Fall Antenna Plans: 80 Meters

Now that the 80 meter half sloper is reconnected (I had borrowed the coax for the 6 meter yagi over the summer) I am reminded how awful an antenna it really is. This is a good time to consider alternatives since the noisy summer conditions are still prevailing on the low bands, and will continue for a few more weeks.

To summarize, here are the problems I have with my half sloper:

• The antenna has a significant horizontally-polarized component in many directions. Despite the use of the tower as a major component of the antenna it seems that the wire can often dominate the far-field pattern. Much of the antenna's radiation is at high angles, which is not what I want.
• There are substantial ground losses which severely cut into its efficiency. I am comfortable claiming this based on its on-air performance, feed point impedance (presence of series ground loss resistance) and the software model. NEC2 often has been reported to underestimate losses from real ground, yet even so the modelled losses are substantial.
• Antenna bandwidth is modest. It is cut to resonance within the CW segment (3.5 to 3.6 MHz) and does poorly in the SSB segment (3.8 MHz). I've tried the FT-1000 MP's ATU and an external antenna tuner with poor results. I can match the antenna for SSB, but the matching and SWR loss seem quite high. While adjusting feed line length might help, I'd rather have a broadband match.

These are problems whether I am contesting with QRP or DXing with 100 watts on 80 meters. Both have been frustrating. I had higher hopes for the half sloper. In retrospect I feel my initial optimism was misplaced. Now it's time to do something about it.

Options

As I move lower in frequency my options become increasingly constrained by my available supports and property. Just moving a factor of 2, from 40 down to 80 meters, I can pretty much rule out all horizontal antennas. They will either do no better than what I have or will destructively interact with may high band antennas. Interaction is unacceptable since 80, for now at least, is less valuable for QRP contesting and for DXing.

Regardless of the antenna I choose, horizontal or vertical, ground losses must be addressed. The ground directly under all my antenna is poor, not the medium ground I typically use in my models. I model that way to make the results meaningful for most readers of this blog. My lot is backfilled with sand (septic tile bed) over shale. Soil is only 12" (30 cm) deep.

Do not be deceived by advertising for commercial vertical antennas with "no radials" designs and that have elaborate matching networks, or any home-built antenna that does not require radials, such as a delta loop or half sloper. You cannot so easily dismiss ground interactions, and the inevitable loss.

Radials are needed, although I don't want them. There is too much traffic in my backyard to have wire lying on the surface, even if it is worked into the grass and weeds. Burial is out of the question at this QTH since it would tear up the lawn for what is likely to be a brief deployment. A vertical would have to use the tower that is centred in the yard since it is the only location where radials of any kind can be placed.

As I said, my options are limited. Whether I like it or not I have to go vertical and find a way to put down some radials. This is the only way I can hope to improve low-angle radiation and reduce ground loss. Reducing local noise (QRN), which can be quite severe during the evening, is out of the question since I have no space for a directive receive antenna. With QRP that's rarely a problem since I am far more concerned with being heard. A separate, directive receive antenna is of little value for the same reason.

My objectives for the 80 meter antenna:

• Low-angle radiation suitable for DX. I only need enough high-angle radiation to make contest contacts with the nearby US northeast and midwest.
• The minimum radial field to reduce ground loss to an acceptable level.
• Feed system to achieve a 50 Ω match from 3.5 to 3.8 MHz, for the tower, top loaded with a tri-band yagi, and assorted cable runs.

With those points in mind we are ready to proceed.

Resonance

There are so many variables to determining the resonant frequency of a vertical constructed from a tower and yagis that it is often best to just go out and measure it. Unfortunately this requires that the radial system be in place. For a small number and length of radials the radials play a substantial role in determining the resonant frequency. With more and longer (λ/4) radials the radials tend toward non-resonance, leaving the monopole itself as the principal tuning variable.

Calculation can get us close, or at least close enough to guide the design of the radial system and feed network for a tower with a yagi on top. There is a formula for this in the 1st edition of ON4UN's Low-band DXing, page II-32:

L = 0.38f ( H + SQRT( S ( 1000 - H ) / 500 )

L is the electrical length in degrees (λ/4 = 90°), H is the height in feet, S is the area of the yagi in square feet, and f is the frequency in MHz. This formula is not in the 5th edition, having been replaced by a graph for a more restricted range of figures. My guess is that this was done to discourage readers from applying the formula to extreme cases where it is inaccurate. Therefore only use the formula as a rough estimate.

Per this formula, my tower plus mast height of 15 meters, with an Explorer 14 at the top, has an approximate electrical length of 105° at 3.65 MHz. It should therefore be resonant below the band edge. This is close enough to λ/4 to allow a simple matching network. I like that.

However there is more involved in getting a good match on a ground mounted vertical. With a small quantity of radials the radial length contributes to the resonant frequency. With more and longer ones the radial system becomes non-resonant. I will have a few short ones, so it matters.

Ground loss

There are ample resources in the amateur literature about ground loss and the mitigation of ground loss. One in particular I like is the 5th edition of ON4UN's book. On the internet, one good place to look is the series of articles by N6LF. Read them if you have or intend to build a vertically-polarized antenna for the low bands. I will only say a few words here that are specific to my situation on 80 meters.

Z = ( Rrad + Rgnd + Rant ) + jX

The resistance term R in the antenna feed point impedance Z is composed of 3 series resistances:

• Rrad: Radiation resistance
• Rgnd: Ground loss
• Rant: Conductor and ESR (equivalent series resistance) loss in the antenna and matching network

For a typical λ/4 vertical monopole with a perfect ground plane the radiation resistance is 37 Ω. Ground loss due to poor ground or ground plane can be larger than the radiation resistance. Conductor loss is typically negligible for an antenna of this type, however capacitors, inductors, transformers and transmission line stubs in the matching network (especially for short verticals) can also be quite large.

The only way to manage loss outside of the near field (far field ground reflections) is to move to a better QTH! This is outside of my control for the time being, as it is for most hams. What I hope to manage is near field ground loss close to the antenna. This is where the radials come into play.

Using EZNEC, I built a model of a vertical with two grounds.The first ground, out to 8 meters distance from the tower, is poor (0.002, 10) to account for the sand fill and bedrock. From 8 meters outward I use a medium ground (0.005, 13). The intention is to approximate near-field ground losses without distorting the far-field pattern. That's the best I can do, knowing that nearby buildings are within the near field. But then that's true for any low band antenna on my property. There is a significant change in ground loss when the media parameters for that inner ground are varied.

Matching network components should be selected for their low ESR. It is a mistake to only pay attention to the component values and their maximum voltage and current ratings. Transmitting capacitors (fixed or variables) and high-Q coils are best. The loss is there at all power levels so don't take shortcuts if you, like me, operate QRP.

Radial system

The radial system is unlikely have more than 8 radials. Their maximum length is limited by the size of my backyard and fixtures. Toward the south I can go quite long. North toward the house allows lengths up to 15 meters, and shorter where I have the deck and and landscaping. The main limitation is east and west, where the maximum possible length is 7 meters. Although my lot is ¼ acre it is only 15 meters (50') wide.


With this constraint my choices are to go long where I can and short where I cannot, or to choose equal but short lengths for all radials. The question is which does better? Radial asymmetry is something I've dealt with before, its good and bad points. Once again, EZNEC helps to answer this question.

In the view at right (with currents plotted), X is east and Y is north. My lot is 15 meters wide along the X axis. My house is about 15 meters north of the tower. Going south, there is about 25 meters of available space.

In this first model wires #2 and #4 are 7 meters long. The diagonal wires are 10 meters long and wires #3 and #5 are 15 meters long. It turns out this is a poor arrangement.

Most of the radial current is in the 6 longest radials, with almost no current in the 2 short ones. When the current is so low their effectiveness is quite poor. Snipping those two wires from the models had a negligible impact on ground loss (-0.1 db). The azimuth pattern is omni-directional for all reasonable arrangements of 6 or 8 radials. It is just ground loss and resonant frequency that are effected.

When the two longest radials are reduced to 10 meters length the current becomes more equalized and ground loss is slightly reduced. The relative current flowing in the 7 meter long radials is also higher. I decided to proceed through the rest of the modelling with this arrangement.

Antenna feed and matching network

For the typical shunt-fed tower it is necessary to use a gamma or omega match since the tower is not isolated from ground. The combination of electrical continuity into the concrete-embedded tower base comprises a Ufer ground. My tower is isolated from ground, though not in an ideal fashion. The preserved wood base is a poor conductor, even when wet, and its ground contact area is less than 1 square meter.

It may be worth an experiment to feed the tower directly. If the feed point impedance at resonance comes reasonably close to 50 Ω I'll take it as an indication that the tower's ground isolation is acceptable (see below).

To begin the analysis I added a radial system to a vertical monopole in EZNEC. The radial system has 8 radials of 10 meters length, except for the east and west radials which can only be 7 meters long (see discussion above). Since the radials in this configuration affect system resonance, the monopole must be tuned once the radial lengths are set.

The SWR plot above has the monopole adjusted to an electrical length that is resonant at 3.6 MHz.Notice that the feed point impedance is 60 Ω. This is 23 Ω higher than the 37 Ω of a ground-mounted vertical with an ideal (zero loss) radial system. Assuming this reflects reality (which is unlikely) the near field ground loss would be approximately -2 db. This does not include other environmental loss, such as nearby houses and ground reflections beyond the near field. The true ground loss almost certainly will be greater.

Ground loss is undesirable. Yet if it can't be avoided we can at least use it to our advantage. As the cliche goes, when life serves us lemons, make lemonade! Here we find that the ground loss makes it possible to achieve a broadband match to 50 Ω coax without a matching network. This is not unlike some commercial tri-band yagis where the trap loss permits a direct match to 50 Ω coax even though the radiation resistance may be half that value.

All we now must do is add a series capacitor (between the coax centre conductor and the tower) to compensate for the inductive reactance due to the tower's resonance at a lower frequency. The capacitor would be adjusted for minimum SWR at the selected centre frequency of 3.6 MHz. Tuning can be done with a variable capacitor, and then substituting a fixed capacitor of the required value.

Should direct feed result in a higher SWR (due to actual ground loss or excessive ground interaction at the tower base), a gamma match is the next best bet. The estimated requirement is a gamma rod (or wire) about 7 meters long, a series capacitor to tune the gamma match and tying the radial system to the tower base.

In the unlikely event this is insufficient, an omega match would be required. Were I to attempt to shunt feed the tower on 160 meters, an omega match would certainly be required since the electrical length of the tower would only be 53° at 1.85 MHz. The additional capacitor would add loss, though it would be small in comparison to higher ground loss of the small radial system.

Transmission line

In an ideal vertical installation the coax transmission would be buried to minimize antenna coupling, and would have a substantial common mode choke at the base of the vertical. My situation is far from the ideal, and that may be okay. The coax will have to run overhead, in parallel with all my other cables out to the tower, to avoid damage to the cable and to people.

Some amount of coupling and therefore common mode current is going to be unavoidable. Even were I to follow the ideal for this one antenna, there would still be coupling to the several cables running up the tower to the rotator and other antennas. I have that very situation today with the loaded half sloper antenna for 80. There is coupling, though not enough to be a problem. Running a kilowatt would change my opinion, but that won't happen.

In all likelihood I will run the coax overhead, with all the other runs, and have it dip down toward the feed point at the tower base. Since I will be using a 130' (40 meter) length of RG-213 there will be enough spare coax to wind a coaxial choke. That choke must not be "scramble wound" because the inter-turn capacitance would render the choke ineffective. However, I am unconvinced that a properly wound coax choke is worth the trouble because I know there will be coupling back to the shack on the other cables. This decision will be deferred until I build the antenna.

The plan

I'll be removing the half sloper when I am ready to install the second 40 meter inverted vee. I plan to do that in the next two weeks (early September). When that is done, and the septic tank is pumped, I'll be ready to proceed with the 80 meter vertical. Allowing time for experimentation and a further delay toward the end of lawn mowing season, I should have radials in place and the antenna ready by early October.

Elevation pattern of my tower vertical with the ground,
radial system and feed system discussed in this article

One problem I foresee is the ability to confirm performance with a reference antenna. Unfortunately the half sloper cannot be kept as that reference. Using a 40 meter antenna with a tuner is a poor alternative since, in earlier testing with this arrangement, its performance is very poor and therefore unsuitable as a reference. I have no good third alternative.

Based on models alone, it appears I can expect at least 3 db low-angle gain improvement, and probably more, in comparison to the half sloper. Some of that comes from the switch to vertical polarization and the rest from reduction of near-field ground loss by using radials, poor as those radials must be.

I may have to roll up the radials when not in use, at least until early November when people traffic in the yard is no longer a factor. Then it'll be safe until spring thaw.

Once the antenna is built, tuned and I have some performance observations from on-air use I will follow up on this article. You can then compare my modelling alternatives with my final choice of feed and radials.

Fall Antenna Plans: 40 Meters

Fall is rapidly approaching. For me that means preparing the antennas for fall and winter contests, and the occasional DXpedition. Summer has been a down time for my radio activities, with travel, home improvements, sports and other activities. The articles in this blog have been sparse. Now is the time to get serious about antennas.

The 6 meter yagi is now out of the way, making room for other antennas. There is little I can do for the high bands (20 through 10 meters) with my current supports so there will be no changes for those antennas. It is 40 and 80, and possibly 160, where I desperately need improvement. This is especially true if I again enter the QRP category in the major contests. On these bands every decibel counts when others can barely copy me, or not at all.

Final decisions have yet to be made. Options are limited, as are the performance improvements. I'll take you through my thinking at this stage so you'll understand my choices. Later, when the antennas are built and tested, I'll relate how I came to do what I will have done. In this article I'll discuss 40 meters, deferring the other bands to future articles.

Pattern

My only antenna for 40 at present is a multi-band inverted vee at an apex height of 14 meters. One end is tied to the tower and the other to the house eaves. It is asymmetrical, though not by a lot. It is enough to skew the pattern, as you can see in the adjacent plot.

An inverted vee is not really an omnidirectional antenna, even if it is often billed as such. It is only more so than a dipole. You can read how I came to choose this antenna in an article I wrote in 2014.

Notice the azimuth pattern, at a DX optimum elevation angle of 10°. I set up the EZNEC model so that east is to the right. The antenna is replete with compromises.

Europe is down -2 db from where it peaks, as is much of the US. Asia is down -5 db and the southern US, Caribbean and South America are even worse. My operating experience tells me quite clearly this is hurting my contest scores and DX performance. I need a better or a second antenna to fill these gaps.

My best options are as follows, as constrained by my property and supports. There will be no new tower at this QTH this year, and perhaps never.

• Inverted vee: Mounted at the top of the tower this antenna would have the same 14 meter apex height as the multi-band inverted vee. Made symmetric with an interior angle of 90° it would be oriented to be at approximately a right angle to the other inverted vee. In this way interaction with the tri-band yagi on 15 meters above it and the vees would be small. While a tight squeeze I have tie off points selected that would make this work.
• Omega-tuned boom dipole: This involves extending the boom of the Explorer 14 by at least 6 meters and making an omega match with the tap being a wire tied to the end of the existing boom and angled downward to the mast just above the mast bearing. This is a tried and true design that I previously considered but rejected because of the complexity of raising the extended yagi. That remains a task I am loathe to tackle.
• Rotatable dipole: The driven element of my recently-purchased Cushcraft XM240 can be mounted alone on the mast and rotated. It would be mounted parallel to the yagi's boom to avoid interaction, which I've modelled and seen that it is quite severe on 15 meters though acceptable on 20 and 10. At 43' long (13.5 meters) it fits within my 50' wide lot but in windy conditions could tangle with the trees that serve as the tower's guy anchors. Some careful measurement would be required. The wind load is substantial (~3 ft²), so it would have to come down after the winter season, before spring and summer storms arrive.

All of these antennas would have a feed point at the top of the 14 meter tower (DMX-52) that currently supports a Hy-Gain Explorer 14. The RG-213 transmission line is what was used for the 80 meter half sloper and was temporarily used for the 6 meter yagi. That coax is now free since I have other plans for 80.

I modelled the inverted vee and rotatable dipole in EZNEC and overlaid them on the azimuth pattern of the existing inverted vee. All are at an elevation angle of 10°.

First, notice that the inverted vee on the tower has less gain at low angles. This is because the interior angle is smaller than on the multi-band inverted vee. The difference is about -1 db. Due to that and constraints on tie off points, it does only a modest job of filling in those pattern gaps. Northwest and southeast are worst.To the north the improvement is just 2.5 db and to Europe there is no difference. Where the new antenna does well is to the south where it is ~6 db better. This pattern of this inverted vee is more omnidirectional due to its symmetry, a symmetry that might not survive real-world interactions.

As expected the XM240-derived dipole does best, since its average height is higher than the inverted vees. Even with the coil loss (-0.36 db) the dipole gain peaks 0.5 db better than the multi-band inverted vee. (NB: in an earlier article we saw that a dipole typically beats an inverted vee with a 120° interior angle by 1 db.)

The performance improvement comes at the expense of wind load and the need to rotate the dipole to get the most from it. Of course with both antennas online it is possible to switch instantly. At times when both high and low bands are open there is the additional matter of the dipole pointing of the side of the tri-band yagi. But it does allow working the US and points north and south while the yagi is pointed to Europe.

Interaction

The model view at right, with currents, shows the high coupling when the dipole is rotated to where both antennas are in the same plane. It turns out that interactions are a major determining factor as to which antenna I will go with. This can, and does, degrade both antennas' performance.

The nearness of the ends of the dipole and inverted vee is not due to perspective; they are ~3 meters apart (the vee is tied off to the tower). For model simplicity the other elements of the multi-band vee are omitted since their effect is negligible.

To test this out in the EZNEC model I fed each antenna in turn to estimate the effect of interaction. I then rotated the dipole to measure how the interaction changes with direction.

Interactions when the inverted vee and dipole are in the same plane (left) and orthogonal (right), at 10° elevation

When orthogonal there is little interaction. Compare the right pattern with the one at the top of this article. (The vee's pattern is not skewed; it has been rotated in the interaction model.) Low current on the inactive antenna confirms this. When collinear (in the same plane) the impact is large. Antenna lobes are no longer where we want them! However there is a gain effect, as in any parasitic array, with the amplitude of the major lobes 1 to 2 db higher than in the non-interacting (orthogonal) orientation. Unfortunately this gain is not useful or reliable.

The SWR for both antennas in the collinear case are poor. Resonance is shifted and bandwidth is reduced for both antennas. Even if it were possible to live with the pattern distortion, the large swing in SWR is not tenable for most operating, especially contests, and would at least require frequent adjustment with an antenna tuner (preferably automatic).

Where I go from here

This analysis demonstrates the importance of checking interactions between antennas for the same or harmonically-related bands. My antenna decision is heavily constrained by interactions. I could not put up a rotatable dipole unless I remove the 40 meter element from the inverted vee. That is not desirable.

In my earlier interaction modelling I was able to demonstrate modest interaction on 15 meters between the tri-band yagi and the 40 meter inverted vee. Again, worst case was when they were collinear (yagi pointed east). I judged the degradation to be acceptable: about -1 db gain, poorer F/B but little effect on SWR. Compromises are sometimes unavoidable. But you can't make an informed decision until the interactions are tested, in a model (preferred) or in the field. Spending time on this analysis saved me time and effort, and disappointment.

My choices now come down to these options:

• Install the rotatable dipole and remove the 40 meter inverted vee. I would lose instant direction switching and have to do some mechanical work to modify the inverted vee and to install the dipole on the tower. The higher wind load is a risk, though I believe it is managable if I take the dipole down in early spring. But then I would have no 40 meter antenna at all.
• Build and install a second, 40 meter only, inverted vee on the tower, orthogonal to the first. I would retain instant direction switching and avoid destructive interactions. The 90° interior angle of the vee reduces gain but is necessary to avoid degrading the yagi's performance on 15 meters. Installation of this vee presents a mechanical challenge in that one leg has to be tied off at some height on a suitably placed tree. There is a wasp nest in the way (I'm allergic) that I'll have to first remove!

I'll report back on what I decide to do. I may come up with a further option to consider.

A subsequent article I will discuss my options for 80 and 160. I have fewer good options for those bands. I may decide to entirely forgo 160 this season.

6 Meter E-season Wrap-up

Over the past couple of weeks the number and quality of sporadic-E openings has drastically declined. While there may still be a few good ones, for me this marks the end of the 6 meter season. The temporary small yagi I built and installed to get back on 6 has done what I intended.

In this article I will recap my brief return to the "magic band", now that it is coming to a close.

Statistics

First, the numbers.

• Contacts: At least 100, but not counted. Most came in the ARRL VHF contest and the Es peak in late June.
• Grid squares: 75+ worked, with over half already confirmed on LoTW.
• DXCC countries: 11 worked, including Canada and the US. The other 9 ranged from XE to the southwest, several in the Carribean, and several more across the Atlantic Ocean. More countries were heard but not worked.
• Continents: North America, Europe and Asia. South America heard but not worked.

I as satisfied with these numbers even though they are not impressively large. Some have reported the season to be below average. That may be true. Although I have lots of experience on 6 meters from years ago my recollection is fuzzy and my poor antenna tended to make every opening this season a poor one.

It was well worth the effort of putting up an antenna and wasting some nice summer weather closeted in the basement shack.

Antenna performance

Running 150 watts I am pretty well able to work what I can hear. I only wish I heard as much as others. Many DX and marginal openings allowed others in and near my own grid (FN25) to work stations I could not hear at all.

The poor performance I'm experiencing is a combination of a compromised antenna -- nestled close to the tri-band yagi -- living in a river valley, and noise level. There is no easy way to disentangle their respective effects, except to not they all limited my results.

I seem to do well on aurora scatter, mostly done aiming across and along the wide Ottawa River. The yagi is small and so has a wide beam width for scattering off aurora well above the horizon. I only suffered on the longer auroral-E paths to VE6, VE7 and KL7, which is more due to poor antenna gain. Stations in all these call areas were heard during one excellent aurora opening.

The same appears to be true for Europe since the northeast direction is unobstructed. It comes down to a matter of antenna height and gain, of which I have little. I was very happy to work the few Europeans that I could. There were others I either could not hear or could not work.

The big problem is south, looking into the hill I mentioned in an earlier article. XE was not a problem, which skirts the hill by aiming southwest. Caribbean and South America were the toughest DX paths. I was happy to work what I could, and dream of what I might have worked with a better antenna.

Noise

With a proper antenna I am able to hear noise much better than before. This is clearly not good. Getting the noise source off the side of the yagi helps, but that is unfortunately in directions with little to no activity. The is typically in the range of S3 to S7 at SSB bandwidths, and occasionally even louder.

I mostly kept to CW where a narrow filter usually cuts the noise to a managable level. The high CW activity on 6, more so than I remember back in the 1980s, made this strategy a successful one for me.

KX3

I use the Elecraft KX3 on 6 meters since the FT-1000MP is HF only. An outboard amplifier raises my signal from QRP to 150 watts. It can now update my earlier opinions of the KX3, which had focused on HF contests and DXing.

In sum, I am not too impressed with the KX3 on 6 meters. There must be some aspects of the DDS and receiver that are different than on HF. I did not delved deeper to discover the reason for what I observed.

• Tuning artifacts: When the VFO dial is spun there is often a loud ratcheting sound as the DDS makes its frequency steps. It can hide the very signals you wish to hear. Sometimes I had to tune more slowly than I'd like The manual talks about this and suggests how to reduce the effect, but not eliminate it entirely. There are trade-offs. Maybe I'll try it someday as an experiment.
• Single signal reception: In what is largely another tuning artifact, when tuning through the opposite side of zero beat, signals bleed through to the AGC. The effect seems less severe when not turning the VFO. The AGC pumping is worse than I've encountered on any of the HF bands.
• Noise artifacts: When tuned to a reasonably loud signal it can often be heard to crackle (sizzle?). It is more apparent on a continuous tone (CW/carrier) than SSB, but it's there nonetheless.
• Spurious signals: Disconnect the antenna and tune the band and I discovered perhaps a half-dozen spurious signals of significant amplitude between 50.0 and 50.2 MHz. Considering the receiver technology (direct conversion) these are not "birdies", so I label them as spurious. When I connect the antenna there are lots more to be heard, but those are not the fault of the receiver.
• Noise blanker: The dreadful noise I am dealing with can be significantly attenuated by the noise blanker (NB). Unfortunately the NB also reduces signal amplitude and adds substantial distortion. Careful adjustment of the NB level can help, though in most cases I get better results with the NB off.

Despite all the negativity in the above list, the KX3 did the job and I still like it just fine. It isn't the greatest rig around, but then that is not its purpose. For a small, portable, high-performance QRP transceiver it does very well indeed.

Hurry up and wait

Years ago it was tedious work to watch for openings. Often when I was home I would leave the receiver tuned to 50.125 MHz (the domestic calling frequency) with the volume set low. If I heard something I might check it out for a potential opening. There was also WWV for the geomagnetic indices that could herald aurora openings. At the height of the solar cycle high solar flux readings promised real DX.

It's much easier today. DX spotting networks are available with any internet connection, including my smart phone. All I need to do is look for spots on 6 meters and judge whether it's worth going down to the shack.

Even so there is time and effort required for success on 6. Most openings on 6 are marginal: signals are weak and fleeting. If you hear something enticing you have to jump. Wait a few minutes and the opening or wanted station can be gone, and may not come back until next year, or longer. Listening isn't enough: someone has to transmit. Many times I would go down below 50.1 MHz and loop CW CQs with the antenna pointed in a likely direction. Someone will answer, eventually, if sporadic-E has been reported by others in my vicinity.

Other times it's tedious tuning of the VFO, with longer stops at every station or beacon spotted. This is not welcomed by those with busy lives, hams who can only operate when life allows and not when the propagation dictates. Be prepared for that if you venture onto 6 meters. The rewards are many, but then so are the sacrifices.

Next up

Temporary means temporary, so the 6 meter yagi's presence will last only a little longer. I expect that by mid-August the yagi will be taken down and stored in the garage until next year, or perhaps even later. My plans for 2016 are unclear.

The feed line I co-opted has kept me off 80 since early June. This was little sacrifice during the summer's high noise level and low activity on the low bands. The coax will likely be reconnected to the 80 meters antenna for at least a short time. I have plans for improved low band antennas before the contest season arrives. Those plans will be the subject of a future post.

Closer Look at the XM240 LCA

For my recently-purchased Cushcraft XM240 40 meter yagi I speculated on modifying it for improved performance. The primary options are to convert it into a W6NL Moxon or to replace the low-Q coils with high-Q coils. I built an approximate model of the antenna in EZNEC to evaluate the second option.

The coil is part of the LCA (loading coil assembly). The coil is close-wound on a fibreglass form, an attached to short aluminum tubes at each end. The LCA with the protective coating removed can be see on VE6WZ's web site. You may want to keep that page open while you read the rest of this article since I frequently refer to it.

Calculating the Q of a coil is difficult due to the many factors at play. It is typically easier and more accurate to measure it. Most hams, including me, do not own suitable test equipment. VE6WZ used software to estimate the coil Q and ESR (equivalent series resistance). As I said in my previous article that, if correct, the loss is as much as -3 db and coil heating is excessive. As I said there, I doubted these figures. But how to proceed? It is important to know the loss since it will be a key factor in whether or how I modify the antenna before its expected use in 2016.

The inside story

A close-up of one end of the LCA is shown at right. The ¾" fibreglass form fits snugly inside the ⅞" aluminum tubes, attached by what appear to be rivets. A screw electrically bonds the coil wire to the tube.

Some internet searching told me that the loss tangent of fibreglass is heavily dependent on the formulation. At the high end of the range I calculated an ESR of 8 Ω for the coil at 7.1 MHz, which is what VE6WZ calculated. Presumably that is the loss tangent for fibreglass used in K6STI's software calculator. The calculated coil Q is very low. However at the other end of the loss tangent range the ESR would be a very good 1.5 Ω. Calculation alone is clearly inadequate to gain the required insight.

Puzzled by this difficulty I did continued searching. A passing remark on a ham forum gave me the hint I needed. That person called the form a fibreglass tube. A tube is hollow, not solid. K6STI's calculator appear to assume that the form is a solid rod. I picked up an  LCA, pointed it at an open window and held the other end close to my eye. I saw daylight. Now the trail was hot.

It was difficult to be certain how the interior was structured because the light coming from the other end cast dark shadows from several dark protuberances from the tube walls. But the small diameter tube does not easily allow illumination from the same end I'm looking into with my eye. Fortunately my smart phone camera has a small lens and an adjacent LED "flashbulb" . With some care I was able to get both positioned within the tube opening. I pointed the far end  at daylight and took the following unusual photograph.

The flash was so bright within the LCA's confined space that the metal reflections stopped down the automatic exposure to reduce the far-end daylight to black! Despite this the interior structure is clear.

The rivets are obviously metal (presumably aluminum), as evidenced by their reflectivity. The fibreglass form is definitely a tube and (not clear in the picture) has a narrow wall thickness. The self-tapping screw that bonds the coil to the aluminum is very evident. As an aside, this reminded me that I need to replace the screw with a bolt that goes through the other side of tube, which is a well-known design flaw Cushcraft has persistently failed to fix. Due to the perspective of the camera and hardware alignment the rivets and screw at the far end of the tube are hidden behind those in front.

The upshot of this exercise is that the coil does indeed have an air core. The note by VE6WZ that some have measured the coil Q to be 200 is now entirely credible. Since fibreglass fills only a small fraction of the coil's interior volume its contribution to inductance and Q is small. This is good news.

Inductance, Q and loss

Since those unnamed sources and VE6WZ's calculations for an air-core coil of the LCA's dimensions agree on a Q of 200, let's proceed on that assumption. We can now compare an ideal, zero-loss coil (Q=∞), the stock LCA (Q=200) and VE6WZ's high-Q coil (Q=767).

First we need to agree on the inductance value. VE6WZ's measurement is ~15 μH. An air-core coil of the LCA's dimensions give an inductance of 11 μH. This is a difference that must be explained. I think it is fair to conclude that, per his pictured test apparatus, there is ample stray reactance due the long test leads and the attached tubes to account for the difference. There is no need here to speculate on the accuracy of the pictured test device.

I am also swayed by my EZNEC model which only works well when the load is set to about 11 μH. While I cannot use the Leeson correction, I did use an average element diameter that is roughly consistent with a stepped-diameter correction for an XM240 element. Whereas an inductance of 15 μH in the model is wide of the mark, requiring unrealistic element truncation.

For a Q of 200 and X of 500 (11 μH at 7.1 MHz) the ESR is 2.5 Ω (R=X/Q). I then chose a test frequency where the radiation resistance is a little above its minimum near the frequency of maximum gain. Recall that in a 2-element yagi with a reflector parasite the maximum gain ought to be placed at the bottom of the target band for optimum performance across the band. Since I am targetting the CW and DX SSB segments I chose 7.05 MHz.

The resulting gain figures versus ESR for the several LCA options are as follows:

• 0 Ω (ideal, zero loss): 5.71 dbi
• 0.9 Ω (VE6WZ high-Q coils): 5.43 dbi
• 2.5 Ω (estimated stock LCA): 4.94 dbi
• 8 Ω (now-invalidated estimate of stock LCA): 3.43 dbi

F/B differences are negligible. Feed point impedance and SWR curve are only modestly different across the first 3 selections. Relative to 7.05 MHz the gain differences (coild loss) will tend higher toward the lower band edge, and gradually decline with increasing frequency. This is due to the radiation resistance change with frequency.

The high-Q coils do very well, being about -0.3 db from the ideal. Compared to these coils the stock LCA is down a further -0.5 db. That's also very good, and better than I expected.

Conclusion

I am now inclined to stick with the stock LCA. In my judgment an additional 0.5 db is not worth the effort involved nor the damage risk due to the exposed and more fragile high-Q coils. The better alternative is to forgo the coils and do the W6NL Moxon conversion which does away with the coils and coil loss while also improving SWR and F/B performance.

However I still need to replace those self-tapping screws on the LCA with through-tube stainless steel bolts. I don't want a coil failure to occur in the midst of a contest during a frigid northern winter.

For Future Consideration: 40 Meter Yagi

In the description of my roughly laid out long term ham radio plans I did say I would like a significantly larger antenna farm. That is a task that takes time, including both planning and action. In particular, unless one intends to buy everything new and hire people to install the lot (very, very expensive) it is necessary to do some scrounging and learn some new skills. No matter the level of ambition (or zealotry) this takes time.

To that end I have been planning and searching for various elements of a bigger station. Some of this should be obvious from certain topics in this blog, such as models of large antennas, stacking, relative advantages of gain versus directivity, and more. To get beyond plans to real results there is a need for action. In particular, I will need stuff. Lots of stuff.

Some things I must postpone for practical purposes. If I were able to acquire a large used tower there is no place I can conveniently store it, nor am I in a position to transport it. Other things I can deal with today, purchasing items and setting them aside for future use. I recently acquired one such item.

If you don't recognize it this is a Cushcraft XM240. It is a short (inductor loaded) 2-element yagi for 40 meters on a 6.7 meter boom. If you been a regular reader you may have noticed my interest in rotatable and fixed 40 meter yagis.

When this item appeared on the used market I was quick to make a deal. Several attributes attracted me to making the purchase:

• It's used, but new. It has never been on a tower. The aluminum positively glows.
• The previous owner strengthened this antenna to address its well-known mechanical weaknesses. I was given the original parts where those have been replaced by something better.
• There are tried-and-tested modifications to this antenna to improve its performance. That is, it makes a great base from which to build a yagi that is competitive with full-size yagis. This gives me a few options to choose from.
• The seller is someone I have met before, and is someone I can trust.

I was able to combine a family visit into a longer trip to pick up the antenna. Several hours of driving saved shipping fees, risk of shipping damage and allowed me to inspect the antenna before taking possession. Considering the identity of the seller I expected no problems and there were none. This is how a ham-to-ham transaction ought to proceed, not what unfortunately sometimes happens.

This antenna will go into storage for the present, waiting for a suitable location and tower. Not only can my present tower not handle the load, the elements would tangle with the upper branches of adjacent trees.

This gives me time to consider which, if any, modification to apply to this antenna. It is also possible that I would install it as-is if time is pressing and other necessary tasks take priority.

Loss

To compensate for shortened elements it is necessary to have loads to compensate for the reactance due to the unloaded element's higher resonant frequency. Loads are never perfect: they are lossy. Sometimes the loss is small and sometimes it is large. This is true whether the load is a coil, a capacitor, transmission line stub, capacity hat, linear loading, something else or a combination of these. The stock XM240 uses a coil and a small capacity hat in each element half (4 in total).

The loss of a coil can be substantial if its shape, wire gauge and core material are not ideal. Most commercial designs have lossy coils and traps since there is a greater emphasis on material cost, size and robustness. Ironically, poor (lossy) coils are low-Q (where Q=X/R) resulting in improved SWR bandwidth and simpler matching networks. Few hams are in a position to measure loss, and many seem not to care. Manufacturers cater to the desires of their market.

Most of these short, lossy yagis are used and enjoyed in their stock configuration. That does not mean those hams are not experiencing losses. Often it is that the yagi replaces a single-element wire antenna or some variety of urban-friendly vertical. Even with the loss the short yagi can substantially outperform what it replaces. If optimum performance is your objective it is often possible to do better, with some extra effort.

I built a simple EZNEC model of the XM240 so that I could estimate the loss in the loads. The critical data required, the coil ESR (equivalent series resistance), is not easy to measure. Like most hams I do not have the means to do so. A calculation can be done, though that too is subject to error due to the need for assumption about coil and environmental properties. VE6WZ used K6STI's coil calculator and got an ESR estimate of 8 Ω for the stock XM240 coils.

Plugging the 8 Ω value into my model predicts a loss of up to -3 db. At least ⅔ of the loss is in the driven element because the current is higher than the reflector, as is typical for any yagi. If his coil ESR estimate is correct the loss in each driven element coil could be as high as 170 watts when the antenna is fed with 1,000 watts. That's a lot!

Even at a typical 50% duty cycle for CW and SSB this is 85 watts of heating per coil. I am dubious about the 8 Ω ESR estimate since that would cause instances of coil damage that I have not seen reported for this antenna. Unfortunately I can do no better estimation. Even so I would strongly consider implementing VE6WZ's modification to reduce the coil loss to a negligible amount. Even -1 or -2 db of loss for such an antenna is undesirable.

Perhaps the only good thing about lossy coils is that the antenna is a pretty good match to 50 Ω coax (the antenna comes with a 1:1 balun). With loss-less coils the radiation resistance would be below 50 Ω and require a matching network such as a hairpin or gamma match. Since the loss resistance is in series with the radiation resistance the 50 Ω match can be good. But at a cost.

Gain and F/B

Perhaps the better way to avoid loss is to replace the coils with a large capacity hat. Unfortunately the size of the capacity hat would have to be large. This adds substantial weight to the elements at a point where it can reduce survivability and cause a lot of sag. It is a project that requires a careful eye to design and implementation.

Luckily for me the design work has already been done by W6NL. He transferred his 2-element Moxon design onto the XM240 antenna, and provided detailed instructions to do the conversion. I am intrigued by the advantages of this design, which inspired me to consider how to deal with its potential drawbacks in an earlier article.

Since my antenna's previous owner has already taken care of strengthening the antenna, it is only required to take the additional measures W6NL specifies for conversion to a Moxon. To recap, the advantages of the converted XM240 include:

• Low SWR across the 40 meter band
• Improved F/B
• Negligible loss

What you don't get is improved gain. Gain and gain bandwidth are comparable to an XM240 modified with VE6WZ's coil substitution. To be more precise, the equalization of element current the Moxon modification provides contributes to improving F/B and match, but do not optimize forward gain. I believe this is a reasonable trade-off with respect to elimination of loss in the stock coils or the fragility of a large, low-loss coil.

Deferred decision

I do not need to decide on what direction to take with this antenna until at least 2016. This is plenty of time to consider the alternatives. I fully expect to implement one of the VE6WZ or W6NL modifications. For the present it will share storage space with a TH6, A50-6 and several rolls of Andrews Heliax. More items may join these over the coming year.

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.