Lifting the 40 meter yagi onto a 43 meter high tower was not the end of the project. It was also necessary to design and adjust the feed system, and then test it on air. I can now confirm that the antenna works. However, the SWR is not what it should be, and that is worth a discussion.
I will start with a discussion of matching the antenna to the transmission line. After that I'll give my initial impressions from several days of use. You can skip ahead if that's the part that interests you.
The reason the antenna elements are lightly loaded with capacitance hats is to defeat interactions with the yagis of the 15 meter stack. That is a particular concern when the 15 meter and 40 meter yagis are pointed towards Europe (northeast), which is likely to often occur during the years bracketing solar maxima. The siting of the towers has trade offs and I knew that I'd eventually run into issue like this.
As I discovered during modelling of the interactions, there is a difference between element resonance and system resonance. That is, the 3rd harmonic of the 40 meter yagi is different from that of each element in isolation. The yagi elements are of course tightly coupled and their mutual impedances determine the system resonance. Modelling is great but a measurement is better.
As the frequency increases any antenna will exhibit an increasing number of minor and major resonances. For this antenna we are concerned with any resonance near the 15 meter band. The VNA plot shows that the design successfully shifted the 3rd harmonic well above the 15 meter band. That's good! The modelling study suggested that pattern distortion of the 15 meter yagis due to the 40 meter yagi interaction with capacitance hats is well below that of interactions due to tower guys.
Measuring the pattern of a yagi is quite difficult so I am relying on the combination of modelling and impedance measurement. I tentatively conclude that I've accomplished my objective.
Gamma match design and challenges
The gamma match is the same one used for the experimental dipole. A few changes make it more suitable for the yagi. Initial adjustment of the gamma match was facilitated with a 500 pf variable capacitor clamped onto the gamma rod. The actual gamma capacitor is a length of coax inside the gamma rod. A long, cylindrical capacitor behaves differently and requires further adjustment to the gamma match.
There are effective methodologies to the design, construction and adjustment of gamma matches. Nevertheless it remain something of a black art. It is a very flexible matching system that can transform a wide range of impedances to the desired 50 + j0 Ω, however that flexibility can lead one to make poor choices. Yes, you may be able to achieve a perfect match at one frequency, but that does not necessarily mean that the match is optimum across the antenna frequency span.
I have yet to find a gamma match design process or algorithm to accomplish the latter. Unfortunately I don't have one of my own to offer. This is a topic I would like to investigate when time allows. Until then I have to rely on vague heuristics, measurement and experiment. Unfortunately that is not easy at the top of a 150' tower. At least the driven element is easily accessible for adjustment, unlike HF yagis with 4 or more elements. For those big antennas you either lower the yagi to the ground to adjust them or you improvise.
The first SWR curve is quite poor. The DE (driven element) is tuned for resonance at 7.150 MHz. This is not ideal since the gamma rod length and gamma capacitor value are larger than I'd like. After re-reading several technical resources, I realized that it is better to have at least -20 Ω or more of capacitive reactance at the centre frequency, just as for the beta (hairpin) match. Although the antenna has good performance from 7.0 to 7.3 MHz, the centre frequency for matching should be 7.1 MHz. There is insufficient capacitive reactance in the antenna as designed.
Modelling confirmed that adjusting the length of the DE changes X without any significant change to R. Changing the resonant frequency of the DE (within quite a large range) has no effect on the gain and pattern, despite the common belief of many hams. Yagi performance is almost entirely determined by parasitic element reactance at the operating frequency and position relative to the other elements.
The DE was shortened by 12" (30 cm) on each half element by sliding the ½" tube into the ⅝" tube; the ¼" tips are less adjustable so they are left alone. The change raises the resonant frequency from 7.150 MHz to about 7.350 MHz, which should add at least -20 Ω to X. Making the adjustment involves rotating the DE on the boom, climbing down the tower ~30', hanging out from the tower to make the length adjustment, and then repeating the process for the other side of the DE.
When I first tried adjusting the DE length the wind was very strong, the temperature near freezing and the element tangled in one of the guys when rotated for the second half-element adjustment. I gave up and completed the adjustment a day later with the antenna rotated a few degrees to clear the guys. The SWR curve was much better, ranging from 1.4 at 7.0 MHz to 2.8 at 7.2 MHz, and 1 at 7.090 MHz. Unfortunately my phone glitched and the picture of the analyzer screen is lost, so you'll have to take my word for it!
Even so the SWR bandwidth is less than what is possible with full size elements. My modelling indicated otherwise but I suspected that was optimistic, careful scaling notwithstanding, because NEC2 inaccurately calculates the reactance for complex antenna shapes, such as the capacitance hat loaded elements of my yagi. The 2:1 SWR bandwidth ought to be better than 150 kHz.
The feed point as currently implemented is quite simple: the gamma match and a bracket with the UHF jack. The RG213 rotation loop to the Heliax transmission line was already there from previous antennas that were on the 150' tower. The weatherproofing was completed after the photo was taken.
Notice that there is no common mode choke. It was expedient to exclude it even though I have a commercial unit on hand with coax wound on a ferrite torroid. Gamma matches are said to inherently provide a measure of common mode rejection, but I have never verified the truth of that. Although a choke is highly recommended it is perfectly possible to escape its ill effects with no measures taken. I will add one next year even though I notice no ill effects.
The gamma rod is a telescoping 6' long ⅝" tube inside a 4' long 0.84" OD pipe. When moving the strap between rod and element I keep the strap bonded to the ⅝" tube and trombone it inside the pipe. Because the final strap position is further inboard the pipe is almost superfluous. It also means that nearly the full length of the gamma capacitor's outer "plate" is the ~½" ID of the ⅝" tube. It is a good fit for RG213 sized coax with an outer diameter of about 0.4". Perhaps I will get rid of the larger pipe and adjust for the different step up ratio due to a narrower rod. If I'm lucky the change will be helpful.
RG213 is a poor choice in this application. Unlike the gamma capacitors of my higher frequency yagis, I use the outer conductor (shield) of the coax as the inner capacitor plate. The problem is that the jacket of RG213 is typically plasticized PVC which is a poor dielectric at HF. The inner conductor surrounded by the PE dielectric, stripped of the braid and jacket, is superior and well suited for this application. The expected loss of PVC at 7 MHz is not high but it makes little sense to go to the trouble of building this antenna and making compromises.
A better choice is LMR400 due to its PE jacket material. The jackets of both are infused with carbon black but not enough to be a flash over risk. The ID of the gamma rod and the dielectric constant are important parameters when constructing a gamma capacitor of this type. Here's what I measured:
- RG213 (PVC) inside a 0.622" ID pipe: 4.7 pf/in (1.9 pf/cm)
- RG213 (PE dielectric, stripped of braid and jacket) inside a ½" ID tube: 2.1 pf/in (1 pf/cm)
- RG213 (PVC) inside a ⅝" OD tube: 8 pf/in (3.2 pf/cm)
- LMR400 (PE) inside a ⅝" OD tube: 5.7 pf/in (2.3 pf/cm)
Voltage across the gamma capacitor is a concern since it can be quite high. The lower the capacitance the higher the voltage across the capacitor. Using TLW to develop an approximately equivalent L-network of the same topology and impedance transformation there is ~700 volts at 1000 watts. The LMR400 jacket is sufficient provided that the far end of the coax is well taped or similarly insulated. So far it is working well although that might change if water enters the gamma rod. I sealed the rod to prevent that from happening.
Proceeding with the last of these options, I used 60" of LMR400 with a measured capacitance of ~330 pf. By a combination of trimming the coax and telescoping the gamma rod I got the ~295 pf needed. Unfortunately the final SWR curve is not as good as with the variable capacitor.
There are two differences between a fixed position capacitor and the cylindrical gamma rod capacitor that may account for the degraded SWR curve:
- As you telescope the large, inner pipe to reduce capacitance (more -X) the wire from the connector to the capacitor get longer (more +X). That makes adjustment more difficult and alters the frequency-sensitive behaviour.
- The gamma rod capacitor is only ~1.5 meters long, but that is long enough to exhibit transmission line effects. Assuming a velocity factor of 0.7 for the jacket, the LMR400 section is over 18° long at 7 MHz. The effect is not large but it is frequency sensitive and the overall impact is difficult to calculate.
All that said, the antenna works. It is cold up there and I had had quite enough for the season. I declared it to be "good enough" for ham work and climbed down for what I hope is the last time this season. The inconvenience of a less than perfect SWR is tolerable until I can deal with it in the spring sunshine.
On the air: initial impressions
Achieving gain on 40 meters is challenging for most hams. For several years running, the most popular articles on this blog are those about 40 meter wire yagis. Articles about bigger antennas may be interesting reads but few hams would contemplate undertaking those projects. Small rotatable yagis with shortened elements, like my Cushcraft XM240, are more common but still a relative rarity.
This 3-element yagi is a revelation. It is performing beyond my expectations. Part of that is the height but I don't remember the XM240 at the same height doing so well. DX signals in comparison to the XM240 at half the height are pretty well without exception stronger. Sometimes by a little and often by quite a lot. Switching back and forth has become one of my favourite activities for the past few days.
Most hams in this region find that there is usually little difference between signals from Europe for the same antenna at 20 meters and higher. The typical elevation angle for the path is 10° to 20°. That is not the case between the XM240 and the 3-element yagi. At worst signals are the same strength. At best European signals are 3 to 4 S-unit stronger. That's a remarkable difference.
As the path length increases the average difference between the antenna is more marked. During our wintertime late afternoons long path openings to east Asia many stations can be heard and worked. A simple CQ is usually enough to attract several callers from Japan. The XM240 at the same height didn't do half so well. Flipping between the antennas, many of these signals virtually disappear on the XM240. It is true for Europe and other directions as well: signals that are barely discernible on the XM240 are solid copy on the 3-element yagi.
I have been having fun this week! The antenna coming online now is like a Christmas present to myself. I keep telling the friends who helped me raise the antenna to come over and try it out. None has as yet, but perhaps a few will once the holidays are over.
I expect the antenna to pay dividends in DX contests to come. My plan is to reserve the XM240 for North America and DX paths off the direction of the bigger antenna. 40 meters has been my most problematic band during contests and that is going to change. This antenna puts a smile on my face. After close to 50 years with a ham radio license it is rare that anything in this hobby can do that.
Improving the antenna
The SWR needs attention. I need it flatter across the band to be compatible with a solid state amplifier. With my current manually tuned tube amps it is not a problem up to 7.2 MHz other than having to touch up the tuning when QSYing more than about 25 or 30 kHz. Ideally, the SWR should be below 1.5 from 7.0 to 7.2 MHz. The antenna does not need to match well above 7.2 MHz since that 100 kHz segment is only used in our ITU region, so the lower XM240 is good enough for the shorter paths.
I will first try variations of the gamma match. Since the voltage across the gamma capacitor isn't very high I may try a fixed position capacitor, fixed or variable, to equal or exceed the better SWR found during the adjustment process. Alternatively, the gamma match can be optimized for CW (7.0 to 7.1 MHz) and install a switched L-network to improve the SWR between 7.1 and 7.2 MHz, and perhaps another for higher than 7.2 MHz.
If I put the gamma capacitor in a box I will have room for an L-network. It has to be an L-network since varying the capacitor value isn't good enough. The R component of the impedance dips too far below 50 Ω as the frequency rises.
Another parameter to be adjusted is the DE length. More capacitive reactance by further shortening the DE may help. Certainly the SWR bandwidth improved by raising the DE resonance 200 kHz, as described above, and it is reasonable to think that a little more can be helpful. It is not so easy to determine the DE reactance to achieve the broadest SWR bandwidth. I have not yet found a definitive technical resource that addresses the issue.
As a last resort, I will take down the DE and convert it to a split element. More matching options become possible at the expense of a more complicated mechanical design. I do not foresee adding a coupled resonator (4th element) to make it an OWA yagi. That would add another 9 ft² of wind/ice area and the capacitance hats might get too close or touch in the breeze.
I'll close with a annotated picture of the antenna farm that includes the 40 meter yagi. The elements are slightly askew and the boom is not aligned with the 10 meter yagi above it. These are simple to fix but will be delayed until spring. The picture has been uploaded to my QRZ.com page.
Have a merry Christmas and a happy new year. There may be one non-technical article to come before 2022 arrives, but no promises.