If you've followed this blog for a while you'll know that 40 meter gain antennas are very much top of my mind. I cannot fit in a gain antenna at this location, not even a wire yagi, and certainly not the 2-element yagi I have in storage. So I plan ahead.
One of the questions I am pondering is the relative performance of 40 meter rotatable yagis with shortened elements. A full-sized 3-element or 4-element yagi is a monster: typically well over 100 kg weight and up to 30 ft² (3 m²) of wind load. Although the tower I recently purchased can handle this size antenna there is the matter of erection and maintenance. I want to be certain the effort is justified. So if comparable performance is achievable with a smaller yagi that becomes an attractive option.
The subject of compact and full-size 40 meter yagis is something I hope to address in future. In this article I will focus on coil-loaded tubing elements. Rather than address a complete yagi with short elements, which complicates the design in several respects, there is some insight to be gained by investigating a single loaded element.
The basic design
With EZNEC I modelled a dipole with 25 mm (1") constant diameter aluminum tubing. This is not a realistic design, which would require tapered tubes. The Leeson correction in EZNEC cannot be properly applied to elements with loads, be they coils, capacity hats and other systems. For the current study there is no need to find the exact length: the NEC2 engine will tell us what we need to learn about performance. Getting the dimension exact can be dealt with when and if an antenna is built.
I placed the loaded dipole in free space to avoid the effect of ground. Ground interaction with the near-field of a yagi is in any case less that than of a single-element antenna, allowing the model behaviour to be most useful. Coils are placed at the midpoint of each half element. This is a typical placement for loading coils since they become less effective and larger further outward and can decrease element efficiency when placed further inward.
Element length is then progressively shortened from full-size to just under half-size. Inductance is set so that resonance (R+0j) in all cases is 7.100 MHz. Gain is calculated with selected values of coil Q from 100 to 800.
The higher the Q the lower the loss in the coil: Q = X / R, with X (inductive reactance) a function of coil inductance and frequency. Since R = X / Q it is a simple matter to calculate the ESR (equivalent series resistance) of the coil for known values of X and Q. As Q declines, R increases. As R increases so does the power dissipated by the coils, lowering performance and limiting high power operation.
Notice the current profile when coils are inserted. In a short element (50% full size shown above) the current decreases only a little from element centre to the coil, then sharply declines to zero at the element tip.
Coil inductance, Q and radiation resistance
The broadside gain of a dipole in free space is ~2.15 dbi. Even with perfect (zero loss) coils the gain decreases as the element is shortened. That power goes into broadening the pattern. Gain will decline further due to coil loss and conductor loss. The latter is negligible for elements made from aluminum tubing, so it is the coils we must optimize.
The radiation resistance of a λ/2 dipole declines as it is shortened. Since the (loss) resistances of the coil and conductor are in series with the radiation resistance, as the dipole gets shorter the loss increases. The matching network to transform the net feed point impedance to 50 Ω also has increasing loss, although this is not addressed in my model. Total loss sets the practical limit to how short an element can be made and still have acceptable performance.
Capacity hats and linear loading also introduce loss, an amount that depends on configuration and, again, on how short the element is made. There is no free lunch. Managing loss has a cost. Our job is to optimize the design to maximize performance and minimize complexity and cost.
As loading increases the antenna bandwidth also declines. This is mainly due to the lower radiation resistance, whereby the impedance Z = R+Xj changes more rapidly as X comes to dominate R. That is, the rate of feed point impedance change is more rapid as the frequency of operation moves away from resonance (Z = R+0j).
When the element is incorporated into a yagi, already a high-Q antenna, the problem can become worse. Since that is my ultimate goal I have an incentive to find a design that is not too long and not too short, but just right.
Putting it all together
With all the design components in place we are ready to run the numbers through EZNEC. In this way we can develop a picture of what to expect from an inductively-shortened 40 meter tubing element. As mentioned earlier, element diameter is fixed at 25 mm and the position of the coil is always at the midpoint of each dipole leg (half element).
For those unfamiliar with how coil Q is affected by its construction I strongly recommend you read what W8JI has to say on the topic of loading inductors. There is no need for me to reiterate what he so describes so well. You can also look at VE6WZ's designs to see what a high-Q loading coil for a low-band yagi looks like.
The chart includes the case of a lossless coil (Q=∞). Although not physically attainable, it shows the maximum gain that a shortened dipole can achieve. W want to get as close as possible to that value with a realistic design. As stated earlier, short dipoles have less than 2.15 dbi broadside gain just because they are short, irrespective of loss. I stopped shortening at 40% of full size since at these short lengths the coil loss becomes unmanagable.
We can summarize what this chart tells us:
- Coil Q is less important when the element is close to full size. That is, the loss may be negligible. So build the coil more for endurance than high Q,
- High coil Q cannot prevent large loss when the element is very short. Q=800 is approximately the best we can attain for a practical coil in this application, and Q=600 may be best achievable.
My own rule of thumb is to keep the net gain above 1.7 dbi, which allows for -0.45 db due to a combination of coil loss and element shortness. When elements above this value are incorporated into a yagi the bandwidth and performance can usually be successfully managed. The Cushcraft XM240 elements are just above this cut-off, with elements ~65% of full-size and a coil Q of ~200.
If your performance objective is more modest a low target may be justified. It's a personal choice, provided the loss does not grow so large that operating QRO becomes a risk. More on this below.
Implications for high power and trap antennas
To be specific about loss let's take an example. You are running 1,000 watts to a 70% size dipole whose coils have a Q of 100. The gain is -0.43 db with respect to one with perfect coils (Q=∞). Coil loss is therefore ~100 watts, or 50 watts per coil.
Depending on the mode and the weather this can easily damage the coils and render the antenna inoperable. Consider that a coil with Q=100 is typically close wound with enamel wire on a solid dielectric core. It may not be easy to shed that much heat in many ambient conditions, especially when combined with a weatherproof coating encasing the coil.
The similar situation applies to trap antennas, including tri-band yagis. On bands where a trap passes the RF it is not doing so without effect. On those bands the traps behaves as an inductor, and all of the above discussion applies. Trapped elements are shorter than full size because they are inductively loaded dipoles.
A tri-band yagi element on 20 meters has both the 10 and 15 meter traps behaving as inductors. The Q of those inductors is perhaps no better than 150. The loss can be significant, limiting gain and dissipating substantial heat. It is for this reason the 15 meter trap on Hy-Gain tri-band yagis rated for maximum legal power are wound from copper rather than aluminum. The lower resistance is needed on 20 meters, not 15.
Construction issues (real coils)
We cannot always design a coil for highest Q. There are practical limits, the most serious being fragility. In climates like mine the effect of ice (freezing rain) is an ever-present hazard. Also consider corrosion and fatigue from bending in the wind.
It must also be built around on outside a non-conducting structural member such as fibreglass which is needed to place the coil in series with the element yet maintain the yagi's structural strength.
These can be dealt with, though as the coils become larger so do the challenges. The coils on an XM240 are not high performance, but get the job done at a modest loss. Think about the trade-offs if you ever go this route. Again, pay close attention to what W8JI has to say on this topic and what VE6WZ has achieved with the coils he's built for a hostile climate.
Last, there is no good way to model a tapered yagi element with loading elements using NEC2, even with the Leeson correction. Be prepared to tune the elements, individually, on the tower. Or invest in NEC4.
My next steps
At some point, perhaps over the winter, I will model a few yagis with coil-loaded elements and see what I can come up with. This has been done before, though not by me and perhaps not with the same set of performance criteria. Even if I go no further than models there will be something new to learn. As usual I will share that learning on the blog.
I will also share my thoughts on other element shortening techniques. There are some I like and others that I do not. In the end I may yet opt for a full-size, 3-element 40 meter yagi, or go with one of the large wire yagis I've previously described.