Stacking HF Yagis - The Basics

Stacking of two identical yagis can provide an additional 3 db gain (doubling). That is, under suitable conditions. There is lot of fantastic information around about the realities of stacking, balanced against a lot of good but incomplete information. There is also lots of nonsense here and there. It all makes for a big mess.

This article is my attempt to add a bit of light to the basics of stacking HF yagis. I figure, why not, winter and the holidays make for a good time to do a little dreaming about big antennas. Although I have never had stacked yagis (for the same band) in my various stations over the years I have used many and helped others design them.

So sit back and join me in a bit of dreaming about big antennas. Keep in mind this is not a construction article, nor is it about choosing the optimum design or a critique of others' designs.

If you already thoroughly know the basics you'll learn nothing new here.

Pieces of the puzzle

The diagram at right includes the main components of a two-yagi stack, as often deployed. It is obviously not to scale or even "anatomically correct". My drafting skills are poor! Hopefully I can get the idea across with my minimum outlay of effort.

The upper yagi is on top of the tower and rotatable. The lower yagi may be fixed in one direction or rotatable with a ring rotor or a hinged arm. The latter would have a dead spot somewhere since rotation would be less than 360°. Then there are those that have rotatable towers.

Each of the labelled components will be covered in the discussion below, in no particular order.

Additive gain from subtractive arrays

Moxon has a nice discussion of these distinct classes of gain (directive) antenna arrays. Here are my paraphrased definitions of both:

• Subtractive: Arrangement of driven and parasitic elements within the antenna's near field designed to reduce or cancel the net field in most directions to achieve directivity; that is, gain and F/B. Its characteristics include: relatively compact size; narrow bandwidth; and low radiation resistance (for maximum gain). The yagi is the usual and perhaps best example.
• Additive: Two or more antennas with low mutual impedance have their patterns combine in the far field to produce directivity. When suitably designed the antennas in the additive array do not "see" each other (small mutual impedance), therefore the characteristics of each antenna in the array are as if they were solitary. A power divider allocates the power among antennas, along with any required phase shifting.

When stacking yagis, the ideal is additive combination of the separate antenna patterns without so much mutual impedance between them that the net pattern is degraded. In the real world the ideal is rarely achieved. The confounding factors are getting the antennas far enough apart and far enough from ground that addition is the dominant factor in pattern determination. A lesser objective is to either accept some degradation or to modify the design of the individual antennas to leverage the mutual impedance to equal or even exceed the ideal (3 db) gain.

It's really just that simple. I have noticed that some (most?) of the literature on this topic does not clearly differentiate how the two array types each affect the outcome in their own way. This omission can cause confusion.

Example: Stacked 3-element Tri-band Yagis

An example will help to elucidate the discussion. The antennas at right are both short-boom 3-element tri-band yagis (yes, you can stack multi-band antennas) vertically spaced 20 meters. I modelled this tri-band trap yagi in EZNEC some months ago. If you like you can refer to that article for design details, although that really isn't necessary for what follows.

Before adding the complication of ground it is helpful to first run the model in free space, eliminating the effects of ground on the near field and the additive effect of the two ground reflections (images). The plots (azimuth on the left, elevation on the right) compare feeding just one yagi versus feeding both in phase. The test frequency is 14.1 MHz. At this frequency the 20 meters stacking distance is ~1λ.

The gain of feeding one yagi is 7.14 dbi, which is a bit lower than the 7.28 dbi it has when the other yagi isn't present. That is the effect of mutual impedance between the yagis. In this instance current in the unfed yagi is ~10% that of the fed yagi, which is pretty good so far as stacks go. The azimuth pattern is not distorted because the array is symmetric in that plane. In elevation the single yagi pattern is distorted (upper yagi, in this case) due to vertical asymmetry. Symmetry is restored when both yagis are fed.

The gain with both yagis fed and no phase shift is 10.49 dbi, or an additional 3.35 db. If there were no mutual impedance between yagis the gain ought to be 10.28 dbi, precisely 3 db more than a single yagi. In free space the gain peaks at 0° elevation since there are no ground reflections (images).

Notice that the shape of the azimuth pattern is almost exactly the same as for a single fed yagi, just with higher gain. As should be apparent that it is from the elevation pattern that the energy is taken for the stacking gain: the main lobe is narrower in the elevation plane. Lucky for us vertical stacking is easier since it has both equal compass coverage and improved low-angle radiation. (The latter will become clear when we come to real ground.) That is, good DX performance without the need to make more frequent adjustments to the beam heading than with a single yagi.

Mutual impedance slightly reduces the gain if only one yagi in the stack is fed but results in more than 3 db gain increase when both are fed. So far so good. While I am not going to deal with stacking optimization in this article it should be obvious that 1λ separation is effective for this particular yagi, at least in free space.

Ground effects

Moving from free space to real ground we introduce two additional factors to our stacked array:

• Near-field interaction with ground
• Far-field pattern due to ground reflections from all yagis in the stack

In the first case we are concerned with antenna impedance and efficiency. Any significant differences among the yagis due to near-field ground interactions (mutual impedance) can cause problems. These include unequal power division and pattern distortion of the lowest yagi. As an absolute minimum the lowest yagi in the stack should be no less than than λ/2 above ground (10.5 meters at 14 MHz). For best results the lowest yagi should be at least 1λ high.

In the second case the stacking distance and the ratio of stacking distance to height affect the superposition (linear sum) of the space waves and ground reflections. First we take the above array of tri-band yagis and place them over typical medium ground, with the lower yagi at 20 meters height (1λ on 20 meters, and 2λ on 10 meters).

As is typical for a horizontal antenna there are more lobes in the pattern as you go higher. The combined pattern therefore has a couple of notable features:

• Fewer nulls in the elevation pattern. Unless deliberately designed the nulls between lobes of the two antennas will not coincide. In my judgment this is to be seen as an advantage since switching of stack feed is less often needed to receive stations on high-angle paths.
• The lowest lobes are the ones with the greatest energy and they typically combine to give the low-angle gain stacks are justifiably famous for achieving. They do not sum exactly since the lobe widths and centres are different due to the different heights. The smaller the stacking distance the better these lobes add.

In this particular example when the two tri-band yagis achieve a maximum gain of nearly 15 dbi at 9° elevation. At very low angles the pattern of the highest yagi dominates the summed pattern.

It should be clear from this discussion that it would be very unusual for stacking gain to be exactly 3 db! This is true even absent near-field ground effects and mutual impedance between closely stacked yagis. Indeed a perfect summation of lobes is not necessarily the best. Although elevation angle peaks can be closely matched when the ratio of stacking distance to height above ground is highest, mutual coupling between yagis can diminish gain.

Counter-example: 4-over-4 on 40 meters

I think it worthwhile to include a stacking example that fails miserably. For this I am using the 4-element 40 meters switchable wire yagi from a recent article. In addition to the original with an apex height of 20 meters (λ/2) there is an identical antenna above it at 40 meters height  (1λ). The effective height of each is several meters lower due to the inverted vee element shape. It is assumed that both yagis are switched in tandem.

The separation between yagis is λ/2, which is very small for an antenna of this gain and boom length. The mutual coupling between antennas is significant though not too bad. SWR is barely affected when only the upper or lower yagi is fed, and is slightly improved when both are fed. Gain is degraded by just under 1 db when only one yagi is fed.

The failure of stacking is readily apparent when we plot the elevation pattern of the stack versus each of the lower and upper yagis.

Here we see the effect of having the lower yagi close to ground, even with a small stacking distance. The main lobe of the lower yagi is of high enough elevation that it adds poorly with that of the upper yagi. The net result is a mere 0.3 db gain at low angles in comparison to the upper alone. Indeed the lower yagi is worsening the pattern of the stack.

It is clearly better to not stack in this instance. The best result comes from simply raising the wire yagi to the greatest possible height. It should come as no surprise that in the super-stations that do use stacks on 40 meters that the upper yagi is typically at 60 meters height (1.5λ). You need to do that to get worthwhile stacking gain. The same reasoning applies to higher bands, with respect to wavelength.

Yagi tuning, power splitting and switching

Yagis of all types can be stacked, provided that the stacking distance is sufficient that the mutual impedance is small. However there are good reasons to use identical antennas that are identically tuned.

• Power splitting: The impedance of off yagis in the stack should be made as identical as possible, across the band(s) of interest. Impedance differences, and even equal but highly reactive impedances, will unequally split source power. Inequalities will show up in the far-field pattern with the yagi getting more power dominating the pattern and a reduction in stack gain.
• Switching: Many stacks feature switching between the full stack and individual antennas within the stack, to allow real-time selection of best matches the path's elevation angle. An impedance difference seen by the transmitter could require tuning after every switch action. This is undesirable.

The simplest setting is where just one yagi is selected. Power does not have to be split, and relays connect the main transmission line to the phasing line connected to the selected yagi. Both lines should be 50 Ω.

When two or more yagis are selected we need a way to equally split the source power and to ensure the yagis are fed in phase. Variations are permitted to create alternative patterns but that is rarely done. We'll stick with the dominant arrangement that calls for equal power and phase.

Equally splitting the power to a two-yagi stack can be as simple as a coaxial T-connector. However that is insufficient in most cases since this places the loads in parallel and, if the impedances have been matched as they ought to be, the summed impedance is half that of an individual yagi. For the ideal 50 Ω case (at resonance) this gives a net impedance of 25 Ω, or an SWR of 2 for a 50 Ω source. The SWR will be worse at all other frequencies.

A transformer solves the problem. Perhaps the simplest is the λ/4 coaxial transformer. If a λ/4 section of 70 Ω coax is connected to each arm of the T-connector the 50 Ω impedance of the yagi is transformed to 100 Ω. I used this type of feed in my design of additive 40 meters slopers.

In parallel (via the T-connector) and with the transformers the summed impedance is the desired 50 Ω. The remainder of the phasing lines (between the yagi and coaxial transformer) are 50 Ω.

For a single band two-yagi stack that is permanently wired (not switchable) the use of λ/4 coaxial transformers is the best and most efficient choice. Even if switching is desired this is still not a bad choice, if we provide a means to cut the transformers out of the circuit when an individual yagi is selected. This can be done by coiling the transformer at the switching box on the tower and using relays on both transformer ports.

In every other stacking scenario it is better to use a high-efficiency broadband toroidal transformer (unun). This includes multi-band yagis and stacks with more than 2 yagis. For two-yagi stacks the transformer is 2:1 (50 Ω to 25 Ω) and 3:1 (50 Ω to 17 Ω) for three-yagi stacks. Two 2:1 transformers or a 4:1 transformer can be used for a four-yagi stack, depending on the desired switching configuration.

There are many commercial products (e.g. Comtek) that include the transformer and relays in one box and a switching unit for the shack. DC power is typically delivered by separate 3 or 4 conductor cable to accommodate the several operating modes. The relays cut the transformers out of the circuit when a single yagi is selected. While these devices aren't difficult to build most hams choose to buy since they are not very expensive and save effort and time better spent building and maintaining these monster antennas.

Phasing

Whatever transformer option is selected it is vital that the phasing lines to the yagis be of equal length. Pattern addition will only give the modelled gain if the yagis are fed in phase. A substantial phase error will decrease gain and otherwise degrade the pattern.

A reasonable maximum error tolerance is 1%, which is equivalent to 3.6° phase shift between yagis for 1λ electrical length of phasing line. The same accuracy goal should be used for λ/4 coaxial transformers. Not only must the lengths be equal the lines should be the same brand and vintage to ensure that the velocity factors are the same. Especially avoid solid polyethylene (0.66) in one and foam (0.8 to 0.9) in the other. For example, a 1% error in a 5 meters long phasing line made from RG-213 is 5 cm (2"), which is easily done.

If  λ/4 coaxial transformers are used these must be directly connected to the switch box, not to the yagis. For permanently wired stacks the transformers can form part of the runs from the T-connector to the yagis. They will not reach all the way since, even with foam coax, the transformers only span 0.4λ, and the yagis are sure to be well over 0.5λ apart.

It should be no surprise that the switching unit and transformer are typically mounted on the tower between and equidistant from the yagis in a two-yagi stack.

Final

Well, wasn't that fun? Stacking may seem like it's only for the big guns yet I know many smaller stations that utilize stacks for the high bands, especially on 10 meters. Even with a 25 meters high tower plus mast it is very possible to get most of the benefit of stacking as low as the 20 meters band. Maybe it isn't so much of a dream after all.

My next article will be my year end retrospective and a look forward to 2015. Unlike my plans for 2014 this coming year is less-well planned since I am running up against the constraints of what I can reasonably build on my suburban property.

40 Meters 4-element Wire Yagi

Earlier this year I showed the design of a 3-element switchable wire yagi for 40 meters. Soon after I expanded the antenna to 4-elements but never wrote it up. Since it's winter and I have some additional time I decided to refine the design and publish it. I was also motivated by the relatively high interest shown (based on page hits) for my various wire yagi designs for 40 meters.

In this article I will only focus on the differences from the 3-element design so please refer to that article for details not addressed here.

Adding a fourth element is straight-forward. Obviously the antenna is larger (longer) but it has some unusual features that are worthy of discussion:

• The antenna has 5 elements, not 4, but only 4 are active at any one time.
• The 2^nd director is fixed, not switched. In fact the active switching is identical to the 3-element design.
• Switching symmetry requires the reflector-to-driven and driven-to-1^st-director distances to be equal. But the distance between directors and length of the 2^nd director can be adjusted for optimum or desired performance.
• It is possible to have 4 elements in one direction and 3 in the other, if some odd behaviour can be tolerated.

Design Process

I started by adding a 2^nd director to the 3-element model. I made it the same length as the 1^st director used the same spacing as that for the driven-to-director. This approach is in keeping with W2PV's modified NBS designs that can achieve optimum results for gain, F/B and bandwidth. Wire yagis work as well as his tubing-based designs but with higher element loss and somewhat reduced bandwidth.

As mentioned above the 2^nd director is not switched; it is a continuous length of wire. For this reason a similar element must be placed on the other side of the yagi for the 2^nd director in the reverse direction.

If it seems odd that a director could be placed behind a reflector do keep in mind that the action of the reflector pretty much isolates the antenna from any resonant conductor behind the reflector. In the above current plot you can see that there is only a small induced current on the 2^nd director when the adjacent switched element is configured as a reflector. The amount varies with frequency -- in fact all element currents substantially vary with frequency. In modelling I found that the position of this element needs no adjustment to compensate for its mutual coupling.

Antenna size

This is not a small antenna! It is 29.6 meters long and requires two tall supports, such as towers supporting rotatable yagis, preferably guyed to deal with tension in the cable "boom". As with any antenna for 40 meters you want this antenna high. This is especially so with inverted vee elements since the ends can come close to ground. I recommend a minimum height of 20 meters (λ/2). A height of 30 or more meters is even better.

The antenna elements have an interior angle of 120°. So not only is the antenna long it is also wide. The "wing span" (or width) of the antenna including tie ropes anchored to the ground is 70 meters, when the apex is 20 meters. Wing span scales linearly with increased height. Vertical supports can be used to reduce wing span and increase safety for anyone walking in the area.

A smaller interior angle reduces the wing span but will require longer elements and retuning due to lower feed point impedance. Performance at low angles will also be reduced due to the lower height of average current.

Ideally the antenna supports, if they are towers carrying yagis, should be further apart than this antennas "boom" length of ~30 meters. This is to reduce interactions that could distort the patterns of one or more antennas. Similarly the cable supporting the wire elements should be mounted no closer than 5 meters below the top of the towers, and preferably more if the directors are positioned near either tower.

Performance

The additional gain attainable with one additional element is not a lot, even with the longer boom. It is an unfortunate truth that with yagis there are rapidly-diminishing returns with increasing size (elements and boom length). Actually it is the boom length that is the critical parameter. It is just that you need enough elements to ensure sufficient inter-element coupling to achieve the benefits of the chosen boom length.

This antenna achieves from 1.4 db to 1.9 db more gain in comparison to the 3-element wire yagi, for the given elevation angle and height -- 10° is median elevation angle for most DX paths on 40 meters. This may not seem like much yet it is enough to be seriously considered for the modest additional effort required. After all, stacking two yagis gives on average 3 db of additional gain, and this wire yagi is far easier to deploy.

F/B has two peaks, but both are outside the band. The average 10 db of F/B is good enough for my purposes. The reason it is so modest is that the effective boom length of 22.2 meters is ~λ/2. As W2PV showed so long ago F/B in a conventional yagi peaks for boom lengths that are odd multiples of λ/4 and is worst at even multiples.

As gain increases the width of the main lobe decreases. The main lobe (azimuth) is 58° at the -3 db points. When centred on 50° bearing I could cover all of Europe and much more. In the reverse direction of 230° I can cover the South Pacific and most of the continental USA.

When raised to heights greater than 20 meters the main lobe's elevation decreases. This further improves the antenna's DX performance. However a smaller secondary lobe appears at high angles. In practice this is not a problem.

All performance figures include I²R loss for elements made from 12 AWG insulated copper wire. The average loss is -0.3 db, except for a steep rise near 7.3 MHz where it climbs to -2 db due to a corresponding steep rise in antenna current in the driven and director elements.

Match

When yagis grow to 4 or more elements it is common for an optimized design to display two "humps" in its performance metrics. This particular design show aspects of that with respect to F/B and SWR, but not with gain. The antenna has two resonant frequencies (where X = 0), one low in the band and one higher. While this can help to achieve a broadband match there is some challenge in taming those two humps.

I settled on a beta match. After some experimentation with network parameters I reluctantly concluded that compromise was necessary. Experimentation included varying the beta match stub impedance from 100 to 600 Ω, and even trying a fixed inductor. The stub impedance matters since the rate of reactance change for fixed values of frequency and stub length is a function of impedance. The idea is to have the reactance at least partially track the uncorrected capacitive reactance across the band. Unfortunately that second hump makes this impossible. A fixed inductor fared no better.

The above SWR curve seems to me to be an acceptable compromise. This required a longer than expected driven element length of 19.85 meters (12 AWG insulated copper wire). The transmission line stub is 1.5 meters of 300 Ω open wire line. If plastic is present in the stub's construction it must be made shorter due to the lower velocity factor.

On the other hand, with 100 meters of RG-213 feeding this antenna the SWR at the shack end of the coax is below 1.5 from 7.000 to 7.275 MHz. Lower loss cable is recommended for the long run that is likely required, at the cost of having the SWR closer to that shown above.

If the antenna is raised higher the SWR profile remains the same. That does not hold for heights below 20 meters since the ends of the elements interact with ground.

Conclusions and extrapolation

I like this antenna. Should I ever have the required supports I would seriously consider building it. Perhaps at an even greater height. One added step I would take before doing so is to improve the match by some means. That could be done with a dual-driven element or a switchable load at the feed point.

If built there would have to be at least one more antenna to cover the azimuth directions outside the reversible main lobes of this fixed wire antenna. A rotatable yagi would likely be the best choice. As should be obvious by now I am talking about antennas in a substantial installation, which is nothing like I could even dream of at this time. Perhaps never, though dreaming is free.

Gain could be slightly increased with further tuning of the parasites and element spacing. But doing so makes the match more challenging since the radiation resistance will vary more over the band. I opted for a design that (barely) makes the match work with a simple fixed network.

The antenna can be further extended. By adding a 3^rd director I was rapidly able to increase the gain to 1.5 to 2.0 db above that of the 4-element design. I kept the same director length and spaced it 10.4 meters from the 2^nd director. In the model (shown at right) I took the expedient step of not adding a 7^th element for reversibility. Its presence in the model would have a negligible effect, and can be easily added when it is built.

The match, unsurprisingly, was a challenge, being a more extreme case of that seen with the 3-element antenna, due to the wide range of radiation resistance across the band that comes from optimizing for gain. The match could be improved by tapering the lengths of the directors, but only if you are willing to sacrifice 0.5 db or more of gain.

The antenna could be extended to 80 meters, and even interleaved with the 40 meter antenna and using a common feed, with some design tweaking. Getting performance on 80 with this antenna is a problem since it requires more height, at least 30 to 40 meters up, and some means of tuning to make it work across the band. The scaled model has a usable bandwidth of no more than 100 kHz. I have some doubts as to whether it could outdo a well-built 4-square on 80. Local ground and topography would play a large role in any meaningful comparison.

I will leave off wire yagis for a while to focus on other antenna designs that currently have my attention. With the holidays around the corner this may have to wait until January. I also intend to expand on why I am so focussed on antennas for the lower bands.

Front-to-Back is Overrated

After looking at Moxon and other directive antennas I realized it was time for a reset. That is, to ask just what it is one is trying to achieve with such an antenna, or indeed with any antenna? It is often far too easy to pick out a commercial product, install it and then declare to the the world how great it is, without ever really thinking through one's needs and desires.

My intention is not to disparage any products or designs, but rather to encourage some reflection. From my own years of observation it is a minority of hams that think through these matters and then can honestly state that their choice of antenna is the best one for their style of operating and personal circumstances. We all have constraints within which we must live.

I will start into this topic with the fundamental metrics of the typical directive (or gain) antenna to which most hams pay attention, and that manufacturers advertise:

• Gain
• Front-to-back (F/B)
• Match

This is a pretty simple set of metrics to deal with. However in most cases there are trade-offs since it is a rare antenna that does comparatively well at all these metrics, or that does so in a way that is economical and not an installation and maintenance burden.

Let's look at each metric in turn to discuss why it might matter in the choice of an antenna. Although the title of this article is, in part, giving away the ending the process of getting there arguably matters more than any conclusion.

Gain

Gain is probably the most sought after feature in an antenna when an antenna of size or expense is considered. A forward gain of, for example, 3 db is equivalent to doubling transmitter power. Since gain is reciprocal it enhances reception by the same amount. There are few hams that don't want this. But why?

First, it increases competitiveness in getting through DX pile-ups faster. It that matters to you and you're running legal limit power, more gain is a reliable means of getting through.

Second, gain draws in more contest QSOs. A louder signal is a more attractive signal. If you doubt this you should reflect on your own behaviour on the bands. Hearing two signals of different strengths you are more likely to call the stronger one, or at least call it first. Since the size of stations relative to numbers is pyramid shaped, there are increasingly more stations of smaller capability. So the higher your gain the greater the score. To a limit since the ham population is finite.

Third, open propagation paths that are otherwise marginal or unusable. This is as true of EME as it is for HF DXing and contesting. For example, from my location the polar path to southeast Asia is relatively difficult. Most often when there is propagation it is marginal for those of us with modest antennas and power. Every decibel counts, even when there is no competition for a particular station.

F/B

Conservation of energy dictates that if you achieve gain in one direction there must be an equal decrease in other directions. This is inescapable. Depending on your objectives this can be a benefit or a problem. First we ought to list the types of signals that are adversely affected (attenuated) due to gain in the desired directions(s).

• Stations other than those within the forward lobe
• Local QRN
• Atmospheric QRN

Why do you want to attenuate signals off the main forward lobe? The usual reason given is QRM that reduced readability of the desired station. I suspect that most hams have more of a QRM problem with stations in the same direction, those within the main lobe rather than other directions.

To make this more concrete think of an opening from my part of North America to Europe. Other NA stations will hear the same European station I am listening to and will, like the large majority of hams, avoid the frequency. That is, most hams are well behaved and avoid causing QRM. However within Europe other stations will often not hear the one you are listening to and may inadvertently cause QRM by transmitting on what to them is a clear frequency. The directivity of your antenna is no help.

In the case of a rare DXpedition it is more likely that the madding hordes will cause QRM, mostly accidental (over-enthusiasm) and some deliberate. Since most of these DX stations operate split the majority of QRM is avoided since they are not transmitting on the DX transmit frequency. F/B and rejection of other directions is only of significant benefit with a fraction of deliberate QRM. Since those stations are typically nearer to you it can take a lot of directivity to be beneficial.

During contests or other times when the band is open in two or more directions at once F/B can be more of an annoyance. Unless you have another antenna that favours directions that are rejected by the first you may have to turn the antenna (assuming a rotatable yagi) often. With a poor F/B you can often work other directions without turning the antenna. This is an advantage for contesters with small stations that need antenna diversity. I use the poor F/B of my yagi at some frequencies to improve contest results.

QRN requires a different approach. In the case of atmospheric QRN, unless there is an intense weather system in a specific direction you will benefit little from antenna directivity. While it may seem like a good idea to attenuate atmospheric QRN is most directions it does not really work that way. If the noise is truly omnidirectional the total noise power within your receiver bandwidth does not change with antenna direction. Again, we are dealing with conservation of energy. A directional antenna that rejects noise is most directions also amplifies noise from the main lobe due to forward gain. They balance exactly.

Local QRN due to switching power supplies for LED lighting systems, arcing power line insulators do have a particular direction allowing one QRN source to be nulled. Unfortunately that direction is often one where you can simultaneously beam toward the desired direction and sufficiently attenuate the noise. This is a problem more amenable to separate receive antennas such as a small loop or Beverage.

Match

Operator convenience dictates that the antenna provide a simple match to the rig at all frequencies over which the antenna is stated to operate. Specifically this means a close to 50 Ω feed point impedance, allowing for efficient transmitter transfer of power without the need for an external or internal impedance matching unit. Yagis, for one, have a feed point impedance that can be far lower than 50 Ω at the frequency where gain is highest.

This is difficult to achieve over an appreciable bandwidth for an antenna, such as a yagi, that develops gain and F/B by cancellation of portions of the antenna's near field. This has made the internal ATU a common feature of modern transceivers, in order to improve the match over a wider bandwidth (preferably the entire amateur band) than the antenna alone can achieve. Arrays that achieve gain by additive techniques, such as the 4-square or multiple slopers, often require no external matching network.

The problem is exacerbated with multi-band antennas since traps and other loading elements further reduce bandwidth. Both subtractive gain and multi-banding increase antenna Q, where the feed point reactance (and sometimes the resistance) rapidly increases away from the resonant frequency (X = 0).

One positive point is that it is usually possible to bring the frequency of best match within the frequency range where gain and F/B are best. The reason is that most impedance transformation networks that are part of the antenna (beta, gamma, delta, etc.) don't appreciably alter parasite behaviour. In my own past antenna articles I often emphasized that tuning a gain antenna during design and construction should focus first on gain and F/B optimization, and last on match.

Trade-offs

Perhaps the greatest performance trade-off for a subtractive array such as a yagi is gain versus match. The reason is that gain is maximum when subtraction is greatest. This result in the lowest radiation resistance (highest antenna current, by Ohm's Law) and highest Q. Yagis can have a radiation resistance below 10 Ω, and commonly below 20 Ω. Both R and X values change quickly away from this frequency because of the high Q. A matching network with fixed component values can transform the impedance to 50 Ω, but with a narrow SWR bandwidth.

More typically a yagi is tuned for lower than maximum gain to reduce the above problems, and that of I²R loss in the elements which can be significant with wire elements.

F/B tends to be influenced more by adjusting boom length than gain. It is especially influenced by element coupling since high F/B requires close to equal element currents. This was discussed in my recent article on Moxon yagis.

Unfortunately that increased element coupling and current equalization does not favour optimum gain, even while it improves both F/B and match. Indeed the comparatively lower gain of a Moxon rectangle should be evident by its good match to 50 Ω coax since, as already mentioned, high gain is associated with low radiation resistance and high, not equal current.

The diamond vee wire yagi I built years ago for 40 meters had very good F/B, almost certainly due to the current equalization brought about by the element ends turned inward. Although I could not measure the gain (which is very difficult to measure in any case) nor compare it to a reference antenna I can still be certain that the gain was no better than my more recent EZNEC model shows. The gain would be comparable to a Moxon and worse than a wire yagi with parallel elements.

So we can't have it all. There are unavoidable trade-offs we much deal with in choosing or designing a gain antenna array.

Common factors

The are other factors that can substantially affect antenna performance in regard to the metrics introduced at the beginning of this article. Since these affect all antennas almost equally I call them common factors, and discuss some important one below. That is, they are not a basis of comparison among gain antennas.

All antennas do better with height. This even goes for vertically-polarized antennas, or at least those that do not have an extensive ground plane that prevents the antenna's near field from directly interacting with ground. However do keep in mind that increasing height requires longer transmission lines and therefore higher loss. If care isn't taken, especially if the match is poor at some frequencies, much of the low-angle gain increase due to height can be lost in the transmission line.

In the usual case of horizontally-polarized gain antennas like yagis height increases gain at low radiation angles and therefore DX effectiveness. Since height affects antennas in an almost identical fashion it does not distinguish one horizontal antenna from any other. The exception is high-gain antennas with a narrow main lobe in the vertical plane, which will put more power at lower angles than an antenna with a wider main lobe for an equal increase in height. Generally speaking it would take a gain difference of at least 3 db for this height affect to become significant. A good example is stacked yagis.

Low gain antennas can have their performance, in all respects, changed or worsened at low heights since a larger fraction of the antenna's near field will interact with ground. This negative effect is lessened at heights above about λ/2 (10 meters on the 20 meters band).

Discussion

When antenna elements are bent from the parallel or otherwise loaded for shortening it is important to beware of comparisons that do not elaborate on the differences. Without knowing this it can be difficult to interpret the results. This also goes for height above real ground (and ground of different characteristics) since these also muddle the comparison. Don't implicitly trust the comparison by just reading the final numbers without knowing how those numbers were reached. In most cases the deception is unintentional, but are just as misleading.

One reason the Moxon has somewhat lower gain is that the elements are shorter than λ/2. Moxon himself notes this in his book. He believes this is a reasonable trade-off with respect to gain and match. I would only agree if shorter elements have a mechanical advantage, such as on 40 meters where a gain antenna can be quite large, and especially if it must be rotatable. In this latter case you would probably be better off with a W6NL design 2-element yagi, either built from scratch or as a modification to a conventionally-loaded yagi.

Once you get beyond a modest amount of F/B (or F/S, etc.) the increased cancellation of fields in various directions has little to no effect on gain. Look at the azimuth pattern comparison at right (Moxon in blue), taken from my earlier Moxon article. All of that additional field cancellation and yet the gain is lower. Where did the energy go if not forward gain?

The answer lies in two places: the shape of the forward lobe and the chart scale. The Moxon rectangle has a broader main lobe, which spreads the available power over a larger solid angle. The chart scale is logarithmic, not linear, so that deep F/B is not what it appears! To go from -10 db F/B to infinite F/B is only 10% additional power available for forward gain (obviously I'm generalizing since the pattern shapes are different). That's only another 0.5 db potentially available. As noted this is spread over a wider forward lobe.

From this it should be no surprise that in pretty much every yagi ever designed the frequency of greatest F/B differs from that for greatest gain. The greatest gain is rather where the current is maximum (sum of driven and parasites, assuming proper yagi design), which is also where radiation resistance is lowest.

Of course that low radiation resistance must be addressed if maximum gain is desired. The match is easy enough to achieve at one frequency but not always across the band because of the high Q associated with the maximum gain condition. This is particularly true with only 2 elements or on 40 meters and below.

Conclusion

To me high F/B is therefore of small value: it helps not at all with achieving greater gain, does little about noise, and limits directional diversity during contests. If match is a concern it is better to increase the array to 3 or more elements so that both gain and match can be had over a broader bandwidth.

Don't blindly follow an antenna's spec sheet or focus too much on F/B in any antenna design. Especially since the quoted high values typically are achieved over a narrow frequency range. Be very certain that the F/B you're really getting is a must-have feature for your operating objectives. Otherwise you'll pay a price, and that price may only be evident in unexpectedly poor results.

Going QRP in CQ WW CW

If you enjoy DXing, QRP or QRO, you owe it to yourself to operate the CQ WW contests. The activity level is phenomenal. You'll hear openings and work DX you never imagined possible. It's not that the ionosphere behaves differently, but that stations are active from places and bands, and at times of day that make it seem as if it's the contest itself causing the openings.

There is something magical about getting on, say, 40 meters and hearing DX from all over the world fill the dial. You can rapidly spin the dial and hear DX. It then only requires that you give them a call and start filling your logbook. QRP works nearly as well as QRO. Everyone is eager to work you. All you need do is clear your calendar for a few hours, lock yourself in the shack and turn on the radio.

The CW contest is of particular interest to the QRPer. It's all about receiver bandwidth and SNR (signal-to-noise ratio). It is therefore no surprise that my results in CQ WW CW this past weekend, and that of other QRP participants, far exceeded those in the SSB contest a month earlier. There is even a RTTY version of this contest for those with a digital interest, and where QRP can also be competitive.

I won't dwell on my detailed results here, and only refer you to the submissions posted on 3830. Instead I'll delve into several topics that I believe are more interesting. My station setup was the same as I described for CQ WW SSB.

80 meters

I entered the LZ DX contest the weekend before CQ WW CW to test out my DX capabilities on 40 and 80 meters, with an emphasis on the latter. I didn't make many contacts on 80, nor did I expect it. The ones I did log were difficult for me and especially for the other operator. Five watts to a loaded half sloper nestled within suburban sprawl is not a good combination.

That said, the dry run was a success in that is showed I could work DX on 80. Not a lot but enough to make a big difference in my multiplier total. To give you an idea of how my DXing progressed on 80 over the past couple of weeks here are my DXCC totals at key times:

• At start of LZ DX contest: 3
• At end of LZ DX contest: 7
• At start of CQ WW CW: 10
• At end of CQ WW CW: 26

It's a modest level of success, but success nonetheless. It helped that conditions on 80 were particularly good on Saturday night. My best opportunities came from following the sunrise line as it advanced across Europe, briefly enhancing signals levels of each European station by at least 10 db. I started with Russia and ended with Spain a couple of hours later. Then I looked south to the Caribbean.

Propagation

There are many subtle and significant differences in propagation between the SSB and CW weekends even though they are only one month apart. For one, the eastward openings to Europe and beyond on 10 and 15 are shorter: the sun rises later here and set earlier there. The high solar flux and quiet geomagnetic field could not fully compensate for the path's reduced duration. Since high rates to Europe can be sustained from here on 10 meters when the band is open it was important to be there in those critical morning hours.

Some bands were open around the clock. The 20 meters band never closed. But for QRP the lower signal levels between midnight and sunrise made this band a poor choice. I nevertheless did make some contacts on 20 overnight just to break the monotony of operating 40 and 80. That I could so at all was interesting.

The story on 40 meters was similar. Even well after sunrise many Japanese and Russian stations could be heard. At this time of year the darkness line is not too far to the north of Ottawa and solar irradiation of the signal-blocking D-layer takes more daylight hours.

While interesting it was useless to me since with QRP and a small antenna, and one that does not favour the northern direction, none of this DX was workable. The difference of -23 db with respect to a kilowatt, zero antenna gain, and a low-angle radiation deficit of -0.6 db/meter of antenna height (40 meters, horizontal polarization) form an insurmountable barrier.

Attenuation of signals on all bands was low. This is particularly favourable with QRP where every decibel is worth gold. Propagation made this weekend's contest one to remember. The QSO and multiplier totals of the big guns are truly remarkable.

Antenna diversity

In this contest I had more success with having two antennas on the high bands than I did during the SSB weekend. With the yagi pointed to Asia, Europe or South America I could switch to the inverted vee whenever I came across a US station and raise their signal level. After working each one I switched back to the yagi for the DX path.

This technique worked less well for DX. This was particularly noticable when beaming to Asia or Europe in the afternoon and early evening when the path to the Caribbean and South America was good. More often it was easier to work southward off the back of the yagi than use the inverted vee; since the inverted vee runs north-south those directions show lower gain. When that didn't work I turned the yagi south to catch the stations I missed. The band map and local "spotting" feature of N1MM+ made the process efficient.

Pile-ups

Getting through a pile-up with QRP is difficult but not impossible. I'll mention a few methods here, most of which I've discussed in earlier articles. In a contest this is most relevant to multipliers. Double multipliers -- zone and country -- are even more desirable. It is an unfortunate fact that multipliers for you are multipliers for everyone else, hence the pile-ups.

• Second call: Unlike in day-to-day DXing the callers tend to toss in their calls once and wait to see who the DX responds to. Since not every one of those operators is a CW expert with the uncanny ability to pull out a call or even a partial call from a pile-up there is often a delay in their response. I look at this as an opportunity. I immediately send my call a second time (easy to do with a function key press). With QSK I can always cancel the transmission by tapping the paddle if I hear the DX underneath. Since a QRP signal is copyable when in the clear this technique is often effective.. Your keyer speed must be high for this to work since the window of opportunity is only one or two seconds.
• Self spotting: Contest logging software like N1MM+ have a band map feature that automatically spots calls that you enter but don't work before QSYing. If there's a pile-up you can quickly flip back to the DX's frequency at intervals, either to check if the pile-up is smaller or even gone, or when propagation raises the signal level.
• QRM blind calling: QRM is common in contests. Big guns, and even littler ones, are always on the hunt for a run frequency. The multiplier you are chasing will occasionally be obliterated by the sudden appearance of a "CQ machine" on near the DX's frequency. Now you can't hear the DX, and probably neither can most everyone else. Often it is the case that by the vagaries of propagation the CQer and the DX station can't hear each other strongly so the path is still available for your use. So toss in your call a time or two even though you can't hear the wanted station, and others are standing by for the QRM to clear. When it does, and you do it right, it's your call you'll be hearing. Be extremely cautious when you do this since you can become the QRM, even though your QRP signal is small in comparison to most others. But it can work. One notable success in this contest was to work a Pacific islander through the QRM of a negligent CQer.

I said it above and I'll say it again: use these techniques with good judgement! It is all too easy to cause problems for others when pile-up busting techniques are misused or abused. Please do not become a part of the problem. Even though you are less likely to cause problems for others as a QRP operator you indeed can still do so. Bad habits are also difficult to break so don't ever start.

Sending fast and slow

One peculiar behaviour I see quite often is operators that are seemingly incapable of grasping the idea that different situations call for different CW sending speeds. Too many (and contesters are some of the worst offenders) choose what they consider to be a suitable speed and never again touch the speed control. There are frenetic contesters who seem to think that the faster they wind up the keyer the higher the QSO rate. Others, often those with small stations, send very, very slowly, worried that otherwise they cannot be copied. Both are wrong. You should adapt your speed to every situation.

Even if your CW skills are not the best it is possible in a contest to do as the situation requires regardless of your ability level. The exchange is usually simple and short, with the greatest difficulty being the unpredictability of call sign suffixes. It is possible to get by in a contest with code speeds 5 wpm higher than you can comfortably receive or send. Try it and you'll see for yourself.

Early in the contest, when everyone's rate is high, it is best to send fast: 25 wpm or higher. You may be surprised at how well others copy you: contesters are often superb operators. If you are answering another's CQ you likely will have more than one chance to copy their rapidly-sent call. So don't worry if you catch ust part of it the first time.

Even if you believe your QRP signal is poor copy on the other end (often the case on the low bands) your first call should be relatively fast. If they can hear you but not copy well they'll let you know. Then you should immediately slow down, by a lot if necessary, to ensure good copy of your call and exchange. I often call at 24 or 25 wpm and slow down to as low as 16 or 17 wpm if readability is poor. Don't be shy about slowing when the situation warrants. Better to slow down quickly rather than slowing in small steps. You'll complete the QSO faster that way.

Later in the contest I tend to go a bit slower just to start things off right. There is less hurry as rates plunge after the first day of the contest. Other than the VFO, keyer speed was the rig control I used most often during the contest.

Running

As always it is S & P (search and pounce) that produces the bulk of contest contacts for the QRP operator. Or at least for the QRPer who is not a rare multiplier. I estimate my QSO split in this contest as 13% run and 87% S & P. Despite the challenges of running it is necessary to reach a high score. There is no other way to work casual operators who never CQ themselves. It also is the only way to boost the modest rate possible with S & P, unless you operate in "assisted" class where you can exploit the spotting networks.

My expectation that 10 meters on Sunday morning would produce the best runs was mistaken. I just could not get anything going despite the good conditions to Europe and the faltering rate of the big guns. Instead I was surprised to find that 15 meters produced good results. It is therefore important to try running at different times and frequencies until you find a combination that works. Don't give up too quickly since it may take a few minutes for the run attempt to show promise.

In one big run on 15 I logged 75% of my total run QSOs, working mostly Europeans through late Sunday morning. My net rate was only about 100 per hour but it contributed over 150 QSOs to the log. You'd be surprised how slow this can seem in the moment. It gets boring to spent most of the run time pressing F1 and listening to my own repetitious CQ. Occasionally several stations would answer and I'd have to pick out a call, or partial call, and quickly clear them before the ones waiting got impatient and moved onward.

I was spotted only twice in this run, in comparison to four times in my big run during CQ WW SSB. This I discovered after the contest when I searched the spotting network history.

QSOs versus multipliers

There is a helpful feature in most contest logging features that tell you the equivalent score impact in QSOs of working one multiplier. In my case this averaged out by the end of the contest to about 3.1. That is, working one multiplier is equivalent to working 3 non-multiplier stations. This is an invaluable tool to ensuring you do not spend too much time in a pile-up pursuing a multiplier. Pay attention to this number if you want to get the best possible score.

I didn't always pay attention to my own rule. I can be very squirrel-like when the DX is rolling in: I am easily distracted by shiny objects, in this case interesting or rare DX. As I trawled the bands for more, mostly-unworkable DX with large pile-ups I was very aware that my score was suffering. There was some guilt about this but I really didn't care. Having fun is more important to me than winning a certificate. So I persisted in unproductive activity. In the time it took me to work 3 more JAs on 15 or fruitlessly sit in a pile-up on a rare Pacific station I could have worked 30 stations on 40.

Your objectives and interests may differ from my own. Watch yourself, and the clock, if you are focussed on achieving a high score. Perhaps I will try to win one day but until then I'll do whatever strikes me at the moment as most interesting. I exclusively focussed on the score when I operated as part of a multi-op effort, where it was more important to me to not disappoint my more competitive teammates.

Finally...

My antenna construction this year was in part intended to make me competitive as a QRP contester. That goal has been achieved. Although better antennas would improve on what I've achieved in 2014, and could be made compatible with my present QTH, it is likely that 2015 will see only modest improvements. The bigger changes may be inside the shack.

I will continue to design and perhaps experiment with new antennas, though more as a technical challenge than with the aim of improving my operating results. The required structures that would deliver improved performance are excluded in the near future. These include a permanent and stronger tower for higher and bigger antennas, and radials for low band vertically-polarized antennas. There are considerations outside of ham radio that limit my horizons for the next year. Looking further ahead...we'll just have to see.