this article is easier to build since it uses inverted vee elements. It requires only one support -- for the boom. The ends of the antenna are tied to ground supports with the aid of ropes from the element ends to the tie point.

The model is identical to dipole array save for the bending of the elements at their centres. I set the interior angle to 120° and left the element centres at the original height of 20 meters over a medium ground.

Symmetry (as I harped on before) remains critical to array performance. The angles of the elements should be equal -- this is more important than adhering exactly to an angle of 120° -- and remain parallel to each other and orthogonal to the boom. This requires some care in the selection of tie points. It is also important to use high-quality end insulators for the elements, and not simply bind the rope directly to the wire ends. What may be acceptable in a single-element antenna can destroy the performance of an array.

The design itself is quite simple. First I took the (EZNEC modelled) reference dipole from that previous article and bent it into an inverted vee with an interior angle of 120°. The SWR was then swept to find the resonant frequency. Bending the elements in this manner raises the frequency at which the antenna reactance is 0.

The resonant frequency rose by 1.27%. For small percentage changes (under 10%) it is sufficient to simply change the antenna length by the same amount. In this case the legs of the vee were increased by ~1.27% (rounded to the nearest centimeter) which moved the resonant frequency back to where it was for the original dipole.

The purpose of doing this was to avoid a lengthy retuning procedure for the yagi which is complicated by the 3 meters of ladder line running from the switch box to each element. Using an educated guess as to the impact of the fixed ladder line length's on the total element resonance I proceeded to add 1% to each element leg before bending them into inverted vees. Scaling elements in EZNEC is something I prefer to avoid since it can be tricky, or at least finicky.

Here is the SWR sweep that I got from this simple procedure.

If you refer back to the earlier article you'll see that the SWR curve is almost identical. What can I say except that I made a lucky guess.

A match is nice but insufficient. We need to look at the yagi's performance. The questions to be answered are: are the frequencies of maximum gain and F/B in the correct positions, and, how does performance compare to the yagi made from dipole elements?

To make the comparison easy I put the performance plots for the dipole yagi (from the previous article) and the inverted vee yagi next to each other. It should be obvious that the two are very similar, with some important differences.

Please note that all gain and F/B figures are, again, at a 10° elevation angle, not at the angle of maximum radiation. I chose this angle because it is a good median value for DX paths.
  • Despite the same SWR curve the frequencies of maximum gain and F/B are both lower by about 25 kHz.
  • The F/B curve, apart from the frequency shift, is nearly identical.
  • The maximum gain is lower by about -1 db. This is expected. However the gain bandwidth is sharper; gain falls off more quickly at higher frequencies. At 7.2 MHz, for example, the gain is -1.4 db versus the dipole wire yagi. This may be difficult to discern in the chart.
  • The gain versus the reference inverted vee is comparable to the gain of the dipole yagi versus the reference dipole. The reference inverted vee is approximately -1.6 db versus the reference dipole.
The gain differences are largely explainable by the difference in the heights of the current averages for the reference antennas and yagis. There is an exception at the point of maximum gain where the gain of the inverted vee yagi is better than the -1.5 db average by 0.5 db. I don't know the reason for this.

Of course the height of average current is responsible for gain differences at low angles. The elevation angle of maximum gains of the reference dipole and inverted vee at 20 meters apex height are 30° and 32°, respectively. However for the dipole yagi and inverted vee yagi these angles are 28° and 29°, respectively.

The yagi gets its gain by narrowing the main lobe in both azimuth and elevation. Thus a yagi at the same height as a dipole concentrates more of its energy at lower angles. This improves DX (low angle) performance versus non-DX QRM (high angles) in the direction the beam is pointing.

My final act with this model was an attempt to raise the frequencies of maximum gain and F/B back to where I wanted them (the same as the dipole yagi). Although the impact of the 25 kHz lowering of these frequencies is not a serious flaw I am interested in how difficult the tuning would be. I tuned these parameters by shortening the length of the reflector stub by 6 cm, from 1.12 to 1.06 meters.

Unfortunately this changed the (above) ideal SWR curve by shifting the minimum SWR point higher by 20 kHz. The tuning of the reflector changes the array resonance in the same direction. Although minor the SWR at the bottom of the band rose to 2.1, which may be a problem with some transmitters. By adjusting the length of the beta match stub I could shift the resonance almost to where it was before. However, this simple act did not change the SWR at 7.0 MHz.

A full tuning procedure would be require per the step described in the previous article. Since this is not an antenna I plan to build I decided to stop and sidestep the additional work. I have one more variation to apply to this antenna to make it something I would be willing to build. That antenna may be worth the effort of detailed tuning. This will have to wait for future article when I have time to do the modelling work.

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.

Tuesday, December 3, 2013

Mast Failure

About a week ago the Site B antenna mast suffered a major failure and came down. It did so without any drama, hardly making a sound and causing no damage to the house and grounds. Of course the multi-band inverted vee it supported is also down.

If you follow the link in the previous paragraph you will find a picture of the antenna mast soon after it was installed. It consists of ~6 meters of aluminum boom from a old Cushcraft 6 meters yagi and 2 sections of army surplus telescoping fibreglass mast below the boom and nested, with shims, into the Schedule 40 steel pipe that is bracketed to the house. The mast is guyed with ropes and a pulley up top is used to raise and lower the antenna.

Care to guess where the failure occurred? The adjacent picture is a big clue. I posed the two sections of mast side by side.

The exact point of failure was the lower-diameter end of the bottommost fibreglass mast section, the one that is mated to the steel pipe. As you can see the fibreglass broke at the collar that rested on the pipe rim. The moderate amount of on-the-ground testing of the fibreglass -- vertical and bending loads -- I performed did not identify this failure mode.

I have no one to blame but myself since I judged the material suitable for the application. This highlights a problem with surplus material: no spec sheet and no documented history of use. Either the mast was stressed beyond its unknown spec or it had been previously compromised. Unlike materials like steel it is difficult to determine which is the key factor by simply looking at it.

My original intention was to use metal but I had difficulty locating steel of aluminum tubing or pipe of the required strength and able to mate with both the bottom pipe (1.9" O.D., 1.61" I.D.) and aluminum boom (1.375" I.D., 1.5" O.D.). Since the fibreglass mast did the job with simple aluminum shims that is what I chose to do. I only expected it to be in use until the spring.

As I said from the start, the mast was deliberately built to be cheap, light and (supposedly) strong enough for the job at had. I wanted to cap my investment in this short-term experiment and avoid the risk of serious damage should it fail. By these criteria I succeeded, except for the longevity.

The combination of wind load and bending stressing are the likely culprits. I suspect, but cannot prove, that these loads caused gradual weakening of the fibreglass as it pressed against the steel rim of the pipe.

Unfortunately the snow we've had in the past week makes it unsafe to work on the roof. All I could do by ladder was to disassemble the mast and inspect the rest of it for damage. I believe I can get it ready for reinstallation with only a little work. A brief thaw will also be needed.

The biggest loss is the antenna. It's physically perfectly alright, just unusable for the present. This limits my operating due to the loss of 30 meters and inability to fill the side nodes of the the other dipole on the higher bands. At least it had the grace to fail after the CQ WW CW contest.

My options to getting the antenna back up include:
  • Installing the aluminum boom directly into the steel pipe. That will cost me 2.5 meters of height.
  • Find a length of steel pipe that is suitable for mating to both the aluminum boom and steel pipe. So far I haven't had any luck. I'll keep looking. Of course this is why I went with the fibreglass in the first place.
  • Move the antenna to the Site C tower. The maximum height I can manage there is 12 meters. The problems include interaction with the 40 meters delta loop and suitable tie points for the ends. The purpose is to mount the antenna at approximately right angles to the TH1vn dipole (up 11 meters), which severely limits my choices.
With the early arrival of cold and snow the fundamental limiting factor is the weather. Unless we get a thaw the antenna will stay on the ground. I am still on the air though with fewer bands and less azimuth coverage.