Performance of the 80 Meter 3-element Vertical Yagi

The 3-element, 4-direction vertical yagi I recently completed is not a perfect antenna although it does perform very well. It has its pros and cons. I learned a great deal designing and building it, which was one of my main objectives apart from putting out a competitive signal on 80 meters. The antenna is a variation of the K3LR array described in ON4UN's Low Band DX'ing book.

No antenna stands on its own merits; every antenna must be compared to alternatives. For this discussion of the yagi's performance I will use the big gun antenna standard for 80 meters, the 4-square.

This is the sensible baseline since it is important how I do relative to other serious contesters and DXers. It makes little sense to compare the yagi to an inverted vee -- of course it's better but the comparison is of little value.

This article is not a mystery novel so I will put the answer right up front: the 4-square is superior on the majority of metrics. That said the details of the comparison can be subtle and enlightening for those with a passion for antennas. A truthful comparison helps direct my future plan for 80 meter antennas. That will be briefly addressed towards the end of this article.

Let's start with the basics before delving into details.

First up is a fundamental of physics: conservation of energy. For antennas of equal efficiency a corollary is as follows:

Gain = Directionality

To achieve gain in one direction requires taking energy from other directions. Conservation of energy informs us that to achieve gain the antenna must be directive, and vice versa. The two are inextricably linked. The 4-square's better directionality largely explains its gain advantage over the 3-element yagi.

However it is not quite that simple. Dropping a secondary lobe from -10 db to -20 db (assuming for the present argument there is only one lobe other than the main lobe) the main lobe energy increases from 90% to 99% of the energy. This is an almost negligible gain improvement of 0.4 db. Reception improves but not transmission effectiveness.

Further gain improvement requires narrowing the beam width of the main lobe. For a non-rotatable antenna like a 4-square or wire yagi too narrow a beam width can be detrimental since there will compass points where gain is poor.

Although the 4-square is more directive than the yagi the gain improvement is not substantial. The better gain of the 4-square mostly comes from other differences between the two antenna types. Both have sufficiently modest gain/directionality that 4 direction switching covers 360°.

With that fundamental observation made let's look at how the antennas differ. There are several factors:

• Element spacing: On a side the 4-square element spacing is 0.25λ, and the diagonal spacing is 0.35λ. For the yagi the element spacing is 0.125λ. The closer spacing of the yagi increases the mutual coupling. This is required in a yagi but not is a 4-square.
• Element shape: It is typical to use straight elements in a 4-square although that isn't necessary. The yagi has a straight driven element and sloped T-top loaded parasitic wire elements. Again, that is a choice not a requirement. Element shape and diameter effects both antennas and we will have to normalize them to make a fair comparison.
• Forcing: Yagis work by mutual coupling alone. The 4-square uses phasing lines and combiners to engineer phase and amplitude of antenna currents. However mutual coupling exists in a 4-square and is a significant factor in its design and engineering.
• Ground dependency: The antennas behave differently for the same radial system (near field). Distant ground (far field) effects are the same for both.

These are the major electrical factors. There are also other factors, such as cost, that must also be considered.

Notes on modelling

All the software modelling is done with EZNEC. Medium ground (0.005, 13) is used throughout even though the ground conductivity in my rural locale is better than that. A fair comparison depend on a standard environment.

MININEC ground is used rather than "real" ground so that the radial system can be easily modelled as a resistance load at the base of each element. MININEC assumes a perfect ground with respect to the near field. The resistance accurately represents the equivalent series resistance (ESR) of the radial system and ground beneath. But you have to know the ESR of your radial system. The model departs from reality for a small number of radials since they affect the antenna resonance. These effects must be compensated for during antenna construction and testing.

There is loss in more than just the ground. Wire elements have non-negligible loss whereas tower and tubing vertical elements have negligible loss. Coil, capacitors, phasing lines and hybrid combiners each contribute loss. In particular the 4th port of the hybrid combiner used in most 4-square antennas goes to a 50 Ω dump load, which can be as lower gain by as much as -0.5 db at the band edges, though -0.1 to -0.2 db is more typically .

Since this is comparable to the approximate -0.15 to -0.2 db resistance loss in the wire yagis elements I will treat them as equal, and leave them out of the antenna comparison. The 4-square model is adapted from one packaged with EZNEC uses lossless phasing lines and no combiner or dump load.

The azimuth pattern comparison is typical. The difference in practice has many factors, as listed above. For my current radial system the 2 db difference of the inner plot is a fair representation. In other configurations the difference can be better or worse and in the ideal can approach equality. We'll come to that later in the article.

The elevation patterns are similar for both antennas. This is primarily determined by ground quality and topography outside of the antenna's local environs.

Turn a yagi on its side

Verticals arrays -- yagis and 4-squares -- have relatively poor side lobes in comparison to horizontal arrays. Many of you know why that is but let's review it anyway.

A dipole has low radiation off its ends. An array made of dipole elements is the same since adding nothing to nothing equals nothing. Therefore the typical horizontal yagi has deep side nulls. In free space the elevation pattern has quite a lot of radiation directly up and down. For a typical 3-element yagi in free space the blue plot is the elevation pattern and black is the azimuth pattern.

Over ground the way to remove the high angle radiation is to place the yagi at a height that is an odd multiple of λ/2 so that the ground reflection is out of phase with the direct wave resulting in cancellation. At intermediate heights there can be substantial high angle radiation, and that is rarely desirable.

Rotate the boom 90° and the elevation and azimuth patterns are swapped. That is in essence what you have with a vertical array: lots of radiation off the sides and very little at high elevation angles. In a conventional vertical yagi like my 3-element 80 meter antenna radiation to the sides is worse than shown in the adjacent plot.

For a driven array such as the 4-square it is possible to reduce the side lobes. Thus a 4-square can have better directionality than a 3-element yagi. Of course the 4-square has one extra element, which may seem an unfair comparison until you consider that the two antennas are of similar size.

Element spacing

Comparing element spacing of the two antennas can be confusing since although they occupy a similar area the yagi has a fifth element in the centre -- the driven element -- and two of the elements are inactive. Further, because two elements are inactive the 0.35λ spacing between adjacent parasitic elements is irrelevant. The element spacing is 0.125λ for the yagi and 0.25λ for the 4-square, a ratio of 2.

The significance is that the mutual coupling between yagi elements is higher than the 4-square. The elements can be more widely spaced to equalize the antenna footprints. This would increase the boom length to 0.35λ (0.175λ element spacing), a length that is near optimum for a 3-element yagi. That does indeed improve the yagi's performance, as we'll see.

In addition to achievable gain the increased spacing modestly improves F/B. Of perhaps greater importance is that the mutual coupling is reduced which increases radiation resistance, and that lowers antenna currents and I²R ground loss. Driven at 1000 watts the typical 4-square element current is ~2.5 A. Currents in the yagi elements cover a wide range, from as low as 1.5 A to as high as 9 A, with more typical values between 2 A and 7 A.

The gain improvement of 0.175λ yagi element spacing is ~0.6 db (perfect ground), which is marginally significant. Reduction in ground loss results in greater efficiency for the same radial system. Gain improvement is greater with a poor radial system and less with a better one.

Element shape

The sloping T-top wire parasitic elements are convenient since it uses the driven element as the support structure. It comes at a performance cost since the element shape is not optimal. There are two problems:

• Radiation resistance: The acute angle on the lower side of the T causes field cancellation with the monopole part of the element. Field cancellation lowers radiation resistance and this increases loss in the radial system and to a lesser amount in the element wire.
• F/S: There is a horizontal component to the azimuth pattern due to the T which lowers overall directionality by increasing radiation to the sides and rear.

The lower acute angle (close to 45°) requires NEC4 for accurate modelling. With the more commonly used NEC2 there is a significant discrepancy so the wire elements dimensions must be determined in the field. NEC4 isn't perfect but you will get close.

Modelling with EZNEC predicts an approximate 5 Ω reduction of radiation resistance from 31 Ω to 21.5 Ω. compared to a straight wire element. With my analyzer I measured 25 Ω including an estimated ground loss no worse than 5 Ω. For a 5 Ω radial system the loss is 16% versus 14% with straight wire elements. Although that's small the loss multiplies for poorer radial systems and in a yagi where the radiation resistance is lower and the current higher.

A comparison of straight wire elements versus the T-top wire elements was discussed in a previous article. Look there for the relevant charts since I won't reproduce them here. You will see that directionality and gain are better with straight elements, especially directionality . Unfortunately straight elements are not easy to make from wire due to the need for suitable supports. A coil loaded shorter straight element is feasible except that efficiency is far worse. If you go to the trouble of rigid parasitic elements I believe it is more sensible to build a 4-square rather than a yagi.

Forcing

Yagis rely on mutual coupling alone to achieve current amplitude and phase for desired behaviour. Current forcing is a feature of driven arrays. Since there is substantial mutual coupling in a 4-square it is not a purely driven array; the elements would have to be much farther apart for that.

Forcing is simple in its basic concept. The generator always sees a single impedance. By tying all the elements to the feed point the amplitude and phase is uniquely determined. Networks between the feed point and elements set the amplitude and phase to achieve the desired behaviour.

It is quite complicated since you want a 50 Ω load for the generator and accurate power splitting and phase across 4 elements with network that must sustain complex loads (high voltage and current) at high power and with direction switching. Elements must be made as identical as possible. Not many hams design and build their own 4-square control systems!

The EZNEC model used in this article is adapted from one provided by W7EL with the software. It uses fixed phase lossless transmission lines. This is impractical for real antennas due to the direction switching challenges and the frequency sensitivity of the phasing lines. Hybrid combiners are more suitable.

More than you could ever want to know about 4-square design and hybrid combiners can be found in ON4UN's Low Band DX'ing book. For the present discussion I will only mention a couple things. First, the phasing lines experience high SWR and have attendant losses, although those are low with good quality coax at 3.5 MHz.

Second, hybrid combiners are not lossless since frequency dependent imbalances among the 4 elements present at a 50 Ω port where a dummy load dissipates the power due to the imbalance. A failure in one element or icing can cause a large increase in the the dump power. Monitoring or protective circuitry is important.

Modern 4-square controllers usually offer an omni-directional mode in addition to the 4 directions, just like I built with my 3-element yagi.

Ground dependency

Ground ESR in series with the antenna impedance is the most important factor affecting the yagi in comparison to the 4-square. For the same radial system the ground loss for the yagi is higher, and it can be substantially higher. That is due to the low radiation resistance due to the aforementioned factors: element shape and mutual coupling. The better the radial system the closer the yagi's performance to that of a 4-square.

The yagi should have a radial system ESR of less than 5 Ω and lower is highly desirable. In my antenna I have twice the number of radials on the driven element as the parasitic elements since currents are highest in that element. Current in the yagi elements can be more than 3 times higher than in the 4-square. If you are limited in how many radials you can put down go with the 4-square.

Measuring the ESR of a radial system is difficult. My estimate for those in the yagi is based on the trend line of element self-impedance as radials are added. This is a common technique and usually the only practical one. The measurements suggest that the driven element radial system is in the range 2 Ω to 3 Ω, and that of the parasitic elements 4 Ω to 5 Ω. For modelling purposes I use the values at the high end of these ranges.

I will keep it simple and state a few modelled comparisons rather than draw up a bunch of charts. As a baseline with a perfect radial system of 0 Ω the 4-square has approximately 0.5 db more gain than my style of yagi, assuming the previously described internal loss typical of the 4-square and yagi. For a 5 Ω radial system the 4-square gain declines by 0.5 db and the yagi gain declines by 2 db. Therefore with a large but not extreme radial system the 4-square gain is better by 2 db. There is frequency sensitivity in these figures for the yagi so I took the average.

That's a substantial difference. With a smaller radial system the difference will be larger. You need a lot of radials to make the yagi perform well. As I said in an earlier article that although the directionality of the yagi is lacking it is of little consequence in contests since I can work stations off the back and sides with good success and that puts more QSOs in the log. Receive performance is compromised so it is occasionally helpful to use a high directionality receive antenna.

Pros and cons vs. the 4-square

This list is a set of subjective and objective observations of the yagi versus the 4-square. You may disagree with some points or weigh their importance differently.

Pros:

• Low cost
• 20% less land use
• Flexibility of direction choice, more than 4 directions, and ability to add more directors
• No dump load or phasing harnesses: all the power is radiated or lost in the ground

Cons:

• Lower efficiency for the same radial system
• Must home brew: there are no commercial control systems
• Directionality and gain

I believe most hams would, and should choose the 4-square. It is possible to build it with wires to reduce the cost with external supports or with elements similar to that used in my yagi.

The decision is not quite so straight-forward since my yagi design is not the only one. The yagi can be improved in various ways.

Alternatives

The yagi will remain as it is for some time. There are too many antenna projects for the next year to worry too much about 1 or 2 db. What I can do, now that I am indoors more often due to the weather, is to explore alternatives. Alternatives range from the highly disruptive to modest.

Taller centre support to allow straight (unloaded) elements

Straight wire elements increase gain by ~0.5 db. Side lobe radiation is reduced almost to that of the 4-square. Directivity is improved so that that it comes close to that of a 4-square though frequency dependent. The taller central tower can serve as an efficient 160 meter antenna with suitable switching to retain its performance as an 80 meter omni-directional vertical and yagi driven element.

Increase boom length so that it covers the same area as the 4-square

Element spacing increases from 0.125λ to 0.175λ, for a boom length of 0.35λ. Gain increases ~0.6 db and directionality is improved. Of course the radials for the parasitic elements must be relocated, and that job takes several days. The increased spacing permits converting the array into a 4-square. The central tower can be used as a simple support, or continue as an omni-directional vertical (if the commercial 4-square controller doesn't have this feature) or as a 160 meter vertical. For the latter case modelling confirms that a central 160 meter vertical does not affect 4-square performance on 80 meters.

Bent elements

Removing the lower half of the sloped T-top loading section on the parasitic elements has several advantages. Parasitic element efficiency because the radiation resistance rises from 21.5 Ω to 31 Ω. Gain increases 0.6 db with the existing radial system. Directionality is within a few decibels of a 4-square. There are no mechanical changes. Parasitic elements must be tuned for different self-resonant frequencies and the L-network adjusted to compensate for the higher feed point impedance.

More radials

This is perhaps the simplest alternative. By doubling the radial count the ground loss is reduced. In addition to a gain increase of 0.6 db the directionality is modestly improved. Apart from laying the wire the L-networks must be adjusted for the lower feed point impedance and the parasitic elements retuned to the desired self resonant frequencies. Wire isn't always cheap and doubling the radials will require 1600 meters of wire and many days to install them.

Paths forward

The described alternatives can be combined for further performance improvement. For example, by doubling the radials, using bent elements and a 0.35λ boom length the gain comes within 0.5 db of a 4-square and directionality is similarly close.

One or more of the alternatives will be explored in depth in future articles. This one is already long enough and I don't have the time right now. Although I may eventually go for a 4-square I am not done exploring yagi designs. Modifying the existing yagi is far easier than rebuilding.

A little more gain and directionality would be beneficial, especially on receive. It would be advantageous during contests to keep receive antennas primarily for 160 meters to reduce contention between operating positions. In contests I often use the northeast Beverage while working Europe to improve copy of the weakest callers.

In conclusion there are many ways in which the yagi can be improved and experimented with. In that light this is an ideal antenna for me and my interest in antenna design. A 4-square with a commercial switching system is not so interesting to me. Others may have different objectives.