Where Gain Comes From

In pursuit of antenna gain it's physical basis is sometimes overlooked. Of course most hams already know that element coupling and phase relationships are among the critical elements. However the details hold some insights. As I write this, it is raining, band conditions are poor and ARRL Field Day is occupying the bands (and in which I chose not to participate). This seems a good time to reflect on fundamentals.

This article is not a rigorous or mathematical look at gain. There are ample texts available for that, both in the amateur radio and professional literature. Instead I will give my approach to understanding gain, with the hope that a few readers will learn something new. You can always delve deeper into the technical literature if you are sufficiently intrigued to want to learn more. While I did double-check the mathematics I present in this article I'll ask you to forgive any minor errors. Major errors are the ones I want to know about.

Update July 1: Errors were found and corrections made. Nothing major, although one equation was bungled. Edits are not marked since they are not earth shaking.

Update July 9: The opening paragraph of the Radiation Resistance section said that phase and current equalization alone limits the gain in an ideal 2-element yagi to 3 db. This is wrong. The error has been corrected, as has the rest of that section. Even though the ultimate conclusions are correct the path there should not mislead. Therefore the correction is warranted.

Conservation of energy

Gain is inseparable from directivity. The mythical radio antenna with no gain is the isotropic radiator which, by definition, has no directivity. Real antennas have directivity, whether accidental or designed. Since it is a fundamental law of physics that energy be conserved, gain in one direction must come at the expense of gain in another. Gain is commonly expressed in dbi, relative to an isotropic radiator.

High gain is therefore strongly associated with high directivity. Typically one strong main lobe with minor side and back lobes.

Radiation is proportional to antenna current

Antenna operating parameters at the granular level include voltage, phase, resistance and current. But in the end it is antenna current that determines the radiation field. The other items are our tools to get there, in that they determine the current magnitude and where it flows. Therefore antenna designers must pay attention to all those parameters.

It is not only current magnitude we care about. The distance over which the current flows matters. For antennas not too long (relative to wavelength) a similar current profile over a longer antenna results in more radiation. Short antennas require a higher current (and lower loss) to match the gain of a longer antenna. In mathematical terms, it is the integral of the current over the element that determines the radiation.

When an antenna has multiple elements the fields from the elements interfere in the near field (mutual impedance) and in the far field (superposition), which determines the pattern. Interference does not destroy energy. There is a difference in how this manifests for near-field coupled elements (e.g. yagis) and far-field coupled elements (e.g. wide-spaced vertical arrays and stacked yagis).

Objectives for gain

With gain as our objective we want to:

• Maximize current magnitude
• Maximize the element length over which high current is maintained
• Phase currents from multiple elements so they reinforce in desired directions and cancel in others

Unfortunately we can't have it all. Compromises are necessary. Let's delve into a few details.

Perfect Front-to-Back (F/B)

The criteria for maximizing F/B are stringent, far more than for gain. This can be illustrated with a hypothetical example.

Let's assume a simple 2-element yagi, with the parasite configured as a reflector, designed for an infinite F/B in the backward direction -- 0° degrees elevation and 180° azimuth, in free space. This is in fact not possible to achieve in a real 2-element yagi, but let's set that aside for the moment for this thought experiment.

We'll pick a typical boom length of 60° (0.167λ). Let's imagine that the current phase on the reflector is 120° ahead (or 240° behind) the driven element (source). When the rearward radiation from the driven element reaches the reflector the reflector current has advanced to 180° (120° + 60°) so the radiation cancels. This is an infinite F/B.

Well, not quite. Complete cancellation also requires the fields to have equal magnitude. This requires equal current in both elements. It is akin to balancing a pencil on its point since the slightest variation in magnitude or phase results in a finite F/B, or the null will skew to a different direction. That's in addition to element diameter, wind, etc. You also can't QSY since these conditions can only be achieved at one frequency; an infinite F/B on CW would not be infinite on LSB or USB! High, yes. Infinite, no.

As we can see, even in the ideal case a perfect F/B is elusive, and one cannot come close is a real 2-element yagi with conventional dipole elements. It is possible to do better in yagis with 3 or more elements, though with some confounding design criteria.

The gain associated with this idealized 2-element yagi with infinite F/B is not perfect. In the forward direction the phase of the field from the reflector does not equal that of the driven element, which is necessary for maximum reinforcement. The phase difference is 60°. This yagi would have less than the ideal 3 db gain for equal and in-phase element currents. One saving grace is that there still is gain when the magnitudes are unequal and the phase relationship is not ideal.

Yet this is only for two narrow directions: exactly rearward and forward. To calculate the complete 3-dimensional pattern of F/B and gain it is necessary to do vector addition of the fields over the full sphere since the far-field phase difference between elements is direction-dependent.

Radiation resistance

If current equalization and phasing are all there is to yagis we could not get more than 6 dbd gain (8.1 dbi) from a 2-element yagi. Yet a real gain-optimized 2-element yagi can only achieve a peak gain of about 5 dbd (7.1 dbi) since element currents cannot be equal and ideal element phase is elusive. Even in a Moxon, where currents are nearly equal, phase inevitably favours F/B at the expense of gain.

Indeed, currents and phasing alone can do no better than ~5.1 dbi forward gain, about 3 db less than the ideal maximum gain. Clearly there must be more to the story. The answer lies in the radiation resistance and its impact on antenna currents.

To get an idea of what is happening it is helpful to modify the source behaviour in our software modelling systems. EZNEC, by default, normalizes the source current to 1 A. It does this by adjusting the source power after calculating the antenna feed point (source) impedance. This is usually the preferred approach since it is helpful to work with a constant reference current when analyzing models. That is, wire and segment currents relative to a constant source current. EZNEC allows us to set the power to a constant and let the source current float. This is how we normally operate our transmitters, provided the SWR does not cause output power to be rolled back. It is also what we need to do to better understand yagis and gain.

When we do this and feed 100 watts to a dipole, a 2-element yagi (60° boom) and a Moxon rectangle we are presented with a set of element currents and impedances per the table at right. The yagi is the 2-element 6 meter yagi I designed and installed a few weeks ago, and the dipole is the driven element of the same yagi. The Moxon rectangle is an optimized design for 40 meters. All are modelled in free space.

There is some variation in feed impedances due to the different wire length to diameter ratio for these 6 and 40 meter antennas, but otherwise scale appropriately for our purposes. The table is a hybrid of EZNEC source data and segment currents.

The dipole impedance is less than 73 Ω due to being made from tubing (low length to diameter ratio). The slight shortness of the dipole (to accommodate a gamma match of the yagi it comes from) does not appreciably affect the current distribution versus a true λ/2 length. Ignore the reactance and you'll see that the current follows from the usual relationship: I = √(P / R).

Adding back the reflector we have a 2-element yagi for 6 meters, gain optimized for 50.1 MHz. Notice what has changed:

• Driven element current is 39.5% higher than the dipole.
• There is a reflector current that is 76.9% of the driven element. It is 153.9° ahead of the driven element.
• Feed point impedance has dropped by about half. R and X are suitable for the designed gamma match.

First, let's consider the driven element. The current increase represents a field increase of 1.95 (1.395²), which is close to 3 db. The impedance reduction is due to the mutual impedance with the reflector element.

This arrangement of parallel identical dipoles is a standard study for mutual impedance since it is a simple case. The mathematics involve solving a matrix (2 by 2 for two elements, and scales with additional elements) of complex impedances. One complication is that the induced current on the parasite induces a current back onto the driven element. A good mathematical derivation targetting the ham audience is by the late Les Moxon in his book HF Antennas For All Locations (Chapter 5). If you don't have his book (why not?) there is also a good description on Wikipedia. I'll simply note that for this 2-element yagi the mutual impedance (Zm) is about 60 - j10 Ω, for both elements. Zm is responsible for both decreased radiation resistance and increased Q.

Real yagis

The currents and phases in the yagi elements maximize neither gain nor F/B. There is in fact no 2-element yagi design that can accomplish both, or either one for that matter. The 3 key performance parameters of yagi design -- gain, F/B and impedance -- cannot all be optimized in the same antenna.

In yagis with 3 or more elements the adjustable parameters rapidly increase yet the same constraint applies. For example, if you focus on gain you will find that the impedance drops sharply, resulting in increased I²R conductor loss and require a matching network that will introduce additional loss.

For our 2-element yagi the reflector current relative phase (154°+60°=214°) and relative magnitude (0.77) differ from the ideal to achieve maximum F/B. This can be seen in the elevation plot below. The relative phase (154°-60°=94°) is also not ideal for maximum gain. In fact most of the gain is from the increased current (~2.9 db, due to the lower radiation resistance) than the element phasing (~1.8 db)!

The Moxon rectangle does better at optimizing all performance parameters. While the gain is 1 db worse than the yagi it does better on F/B and impedance. The free space elevation plots of both antennas are overlaid in the adjacent elevation plot.

The high F/B is due to the near equal currents (0.95 relative current in the reflector) and near-ideal rearward relative phase: -4.6°-(48°+124.9°) = 182.5°.

Current gain in the Moxon rectangle delivers only ~1 db, because the radiation resistance is higher than the yagi. The rest (~2.7 db) comes from reflector current and phase: 124.9°-(-4.6+48°) = 81.5° in the forward direction.

Note: For simplicity I am ignoring the forward gain and overall pattern impact of the inward-turned ends of the Moxon rectangle elements. The effective element lengths are shorter than in a conventional yagi, which reduces the broadside field strength. The effect is small since there is little current at the element ends.

It is not surprising that many hams prefer this compromise for small antennas. Larger antennas that incorporate high element coupling for optimum F/B and match include the Spiderbeam style of yagi and the OWA yagis used in some contest super-stations.

Stacking gain

Although I've written about stacking gain in an earlier article, I want to revisit it in the context of the current discussion. Let's place two identical yagis in free space, stacked far enough apart that their mutual impedance is 0 Ω. In the forward direction (centre of the main lobe) the far-field gain will be 3 db. I will break this down, step by step, to highlight interesting relationships between antenna current, radiation resistance and field strength.

Start with feeding just one of the yagis with 1 A source current. We then imagine a distant centre-fed dipole that has induced on it a current of 1 μA. For a receive antenna radiation resistance, transmission line and load (receiver) all 50 Ω, the voltage at the antenna terminals is 50 μV (S9). This follows from the Ohm's Law relationship: E = IZ.

Now we hook up the second yagi and split the transmitter power between them. The source current in both yagis will now be 0.707 A since we've halved the power and I, E ∝ √P. That is, I' = I / √2.

In the far field, directly in the centre of the forward lobe, the phases and magnitudes of the fields from both yagis are identical and can be summed (superposition) as scalars. Field strength will be proportional to 2 x 0.707 A = 1.414 A, or √2 A. At the receiving antenna the induced current will be 1.414 μA and the terminal voltage 70.7 μV. The equivalent power of the induced power is doubled, or S9 + 3 db, since for a constant load impedance P' = (E'√2)(I'(√2).

As always, conservation of energy applies, so that power must come from elsewhere in the antenna pattern. For vertically stacked yagis the main lobe is narrower in the elevation plane than for each individual yagi.

Ground reflections

It is widely known that over real ground a horizontally-polarized antenna exhibits gain over free space due to the sum of the space wave and ground reflection of equal angles. We are achieving gain by, in effect, constraining the free space pattern to one hemisphere. However, the doubling is only seen when integrating over the full hemisphere, and if the ground is perfect (zero loss). The gain and pattern depend on the antenna's free space pattern, height above ground, ground characteristics and local terrain.

One interesting difference from the stacking case is that in the case of perfect ground reflection the nominal gain is 6 db, not 3 db. This has two causes which we will look into. The first is height above ground.

For an antenna like a dipole or yagi the free space elevation pattern is symmetrical (mirror image) above and below the horizontal plane containing the antenna. For each ray of the upward space wave (positive elevation angle) the gain of the antenna is the same as the ray headed ground-ward at the same, but negative, elevation angle. Since the incident and reflection angles are equal these two waves will interfere in the far field.

For a phase difference of 0° the two rays deliver maximum gain (lobe centre). For a phase difference of 180° they will completely cancel (null). At all other phase angles the field strength will be intermediate between those values. Thus are lobes and nulls formed. Were it possible for the reflection to combine in phase throughout the hemisphere the broadside gain of the dipole would be 2.15 + 3 = 5.15 db at all elevation angles. Since the actual pattern has lobes and nulls and we are assuming perfect ground at least one lobe must have a gain in excess of 5.15 db.

Primary is a dipole 1.25λ above perfect ground; blue is a height of 1λ

A comparison of a dipole at different heights above perfect ground illustrates what occurs.

Since perfect ground inverts the phase of the reflected ray by 180°, in-phase superposition requires the path lengths of the space and reflected waves to differ by ½λ or every 1λ increment beyond that. Similarly, the first null has a path length difference of 0λ and there is a null at every 1λ increment. We'll place the dipole at heights of 1λ and 1.25λ, then compare their elevation patterns.

The dipole has a null at an angle of 0°, no matter its height, since the paths lengths are equal and the reflected wave is phase shifted 180°. All lobes have a peak gain of 8.15 dbi, which is the expected 6 db above that of the dipole in free space. The displayed 0.1 db gain difference of the two patterns is due to a plotting anomaly.

For the dipole up 1λ there are 2 lobes, for path length differences of 0.5λ and 1.5λ. More lobes require more height since the maximum possible path difference is 2λ, towards the zenith. For the dipole up 1.25λ there are 3 lobes, for path length differences of 0.5λ, 1.5λ and 2.5λ.

Clearly the 6 db gain in the lobes exceeds the simple reflection average of 3 db, and must be due to the pattern gaps caused by those deep nulls. It is the precise mechanism I want to focus on with respect to in-phase superposition of the space and reflected waves in the centre of those lobes.


Unlike stacking there is no power splitting. If the antenna current is 1 A the current in the dipole's image (ground reflection) is also 1 A. When the space and reflection rays are in phase the field strength due to superposition is now proportional to their scalar sum: 2 A. Thus the gain is 2² = 4, or 6 db. This is why the lobe peaks of the dipole are 8.15 dbi.

Over real ground there is some absorption of downward directed radiation. Ground absorption increases at low angles and poor ground.Also, phase inversion is no longer 180°. Phase increasingly shifts from that ideal as ground quality worsens.

Additional factors are that ground is non-homogeneous and terrain can be far from flat. Tools like HFTA are employed by many hams to get a true picture of pattern formation and ground reflection gain using detailed topographic data for their QTH. Fresnel zones for low (DX friendly) elevation angles come into play. At low incidence angles, reflection can be from a large area, not at a single point on the ground.

Yagi ground reflection gain can be very sensitive to ground quality and terrain since so much of the total radiation is concentrated in a narrow beam width. Since the (height dependent) lowest angle at which the space and reflected waves are in phase is not at the centre of the free space main lobe (the main lobe for a yagi in free space peaks at 0° elevation) the gain due to ground reflection in the first lobe will be less than 6 db. The higher the yagi, the closer one comes to the ideal. However, higher angle lobes are small since the yagi's main lobe has a narrower elevation beam width. Therefore picking an ideal height to reduce high angle radiation is less critical for yagis than for dipoles or other simple antennas.

Conclusion

The physical mechanism by which yagis develop gain and F/B are easily understood with the help of some mathematics and geometry. I believe this is useful knowledge to keep in mind when we design antennas or plan our antenna farms, whether large or small. Software modelling tools and the ready availability of the optimized designs can blind us from an understanding of important details of how real antennas behave, and how to best optimize gain.

Back on 6 Meters After 20+ Years

With about 50 QSOs and about 30 unique grid squares in the log (most in the ARRL VHF contest) since recently installing a small yagi I can truly say that I am back on 6 meters. Apart from 2 or 3 marginal QSOs made over the last year using a non-resonant HF dipole, my last activity on the band was in 1992. It was then that I dismantled my station for my long QRT period.

As I said in my yagi article, 6 meters was one of my favourites. My first experience was ~1974 with a borrowed AM rig (keying the carrier for CW-SSB cross-mode) and a dipole. That was enough to hook me. The next year I bought an FT-101B and found a used matching transverter, the FTV-650B. I operated occasionally until forced to QRT in 1979 when I moved to Ottawa. In 1985 I purchased a used fully-loaded FT-726R and a Cushcraft A50-6 that I mounted at 22 meters height. That's when the real fun began.

Some of the over 400 grids I worked on 6M from 1985 to 1992

I still have the A50-6 (I used bits of it to build the current 2-element yagi) but the FT-726R is long gone, being one of the few items I sold during the intervening QRT years. But enough reminiscing! I will now recount a few things about my current setup and how my experience compares to that of decades ago.

Activity level

There are a few changes I've noticed:

• The universality of HF+6M rigs encourages many more hams to at least experiment with 6 meters.
• The baby boomers are retiring, so there is more activity throughout the day.
• Many of those same hams, contesters and DXers looking for new challenges beyond HF, have been attracted to the diverse challenges of 6 meters.
• Global spotting networks alert everyone to openings. This is preferable to having a receiver sitting on 50.125 MHz hissing in the background all day long.
• There is more CW than I remember. This is good since so many of the openings are marginal.
• There is significant activity on weak signal digital modes (e.g. JT-65), allowing QSOs that might not be possible even with narrow CW filters.

These are all good things.

My particular challenges

My QTH is not ideal for VHF work. I live adjacent to a major river: the Ottawa River which divides VE2 and VE3. It should be obvious that is a low spot in the local terrain. Since the river is very wide there is no impediment to low-angle radiation over 3 quadrants, ranging (clockwise) between the southwest and the southeast. The fourth quadrant faces a hill and extended ridge line with a local peak higher than my tower about 500 meters to the south.

On HF this is not a concern for my operating. For contests the F-layer angle to the US is quite high. Beyond that, there is a negative effect to South America and long path Asia. I can live with that. However on VHF that ridge line blocks low-angle paths to the major source of QSOs. On VHF and up it's almost all low angle work. I often notice others in this area (grid FN25) hearing better than I do. This was also true when I had the larger tower and antenna years ago.

Another difficulty which I mentioned in the previous article is the long run (40 meters) of RG-213. This is a poor choice for long transmission lines on VHF. I estimate (not measured) up to -3 db of loss. Coupled with the 8 watts of my KX3, gain loss due to yagi interactions with the HF tri-bander and the modest tower height, I am at a disadvantage. I notice it. For example, stations worked by others in the same grid are too weak here or not heard at all.

Loss compensation

I have a deep junk box. It is full of parts and pieces of equipment collected over the decades. Although it's been a while I did remember something I once owned and could not remember selling. Some rooting around in various boxes yielded a small device that was sure to solve my problems. If it still worked.

That item is lurking behind the KX3 in the picture above. It's a 30-year old brick amplifier for 6 meters, made by TE Systems (it seems they're still in business). Years ago it was paired with the FT-726R to boost that rig's 10 watts to 170 watts. With 8 watts from the KX3 it would manage around 150 watts. But first I needed to find the manual and the interconnect cables.

The manual was found after another 10 minutes of searching, and another 10 to find the power cord with the correct connector for the amplifier. If there were other cables for other functions they are nowhere to be found. Luckily this amp has an RF-sense circuit to switch between receive and transmit.

Perhaps it was a miracle that everything worked perfectly, and perfectly together. The +13 db boost ensured that I could work pretty well everything I heard. More power would be overkill since my QRN level on 6 meters is up to S6 (SSB bandwidth) in the most important directions. The KX3's noise blanker does little to improve the SNR on this noise source. The TE amp's LNA is of no value due to that noise.

Culture

Because of who is on the band you find a variety of operating styles, associated with the culture from whence the ham comes. If it's a contester the speeds are high, the operating fast and efficient. The casual operator, who may have come to 6 simply because it was there to be used on a late-model transceiver, is slower, more prepared to chat and may need reminding to tell you his grid square.

The variety is itself very interesting though can cause some culture clash. A recent example is the ARRL VHF contest where some operators would send their name and state, which are not part of the exchange. So I give them my name as well. It's better to reciprocate than to appear rude. Others collect SMIRK numbers, but I don't have one to give.

I thing I would like is faster CW speeds by everyone. Although not everyone is capable of it, there is justification for speed. Conditions change fast on 6 meters. By sending at 20 wpm or less it is very possible to not complete the minimum information exchange for a VHF QSO -- signal report and grid square -- not to mention name, state and perhaps more. Among those with better CW skills some will send slower when conditions are marginal with the thought that it is more effective. That's true but often irrelevant if 15 seconds later the opening disappears! Perhaps this behaviour is due to an HF acculturation.

Time

Counter to the interesting challenges and rewards of 6 meters is one big disadvantage: time. Time to monitor, time to get on when the opening occurs, and time to catch that seconds-long signal burst for an elusive QSO. It's a good thing that real openings are concentrated from late May through July (Es) and around solar cycle maximums (F). It is no fun to be at the mercy of a fickle ionosphere.

I remember one time, two cycle maximums ago, when in mid-afternoon another 6 meter enthusiast called me at work. He held the phone next to the radio, so I could hear the band full of Europeans. He cooly advised me to go home and get on. This was a rare event. After hanging up I fretted. Eventually I gave my boss a semi-credible story, promising to make up the time later, hopped on my bike and hurried home as fast as I could. Luckily I caught enough of the opening to fill the log with plenty of DX.

The thing is I hate that: a band that decides when I must operate and not when I want to operate. At least in HF contests it's a calendar event that can be well planned in advance. Be wary of seeing your free time frittered away should you venture onto 6.

Even when there is an opening you can spend a lot of time scanning around and hearing nothing. When you hear talk of all the openings during Es season do keep in mind that the majority of marginal. You listen and listen, then you call CQ and call again. Turn the beam a bit and repeat. When that weak signal pokes above the noise and you log one from across the continent or across the ocean it does feel good. However the time involved can be ridiculous.

Nowadays it helps that global spotting networks can be monitored on a smart phone so you can be alerted of an opening no matter where you go. Then you have to decide whether to head to the shack to work (or fail to work) someone.

Be prepared for the time investment to get the most out of 6 meters. Only you can decide if the rewards are worth it.

Finally

As I listen and call, again and again, I ask myself whether 6 meters is worth the effort. I am trying to limit the time I pay attention to the band, and I am not shy about tuning HF while also calling CQ on 6. If the band is marginally open, or open to someone not too far from my QTH, sometimes someone will answer. For example, today I worked a few stations on the US southwest (double-hop Es) just that way.

By budgeting my time I hope to avoid burning more time than I ought to on 6. But then it's only for another month. Then the antenna comes down for the season. I don't want the additional wind load for most of the year when prospects for an opening are poor. Yet, as I write this, HF conditions are rapidly degrading. This is another reason to give keep the antenna up, by allowing me to get on the air when HF opportunities are poor. Who knows, with the rapidly increasing geomagnetic storm conditions there may even be an aurora opening very soon.

Solstice Antenna for 6 Meters

From 1985 to 1992 I was very active on 6 meters. I enjoyed the propagation surprises it offered, including some fascinating DX. I worked hundreds of grid squares, worked every province and territory, all US states, all but one continent and about 65 countries. I'd have worked many more countries had there been more countries that permitted the band to their hams back then. In short, 6 meters was one of my favourites.

Since returning to the air in late 2012 after 20 years absence I occasionally pondered putting up an antenna for 6. I have made a few contacts using my KX3 and antennas for the HF bands though not without difficulty. After putting up the new tower in 2014 there was no point since the sporadic-E season was long past its peak. So 2015 is the year to get it done.

With the CQ WPX CW contest out of the way and no other HF contests I want to enter the rest of the summer I have an opportunity. These seemingly unrelated endeavours are connected by the availability of transmission lines on the tower: a yagi for 6 will need to use the coax currently feeding the 80 meters half sloper. Of course that means this is a temporary configuration that I will undo once the mid-summer (solstice) sporadic-E season is over.

Thus my objective of a "solstice antenna". It has to be small yet effective. Some trade-offs are allowed since it will be in place for only 2 months. These are the challenges I must deal with:

• Use only parts on hand. This, as we'll see, is the easy part.
• It must go up fast and easy. Sporadic-E season is right now so time is of the essence.
• Design or copy the design of a small yagi.
• Tune and optimize performance.
• Interactions with the Explorer 14 antenna sharing the same mast.

I'll walk through the steps to get myself back on "magic band".

Parts on hand

As I said above, this is the easy part. It's easy since I still have the yagi I used so many years ago: Cushcraft A50-6. That's a big antenna (1λ boom length) and unsuitable for the present circumstances. But with all those parts it is quite easy to build a smaller yagi.

In fact all of the parasites are mechanically identical, only requiring adjustment of the element tips for tuning. The centre section is 4' ( m) of 3/4" (19 mm) tubing and the tips are 5/16" (16 mm) tubing. The boom can be built by selecting tubes of the total 20' (6 m) original boom length. Alternatively another tube, aluminum or other non-conducting material can be substituted. There are numerous options to choose from my junk box.

Speed

I will not dawdle with this antenna. I aimed for fast turnaround from concept to on-air. This objective not only explains why I would only use parts on hand but also my focus on tried and true designs. For example, while a Moxon rectangle is light, small, easy to feed and simple it would require fabrication and some experimentation with design and tuning.

For this reason I chose to stick with a yagi, one based on an existing Cushcraft design. If that latter point seems odd keep in mind that the tubing schedule affects element resonance and I have Cushcraft elements. So all I needed was a Cushcraft manual for a yagi smaller than the A50-6.

Primarily for reason of interaction with the Explorer 14 (see further below) I opted for a 2-element yagi rather than a 3-element yagi. Other reasons are to keep wind load to a minimum (1 ft² in this case) and a 1 meter long boom is easy to lift straight up the tower between the guy wires. The 2 meter boom of a 3-element yagi would require more work to get past the guys. The sacrifice of up to 2 db gain is acceptable for this temporary antenna. Bandwidth and F/B are unimportant and were ignored in the design.

Design process

With the decision made on the antenna type I looked online for an A50-2 manual and...there is no such product. The smallest Cushcraft yagi is the A50-3. Unfortunately you cannot make a 2-element yagi from that by simply removing one of the parasitic elements. Antenna resonance will drastically shift. This called for some computer modelling.

In a typical 3-element yagi the director and reflector elements are resonant at equal distances from the centre operating frequency. In the case of the A50-3 these are approximately ±4%. Since in a 2-element yagi with a reflector the reflector should be resonant at the centre operating frequency, or +4% from where it is in the A50-3. However that is an approximation.

Dimensions for the Cushcraft A50-3

What I did was take an optimized 3-element yagi model of similar dimensions and remove the director. I then adjusted the reflector length to re-centre the antenna at the desired frequency. I found that for a gain-optimized spacing of 0.17λ (1.0 meter at 50.1 MHz) the resonant frequency needed to be shifted upward by 3%. Since I don't know that the A50-3 dimensions for the low end of 6 meters are what I want it is risky to shorten the reflector by 3% and expect the tuning to be correct. The element must be precisely modelled.

Unfortunately NEC2 does not correctly calculate reactance on wires made from telescoping tubing. It is necessary to use EZNEC's Leeson stepped diameter correction feature. I did this, following the necessary design steps to ensure the correction can be applied and would be reliable. The metal boom was added to the design since that can have a small effect -- the boom increases the effective element diameter where they cross.

I modelled the A50-3 reflector as a standalone element, confirmed the frequency of resonance was where it ought to be (~49.8 MHz), then shortened the outer tube sections by 3%. I added the driven element, using the A50-3 dimensions, 1 meter in front of the reflector. The boom was extended up to, but not touching, the driven element. The boom cannot connect to the driven element in a model with the split source required for the Leeson correction.

To my surprise the gain and F/B performance centred right where I wanted them. Free space gain is 6.9 dbi. The antenna impedance was also as expected from theory, ranging from 33.8+11j Ω at 50.0 MHz to 37.0+18j Ω at 50.3 MHz. The reactance is likely inaccurate, due to the boom. Even so I expected the impedance would be within the adjustment range of the gamma match -- I was almost right, as we'll see. Impedance declines as the boom length is shortened, and might be required if a match cannot be obtained (the A50-6 has a lower impedance and this gamma match is from that antenna).

The elevation plot of the 6 meter yagi at its intended height of 14.1 meters is on the right. There are many minor lobes at higher angles due to the wide beamwidth and being 2.4λ high. For the same reason the modelled ground loss models as -1 db.

Tuning it up

The antenna does not need to be high off the ground for tuning. Even 2 meters (0.35λ) is enough to ensure that the tuning will be the same when raised onto the tower. Adjusting the antenna at this height is easy. It is only necessary to get your body out of way to take measurement (your body couples to the antenna) and to keep some free air around the antenna so that the environment does not interact.

The test setup is shown at right. Antenna work on the deck on a sunny warm day is a pleasant activity. The KX3 and an SWR bridge are on a table. Notice that the reflector is nearest the house so that open air is in front of the antenna. This minimizes interactions with the house and deck. A step ladder is used to make adjustments to the elements and gamma match. It must be moved out of the way each time to avoid interactions. A fibreglass ladder would be a better choice.

I adjusted the reflector tip length to 83 cm per the model as adapted from the A50-3, as discussed above. For now I have to trust that this will place maximum gain at 50.1 MHz since I have no easy way to confirm it. If I'm off even 1% (500 kHz) the gain remains near maximum. One way to test that reflector tuning is not wildly off is if the gamma match can't come close to achieving a good match at 50.1 MHz.

I couldn't get the SWR lower than 1.2 at 50.1 MHz with the gamma match alone (maximum capacitance at the best impedance tap point). I shortened the driven element 5 mm per side to get the job done. SWR is no more than 1.1 at 50.15 MHz. Since the required bandwidth is narrow (0.5%) the SWR is near perfect from 50 to 50.2 MHz.

I did have a bad interconnect cable that created an impedance bump between the rig and SWR bridge so the rig's SWR bridge read a higher value until I fixed that problem. I recommend testing all coax or you could end up wasting a lot of time with fruitless tuning. Sometimes coax that tests good at HF shows an anomaly at VHF.

As a last test I raised the antenna by one more 4' fibreglass mast section. As expected the impedance was unchanged. If 6 meters had been open I should have been able to work someone. The band was dead so I dismantled the test setup.

Interactions with the tri-bander

This antenna will have to be positioned close to the Explorer 14. When mounted directly atop the mast bearing it is only 80 cm below the tri-bander. Interactions are inevitable. The expected risk was more on 6 meters performance since it's the smaller antenna. However I did have some concerns about the Explorer 14 para-sleeve, which is short and could compromise 10 meter performance.

I used EZNEC to place a model tri-bander and the new 2-element 6 meter yagi together as they will be on the tower. Although I know that the model cannot be accurate I want to at least identify areas of concern. The model should be sufficient for that even though the Explorer 14 is not the same as the model tri-bander.

The current plot above is with the 6 meter yagi fed at 50.1 MHz. This is the worst case condition which I will further analyze. I was gratified that the effects of the 6 meter yagi on 20, 15 and 10 gain and impedance were negligible. Even the F/B, which is the most sensitive performance parameter, was little affected, even on 10 where interactions are maximum.

The presence of the tri-bander has a more profound effect on the 6 meter pattern. Somewhat surprisingly the effect on impedance was very small: only 2 or 3 Ω in both real and imaginary components. When the antenna goes up this can be easily confirmed, more easily than gain can be.

While small in magnitude the current induced on each of the tri-bander's elements has a significant impact on all aspects of the pattern. To see this more clearly I moved the model to free space then overlaid the patterns with the tri-bander absent and present. It is perhaps unsurprising that the tri-bander elements acted as weak reflectors, tilting the elevation pattern downward. More interesting is that the side nulls common to any dipole or yagi with dipole elements have been filled.

When returned to real ground and the stack at the design height the 12.57 dbi gain shown earlier was reduced by -1.5 db. This is not desirable though I am prepared to live with it as a temporary way to get on 6 meters this summer.

Since I did not include a boom in the tri-bander model I chose not to model interactions with the 6 meter yagi rotated 90°. I may try this arrangement after the antenna if the interactions prove to be a significant problem.

Up in the air

Not a pleasant perspective for those with vertigo

From start to finish this project spanned 7 days. Design and testing were the largest tasks. Actual time spent was minimal. The biggest gap in that week was between completing tuning and hauling it up the tower. The weather was fine Sunday morning and I had a couple of free hours so I went ahead and installed it.

The first thing was to orient the antenna so that it would not tangle the guys during lifting. Without help on the ground to pull the antenna outward at critical points this can be a problem. I had just such assistance the previous day when I put up an antenna for another ham that had to be steered around various obstacles.

I rigged the rope so the element ends were pointing upward. Of course it all went awry when I got to the top of the tower and pulled. With such a short boom I was still able to maneuver it by jostling and swinging the rope. This would have been much more difficult if I had built the antenna with 3 elements. So far so good.

The next problem was the stacking distance. I neglected to account for the mast bearing height and tri-bander distance below the mast apex in my interactions model. Even with the small boom-to-mast clamp the vertical distance between the yagis is 60 cm (2'). Not surprisingly this increased interactions, easily seen by the increased SWR.

The coax for the drip loop is a bit short. I chose it anyway to avoid having to make a new one. To compensate I slid the boom so that the driven element is closer to the mast. I couldn't get too close or the gamma match would touch the tower! Asymmetry in such a small antenna will not unduly stress the rotator.

After sealing all the coax connections and securing the cables I came down the tower to test out the antenna.

Testing it out

The 40 meter (130') run of RG-213 is less than ideal for VHF. The loss for this run calculates to -1.9 db. Although the cable is good it is old so let's say that the loss is -3 db. With a shack-measured SWR of 1.3 the overall transmission line loss is still approximately -3 db. The 8 watts from my KX3 is only 4 watts at the antenna. Receive sensitivity is reduced by the same amount.

There was a marginal sporadic-E opening at the time I was testing the antenna. I did not attempt a QSO since signals were weak and fleeting, unworkable with my low power. Instead I compared received signal strengths versus my other, non-resonant antennas. On that basis the antenna was working, though perhaps not as well as I hoped. A better assessment of gain is difficult form this test since the Explorer 14 on 6 meters is so large that its pattern would be quite complex, and likely has gain in some directions.

To be continued

Later Sunday there was another opening. This time I made one QSO. That at least showed it is doing something right. For what it's worth I was complimented on my QRP signal.

Since this is a temporary antenna I declared that, for good or ill, this project is a success. I'll be back with an update once I get to work a better opening, including checking its F/B. I am even considering playing in next weekend's ARRL VHF contest. If 6 meters opens.

CQ WPX Contest: To Love It or Hate It?

I did a semi-serious QRP effort in this past weekend's CQ WPX CW contest. This is in any case a relatively relaxing contest for a single operator entry with its 36 hours operating time permitted out of a possible 48, I was also not fully committed to putting in an effort until well into the contest period. So I was in mellow mood. That the weather was less than ideal I was comfortable with the idea of staying indoors at a time of year when I'd rather be outside.

As it turned out I operated for 30 hours. Propagation was such that I took frequent breaks during the day due to poor propagation for QRP (good long openings but with poor signal strength), including a lack of 10 meters due to the low solar flux.

CQ WPX is a fun contest, though it is not without its peculiarities. What follows here is not a criticism of the contest or its exceptional management. It is just that the environment has changed around it. Let me start with a brief background for those unfamiliar with the contest, the WPX operating award with which it is bound and how amateur radio licensing has changed over the years.

A brief history

When I was contesting more seriously in the 1980s the WPX contests were 2 of the 4 major contests with a truly global feel and participation. the others were the CQ WW contests also sponsored by CQ Magazine. In comparison the ARRL DX contests were, and remain, second tier contests due to their effectively being large North American QSO parties.  The 4 majors were the sole focus of a multi-op team effort I was part of in the early 1980s: VE3PCA.

Many other contest teams around the world had a similar focus. If you were a DXer and also a serious competitor these were the contests you most cared about.

The rules are simple enough: everybody works everybody. QSO points are roughly proportional to QSO difficulty (country, continent, band), with multipliers being call sign prefix. For example, my prefix for a multiplier is VE3. Others would include W3, UA0, UA9, PY1, and so on. Obviously just by virtue of being in a country affords you a distinct call sign and therefore multiplier value. Larger countries with more hams have more prefix ranges assigned, allowing more equitable distribution of multiplier value. This means that a W1 or a WA2 can be as valuable as a G8 or a BY1.

What changed

In the 1990s in the wake of political changes amateur radio energies were fully unleashed in a wide swath across Europe and Asia. Lots of new super-stations sprouted up over the following decade. Elsewhere in the world rapid development in formerly third-world countries amateur populations rose and added new ranks to the global pool of contesters, and newly workable prefixes.

Just as many contesters flock to semi-rare and rare countries for CQ WW contests to become an attractive multiplier, and so boost their scores, something similar occurred in CQ WPX. Many countries' governments were persuaded that supporting radiosport was desirable. That they could do so by a simple and inexpensive administrative procedure was attractive. Thus the appearance across the world of "contest call signs".

Contest call signs, often only permitted during contests, were designed to be beneficial. Typically they are 1x1, 1x2 or 2x1 calls that are easier to copy and faster to send. This is good for them and for those contacting them. Examples include: G9W, LY2A, C4Z. There are countless others. These stations are in addition to the entrants using their usual call signs. Prefix multipliers proliferated.

Other countries, notably the US and later Russia, made the issuance of 1x2, 2x1 and 2x2 call signs routine for higher-class licensees or by application.

The result

Prefix diversity is exceptionally high today. It is so high that it is common in CQ WPX contests to have almost every QSO count for a prefix multiplier until well into the contest. The multiplier acquisition rate never does slow down that much throughout the weekend. In my case I logged 823 QSOs and 488 of those were multipliers. That's a phenomenal 59% of QSOs that were multipliers!

Among the top scorers a multiplier count over 1,500 is becoming common. Their multiplier to QSO ratios are still 20% to 25% despite working as many as 8,000 stations.

In my opinion multipliers in CQ WPX have become too easy. When everyone is a multiplier no one is a multiplier. To win in this contest you have only to focus on bulking up on QSOs. Taking time to find and work multipliers is not worth the time investment. The new strategy is to be as loud and fast as you can be. That creates long, deep runs to run up the QSO totals.

As I put it in my soapbox comments accompanying my entry for this weekend's contest:

My strategy was to ignore most of the world to focus on Europe and the US. Prefixes aplenty were there without chasing DX with weak propagation. Put another way, I solely focused on QSO total and let the multipliers take care of themselves.

It works as well for QRP as for the super-stations to focus on QSO-rich areas.

It doesn't require great intelligence to discover this strategy. This contest is widely understood to be one about high rates and dominating signals. While these are winning factors in any contest it is more true in CQ WPX. A modest station from a perfect location on an African shoreline is worth no more a VO1, and both will struggle to do well in this contest.

The proliferation of prefixes has perhaps done some damage to this contest by making it less valuable to be in a relatively-isolated global locale such as Japan or one with only modest amateur numbers such as South America. There is little downside in score potential by not bothering to turn the yagis in those directions.

I know that it reduces the contest's appeal to me, and it would seem many others in many less-populous regions who choose not to bother with it. Many would fervently disagree with my opinion. The fun and success they experience is not something I would want to dampen. However, as things stand I have more fun entering an ARRL DX contest than CQ WPX.