With modern software tools such as NEC2 it is entirely feasible to do so. However that is only true for unloaded elements to which you can reliably apply SDC (stepped diameter correction). Otherwise your options are more limited: NEC4 (expensive); or, purchase a commercial yagi (also expensive) from a company that has (hopefully) designed it properly. EZNEC version 6 supports SDC when using discrete loads (e.g. coils) but not appurtenances like capacitance hats.
If you have a friend with NEC4 you can ask for their assistance. I don't and in any case I would like to do the entire job myself for the challenge and for the education. Therefore another option is required.
In an earlier article I went through the mechanical challenges of building a 40 meter element. The small capacitance hat reduces the length to approximately 90% of full size and shifts the third harmonic resonance well outside the 15 meter band. This element is the basis for a 3-element 40 meter yagi.
Before liftoff: model calibration
I am using EZNEC with the NEC2 engine and using a combination of model extrapolations and in-the-field experimentation to generate the required data. The experimental element is critical to the process. It is split for dipole feed to allow accurate measurement with an antenna analyzer.
Although NEC2 cannot model this antenna it does inform the design. It is desirable to get close to the target frequency before the antenna is lifted into the air. Relying solely on trial and error will result in a lot of extra physical work which I want to avoid!
The first task is to estimate the error due to the lack of SDC. To do this I modelled the element without capacitance hats and plotted the impedance in free space with and without SDC enabled. The difference is stark.
For SDC enabled the antenna resonates (X = 0) at 8.03 MHz and it drops to 7.62 MHz when SDC is disabled. That's a shift of 410 kHz or 5%. This is an effect that should never be ignored or guessed at.
Note: For shifts greater than 2% or so it is better to use a ratio rather than an absolute (linear) frequency offset as an accurate scaling factor. Yagi parasitic elements are almost always offset more than that relative to the design (centre) frequency.
The other important effect is that of ground. A 40 meter dipole up 30 meters (¾λ) is strongly influenced by the presence of ground. Therefore we must inspect the R and X components of the impedance; however we need not be concerned about the effect of ground on the far field pattern.
For a yagi the effect of ground is small at this height so we need to know how much the experimental antenna is effected by ground and subtract the difference to know how it will behave as a yagi parasitic element. That is also why it is routine to model a yagi in free space and expect it to work the same on the tower.
For the dipole at this height the model calculates that resonance is lowered by 45 kHz (0.7%) compared to free space -- from 6.730 MHz to 6.685 MHz. For example, the actual measurement of the antenna as modelled in EZNEC is resonant at 7.110 MHz. We add 0.7% kHz to get 7.160 MHz, which more accurately describes its behaviour within a yagi. The adjustment to free space is desirable since a 45 kHz frequency shift of a 40 meter yagi's optimum pass band is quite large.
Also notice that the absence of SDC lowers the resonant frequency from the measured 7.110 MHz to 6.685 MHz in the model, or 6% lower. This is almost equal to the modelled 5% done without capacitance hats (see discussion above). The large difference exemplifies how challenging it is to calibrate for loss of SDC. Measurements are superior to relying solely on model calibration for complex elements.
As we'll see in the measurements the model's R value is also incorrect when SDC is disabled. It is more than 20 Ω lower than the correct value. The radiation resistance is less affected by the slight shortening of the element than the model calculates, which is important for antenna efficiency and gain.
With these model predictions in hand we can proceed to finalize construction of the experimental element and lift it into the air.
The element is as described in the previously provided link. One additional style of joint was added to extend element tips and capacitance hats with ¼" aluminum rod: a set screw. It is only suitable for experimentation since it is not mechanically sound. A slot and gear clamp or compression clamp are recommended for a permanent joint.
A hole is drilled near the outer end of the ⅜" tube and tapped for a 6-32 screw. It is a delicate operation since just 2 threads fit within the 0.058" tube wall (thread pitch is ~0.03"). I used ½" long screws since I had them but ¼" are better. The nut locks the screw after it is tightened against the rod. Since the fit is sloppy the nut should be little more than finger tight to avoid damaging the threads or lifting the screw off the rod.
The ¼" rod was the easiest and cheapest way to extend and adjust the element and hats. The rod is cheap and I have a bunch of it from a previous antenna project so there was no need to sacrifice more expensive tubing for the experiment. I hadn't expected to extend the capacity hats until I ran into an issue that I'll describe later in the article.
Rigging and lifting
The size of the antenna made for a cumbersome lift. I needed a location in the hay field with a clear path by tram line to 105' (34 m) that would keep the tips and capacitance hats from fouling in the guys of both tall towers, antennas and tree and with a convenient anchor for the tram line, ropes and related equipment. I chose the best location that didn't require the effort of screwing an augur style anchor into the ground
You can see in the above picture (with Alan VE3KAE steering the antenna) that the tram line anchor is the base of the 140' (40 m) tower with the 15 and 20 meter stacks. The tram is pulled tight with a winch and the antenna is manually hauled up by rope. It isn't too heavy at 52 lb (plus rigging) but it is tiring for one person. For the second session we had a larger crew to share the work.
Tag lines were added to steer the antenna around the guys you can see on the right. To protect them the capacitance hats were spread when the antenna was lifted a few meters off the ground and folded before touching down. I do the same for the XM240 and its smaller though more fragile capacitance hats.
We had minor tangles with the guy set whose attachment point was just a few feet below the top of the tram. Had we gone any higher the top guys would have been a more serious hazard.
It was awkward but worked surprisingly well. Tangling was easy to rectify without damaging the antenna. Chains and shackles connected the centre plate to the tram line pulley and haul rope.
The binding posts were attached to the feed point on the ground since it is an easy item to drop from the tower. The more fragile analyzer was carried up with me. It's amusing to see a tiny feed point on the fat pipes of the antenna.
The antenna survived multiple ascents and descents despite some guy tangling and bouncing on the tram as the haul rope was pulled. The improvised split and insulated element centre withstood the abuse without any problems. The antenna was blown off its ground supports twice during high winds between the two trial dates and suffered no damage, not even to the relatively fragile element tips and capacitance hats. That bodes well.
Trials, measurements and implications
In total we did 6 lifts of the antenna to gather the required data. That should be enough to confidently interpolate and extrapolate the dimensions of the 3 yagi elements using EZNEC without benefit of SDC.
The first measurement was to set a base line. From a rough extrapolation from the software model I expected the antenna to resonate higher than band centre. In that I was correct since it resonated at precisely 7.300 MHz. Correcting for the modelled ground effect the free space resonance should be close to 7.350 MHz.
For each trial I determined the resonant frequency, the impedance ±350 kHz and the frequency of minimum SWR for the third harmonic. The 5 subsequent trials explored variations of the following parameters:
- Length of the inner (largest) diameter section, which also shifted the position of the capacitance hats
- Length of the outer (smallest) diameter section (element tips)
- Length of the capacitance hat arms
- Test approximate dimensions for director and reflector elements
Only one variable was changed at each trial. This is necessary to avoid confounding factors that will leave you wondering the magnitude of two or more changes. You may think you're saving time but you are in fact creating doubt and ultimately making more work for yourself.
I was careful to orient the antenna so that there was minimal interaction with the guys above and below the antenna. The measured difference was only a few ohms yet that can make a difference for optimum yagi performance. You can get away with inaccuracies for a single element antenna that you cannot for a yagi. Don't deceive yourself into believing you can take shortcuts.
For the second trial the 1.9" pipe was extended outward 6" on each half-element. This simulates a 5' centre section of 2.375" pipe. The modelled difference of extending either diameter of pipe is only a few kHz using the baseline SDC model. The longer centre section may only be required for the reflector element. The third trial extended the tips by 6" using ¼" rods; there was not enough spare length in the outermost tube sections and I didn't want to unnecessarily waste new tubes cut longer.
As expected the rate of resonance shift differed for equal length changes at the centre (large diameter) and tips (small diameter). Within the 40 meter band a 6" length adjustment shifted resonance by 90 and 100 kHz at the tips and centre, respectively.
What surprised me was the large effect of small changes to the lengths of the capacitance hat arms and (per the model) their diameter. With the arms of the capacitance hats increased from 43" to 48" with ¼" rods resonance in the fourth trial was 155 kHz (2.2%) lower and the resistance (R) dropped from 76 Ω to 69 Ω (9%). I did not confirm the modelled effect of different diameter tubes in the hats.
The resistance drop indicates that, as expected, the more an element is loaded the lower its radiation resistance. In this case the decrease is not enough to noticably effect antenna efficiency. It can be substantial for elements significantly shorter than 90% full size, and will vary with the loading method.
My conclusion from the data is that the capacitance hats perform as expected to eliminate the destructive 15 meter interaction. Further modelling is required to confirm that this result applies to the yagi. The longer 48" hats will likely only be used for the reflector.
Length choices for the frequency extremes are greater than required for the director and reflector. These were deliberately chosen to bracket the targets during the trial to allow more accurate interpolation versus extrapolation. I am now confident, for example, that tip and hat extensions are only required for the reflector element. I prefer not to use ¼" rods even though I know others do so successfully in similar climates.
The ±350 kHz impedance measurements were approximately 45 - j35 Ω and 120 + j35 Ω. The reactance values were a little higher at the highest resonant frequency tested. These values were expected at the ±5% frequencies and their confirmation will help with designing the yagi.
Recall that tuning of the parasitic elements is to achieve the correct phase, not resonant frequency, since that and the element spacing determines the mutual impedance and the far field pattern. The reactance determines the phase shift. Tuning by resonant frequency is an heuristic that is only valid for unloaded dipole elements; it is not a general solution. The reactance measurements are critical.
I may conduct one or two more trials, but not immediately. It would be helpful to confirm the effect of tube diameters on the 48" capacitance hat arms since they are acutely sensitive to the diameter. These will have longer ½" tube centres and not ¼" tips to keep the joint count to a minimum. Other than this case I expect to rely on interpolation from the current set of measurements.
I will build an element resonant near 7.1 MHz with a continuous 2.375" centre pipe and gamma match. Although gamma matches are not usually employed on simple dipoles it avoids splitting the element for dipole feed (also required for a beta match) for a robust mechanical design.
Modelling the 3-element yagi has already begun. However there is no rush since I don't intend to build it this year. For now it is enough to generally characterize element parameters to achieve the yagi design I want. I am encouraged that the modelled performance parameters -- gain, F/B, bandwidth and SWR -- are close to that of a 3-element yagi employing full size elements.
Proceeding in small steps is a sensible way to custom design and build an antenna of this size. Later this year I will lift the dipole to the top of the mast of the 150' tower, where the XM240 was once located and performed well. This will give me a high 40 meter antenna until I am ready to build the yagi, albeit one with no F/B and less gain than a yagi. The yagi will be my major antenna project in 2021.
The dipole will test the robustness of the element design in severe weather through a cycle of seasons. Intensity of wind, electrical discharges and ice are greater at that height and I want to be certain that the element is equal to the challenging conditions. A 3-element yagi made from these elements will experience even greater mechanical stress.
I want to build this antenna well. It has to last a lifetime: mine.
|Heading down after a job well done|