Tedium of Single Band Contests

As I write this, the 2022 CQ WW 160 Meter contest is not over. But it's over for me, and has been since Saturday evening. The endless tedium wore me down. Better DX conditions would have helped, since without that the prospect for contacts is severely limited.

Some people like that and will work with whatever the propagation gods (or devils) provide. I can live with that in most contests. You make do since you know that everyone else is in the same situation. Skill and technology are what make winners.

In a single band contest the application of skill is narrower. When the DX isn't there on top band you have two things you can do: call CQ endlessly and trawl the bands (and cluster/skimmer spots) for fresh meat. I can maintain my enthusiasm for a while. Eventually the tedium gets me down. I have regularly bailed early from contests such as these. This isn't a new problem for me, since it was the same when I first got into contesting as a teenager in the 1970s.

My strategies for countering the tedium have been to operate with a handicap like QRP or as a member of a multi-op team. With an inferior signal every QSO is an accomplishment. There are always more stations to work and challenges to overcome. With a kilowatt and a full size vertical on top band the QSOs are not so difficult. After the first 600 to 700 QSOs you have milked at least 80% of the available stations and the rate falls off a cliff.

I had over 700 QSOs in the log when I shut down in the wee hours of the first night of the contest. I worked every available state/province multiplier and over 50 countries, despite the mediocre conditions. Many other countries were heard but they did not hear as well as the hordes calling them. Productivity suffered and the long tedium had begun.

When I resumed Saturday evening the rate improved as many stations made their first foray into the contest. Very soon that pool dried up and the tedium resumed, worse than before. Many contesters love the challenge of scrapping for every contact. The best operators scan the bands or jump on spots with one receiver while listening to answers to their CQ machines on another receiver. A few have sophisticated equipment to allow them to do both concurrently. The rest of us can only listen on the second receiver when the CQ machine isn't transmitting.

I am not happy with that style of operating. DX conditions were worse the second night and that accentuated the tedium. So I quit the contest. I never had the inclination of winning in any category and, frankly, my station, good as it is, is inferior to many others. There is added frustration from the Beverages which allow me to copy too many stations that cannot hear me. Oftentimes a kilowatt is no more productive than QRP. At least the amp keeps the shack warm during winter weekends.

I can sustain my enthusiasm in a multi-op because off times break the tedium. Every time I sit down to do a shift I am refreshed and able to dig in and get the job done. As a single op the tedium is unremitting and it wears me down. I admire the operators who deal with it better than I can.

This problem is common to most single band contests. It also occurs in contests with limited participation. I place ARRL Sweepstakes in a similar category since you can only work stations once regardless of band. The outcome is much the same, but with more spectrum to cover.

For the contests I most enjoy you respond to conditions and ever-changing activity levels by band and mode changes, alternating CQ and S & P, SO2R, watching signal strengths and spectrum scopes, among other strategies. Building and operating a multi-faceted station that permits these tactics sustains my interest and enthusiasm before, during and after the contest. In many respects I enjoy that more than operating in contests.

Single band contests rarely suit my desires. There are exceptions. Examples in 2021 include my 15 meter single band assisted entry in the CQ WW SSB contest and my (unofficial) 20 meter assisted entry in the ARRL DX SSB contest. I had fun putting to the test the recently completed stacks for 15 and 20 meters. I may do the same on 40 meters in one of the upcoming ARRL DX contest weekends to see what I can do with the recently completed 3-element yagi.

I will continue to operate the ARRL and CQ 160 contests but probably never with the objective of winning. To become competitively oriented I would need to make it a multi-op operation. As a single op, it's mostly an opportunity to work DX that is otherwise sparse on top band and to compare my antenna and station capabilities to those of others. The latter spurs my technical side to improve my station. 

Outside of contests, there is now far more top band DX to be worked on FT8, and I do make regular appearances. That's a story I'll defer to a future article.

Yagi Side Resonance

RF is very sociable: it happily interacts with everything in the universe. A few interactions are significant, some are minor and the vast majority are negligible. As hams we discover or predict interactions, then deal with the problematic ones and ignore the rest. Often, interactions are unknown or dismissed, and only addressed when they are too severe to be ignored. 

As deliberately radiating devices, antennas are especially prone to interactions, as the perpetrator or as the victim, or both. As the victim, an antenna's pattern and efficiency can be degraded by interactions. Those interactions can be with structures, utilities, trees, ground other antennas within a couple of wavelengths.

When I designed my 3-element 40 meter yagi I paid particular attention to its interaction as the perpetrator and the 15 meter stack as the victim. It is big and high enough that it is not particularly prone to be a victim. This is helped by the vertical polarization of the 80 and 160 meter antennas: orthogonal antennas interact little.

Here you see a simple 80 meter dipole excited at 3.6 MHz. It is positioned 200' (60 m) laterally from the centre of the 40 meter yagi and 50' (15 m) lower. The 40 meter yagi has a substantial mutual impedance and is happily interacting. How is this possible? 

It is no surprise that the pattern of the 80 meter dipole is distorted. For an 80 meter yagi with 2 or more elements the pattern degradation would be substantial. This is of particular interest to me since I am considering a wire yagi for 80 meters suspended between my two tall towers, including the one supporting the 40 meter yagi.

A ham in the distant past had the interesting idea of making a yagi into a dipole for the next lower band. Viewed from the side a yagi is a short dipole with large capacitance hats. A typical 3-element yagi resonates at about half that of the design frequency. That is, a 3-element 20 meter yagi is resonant within or near the 40 meter band, and the same is true of a 3-element 40 meter yagi on 80 meters.

The trick is with the feed point. You must excite the boom and not the driven element. Although they are mechanically and electrically connected the 40 meter feed is neutral with respect to the boom. As is common knowledge, the elements of a yagi are electrically independent of an orthogonal boom that crosses their centres.

Yagis with elements insulated from the boom do not have this attribute. At least the outermost parasitic elements -- reflector and last director -- must be electrically connected to the boom. 

Since the boom is a continuous conductor a similar feed system is required as for a yagi with a continuous driven element. A gamma match may work. More often an omega match must be used since the yagi cannot be adjusted to be compatible with a gamma match. In an earlier article I referenced a couple of construction articles by those who have done this.

Were the elements of the yagi insulated from the boom, its 46' (14 m) length would serve pretty well as a dipole on 30 meters.  

For those modelling these effects it will be necessary to add the boom to the model. It is ordinarily omitted from the model because, other than the element-to-boom clamp, the boom is neutral. To model the boom dipole I had to split the centre wire of each element to allow connection of the wires that comprise the boom. SDC (stepped diameter correction) and other NEC2 limitations that confound accurate yagi modelling are a relatively minor source of inaccuracy when the elements are employed as capacitance hats.

Both matching networks are difficult to retrofit to an existing 40 meter yagi due to its size. For example, the calculated gamma rod length for the impedance at 3.6 MHz is 13' (4 m) long. There is no good way to do that without a crane and basket. More capacitive reactance can reduce the length by several feet but that requires rebuilding the 40 meter yagi! Perhaps a "long enough" but short gamma rod and an L-network will get you to 50 Ω.

Notice that there are other resonances, which is not unusual for an antenna with many protuberances. There is a resonance at 14.4 MHz that, due to model inaccuracies, might actually fall within the 20 meter band. I have not done the modelling to determine the magnitude of the 20 meter interaction.

Although the antenna can have a DE feed point for 40 and a boom feed point for 80 meters, it is not advisable to operate both bands concurrently without band pass filters that are up to the challenge. However this is usually only a concern for multi-op and SO2R contesters. Everyone else can utilize two transmission lines (one terminated) or a switch at the antenna.

There are pros and cons in this situation. The major benefit is the possibility of a high dipole on a band where one might otherwise only be able to deploy a wire antenna like an inverted vee at a lower height. The major disadvantage is that a yagi can interact with a horizontal antenna for the lower band when the boom is broadside to that antenna. There is no one solution since every station is different with respect to operating objectives and favoured beam directions.

That lower resonance is there whether you feed the boom or not. Putting that lower band resonance to use as a dipole may involve significant effort. The boom resonance can be defeated in the same manner as for a tower. However I've never heard of someone taking the trouble to do so. Interactions are silent so that their impact is easily mistaken for other things and therefore may never be addressed.

Out of interest I created a boom model for my 5-element 20 meter yagis. The resonance is lower than half of 14 MHz because, with 5 elements, the boom is electrically longer. The boom resonance surprisingly falls right inside the 60 meter band. Of course it almost certainly doesn't but it should be nearby. But I have no interest in that band and the interaction isn't important since it isn't a contest band.

Notice how the elements adjacent to the feed point at the boom centre are very active (directors 1 and 2), but not so for the other 3 elements. There isn't much current flowing at the extremities since the most active elements introduce a current distribution discontinuity. That is in the nature of capacitance hats. There is a similar effect with loading coils. That is why they are effective at their job of shortening an antenna.

More can be said of unusual yagi resonances, how to positively exploit them and the downside of interactions with other antennas. But I won't. Every antenna and station is unique so it's enough to raise awareness of this little understood issue. Look around your antenna farm, whether it is big or small, and consider what might be at play. Most will shrug it off since characterizing the scope of the problem and taking mitigation measures is neither easy nor straight-forward.

If I build the 80 meter wire yagi that I have tentatively inserted into my 2022 plan there are factors that lessen my worry. First, most of the time the boom of the 40 meter yagi will not be parallel to the 80 meter elements. Second, yagis have enough directivity to reduce interaction when they are at different heights. Third, I still have the 80 meter vertical yagi should a problem arise when the 40 meter yagi is pointing in a direction that increases the interaction.

When I get serious about building an 80 meter wire yagi I will develop models to explore the matter in more depth. I have no plan to convert any of my yagis as lower band dipoles since I have enough antennas to meet my needs. My concern is interactions.

Gamma Match Peculiarities & Challenges

After a brief struggle with the gamma match on the newly installed 3-element 40 meter yagi I thought to myself that there has to be a better way of doing this. Unlike many other ways of feeding yagis, the gamma match remains an enigma. Calculating its dimensions is at best an estimate and it can be off by quite a lot. 

We can get by despite this because the gamma match will match a wide range of feed point impedances. A bit of trial and error usually does the trick. It is interesting that it can be so difficult to analyze and accurately predict its behaviour!

The most common style of gamma match is shown below. A reference diagram will help to avoid the possibility of confusion even though most hams have encountered the gamma match.

Unfortunately I do not have the relevant education to dive too deep into the transmission line and antenna theory to properly understand the gamma match. I can get through partway and then I will inevitably hit a wall. I have not been successful, so far, with published material on the gamma match since they tend to touch lightly on important theoretical points, make assumptions that overlook the general case, or crunch through the complex number equations and hyperbolic trigonometry without explaining what is being done and why.

The basic behaviour of a gamma match is as follows. I am paraphrasing an article that like by Healey W3PG in April 1969 QST. His figure 4 is reproduced above. ARRL members can pull the article from the QST archive.

1. As a short or partial folded dipole, the current split on the DE (driven element) and gamma rod multiplies the feed point impedance (both R and X components) by a step-up ratio. The ratio is determined by the tube diameters and spacing. 
2. The impedance is raised before being stepped up because the DE tap point (gamma rod strap) is off centre. This occurs due to the current and voltage gradient along the element, with voltage rising and current declining as you move toward the element tips. The increase isn't large -- a typical value is 5% -- but well worth taking into account.
   
3. The shorted stub formed by the gamma rod and element adds parallel inductive reactance Xp to the stepped up impedance Z₂ at the DE tap point and also transforms the net impedance since it is a transmission line. 
4. In a typical gamma match, the reactance at the feed point is inductive. The series gamma capacitor -Xp cancels that reactance at the design frequency.

When properly configured the feed point impedance is 50 + j0 Ω, at one selected frequency, usually near the centre of frequency range of interest. The SWR curve across the band should be similar to that of other antenna feed systems. As Cebik W4RNL points out in "Some Preliminary Notes on the Gamma Match", and I found with my new 40 meter yagi, getting the gamma match to do that is not as straight-forward as for other common feed systems. The mathematics are more difficult, the physical dimensions are critical and the (dipole) feed point impedance we seek to transform may be impossible to measure. (Search for the Cebik article in a search engine to locate an extant archive.)

I would like to better understand the gamma match. I have most of the mathematical training required but not enough of the electromagnetic physics and engineering. I sometimes joke that I've forgotten more mathematics than most people have ever learned. There is a thin layer of rust coating my neurons. However I never formally studied electromagnetism. 

Bear with me as I plow through what I can of the subject without delving deep into aspects that I am not yet qualified to comment on. After designing a number of yagis and gamma matches, and then modelling, measuring and adjusting them, there are several challenges about gamma matches that I've been contemplating:

• Achieving a perfect 50 + j0 Ω match at one frequency is not difficult. Since a yagi is a high Q antenna its impedance changes rapidly with frequency. There is no gamma match design process that I'm aware of that optimizes the SWR across an amateur band. Is there a best set of driven element length (pre-match R + jX Ω) and gamma dimensions that maximizes the SWR bandwidth? If there is one, how large an improvement is possible?
  
• For a yagi like the one I built for 40 meters that cannot be accurately modelled with NEC2, it would be helpful to reverse the calculations. That is, knowing all the dimensions and the impedance at the gamma match feed point, what is the dipole feed point impedance? Since the element is continuous rather than split there is no good way to measure it directly; I used a split centre for my early experiments. We most often rely on models and heuristics to estimate the impedance to be matched. But I have no accurate model of the antenna impedance and I need to know the actual impedance across the band to fully understand the antenna's behaviour.
  
• Reliability of the gamma match calculations is sensitive to several mechanical design parameters that are difficult to control in practice:

• The "open stub" between the gamma rod beyond the shorting strap and the driven element
• Tube diameter steps along the driven element and gamma rod that are typical of large yagis
• Asymmetric lengths (imbalance) between the coax connector and the connections to the DE and gamma capacitor
• Transmission line effects of a long, thin tubular gamma capacitor versus a fixed capacitor (lumped constant)
• What is the best gamma match topology to allow a minimum number of supplemental switched reactance elements to improve the SWR at the high end of the 40 meter band? The gain and directivity are very good high in the band but the rapidly declining radiation resistance prevents achievement of a low SWR across the full band with a static matching network. Yes, an OWA design with a coupled resonator does far better but that is not the problem I'm trying to solve.
  

The challenge is greater for the 40 meter yagi than I experienced with my yagis for 20, 15 and 10 meters because of the increased mechanical complexity, physical size and the greater bandwidth of the band. For example, there are 4 dimension steps along the gamma match, and the 300 kHz bandwidth of the band is equivalent to 600 kHz at 14 MHz and 900 kHz at 21 MHz.

Restricting ourselves to the bottom 200 kHz of the band helps to manage the SWR bandwidth but it is still a greater matching challenge compared to yagis for the higher bands, especially since having more than 3 elements makes it easier to achieve a wider SWR bandwidth. 

I ran into issues with the gamma match on the 40 meter yagi that were not as easy to deal with as they were for the higher band yagis I constructed over the past few years. The greater bandwidth requirement is one of the reasons. Since it's cold and snowy this time of winter I am taking the opportunity to better understand the gamma match and plan for improvements. When warmer weather arrives and I can comfortably climb the tower those steps can be taken.

Instrument choice

Let's assume you measure a perfect 50 + j0 Ω with your antenna analyzer connected to the gamma match feed point using a variable capacitor for the gamma capacitor. Now swing the capacitor back and forth until you get, say, -100 Ω and +100 Ω reactance. You will notice that the R value also changes.

There are two potential causes for the varying R. One is that the mismatch causes standing waves through the components of the gamma match and antenna. In practice this is really not an issue for a typical antenna utilizing a gamma match.

The other cause is the measuring instrument. Measuring antennas is usually done with a handheld single port analyzer. These common instruments run the gamut from horrendously inaccurate to very good accuracy. The Rig Experts AA54 I use is middle of the pack in expense and quite accurate for the price. That is, to a point. Every antenna analyzer and VNA will exhibit decreasing accuracy as R and X depart from their nominal port impedance of 50 + j0 Ω.

In the case of the AA54, when I achieved a 50 + j0 Ω match at about 7.085 MHz with 290 pf of series capacitance, I swung the 500 pf variable capacitor from one extreme to the other. R varied by a few ohms, in the range 46 Ω to 54 Ω. 

One investigator who I will not name noticed a far greater range of R when using an inferior instrument and concluded that the various mathematical models of gamma matches were unreliable! I was amused since it was obvious that he was really measuring the poor accuracy of his antenna analyzer and not the antenna. That did not appear to occur to him since he questioned none of the measurements.

Since the antenna analyzer has that inherent inaccuracy it is better in most cases to adjust the capacitor to get X = 0, measure the capacitor's value and calculate the capacitive reactance. The R value, if it's not too far from 50 Ω, will be quite accurate even on poor instruments.

You should invest in an instrument that is equal to the task you require of it or you should modify your use of it to mitigate its limitations. Compared to the problems you'll run into with a poor instrument the modest expense is worthwhile. I know far too many hams, some of whom have reached out to me after reading my blog, that use poor antenna analyzers and then make excuses when they see nonsense readings rather than invest in a better instrument. Please don't be one of those hams.

Gamma section stepped tubing

The DE and gamma rod dimension steps along the gamma match length, and the Z₀ of the 2-wire transmission line they form, are:

• [4"] 7.5" element-to-boom plate & 0.84" rod: Z₀ = ~270 Ω & step-up of ~13
• [26"] 2.375" DE & 0.84" rod: Z₀ = 340 Ω & step-up of 6.0
• [18"] 1.9" DE & 0.84" rod: Z₀ = 350 Ω & step-up of 5.4
• [variable] 1.9" DE & 0.625" rod: Z₀ = 370 Ω & step-up of 5.9

This is mathematically messy. Aside from the boom clamp, most HF gamma matches do not have steps on the DE and gamma rod. Perhaps a weighted average is a good enough estimate for those critical parameters. I hope so since that's what I've been doing.

You can certainly find a match by combining a naive estimate with trial-and-error adjustments. For the majority of cases that is good enough. However, it's a problem if you would like to reverse the gamma match equations to find the dipole impedance of the unmodified antenna. As already said, "plumber's delight" construction of the DE does not allow a direct measurement of the dipole impedance.

Gamma capacitor

There are two common types of series gamma capacitor: lumped constant (fixed or variable capacitor) and cylindrical (insulated wire or tube inside the gamma rod). They are only roughly equivalent, yet few hams consider the inherent peculiarities of cylindrical gamma capacitors. I have run across a few cautionary notes about the cylindrical capacitor, like that by W8JI, but nothing specific. The linked page is long so here's the relevant paragraph:

The above example of decreased power rating is especially important to Amateurs using coaxial cables as capacitors. Voltage is NOT constant along the length of a long coaxial capacitor. Maximum voltage in the component is always HIGHER than the actual voltage across the terminals of the "capacitor", and it is higher than the voltage calculated by the current through the capacitor! Coaxial capacitors or linear stubs used as reactive elements always have significantly lower operating Q, higher power loss, and operate under more electrical stress than a well-designed lumped component. Stubs and linear loading does have the advantage of spreading heat out. You won't notice the heat as much, even though there is a lot more heat energy! Just don't let the smaller temperature rise fool you into thinking the system has less power loss.

Without worrying about the theory, let's look at a few measurements I took. I used the best instrument I have: the VNWA3 by DG8SAQ. The calibration point is at the end of the short cable terminated with a male BNC (on the right). The calibration error due to the barrel connector, binding posts and short wires to the capacitor is small at 7 MHz. Despite the calibration it will be seen that the 13" from the VNA port to the gamma capacitor is significant.

Before doing the measurement I tested the capacitance read by the VNA with two different high Q capacitors designed for moderate to high RF current. They read almost exactly flat up to 30 MHz, with a gradual rise up to 100 MHz. They are boring charts so I omitted them from this article.

The gamma capacitor is 43" (1.1 m) of PVC jacketed RG213 inside a 6' length of ⅝" × 0.058" tube. I previously measured this capacitor as ~340 pf (8 pf per inch) with a lower quality RLC meter that uses a low frequency signal to measure coils and capacitors. I replaced it with LMR400 in the gamma match of the 40 meter yagi since PE is a superior dielectric material compared to PVC (lower loss).

The gamma capacitor is far from an ideal flat line! I placed markers at points of interest. The RL (return loss) plot hints at the loss due to the PVC dielectric.

At very low frequencies the capacitor value is about what it should be. However, notice the loss shown by the RL. The loss peaks at ~8 MHz before moderating, and then becoming extreme between 80 MHz and 120 MHz. I did not compare a length of LMR400. The test RF capacitors have negligible RL.

The first capacitance peak at 26 MHz is near where I estimated the frequency at which the gamma capacitor is an ¼λ open transmission line stub. The VF within the capacitor is difficult to estimate, and I didn't bother trying to measure it since it requires subtracting out the VF of the VNA coax and connections to the capacitor. The stub begins at the VNA port, not at the gamma capacitor, so it is 56" (43" + 13"), with VF changing at cable junctions. Although I did not verify the source of the high loss 100 MHz resonance, there is one candidate that I strongly suspect.

The ¼λ stub frequency will be different when installed on an antenna. It is far enough from 7 MHz that it is probably not a problem. However, notice how the capacitance rises dramatically at half the stub frequency. That may be noticable.

Open stub beyond the shorting strap

Most analyses of gamma matches ignore the open stub formed by the gamma rod and DE outside the shorting strap. After many trials of building and adjusting gamma matches I feel the same. My model of gamma matches also indicated little effect. I thought it still worth a calculation.

For the 23" of ⅝" gamma rod beyond the strap on the 40 meter yagi DE the calculated parallel reactance is approximately -3700 Ω at 7.1 MHz, for a capacitance of 6 pf. Since the magnitude of the reactance is much larger than the stepped up antenna impedance the effect should be small. It is also swamped by the larger reactances of the gamma match's shorted stub and series capacitor.

That said, it is best to keep the length of the rod only long enough for the gamma match to have a moderate amount of adjustment room. That minimizes any potential effect and reduces wind load.

Lumped reactance vs. transmission line sections

Unlike the cylindrical gamma capacitor, a lumped constant (fixed or variable capacitor) should provide a better all-band match. It's simply more predictable. One factor that may have played a role in my matching woes is that the length of LMR400 is just shy of 60". That would lower the ¼λ stub resonance of the cylindrical capacitor, perhaps as low as 20 MHz, and the capacitance gradient would begin its rise at a proportionately lower frequency. 

There is a slope to the capacitance curve at 7 MHz with the shorter RG213 gamma capacitor. That is in part due to transmission line effects that worsen as the ¼λ stub resonance is approached. The higher capacitance lowers the reactance of the series capacitor. The reactance of any capacitor decreases as the frequency increases since Xc = 1/(2πfC). 

I would like to measure the series capacitance needed to cancel the inductive reactance at several spots across the 40 meter band. Then I can tell whether the sign of the decreasing reactance of a fixed capacitance is the same or opposite to that of the inductive reactance. The first makes the SWR worse and the second makes the SWR better. However, I won't climb the tower in winter to do the measurement.

The deviation of the capacitive reactance across the 40 meter band is likely to be smaller than ±10 Ω from the mean value of ~75 Ω. That's significant but not disastrous. Until I take those measurements I don't know for sure if this effects are responsible for the worse SWR curve with the cylindrical capacitor versus the variable capacitor I used for the initial adjustment.

There may be other effects that a measurement would uncover. There are certainly several quirks shown by the VNA measurement.

There is another curious effect of the cylindrical capacitor we need to consider. When the capacitance is reduced by sliding the gamma rod outward the lead in wire from the feed point is lengthened by the same amount. We are therefore increasing XL while increasing Xc. If the magnitudes are similar the adjustment does not go as expected.

For the capacitor on the 40 meter yagi gamma match we have the following. For a capacitor value of 300 pf, a 1" movement of the gamma rod changes the reactance 1.5 Ω. The inductive reactance of the lead in wire is ~0.7 Ω per inch. The former is pretty exact but the latter is estimated from coil forming equations. Therefore sliding the gamma rod will have about half the expected effect.

The rate of change of capacitive reactance depends on gamma capacitor construction, frequency and length relative to wavelength. I have run into adjustment trouble with a couple of yagis due to the magnitudes of XL and Xc being too close. One solution is to alter the DE length so that a different capacitance is needed. The rate of change of a capacitor's reactance is inversely proportional to its value, and in that way the rates of change can be made to diverge.

Methods to reverse the gamma match calculations

The best way to determine the dipole feed point impedance of yagi is to temporarily substitute a split centre to the DE. That is how I conducted my experiments in 2020 with the 40 meter dipole. That isn't always possible or effective use of time and materials, especially for the size of a 40 meter yagi element.

With exact measurements of the feed point impedance and gamma match dimensions there are several methods to calculate the dipole impedance of the antenna:

• Reverse the gamma match design equations and solve for the feed point: Z₀ = R + jX
• Build equations from the fundamentals to calculate the dipole impedance Z₀
• Using an existing gamma match calculator, manually enter R and X values until the design parameters match the dimensions of the built gamma match; alternatively, automate the process with a software algorithm

I gave up on the gamma match calculator distributed with the ARRL Antenna Book because it is difficult to use. Each iteration requires re-entry of all the parameters, which is absurd. It is also not possible to inspect the algorithm. For my most recent calculations I used the TNL (Tolles, Nelson, Leeson) algorithm programmed by Cebik in an Excel spreadsheet. 

Cebik is gone but his articles and files have been archived in several places. I won't give any URLs because they likely have a short lifetime. Use a search engine to locate copies extant at the time of your search. After all, you could be reading this article years after it was written.

I converted the Excel spreadsheet to Open Office and plugged in the dimensions of the gamma match. I hoped to see the best fit with the NEC2 model of the yagi's dipole impedance. That didn't happen.

I manually adjusted the dipole Ra and Xa values in the spreadsheet until it churned out the measurements of the matched antenna to within a few percent. The final values of Ra and Xa that resulted in the actual gamma match dimensions do not look realistic (see the screenshot below). Even so, the TNL algorithm's estimate based on the modelled impedance was a pretty good starting point to build and adjust the yagi's gamma match.

As previously discussed, there are anomalies introduced by the cylindrical gamma capacitor and other components of the built antenna and match. For example, the precise location of the feed point (coax connector and wire leads) and using 2" as the average DE diameter. I found that small changes to Ra and Xa cause relatively large changes to the gamma rod length Lgr and gamma capacitor Cs.

The values of Ra and Xa are not correct. Ra ought to be closer to 20 Ω and Xa nearly twice as large. But I don't really know, and that's why I want the ability, with reasonable accuracy, to reverse the gamma match equations. I copied out the equations from the spreadsheet cells to see how difficult it would be to reverse them. I successfully reversed the less complex of the equations but without better fundamental knowledge of RF network theory I am unlikely to be successful. Besides, the manually discovered Ra and Xa diverge from reality enough that I doubt the work would be worthwhile.

I heard that there are improvements to the version of the TNL equations encapsulated in Cebik's now old spreadsheet. Unfortunately I don't have them and a cursory search didn't turn them up. The sensitivity of the equations to diverse physical parameters are also a concern. I don't plan to pursue the reversing project further at this time.

Next steps

Gamma matches are fun, if you like that sort of thing. They are useful, simple and terribly enigmatic. The opacity of their behaviour may delight the many hams of the trial-and-error brigade while horrifying those of us who prefer exact specifications and predictable behaviour. I keep making them even though they frustrate me to no end. I wish there was a more accurate design procedure.

When warm weather returns I will climb the tower and take a host of measurements at the feed point of the 40 meter yagi. I have two purposes. One is to improve the SWR bandwidth. The second is to determine the dipole impedance across the band so that I can verify my model of the antenna. The latter is not particularly necessary since the antenna performs very well. But I'm curious.

With the measurements in hand I will redesign the gamma match to improve the SWR curve and design a switching system to extend the low SWR range to cover more of the SSB band segment. There is no rush since it works well on CW and CW is my most common mode. I rarely venture onto 40 meter phone except during a handful of contests.

If I get very ambitious I'll resume my attempt to reverse the gamma match equations.

2022: Chasing Loose Ends

It is time for my annual look back on the year that was and year that has begun. You'll find that this is a tradition when you look back in this blog for January of each year.

Undertaking the construction, maintenance and use of an amateur radio station of the size that mine has become does not happen by accident. Well, you might accidentally arrive at a worthy destination by directionless wandering, but I'm getting too old to waste time. So I plan.

A plan is worthless unless it has clear and measurable milestones to track your progress. That makes many people so uncomfortable that they conveniently forget their stated intentions or they "move the goalposts" and hope that no one notices. People do notice, though in most cases they will remain diplomatically silent. I am too honest with myself to engage in self-deception. Putting my plans in the blog at the start of each year helps to keep me honest.

So, how did I do in 2021? For those with time to waste and a penchant for fact checking have all the raw data at hand: my stated plan and where I ended up on December 31. I am not surprised that my success rate for the line items is not high. I like to aim high but I won't sacrifice my life to get there.

What is important is that the major projects were completed. The items in my plan are not intended to be equally weighted. The following statement from my 2021 plan remains valid:

"Beyond 2021 no major antenna projects are planned. There will continue to be refinements and improvements, and I will likely dabble with experimental antennas and related projects."

By far the largest project was designing, building and raising the 3-element 40 meter yagi. The 5-element 10 meter yagis were a lesser challenge that consumed more time than I anticipated. Difficulties getting the rotatable, side mounted TH6 working properly took time I'd have preferred to spend elsewhere. Nevertheless the year was reasonably successful.

One important change to the plan was that the rotatable side mount was done for the TH6 and not the XM240. I left the small 40 meter yagi where it was because I determined it was more productive to have it fully rotatable (360°) and the TH6 was really only needed for the shorted North American paths and as a rapid choice to work Caribbean and Central America multipliers and to work South America. By doing it this way I was able to avoid building the more complex swing arm (300° rotation) for side mounting the XM240.

Lesser projects completed in 2021 included:

• New amplifier for high power SO2R (with BPF) and 6 meter DXing
• Correcting the mismatch of the upper 5-element 20 meter yagi
• Reversible east-west 156 meter Beverage
  

Of these, the only one I have yet to discuss is the BPF (band pass filters). There is a reason for the deferral, and I hope to correct the omission in the not too distant future. Numerous repairs are omitted from the list since those are unavoidable maintenance tasks for those with large stations. There's always work to be done. 

To give examples of the maintenance that must be done, this week I repaired a Beverage that a tree fell onto. A dead limb of that tree is hung up in another tree, out of my reach, that is certain to fall in the near future. On the 15/20 meter tower the prop pitch motor has become unreliable in cold weather. It will need service (again), but I will live with the problem until warm weather returns.

2021 projects that were deleted or deferred included:

• Stack switch for the 10 meter yagis
• More radials for the 160 meter antenna
• Efficiency improvements for the 80 meter vertical yagi
• VHF antennas: longer boom 6 meter antenna, and an antenna for 2 meter DXing
• Antennas for the WARC bands: 30, 17 and 12 meters

The 10 meter yagis were raised late in the year while the 40 meter yagi was under construction. The latter was the priority so the 10 meter stack switch was put aside to the new year. All the parts are on hand and construction is straight forward since it is no different than for the 15 meter and 20 meter stack switches.

Laying more radials for the shunt-fed tower on 160 meters is easy enough, if I had the wire on hand. I didn't so it didn't happen. Eking a fraction of a decibel on 160 meter was not a priority. Of even less urgency was improvement to the 80 meter array. I have alternative ideas to mull.

The same lack of urgency applies to VHF and WARC antennas. Maybe in 2022.

I previously published an annotated version of the following photo on the blog and on my QRZ.com page. It will be interesting to compare how different the station looks a year from now. I doubt that it'll looks very different from this visual perspective. Most of the changes will be in the shack, electronics on the tower and antennas, and relatively minor antenna changes or additions.

Many hams have told me that it is impressive. I suppose it is, however I get exhausted looking at it. It was a lot of work over the past 5 years since moving to this rural QTH. What I can celebrate is that the bulk of the big projects are now done. All of it must be maintained, and that is a never ending job. 

I didn't get here with a firm plan from the outset, as long time readers will know. There were too many uncertainties in my mind about what I really wanted and what I could realistically accomplish. I wanted "big" with no clear definition of what that meant. There were too many alternatives to explore. 

Each next step was well considered but not always the step after that. This is not a commercial enterprise so I allowed myself to be influenced by whims and opportunities, and by the adventure of exploration. Every ham with a large antenna farm has their own story.

Future projects will be less arduous. I am contemplating the addition of a small tower in future to avoid interaction and mechanical challenges of antennas on the existing towers. I also want a small tower with few encumbrances for antenna experiments. The station will not reach stasis for a long time since there will be new antennas to explore and improvements made to existing ones.

With a sigh of relief that I've made it this far, let's look at what I have planned for 2022. Although the projects will be less visually impressive they will have a impact on contest competitiveness, among other advantages.

• Prop pitch rotators: I am having more difficulties with the motor that turns the 15 and 20 meter yagis. The gearbox is the problem this time. Service will wait until warm weather returns. I must also finish building the direction pot for this rotator and improve the one for the chain drive prop pitch motor on the 40/10 tower. Once those are done a new controller in the shack is needed to make them ergonomic and more reliable. The controller will be home brew, including software.
  
• 160 meters: There are two options to improve my top band signal. One is to shunt feed the other tower and feed them for switchable end-fire and broadside configurations. The second is a parasitic array using a wire driven element between the towers or adding wire elements to the existing antennas. There are pros and cons to be weighed. A large consideration is for ease of deployment each fall and removal in the spring for haying.
  
• VHF: At minimum I need a 2 meter yagi suitable for DXing and occasional contest use. It will go on the Trylon, just below the 6 meter yagi. A superior 6 meter antenna is possible this year but may be deferred to 2023. Extending my DXCC count on 6 meters will not be easy.
  
• WARC band antennas: My primary interest is chasing band-countries for general DXing on 30, 17 and 12 meters. I have no specific plan at present and there are too few major DXpeditions expected this year due to the ongoing pandemic. I use a tuner on the XM240 for 17 meters and the 80 meter vertical for 30 meters, and on 12 meters I load whatever high band antenna is broadside to the station I'm calling. While far from ideal at least it works well enough, for now.
• 40 meters: The matching system for the 3-element yagi needs work to improve the SWR and it needs a switchable network to make it more usable on SSB. It's just a matching problem since performance is excellent.
• 80 meters: I am contemplating a reversible 3-element wire yagi with a rope catenary strung between the towers. A horizontal yagi could pay dividends by being more efficient and to exploit high elevation angle DX paths. It would point northeast to Europe and southwest to cover most of the US. The main lobe of a 3-element yagi is broad enough to work well for most stations I can expect to work. A second 80 meter antenna provides a backup in case one fails before a contest.
• Station automation: I am making slow progress on the hardware and software. Some of what I need should be complete by early spring. The rest can wait until I can begin inviting others to do multi-op contests. COVID's resurgence will delay multi-ops for a while longer.
• Station modernization: A new SDR transceiver will replace the FT950 which has long overstayed its welcome. More extensive software control of equipment and antennas is planned. Other equipment changes are being contemplated.
• Receive antenna: The Beverage system is performing well, although it demands regular maintenance. Completion of the desired 8 directions with a future NW-SE reversible Beverage is doubtful because it's benefits are at best incremental. These antennas are not so directional that more than 6 directions are strictly necessary. Instead I would like a second receive system, probably a multi-direction vertical array. The benefits are diversity reception and for low band multi-op contests. Planning and design can proceed this year, and construction to follow in 2023.
  

This list is vague in comparison to those I've made in previous years. That's deliberate. From here on I will be more relaxed about my station plans. Major projects were never intended to continue forever! Speculative projects for fun and for experimentation will be undertaken when I feel the motivation and interest. 

I will spend more time this year and in subsequent years for non-ham retirement activities.

With that I will end the annual retrospective and look forward. I hope to meet more of you on the air. It's always enjoyable when a contact, during a contest or other times, tells me they read and enjoy the blog. Thank you for following along in my journey. Major contests are on the horizon, the 6 meter summer sporadic E season is only 4 months away and the sunspot count is climbing. Pandemic or not, 2022 will be a great year.

Where Is My Straight Key?

A bunch of the local hams operated SKN (Straight Key Night) on new year's eve. Although I didn't plan to participate I enjoyed reading about their plans and the keys they'd be using. Afterwards came the stories of who they worked. It brought a smile to my face.

It also made me wonder: where is my straight key? I do have one...somewhere. It's very old and not in good condition. Some work would be needed to make it usable. I had an urge to see it again so I dug through boxes of disused gear and parts and I eventually found it.

Doesn't look like much, does it? I have little sentimentality for old things and I am happy to see them go when the time comes. I kept the key because it is the only one that I ever owned. Besides, no one would buy it and I doubt I could give it away. I must have been 14 when I bought it or it was given to me (I don't remember).

My father gave me a scrap of wood of the size I wanted. I sanded and stained the wood, and then screwed down the key. Three plastic feet underneath with pins for nailing into the wood complete the project.

I used it for sending practice until I got my license at the age of 15. One old tube transmitter put a bit of voltage on the paddle and delivered a mild shock when I would accidentally touch the metal lever. It was important to carefully grip the non-ergonomic knob by the rim! I used that key, as you see it, for the first 2 or 3 years that I was licensed.

Then came the contesting bug. The straight key was pushed to side and replaced by an early generation digital keyer with memories. The electronic iambic keyer was a blessing for allaying the fatigue of pounding out hundreds of contacts over a weekend. The key also improved my speed and QSO rate. I never looked back.

I know that I used it from time to time over the years, but those occasions soon became rare. I no longer recall when I last used it. It follows me around as I go about my life, packed in a box most often. It has moved with me numerous times. 

It does not work well. There are a couple of ball bearings missing from a cleaning and oiling incident in the distant past. They popped out, rolled away and apparently not all of them were recovered. The lever wobbles. This is a less than ideal condition to achieve a good "fist".

I always meant to replace the lost bearings but I never did. There was no urgency for an item that I never use and that I am unlikely to ever use. However, I do think about it from time to time. I could buy a new or used key -- they aren't expensive -- yet I haven't done that either. Perhaps I never will.

The memories it elicits have value and that's what really matters. Repairing and using it are less important. Maybe for the next SKN.

Happy New Year!

Lighting Up the 3-element 40 Meter Yagi

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.

Interaction mitigation

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 3^rd 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 3^rd 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 (4^th 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.

The Mother of All Tram Lines

The title is the answer to the following question: how do you lift a 300 lb 3-element 40 meter yagi onto a 150' tower?

When we last saw this new antenna it was partially assembled at the launch point for raising onto the tower. A lot of work has gone on since then. There is a great deal of preparation required for a lift of this magnitude go smoothly and safely. I am happy, and relieved, to report that the antenna is on the tower and working. It has already been subjected to high winds and survived the experience.

We need to rewind a few months to understand how I proceeded to design and build the tram line to bring this project to fruition. Don't expect a full blueprint, just enough detail to give you a good idea of how to do it. This is not a project for a novice. Mistakes can be lethal. How?

• If insufficiently strong without supports (e.g. boom truss) the antenna can break, fall and damage the rigging.
• Steel cables under tension will whiplash at high velocity if they kink and break, a mechanical connection fails, or a winch or come-along fails. The cable can maim and kill.
• The tower, mast or ground anchor can fail if improperly engineering or used. Property damage is guaranteed, and life is also at risk. No, you can't run out of the way fast enough and a hardhat won't save you.
• A falling 300 lb antenna striking a guy wire will very likely bring down the tower. See previous bullet.
• A vehicle hauling an antenna up the tram line has sufficient power to break the tram line, haul cable, mast, pulley blocks and mechanical connections if it happens suddenly and power is not removed immediately. See second bullet.
• No matter what you say, crew members (and probably you as well) will remove personal safety equipment and step under the antenna and rigging, usually for no justifiable reason. There is no good reason except under strictly controlled conditions.
• No one should be on the tower during the lift. Leave that until after the antenna is in position and all but the critical cables are slack. If you must be up the tower to facilitate the lift you're doing it wrong.
  

A professional rigger who loaned several items that I needed for the tram said that for commercial work they strive to use cables, ropes, tools and fasteners at no more than 10% of their breaking strength. This is very conservative since 20% is more typical. When you consider the liability for injuries and property damage for failures of large towers and while lifting heavy loads up those towers the conservatism is well justified. As a ham I am willing to venture higher than 10% but rarely more than 20%. At 30% the alarm bells should be ringing no matter who you are or what you're doing. Don't even think about it.

Amateur radio is a hobby. Be conservative and be safe. There is no shame in admitting a procedure is beyond your ability. Hire professionals.

Do you feel suitably chastened? Sorry to put you through that but it really needs to be said. Repeatedly. In my long experience too many hams have misplaced optimism. 

Note on photos: Most of the best photos in this article were taken by Alan VE3KAE. He came over several times to help with antenna and rigging assembly, rigging tests and for the final lift. The worst pictures are by me and my not very good smartphone. I don't show credits on each photo. I also have a new phone that I'll try on upcoming projects.

Taking the time to get it right

I started the rigging in October and the lift was done on December 1. I proceeded carefully, taking all the time I needed to be absolutely certain. I am no novice but this is not a job to be done rashly.  We then waited for agreeable weather, and the weather is rarely cooperative this time of year. 

I cancelled the first scheduled lift day because I wasn't fully satisfied with the rigging. That was easily remedied but a week passed before acceptable weather returned. There was also snow on the ground.

The setup

A lot of space is needed for the big tram. The diagram below has been supplemented with an aerial view (overlaid on a Google satellite image) and photos of critical components.

The tram line anchor on the ground is a large tree wrapped with chain. The upper end of the tram line is halfway up the 10' mast and is comprised of several commercial rounded mast plates. Due to the required force to withstand the weight of the antenna and tram line and the tension of the tram line and haul cable there is a back stay. The back stay is essentially a temporary guy. I was lucky to find a suitable tree (large and healthy) that is ~1° off a direct line through the tower. The mast pulley is placed on the other side of the mast to compensate, but that wasn't really necessary.

The haul cable is 500' long to traverse the large distance from the launch point, over the tower to the guy anchor and then horizontally to the vehicle. My preference was to have the haul cable run straight down the tower, as I've done many times before. That required a cantilever and second pulley that would be under high stress. Taking the cable outward from the tower is easier but adds complication during the lift, as we'll see later.

The overall procedure is to crank the winch to lift the antenna far enough that when the haul cable is pulled tight the rear tips of the long elements don't strike the ground. The back stay is tightened to keep the mast vertical. The antenna is hauled up until the forward tips approach the forward guys. The tram line is again tightened and the tag line pulled to tip the element to be more vertical. When the antenna reaches the tower the tram line and back stay are slacked so that the boom rests against the mast plate. We climb the tower and bolt everything together.

There are two lifts. The first is the antenna without the driven element. That reduces the weight to less around 250 lb, which includes the rigging. It also prevents severe interference between the driven element and its fragile capacitance hats, the cables parallel to it, the tower and mast, and the 10 meter yagi at the top of the mast. The driven element is lifted end first, just as it was for the dipole that was lifted last year, and taken down the same way earlier this fall.

That's the summary. Details follow.

Equipment choices

EHS 7×1 guy strand is not ideal tram line material because of the bend radius imposed on it by the antenna weight pulling on the tram line pulley blocks. However it is strong and I have a lot of it scavenged from commercial towers. The tram line and the tram line extension to the anchor is ¼" EHS. The extension is needed since the longest length in my stock is 200'. It is the same cable used a year ago to tram the 5-element 20 meter yagi to the top of the 140' tower.

The breaking strength of ¼" EHS is 6000 lb. Tension during the procedure never exceeded 800 lb, or 13% of breaking strength. The winch is rated for a 1750 lb working load and its cable is ⅛" aircraft cable with a breaking strength of 2000 lb. A come-along was used on the tram line when the tension exceeded 400 lb (20% of breaking strength). Shackles, chains and other cables in the rigging are used within their working load limits.

The haul cable is 500' of 7×19 3/16" aircraft cable with a breaking strength of over 4000 lb. A smaller cable could have been used since the weight it would have to support is no more than 250 lb. I followed the advice of the professional to buy the bigger cable as a safety margin, both for the lift and in case there was tangling with the rest of the rigging.

Rigging the antenna

For the initial test of the rigging the connections to the antenna were partially improvised. I used materials that are easy to work with but that are not of adequate strength for the lift. Once we were satisfied with the overall setup, stronger materials were substituted.

With the first version of the rigging the antenna was lifted by the winch. The element tips and capacitance hats were not attached to protect them during the trials. As the tram line is tightened the antenna moves backward and can spear the element tips into the ground. The tips, though tough enough on their own, cannot withstand the weight of the antenna bearing on them. I had a friend (Alan VE3KAE, seen below) help with the test of the rigging.

Notice the bowing of the boom. The boom must support its own weight of 110 lbs and 45 lb of element and clamps at each end. The boom can withstand the static stress. It is important to install the boom truss as soon as possible after it is on the mast since the boom isn't likely to survive a high wind without it. On its own, it can handle the weight or the wind load, but probably not both.

The antenna is unbalanced in this test. The reflector (nearest element) is heavier than the director by about 3.5 lb, and about 4 lb with the tips installed. Finding the centre of gravity (CoG) by experiment alone is tedious so I developed a spreadsheet to calculate the moment on each side of the tram line. When the antenna was assembled and the exact CoG found, the calculation was off by just 1". Balance helps to steer the element tips clear of the top guys and the 10 meter yagi atop the mast. The 10 meter yagi is 24' long, which is only half the boom length of the 40 meter yagi, so the reflector and director clear the 10 meter antenna with room to spare.

Below is the final rigging of the boom. It is worth describing a few details.

The are two ¼" commercial steel plates to secure the rigging to the boom. One chain attaches to the tram riding trolley and the other to the haul cable. The chain for hauling is shackled to the plates. When the cable is pulled the plates align with the tram line and that tips the elements up. The trolley is ½" steel plate with shackles to hold the pulley blocks that ride the tram line. 

Although small, the pulley blocks are rated for a few tons of working load. I used two to spread the load on the EHS, to reduce deflection and point stresses that can damage the cable. After the rigging was dismantled I found a couple of small kinks near the bottom of the tram line, where the trolley was positioned most of its time the antenna was off the ground.

The truss cables and turnbuckles are tied together and to the boom plates, and held to the boom with cable ties. It is important that they don't escape or the antenna would probably have to be lowered to retrieve them. After it is raised the extra rope length is looped over the tram line to keep the truss half tied together and free to reach the mast clamp.

The light duty steel angle and attached tag line are used to tip the elements further upward to clear the top guys. After the boom is bolted to the mast plate the angle stock is a lever to rotate the boom and level the elements. The alternative is to wait for the driven element and use that as a lever.

The lift

The tricky parts of the lift are the beginning and the end. Watching the huge antenna slide up the tram line is awesome but requires no work other than keeping in communication with the driver. The first step is to lift the antenna by pulling in the slack in the tram line. During this process the tension rises only slowly. We stop when the winch is too difficult to turn or the tension reaches 400 lb. There is a Loos tension gauge on the ¼" EHS tram line extension cable. The come-along is attached to the extension cable with a sacrificial pre-form and the tightening continues. 

What we're really doing is raising the antenna rather than increasing tram line tension. That is because the antenna is so far along the tram line. The loading is very different when the launch point is closer to the ground anchor and when the antenna approaches the top of the tower. It was interesting to watch the tension gauge hold steady as the tram line is tightened. That isn't what most people expect to occur.

Once the antenna is a few meters off the ground the car rolls forward a foot or two to take the weight of the antenna. One person watches each rear element tip to keep them from spearing the ground. When it's high enough we spread the capacitance hats.

I confirmed in the model that the hat arms don't have to be at exact right angles to accurately reproduce the loading effect measured last year. We did it anyway since it looks prettier that way. Helping me out (above) are fellow contesters Vlad VE3JM (left) and Greg VE3PJ (right).

We did have an accident when one of the arms broke. I believe it was the arm that snagged and bent when it was lowered from the tower earlier this fall. An hour was spent building a new one. Before resuming we stopped for lunch. The antenna was left hovering above the ground.

John VE3NJ is driving his car in reverse to haul the antenna because the tow hooks are at the front of the chassis. The car may seem small for the job but it is in fact perfect. The peak towing load is only slightly more than the antenna weight and that is only reached when the antenna nears the top of the tram line. The engine's moderate torque capacity gives the driver an excellent "feel" for the load and mechanical snags that might occur. 

The automatic transmission is particularly helpful to control torque and avoid sharp acceleration and deceleration. My car has a manual transmission which makes torque control difficult. I salute John for his willingness to drive into the snow filled hay field.

The unevenness of the hay field caused some difficulty. Two of us had to push the car when it entered a small depression and the drive wheels spun in the deeper snow.

The tension on the tram line drops to a low value as the antenna approaches the top of the tram line. That can come as a surprise. The weight of the antenna at this point is almost entirely on the haul cable, so the tram line carries less of it.

The partially slack tram line must be tightened at this time to raise the antenna to help it clear the top guys and the prop pitch motor platform (it's the blob just below the top guy station). Turning the winch crank quickly raises the tension, so we again switched to using the come-along on the heavier EHS. A guy grip locks the tram line to the chain around the anchor tree. The back stay must be adjusted to compensate for the increased lateral force on the mast.

I put most of my weight on the tag line to raise the forward tips well over the top guys, while at the same time shouting instructions at John (with others relaying my words through the car window). We all had radios but without VOX I can't transmit when both hands are occupied.

The boom briefly tapped the top guys and then cleared the prop pitch motor. The boom bumped into the top few inches of the tower but in a moment it was over the top. We slacked the tram line and back stay so that the boom hung straight down at the level of the mast plate. 

The top safety rope now comes into play. Look at the top diagram to visualize the forces at play. With the tram line and back stay tension eased, we are left with the lateral force of the haul cable due to the ground pulley being 120' from the tower base. The safety line is there in case the mast bends backward more than I'd like. It turns out that it wasn't so bad and the safety line may have been unnecessary. Knowing what might happen is why I took this precaution. The inset photo (diagram above) shows the mast rigging after the safety rope was moved out of the way of the truss clamp.

Securing the antenna

I climbed the tower with the 4 u-bolts to attach the boom to the mast plate. It was remarkable that I had to instruct John to lower the antenna only 1" to align the boom with plate holes. They went in with no drama at all. The antenna was secure at the top of the 150' tower. The car moved forward to fully slack the haul cable.

The chains from the tram line trolley and haul cable were removed and the tag line transferred to the trolley. I sent the lot of down the tram line. With the tram line slack, the dangling chains strike the ground to slow it down and prevent damage. 

Free of the pull of the trolley and haul cable, the boom was rotated with the lever. The elements couldn't be completely levelled until later when the rigging plates on the boom were removed. That was done after the boom truss was connected to the mast.

The position of the rigging plates up the mast made it difficult for one person to attach the boom truss cable to the mast clamp. Vlad VE3JM joined me on the tower to lend a hand. One of us pulled in the truss cable and the other drove the bolt through the clamp and turnbuckle eyelet. We then levelled the elements. By tightening the turnbuckles we levelled the boom. 

The sun was setting so that was it for the day. We took pictures, climbed down and my friends left for home after a very productive day.

These are the pictures Vlad and I took of each other, and one that Alan VE3KAE took of us from the ground. They make a pretty mosaic.

Driven element

The weather worsened so we could not raise the driven element for two weeks. During that time we had two wind storms, one of which hit on Dec 11 with gusts of 100 kph and higher. My imagination did run a little wild since it was nighttime and I all I could do was listen to the wind roar for several long hours. In the morning light I was relieved to see that the antenna and tower were unharmed. The tower and antenna are designed for survival, but that never completely allays one's fears.

Wind on the scheduled day was gusting to 50 kph on the ground and higher on the tower. We went ahead because there was a problem finding a day with better weather when I could gather enough helpers. Good tower work weather is uncommon this time of year. For this last step we were the same group as before, less one person. 

The wind was really strong so we had to alter the rigging to lift the driven element safely. It is going up end first and by muscle power using the same tram line. The steel haul cable was replaced by rope since it is far easier to work by hand. It went up end first to thread the triangular gap between the boom, mast and boom truss. The leading capacitance hats are only unfurled once they're through the gap. That was my job.

The element was whipping around so much that I tied the haul rope to the leading edge of the element 1" tube just inboard of the capacitance hats. With that simple addition the tip pointed straight ahead and parallel to the tram line. The tip points at the mast where the tram line anchor and haul pulley are mounted. I removed the wire and gently pushed the capacitance hat arms around the mast.

There were tense minutes after I saw that the capacitance hats were above the tram line and a fix was required. At some point near the ground, when the element was swinging in the wind it someone twisted up and ended up on the wrong side of the tram line without any of us noticing. 

Choreographing a few acrobatics with the capacitance hats I was able to get them back under the tram. Hauling continued until the element-to-boom clamp was on the boom. Getting that 60'+ element steady enough in the gusting wind to thread the u-bolts was a challenge.

With the element bolted down I loosened the boom and used the driven element as a lever to better level all of the elements. I couldn't yet slide the DE into its correct position because the slack tram line was lying across it. It was getting late so we called it a day. The sun set early this time of year.

The next day I dropped the tram line on my own and slid the DE to its position on the boom. I then did the first test of the SWR, using a variable capacitor in place of the capacitor inside the gamma rod. The measurement after adjusting the capacitor indicated that the antenna was behaving as a yagi, but with a couple of surprises. 

More on adjustment and getting the antenna on the air in a future article. The weather this week has been continuing warm, if wet and windy at times. I have to move quickly to beat the weather. The rigging is now been completely removed from the tower, and work on the yagi feed is ongoing. Whether it works or not the antenna is going nowhere until warm weather returns.

I'm pushing it to the deadline but this antenna will be working and on the air this year and before the serious winter weather rolls in. This is the pinnacle moment of my 2021 station plan and I intend to get it done right and on time. I let other items slide but not this one.

While the work was going on we were so wrapped up in the details of getting it done that it was easy to forget how big this thing is. It is no surprise that very few hams have a 40 meter yagi with 3 or more elements. It was a shock to look out the window the morning following the big lift and see that monster perched at 150'. It's impressive and intimidating. However, an antenna is meant to be used and not merely admired as an ornament. 

I hope that this story about large antenna tram lines has been of interest. Not many would choose to raise an antenna of this size without hiring a crane.