Skewed Wire Yagis

So you want to put up a wire yagi for the low bands. All you need is two sufficiently tall structures -- trees or towers -- tie a catenary rope between them, hang wire inverted vee elements from it and run coax along the catenary to the driven element. Simple and cheap high performance fixed yagis for 40 or 80 meters can be yours.

But what if those structures aren't positioned where you need them. If they are not on a line that is close to the direction (or directions if the yagi is made reversible) that is your objective it could kill the project or you'll have live with reduced performance due to the desired direction being off the centre of the main lobe or by reducing the number of elements to broaden the beam width.

For the case where the structures are towers (or just one of them is) and you plan well in advance you may be able to place the tower or towers to suit wire yagis. Otherwise you can only count on luck to have them where they're needed. I expect this is a dilemma that some readers have faced or will face since the all time most popular articles on this blog are designs for 2, 3, and 4 element 40 meter wire yagis.

The left diagram demonstrates the problem. The greater the angle between the catenary and the desired direction (two directions for an electrically reversible yagi) gain will suffer. The effect increases with the number of elements since the main lobe will be narrower. A 2-element yagi is therefore the least affected by direction error.

On the right is the hypothesized solution. The elements have been turned so that they are broadside to desired direction(s); they remain parallel to each other even. The questions to be answered include:

1. Is the main lobe (if it survives this abuse) along the catenary (a line through the element centres), broadside to the elements or somewhere in between?
2. How much are gain, F/B and SWR affected as the skew angle increases?
3. If the pattern does shift direction how great an angle can be achieved while maintaining a clean pattern an similar SWR band width?

In this article I will explore the problem with wire yagi models where the elements are askew from each other, as they would be when the catenary runs at an angle to the desired compass point. This computer model study should be enlightening and may give hope to those with unfortunately located support structures.

Model parameters

Since a 2-element wire yagi has a wide main lobe and wire yagis with 4 or more elements are uncommon and take more time to deal with in the model I will restrict myself to a 3-element reversible wire yagi for 40 meters with inverted vee elements. The antenna is one I've described in detail before, and indeed is the all-time most popular article on this blog according to web site statistics.

The diagrams above are based on my EZNEC model of the antenna. Refer to that earlier article for details on antenna design and performance since I will not repeat that data in this article. Apex height of the inverted vee elements will be fixed at 25 meters since I don't expect that height will significantly alter the effects of element skewing.

The yagi is reversible by switching a coil at the centre of the two parasitic elements, such that one becomes a director and the other a reflector. The driven element is at the centre of the array so that the performance metrics are identical in both directions (symmetric). Therefore we only need to examine the model in one direction.

Skewing the elements can be done in two ways:

• Rotate the elements in place. The greater the rotation angle the shorter the effective "boom" length. That is, the element spacing is reduced along a line broadside to the elements.
• Constant element spacing. The distance between element centres increases with rotation angle so that the element spacing remains constant.

A 2-element reversible yagi has transmission lines between the feed point and the elements. Therefore when you skew a 2-element yagi the electrical design must be adjusted for the latter method because the physical length of the transmission line must increase. Worse, the lines will be unbalanced due to the loss of left-right symmetry. In my opinion this is more trouble than it's worth. The 3-element yagi is far simpler since it has only DC control lines running to the parasitic elements. Common mode currents due to the asymmetry can be addressed without affecting antenna performance.

For the 3-element 40 meter wire yagi I will examine both skewing methods for angles up to 30° in steps of 5°. Patterns are only computed at 7.1 MHz, which is approximately the midpoint of the yagi's design range for best performance. Based on my modelling I don't expect any surprises in performance at other frequencies over the antenna's range of 7.0 to 7.2 MHz.

For the constant element spacing method I will not compute the increased "boom" length -- distance between element centres along the catenary. This is easily accomplished with elementary trigonometry if you are interested in building an antenna of this type.

Modelling results

As I increased the rotation angle (skew) in the models I was surprised by the yagi's resilience. Performance is sustained better than I expected. However the skewing is not entirely without cost. Scan the table of the calculated key performance metrics before you continue reading. The tables have been normalized to compensate for shortcuts and orientation oddities in my rotation methodology. None of this affects the results but did reduce the time I spent modelling.

There are several conclusions we can make based on the data:

• Gain, F/B and main lobe beam width are largely sustained for angles up to 30°. I didn't expect that I could push that far without negative consequences.
• The centre of the main lobe is between the catenary direction and broadside to the elements, and is the same for both skewing methods. The main lobe skew is ~60% of the physical skew in all cases.
• Although SWR bandwidth is unaffected the resonant frequency increases slightly at the largest skewing angles. Adjusting the matching network should be easy, or at least straight-forward.

Despite these promising results it was disappointing that the pattern skew fell short of the physical skew of the yagi. For a 30° physical skew the skew of the main lobe is 18° ±1°.

The azimuth patterns at a skew angle of 30° show a difference between the skew methods -- original in black and skewed antenna in blue. The rearward pattern is cleaner when the elements rotated in place. With constant element spacing the F/B and F/R are slightly worse. The F/B figures in table also clearly favour rotating the elements in place. [Note: The small skew in the left pattern plot is an artefact of my modelling shortcut discussed previously, not a true difference between the skewing methods.]

Application and items for further study

Hopefully this study can act as an incentive to a few readers with seemingly inconvenient supports for high performance wire antennas. It can pay dividends on the low bands as we survive the next 2 or 3 years the solar minimum will last.

To start, consider how far askew the line between supports is from what would be ideal for you operating objectives. Let's say the amount is 20°. Choose a skew angle of 30° and the pattern will be almost exactly where you want it. If the desired direction is 30° off the catenary you can get most of what you want by skewing 30°, since the pattern will be 18° closer to the ideal than it would otherwise be.

You can even do this with conventional yagis. The application I have in mind is side mounting a yagi flush to a tower face but have its pattern in a different direction when no tower face is suitably oriented. However this would require custom boom-to-element clamps and there may be awkward questions from visiting hams about your peculiar looking antenna. The skew of a wire yagi is less obvious to the casual observer.

If the desired skew is greater than 30° I strongly recommend developing a model rather than extrapolating from the models in this article. At some point I expect performance to rapidly degrade. I didn't attempt to find that point, but be assured that it exists. The same goes for wire yagis with more elements: do a model before jumping into construction.

Depending on my own interest I may extend the skewing concept to wire yagis with more elements, yagis with a coupled resonator and wire yagis with loop elements. It is reasonable to predict that all will benefit to a degree though it will require modelling to find how far each yagi design can be skewed before performance deteriorates.

The primary message of this study, I believe, is to use the supports you have and exploit skewing to make the best of your circumstances. Perfection is rarely necessary or even desirable. I would only caution against deployment of novel skewing arrangements without modelling beforehand to determine what you can expect and so avoid wasted effort.

Motivation

Skewing yagi elements may seem an odd idea and I admit it never occurred to me until about two weeks ago. I was walking back and forth in the hay field armed with a compass, wood stakes and a 200' tape measure looking for the ideal location to plant my second big tower. Tower siting is a compromise between safety, transmission line length, yagi side mounting, interactions and wire antennas. It is rare that all objectives can be fully satisfied.

This tower's placement in my original site plan for this QTH was based on these criteria. Details matter when one moves from a rough plan to literally pounding a stake into the ground, hence my recent surveying activity.

I expect to place the tower such that there will be some skewing required for wire yagis hanging off a catenary between the towers to make the project more tractable and to minimize interference from side mounted yagis pointing directly at antennas on the other tower (towards Europe). Shifting the tower site ~20 meters solves these and several other problems.

Thus was born my motivation to study skewing. A few hours later I sat down in front of the computer to study the implications and possibilities.

That tower project is now well into the planning stages with a tentative schedule. Wire yagis for the low bands may be in my future now that I have skewing data in hand. Stakes are in the ground.