Buying a Used Tower

A few hours before the start of WPX CW this past weekend a tower arrived on my doorstep. Back in January I did say that a taller and stronger tower are part of my plans for 2014. To that end I have been shopping the used tower market for the past couple of months. Below is a picture of the tower loosely assembled in my back yard.

This is a used Delhi (now Wade Communications) DMX-52. Tower weight is ~120 kg and it stands 14.1 meters (6 x 8-foot sections, with 5 x 4¼" overlap between sections). The tower is typically erected as a free-standing tower but it can also be bracketed or guyed. I will be guying it since I don't want the cost and inconvenience of planting it in concrete. It may only be in use for 1 or 2 years.

You are most likely unfamiliar with this tower if you are not Canadian. They can be found from one coast to the other in both ham and non-ham applications, both residential and commercial. Like many towers it is uncommon to find them far outside their countries of origin. For example, while Rohn towers are very common in the US they are a rare sight in Canada. The same is true of DMX towers in the US. This is despite the extensive commerce between the two countries.

Coincidentally this tower model was my very first tower, back in 1974 when I was in high school. It served me well for several years until I graduated from university and moved out of my parents' home. I didn't have a tower again until 1985. During those intervening years about the only times I got on the air were as part of multi-single and multi-multi contest teams at other hams' stations.

Since all of us like to save money I thought that it would be helpful to say a little about the right way of buying a used tower. Even if you buy new you may find something useful here as well. This is not a comprehensive list, just some points that some might benefit from.

There are no bad towers

There is an old saying: there are no bad dogs, only bad dog owners. The same is true of towers. That doesn't stop many hams from declaring a tower to be "bad" when in reality they are responsible for ignoring the engineering limits and installation and use instructions, only to have something unfortunate happen.

All they're doing is shifting blame for their own poor choices and behaviour. Please don't be one of those hams. Choose the right tower for the task at hand.

Availability vs. need

When looking for a used tower you are at the mercy of the market. Often you can't get exactly what you want. Don't use that as an excuse for buying a tower that is not adequate to your needs. In the long run that can cost you dearly. Know your local market and the specifications for types of towers that come on the market so that you'll know what to pursue and what to pass over. Around here those are mostly DMX and Golden Nugget towers by Wade Communications. The latter is what I put up last year to support a high-bands dipole and delta loop for 40.

The residential OTA (over-the-air) television market is much larger than the ham market so don't only focus on buying from hams. Many non-hams will give away unwanted towers if you'll only take them down. This is less true in Ottawa this year than last year, probably due to increasing numbers of people "cutting the cord" to sate their television appetite. If you've never done tower work before don't start your education by offering to take down someone's unwanted tower for free. At least not without experienced assistance.

Consider buying two imperfect towers if the prices are very attractive and you can mix and match pieces to make up one good tower. You can endear yourself to your ham friends by giving away the pieces you don't need. Your family will appreciate that you don't clutter the yard with unwanted tower sections that slowly surrender to entropy.

Nothing is forever

No tower lasts forever. Every product has a limited lifetime. When you buy a used tower you are buying a tower that has less life in it than a new one. That's one reason you pay a lower price. Always keep this fact firmly in mind: a used tower will not last as long as a new tower. Worse, there is no easy way to estimate the remaining service life.

Never buy a used tower sight unseen, even though that may restrict you to the local market. Too many towers are misused, overused and abused by their previous owners. This goes for both hams and non-hams. The dreadful things I've seen done to perfectly good towers over the years continues to amaze and disgust me. While you may not be able to estimate the service life of a used tower you should be able to identify abuse and neglect. But to do so you or an acquaintance who knows towers needs to be able to inspect it firsthand.

What you can't see can hurt you

Stresses from handling, normal use and even poor storage conditions can result in micro-fractures that are impossible to see in a visual inspection. Aluminum in particular is prone to invisible flaws since stresses below the metal's yield point can weaken it.

An example of fatigued aluminum can be seen in the tower I just bought. Aluminum rivets attach the cross braces to the tower legs and to each other. The action of the harder metal (steel) against the aluminum rivets is hidden from view. That is until a rivet breaks. This problem commonly afflicts DMX towers of a certain age, especially when they are overloaded.

It is a simple matter to drill out the remnants of a broken rivet and replace it with a bolt. But first take note of any bends or breaks in the steel braces themselves that would indicate a more serious problem. If there is a problem you need to closely inspect the rest of the section, and even other sections since it is rare that excess stress on the tower causes just one problem. That is, when you can see one rivet that is broken due to fatigue or steel abrasion you can be sure that others are not far behind.

The one broken rivet in the tower I purchased (picture at right) has now been fixed. It appears to be an isolated failure and therefore of no undue concern. However I will still periodically inspect the area after the tower is raised.

In a tower made of formed sheet metal such as the DMX pretty well every part and surface is visible. In a tower with tubular legs (e.g. Rohn or Golden Nugget) there are areas that cannot be easily inspected. There are many ways for water to get inside the legs and gradually, over many years, to find any flaw in the steel coating through which rust can get a toehold.

The problem of inspecting inside tubular legs gnaws at me and I therefore tend to distrust the integrity of used tubular towers. One quick though imperfect test is to look for rust stains on the inside bottom of tubular legs. These are caused by loose rust transported downward by moisture. You need to establish how serious the problem is and reject the section if there is any doubt. One weak point can bring down the entire tower.

Galvanizing

Pretty much all towers are made from galvanized steel. This is typically a zinc-based coating put there by hot dipping (best) or electroplating (not as good).

Depending on local climate the coating will wear off sooner or later. Once the base metal starts to rust it is difficult to stay ahead of the problem. If you've ever tried to paint a standing tower you'll understand. It's a messy and difficult job. In fact painting a tower on the ground is tedious work due to the intricate structure.

Reject a tower that has more than small patches of rust, or where just one spot has eaten deep into the steel. A badly-rusted tower is too expensive even if it is freely offered. It is well past its service life. Even if you repair the visible rust it still indicates that the coating is wearing thin and rust will soon appear elsewhere.
 
At right is a picture of the top section of my newly-acquired tower. The rust you see is due to attached clamps, not within the tower itself. This is nothing more than a cosmetic issue. Learn to distinguish between base metal rust and rust that "drips" onto the tower.

Hardware

Towers are engineered structures where every piece of it is designed or selected to a set of specifications. Violate those specifications and the tower will not perform as advertised. One of the most common violations I have seen is the use of improper hardware. In particular the bolts which connect the tower sections. This is a topic I talked about last year.

Tower bolts have a couple of properties that are especially important: shape and strength. In the picture at right are a few bolts from DMX towers and related equipment.

At the top is one of the bolts that came with the used tower I just bought. There is some corrosion but it is usable with some cleaning. Below it is a new bolt of the same type. These bolts have a ½" shank (outer thread diameter) and are Grade 5 strength. Although only the bolt head carries the Grade 5 marking (3 bars on the head) the nut and lock washer are the same strength.

None of the hardware on the used tower came with lock washers. What happened to them I don't know. The fellow who sold me the tower is a construction professional and came across as very honest and careful. But he does not know towers especially well. He is not the original owner and so I expect that the lock washers were not present when he acquired it. They must be replaced. I purchased new Grade 5 lock washers for $0.09 apiece (and $0.05 for the sections which use ⅜" bolts).

The bolts are not standard. Notice the bevelled shank just below the head. The bolt holes in the tower sections are slightly larger than ½" so the threaded part of the bolts fit loosely within the holes. When the bolts are tightened the bevel creates a small dimple in the tower leg underneath the bolt head and forces the other tower leg into alignment.

A standard bolt does not do this and so cannot properly secure and align the sections. Get replacement bolts from the manufacturer whenever specialized bolts are missing or badly corroded. They will cost more but the price of an improperly built tower can be far, far higher. If you don't want this expense you should reject a used tower that does not come with a complete set of bolts that are in good condition.

The bottom bolt in the above picture is also for a DMX tower but has a standard shape. It comes as part of guy station kits. These longer bolts are used in place of the lower of the pair of bolts at the section joint where the guy station is mounted. The other, bevelled bolt should be torqued first since only it can align the sections.

Bolt holes

Improperly secured tower sections and excessive load are often visible in the bolt holes of the disassembled tower. Bolts that are insufficiently torqued and slip due to weight pressure or tension due to high wind loads will show up in wear and stress marks in the bolt holes.

Some wear is normal so don't expect the attachment points to be pristine. One common problem is wear around the hole due to rotation of the bolt head during installation and removal, which scrapes off the steel coating and even the steel underneath. The bolt head should be held still and the nut turned during both installation and removal. The lock washer under the nut prevents abrasion of the tower when the bolts are tightened and loosened. Excess metal loss due to improper bolt handling is a problem.

Galling and elongation of bolt holes are a clear sign of abuse, inadvertent or otherwise. All the bolt holes on the tower I bought show normal wear except for the bottom holes of the bottom section. This is where the tower is normally attached to the base (engineering stubs in concrete).

This wear does not appear to be due to movement caused by insufficiently torqued bolts. The visual evidence coupled with the seller's story of the tower condition he found when he took it down seems to indicate that a non-standard mounting method was employed that involved shaving material from the holes. This is not good.

Since I need to build a custom, ground-surface mount for this tower this damage is something I can work with. If it were to be installed with a traditional concrete base as a free-standing tower or off the ground with larger sections underneath I would be more concerned. I must ensure that the tower is capable of supporting the combined static and live load of the tower itself, antennas and the climber (that is, me).

Modifications

Beware of modified towers! Too many people imagine that they're smart enough to cut, attach or pierce the structure to suit a unique application. They are almost always wrong. Unless there is good evidence that all modifications meet a high engineering standard a modified tower should always be rejected.

Next steps

Apart from minor repairs to the tower I need to construct a base and a gin pole, and buy or build the guying hardware. I plan to use the same guying system as for the current 30' Golden Nugget tower. In fact it will replace that tower at that same spot (Site C).

When all is ready I will completely dismantle all antennas and support structures. Everything will be rebuilt from the ground up. This will not prove as large a task as it might seem. In any case I have less interest in operating during the summer so it will not be an inconvenience to be off the air for a few weeks. Other activities get priority this time of year.

Once I complete the dismantling I'll say more about how I will go about building the next iteration of my miniature antenna farm. By summer's end I expect to have a moderately competitive QRP DX and contest station.

40 Meters 3-element Wire Yagi

The most popular articles on this blog are a surprise to me. They are the articles I wrote over a year ago on small 40 meters single-element antennas that are effective for DXing. In retrospect I should not be so surprised. Commercially-available rotatable yagis are common on 20 meters and above, but once you drop down to 40 meters there are relatively few hams with the ability to erect a rotatable yagi.

There are indeed small (loaded) commercial yagis for 40 but they are relatively expensive, carry a large wind load penalty and need to be at least 20 meters above ground to compare favourably to a single-element vertically-polarized antenna.

This is not another article about small 40 meters antennas. Rather it is about a large antenna that should be within the reach of many hams. What you will need is 2 high supports, such as a pair of modestly-tall towers, enough space to string out a few wire elements, and the motivation to make the necessary effort. This antenna should prove of interest to those hams that want more than what a single-element can offer but are unable for whatever reason to install a rotatable yagi.

Motivation

Although I have no plans for an antenna of this size anytime soon it still serves a purpose. Yagis with 2 elements (wires or rotatable) have significant compromises. These relate to key performance metrics such as gain, gain bandwidth, F/B, SWR bandwidth and some complexity in making it switchable (between broadside directions). A 3-element yagi ameliorates much of these concerns.

A wire yagi is in many cases a favourable alternative to a rotatable yagi. A typical 3-element full-sized yagi on 40 meters weighs at least 100 kg (225 lb), 10 to 15 ft² of wind load, and costs upwards of US$2,500. There are few used yagis in this class since they frequently fall victim to wind and weather before they can be sold. They are not for the faint of heart.

A rotatable yagi is usually unnecessary. From my QTH a fixed, switchable wire yagi oriented 60°/240° true bearing addresses 80% of the important paths for DX and contesting. Toward the northeast its main lobe covers Europe, western Russia, the Middle East, south Indian Ocean and north Africa. When reversed it covers most of the continental US and the southern half of Oceania. Considering the low cost and high performance a wire yagi can be an ideal choice for 40 meters. It should be complemented by either a small rotatable yagi or other wire antennas to cover other paths and for contest flexibility.

Structure

By making the elements from inverted vee elements it is possible to build a yagi with any number of elements by tying a cable between two towers. A steel cable should be insulated from the towers, and even broken into smaller sections to minimize interactions with other antennas, including shunt-fed towers.

Of course the towers should be far enough apart and high enough to maintain some separation between yagis atop the towers and the wire yagi. Although trees can be used it is rare to have trees of suitable height and position, and they are difficult and dangerous to work with at these heights.

As you can imagine it is quite important that a line through the towers points in the most desirable direction since the main lobe's centre will fall on that line. If you ever do plan to put up a second tower you might want to consider placing it to allow for the possibility of low band wire yagis, and not just for 40 meters. With even taller towers (40+ meters) a similar yagi can be built for 80 meters. While simple, this clearly is not an antenna for a modest station! My present station included.

On 40 meters we should strive to achieve a minimum height of 20 meters (½λ). If the towers are 25 or more meters high and 25 or more meters apart we can achieve sufficient separation to minimize impact on high-bands yagis at the top of the towers.

It is important that the elements be placed so that they are parallel to each other and orthogonal to the support cable, and that the interior angles of the vees are identical. Carelessness will compromise performance so take care to get it right. Use high-quality insulators between the element ends and tie-down ropes to reduce detuning and losses to the environment, especially in the rain.

Don't over-tension the support cable, especially if the towers are self-supporting. You can compensate for sag to keep the elements at the same height by hanging the parasites lower below the cable than the driven element. The cable also serves as a messenger cable for the coax feed line and the relay power cables. Induction of antenna current on the coax exterior and the DC cables is small because they are at a right angle to the elements.

Design

I chose the same basic design as for the 3-element reference 20 meters yagi from my series on choosing a high-bands yagi. That antenna was adapted from a W2PV design that itself was a variation on an NBS yagi optimization process. I chose 1.04/0.96 for the respective lengths of the reflector and director. The centre frequency is 7.1 MHz. The "boom" length is 0.35λ, or 14.8 meters (48.5').

My intention with these choices was to ensure that the antenna would work well across the 40 meters band with respect to gain, F/B and, to the extent possible, SWR. The last is the most difficult since the yagi is a high-Q antenna and the band has a 4% frequency range.

I first created an inverted vee in free space that resonated at 7.1 MHz. In a 3-or-more element yagi the gain tends to peak high in the band while F/B peaks low in the band. Unlike the aforementioned 20 meters reference yagi it is necessary for the element separation to be equal (7.4 meters). The antenna will be switchable and therefore must be symmetrical with respect to both broadside directions.

The interior angle of the inverted vee is 120° so that it is most efficient and to keep the ends from getting too close to the ground. Ground proximity reduces low-angle radiation (bad for DX) and increases ground loss.

Once I had the driven element designed I made two copies of it, placing each in position as a parasite. I then adjusted their lengths to the calculated dimensions for the reflector and director. Each element has a 10 cm (4") horizontal segment at the centre to facilitate connection of transmission lines and loads.

I next confirmed in EZNEC that the antenna model worked as intended. There was some risk that it would not since the design parameters I chose were for horizontal elements, not inverted vees. It worked just as expected.

I then added copper wire loss and placed the antenna 20 meters above real (medium) ground. It continued to work as designed. Further adjustment should not be required at greater heights. The same is not true if the antenna apex height is moved more than a few meters lower (element ends lower than ¼λ above ground).

Switching

You can use this wire yagi as a unidirectional antenna by leaving the reflector at its full length. However it seems a shame to erect such a large antenna and not make it switchable. Depending on geography perhaps only one direction is needed in some cases. It's your choice. From the above azimuth plot (taken at 10° elevation and a height of 20 meters) the -3 db beamwidth is 67°. Making it switchable increases the total -3 db beamwidth coverage to 134°. That's so attractive that I am unwilling to lose half of that.

To make the antenna switchable I chose to use a coil to tune the parasites. This is quite simple to do. First, cut the length of the reflector to equal that of the director. Second, calculate the inductance of a coil that has ~70 Ω reactance at 7.1 MHz (the centre frequency). Finally, check the values of gain and F/B to ensure that the yagi performs as it did with the reflector at full length. As it turns out I had to increase the reactance to over 90 Ω to get the performance back to where it had been. This requires a coil inductance of 1.8 μH at 7.1 MHz.

To make the antenna switchable each parasite has this coil at its centre and an SPST or DPDT (shown) relay configured to short the coil. When the relays are not energized one coil is in series with the parasite (reflector) and the other coil is shorted (director).

When the relays are energized the action of the coils is reversed, and therefore the direction of the yagi. Since the antenna is symmetric its performance and SWR should be identical, unless there are asymmetric interactions with the environment between directions. It is recommended that when the relays are not powered that the yagi be configured to point in the direction most often used.

Unlike the 2-element yagis I previously designed there is no need for transmission lines between elements. It is only necessary to run a 2-wire low-voltage cable to the centres of the parasites to power the relays. A small plastic box hung from the cable at the centre of each parasite should be used to contain a relay and coil, and another at the driven element to terminate the coax feed line and split the DC relay power from the RF. A separate low-voltage DC cable can be run from the shack in parallel with the coax if preferred.

The final task is to match the feed point to 50 Ω. I chose a beta match. This involves shortening the driven element and placing a open-wire shorted stub across the feed point.

Dimensions

Final design dimensions:

• All elements made from insulated 12 AWG (2 mm) copper wire
• Director and reflector length: 19.66 meters
• Driven element length: 19.94 meters
• Parasite coil: 1.8 μH
• Beta matching stub: 2.3 meters of 150 Ω open wire line shorted at the end, or a coil having the equivalent inductive reactance

When constructing the antenna it is a good idea to first build a driven element and tune it to resonate at 7.1 MHz. Measure it and then cut both parasites to 0.96 of this measured length. Adjust the length of the driven element in proportion to any differential between the parasite length and the parasite design length of 19.66 meters. This last step should simplify tuning of the beta match.

The impedance of the beta match stub is somewhat critical so choose stiff wire (or rods) of a diameter and separation to achieve 150 Ω impedance. At other impedances the length of the stub must be adjusted and the SWR bandwidth may be a little worse. The stub should employ a shorting bar for adjustment. If a coil is used instead it, too, will need to be adjustable either with a movable tap or by spreading/compressing the coil.

Performance

At an apex height of 20 meters and 10° elevation (median of DX-friendly angles on 40 meters) this 3-element wire yagi outperforms a 2-element wire yagi (with inverted vee elements) by 2 db and one with dipole elements by 1 db. Better yet the gain is more consistent across the band than any 2-element yagi. F/B bandwidth and depth are also improved in comparison to 2-element yagis.

This performance differential is sustained as height is increased.

F/B peaks a little below the lower band edge. It can be moved higher but at the cost of lower gain in the CW segment. I consider this a poor trade-off though others may feel differently. As designed the 10° gain is 6.85 dbi at 7.0 MHz and gradually rises to a peak of 7.25 dbi near 7.2 MHz. Moving the antenna from free space to 20 meters over medium ground shifted the frequency of maximum gain by only 30 kHz.

At 7.180 MHz the main lobe peak is 12.04 dbi at an elevation angle of 27°.

The uncorrected radiation resistance of the antenna is ~24 Ω. A beta match was designed in EZNEC to match the antenna to 50 Ω coax. Dimensions were noted earlier in the article.

The 2:1 SWR bandwidth is 160 kHz. In practice the SWR bandwidth will be wider due to transmission line attenuation and environmental losses in the antenna's near field. An antenna tuner can be used to tame the modestly high SWR up to about 7.250 MHz, which would allow this antenna to pretty well cover the entire 40 meters band. Despite the high SWR, the gain remains good right up to 7.3 MHz.

It is a simple matter to shift the frequency of minimum SWR to better favour CW or SSB band segments by adjusting the beta match parameters. Gain and F/B will stay the same if the parasites are left as they are.

About wire loss and gain

It is possible to get more gain from this antenna. At least in theory. By spacing the resonance of the parasites closer together the free-space gain can be boosted from 8.7 dbi to 9.2 dbi. Unfortunately this requires a type of wire that is not currently available: zero loss.

The average I²R loss in this antenna built with 12 AWG insulated copper is -0.3 db. The quoted performance include this loss. When the gain is maximized by tightening the parasite tuning the average loss increases to around -0.8 db. In other words the increased gain is entirely erased by the increased wire loss!

This is one of the trade-offs of wire yagis we must learn to live with. Gain has an inverse relationship to radiation resistance in a yagi: the lower the radiation resistance the greater the I²R loss. Heavier gauge wire can be used, of course, but the expense (and weight) quickly rises.

I believe that 12 AWG wire is the largest that makes sense in antennas of this type. Smaller gauge wire should be avoided, not only for the increased loss but also tensile strength. Insulated copper-coated steel wire is available which both lowers cost (steel is cheaper than copper) and increases strength, so consider that choice if you decide to build a wire yagi.

Choosing a High-bands Yagi (Part 5) - Comparisons and Wrap-up

To close this series about choosing a high-bands yagi I will do some comparisons, review some of the key trade-offs and then consider antenna height. Recall that the reason for this series is my need to choose a commercial small tri-band (or 5 band) yagi suited to a small tower, which is my plan for 2014. Hopefully others get some value from this exercise as well.

First, below is an index to the preceding 4 parts of the series. This will make it easier to follow the references in this final article in the series.

• Part 1: Introduction and reference 3-element yagi
• Part 2: 2-element trap tri-bander
• Part 3: 3-element trap tri-bander
• Part 4: Rotatable wire yagi

Now then, why choose a yagi at all? I know many hams that do so with hardly a thought; it is just what they believe they need to do to get on the air. This is clearly not necessary. In my own way I have proved over the past 16 months with wires alone. I have not only been effective in contests (QRP category) but have also worked close to 200 countries. It is likely that I will reach the 200 DXCC mark before I get around to putting up a yagi.

Everyone has their own reason to put up a yagi. At least there had better be a reason, and a good one at that, to undertake the expense, trouble and risk of erecting a tower, complete with antenna and rotator. My own reasons are clear enough:

• Be more competitive in contests, or at least have more fun by working more stations and multipliers.
• Work more DXCC countries, including those over long and difficult paths, and to have more success in pile-ups on the rare ones.
• Less struggle to make contacts, even on a casual basis, especially on SSB or when conditions are less than favourable.

The critical need is effective radiated power (ERP) at the required elevation angles and directions. Apart from changes within the shack (transmitter power) this comes down to antenna gain and height. F/B and SWR match are nice but are secondary to my objectives. That is, I am ready and willing to sacrifice F/B and some SWR bandwidth to squeeze more gain from an antenna.

With that in mind let's recap the gain performance of the antennas in this series on 20, 15 and 10 meters. You can refer back to the articles listed above for more information about F/B, SWR and model details. The charts at right only show gain.

An "optimal" 3-element full-sized reference yagi is only shown for 20 meters, which was presented in Part 1. Similar performance can be expected on 15 and 10 meters for the same antenna scaled to those bands. The gain-optimized spider beam was also only modelled for 20 meters (3-el spider+ in the chart). It was presented in Part 4.

From an inspection of the adjacent free-space plots of gain we can deduce the following points:

• All small tri-band yagis require a compromise in performance in comparison to a full-size yagi. In some cases the compromise is profound.
• 2-element designs have maximum gain at the low end of the usable bandwidth while 3-element designs lean the other way. However, the introduction of traps skews this theoretical attribute due to equivalent series resistance (ESR) loss in the traps.
• Traps reduce performance bandwidth on 15 and 20 meters. It is especially important with these antennas to tune the elements for the band segment(s) of interest.
• With respect to maximum gain the difference among these antennas is not very large. This is misleading since for the 2-element and trapped yagis the gain curve has a sharp peak and can be quite poor elsewhere in the band.
• Excellent gain and F/B are often present even on band segments where the SWR becomes problematical. This can be matched in the shack at the cost of increased transmission line loss. This should not be a concern in most installations if the SWR if less than 3 or so and RG-213 or better coax is used.

Let's also recap some important points about the design of these antennas:

• Traps must be well designed to minimize loss due to ESR. Loss is greatest where the gain is highest since that is where radiation resistance is lowest.
• Broadband SWR comes at the cost of gain. You can't have both, so you must choose. That gain and smaller SWR bandwidth requires a matching network (e.g. beta match or balun) to raise the impedance to 50 Ω. The matching network, when required, must work on all 3 bands, and with a common feed point. Most commercial products in this category already do so, saving us the trouble.
• Rotatable wire yagis have a somewhat complex physical design that can make them difficult to install on towers that are guyed or that support other antennas.

Effect of height over ground

All the forgoing modelling and analysis has been done in free space. This is useful since it removes variables to do with antenna interactions with the environment. Once we introduce the ground a number of subtle differences creep into the picture. That is what we will now look at.

First, provided that any of these yagis is higher than 5 meters above ground there will be little impact on SWR, gain or F/B performance. While it is true that height affects gain and F/B versus elevation angle the overall gain and F/B performance are pretty much the same as in free space. This behaviour is common with directive antennas. If the downward radiation (as measured in free space) is small in comparison to the main lobe there is less interaction between the antenna's near field and ground. Get up high enough and even other houses and utilities in the vicinity can effectively "disappear".

For the height analysis I will in any case keep the antenna even farther above ground, at least 10 meters (½λ on 20 meters and 1λ on 10 meters), so we can comfortably assume that the preceding free-space antenna analyses are both valid and height invariant.

Since most of the modelled yagis have significant frequency-based performance variability I selected a frequency where the performance is representative or close to average for each antenna. On 20 meters this is typically in the range of 14.100 to 14.150 MHz. You can judge for yourself whether this choice is appropriate by reviewing the gain charts shown above.

On 40 meters I chose an elevation angle of 10° for the gain comparison since that is the empirical (experimentally measured) median angle for long and medium length DX paths on that band. On 20 meters the median is lower at about 5° -- the angle generally declines with increasing frequency. That will be the basis for the comparison.

The elevation angle of the main (or lowest) lobe is misleading since that is not the angle for the DX path. The ionosphere determines the path direction (azimuth and elevation) which then informs the optimum antenna design. It is never the other way around! If the main lobe is in a different direction you are wasting energy since it is not going where you need it.

It is no surprise that the 5° gain increases with height for all of these yagis, and indeed for any horizontally-polarized antenna. It is therefore also unsurprising that the performance differentials for the most part remain the same at a variety of heights. There are subtle height-dependent variations due to the different shapes of the main lobe, but we can ignore these since they are quite small.

The full-size 3-element reference yagi is the clear favourite. This is expected since all the tri-banders involve compromises that affect gain performance. The gain range among the candidate tri-banders is ~2 db, but, again, keep in mind that some of these antennas do less well over much of the bands of interest. As I said in Part 1, it is important to compare tri-banders against a superior standard rather than only against other "compromise" antennas; we need to look reality in the face, and know what we are, or aren't getting.

It is interesting that my gain-optimized 20 meters spider does quite well. The unmodified Spiderbeam is less impressive, even though it is most like the reference yagi in that the gain holds up pretty well across the band.

There is another quite interesting way we can interpret the above chart. That is to look at how much higher each antenna must be raised to equal the gain of the reference yagi at a lower height. The approximate round numbers for the range of heights plotted in the charts are as follows:

• 2-element trap tri-bander: 6 meters
• Spiderbeam (unmodified): 5 meters
• 3-element trap tri-bander: 4 meters
• Modified 3-element spider: 3 meters

For example, if the reference yagi is up 15 meters you would have to place a TH-3 (or equivalent product) at 19 meters height for similar gain performance at 5° elevation. It is a simple matter to calculate the equivalent height differential for any other pair of antennas in the list.

That's some food for thought should you ever have to decide between bigger antennas (e.g. stacked monobanders) versus a taller tower. If you consider what is involved it is almost always better to place a tri-bander on a taller tower. Up to a point. Once you start talking about serious height, say 30 meters or more, the objectives and comparison can be quite different. Even so it is no surprise that some smart hams who build competitive contest or DXing stations will often complement their antenna farms with a large tri-bander such as the TH-6 or TH-7 on one of their towers.

Conclusion

That's all I have to say on this topic. I still have to buy a 15 meters high tower and small yagi if I am to fulfill my objectives for 2014. When I'll do so is unpredictable since I am looking for used equipment that can be acquired locally. I won't spend a lot since I might only be using them for a year or two. My antenna choice may come down to what's available on the local used market rather than choosing the best.

Choosing a High-bands Yagi (Part 4) - Rotatable Wire Yagi

Rotatable wire yagis have some attractive advantages:

• Light weight
• No loads or traps
• Moderate wind load

Unfortunately these advantages are counterbalanced by several challenges, which include:

• Unlike aluminum tubes the wires don't support themselves, and therefore require a (usually) complex mechanical design with little to no metal in the structure
• Elements cannot in general be parallel, resulting in reduced performance and increased complexity of electrical design and behaviour

The question is whether the trade-offs are favourable in comparison to alternative small size rotatable yagis such as the 2-element or 3-element tri-banders, covered in the previous two parts of this series.

There are 2 especially popular designs in this category of rotatable wire yagi: the Hexbeam and the Spiderbeam. The former is typically limited to 2 elements due to its structure, while the latter is more flexible with regard to element count. This article will focus on the Spiderbeam since it is the more expandable design and has all the elements on one horizontal plane. The vertical stack height of the Hexbeam design requires a shorter tower to stay under the Industry Canada exemption limit of 15 meters structure height. There are enough jurisdictions outside Canada with similar limits that this issue has more than local applicability.

In an earlier article in this series I mentioned that I had found an EZNEC file on ARRL's web site for a tri-band Spiderbeam. Some aspects of the model did not follow best practices for a NEC2 model so I made adjustments to the segmentation and elsewhere, but did not alter the wires in any way.

Although wire lengths are not exactly the same as found in the Spiderbeam construction guide I was able to verify that after compensating for use of non-insulated wire in the model that the parasitic tuning is identical. The use of 1 mm diameter wire (18 AWG) is the same.

The model uses transmission lines to connect the roughly-parallel elements of driven element fan dipole. This is a subject I covered earlier. This method is superior to modelling the element connections using wires in NEC2.

In the adjacent view of the EZNEC model the antenna points in the 'X' direction. There are reflectors for 20, 15 and 10 meters at the rear (wires 10 to 15) and the same for directors at the front (wires 16 to 23). There is a second director for 10 meters so there are in fact 4 elements on that band. The 5-band version of the commercial product (not covered here) has 2 elements on 17 and 12 meters.

There are no traps or other loads in this antenna, and therefore no associated losses. There are I²R losses in the wires which are higher than in a yagi made of aluminum tubing. This can be reduced by the use of heavier gauge wire. For this model I will use the AWG 18 wire as in the found model so that I can avoid the subsequent necessity of adjusting wire lengths.

Design Issues

The Spiderbeam is a good antenna. So when I say 'issues' I am not dismissing the design or the designer. Every antenna includes compromises. This one is no different. Let's look at them now so we can understand the (model) measured performance.

• Non-parallel elements: I have never been able to get an antenna with parasitic elements bent in the fashion of this antenna to approach the performance of a conventional yagi with parallel elements. It may not be possible. I have experimented with shorter and longer booms with not much better luck. The Spiderbeam choice of 10 meters for a boom length (on 20 meters) looks about the best possible for this style of antenna. Alternatively, parasites that are more rectangular (straight but with the ends turned sharply inward) as they are in a Moxon 2-element antenna generally perform better.

Spiderbeam Construction Manual caution: element lengths are critical (yes they are)

• Element tuning: The ends of the parasites are close to the driven element and, except on 20 meters, are close to other parasites. Element tuning is altered (electrically lengthened) when its ends are close to any metal or other elements. Tuning is difficult since the resonant frequency is obscured in any array and is further muddied by this coupling. Adjusting the element length is further complicated if the distance to other metal objects changes when the wire length is changed. As the above warning Spiderbeam includes in the manual says, element length and placement is critical to proper operation.
• Element interaction: There are no traps or trap losses in this antenna but there are many more elements than in a 3-element tri-bander. More elements means more interactions. NEC2 and its cousins are very good but cumulative errors inevitably creep into any numerical model with lots of close-spaced wires. Building an antenna like this from a numerical model inevitably requires wire length adjustments during construction and tuning. Further, there are also small induced currents on the many non-resonant elements (those not active on a specific band) that complicate and slightly degrade gain and F/B performance.
• Match vs. gain performance: As we will see the commercial version of the Spiderbeam is designed for a good match (low SWR) across all 3 bands. This is at the expense of forward gain. That is true of any yagi. It can be corrected, at a price. I address this further along in the article.

Another issue with this antenna is its mechanical structure. Its 3-dimensional "closed" format makes it difficult to raise and install on many towers. You may have to use your imagination a bit to understand what I am about to say since I haven't drawn any pictures to illustrate the following points.

Unlike a conventional yagi this antenna must be lifted and installed as if it were a solid, 1-meter thick plate. This is because there are no openings in the structure; the entire space is filled with wires, ropes tying the wire ends, fibreglass tubes and ropes that tension the tubes to a central mast. That is, the antenna must be lifted over guys and other antennas and dropped down over the top of the mast.

In fact, the mast itself is an integrated part of the structure. This antenna does not play well with more than one antenna on the same rotated mast. For many hams this is acceptable. It is not acceptable to me.

If you have a guyed tower, other yagis on the rotator mast or wire antennas hanging from the tower you will have grief installing this antenna. Even if this is the only antenna on the mast today, if you decide to add another antenna in future it will have to placed below the Spiderbeam, and do so carefully to avoid tangling and damage during installation.

Performance

The fact that this antenna is a good broadband match to 50 Ω coax is a danger sign. That is, with respect to gain. If gain is the primary reason you choose a yagi for an antenna this should concern you. It certainly concerns me. Let's look at the performance charts produced from the EZNEC model. Keep in mind that the model has been verified against the manufacturer's construction guide so it should be a good reflection of reality.

On 20 meters the gain is a full -2 db below that of the reference 3-element yagi introduced in Part 1, never rising above 7 dbi. The F/B is, however, quite good across the band, even better than the reference yagi in many respects. Although I can't say that it is generally true, I have noticed from my various modelling activities that I can never get good gain from an antenna with inverted vee elements (which these effectively are) but I usually do get good F/B performance. This is on a boom that is 35% (2.6 meters) longer than the reference yagi.

In contrast the SWR bandwidth is definitely better. The good match comes with a cost in performance.

This is not an immaterial concern. Most hams will spend a lot of money in coax or tower height to gain another 2 db, or even less, of forward gain. To then throw it away at the antenna makes little sense to me.

On 15 and 10 meters the performance is a little better. While still not rising above 7 dbi gain on 15 meters it is ruler straight across the band at just a hair under 7 dbi. F/B on 15 is also very good, as is the broadband match. Again, the gain is -2 db worse than an equivalent reference 3-element yagi. However in this case the difference is not so bad since the reference yagi has a broad gain peak such that over much of the band the difference is no worse than -1.5 db.

The SWR bandwidth on 10 meters is narrower than on the other bands but still very good. Gain is also better, but peaks at 8.5 dbi very high in the band (29.5 MHz). The gain is still disappointing since there are 4 elements on 10 meters (2 equal-length directors), yet doesn't quite reach the gain performance of a reference 3-element yagi. F/B performance is, again, very good.

Using 1 mm wire as specified the typical copper wire I²R loss is -0.3 db. This is included in the modelled performance.


Designing for gain

I think it is worthwhile to see how far this style of antenna can be pushed in the pursuit of gain. I created a mono-band 20 meters model by eliminating all the other elements. It was then a simple matter of altering the ratio of reflector to director lengths to optimize the gain.

The simplest way of proceeding is to increase the length of the director in small steps. To minimize the impact of varying element interactions I did this by moving the director's endpoints (wires 6 and 7 above) outward on the 'Y' axis. Changing the distance between the ends of the director and the driven element would complicate matters since this would add a second variable to the tuning process. The boom length was fixed at 10 meters (distance between parasite apexes).

Once I found the optimum director length (maximum gain) I adjusted the reflector and driven element to compensate for the longer director and the absence of coupling with 15 and 10 meters elements.

The gain was increased by ~0.7 db at a centre frequency of 14.075 MHz. This includes copper wire loss of -0.7 db due to the lower radiation resistance. Heavier gauge wire can tame this loss. For example with 2 mm wire (12 AWG) the I²R loss is reduced to -0.3 db.

Gain and F/B remain very good up to perhaps 14.250 MHz, above which the F/B in particular rapidly degrades. Even when optimized in this way, and using 12 AWG wire, the gain is still -1.1 db worse than the reference 0.35λ 3-element yagi made from parallel aluminum tubing.

The ratio of reflector-to-director length in the gain-optimized antenna is 1.038. While this is quite narrow for a conventional yagi (±1.9%) it is less so in this case. To determine the actual reactance of the parasites I isolated each of them in the model and fed them directly to find their impedance curves. Their reactances are equal and opposite (±29 Ω) at 14.350 MHz. The resonant frequencies of each separate element are 14.100, 14.525 and 14.600 MHz for the reflector, driven element and director, respectively. From this the actual ratio of parasite resonant frequencies is ±1.8%. Compare this to the ±4% ratio of the 3-element reference yagi.

The frequency of maximum gain is (as shown above) 14.075 MHz, far from where the frequency where the reactances cross at 14.350 MHz. Either the use of bent parasites causes this difference from standard formulae for yagis or (far more likely) the nearness of the element ends to the driven element electrically lengthens those elements by ~2%. This can be a difficult antenna to design from scratch. I also know this from trying a similar approach several months ago for an unrelated antenna concept.

In the gain-optimized yagi the match is, as expected, more challenging. Feed point impedance drops to ~25 Ω. The antenna requires a 2:1 balun or a beta match. Either should work well since the radiation resistance changes slowly across the band.

It should be possible to do the same optimization on all 3 bands at once while continuing the use of a common feed and matching system. To do so would require paying attention to feed point impedance. It is a personal decision whether to undertake this change or to go with the manufacturer's design choice for broad bandwidth performance and simple match to 50 Ω coax.

An alternative approach for improved performance is a pseudo-Moxon design where the central section of the parasites is parallel to the driven element. I may try this in the future. If I do I'll write an article about it.

Conclusion

I am holding off on selecting from among the various type of small, high-bands yagis until the end of this series of posts. For now I will say that I am disappointed with the Spiderbeam's performance. The very good match and F/B performances are nice but, for me, do not compensate for disappointing gain.

As I showed it is certainly possible to change the antenna so that it has higher gain on all 3 bands. It would require tighter parasite tuning, 14 AWG wire and a 2:1 balun or beta match.

Even so the mechanical issues concern me. This is not an antenna that plays well with other antennas on the same mast or on a guyed tower, which is my situation for the near term. Your criteria may be different from mine. Many hams have bought and love this antenna. It's an especially popular choice for DXpeditions.

Choosing a High-bands Yagi (Part 3) - 3-element Tri-bander

Continuing on from Part 2 of my analysis of small high-bands yagis, it is time to evaluate 3-element tri-band yagis. In this category I include those antenna with 3 elements (reflector, driven and director) that are each active on 20, 15 and 10 meters. Traps for 10 and 15 meters are employed to achieve tri-band resonance. Examples include the TH-3, TA-33, A3S, among others. They typically have a short boom, usually between 3.5 and 4.5 meters.

As with 2-element tri-banders the boom length must be a compromise since it varies by a 2:1 ratio between 20 and 10 meters, as measured in wavelengths. At a typical boom length of 4.2 meters (~14') this is 0.2λ, 0.3λ and 0.4λ on 20, 15 and 10 meters, respectively. Tri-band yagis with booms longer than 4.5 meters typically have additional elements for one or both of 10 and 15 meters since otherwise the boom is too long for effective element coupling, and therefore reduced gain. Examples of these include the TH-6 (the antenna I have stored in my garage) and CL-36, among many others.

Before we delve into the design and evaluation it is worth a moment to review the parameters which effect 3-element (and larger) yagi performance:

• Boom length: Maximum achievable gain is a function of boom length - the longer the boom the greater the gain. There is likewise an optimum boom length (in wavelengths) for a yagi comprised of a chosen number of elements. For a 3-element yagi the optimum boom length is ~0.35λ, per the reference yagi introduced in Part 1. Maximum F/B is a more complex function of boom length, but shows a periodic behaviour with peaks at odd multiples of λ/4. For a 3-element yagi there is just the one peak at 0.25λ since the next odd multiple is too long a boom for 3 elements.
• Parasitic element resonance: Maximum gain and F/B are achieved when the resonant frequencies of the parasitic elements are close together -- but not too close -- with lengths of 0.49λ and 0.47λ for the reflector and director, respectively. However this is a poor choice since the gain, F/B and SWR bandwidths are narrowest in this case. Better choices are 0.502λ and 0.463λ, where we sacrifice ~0.5 db of maximum gain and, perhaps, ~5 db of F/B in return for good performance across all 3 bands. The use of traps will further narrow bandwidth performance so we want to start with a reasonably broadband design choice. These choices help to avoid sharp radiation resistance dips at maximum gain which make it difficult to achieve a broadband match.
• Element separation: It is assumed that for the 3-element yagi the separation between reflector and director elements is equal to the boom length; that is, they are at opposite ends of the boom. The only remaining separation variable is the position of the driven element. To avoid mechanical interference with the mast clamp the driven element is typically offset from the centre position towards the reflector. As the separation between driven and reflector elements is reduced the gain increases and the impedance falls, but only to a certain point. A small offset is optimal.

Notwithstanding the above points it is not my intent to design an "optimal" 3-element trap yagi. What I am doing is creating a benchmark to serve as a proxy for the better commercial products in the category. Since there is strong market demand to optimize SWR (match) performance it is to be expected that products may have an incentive to sacrifice more gain and F/B performance than I'd prefer.

Unfortunately there is no certain way to judge yagi products for their performance. Published specs are incomplete and graphs too often look a little too perfect to be accepted as presented. This is the case even when the specs are mostly true. We can use the laws of physics (electromagnetism) to explore what is theoretically possible (and probable), knowing that no real product can exceed the performance of an ideal antenna. That is, we can use physics as a sanity test. That is one of my purposes for modelling a variety of small yagi antennas. The hope is that the best small tri-band yagis approach the ideal.

Design Process

The design process for a 3-element tri-bander is straight-forward, though more complex than for the 2-element version. Gain and F/B in the 2-element yagi is solely determined by the boom length (for a fixed style of element design). With 3 elements it is necessary to coordinate the relative resonance of the reflector and director elements to achieve a desired gain and F/B profile over the band of interest, as was described above.

Once the desired gain and F/B profiles are selected per the reflector and director tuning we can think about the match. This is done by adjusting the driven element and matching network (e.g. beta or gamma match). This matching process does not affect gain and F/B, provided the driven element does not get excessively short and the matching network is low loss.

Keep in mind that a lot of the work has already been done for us. Starting with the venerable work of the NBS many years ago, extensive theoretical modelling by W2PV around 1980, and more recent work by many others utilizing state-of-the-art software and high-speed computers. I am leaning on that work when I select design parameters. There is no need for me, or anyone, to design a yagi from scratch. It would be a waste of time. There are no undiscovered secrets left to be ferreted out by aspiring mavericks.

With all the forgoing in mind here is how I went about the design:

• Choose the resonant frequencies for the reflector and director, in relation to a centre frequency. You can either look up the performance figures or experiment with EZNEC or a similar tool. If you experiment always tune both reflector and director so that they maintain the same ratio with respect to the centre frequency. This will simplify matching. Note that as in the reference yagi it is not possible in a 3-element yagi to get the maximum gain and F/B anywhere near the same frequency, so choose the centre frequency with care.
• Develop two antenna models: one for the yagi and one for element tuning. Once an element is inserted into the yagi it is very difficult to tune it due to mutual coupling. It is better to tune it in a separate model and copy it to the yagi model. Do the element model in free space.
• For the trap elements we are using it is necessary to tune the reflector and director on all 3 bands. Calculate the target resonant frequencies on each band and get the element resonance as close to those frequencies as possible. Resonance is the frequency where the reactance is zero, not where the SWR is minimum. Don't fuss over it too since there are other factors not included in the model that affect element tuning: tubing taper schedule; element-to-boom clamps; trap dimension; coupling to other antennas, etc.
• With all 3 elements in the model the performance curves can be shifted up or down in frequency by changing resonance of both parasitic elements by the same amount.
• Alter the placement of the driven element and resonance of the parasitic elements in small increments to adjust performance (gain and F/B). Remember to do all resonance tuning in the element model and copy its parameters to the yagi model. You may want separate models for the director and reflector (as I did) to speed the design process.
• Adjust the driven element in the yagi model to place the SWR curve consistent with your design objective. Add a beta match or similar network if the feed point impedance is too low for a direct match to 50 Ω coax -- this is mandatory in the antenna we are designing. Tuning of the driven element and match has little to no affect on gain and F/B performance, which is why it is done last.

Of course I say you can do all this work but few will and will even want to do so. Since this is my project I will cut to the chase and present the antenna that I designed by this process. As with any yagi antenna it is a compromise, but one that I believe reflects the best computer-designed small tri-band yagis on the market. I will only present the performance figures since the physical dimensions and trap designs are unlikely to be an exact reflection of any commercial product. For example, my model has no boom, and that has an effect on element length. Further, the trap (load) model has no physical dimension, and although the trap performance might be similar the design is almost certainly different from all commercial products.

I chose the following centre frequencies to optimize gain and F/B for CW and lower SSB segment of each band. These frequencies require careful selection since the relationship of optimum frequency for gain and F/B are boom length dependent, and are therefore different on all 3 bands. They are derived from the models developed by W2PV.

• 20 meters: 14.000 MHz
• 15 meters: 21.200 MHz
• 10 meters: 28.600 MHz

Other design parameters:

• Boom length: 4.2 meters: 0.2λ on 20 meters, 0.3λ on 15 meters and 0.4λ on 10 meters
• Driven element spacing: 1.9 meters from the reflector, which provides enough space at boom centre for a boom-to-mast clamp but does not result in excessive torque due to wind load asymmetry
• Reflector element resonance: 13.440, 20.350, 27.450 MHz (0.960 of centre frequency, or 0.502λ length equivalent)
• Director element resonance:  14.560, 22.050, 29.740 MHz (1.040 of centre frequency, or 0.463λ length equivalent)

TH-3MK4 (from online manual)

The parasitic element lengths can be made similar on all bands despite the different boom lengths on each band as measured in wavelengths. They could be further optimized for the respective boom lengths on each band but since the potential improvements are minor I am opting to keep it simple.

The final design looks a lot like the Hy-Gain TH-3MK4, the schematic of which is shown here. Of course other 3-element tri-band trap yagis look similar and, probably, have similar performance. My choice of the TH-3 as a model is not a recommendation of this antenna. It's just that I know Hy-Gain best and their traps seem to measure well. I have never used a TH-3.

Avoiding Maximum Gain

Before getting into the modelling results for the "optimum" design it is worthwhile to explore what it means to design for maximum gain, and why this is a bad idea. Just for the fun of it I ran the model with identical elements, all being copies of the driven element. This is a symmetrical yagi that will exhibit 0 db of F/B but has bidirectional gain.

The antenna resonated at 14.140 MHz. At right is the free-space elevation pattern of the antenna. Notice that the gain is quite poor, worse than a dipole, but is reasonably directive. Where did the power go?

At resonance the impedance is 1.9 + j0 Ω. This is exceptionally low. The radiation resistance rises steeply on either side of resonance, so this is a sharp dip. Not only does this make it difficult to design an effective, low-loss matching network the low R value is an invitation to other losses. In particular the traps (modelled at 0.3 Ω ESR, the same as in Part 2) contribute -3.8 db of loss. Even with large aluminum tubing for the elements we get -0.3 db of loss. If there were no losses the bidirectional (broadside) gain would be 5.1 dbi.

There are similar losses on 15 meters, where the traps are most active. On 10 meters the trap loss is small, however the aluminum I²R losses are still present.

This demonstrates why a yagi with 3 or more elements should never be designed for maximum gain. The gain bandwidth is narrow and the target gain cannot be achieved in any case due to losses caused by the low radiation resistance. This is true even in an antenna without traps or other loads.

Trouble with traps

In the interests of sharing what I learned I will confess that the process I came up with above to tune the parasitic trap element did not work well. While I did suspect the possibility of problems, especially with director tuning, I was unprepared for the magnitude of the resulting errors. In the case of 10 meters the performance was mediocre and the performance curves were shifted 1 MHz higher. The same happened on 15 meters, although the curves shifted less than 200 kHz higher. On 20 meters the frequencies came out right but the performance was poorer than expected.

What happened? I know the design process works on yagis comprised of unloaded elements, and in fact got a textbook result with the reference yagi I developed in Part 1. To understand the source of the problem it is useful to make a brief detour to look at how yagis work.

The far-field pattern of a yagi is the superposition of radiation from all of the antenna elements (plus ground reflections). When these are in phase in a specific direction they add, resulting in gain. The amount of gain depends on how close their phases are, and their magnitudes as well. When they are exactly out of phase (180° difference) and the magnitudes are equal there is no net radiation in that direction.

The phase and magnitude of the radiation from a parasitic element depends on:

• Separation: It takes time for the field from the driven element to propagate to the parasite, a time that is proportional to distance. The phase shift is proportional to the separation measured in wavelengths of the radiation. For example, for 0.2λ separation the phase differential is 72°. That is, by the time the field reaches the parasite the phase angle at the driven element has advanced 72°. In all other directions the phase relationship differs, and therefore the field strength is dependent on the elevation and azimuth angles.
• Reactance: In general, the closer the parasite resonant frequency (where reactance is 0 Ω) is to the driven element the greater the magnitude of the induced current. When the parasite is tuned to another frequency the reactance causes the magnitude of the induced current to fall and, importantly, the phase of the induced current will be shifted. This determines the phase and magnitude of the radiation from the parasite.

The dynamics are actually more complex since it is a recursive process. Radiation from the parasites induces current in all the other elements, including the driven element, which then combine with the currents on those elements and are again radiated. This is a continuous process while the source is active and energy from the induced fields is available (not yet launched into space or dissipated by I²R losses). EZNEC shows the data for the steady-state current magnitude and phase for every wire segment in the model.

Another important facet of the dynamics is that the mutual coupling lowers system impedance and thus raises the total current in the system for a given source power. Gain is therefore not only a function of superposition but also the system impedance. (EZNEC normalizes the current to 1 A at the source by adjusting the source power unless you tell it to keep the power constant instead.)

When we specify a parasitic element by length relative to a resonant λ/2 element (or the equivalent resonant frequency) it is merely a calculation shortcut. What matters is the reactance. In a loaded element, whether done with coils, capacitance hats or traps, that shortcut is invalid. That's where I went wrong on the first try. Once again it's those traps making my task more difficult.

Because of the complex contribution to phase by the traps it is not possible to tune the parasitic elements by frequency or length. I worked around this by modelling a tube, without traps, to the target director and reflector resonant frequencies on each band (as shown above). I then read off the reactance at the centre frequency -- the X in Z = R + jX.

• 20 meters: Reflector [+41 Ω]; Director [-37 Ω]
• 15 meters: Reflector [+38 Ω]; Director [-35 Ω]
• 10 meters: Reflector [+36 Ω]; Director [-33 Ω]

I retuned the models of the reflector and director, adjusting them so that their impedances showed these reactances at the centre frequencies of all 3 bands. With some trepidation I copied these elements over to the yagi model and observed the gain and F/B across the bands. Lucky for me this worked beautifully.

Small frequency shifts were still required on 2 bands but otherwise the gain and F/B performance were per the textbook. I then proceeded to set the trap ESR to 0.3 Ω (just as in the 2-element yagi) and match the system to 50 Ω.

Performance

To avoid boring you with the processdetails, I will directly proceed to the results. These are visible in the collection of charts on the right.

I used the same chart structure as for the 2-element antenna to make comparison easier. I will do a more direct comparison at the end of this series (Part 5?) if you don't want to bother flipping back and forth as you read.

All measurements are made in free space. All of these antennas, including the 2-element version will respond to height above real ground in much the same way so this approach avoids confusing height for raw performance. We will come back to antenna height in a later article in this series.

My observations on the performance models:

• Gain and F/B bandwidth are superior to the 2-element tri-bander model. Although the maximum gain on 15 and 20 meters is only modestly better, it is available over more of each band.
• Gain on 10 meters approximates that of a full-size 3-element yagi, reaching a maximum of more than 9 dbi.
• 15 meters is, again, the worst performer. Bandwidth is narrow, both for performance and SWR (not shown). At the top end of the band the yagi reverses direction, as indicated by negative F/B. Peak F/B is excellent since the boom is close to an odd multiple of λ/4 (0.3λ).
• Loss due to trap ESR (equivalent series resistance) is, as always, highest around the frequency of maximum gain. In the case of 3-element yagis this frequency is high in the band, whereas it is low in the band for 2-element yagis. This is a general rule for 2 and 3-element yagis, and is unrelated to the use of traps.

You may have noticed that I did not plot SWR. Coming up with a beta match that would give a low SWR on all 3 bands became tedious and I gave up after working on it for a time. Surely that ideal beta match does exist -- most commercial products have done so -- but there was no point in discovering it in this model since I am not planning on building this antenna and it has no impact on gain and F/B performance.

I got close enough to the ideal by playing with beta match parameters (stub impedance and length, and driven element length) to discover the implication for match bandwidth. It is good on 10 and 20 but not good on 15 meters. Once again it is that middle band that causes problems, just as it did on the 2-element tri-bander and even the trap dipole. I do know that Hy-Gain uses different 15 meter traps on the driven and parasitic elements so they presumably have learned something that I have not.

Trap ESR Loss

That last point brings us to the impact of traps on performance. I did the same sensitivity analysis as for the 2-element tri-band yagi. You can go back to Part 2 to see what I had to say on the topic. Here I will simply present the charts that show the impact of trap ESR.

As a reminder, I used 0.3 Ω as the traps ESR for the above performance analysis since that appears to be in the range of the best commercial traps in tri-band yagis. An ESR of 0 Ω represents a lossless trap, which is useful as a theoretical benchmark but is impossible to achieve in the real world.

Loss is highest where gain is maximum since that is typically where the radiation resistance of the antenna is lowest. On 20 meters this is the high end of the band and on 10 and 15 meters it occurs mid-band. On 15 meters the loss is especially high since the radiation resistance is below 10 Ω over a large section of the band.

Apart from 15 meters the impact of trap ESR is modest. Traps are a great convenience in designing a compact tri-band yagi with good performance, but this is a cost that must be paid.

Note: The charts say the reflector tuning is 1.05 Fc, but it is 1.04 Fc as stated earlier in the design process. Or (more correctly) tuning is per the exact reactance values stated above.

Next up...

In Part 4 I will evaluate the Spiderbeam category of multi-band yagi. This is a promising antenna since it has no traps or aluminum tubing. However, as we will see, there are still compromises and trade-offs.

Choosing a High-bands Yagi (Part 2) -- 2-element Tri-bander

Having established a reference yagi in the previous article I now want to explore the first of several categories of small-sized yagis: 2-element tri-bander.

There are any number of commercial products that fall into this category. Perhaps one of the best known is the Hy-Gain TH-2MK3. I will use this antenna as a design template. This as not a product endorsement. As we will see all antennas of this type are difficult to assess with software models, or at least without knowing all aspects of the technical specifications. The traps are the major unknown.

There are several concerns I had with these antennas and were a particular focus on my modelling effort:

• Boom length: It is not possible to choose an optimum boom length (element separation) for works for all 3 bands of interest. We must learn how severe a reduction in antenna performance results from a compromise length.
• Trap efficiency: There are 8 traps in this antenna, so even small losses can add up. Their efficiency is frequency dependent and highly sensitive to electrical and physical parameters. The data for the traps is typically not publicly disclosed by manufacturers, so it is necessary to make a few intelligent guesses.
• Match: The uncorrected feed point impedance is different on each band since this parameter is sensitive to boom length (as measured in wavelengths).
• Bandwidth: These antennas can exhibit a narrow bandwidth, especially when adjusted for optimum gain. The inclusion of traps exacerbates the problem.

The above list is derived from the issues I enumerated in Part 1 since, in my estimation, they are the greatest challenges in this class of small yagis.

Traps

The first step is to design the traps for inclusion in the EZNEC model. This is an interesting challenge since there are an infinite number of L (inductance) and C (capacitance) parallel circuits that resonate at any given frequency. This is constrained to a smaller range of values by physical design, and then constrained further by impacts on efficiency and reactance on lower-frequency bands.

I modelled a dipole in free space with 4 traps (2 for 10 meters and 2 for 15 meters). As a starting point I made the dipole of similar length to the elements in the TH2, then did the same for trap placement.

Above is the current plot taken at 21.1 MHz. You can see the current "glitches" at the traps. The 10 meters traps act as inductive reactances at 15 meters, and the 15 meters traps "leak" some current since the trap is resonant above the band. The 15 meters traps have noticable loss, helping to lower the gain to 1.8 dbi, or about 0.35 db lower than a dipole.

Which brings me to the trap calculations. This is outside my area of expertise so I had to turn to other sources. One excellent resource is by W8JI (whose material I've linked to before). It was based on his measurements and theory exposition that I decided to normalize on the Hy-Gain tri-bander designs. I placed the trap resonant frequencies outside of the bands of interest, and specifically chose the frequencies that he measured for the Hy-Gain traps:

• 10 meters: 29.7 MHz
• 15 meters: 22.3 MHz

Although this worked out well in the model, I did not see the increase in trap loss near those frequencies to which he alludes. Where I did see increased losses...well, I'll come to that further along.

In a parallel resonant LC circuit the values of reactance are equal (and opposite). But what value of reactance? If we ignore physical constraints on trap design it is easy enough to choose from a wide range of values. One difference is the amount of inductive reactance the traps exhibit at lower frequencies. This affects the length of the element outside the trap. For example, with a higher value of inductive reactance contributed by the 10 meters trap the rest of the element must be shortened to compensate. Another difference can be loss: the higher the inductance the larger the ESR, and therefore the loss (all other things being equal).

Making the element too short has an effect on element gain (gain versus a dipole declines as the element gets shorter) and it can squeeze the traps together more than can be accommodated in a physical design.

Most trap calculators I've run across on the internet typically use a reactance target of 200 Ω. From my reading of related material this value correlates with achieving inductor Q of anywhere from 100 to 500 and ESR (equivalent series resistance) of less than 1 Ω. The ESR plays a key role in trap loss, so we want it to be as low as possible while not requiring an impractical coil design.

EZNEC supports loads that are configured as traps and will calculate the loss in the traps. What it will not do is tell you the ESR. You must supply that value from calculation or measurement. Not being able to do either very well in this theoretical exercise I tested what I believed would be the approximate ESR for Hy-Gain traps, which I suspect are in the range of 0.3 to 0.5 Ω. As we'll see even within this small range the results can vary quite a lot. Traps made from coax or small coils and capacitors have higher ESR.

All loads in EZNEC are distributed/centred on the segment where it is placed. Real traps have a finite width and height. In the case of Hy-Gain traps (and many others) the exterior of the trap is continuous with the element, with the outside being part of the radiator and the inside being one plate of the trap capacitor. The overall result should otherwise be similar in a realized antenna.

Boom Length

This one must be a compromise. A typical and preferred boom length for a 2-element yagi with a reflector centres on 0.14λ (3 meters long on 20 meters). This is the length I normalized on for my series on 2-element wire yagis for 40 meters. But if you select this boom length for 20 meters then the boom length is 0.21λ or 0.28λ on 15 and 10 meters, respectively. This can be a problem, especially on 10. Conversely, if the boom is optimized for 10 meters, the boom length is 0.07λ or 0.11λ on 20 and 15 meters, respectively, which can cause problems on 20 meters.

When the boom is too long the mutual coupling can be too small to achieve optimum gain. For a short boom the gain can be achieved but at the price of F/B and, more seriously, low feed point impedance. It should be no surprise that commercial products tend to choose boom lengths around 2 meters, which is midway between those extremes. For example the boom of a TH-2MK3 is 1.8 meters (6'). This is near optimum for 15 meters but workable for the other bands. The question to be answered is how severe a compromise is involved? This affects not only gain and F/B (the key performance measures) but also matching; the feed impedance (and SWR bandwidth) will vary greatly across the 3 bands.

Design Process

Once the trap dipole is adjusted to the preferred resonance on all 3 bands it is a simple matter to duplicate the element and space them apart by the chosen boom length. Remember the rule: to construct a 2-element yagi with a reflector element you make the parasitic element the same length as the original, resonant element. When I did this for the trap dipole I had a tri-band yagi that needed only small adjustments to optimize gain and F/B at the design frequencies. All of that adjustment is made to the parasitic. The driven element is only modified, later, to achieve a 50 Ω feed point impedance.

As with the trap dipole the yagi was designed in free space. Except in this case it is a good proxy for a yagi above real ground, provided it is not too close to ground. For example, the reference 3-element yagi in Part 1 maintains its gain, F/B and SWR bandwidth to heights as low as 5 meters (0.25λ). What's different is the far field pattern, in particular the performance at low radiation angles.

In the EZNEC model view notice how close together the traps must be. The inductive reactance of the 10 meters (inner) trap shortens the required length on 15 meters. With the inductive reactance contributed by the 15 meters (outer) trap only a little more tubing is needed to resonate on 20 meters. To see how this affects the current distribution on the element notice how when excited at 21.1 MHz the current jumps in the areas between and beyond the traps. On 20 meters (not shown) the current distribution curve is closer to normal, just compressed a bit between the 10 meters trap and the element end. As it turned out 15 meters was the most difficult band to adjust in the model.

The following construction diagram of the TH-2MK3 is almost identical to the yagi model, demonstrating that trap placement is no mere modelling artifact. I omitted the metal boom in the EZNEC model since other than change the resonance of the reflector element a small amount it otherwise has no performance impact I opted for simplicity. The driven element does not contact the boom.

At a separation of 1.8 meters it only takes a small change in boom length to cause significant changes in the antenna's behaviour. While the shifts in resonance are easy to correct the same is not true of the antenna's impedance profile, particularly on 20 meters where the boom length is shortest in terms of wavelength (0.9λ).

With both elements in place the next step in the design process is to adjust the centre section of tubing to achieve the gain and F/B curves for the band segment of interest on 10 meters. I followed my usual inclination of optimizing the antenna to the CW segments on all bands but ensured that there is still good performance at least up through the lower part of the SSB band segments. This proved difficult since on 20 and 15 meters the bandwidth can be narrow, whether measured by SWR, gain or F/B.

After tuning the reflector on 10 meters I did the same for the other bands, first 15 then 20. Then I did it all again since adjusting the outer parts of the element affect the higher bands a small amount.

I added a shorted transmission line to the feed point of the driven element to model the beta match on the TH2. Although its impedance is not specified it appears identical to that of the TH6. So I took a ruler out to the garage where the TH6 is stored, measured the dimensions and calculated its impedance: a little over 300 Ω. With that in the model I adjusted the driven element dimensions for best SWR in the selected segments of all 3 bands. This is, again, an iterative process, including adjustments to the beta match since my model does is not identical to that of the TH2.

Performance

I'll say up front that I was pleasantly surprised by how well this antenna performed in the model. I had to review the theory to understand what I'd missed. The main thing is that excellent gain and F/B can be achieved over a wide range of boom lengths, which allows the antenna to work well on 20, 15 and 10.

As alluded to earlier the critical items are trap ESR and low feed point impedance on 15 and 20. The first limits the achievable gain and the second limits the SWR bandwidth. On 10 meters neither item is a concern so the antenna does quite well.

Before I dwell on these concerns I will summarize the antenna performance in a few charts. For this analysis I set the trap ESR to 0.3 Ω at the resonant frequency of the trap. EZNEC does the rest.

The gain and F/B curves are typical of 2-element yagis with their respective boom lengths as measured in wavelengths. The theoretical maximum gain is a little over 7 dbi, to which we get close on 10 and 20 meters. Since in these antennas the frequency of maximum F/B is higher than that of maximum gain it helps to place the maximum gain at the low end of the desired range, which sacrifices F/B at these frequencies. The presence of the traps does not appreciably affect the performance curves, except that the trap loss limits achievable gain.

Look at the comparative gain and F/B curves for the 20 meters 3-element reference antenna (from Part 1) and the trap tri-bander on 20. The gain of the full-sized 3-element yagi is pretty flat across the band. While the gains are close together (< 2 db) where the 2-element does best they are far apart higher in the band. Expect similar results for 15 and 10 when compared to full-sized 3-element yagis. In contrast the F/B curves are not very different, although the F/B bandwith and maximum is better for the 3-element yagi.

SWR is excellent only on 10 meters. On 20 and 15 meters the usable bandwidth is narrow. The beta match can only do so much for us. This is especially true on 20 meters where the boom length is only 0.9λ, resulting in a low feed point impedance where gain is maximum with large percentage swings in radiation resistance away from that frequency. I could have fought the SWR lower on 20 meters but it would improve SWR bandwidth only a small amount. Users of this category of antenna must accept that. Use of the rig's ATU can help extend the usable bandwidth (gain and F/B are decent across all bands), but don't expect miracles at the high ends of 15 and 20.

About those traps...

Hy-Gain, Cushcraft, Moseley... the traps of all tri-band manufacturers look similar, and they are similarly placed on the elements, whether 2 or 3 element yagis. They are not the same. But how different? I can't say. In the trap article by W8JI that I linked to above there are some indications but no hard figures on the performance impact. Specifically the loss.

In the above evaluation I used an ESR of 0.3 Ω since, so far as I can tell, it is a value that is likely not to be too far from the truth. I used that value for all the traps but that isn't true. Expect different values for different traps -- even for the same band on the same antenna -- and especially across manufacturers.

This leads me to finally make a brief exploration of how trap ESR can impact 2-element tri-bander performance. I will focus on gain since it is overall antenna efficiency that is paramount. SWR is also affected by higher ESR values but (as is typical with all forms of loss) it improves SWR performance.

Perfect, loss-less traps (a useful fantasy!) are those with an ESR of 0 Ω. It tells us what can be achieved in an ideal tri-bander. We must aim a little lower. The charts show the gains at 0, 0.5 and 1.0 Ω. The value of 0.3 Ω I used in the performance evaluation is, I believe, typical of the best traps. A value of 0.5 Ω is less than ideal and 1.0 Ω is a poor trap. ESR is even higher in the worst traps, such as in many traps made from coaxial cable.

There are a few interesting things we can learn from the calculated effects of ESR on antenna efficiency (for which gain is a proxy).

• Loss is highest near the frequency of maximum gain. This is because radiation resistance is lowest at that frequency. This is I²R loss since, for a given source power, the current (I) increases as the radiation resistance decreases. Radiation resistance tends to decline as the element spacing is reduced, so this can be managed by increasing boom length. For the same reason a trap dipole has low loss even with poor quality traps since the radiation resistance is much higher than in a yagi.
• The gain of a 2-element yagi can exceed 7 dbi, but this cannot be achieved with traps. Although I don`t address the topic here, linear loading does not allow us to escape from such losses. It`s just a different manifestation of loss. There is no free lunch.
• Poor quality traps can reduce gain by several db. But even then the loss is more moderate the farther you operate from the frequency of maximum gain.
• Loss increases as antenna current flows through more traps. This is why the losses are smaller on 10 meters.
• Trap loss can shift the frequency of maximum gain. This is an artifact caused by high trap loss. It is just that the gain near the "true" maximum gain frequency is greatly reduced by trap loss.
• Managing performance on 15 meters is especially challenging. The closeness of the traps to each other has an odd effect on antenna current. This may be a necessary sacrifice in this category of antenna.

Conclusion

Performance of 2-element tri-band yagis is moderately good, but short booms and traps limit their performance. In the ideal case they compare favourably to the reference 3-element full-size yagi. Alas, we do not live in an ideal world.

In the next article I will explore 3-element short-boom yagis. Hopefully it will be shorter since the material on traps will not need to be repeated.