The Challenge of Wire Yagis is...Wire

I receive many inquiries about wire yagis. This corresponds well with the blog statistics since the most popular article over the 8 year run of this blog is the 40 meter 3-element wire yagi. There are several other related articles that are almost as popular. This isn't surprising because for most hams a yagi for 20 meters and higher bands is not difficult to buy and install, but once you go down to 7 MHz the size of a rotatable yagi, even one with shortened elements, is beyond possibility for most hams. 

Yet there is a desire for better performance on 40 meters than a simple antenna like an inverted vee, vertical or loop. A wire yagi is enticingly within reach. Few bother to contemplate multi-element, higher performance antennas on 80 and 160 meters and, again no surprise, those articles on the blog are far less popular. Many are willing to try on 40 meter wire yagis because they are easily supported and inexpensive, and with a little ingenuity can be electronically switched between its two broadside directions.

In reality it is never quite so simple, as many have discovered. Many hams abandon the project midway through. One of the difficulties is that many hams do not really understand yagis and their subtle complexities. They do not have the technical knowledge, the required test equipment, don't know how to use the equipment or don't know how to interpret what they see. A 2-element yagi is not twice as difficult as a dipole or inverted vee: it is closer to 10× more difficult.

That said, I don't mean to discourage anyone from embarking on a project like this! It can be a very satisfying experience, from the knowledge gained to the on air results. I built my first 40 meter wire yagi over 30 years ago and I got it working despite my (then) limited knowledge of antenna theory, nothing more sophisticated than an SWR bridge for test equipment, ELNEC software (precursor to EZNEC) and a lot of motivation. 

The antenna worked and I was hooked on the potential of these deceptively complex antennas. Readers may be surprised to next hear that I've only ever had two of these antennas. Many designs I did for other hams or they were modelled and never built. I've learned a lot on this journey.

In this article I want to focus on one particularly fundamental challenge of wire antennas: the wire itself. This is the one thing almost everyone takes for granted and should not. A lot of the trouble people run into is that they don't understand the surprisingly large impact of wire specifications and usage on the project. You can easily ignore or remain blissfully unaware of these issues with a single element antenna -- test, prune and you're done. Yagis are not so forgiving.

Before we jump in, a word about the common rotatable yagi with aluminum tube elements. In contrast to wire yagis these antennas are can be modelled to an absurd degree of accuracy and predictability. I recently gave an example of this phenomenon. NEC2 supplemented with an algorithm to correct for stepped diameter (telescoping) tubes works extremely well. 

Whether you can model it in free space or a modest height above ground the result are reliable, and indeed almost exactly the same. Commercial vendors love this since individual hams don't have to adjust their products as long as they're installed at a modest height of at least, say, λ/2: approximately 30' (10 meters) for a tri-band yagi.

The following is a brief list of wire difficulties builder of wire yagis are sure to encounter. All will be discussed in this article. After giving you lots to worry about I'll make proposals on how to deal with the uncertainties when building wire yagis.

• Insulation: material; thickness; stability; or bare wire
  
• Material: copper soft drawn vs hard drawn; copper plated wire; other conductors
• Conductor diameter
• Stranding: solid; number of strands
• Sag and tension
• Wire termination method
  

Let's begin with must seem to be a elementary description of what a wire is. The following diagram is of a THHN electrical wire often used in Canada and the US since it is ubiquitously available in bulk and usually at good prices. It is from a randomly selected web site. There are of course countless varieties of wire in the market, and this is no way is a recommendation to use THHN.

Wire material and construction

For almost all electrical wire the metal is soft drawn copper. Unless alloyed or hardened copper is a soft metal. Put it under tension and it will stretch, and in the process it will also harden. Do it under controlled conditions and you will have made less stretchable hard drawn copper. Some hams do that. It's a good idea although I've never done it. If you do there will be a slight diameter reduction of (usually) no more than one AWG number. Hard drawn copper wire for antennas is commercially available at a higher price than electrical wire.

As soft drawn wire stretches the resonant frequency will be lower due to its longer length. Under moderate tension and the load put on the wire by wind and ice you will find that the antenna will have to be adjusted because it stretches and sags. Expect to do it more than once.

Stranded wire will stretch more because the individual strands do not lie quite flat against each other. Under tension the strand spirals will draw inward and lengthen. This is independent of the each strand stretching as it hardens. Guy strand and rope compress in a similar fashion. The impact of this behaviour on wire yagis is quite and can almost always be ignored.

Another problem with stranded wire is that for the same gauge the rate of corrosion is higher. Chemical reaction rate is in proportion to the surface area, and that is always higher for stranded wire. 

On the positive side, stranded wire is more flexible. Some believe their wire antennas survive better for that reason, although I haven't noticed any difference from solid copper. Of more immediate concern is that careless handling of solid wire is more likely to result in kinks that will weaken the wire. Copper will break from the fatigue of repeated bending. Repairing just one kink will weaken the wire.

I used to believe stranded wire was better and that's what I used. Like many other hams I now build wire antennas almost exclusively with solid wire.

One of the worst choices in my experience is bare stranded copper plated steel. Copperweld and similar products corrode faster and are prone to rust as the copper plating develops fissures. Sanding the corroded wire can remove the copper plating. On the other hand it takes tension well, and that allows construction of predictably stable wire antennas. I know hams who are happy using plated wire for their low band antennas that have survived many years.

Non-copper wire such as aluminum and galvanized steel are rarely used for HF antennas. The lower conductance of aluminum and zinc for low radiation resistance wire yagis is not desirable. There are other concerns I will pass over, such as skin effect (for any plated conductor) and robustness. Copper wire copper plated wire are almost always the correct choice for wire yagis.

Wire diameter

Wire diameter affects reactance and therefore affects the resonant frequency. As the wire thins the resonant frequency rises, and on 40 meters every wire we use is thin with respect to wavelength. As an example, a tube element of 25 mm (1") diameter that is resonant at 7.1 MHz will resonate at 7.2 MHz when made from 2 mm diameter wire (AWG 12). We cannot ignore diameter for our wire yagis.

The ratio of wavelength to wire diameter is the K factor. At 7 MHz the K of the 25 mm and 2 mm elements are 0.0006 and 0.00005, respectively. These are small numbers. On 10 meters they would be only 4 times larger. There's no escaping the very small K factors of wire antennas on all HF bands. Be sure to specify the correct wire diameter in your NEC models to avoid mistakes.

Insulation

In the THHN link above you will find a table containing specifications for the insulation layers. One of the words used should give you pause: nominal. Insulation dimensions will vary for many reasons: manufacturer; forming equipment; business decisions; among others. Provided the wire meets critical requirements like voltage rating, weather and environment, failure rate, temperature/loss at rated current, etc., the product will almost always be accepted. 

Electrical wire is not intended for antennas so expect surprises with the insulation. I've tried using calipers to measure insulation thickness with little success. Insulation is compressible and difficult to make straight enough for the calipers to seat properly. I have done better using the published tables for my EZNEC models despite the variability.

Insulation is a critical factor for antenna design, so we must deal with the details. Since we can't rely on the insulation specs we must adapt to them. The biggest concern is velocity factor (VF). Insulated wire typically has a VF of 0.97 to 0.995. Hence the rule of thumb to shorten a wire antenna by 0.5% to 2%. This is not enough accuracy for yagis. A 1% change is 70 kHz at 7 MHz, and that is unacceptable for those aiming for performance. I assume that anyone building a 40 meter wire yagi has performance as an objective, since otherwise why bother investing the time and effort.

A nice thing about insulation is that corrosion is slowed. Moisture will still get in there if the ends are not sealed, and as the antenna wears under environmental pressure the nylon shell will break off (increasing the VF) and the base insulation will develop micro-fissures. Avoid the more colourful wire and always choose black since the (typical) carbon black pigment resists UV deterioration better than other pigments.

The VF of bare wire is far more predictable, at the price of corrosion due to complete exposure to the weather. If you live in an area with high levels of air pollution or near a sea or ocean the rate of corrosion will accelerate.

NEC2 supports specification of insulation for wires. Use the specifications of the wire if you can find the needed data. The important ones are the insulation's dielectric constant and thickness. The dielectric constant is determined by the insulation material. When I am not sure I use 3.5, and it is usually close enough.

Termination

The method used to secure the ends of a wire affects its electrical length. It is easier to get accurate results with bare wire than insulated. 

Consider the termination at right. Since it is insulated, the entire wire length contributes to its electrical length. That loop is next to impossible to model with NEC2. The wire loop is too small relative to wavelength to break into segments.

The actual end of the wire is the true end and so the small loop has a measurable effect. Since the current magnitude is close to equal in the loop and the phase is opposite on opposite sides of the loop, there is field cancellation that partially negates the wire length comprising the loop. But, as already said, it's difficult to model or predict.

Predictability requires stripping the insulation at the termination and wrapping the bare wire loop onto itself. Now the electrical length is to the outer edge of the loop. It is also easier to make a wrap from bare copper wire that will hold under tension. Plastic insulation is springy and can unwrap -- it has happened to me -- and it's worse with stranded wire. If you leave the loop insulated it is important for consistent results (after calibration, discussed below) that the insulator type, loop size, and length or the wrapped wire be the same on all elements. Follow the same procedure at the centre insulator.

Tension

Sag matters in a wire yagi since it lowers the interior angle at the apex. That increases the resonant frequency and lowers the radiation resistance due to increased field cancellation. 

Under tension wire will stretch (see above) and the resonant frequency will be lower. Unfortunately the frequency lowering action of wire stretch does not equal the increase due to sag. You'll have to adjust the yagi or its elements when either or both occur.

Some numbers will help. Making soft drawn wire hard drawn with tension can increase its length from a few percent to as high as 10% before it breaks. Soft drawn copper under ordinary use will stretch less than that. This is not a minor consideration especially as you go down in frequency and a wire antenna is long and heavy. Wire has to support its own weight in addition to support tension. Consider that 1% at 7 MHz is 70 kHz. That's a lot for a restricted bandwidth antenna like a yagi.

Tension is often more than you might imagine. A few years ago the ground anchor of my T-top vertical for 160 meters pulled out of the ground when the wind speed was 70 to 80 kph. It was just a wood stake pounded into the ground. To prevent further damage I went out in the wind storm to pound the stake back into the ground. I couldn't. The wind load on ~47 meters of 14 AWG insulated wire and the rope catenary was too high. I temporarily tied off the stake instead. After the storm I put it all back together and noticed only a small shift in the resonant frequency. For a single element antenna it was not a problem, but for a yagi it might be.

Straight lines are easy to draw and in modelling software. The ideal angle we get is not the reality. The interior angle of the antenna will be smaller due to sag. Modelling the curve in the wire is quite difficult and nigh impossible to get it right, and this is another problem setting the resonant frequency accurately.

We have a few options available to deal with sag:

• Increase tension: That may stretch the wire and you'll soon be repeating the procedure. Choose stronger wire or avoid excess tension.
• Pull the ends of the vee farther apart: With the inevitable sag you can get closer to the desired interior angle.
• Include a centre tube: Sag is moved outward from the high current center to where its impact is less.
  

Radiation intensity is in proportion to current and that is highest at the centre of a λ/2 antenna like an inverted vee. That is why centre sag is significant. Removing sag improves performance by way of a higher radiation resistance and higher height for the average current. The centre tube option nicely deals with the problem even if it isn't very long. As a bonus, as tension changes the tube will rotate from its horizontal position. It's a highly visible indicator that you have work to do. 

On the negative side, the tube must be split for the driven element and for the switching of a reflector coil. Split wire elements are much easier to build.

If there are no convenient supports for the ends of all elements in a wire yagi with 3 or more elements it is possible to use a catenary rope to support the ends of all the elements. Equalizing tension to avoid excess sag can be difficult. Here is a picture of such a catenary in action that someone brought to my attention. I've contemplated one of these to avoid ground anchors in farm field surrounding my towers for any wire yagis I might build at this QTH (none so far).

A further consideration for setting and maintaining wire tension is selection of the rope. It should not expand or contract in any weather and it should be UV resistant. Black dacron is a good choice that is available from many amateur radio retailers and suppliers. I have a large spool on hand for wire antenna project. 

Avoid polypropylene, nylon and natural fibre ropes that will not fare well outdoors and that will stretch with the weather and with age.

Since tension adjustment is unavoidable you should use knots and devices that allow easy release and adjustment. I am not very knowledgable about knots and mechanical tensioners so I will make no recommendations. I use a combination of knots and rope cleats.

How to get it right

It may sound counter-intuitive that wire yagis with 3 or more elements are easier to design, build and adjust than those with just 2 elements. One reason is that 2-element yagis have narrow bandwidths for gain, F/B and SWR. A second reason is that reversing a 2-element yagi requires a more complex switching system for symmetrical performance.

Yagis with 3 or more elements have simpler switching and the bandwidth is larger. A tuning error of 50 kHz is far less detrimental, to the extent that you might not notice it. You will notice it with a 2-element yagi. The Moxon rectangle variety of 2-element yagi does better with its larger F/B and SWR bandwidth. Its gain bandwidth is the same as a conventional 2-element yagi. If we want the best gain at our favourite frequency with a 2-element wire yagi or Moxon the tuning must be accurate.

How can we adjust a wire yagi to get the promised performance? As we've seen above, the variability due to wire choice and usage is surprisingly large. I follow one of two approaches: calibrate the wire or calibrate yagi performance markers. Let's look at both.

To calibrate the wire we first construct an inverted vee (assuming the yagi will use inverted vee elements) using the wire of your choice. Make the centre and terminations as identical as possible. Details matter. Attach coax of known length and type to the centre feed point. The coax should run straight down or orthogonal to the inverted vee to minimize coupling. Use a common mode choke to prevent the coax from becoming part of the antenna. Put tension of the ropes and measure or calculate the interior angle. Note the heights of the apex and the lower ends.

Measure the impedance of the inverted vee. Use a application like TLW (packaged with the ARRL Antenna Book) to transform the impedance to what it is at the feed point. Shift frequency up and down as required until you locate the frequency at which the feed point reactance (X) is 0 Ω. That's the resonant frequency. Do not adjust the element length at this time.

Construct a NEC2 model of the inverted vee. Take care that the dimensions exactly match the built antenna, for the layout and for the wire diameter and insulation. Set the real ground to what you believe you have in actuality -- medium is a good choice for most horizontally polarized antennas even though many urban/suburban locales have worse ground than that. 

The resonant frequency of the model should equal that of the antenna measurement, but almost certainly won't. If they are far apart, stop to ask yourself why. Investigate and redo as needed. If the frequencies are close adjust ground constants or wire insulation properties until the resonant frequencies agree. You will have to use your judgment. Don't just enter numbers at random!

Move the model to free space and locate the resonant frequency. It will have moved because the ground coupling is absent. Note the difference and adjust the real antenna so that its resonant frequency differs from your desired centre frequency by the same amount (the frequency could be higher or lower). This will get your real inverted vee close to what its resonant frequency would be in free space. This is the procedure I am using to calibrate the elements for my planned 40 meter 3-element rotatable yagi.

As noted many times in this blog and elsewhere, a yagi at a modest height behaves as if it were in free space since there is significant field cancellation in the vertical direction. You could say it doesn't "feel" the ground very strongly, or at least its effect becomes small in comparison to the mutual impedance between the yagi elements. 

Unfortunately it is very difficult to measure each element when it is in a yagi due to that mutual impedance, so we do it indirectly using the method described. All the elements can now be scaled from the calibration data. You must be careful to use the exact same wire and construction technique for the calibration to be effective. An extra inch of insulated wire on the end egg insulator is an inch too much.

The second calibration method is done after the fact. First, build the complete yagi. By whatever means get it close to the desired frequency range as possible. Err on the long side because it's easier to prune elements than to lengthen them.

Work with a friendly ham located broadside to the antenna (in the direction of the main lobe) to find the frequency of maximum F/B. Should that be inconvenient, an alternative is to find the frequency where the feed point resistance component of the impedance (Z = R + jX) is minimum. On the computer model find that frequency. The difference is the tuning error. I used this method to adjust my long boom 15 meter yagis.

To adjust the antenna, scale all elements by the calculated frequency ratio. For example, if the measured frequency of minimum feed point resistance is 7.350 MHz and the desired frequency is 7.275 MHz the ratio is 1.01 and the elements need to be 1% longer.

Dealing with uncertainty

I have been asked several times for the wire dimensions of the wire yagi designs found in this blog. My answer typically resembles what you've read in this article, and I can tell you that it satisfies few of them. The point is that I should not and cannot specify the lengths for the elements of a wire yagi! I don't know your wire, your environment or your construction techniques, and those are critical parameters for the reasons explained in this article. 

Sometimes I have shown lengths, and when I do I also specify the wire and mention that you will very likely have to adjust the lengths. I sometimes wonder if the message gets through to many readers. All I can do is provide guidance and show what can be achieved by those who put in the effort.

That, really, is the point of this article: wire yagis require work! If you must have an exact construction guide you should look at alternatives. Despite the challenge, building a wire yagi can be very rewarding, and educational. I enjoy the learning experience. Maybe you will, too.