Thursday, September 30, 2021

Building the 5-element 10 Meter Yagis

The project for a 5-over-5 stack on 10 meters is progressing well. The yagis are built, tested and adjusted, and are slated for raising in October. Although they are smaller than their 5-element 20 and 15 meter cousins that I built two years ago, the performance is similar and the construction techniques and challenges are identical.

To make best use of aluminum on hand I changed the original element design to use ¾" tubes for the centre sections. The final taper schedule for each half element:

  • ¾" × ⅛" : 30"
  • ⅝" × 0.058" : 33" (+ 3" overlap)
  • ½" × 0.065" : variable length tips

The taper schedule was modeled in EZNEC to adjust the tip lengths to resonate the elements (X = 0) at the same frequencies. Scaling is necessary to preserve performance and frequency range when you deviate from the design. For the SDC (stepped diameter correction) I calculated the effective diameter of the element-to-boom clamps using the W6NL equation. For a ¾" tube on a 4" × ¼" plate, the effective diameter is 2.4". The clamp length for each half-element is 2".

I had a challenge ordering suitable clamps for the element-to-boom clamps. Importing of the ideal fasteners from elsewhere is either prohibitively expensive or the dealers refuse to export. Canadian dealers are not as willing as they have been in the past to do special orders. Other options involved calling in favours to use non-retail suppliers, and I didn't want to do that. I resorted to online sites like eBay to find what I wanted. Once I had the parts I drilled the plates to match the hardware.

To further economize I made the booms out of pipe in my stock. The weight is higher than needed for these yagis but since it's 10 meters the overall weight increase is small. The pipes are 1-½" schedule 40 or 80 (1.9" OD), joined by sections of 2" schedule 80 pipe (2.375" OD, 1.939" ID). The fully assembled yagis weight 43 lb and 52 lb. The lighter one will be the upper yagi of the stack, that will be mounted at the top of the mast on the 150' tower above the planned 3-element 40 meter yagi.

The SWR bandwidth of the yagi is around 900 kHz. That is good enough for DXing and contests. If you operate above 29 MHz (e.g. FM) the antenna should be scaled accordingly. However, you will lose performance at the bottom of the band. 

I adjusted the design optimize to my requirements and make the best use the available bandwidth. One change was to shift the antenna up by 100 kHz to get closer to 1 MHz SWR bandwidth with negligible impact on gain and F/B performance.

The model uses a beta match (hairpin) for ease of modelling and for compatibility with SDC (stepped diameter correction). The gamma match I use is functionally the same, and so are a variety of similar "transmission line" matching networks. We'll see the proof shortly.

Construction of the element was no different than that of the 20 and 15 meter yagis so I'll point you there rather than repeat myself. Since there are two of these 5-element yagis, there were 10 elements (20 half elements) to be built. That entailed a lot of cutting, drilling, reaming and filing. I started in August and finished in mid-September. It was a lot of work.

The element-to-boom clamp plates are shorter at 4" × 4" × ¼" but otherwise the same. Due to poor planning, D2 (director 2) on one of the yagis was on a 2.375" pipe. Since the plates were already drilled, I experimented in software with D2 shifted several inches so that it would sit on a 1.9" pipe. By adjusting its length a small amount the performance was close but not the same. Since the designs are already greatly optimized any alteration has an effect. I decided to leave D1 where it was and made a new plate to fit the larger saddle clamps.

I was careful to adjust and measure the half element lengths to be within ⅛" of the modelled lengths. As the frequency increases the need for accuracy also increases. There is little sense investing a large effort to design and build a high performance yagi to then get sloppy and lose some of that performance.

The antenna is large but smaller than many of my earlier projects. It was still a challenge moving them from the driveway, where they were assembled, to the the hay field where they were to be tested and then lifted onto the tower. A friend and I had to carry the heavier one the long way around because of the difficulty of navigating trees and other obstacles. Although the antenna isn't terribly heavy it is no easy job to carry it a few hundred meters by myself, as I did for the lighter of the two.

The rigging to tune and adjust the 10 meter yagis is similar to what was done for 3 of the 15 and 20 meter yagis, except that the antenna size and required height are lower. This is the same rigging used to lower and lift the TH6 recently, which is no accident: I planned it that way to minimize the work. After raising the height of the tram line and lift pulley, the same rigging will be used to tram the side mount 10 meter yagi to 110' (actually about 33 m).

The short length of coax looks silly with the antenna analyzer hanging off it in midair. It was an expedient choice since I didn't have a ready made length of coax that would do the job. What I did have was the recently assembled delay line for the lower 20 meter yagi -- 6.9' of RG213 -- so that's what I used. I'll install the delay line when tuning the 10 meter yagis is compleete.

Despite the short bit of coax and with the help of a step ladder it was possible to adjust the gamma match and measure the impedance with the antenna as high as 15' (4.6 m or 0.43λ) which is high enough to put it in virtual free space.

The shorter gamma rod separation helped to place the coax connector at the same level. For the greater separation on the 15 and 20 meter yagis the connector was higher (closer to the boom) with a vertical wire down to the capacitor. With careful calculation and construction it is a very good fit. I prefer this approach since it improves mechanical robustness.

For initial tuning I used a temporary strap and the gamma rod and capacitor are longer than required. I have learned to distrust gamma match design software. To my surprise the calculated dimensions turned out to be quite accurate, to within 1" (3 cm) and 3 pf (4 cm of RG213 inside a ½" gamma rod) for centre-to-centre spacing of 3" from the ¾" element centre tube.

Further playing with the software suggested, if reliable, that the antenna impedance at 28.5 MHz is 30-j35 Ω versus the 30-j30 Ω predicted by EZNEC. Design and measurements are done at 28.5 MHz since that is where the SWR is predicted to be minimum (1:1), and the SWR over the band should be as designed.

Compare the measured SWR from 28 to 29 MHz at 12' height to the free space SWR predicted by EZNEC above. They are almost indistinguishable. Modern software tools are truly awesome. There is a glitch right at 28.0 MHz that isn't there in other trials. I think the coax connector to the analyzer wasn't tight enough at the time. When the antenna was raised 3' higher to 15' the gamma match required a slight tweak.

The gamma match was subsequently altered to make the components smaller. I did this by shortening the each half of the driven element by ½" to increase the capacitive reactance. This allowed shortening the gamma capacitor, which is desirable for mechanical robustness. The capacitor length was trimmed so that the rod could be shortened while leaving room for further adjustment if needed. After adjustment the SWR curve was almost exactly the same. Perfection is not the objective since. For the side mount yagi, there are almost certain to be guy interactions that will alter the impedance and pattern a small amount

Pieces of the final version of the gamma match are shown above. Construction is similar to that of the 15 and 20 meter yagis, but with a strap that is only ¾" wide. I unsuccessfully tried to form a harder aluminum alloy for the strap but I could not easily do it with the tools I have. So I used same softer alloy as for the straps on the lower band yagis.

With the antennas built and tuned the remaining parts were the boom-to-mast clamps and boom trusses. In my junk box I found a ¼" aluminum plate with holes in exactly the positions needed for the lower, side mount yagi which uses a short length of 1.9" pipe for the mast. 

For the upper, rotatable yagi I chose a ⅜" aluminum plate from my junk box. As for the upper 15 meter yagi, there is an integrated boom truss support. This allows it to be placed at the very top of the mast, as far as possible above the planned 40 meter yagi. 

At the time the picture was taken the fittings for the clamp are incomplete. There were a few more holes to be drilled and saddle clamps selected. One of the 3" DXE clamps for the 2.875" mast is shown, while a second had to be rescued from a "temporary" use on one of the towers where it's been for 3 years.

Still to be done are the coax chokes and boom trusses. For the latter, I am using what I can find in the junk box. The current plan is for short lengths of plated chain anchored on the boom with old muffler clamps, ⅛" aircraft cable as the truss cable and galvanized turnbuckles connected to the mast. It won't be pretty but it will work and nothing has to be purchased.

Coming up is the raising of the yagis and construction of the stack switch and phasing harness. That will have to wait until the antennas at the top of the tower are removed -- TH7 and 40 meter dipole -- and the tower is rigged to lift the as-yet incomplete 40 meter 3-element yagi. Other project have intervened so it will be two weeks or more until both 10 meter yagis are raise.

Monday, September 20, 2021

Side Mount for a Limited Rotation Yagi

For the past few years I have had a Hy-Gain TH6 side mounted at ~72' (22 m) on the 150' tower, fixed south to W4/W5, the Caribbean, Central and South America. It has been used as a multiplier antenna in contests, and it has proven to be very useful in the intended application. That said, having it fixed is less than ideal. I would to use it to cover more of North America to earn more contest points working the US when my bigger antennas are pointed to more distant DX locales.

I have written previously about different methods of side mounting yagis on towers for partial compass coverage. This year I decided to do it for the TH6. A rotation of a little more than 120° allows coverage from 150° (Brazil) to 285° (VE7). That's perfect for my purposes.

I have more to say about the TH6 that will be deferred to a future article. It had to come down for reasons other than the new side mount system: to permanently repair a wire bond that could not be done on the tower, and to flip the boom to mast clamp since the rotatable side mount is on the opposite side of the tower from the fixed side mount bracket.

It is amusing to note that the antenna and rotator were manufactured not long after I was licensed almost 50 years ago. I acquired them secondhand in 1985 when I bought a house and could put up a tower after moving Ottawa as a young man several years earlier. Both went into storage when the tower came down in 1992, where they remained for over 20 years. 

The rotator, a CDE Ham-M, was refurbished and used when I returned to the hobby and put up a tower and tri-bander in 2014. In 2016 they went back into storage.

Looking around at my stock of metal and hardware I formulated a plan. I have a large stock of scavenged material that tends to find its way into projects or gets passed on to others. Nothing needed to be purchased for this project other than a few bolts. 

The tasks to be accomplished included:

  • Take down the TH6 and its side mount fixture for service
  • Service the rotator
  • Select a mounting geometry that would achieve the desired rotation and not interfere with climbing and the numerous cables affixed to the tower
  • Build a side mount system that is sturdy, servicable and meets the objectives
  • Design the cabling system (about 230' long) to use the minimum amount of new cable and provide adequate current capacity
  • Raise the refurbished TH6 and test the system

Getting the TH6 down was straight-forward. For simplicity I used my lawn tractor as the tram line anchor. You back up until the rope is taut, then block the wheels. I can do this for antennas up to around 70 lb, and more if the slope of the tram is low. For heavier antennas and the requisite greater tram line tension, the wheels lift off the ground. Lawn tractors aren't very heavy.

There is some difficulty rigging the antenna for proper balance since, unlike going up, you really only get one chance. The TH6 was a little unbalanced and a couple of tubing clamps snagged a guy. Jiggling was enough to free the snags. The entire job was quickly done with the help of just one friend as the ground crew. Less muscle is needed to tram antennas down, and is further helped by the shallow slope (under 25°) of the 200' long tram line and a height of 75'.

The new side mount went up the same day that the TH6 and the old fixed side mount bracket came down. It had been fabricated over the previous weeks in my workshop where I have a spare tower section to use as a jig. At 10' tall the tower section rests against a roof rafter. I use a step ladder to comfortably work at the top of it.

Laying the tower section horizontally makes it easier to for work on it in some respects. The negatives are that floor clearance is needed for tower projections, visualization is more difficult and levelling and supports can behave unexpectedly. Keeping it vertical help with visualization, and levelling and alignment are the same as when it is on the tower. I shim the wood plate under the tower section to make it level and vertical. Garage floors are sloped for drainage.

On the left is the basic structure. The angle aluminum (⅜" × 3") attaches to the tower girt with two grade 5 ½" bolts. Although A325 hardware is a better choice, the shear force in this application is well within the rating of bolt, nut and tower girt. Large fender washers provide a larger bearing surface for the bolt heads, which helps to reduce point stress on the tower girt and aluminum arm. The aluminum angle was cut to a length that is long enough to mount the rotator, and not too long for excess bending stress due to the weight of antenna, rotator and mast balanced at the end of the arm. 

Not seen in this picture is a vertical support cable for the arm, running from next to the rotator to a tower strut. You can see it below after it was installed on the tower. The cable reduces stress and the turnbuckle allows for exact levelling of the system when it is under full load. Even without the cable the support easily handles my weight when I stand where the rotator is located.

That 3" width of the aluminum angle is a tight fit for the Ham-M bolt pattern so I attached a short length of steel angle to the aluminum. The rotator is centred on the joint between the two to keep it in line with the tower face. Levels were used to keep everything aligned. On the right a pipe (mast) goes from the rotator through the upper support arm affixed to the next higher girt. Detail can be seen in the picture below.

The multitude of holes in the aluminum angle were already there. There are a couple of holes directly under the rotator that are used to fish the 8-wire cable to a terminal strip on the angle, where it is partly sheltered from the weather. The aluminum angle was rescued from a dumpster for free. I had no particular project in mind when I claimed it, but I was sure that it would find a use. There is more in my stock for future projects.

The support girt is at the 75' level, which is 5' above the second set of guys. The upper support arm is at 80'. These are nominal figures that ignore tower section overlap, and the actual values are closer to 72' (22 m) and 75' (23 m). This is a good height to minimize guy interactions and to match the elevation angles needed for the intended coverage area.

On the left you see the support cable and the level used to adjust the turnbuckle. It has to be tightened a tad when the antenna is mounted. The rotator cable and terminal strip are visible below the level.

The steel angle arm supports a mast bushing. A bearing is not really necessary for horizontal wind thrust when there is no vertical force. Also, a bushing is cheap to fabricate. For the 1.9" diameter of the mast the bushing is a short length of 2" schedule 80 aluminum pipe with an ID of 1.939". The fit is so close that the bushing must be carefully aligned. A burr present on the mast had to be filed flush to the pipe surface so that it would slide through the bushing. The mast diameter is probably closer to 1.91" due to the galvanizing for an even closer fit. 

Time will tell how the bushing wears in service; it is aluminum so that it will wear rather then the steel mast. The bushing is easy to replace if necessary.

The thrust arm is steel angle (⅛" × 1-½"). It pivots on the rear bolt to the girt for one degree of adjustment (there are 2 bolt holes on girt that can be selected) and another degree of adjustment is made by moving the nuts on the ⅜" threaded rod between the arm a short and heavy steel angle bolted to the girt face (not shown). The adjustment range was tested on the jig and determined to be sufficient.

Once everything is tightened the arm is very stiff. It will be periodically inspected it to check that it doesn't shift. I will add lock washers and other hardware if the need arises.

Hy-Gain rotator clamps are not very adjustable and a mast has to be about 2.1" diameter to be properly centred. The 1.9" OD pipe can be shimmed to meet that spec. I don't see the need since the distance to the bushing is far enough and the restricted rotation angle small enough that mast misalignment is unlikely to cause binding at the bushing.

After the TH6 was repaired it was trammed to the new side mount. The picture contains several items worth noting. First, notice that the mast clamp is low on the mast, close to the rotator. Although the bushing prevents bending stress on the rotator, an extreme wind can "bow" the mast. That increases bending stress and it is maximum at the midpoint of the mast. It's not a major concern but why take chances. A second benefit is that a shorter mast can be used to secure the boom truss. In this case the mast clamp for the boom truss is just below the bushing.

For a swing arm you must use thrust bearings above and below the swing arm for support and to protect the rotator. In my side mount article the diagram I drew of the swing arm is incorrect; I know better but the mistake crept in anyway.

Geometry and utilization of the tower faces dictated that the side mount would be placed on the tower's one climbing face. One of the other faces is dedicated to cables, which excluded it from consideration, and the other face was not ideal for the desired compass coverage and there is the risk of the antenna boom striking the cables. Putting it on the climbing face raised the problem of having to climb over the wide aluminum strut (see above). In practice the 3" projection from the tower face turned out not to be a problem. Not only do I not accidentally bump into it, it is comfortable to stand on when I'm working at that level.

The pulley for the haul rope is suspended directly above the mast with an arm attached to the tower. Depending on the geometry of the tram line this may be necessary to ensure the mast clamp aligns with the mast when the tram line is slacked. It is easier to bolt together the clamp halves without having to use muscle to align them to insert and secure the long bolts. Alternatively, have a friend join you on the tower. Yagi wrestling isn't fun.

The longer the side mount the further the rotator is offset from the tower. This can be tempting since you can eke a few more degrees of rotation. With my mount I have approximately 135° of rotation available. Placing the boom on the outside of the mast adds another couple of degrees. However, go too far with most antennas there will be a problem: the elements on either side of the mast can strike the tower. That's a bad idea.

Rubber cushions will be put on the boom so that it softly strikes the tower at the rotation limits. The Hy-Gain rotators have too little torque to do any damage and the motor will halt when contact is made.

Side mount rotation, whether a fixed mast or a larger-rotation swing arm, requires an antenna with elements spaced far enough from the centre so that it is the boom and not the elements that limit rotation. Smaller yagis and those for higher frequencies are more problematic. 

The Hy-Gain Explorer 14 that I recently sold is not compatible with a side mount because the driven element is close to the mast (boom centre). The TH6 has adequate space for this system (see diagram, above, copied from the TH6 manual). I opted to use the TH6 rather than the TH7 because there is inadequate space between the two driven elements of the newer antenna. The mono-band yagis I built for 10, 15 and 20 meters are compatible with rotatable side mounts, should I choose to do that in the future.

In addition to mechanical clearance there is electrical interaction of the innermost elements and the tower as they come into proximity during rotation. In most cases it is minor, and when it's the driven element the effect is mostly on the feed point impedance (SWR) and not the antenna pattern. The benefits of rotation typically far outweigh the negatives of pattern distortion. I ran several models to judge the potential magnitude of the interaction for the side mount article, and I reported my general findings. Exact determination of pattern distortion is difficult to do in a software model.

In a future article I'll say a little more about the side mount rotator and rotation. As of this writing the rotator is not wired back to the shack. Indeed, the TH6 is oriented so that the tram can remain in place to lift and adjust the 10 meter yagis that are now built. I should have everything working by early October.

Sunday, September 12, 2021

Fighting Flora and Fauna

This is not the first time I've written about my troubles with wildlife. While a rural QTH is great for antenna farms, the majority of animals are not accustomed to seeing or dealing with humans. Unlike they behaviour changes they exhibit in and near urban areas, they proceed as if in the wild. 

They come close and satisfy their curiosity by chewing or walking on cables, dig in the loose soil of recent excavations and make their homes in shelters built for antenna and cable switches and junctions, and inside tubes and pipes. Deer and their predators follow the trails I make through the foliage and snow. The predators are intelligent enough to respect humans, and their firearms, and keep their distance.

Dealing with animals, vegetation and insects is an unavoidable part of regular station maintenance. Sometimes it is damage I must prevent or repair, and other times nature must be tackled in pursuit of my antenna farm projects. Read on for my latest adventures.

Many insects like dark enclosed spaces in which to build their nests and to store food and eggs over the winter. To their delight, all of my outdoors enclosures for matching networks, switching and cable junctions have weep holes to allow moisture (rain or condensation) to exit. It seems that no matter how small I make the holes there is an insect that is smaller yet. I can't make the holes too small or the surface tension of water will prevent drainage.

Even so, when I built the Beverage antenna remote switch early in 2020 (see article for pics) I made the weep holes smaller than usual and the hole for the Cat5 control cable a snug fit. In early summer the switch exhibited intermittent short behaviour (excess current to the relay coils). A few weeks later when the hay was harvested and I could safely access the switch.

As I slid the cover off after removing the screws an enormous number of ants came scurrying out. They crawled around the enclosure, over my hands and up my arms, with most jumping off when they realized they were on an animal (me). In the 30 seconds or so that it took me to pull my phone out and take a picture only about half the ants were left inside.

You can see the cocoons under the ant mass. These had to be scraped off after the the ants were cleaned out. The funny thing is that the ants were not responsible for the switch failure. After bench testing in my workshop the likely culprit is a secondary lightning strike. Long Beverage wires are notorious for building up large induced voltages from nearby strikes, and in this case the integrated suppression diodes in the relays had failed. 

Unfortunately, as I discovered in a similar case, the diodes fail to a low resistance value (not a complete short) when their PIV rating is exceeded. I was further irritated that the specs for these Littlefuse reed relays do not state the PIV rating of the suppressor diodes. I didn't notice that when I selected them. For the interim I have more of these in my stock so I will be installing them shortly, in time for the fall 160 meter season. I would like to replace them with relays that use my choice of suppressor diodes.

Despite the diagnosis the ants are not innocent. They brought a lot of moisture into the small enclosure that left its mark. Notice that all the bare copper wires are heavily corroded (green). Tinned wire and hardware is unaffected. When I rebuild the switch the bare copper will be replaced by tinned wire. Wire that than cannot be easily replaced (e.g. transformer windings) will be coated to inhibit corrosion.

It is interesting that one of the two styles of coax jacks corroded (on the left) and the other did not. Application of dielectric grease to the threads should inhibit further deterioration.

The ants were a surprise since it's earwigs I typically have to deal with. Earwigs will climb at least several feet to find a nice comfortable hole to lay their eggs in late summer. At last count there are 6 enclosures with earwig infestations (including every one in the 80 meter vertical yagi). I am not yet able to reach the Beverage antennas which each have two enclosures (head end and reflection transformer) to be inspected.

The picture shows the 80 meter yagi switch box with the largest earwig infestation. It is the one at the base of the southwest parasitic element. All the covers were removed and the units left open for a few days until the eggs dried and could be cleaned out. Try it when they're fresh and you will only smear the black goo everywhere. 

A bit of rainwater while they're uncovered won't damage the relays and coil. Neither will a water rinse. Sealed relays can put up with a lot of environmental abuse.

Before winter I plan to deer-proof the cables and support ropes in the 80 meter yagi. They do like to chew things, much to my surprise. In my station they are far worse than rodents. Squirrels, mice and their kin have molested none of the on-ground cables. Sometimes a chipmunk will dig a home along a trench line but they have not damaged anything. Perhaps they favour recently disturbed soil.

In the picture above you may be wondering what the problem might be. It is an after picture, once the problem was resolved. When I put up my first big tower in 2017 the ideal location for one of the guy anchors was behind a short spruce tree. It was not really in the way so I ignored it. Little trees grow into big trees and that's when the trouble begins. 

First it gobbled up the lowest guy. I trimmed branches to avoid contact with the guy. The tree continued to grow and soon gobbled up the second guy and was well on its way to the third. I like trees so I avoid cutting them down when possible, especially an attractive tree in a pleasant setting like this one. 

My patience was exhausted when climbing vines that infest trees grew over the guys. Vegetation in contact with steel, including galvanized steel, promotes rust. With the help of a friend the tree was dispatched and roots cut out below ground. They guys are now free and ground levelled where the tree once stood.

There is a ham I know (call withheld to protect the guilty party) who installed a guy anchor near a seedling many years ago. The tree grew and grew until the anchor and equalizer plate were embedded in the trunk of the now large tree. Neither the tree nor the anchor seemed to suffer from the experience, or at least not yet. I would have loved to take a picture but did not to avoid offending the ham in question. It would have made a great picture, and an instructive one.

Speaking of anchors and trees, there is one last item that is a little different. In this case the tree in question is very much wanted.

A few years ago I opened a path in the bush at the east end of the hay field to use a tree as an anchor for tramming yagis up and down the 150' tower. This worked well. I want to do the same this fall when I decommission the TH7 and bring down the experimental 40 meter yagi element. 

If the latter passes inspection for its mechanical soundness it will become the driven element of a 3-element 40 meter yagi. That project is proceeding and if all goes well it will be built and raised to 150' later this fall. The yagi will weight close to 300 lb (135 kg) and will require a tram line that is equal to the challenge.

There is a large and healthy tree deeper in the bush that appears to be ideal. Equally important is that it is directly opposite the guy anchor discussed earlier. The guy anchor, which has a spare eyelet for this purpose, will hold a back stay cable to the mast to balance the large force of the tram line tension and the yagi's weight.

Clearing of the bush to access the tree and make a path for the skyward pointing tram line is ongoing. The above picture shows the current progress. The tree itself is hidden in shade at the centre of the frame. I'll have more to say about it when it is ready. As a trial run the tree will be used as an anchor to lower the TH7 and 40 meter yagi.

I'll close on a more amusing note. Wild turkeys are common in the area. They roam the lawns and harvested fields almost daily this time of year. They step around guys and over radials and, so far, have done no damage. I leave them alone.

The big birds are shy and run (or fly) when they see me. This one was taken through the window. One day earlier this year there were more than 20 of them in the driveway.

Sunday, September 5, 2021

Correcting the Mismatch of the Upper 20 Meter Yagi

To summarize a long story, after the upper 5-element 20 meter yagi of the stack was raised I discovered that the gamma match had somehow slipped out of adjustment after being tuned. This probably happened while weatherproofing the gamma capacitor. Since the antenna is very large and heavy I decided to correct the mismatch and not to take the antenna down for repair. Taking the antenna down, adjusting it and raising it again would take 3 full days with the help of several friends. Correction is the easier and safer alternative.

I developed models to determine the effect of a matching network. A simple L-network is all that is required, and it can be made very efficient. For convenience my plan was to mount the network at the stack switch. Since the network and the gamma mismatch both shift the phase of the upper yagi it is also necessary to bring the yagis back into phase. The existing phasing lines assume that the yagis are identical, per the design of the antennas and stack.

Although the problem I am solving is specifically for my antenna system, the techniques and tools are applicable to other antenna challenges. Since these may be of use to readers, it is worthwhile to describe the resolution in depth.

Danger of calculation versus measurement

I keep so busy with my many projects that I don't always remember what I've done and my notes may be missing or difficult to understand. I had a set of impedance values across the band for the upper yagi in my notes and I assumed they were measurements. It turned out that they were calculated for the length of the phasing line to the stack switch based on measurements at the coax joint on the boom where it connects to the rotation loop.

The impedance is determined by the electrical length of the transmission line. The phasing harness lengths were calculated from the physical lengths and the VF (velocity factor) of the coax. For the upper yagi that includes 11' of RG213 (rotation loop) and 30' of LMR400 (tower run). This is approximately equivalent to 44' of LMR400. The total length is 66' including the 22' length of LMR400 from the feed point to the tower.

Physical lengths are easy to measure and mine were done with great accuracy. Unfortunately the published VF of coax is not always exact for a variety of reasons. When the phasing harness segments are from the same coax reel the VF is usually equal. In other cases, the VF can differ and the yagis will not be properly phased.

Under the misconception that the recorded values were measurements I used TLW to design the L-network. It turned out to be a degenerate case where the network reduced to a single component: a series inductor. 

I dutifully built it (see above) and tested it with an analyzer (at right). The box must be closed since the inductance is reduced by the aluminum enclosure. To compensate, the coil is designed with a higher inductance. The required 31 μH of series inductance is what I got after adjusting the coil turns.

I discovered my mistake at 110'. Thoroughly confused and out of time that day I descended the tower.


Several days later I went back up the tower with an antenna analyzer to measure the upper yagi impedance at the stack switch. It was a windy day so I had to visually integrate the readings as the elements wiggled and waggled above me. A few ohms either way is not a serious issue since the L-network can be fine tuned once it is installed.

Taking care not to lose the piece of paper with the numbers in the brisk wind I came down and ran them through TLW. With a bit of experimentation the measurements and calculations matched for a 40.5' physical length of LMR400. That's an error of 8%! This implies a VF of 0.78, far less than the specified 0.85. This is so surprising that I plan to take a tape measure up the tower to recheck the lengths, despite having triple-checked them on the ground.

At right are the measurements, taken at every 50 kHz across the 20 meter band. From a cursory examination of the impedance values it might appear to be impossible for a fixed network to properly transform the SWR across the band. Appearances can be deceiving.

Accounting for frequency, one network can transform a disparate set of impedances to a fixed target impedance. That is approximately true in this case where one network restores the designed SWR curve for the 5-element yagi: about 1.5 at the 20 meter band edges and 1 in the vicinity of 14.1 MHz.

Achieving a perfect 50 Ω impedance is not possible nor is it desirable. Careful design should result in a close match to the lower yagi's SWR, and therefore equal power division and near equal SWR when switching among upper, low and both yagis in the stack. There are software tools to ease the design process. Having one antenna exactly 50 Ω across the band does not achieve either objective.

Designing and testing the L-network

An L-network consists of a capacitor and a coil, one in series and the other a shunt on either the 50 Ω or the antenna port. There are two optional configurations, usually called low pass or high pass since they also behave as filters. Its filter performance is unimportant for this application so I chose a low pass network because the calculated L and C values were easy to work with. By this I mean a low value for L (small coil and low loss) and for C close to a capacitor value and power rating in my junk box.

As for the gamma match, I designed a network to transform the impedance to 50 Ω at the same frequency, a little above 14.1 MHz. For the gamma match that gave an SWR below 1.5 across the 20 meter band. It is a little more complicated for the mismatched upper yagi. Some experimentation was required.

I used a combination of TLW and SimSmith. Using the actual impedance measurements, I designed an L-network for 14.150 MHz. I plugged the network into SimSmith and checked how it performed against the measured values across the band. The SWR curve was good but not great. For the best SWR the L-network was set to match at 14.100 MHz. The result was an SWR of 1.3 at 14 MHz and 1.7 at 14.350 MHz.

I picked a vintage 100 pf transmitting mica capacitor from my junk box for the network. These capacitors are old and require testing, but I have had good success with them. A modern transmitting ceramic doorknob is a better choice. A variable capacitor can be used but you'll need a larger box and adjustment will require extra work. It really isn't worth the trouble for this application. But if you choose to use a variable capacitor, pay attention to the voltage calculated by TLW. The variable capacitor must meet the requirement for your maximum power, plus a safety margin.

Since the capacitor measured as 102 pf versus the required 96 pf it was necessary to return to SimSmith to check the network performance across the band with the larger capacitance. The capacitance may be even higher due to stray capacitance within the enclosure.

It is no surprise that a perfect SWR of 1 cannot be achieved at the design frequency. The best I got was the depicted 1.1. That is not really a problem since it has negligible effect at the band edges where the SWR is highest. This is typical since the mismatch at the band edges is dominated by deviations of R and X from 50 and 0 Ω, respectively, of the load's complex impedance rather than the small deviation due to the capacitor being off by a few percent. With this network SimSmith calculates the SWR as 1.4 at 14 MHz and 1.8 at 14.350 MHz.

The inductor was designed with Coil by K6STI. It is 7 turns of AWG 12 bare copper wire, with a diameter of around 0.8" (2 cm) and 1.25" long (3 cm). To wind the coil I used a ½" PVC pipe that has an OD of 0.84". The calculated Q is about 350, which is quite good. TLW predicts very little power will be dissipated. I took the old coil out of the enclosure and substituted the new one. A 50 Ω load was connected to the antenna port (the same setup as was shown earlier) and measured by an antenna analyzer at 14.1 MHz. 

To adjust the coil I opened the enclosure to squeeze or spread turns. The measurement must be done with the enclosure closed since the aluminum reduces the inductance. For this reason the coil design was for an inductance of a little over 0.5 μH. Once the measured inductance was 0.46 μH the shunt capacitor was installed. It's a tight fit but that's okay; the coil and capacitor can be close, or even touch, and the only effects might be slight increases of C and L. The coil can be adjusted during final turning of the network.

For tuning the network a simulated complex load is helpful. It is not really required if you enjoy doing this work 110' up the tower! My preference is to minimize the tower work by simulating the load in my workshop. For the measured impedance of 82-j9 Ω I put a 75 Ω resistor in series with a 1000 pf capacitor. Although 75-j11 is not exact it is close enough to test and coarse tune the network.

The simulated load only permits adjustment of the network at the 14.1 MHz design frequency. You would need to build loads to simulate the impedance at other frequencies to fully bench test the network. I didn't do that since it isn't strictly necessary. If the measurements are correct the software calculations for its behaviour over the rest of the band should also be correct.

Testing of the completed network is shown at right. The SWR is a little high because the enclosure is open for the purpose of taking a picture. With the enclosure closed the SWR is 1.1, which is quite good for the inexact simulated load.

The network was further examined with SimSmith by substituting the simulated load and seeing what the measured impedance would be. The impedance measured by the analyzer was within 1 Ω for both R and X. That's less than the accuracy of the analyzer so we can't expect to do any better. 

I do have a better instrument (VNWA3) but that degree of accuracy is overkill for what this project requires.

On a final note, look above at the image from TLW. Notice the RF voltage across the shunt capacitor. It is not much higher than for a matched load at a kilowatt. The transformation ratio is small so there are no high impedance points in the network and therefore no especially high voltages.

A physically smaller capacitor than the one selected is not advised. The current is high and you want a capacitor rated for high power RF so that the loss is low and within the physical heat dissipation rating of the component. 

The low risk of flash over to the aluminum enclosure permits a tight fit, and that will come in handy during installation on the stack switch. The high power test would have to wait for installation since there is no easy way to simulate a high power complex impedance load for bench testing.

The time had come to go for a climb.

Installation of the network

Through the miracle of software and bench simulation the work on the tower was brief and successful. I plugged the coax to the upper yagi into the antenna port of the network and the analyzer to the other port. Take care because the network is not symmetrical. Label the ports if that help you to remember.

I fiddled with the coil to see if I could do better. For reasons described earlier, it was not to be. The match was near perfect at 14.1 MHz and behaved as calculated by SimSmith elsewhere across the band. It is a little high at the top end of the SSB segment, a place I only venture during popular SSB contests with heavy activity. I can live with it.

The enclosure I chose for the L-network was no accident. It fits very nicely onto the stack switch antenna port with a male UHF barrel connector without striking the connector for the other (lower) antenna port. Weatherproofing is a challenge since there is little space between the upper and lower yagi ports to wind tape. I will have to improve the temporary job before autumn's cool, wet weather.

The enclosure is oriented to allow water to leak out the bottom edges. The bottom two screws were not installed to help with that. Tape placed across the top edges limits water incursion. There are better enclosures available but I used what I had on hand, and it really is good enough. It's 110' in the air and no one will see it but me.

Back in the shack the SWR of the upper yagi was nearly identical to what I measured on the tower. Some reduction of SWR can be expected and is not unusual due to the very lengthy transmission line. The LDF5 Heliax is doing its job well. 

When in lower + upper stack mode (BIP) the parallel SWR via the stack switch L-network is even better (see picture to the right). 

I tested the completed system with a kilowatt to be sure there are no weak components or poor arc tolerance. All is well.

Phase compensation

The misadjusted gamma match and the upper yagi's matching network both exhibit a phase shift. In this case they are in the same direction so they add. A delay line for the lower yagi is required. Should I ever fix the gamma match on the upper yagi the network and delay line must be removed.

Measuring the phase of the antennas is impractical, so I rely on calculation. Unfortunately, it is easier to calculate the delay line length in software than in reality. On the other hand, forward gain is not overly sensitive to modest phase error. Where we can lose is with the size of minor forward lobes, as shown in the previous article on this topic.

Phase shift in the L-network can be accurately calculated. You can see this (above) for both TLW and SimSmith. The phase shift in the mis-tuned gamma match is more difficult to ascertain. Modelling of the net reactance at the feed point is the best bet, and what I previously did with a model. That is what I will use: varying between 10° to 20° across the 20 meter band. 

The L-network phase shift (before substituting a 100 pf capacitor) is 39° at 14.1 MHz, and it, too, varies with frequency. Since this network is almost identical to that in the modelling exercise, and I have had difficulty developing a model that corresponds well with the real antenna measurements, I estimate the phase shift ranges between 49° and 58° across the band, including that of the gamma match. 

They add because both phase shifts have the same sign, which is to advance the signal to the upper yagi. Correction therefore requires a delay line of around 54° to the lower yagi. This is a almost exactly what was found for the earlier modelling exercise, and that is not surprising. Software modelling works and it can save a lot of time.

For the average phase shift of 54° the length of the delay line is 0.15λ, or 3.2 meters in free space at 14.1 MHz. That must be multiplied by the VF of the coax used for the delay line. For example, 2.1 meters (6.9') for RG213 and 2.7 meters (8.9') for LMR400. All that said, the length is not critical since the phase shift is frequency dependent. No fixed length can be a perfect solution, and an average value is good enough in this application.

My plan is to use RG213 and insert it at the tail from the lower yagi's feed point at the tower. Should I not repair the gamma match on the upper yagi and the delay line continues to be used, the RG213 will eventually do double duty as a rotation loop. I hope to make the lower yagi rotatable in the next year or two. It is currently fixed on Europe.

This is easy to implement, and yet I haven't done so yet. The degradation of the stack pattern without the delay line is small, but with careful A-B testing on the air it is noticable. The modelled deficit is about 1 db of gain and the appearance of a higher angle minor forward lobe.

Good performance without the delay line may seem odd but when you add in the larger uncertainty of terrain on the yagi patterns the phase error is not a major concern. SWR is the more important concern since amplifier tuning can be a problem when switching among the stack's 3 modes. Correcting the mismatch also restores the equal power division required for optimum stack performance.

Time is a concern now that autumn is fast approaching and my many antenna projects require my attention. Those are the priority now that the SWR of the 20 meter stack has been corrected. The delay line can wait a few more weeks.