Regular readers will know that a 3-element 40 meter yagi is in my 2021 plan. That remains true. It is a large project that is well beyond the means of all but a small minority of hams. I am stretching my abilities to execute this project. The antenna is intimidatingly large. My tower and rotator are up to the challenge, and were chosen for this long-planned antenna, but this is new territory for me.
It is vital to get the design right, mechanically and electrically. Lifting one of these monsters is difficult and mistakes can be costly. It is daunting to consider lowering and re-raising the antenna should it not perform as expected. Consider the dilemma I faced when the stack's upper 5-element 20 meter yagi suffered a matching problem after being raised. Yet it is a far smaller antenna than this one.
Construction of the yagi and rigging for the lift are proceeding well. I am combining my own abilities with the knowledge I can glean from hams that also have one of these big antennas.
One thing I will say about hams is that they are almost always eager to help. Heaven knows that I've pestered enough of them. Professionals in the tower business also have a lot to teach, if you know one well enough to approach. I am fortunate to know such a person, and he's been generous with his time, his advice and the loan of his tools. I've learned a great deal and I am increasingly confident that I can accomplish this project.
Performance objectives
My original intent was to limit the boom to 40' or 42' (~13 meters). After modelling the antenna I reluctantly lengthened the boom to 46.5' (45.5' from director to reflector). Those few feet increased the gain a modest amount, had little effect on F/B and improved the 2:1 SWR. The optimum 200 kHz for my needs is 7.0 to 7.2 MHz. The SWR rapidly rises above 7.2 MHz.
I decided the greater size and weight are worth it. Whether I notice the incremental performance on air is another matter.
My performance objectives for this antenna include:
- 2:1 SWR bandwidth of at least 7.0 MHz to 7.2 MHz: improved SWR above 7.2 MHz for those occasional domestic phone contests can be achieved with a switched matching network
- Free space gain of at least 8.0 dbi across the band
- F/B no worse than 10 db
- Optimized for CW and also effective on the international phone segment
- Move the 3rd harmonic well beyond the 15 meter band, using capacitance hats, to avoid significant degradation of the pattern of the yagis comprising the 15 meter stack
I reviewed the yagi designs in the ARRL Antenna Book and rejected them. Their large 3-element design favours SWR bandwidth over gain, and there is little improvement of F/B compared to other optimized designs.
An OWA antenna with coupled resonator has superb cross-band SWR at the mechanical cost of a fourth element, and I rejected it for that reason. A fourth element can always be added later without having to take down the antenna.
I spent several hours with an EZNEC model without capacitance hats -- for accurate SDC (stepped diameter correction) -- to explore a range of options. The important parameters are:
- Tuning of the director and reflector (resonant frequencies)
- Boom length
- Position of the driven element
The design I settled on has the following parameters:
- Boom length of 46' (45.5' from director to reflector)
- Driven element 21' from the reflector
- Centre frequency of 7.150 MHz, with feed point matching optimized for CW
- Parasitic element tuning of ±5.2% from the centre frequency
The performance metrics were verified by careful modelling. That process is discussed in a later section. I am confident that the real world performance will closely match the manually-calibrated NEC2 proxy model, with has the capacitance hats but with SDC necessarily disabled.
Modelling challenges
Capacitance hats exclude the possibility of accurate modelling with NEC2, alone or with the enhancements in EZNEC. For example, SDC does not work. This is why we repeatedly raised an experimental dipole last year to collect real world data. The NEC2 model can, with care, be mathematically calibrated using that data. When done well the combination of modelling and measurements can a design that performs to expectations.
The parameters determined with the experimental dipole include:
- Resonance shift with capacitance hats, including arm length and diameter
- Resonance shift for a given length difference of the fat diameter pipes at the centre of the element and the thin diameter tubes at the tips of the elements
- Determination of the 3rd harmonic to see where it falls relative to the 15 meter band, for elements tuned as a driven element, director and reflector
The effect of ground must be manually adjusted. The resonance and impedance of every single-element horizontal antenna is strongly affected by ground quality and height. This is done by moving the model dipole between free space and over ground of approximate characteristics. In my case the modelled free space resonance (where X = 0) is 45 to 50 kHz higher in free space than what was measured. For example, when the experimental dipole resonance was 7.300 MHz the free space resonance is around 7.345 to 7.350 MHz.
The next step was to model the dipole, exactly as built. Due to the absence of SDC and an error due to the capacitance hats the resonant frequency was calculated to be 0.938 that of reality. That is more than 6% low. The model's resonant frequency of ~6.700 MHz is the equivalent of 7.150 MHz in the ground-adjusted experimental dipole. The equivalent 40 meter operating range is 6.55 MHz to 6.85 MHz. Actually it's a little narrower due to scaling.
However, that's only true per the calibration procedure. Altering the dimensions changes the calibration. It is not usually possible to adjust the elements and then use the same scaling factor back to the real world. The adjustments should only be made to full-size elements and then scaled to the NEC2-based proxy model.
The director and reflector are scaled in a similar fashion to the driven element. Each was modelled in free space to set their resonant frequency relative to the model's centre frequency. Then it was moved to the yagi model. The complete yagi was adjusted to find the optimum design per my design objectives. Elements were isolated and adjusted, in the optimization process, and replaced in the proxy model.
Performance and relative performance
I was delighted to learn that the performance of the yagi, with its capacitance hat loads, is close to that of full size elements. This is not surprising since the loading is light to keep the elements to ~90% of full size. Shifts in the behaviour and performance become significant as loading increases.
The parasitic element tuning I ultimately settled on is ±5.2% of the centre frequency. Those are the parasitic element free space resonant frequencies. Tighter spacing of the parasitic elements increases gain at the expense of SWR bandwidth, and F/B at the band edges. There is no perfect choice: do what works for you and your operating objectives. SWR bandwidth and F/B matter to me, but not as much as gain.
Per
the model, and accounting for the average gain test in EZNEC, the gain
of the yagi relative to the equivalent with full size elements is -0.3
db at 7.0 MHz and falls to -0.6 db at 7.3 MHz. The downward correction is included in the charted gain. It is almost certainly a result of NEC2 limitations due to the capacitance hat arms connecting at right angles partway along the dipole elements. The average gain test is a feature of EZNEC that is well worth your close attention.
The comparison azimuth plot at 7.05 MHz (below) does not include the correction for average gain. The primary trace (black) is for the equivalent yagi with full size elements. Notice the slight broadening of the azimuth pattern of the loaded yagi. This is expected for shorter than λ/2 dipole elements, and it is responsible for the gain reduction.
The F/B is a closer comparison and almost certainly immaterial. A few decibels difference at the peak is dominated by modelling accuracy, construction accuracy and real-world interactions. We'll come to the SWR curves later in the article.
From my perspective and with my stated design objectives, I am happy with the calculated performance with respect to my objectives. The slight sacrifice in gain is worth it to reduce the interaction which would degrade performance of the 15 meter yagis even more.
Ignoring these trade-offs does not make the problems go away. They should be dealt with or at least acknowledged. Don't fool yourself.
Fine tuning the design
We are not done. Pushing NEC2 + SDC in the manner I've done has consequences. These are worth discussion since they are applicable to any yagi design, and not just big ones like this one.
The proxy model element dimensions are not the basis for the elements in the physical yagi. There is too much uncertainty in the scaling to trust the model too deeply. Instead the element were scaled from the experimental dipole measurements, as informed by the findings of the model.
The free space parasitic element resonant frequencies are 7.515 MHz (director) and 6.800 MHz (reflector), which are the ±5.2% offsets from the 7.150 MHz centre frequency. Due to the mechanical design the dimensions of the elements that can be varied are:
- Centre 2.375" pipe
- ½" tube
- ¼" tips
- Capacitance hat arm lengths
- Element-to-boom clamp
Since the experimental dipole survived so well for the year it was perched atop the 150' tower I do not want to risk major alterations to the yagi elements. What is easiest to change without unduly disturbing the electrical behaviour and mechanical robustness are the element centres, tips and the capacitance hats. The director is easy since it is smaller. The reflector requires more care.
The experimental dipole is now the director of the yagi because of its short 4' centre section (2' per half element) of 2.375" pipe (2" nominal, schedule 80). These lengths are extended to 5' for the driven element and 6' for the reflector. Each foot (6" per half element) lowers resonance by 100 kHz, weighs 1.8 lbs and adds 0.2 ft² of projected cylindrical surface for wind and ice loads.
There are ¼" tips on the driven element and reflector but not the director. Capacitance hat arms are 42" on the director, 43" on the driven element and 48" on the reflector. I had originally intended not to use ¼" tips since I was concerned about ice loading. Hearing about others' real world experience calmed that fear. The ⅜" section is fixed length so tip adjustment comes from telescoping the ¼" tip (if present) and the ½" tube into the next larger tube.
All the elements include ⅜" tubes, either at the tips or between the ½" tubes and ¼" tips. The rest of the elements are identical to the experimental dipole. One exception is that the overlap of the 1.9" pipe inside the 2.375" pipe is 8" rather than 12". The additional 4" per half-element lowers the resonant frequency 65 kHz.
The position of the capacitance hats along a tapered element is critical. The SDC algorithm in EZNEC replaces the tapered element with an element of the equivalent diameter. The "bumps" at tube transitions and the rate of current phase and amplitude change along the element are not accounted for. That is one reason why capacitance hats cannot be reliably modelled with NEC2 + SDC.
The SDC algorithms works very well for elements that are not in contact and are not close to other conductors, such as for yagis with full size elements. NEC2 also has difficulty accurately modelling wires that connect at acute angles and even for right angles. You can read more about this in the EZNEC manuals at W7EL's web site.
When I extended the capacitance hat arms from 42" to 48" during last year's experiments the resonance shift at 7 MHz was 155 kHz downward. The EZNEC proxy model for these hats at the same location predicts a shift of about 130 kHz. For the adventurous this can be scaled from the SDC-incompatable proxy model (where 6.55 MHz is equivalent to 7 MHz) to 138 kHz. We still have an error of more than 10%. I therefore rely on the real world measurements, not the proxy model, to calibrate the capacitance hats for this antenna.
Dealing with the vagaries of element taper and loads in NEC2 is a very interesting subject on its own. Perhaps one day I'll write an article to give a qualitative explanation. I'll leave the quantitative explanations for those better qualified to do so. With that said I'll move on.
I'm showing the EZNEC wires table for the proxy yagi's director. This will give readers an idea of what the model looks like. Do not take the dimensions of the tips and hats at face value. The built yagi uses dimensions extrapolated from the experimental yagi measurements. Again, the proxy yagi model informs the design but does not dictate the design.
The element-to-boom clamps are ⅜" galvanized plate approximately 7.5" per side. The equivalent diameter with a 2.375" centre pipe is ~5.2" using the W6NL equation for a round tube on a flat plate. Since it is less than 4" of a 30' to 33' half-element the impact on resonance is small. It is less than the uncertainty in the calculations. I ignored the +10 kHz model-derived shift to the resonant frequency. Don't ignore the effect for longer plates, or in yagis for higher bands.
If all that sounds complicated enough, well, it gets worse. My documentation of the measurements of the experimental dipole were not as good as I thought. Looked at weeks and months later the scribbles jotted down atop the tower were cryptic. My blog article wasn't entirely helpful since I did not include every detail.
The most perplexing errors and ambiguities were the lengths of ½" tube at each measurement and the original length of the capacitance hat arms (42" vs. 43"). I won't bore readers with the tedious work I did to resolve all those difficulties. This is not usually a problem with full size elements since NEC2 with SDC within EZNEC is astoundingly accurate. A yagi with loaded elements is more challenging, even for the lightly loaded elements in my yagi, as I discussed earlier.
Matching
I plan to use the same gamma match from the experimental dipole. This will be supplemented with a commercial common mode choke since a coax choke for 40 meters is large, and it is a hazard with the driven element so close to the tower.
The resonant frequency of the driven element is not critical. It is only necessary that it is of similar size to the other elements and that the raw feed point impedance of the yagi is within the range of a gamma match of reasonable dimensions. I will have to experiment with the gamma match after the antenna is raised. The element tips may require adjustment for a good match.
One nice thing about this antenna is that the driven element is within easy reach of the tower. The matching network doesn't have to be built, installed and adjusted before the antenna is raised. I can play with the gamma match and driven element at my leisure after it is on the tower.
Here are the calculated SWR curves for the 3-element yagi with full size elements (top) and that of the frequency calibrated proxy model for the real antenna (bottom):
The SWR bandwidth is better for the proxy model of the real yagi. That is suspicious. The mystery will remain a while longer until the antenna is up, the matching network built and adjusted and then measured. Although an L-network is used in the models -- since it is easy to accurately model and doesn't interfere with the SDC algorithm -- we've seen before that any of the common matching networks vary little in the SWR curves they produce.
For improved SWR above 7.2 MHz I plan to have a switchable matching network. The gamma match or a T-match must be used in combination with that network since the driven element is a continuous conductor. Due to the high rate of impedance change above 7.2 MHz a single network can likely only achieve a bandwidth of 50 kHz. That is enough for my purposes.
As we've seen above, gain is excellent at the high end of the band despite the matching challenge. Maximum gain at the high end or above the band and best F/B towards the bottom of the band is typical of 3-element yagis. High gain correlates with a low impedance, and that is why a broadband match is impossible with one network.
Ideally the network is mounted at the feed point but that is not strictly necessary. It can be closer to the shack for convenience. The loss of LDF5-50 Heliax at 7 MHz is very low and its SWR tolerance very high at 1 kilowatt so that the high SWR above 7.2 MHz is tolerable over the long transmission line out to the tower and 150' upward. I have not yet done the calculation.
Mechanical considerations: weight, wind load, ice load
40 meter yagis are big, really big. They only look small when they're seen on top of high towers. On the ground they are intimidating. I remember helping a friend assemble a full-size 3-element 40 meter yagi over 30 years ago and, at the time, I couldn't imagine lifting it onto his 140' tower. Well, he never did follow through but I remember that antenna very well. These are antennas that demand respect.
The projected cylindrical wind area is easy to calculate so I'll skip over the details. The boom and mast plate have an area of about 12 ft². Each element is about 9 ft² (more for the reflector and less for the director) for a combined 27 ft². At the nominal maximum 135 kph (85 mph) wind in our wind zone the lateral force is 250 lb on the boom is and 550 lb on the elements.
Depending on orientation to the wind the force will fall between those values. The standard multiplier of 2 to account for gusts, turbulence and oscillations raises the peak forces to between 500 and 1100 lb. Consider that when you listen to the weather forecast!
Ice is another matter. Element taper lessens the bending stress as you move outward from the boom. With high tensile strength aluminum alloy the antenna will survive substantial ice load, perhaps to ½" or more. If a wind storm hits when the antenna is coated with ice we may not be so lucky. Ice on the boom is not an issue since the truss provides support, however the boom must be strong in compression to withstand the horizontal force due to the higher tension on the truss cables.
I have a draft article in my files that I've sat on for a few years. In it I do a mixed qualitative and quantitative analysis of forces on a tower with a large 40 meter yagi on top. I may pull it out this winter to finish it and put it on the blog. I haven't because I am not a mechanical engineer and I don't want to make readers over-confident (or under-confident) should they choose to do something similar. I have to be careful with my approach and explanations.
All that said, I am confident that the tower, antenna, mast and rotator are up to the challenge. I know at least one other ham with the same system that has survived a very long time. I knew this from the start since I have long planned this antenna, and I chose the tower and hardware to be ready when the time arrived. That time is now.
In the next section I discuss the antenna mechanical design and not the rest of the system. Just keep in mind that the entire system has been designed with survival in mind. However, it has not been assessed by an engineer. That is why I will stop here with the discussion. Look through the blog archives to find articles about the prop pitch rotator system and the tower to discover what I am using. But don't expect to find calculations.
Mechanical design
The elements are structurally little different from the experimental dipole, and use the same pipe fitting methods. The only change is the joint between ½" and ⅜" tubes. Because the ½" tube has 0.065" walls the ⅜" tube won't telescope. Previously I reamed the larger tube enough for several inches overlap, cut a slit and used a hose clamp.
Now there are two #6 screws and a nyloc nut. A short slit ensures firm electrical contact. There is no adjustment needed or necessary since other tubes in the tips will telescope. I prefer this style for fixed joints. All the tips and capacitance hat arms have this change.
The 46' boom weighs 110'. There are two 20' lengths of 2.875" pipe joined by a 10' length of 3.5" pipe, all schedule 40. A shim reduces the gap along the 21" overlap to about 0.003" all around. The pipes are joined with 3 grade 5 ⅜" bolts each rotated 60° from its neighbours. Play is thereby minimized. This is far easier than fabricating and fitting a tighter shim.
The shim is a 2.5" × 1/16" tube that is surplus from an XM240 boom. It is split and spread to cover the pipe. Opening the tube so that it fit over the pipe was not easy for a large tube of high tensile strength. The sledgehammer in the picture (below left) played a role. The centre picture is of the element sections being joined, and the same was done for the boom sections.
I know hams who have used heftier pipes for the boom of 40 meter yagis. You should not use pipe that is smaller or of lesser tensile strength than what I used (6061-T6). The 2.875" diameter pipes were purchased used for a good price but the 3.5" pipe had to be purchased new. Aluminum is not cheap at these sizes and weights.
The boom truss is ¼" EHS and attaches to the mast approximately 6' above the boom. It is broken up with insulators since there is a 10 meter yagi directly overhead at the top of the 10' mast. Interaction is not really a problem since the truss is orthogonal to the elements. But why take chances when the cable, insulators, grips and turnbuckles are close at hand.
The element-to-boom clamps are ⅜" galvanized plates with ½" galvanized u-bolts. These are standard parts in the tower industry. The plates and the bolts are so strong that you must be careful not to distort the aluminum pipes when tightening the bolts. The one for the driven element has 3-½" bolts for the centre boom section. I did the machining for the driven element clamp and for the boom-to-mast clamp.
The boom-to-mast clamp is 12" × 12" × ½" galvanized plate. It took over 2 hours to punch those ½" holes for the various bolts. There are 4 clamps for the boom and 4 for the mast. We don't want anything to slip, vertically or by wind torque. The centre two mast clamps are commercial tower products with a large surface area for a stronger grip. The boom-to-mast clamp is already on the tower, as you can see.
The plates do not need to be larger than what I chose. There is ample evidence of their durability in other 40 meter yagis and in commercial tower applications with even greater wind and ice loads. The heavy pipes at the centres of the boom and elements also contribute strength at those major stress points.
The boom attachments for the truss are 3/16" galvanized angle stock that cost me nothing except for time in my workshop to punch the holes.
And last, with two more elements there are 16 more capacitance hat arms, with two pairs per half element. Since they worked so well I made more of the custom clamps that I used for the experimental dipole.
Coming up: raising the antenna
A sane person would call in a large crane to lift an antenna this size onto a tower. A crane that size would be expensive and could easily run into trouble in a wet hay field. Besides, it wouldn't be as much fun as doing it without heavy equipment. So I've designed a tram system to lift this behemoth onto my 150' tower (true height is ~43 meters).
As I write this article the tram and rigging are installed and have passed their initial tests. I don't know if the antenna can be raised before CQ WW CW due to the weather and the difficulty of coordinating friends' schedules. If it does go up in the next few days it is unlikely that it can be connected in time for the contest, or made rotatable since it takes time to disassemble the rigging. That's unfortunate but it is not a job to be rushed.
This picture taken two weeks ago show the partially assembled yagi at the launch position. It's now a race against winter. Once I have succeeded (or failed) to raise the antenna I'll write it up for the blog.
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