Tuners Do Not Solve All Ills

I do not have antennas for 80 and 160 meters.

That may not sound like a profound statement yet, for me, it is. As far as my DXing goes it simply means I don't go there. Until I am in a position to raise effective DX antennas for those bands I stick to 40 meters and higher bands. The dilemma comes from contest operating. If I don't operate on those bands I miss out on some easily-acquired multipliers, whether it be CQ/ITU zones, countries (VE & W), ARRL sections, or states/provinces.

For my proximate need there is no need for a great antenna on those bands. It is minimally sufficient to work only a few stations to give the contest score a big boost. For example, in my report on the CQ WW CW contest in 2013 I mentioned that I used a tuner to put enough of a (poor) signal on 80 meters to work a couple of stations and add 4 multipliers (VE, W, zones 4 and 5). Yes, that really does make a difference to one's contest score and is well worth several minutes of effort to re-cable and fiddle with the tuner.

As it turns out it isn't as easy as it sounds. Certainly I have a tuner, several in fact, including one that is big enough to have only modest losses at high SWR. It has no trouble at all getting a 1.0 SWR match on 80 meters for my currently largest antennas: multi-band inverted vee (30 through 10) and delta loop (40). However the results were not at all equivalent, or even what I expected.

Neither antenna is even close to resonance on 80 meters. The SWR is high, very high. It is so high that EZNEC gives up on the calculation, only indicating that it is above 100. That is the feed point SWR, not what you see in the shack. At such high mismatches there is considerable loss due to transmission line attenuation. It may seem odd but this can be viewed as an advantage since the resulting high (not extremely high) SWR means that the tuner can achieve a match without risk of excessive loss in the tuner.

To give you some idea of how high the SWR is on 80 meters with those two antennas I used EZNEC to quantify the antenna feed point impedance at 3.525 MHz.

• Delta loop: Z = 0.5 - j80 Ω. For 50 Ω transmission line this gives an SWR of ~6700!
• Multi-band inverted vee: Z = 3 - j1000 Ω, for an SWR of ~350.

Since the true SWR is very sensitive to environment factors at these extreme impedances these are at best only rough estimates. The point is that the SWR is pretty much off the charts, and it has consequences.

The drawing of the setup gives us an idea of where to look for trouble spots.

• Tuner loss: Regardless of whether the feed point SWR is 350 or 6700 the SWR at the shack end of the coax will be much the same, since the dominant factor is transmission line loss. Since the actual value is not extreme (measured to be, very roughly, 10 or somewhat less) and is similar for both antennas I will ignore this factor in the analysis. If you like, assume a loss of -2 db, which is typical of a mid-sized tuner matching a high SWR at 3.5 MHz.
• Transmission line loss: There are two components to the loss. The first is the matched loss, when the SWR is 1 (load impedance is 50 Ω). The second is mismatch loss due to the signal reflecting back and forth between source and load, where attenuation is suffered on each reflection.
• Antenna I²R loss: The radiation resistance of an antenna rapidly declines below its resonant frequency. Since the conductor resistance is in series with the radiation resistance, as the latter gets very low more of the source power is dissipated in the conductor.
• Ground loss: As you go lower in frequency the antenna is closer to ground when measured in wavelengths. Near-field losses increase due to interaction with (typically) lossy ground.
• Pattern loss: The radiation pattern can tilt upward due to the lower height in wavelengths, especially for horizontally-polarized antennas. With more power radiating at higher angles there is less going toward low angles. If your objective is DX this factor can be viewed as "loss" even if the antenna is perfectly efficient.

Having dispensed above with the loss due to the tuner I will first turn to the radiation and ground loss. After all, the title of this blog is Pattern and Match and I often emphasize putting the priority on pattern.

In the above patterns I have normalized the gain to 25° elevation. It should be no surprise that the horizontally-polarized inverted vee directs most of its radiation straight up since it is very low to the ground on 80 meters. The pattern suffers less when using the 40 meters delta loop, remaining primarily low angle and vertically-polarized. Both antennas are close to omnidirectional on 80 meters since they are quite small in terms of wavelength.

Even with its excessive high-angle radiation the low-angle radiation (25°) is 1 db better on the inverted vee. The reason for this is due to ground loss: the modelled loss over medium ground is -1.5 db for the inverted vee versus -6 db for the delta loop.

The antenna I²R loss is low in both cases despite the very low radiation resistance. It is no more than about -0.2 db with 12 AWG insulated wire. I expected worse, so that is one positive outcome.

Now we must deal with transmission line loss. This can be difficult to model since many of the more common equations in use become increasingly inaccurate at very high SWR, and the SWR of these antennas is very high indeed.

Unfortunately the VK1OD transmission line loss calculator I've used in the past has been taken down by the author. There are other calculators on the internet but may suffer from the inaccuracy cited above. Nevertheless that is what I went ahead and did with a couple of online calculators. The true loss could be higher than the figures I am going to report.

• Multi-band inverted vee: -11 db
• 40 meters delta loop: -23 db

Both figures include the sum of matched loss and mismatch loss for ~25 meters of  RG-213 coax between the tuner and antenna feed point. I did not compensate for the λ/4 of RG-11 matching section on the delta loop since with these levels of mismatch the difference on the results is unlikely to be significant.

Gaze at those loss figures for a moment and think what they mean. If you transmit 1,000 watts on 3.525 MHz on the delta loop more than 990 watts is dissipated in the transmission line. In a way that's a good thing since at these levels of mismatch the high voltage points along the coax could otherwise punch through the dielectric and destroy the cable.

Summing all the losses, at 25° elevation the gain at 3.525 MHz on the inverted vee is -11 dbi and on the delta loop is -24 dbi, minus any tuner loss you wish to include. Most of the loss components are already included in the EZNEC model. I did not use EZNEC to model the transmission line loss. These loss calculations explain why, while both antennas performed poorly on 80 meters with a tuner, I could make a few marginal contest contacts with the inverted vee but not at all with the delta loop.

Lessons learned

Using a shack-based antenna tuner can produce far worse results than you might imagine since the SWR can be extraordinarily high. Do not be deceived by the facility with which a non-resonant antenna can be matched in this way. Tuner and other losses pale in comparison to transmission line losses for all but the shortest runs.

In retrospect this is why I was able to do so well with my eaves trough antenna, including making contacts on 80 and 160: there was no transmission line between the tuner and antenna. Although I cannot easily do an A/B comparison, I believe that the eaves trough antenna performed better on 80 meters than either the delta loop or inverted vee. This is despite its low height (6 meters), bends, corners and attachment to a conductor- and dielectric-ridden house.

The options to deal with this problem should be clear. I will list them anyway.

• Put up a resonant antenna (duh!). Even if you have to use loading coils or a matching network at the feed point it will almost always do better than a non-resonant antenna with a long run of coax and matched in the shack with a tuner. A large, efficient tuner makes almost no difference.
• Only use a shack-based tuner for small excursions from resonance for coax-fed antennas. Don't rely on the SWR you measure from the shack since transmission line losses reduce the maximum SWR you'll measure in the shack, telling you nothing about the severity of mismatch at the antenna feed point.
• You can use open-wire line to tame the transmission line losses, but is a lot of trouble to do right. Plastic-encased ladder line is not low loss; you must use true open-wire line, and you'll probably have to make it yourself. Open-wire line is fraught with difficulties, including getting through walls, preserving the differential phase between wires, corrosion, precipitation and coupling to metal obstructions.

There are other conceivable solutions to specific circumstances. For example, a switch or relay can be used to break the 40 meters delta loop into two separate arms, resulting in an asymmetric λ/2 doublet. Unfortunately it does not resonate at half the 40 meters resonance, and for anything other than QRP the switch (relay) will very likely flash over when transmitting since the voltage at the ends of a doublet can be very high.

Another possibility (one that many have tried, including myself) is to unscrew the coax connector so that only the center conductor of the coax is connected. Then ground the tuner (or transmitter) side of the outer conductor. While there is the risk of RFI, hot grounds and higher ground losses, the antenna can become much more efficient when matched by a tuner. The transmission line becomes part of the antenna. When it does work it usually only works on 160, and not so much on 80.

Final thoughts

Non-resonant antennas in typical use are poor performers, as measured by system efficiency and pattern. Unless designed for a specific purpose, a non-resonant antenna that is opportunistically tuned to make QSOs may suit in a pinch but is otherwise a bad idea. It will net a few multipliers in select contests, but nothing more.

If you want an effective signal for DX, contests or other interests, design and build an antenna that will achieve your goal. Opportunistic use of a tuner is rarely effective. You may be better off locking up or selling your tuner so that you never succumb to temptation.

Late-winter Doldrums

Too cold to work on antennas but so close to warmer weather that I can't bring myself to only plan but not do anything outside. I have pretty much convinced myself that I need to take a step up with antennas and possibly with power. QRP with small antennas has been great fun this past year, it just isn't what I want to do forever.

The spring equinox is as good an opportunity as any to look back at my DX accomplishments over the past 14 months with QRP (10 watts maximum), CW only, and simple, low wire antennas, since ending my 20-years hiatus from amateur radio. That will be a good base from which to look forward to the rest of 2014 and beyond.

DXCC

I now have over 100 countries on each of 40, 30, 20, 17, 15 and 10 meters. The last band on which I achieved this mark was 17 meters, where I now have 102 worked. I was surprised at my low country count on 17, so I had to catch up. This is most likely due to it not being a contest band. I have mostly worked 17 meters to catch some rare DXpeditions (FT5ZM, VU7AG, etc.). I have yet to work F and G on that band. Go figure.

Unsurprisingly 20 meters is my best band with 153 worked. All other bands are in between. I don't have antennas up for 6, 12, 80 and 160 meters so apart from a smattering of contacts using a tuner my efforts there are approximately nil.

My overall total countries is 193 worked. It's slow going at this point. I have heard lots of workable stations in perhaps 50 more countries but my puny signal was not heard. My objective of reaching 200 countries with my current station may not happen before I begin antenna work this year.

LoTW

Logbook of the World has proved to be a great way to confirm countries for DXCC credit. As of my last upload at the end of February I have 145 countries confirmed through LoTW. A confirmation rate of 75% is quite good.

On a per-band basis I have noticed an interesting trend. On the bands where contests are held (80, 40, 20, 15, 10) my confirmation rate is ~65%. On the other bands (30, 17) the rate is ~50%. I suspect the reason is that contesters are more likely than others to upload their logs to LoTW. Many DXpeditions delay uploads or do not use LoTW.

Contests

My DX totals were enhanced by participation in contests, both semi-serious and serious. However on deeper reflection my results mask an unpleasant truth: I am mostly working only big-gun contesters, especially on 40 meters.

It is by working the big guns on every band that my QSO totals get as high as they do. I can't run stations (sit on a frequency and call CQ or QRZ, and get answers) and I don't work many of the stations that have similarly puny signals or even those with average signals. I remember one very weak European on 15 meters that answered my CQ, and later discovering he's a regular contester in the same QRP category as myself. That's how I must sound to most stations that I call. That's why I have to call the big guns.

This is easily noticed in the logging software by the number of big guns that I've worked on every band. All it takes is working 100 of these stations across the bands to reach 500 QSOs. In DX contests where VE can work W/K there are even more of these stations to work.

Whether for purely contesting objectives or as a path to DX success I need better (bigger) antennas.

***

Looking forward to 2014 I will briefly outline the topics that are of interest to me in my pursuit of better antennas. If you follow the blog you will likely see one or several articles on each this year.

Tower

With some reservations in advance of a post-winter inspection, I believe that my opportunistically-guyed small tower passed the weather challenge quite well. This included not only cold and ice, but also some strong winds. If it checks out I plan to install a more substantial tower, though still one that would be considered light duty.

My objective is simple enough: a 3-element yagi at 14 or 15 meters height for 3 or more of the high bands will provide 10 db or more of gain over the multi-band dipole and inverted vee I currently use. Part of the improvement is antenna gain and part is greater height. If I decide to stay with QRP this change alone will make me significantly more competitive in DX pile-ups and contests. Jumping up to 100 watts would add a further 10 db gain.

My plan, if I come across something cheap and used, is a Delhi (now Wade) DMX-52. I can mount this in the same location and manner as the current Golden Nugget tower (Site C). I prefer this approach so that no concrete base is required and I stay under the municipal/federal "duty to notify" regulatory requirements that are in effect for structures higher than 15 meters above grade.

If that goes well (and I don't again lose interest in the hobby) I will consider a more permanent, stronger and higher tower in 2015. Any such tower must go to Site D in order to be clear of the septic system tile bed, yet keep a decent distance from the rear property line.

High-performance yagis for the high bands

A light-duty tower requires an antenna (or antennas) that don't stress the tower plus guying. The TH6DXX I have in storage is heavy and has more wind area that I am comfortable putting on a tower of this class. It also doesn't include 17 and 12 meters.

A rotatable wire yagi is more suitable. I am beginning to seriously look at the 5-band Spiderbeam. From people I've talked to it appears to be up to surviving our local weather and its performance claims appear to be legitimate. I found an EZNEC model of the 3-band version (20, 15, 10) and have started experimenting with it. A Hexbeam is also a possibility, except that it has a large vertical height that would easily put it over my 15 meters height limit when placed on a 14 meters high tower.

If I get ambitious I'll also put up a short yagi on 6 meters. If I don't get around to it by July I will probably not do so at all this year since sporadic-E season will have already come and gone.

Low-bands antennas

For 40 meters I may replace the delta loop with a 2-element switchable array, probably the diamond loop array I have already designed. I will need to supplement this with a dipole, possibly on the house-bracketed mast, to fill the side nodes of the array and to effectively work the northeast US in contests.

Getting an effective DX antenna on 80 meters will be difficult. Something like an inductor-loaded half-sloper might work out. However there is the potential to interfere with the performance of the 40 meters array, and there is an unknown capacitive loading due to the wire high-bands yagi. I don't need a great antenna for 80 meters, just one that will collect multipliers in contests and allow me to do some DXing.

I have no plan for 160 meters in 2014.

I have been idly playing with EZNEC to model a variety of potential 40 and 80 meters antennas for 2015, in the case that I put up a proper tower. The main challenge is getting a high-performance antenna to fit the 15 meters (50') width of my property. For instance, a rotatable 40 meters yagi cannot have elements longer than 13 meters. Managing loss in short antennas is the objective, and therefore I have started to explore in that direction.

When these models reach a suitable level of maturity I will write about them.

Antenna interactions

My immediate interests with respect to antenna interactions fall into two categories:

• Interactions among many antennas sharing one tower
• Interactions among stacked, rotatable yagis

In 2014 the first category is of most interest to me. That is why I spent some effort investigating how a vertically-polarized low-bands antenna interacts with a tower, and how to resolve problems.

The second category is more of a future concerns, but an important one. There are specific ideas I want to dig into that may shed more light on this question. Most hams go by rough, and often unverified rules-of-thumb, while other elect to ignore the issue or go to unfortunate extremes. For example, loss of structural integrity by using masts that extend far above the tower top.

Wind load

Because of my choice of tower and guying arrangement I have a renewed interest in acquiring a better understanding of wind load. In particular, the quantified wind load of antennas and other tower loads, and the behaviour and real carrying capacity of towers. This will also be useful should I erect a larger tower in 2015.

The big problems with wind load is that the marketing of antennas and, to a lesser extent, towers does not provide reliable figures. It is quite easy to find quoted square footage of popular antennas that cover an almost 2-to-1 range of values. Towers manufacturers are typically better at providing good data, if you know how to interpret and apply the data. These data are critical not only to build a robust installation but also to pass the requirements for a building permit.

This is not an unfamiliar area to me since I have put up countless towers and antennas over the decades. I have seen many towers and antennas fail as well. There is good information out there, which I have begun to collect.

Moving Into the Shack

As you might be aware the winter in central and eastern North America has been long, cold and snowy. This makes it difficult to put antenna designs into effect. At this point I am getting tired of modelling antennas. Unfortunately that's all I can do. Well, not quite. Surprising as it sometimes seems to me there is more to this hobby than antennas.

Which brings me to this article's topic -- moving into the new shack -- just for a change of pace.

I have been gradually working towards finishing my basement shack over this winter. Progress had to be gradual since I've been busy at many things, not least of which is the antenna articles I've written over the preceding months. Now that the end is near I was able to finally move back into the shack and set it up as a more permanent area for radio operation. The critical finishing pieces were the door, trim and (very important) the floor.

Once that was done all I had to do was put in an operating desk and reinstall all the equipment. The room was designed as a shack when the house was constructed in 1993 so it has all the necessary infrastructure, including dedicated electrical circuits and two 240 VAC outlets for amplifiers. It sat mostly neglected when I decided to not continue with the hobby. Now, 21 years later, I've finally moved in.

Rather than go back to a simple desk I have restored the custom operating desk that I built 30 years ago. It was used in my first station (1984 to 1992) since moving to Ottawa from VE4. I supplied the basic design parameters to my old friend and excellent amateur woodworker VE3NVM, from which he came up with a construction template. With his help and workshop the desk quickly came together.

Here it is in my new shack, already celebrated with some contacts, including one new QRP country: 5H.

The tabletop measures 84"x30", so it is an imposing presence in the modest-sized 120 ft² room. Made from plywood and seasoned maple it can not only support a lot of equipment, it is perfectly safe to stand on. The only equipment it didn't support was my old Collins 30S1 amplifier, which was meant to stand on the floor. Notice how the KX3 is dwarfed by space meant to hold an older generation of transceivers and accessories.

Let me take you through the design parameters I came up with all those decades ago so that you can get a sense of what I was attempting to accomplish with this desk. The effort I expended is more than most hams would bother with, yet the concepts are equally applicable to the selection and assembly of "off-the-shelf" products.

• Surface height is measured to fit my body. When seated in a chair, with its height set so my thighs (femur) are parallel to the ground, the desk height is such that grabbing the paddles and sending CW is almost effortless. Almost every commercial desk has a higher surface. This can lead to fatigue, especially during a weekend-long contest. One reason the surface is only ¾" thick is to provide sufficient leg clearance despite the comparatively low height. Maple is used to brace the surface due to this choice, yet still support a lot of heavy equipment.
• The lower shelf is for power supplies and other equipment which do not require operator interaction other than being turned on and off. The power bar (bottom right) is used to power them all on with one switch. Right now there is just the 4 ampere DC supply to power the KX3, and the AC power supply for the laptop. Back in the day that shelf was crowded. Its height and placement is designed to not get in the way of your feet. For SSB I had a foot switch on the floor beneath the power supply shelf.
• The rigs I used most often went into the lower bays of the upper shelf unit. I chose an antenna switch that permitted the coax cables to exit straight back. This saves space and has a clean appearance, but at the cost of some difficulty in attaching and removing those cables. The B&W switch is, regrettably, intermittent. This is a design flaw and not due to ordinary wear and tear. Worse, the unit is sealed and difficult to repair.
• The middle deck was used to hold VHF transceivers, pre-amps and amplifiers, plus an assortment of measuring devices. All I have there now is an SWR/watt meter. In the centre is a slot that held the logbook, countries list and other paper resources. All of that is now done with software.
• The upper shelf was for everything else, such as a world globe and spotlight lamp.
• On the right side is a longer open area which I used to work on equipment. It had its own power bar and lamp. When I bought my first PC in 1991 (a speedy 16 MHz) it went in this space. Thus began my obsession with antenna modelling, starting with the DOS-based of ELNEC. Even simple models could take many minutes to run on that PC.

There is one terrible lack in this otherwise functional operating desk. Do you see it? There is no place to install a flat screen PC monitor. This ought to be easy to remedy. Some of the upper shelf space will be covered by the monitor, but since today's equipment is smaller that shouldn't be a problem. Then I'll be able to put a keyboard up front and make it easy to arrange things as in any modern PC-centred ham shack.

Since this desk (less the upper shelf unit) was the centrepiece of my upstairs home office for the past 20 years I had to replace it, and fast. My new office desk is a bizarre hybrid of an old, small Ikea desk and odds and ends from Home Depot. I worked quickly this weekend to both rebuild the shack operating desk and construct and install a new office desk. Now I am not only on the air with my old and trusty operating desk but also ready to get down to work Monday morning.

Detuning a Tower from a Vertically-polarized Antenna

In my previous article on a 2-element loop array for 40 meters I issued a caution regarding the potential harm from a tower that is resonant, or just near-resonant, on the band of interest. This type of interaction can destroy the performance of a directive low-bands antenna that is vertically-polarized. Although even a single-element vertically-polarized antenna will excite a tower resonance the impact is typically not a major concern other than the effect on impedance matching. I have a particular concern with tower resonance since that may be only way I can achieve higher performance with a low-height antenna for 40 meters.

As W8JI describes it is possible to detune the tower so that, at least on one band, the tower can be made to effectively disappear. That is, become non-resonant on the band of interest. This allows the vertically-polarized low-bands antenna to meet its potential.

Of course the tower (plus ground and loading due to yagis mounted above the tower) might not be resonant on the target band and therefore there is no cause for concern. But you can only know for certain by exciting the tower with a nearby vertically-polarized antenna for that band. It would be a shame to go to all the effort of designing and building a high-performance antenna that isn't going to work out.

A better strategy is to remove the tower resonance once it is found, and ensure the antenna fulfills its potential. This is not only a one-time concern since, after all, the tower's resonant frequency will not stay fixed for all time: changes to other antennas on or near the tower will shift the resonant frequency, and we all add and remove antennas on an often yearly basis.

Since the weather is continuing to stay cold, windy and generally miserable here in Ottawa I decided to do a little more computer modelling to test methods for detuning the tower. It would be good to know this since if I erect a larger tower this year I will want to build a directive antenna for 40 meters, and due to its inevitable low height I prefer to go with a loop array rather than a yagi.

W8JI provides some general guidelines for designing and tuning what is effectively a trap on the tower. What is missing are specifics. This is understandable since there are many variables that are installation specific. However I don't want to just wing it. This is where EZNEC comes in handy, allowing us to parameterize the design so that we can succeed faster when we spring into implementation.

For the following discussion I will stick with 40 meters and the switchable 2-element narrow diamond loop array from the previous article. The lessons learned should be applicable to other bands and antenna configurations.

The basics of the trap design model are shown at right. Tom suggests a trap length of no more than 3/16-wavelength so I made my trap 5 meters long (A, wires 10 & 14), 0.5 meters wide (B, wires 12 & 13), and centred on an 18-meters tall tower (wires 9-11, with 10 as part of the trap). The 3 wires are ¼" aluminum rod, which make the trap rigid and adjustable. Heavy-gauge copper wire can be substituted for wire 14. The 18 meters tower height was selected since it is the worst case for 40 meters resonance that I previously discovered.

Currents are shown on the EZNEC plot for the case of trap resonance. Notice that the while the current in the trap is high the current in the tower segments above and below the trap are low (they decline to 0 at each tower end). In this view you cannot see the currents on the elements since EZNEC plots those at a right angle to those shown here.

A series capacitor is positioned at the lower-right corner of the trap, where it is most accessible for tuning. I assumed that the capacitor is a fixed, transmitting "door knob" capacitor or an air variable that is both low loss (small equivalent series resistance, which I inserted into the model) and can withstand the voltages present with high power. The capacitor should be protected from the weather with a cover or enclosure, and protected from mechanical strain by, for example, placing it in parallel with an antenna wire insulator.

Safety note: Place the trap high enough that it is out of arm's reach from the ground since there can be high voltages present on the trap when transmitting high power on the test antenna for which the trap is tuned.

The model was developed without doing any calculations. I simply made an educated guess at the inductor dimensions (length and width) and then adjusted the capacitor value (using an RLC load in EZNEC) until the current was maximum at the initial test frequency. This was easier than determining the trap's resonant frequency, even though in practice the latter is usually easier to measure -- I have a dip meter but not a suitable RF ammeter. Either ought to work since maximum current in the trap should coincide with the resonant frequency.

It only took about two minutes of value substitution to find the capacitor value for the test frequency: 49 pf. That's a useful value since I have several 50 pf transmitting ceramic door knobs in my junk box.

However this, as it turns out, is inadequate. I chose a test frequency of 7.02 MHz since that is the frequency at which the antenna gain is maximum. When I checked across the band I found that the F/B and higher-frequency performance were degraded. The F/B is the most valuable metric since any extraneous current will disturb the fine balance of current phase and amplitude between the antenna elements: a F/B of -20 db requires a power subtraction of 99%. Gain is less sensitive to minor phase and amplitude deviations.

Following further experimentation I found that it is possible to adjust array performance by changing the resonant frequency of the trap:

• Frequency of maximum gain (7.02 MHz, 49 pf): The result is as described above. The gain went up by a small amount, about 0.1 db, which is negligible.
• Frequency of maximum F/B (7.08 MHz, 45 pf): This gave the closest match to the gain and F/B curves for the model that has no tower, as was done in the previous article on this antenna. There is some degradation of gain and F/B at the top end of the frequency range (7.2 MHz).
• Frequency higher than maximum F/B (7.14 MHz, 35 pf): Maximum gain dropped -0.1 db (which is negligible) and the frequency of maximum F/B rose to almost 7.1 MHz. Gain and F/B improved a small amount at 7.2 MHz.
• 7.2 MHz (~30 pf): Maximum gain dropped a more significant -0.3 db and the frequency of maximum F/B rose a bit further than the preceding case. Gain and F/B made further improvements at 7.2 MHz, though not by much.

From this I conclude that precise tuning of the trap is not necessary. If you do want to eke out every decibel per my original antenna design objectives the trap should be tuned for resonance between 7.05 and 7.1 MHz. Matching is not a concern since the SWR curve shifts a managable amount as the trap is tuned across the band.

Tuning the Trap

Although this is a purely software model, one I have yet to build and use, the design must be amenable to tuning. Since it is difficult to directly measure the degree of interaction between the tower and the antenna it is best to focus efforts on the trap. Luckily this should work well, as W8JI said and as my modelling seems to demonstrate.

NOTE: If you see evidence of tower interaction during the initial setup and tuning of the loop array you must put that aside until the tower trap is installed and properly tuned. You should only continue tuning the antenna (per the procedure in the loop array article) when the trap is tuned.

Construction and configuration of the trap are the foundation of the tuning system. The horizontal arms (B) are modelled as solid aluminum rods not only for strength but to allow the inductance to be varied. I kept the arms short enough that the entire trap can be reached from the tower.

The vertical arm, A (parallel to the tower), can be wire, just take care that the copper to aluminum junction is solid and protected from corrosion. Solder lugs are a good choice, much better than clamping the wire directly to the aluminum.

The capacitor is placed at the bottom of the trap for a reason: to allow adjustment with the minimum possibility of coupling between the trap inductor and your body. It should be solidly attached to the bottom arm so that it is robust against abuse and tuning (if it is a variable capacitor). Tune it with your head below the level of the bottom arm and good insulation between your hand and the body of the variable capacitor.

If you choose to use a dip meter to tune the trap a small pickup loop should be inserted at the bottom of A. This is easier to do when vertical arm A is wire.

C vs. L -- The trap can be tuned by varying either the C or L component, although until now I've only discussed C. The L value, although not directly measured and difficult to measure in practice, increases as the A or B dimension (see above plot) increases, and vice versa. For example, if the B dimension is shortened from 50 cm to 30 cm (1 ft.) the required C value must be raised from 45 to 50 pf to counteract the reduced inductance and keep the trap resonant at 7.08 MHz.

It may be preferable for trap robustness to use a fixed C and a variable L. To vary L you slide the rods in and out of the tower or slide the taps for the A arm along B rods. Adjust both ends of A at each step so that the A wire is parallel to the tower.

If a variable capacitor is used you can opt to remove it from the trap after tuning is complete, measure its value with a capacitance meter and substitute a suitable transmitting capacitor of that value. Getting an exact match will be difficult so you should adjust the trap inductance afterwards to compensate. Whether a fixed or variable capacitor is used you must protect it from the weather to prevent damage and so that precipitation does not alter its value or breakdown voltage.

After tuning you must test the antenna from the shack. Confirm that the F/B has a sharp peak and that the SWR curve and resonance are as per the design. You can then complete tuning the of antenna, confident that the tower is no longer interfering with its performance. The trap should not need further adjustment after the antenna is tuned.

Variations on a Theme

Trap orientation -- As modelled the plane containing the trap inductor is orthogonal to the loop elements. While this is largely immaterial to the design and tuning of the trap there is a small affect on the antenna pattern. When the plane of the trap inductor is parallel to the loop elements the pattern becomes asymmetric near the pattern's nulls and rear direction. The effect isn't large so it can be ignored. However it does demonstrate how fine a balance between element currents is required to achieve a large F/B.

Vertical trap placement -- The trap can be moved up and down the tower, but does it make it difference? In my model I centred the trap on the tower, so that there is 6.5 meters of tower both below and above the 5 meters high trap section. I tested this by first moving the trap so that its bottom is 3 meters off the ground. This might be preferred to make it accessible from a step ladder.

I again tuned the trap to 7.08 MHz, and it turns out that the value of C is unchanged. I had suspected that by proximity to ground would alter the inductor value. Unfortunately the frequency of both maximum gain and F/B shifted downward by ~25 kHz and the F/B curve across the band degraded by several db. This isn't a large problem, but still. On the plus side the SWR curve improved! There is now another dip to 1.0 at 7.2 MHz (see chart). However the antenna performs almost no better than a single loop above 7.2 MHz.

Next I moved the trap higher on the tower, so that the top of the trap is 3 meters below the tower top. Interestingly the pattern and match behaviour was almost identical to that with the trap low on the tower. The significant differences are that the SWR is even better, staying below 2 even at 7.3 MHz. This time, to my surprise, it was necessary to raise the capacitor value from 50 to 63 pf.

In both cases the worse performance is visible in the currents plot. The longer section of tower outside the trap develops a higher current which interferes with the desired performance of the array. Of course if you're willing to sacrifice pattern performance (primarily F/B) for full-band matching you now have an option. However keep in mind that this is only a simple model, and once you add in the capacitive action of high-band yagis above the tower what you are likely to achieve in reality will differ, no matter which height you place the trap. My guess (which I won't bother modelling right now) is that with yagis in play the trap ought to go above the half-way point so that the electrical length of the sections above and below the trap are approximately equal.

Trap versus No Trap

Building, tuning and maintaining a tower trap requires effort, some expense and ongoing maintenance which, I believe, should only be undertaken if proven necessary. Since the resonance of the tower (plus ground and other attached antennas) is typically too difficult to predict it is best to try the vertical array (or just a single test element) first and determine whether the tower can degrade to the loop array performance. Do this by looking for anomalous SWR -- where the impedance curve and resonant frequency significantly departs from the model. Anomalies in F/B and gain are more difficult to discern.

If a trap is warranted don't hesitate to do it. When you go to all the trouble of building a large antenna to improve low-band performance it is unwise to ignore the signs that the antenna cannot perform as intended. This is too often easy to overlook (and convince yourself otherwise!) when a second antenna for the band is not available for comparison.

Even after you do build the trap you might not yet be done: solving one problem can introduce others. The placement of a trap for 40 meters in the tower could alter the performance of nearby 80 and 160 meters antennas by introducing a tower system resonance on those bands. As with any trap, on lower frequencies it acts as an inductive load which could lower the antenna system resonance to one of those bands, creating a destructive resonance that was not present before installing the 40 meters trap.

Of greater concern is any antenna for 80 or 160 meters that incorporates the tower as part of the antenna. Examples include half-slopers and shunted towers. At the very least those antennas will require retuning once the 40 meters tower trap is installed and tuned.

2-element Narrow Diamond Loop Array for 40 Meters

In my recent survey of 2-element loop arrays for 40 meters I focussed on the potential but not the actuality of real-world designs. In particular, getting these antennas to a 50 + j0 Ω match requires effort I was not willing to undertake without first knowing their performance. That is, I focus first on the pattern and then, and only then, do I consider the match. Never confuse the relative importance of pattern and match: if the pattern doesn't meet your particular operating objectives the match is irrelevant. In other words, a nicely-matched antenna is nice but if that's all you want you can invest in a dummy load or, for that matter, a variety of poorly-performing commercial antennas. Thus the title of this blog.

In this article I take the most promising of the 2-element loop arrays, the one made from narrow diamond loop elements, and turn it into a usable design. The objectives of the design include:

• Achieving an SWR close to 1.0 at the frequency where gain is maximum.
• Favour the CW segment, my favourite.
• Pattern switching, from one broadside direction to the other.
• Mechanically robust.
• Reliable performance.

Of these objectives the last is the most difficult. Vertically-polarized antennas on a metal support (e.g. tower) are prone to interaction with the tower and cabling that runs along the tower. The performance of a directive array is sensitive to any resonances, which can reduce or obliterate the theoretical performance. Unfortunately these interactions are installation dependent, so the best I can do is provide some insight on what to watch for. I cover this topic last.

Now on to the design specifics. I took the "raw" design from the survey article and modified it in the same fashion as I did for the switchable wire yagi antennas. The challenge was to move the array's resonant frequency to coincide with that for maximum gain, and to change the impedance to 50 + j0 Ω. While I did not show it in the survey article, with the maximum gain at 7.000 MHz the resonant frequency is 6.915 MHz (57 + j0 Ω).

The survey antenna and the one described here have an apex height of 15 meters. The supporting structure is assumed to be non-conducting or sufficiently non-resonant to allow it to be absent from the model. This is a matter we'll come back to later, as promised above. The boom length is 7 meters, which is the optimum length discovered in the survey article.

It took close to one hour of adjusting the design on EZNEC to get the frequencies of resonance and maximum gain on the same frequency. The antenna is optimized for CW. For a 2-element parasitic antenna using a reflector element this allow best performance for CW (lower part of the band) while still performing reasonably well higher in the lower part of the SSB segment.

Each loop is 40.46 meters in circumference (10.12 meters per side) when made from 12 AWG insulated copper wire. This is smaller than the 43.9 meters circumference of the survey antenna. As I indicated in the survey article the loop size in a switchable design would be smaller because of the inductive loading of the transmission lines running from each element to the switch box. With an apex height of 15 meters the bottom of the antenna is up 3.94 meters for interior angles of 120° at the top and bottom.

To keep the switch box close to the element feed points I assumed a rigid 7 meters long "boomlet" running between those corners of the elements. This allows for 3.5 meter runs (the minimum possible) of 300Ω ladder line (0.9 velocity factor). A switch box placed anywhere else, such as on the tower, requires longer runs of ladder line, thus smaller loops and poorer performance. The right angles between ladder line and elements also reduces the potential of common-mode currents on these lines. The boomlet not only supports the switch box it also serves to reliably hold the array's shape, as will be described later.

The resulting array has a maximum gain that is only -0.03 db inferior to that of the full-sized elements of the survey antenna, which is negligible. Maximum gain of 3.44 dbi at 10° elevation is set for 7.02 MHz. The maximum F/B is about 60 kHz higher, just as it was in the survey antenna.

The SWR at resonance is 1.1 (56 + j0 Ω) at 7.025 MHz, and slightly lower at 7.015 MHz where it reaches its lowest value. As can be seen the Q of the antenna is higher than that of a single loop antenna, and the SWR rises significantly away from resonance. Since the rise is quite sharp at lower frequencies it is best to set this frequency close to band edge. The SWR (and gain) degradation is more gradual at higher frequencies.

Unlike the 2-element yagi designs there is no need for a beta match or other matching network to match the antenna to 50Ω coax. The naturally high radiation resistance of a full-wave loop combined with the array's high Q takes care of the match for us!

To tune the reflector there is either a transmission line stub (again, using 300Ω ladder line) or a tapped coil inside the switch box. The length of the reflector stub, which is shorted at the far end) is 0.8 meters. It will have to be tuned when the antenna is first installed. Since the design, construction and use of the switching and tuning system is, aside from the removal of the beta match, the same as that for the switchable yagi designs I will point to that earlier article rather than repeat the material here.

The gain and F/B performance figures are nearly identical for the survey version of this antenna, right across the band. The plot stops at 7.2 MHz to capture the frequency range where the antenna performs best. To get both the gain and F/B on the same plot the gain is multiplied by 10. As mentioned above, the maximum gain is 3.44 dbi at 7.02 MHz (shown on the chart as 34.4).

Construction

Next, let's turn to the construction of the array. No matter how you look at it a switchable loop array is more structurally complex than a switchable wire yagi. On the other hand it is electrically simpler, mostly due to the ease of matching to a coax feed line. The feed point is also closer to the ground, and can be made closer to the shack by suitable selection of which side of the array to feed. Although transmission line losses are small at 7 MHz there is the expense of a long run to be considered.

The antenna boom is assumed to be tower mounted and trussed in much the same way as was done for the wire yagis. The boom is 1 meter longer and is not cluttered with a feed system. The element bottoms can be secured with a similar type of boom (boomlet) lower down the tower, though trussed from the bottom since the tension is upward.

The two corners of each element are more difficult to secure. While a simple tie-down rope can be used it must be run at an angle shallow enough to apply tension to both the lower and upper quarters of each loop, and to precisely position each corner. Symmetry and parallelism are paramount in a switchable array.

For the side containing the feed and switching system it is preferable to use a boomlet as described above. It can be used for the other side of the array as well. It should be both lightweight and rigid.

Consider the design at right. The boomlet is divided into 3 sections with truss ropes tied at each of the 4 edges. The centre third is aluminum tubing and the outer thirds are telescoping lengths of plastic or fibreglass. The aluminum tube and the rope truss ensure rigidity when the elements are tensioned.

The 4-point tying to a common point, then utilizing a common tie-down rope to a suitable anchor, is similar to that for the diamond vee wire yagi.

The switching and feed system can be mounted on the boomlet as shown at right. The coax can use one of the adjacent truss ropes for support (not shown, so reference the previous drawing).

Other construction details for the boomlet plus switching and feed system, and the tuning procedure, are as earlier described for the switchable wire yagis.

Tower Interaction

By feeding the array at one corner and the use of a common-mode choke in the transmission line there should be negligible interaction with the coax. Horizontally-polarized yagis mounted atop the tower may noticably interact with the 40 meters loop array, but the reverse is typically not a concern. However the tower and cables running along the tower can significantly interact with the vertically-polarized loop array.

How large an interaction we can expect? There is no simple answer since every installation is different. There is not only the resonance of the tower but the tower as loaded by rotatable yagis above the the tower. Even if the antennas are electrically isolated from the tower (e.g. Spiderbeam), the vertically-run feed line, and its capacitive coupling to the tower, can still interact with the loop array.

To gain some insight into the interaction I modelled a tower running up the centre of the array. This is an imperfect model for several reasons:

• The effective diameter of an open lattice tower is not the same as a solid cylinder.
• The tower may be directly connected to ground (lightning protection), but NEC2 does not support this configuration.
• Cables and yagis on the tower will, in general, increase the effective length of a tower since it all looks like capacitive loading.

In my model I made the tower a 60 cm (2') diameter conductor that starts just above ground and is then varied in height. I started at a height of 15 meters (the minimum to support the loop array) and went up to 25 meters. Even if the tower is shorter than 25 meters the capacitive effects of cables and yagis can easily result in a similar effective height.

What I found is that at 15 meters height the interaction was modest. The gain was not affected in the CW segment, gain dropped -0.5 db near 7.2 MHz, F/B was slightly reduced, and the SWR surprisingly improved above 7.15 MHz.

At 25 meters height the interaction was very minor, enough so as to not be a concern.

Between 16 and 23 meters height the interactions range from modest to debilitating. The peak effect (induced current on the tower -- see EZNEC current plot at right) is around a height (or effective height) of 18 to 19 meters. At these heights the impedance is a mess as the following SWR curve demonstrates. Gain is reduced by -1 db or worse and F/B is poor to non-existent across much of the band.

Unfortunately it is difficult to predict what to expect in any particular installation. With luck the effective height of the tower will be sufficiently raised by capacitive cable/yagi interactions to avoid the danger zone.

Update Feb 26: I ought to have mentioned that it is possible to detune a tower with a resonance on one particular band. I skipped over this possibility since I didn't have or know of any good references, and assumed it might be too difficult. One that I since found is this article by W8JI. It's worth a look.

Conclusions

At a height of 15 meters the 2-element narrow diamond loop array has ~1 db better gain than its structurally-closest wire yagi competitor, the inverted vee wire yagi. When account is taken of structural complexity, uncertainty regarding severity of interactions, or the ability to place either antenna at an apex height above 15 meters, the wire yagi may be the better choice.

Where the loop array excels are F/B and feed simplicity, which may sway one's decision. The choice is yours. As they say on the internetz: YMMV. I'll be carefully thinking this over before deciding what if any wire array to build when I am in a position to do so. That time may come later this year.

ARRL DX CW 2014

In my 2013 summary I said that one reason to quickly repair the mast for the multi-band inverted vee was to be ready for the ARRL DX CW contest in February. That weekend event has now come and gone. Although this is not an antenna article it is relevant since, after all, what is the use of antenna if not to make lots of contacts? This article is one ham's perspective on the DX contest possibilities with 5 watts and a few wire antennas at a modest height.

Unlike the CQ Worldwide CW contest in the fall, I decided to get beyond casual and dedicate the weekend to the contest. I took many breaks and got plenty of sleep so this was hardly a hard core effort. That would in any case have made little difference since when conditions were unfavourable to my little pistol station there was no benefit to continue sitting in front of the radio.

My objectives for the contest:

• Top ten in the unassisted QRP all-bands North America category.
• Finally cross the 100 countries mark on 40 meters with my current QRP station.
• Work as many new band-countries as possible.
• Have fun.

To my surprise I may have achieved the first objective, the second I definitely met and I had good success with the third and fourth.

The generally good conditions were a tremendous help of course, though the unsettled geomagnetic conditions from Saturday late afternoon onward negatively impacted my results on 40 and 10 meters. Since at best my signal is marginal on the other side of each QSO even a small increase in ionospheric absorption causes extreme difficulty.

Competition in the QRP category is less than in most others. It is therefore not that noteworthy an achievement to place highly: this speaks to the parable of a big fish in a small pond. That my claimed score in CQ WW CW placed me in the top ten with only a modest effort gave me the confidence to think I could do the same in the ARRL DX CW contest. However it will likely be months until I know. If I go by last year's results I have a reasonable shot.

My choice of contest logging software is N1MM. I like its uncluttered user interface and reliability. However I use only a fraction of its features. For example I do not yet use its programmable CW memories feature, which requires a PC-to-rig interface that I don't have. Instead I used my trusty 30-year old keyer that served me well in contests long past.

The score summary produced by the software is shown adjacent. The claimed score is exaggerated by 2,000 to 4,000 points due to one miscounted multiplier on 10 meters and a small number of suspect QSOs. This is not unusual. The score will be lowered by the log checkers after I submit the log. I had more country errors to correct when I imported the contest log into my old version of HRD 5 (Ham Radio Deluxe).

Unlike CQ WW the ARRL DX is more like a QSO party. For Canadians, that means we cannot work VE and continental US stations. That is, every QSO is DX, and there is no temptation to spend time hunting or running US stations. If your objective is purely DX, this can be an excellent opportunity to add to your band-countries totals. If you live outside of W/VE this is not a real DX contest since you are only allowed to work W/VE. That is why the ARRL DX contests are less popular than CQ WW.

On 40 meters I worked 7 new countries to raise my DXCC count from 95 to 102. That brings me to the bottom rung of DXCC award status with only a little over 4 months of operating. I am pleased with this achievement since it is with a maximum power of 10 watts (5 watts during contests) and a delta loop. The new ones I worked included 3V, FP and ZL, but also more common entities such as OE and a few in the Caribbean region.

On 10 meters I managed to squeak out 12 new countries, though nothing rare. On 15 and 20 the additions to my countries worked were less, but enough to put me within reach of 150 on 20 meters.

I had my best QSO productivity on 15 meters. Once the geomagnetic conditions worsened late on Saturday, the signals on 10 meters were only mediocre on Sunday. So I focussed on 15 where I got good results. When I exhausted the possibilities there I searched for new multipliers on 10 and ran up QSO totals on 20. I had poor luck on the north polar path on 20, not managing to work even a single JA.

Unfortunately this time around I worked no new countries. I heard a few but could not get through with my small station. My DXCC total sits at 190, and slowly inching toward 200. This is my total since the beginning of 2013 with my current QRP station, not my all time count which is well over 300.

I've included a picture of my temporary set-up in my not-yet-completed basement shack. The KX3 transceiver is the smallest item! I didn't plan my station around contests so there are some ergonomic problems with the pictured arrangement. In particular the paddles and keyboard are too far apart.

The reason for the two sets of paddles was due to expediency: only my 40-year old Brown Brothers paddles had the proper connecter to plug into my 30-year old keyer. The keyer is homebrew, built from an article in October 1981 QST: The CMOS Super Keyer. I jammed the Brown Brothers paddle between the rig and Bencher paddles since the base is light enough that it slides around a bit on the plastic tabletop.

The antenna switch selects between the TH1vn (favours north & south), the multi-band inverted vee (favours east & west) and the delta loop. I did a lot of switching of antennas while operating 20, 15 and 10 meters to get the best signal on many QSOs. The path often didn't agree with the predicted great circle route, especially around sunrise and after sunset. Although neither high-bands antenna has the performance of a yagi I do have better agility than other stations since I can switch antenna heading instantly.

And with that I'll close off this article. I hope I succeeded in communicating the message that you can have tremendous success as a DXer with QRP and simple wire antennas. You should stick to CW and jump into contests to work lots of DX, including rare ones (stations that will work hard to pull you through for the points!) in a short period of time.

You don't have to be a contester or even enjoy contests. If the wanted DX is in a contest that's where you need to be. Who knows, you might learn to enjoy contests. When DX no longer motivates as it once did, contests may be the stimulus you need to build bigger and better antennas.

Ground Loss and Vertically-polarized Antennas

I made passing references to high ground losses suffered by all of the limited-height, vertically-polarized 40 meters loop antennas in the recent series of articles on DX performance of 40 meters antennas. This is an important topic so I thought it would be interesting to delve more deeply into the subject with the objectives of attempting to quantify the loss contribution and, maybe, see if the loss can be managed.

To do this I will standardize on the 40 meters delta loop antenna I am currently using. Its apex is 15 meters above a typical suburban lossy ground and vertically-polarized by being fed λ/4 down from the apex on one of the delta loop's legs. The adjacent current plot shows how the currents in the two legs are in phase and ideally configured to cancel all but the vertical radiation component. This is our reference for what follows.

To begin we had better be clear on just what we mean when we use the term "ground". Ground is not a magical box to which we connect our electrical supply and equipment for safety, where all the unwanted electrons are shunted off. Of course it can do this if we do it right. It can also help us avoid much of the damage of lightning strikes. Ground also reflects RF radiation and, ominously, absorbs and dissipates RF. Verticals are often said to need extensive radial systems as some sort of talisman to trick the ground into not eating RF.

In reality ground is just a very (very!) big lossy, non-resonant body that conducts, resists and reflects radiation, and it will do so not matter what. That is, ground interacts with all antennas, not just verticals, in both the near field and far field. It just happens that ground has a particular affinity to vertical E-fields and therefore can have a more pronounced impact on vertically-polarized antennas.

Consider the veracity of the following statements. You have probably heard (or spoken) one of more of these yourself.

• Attaching several λ/4-radials to a λ/4 vertical monopole removes much of the ground losses of a ground-mounted or elevated vertical.
• A λ/2 vertical dipole, whether full height or shortened (loaded) not only requires no radials it also has little or no ground loss.
• Horizontal antennas have no ground loss.

All the above statements are false. Let's look at them one by one.

The currents in the elevated ground plane peak at the feed point just like in any vertical or horizontal dipole. The antenna is a λ/2 in length, with half of that vertical and half of that horizontal, though split 4 ways: the current in each radial is ¼ the current in the monopole element. It is the right angle between the antenna halves which give the ground plane antenna its low feed point impedance of 30Ω, not the ground.

With the antenna raised to 3 meters above ground (about the same height as the bottom of our reference 40 meters delta loop) the EZNEC-modelled ground loss is -5.5 db. This is almost identical to that for the delta loop and, for that matter, all the other close-to-the-ground loops and verticals I've modelled. As for its DX performance, it is awful: the gain at 10° elevation is -1.9 dbi, worse than every antenna in the recent summary article. The only remarkable thing here is that a vertically-polarized antenna such as a delta loop can be so competitive versus dipoles and inverted vees even though most of the radiated energy heats the earthworms.

Just to show that ground is not in play with the ground plane antenna I raised its height to 100 meters above ground (easy to do with software, though not in real life). The impedance dropped a few ohms, ground loss improved to -2.5 db, and the pattern remained omnidirectional, but gained several vertical lobes as happens with any high antenna. The ground plane antenna even works fine with just one radial, except that it becomes somewhat directive. Using 4 radials makes the pattern omnidirectional. A ground plane is similar to an inverted vee tipped on its side.

As I said, this loss of -5.5 db is also true of every low vertical antenna I modelled, which include full-size and shortened verticals. So that takes care of the second statement as well.

As for the final statement, horizontal antennas do indeed have loss. It's just that the loss is typically small, and therefore not often worth discussion. To give two examples, the reference 40 meters dipole and inverted vee reference antennas in the previous antenna comparison have losses of -0.6 and -1.2 db, respectively, at an apex height of 15 meters. The loss rises at lower heights and drops at greater heights.

In short, the factors which affect ground loss for any antenna at a particular frequency are:

• Polarization: vertical is worse than horizontal polarization, often by 5 or more db.
• Ground type: loss rises with lower conductivity and higher dielectric constant.
• Height: the farther an antenna is from ground the lower the loss.

To gain an insight to the magnitude of the loss I created an EZNEC model with two grounds. This is a nice feature of the software that allows the study of artificial ground treatments that affect antenna performance.

Each ground has its own set of characteristics: conductance, dielectric constant and height. They must be concentric, each with a fixed inner and outer radius. The outermost ground extends to infinity. I set the heights to zero so that they are coplanar. The test antenna shares the same origin as ground so the delta loop is centered above the ground plane.

The outer ground is the same medium ground I've used all along. For the inner ground I made some rough estimates of the characteristics of a metallic ground plane made of something like open-mesh galvanized steel chicken wire. Although I would never pave my yard with this stuff I wanted to make the experiment somewhat plausible. I chose a conductivity of 100 S/m (better than seawater but much worse than a solid metal sheet) and a dielectric constant of 10. Since the mesh is open the field associated with currents on the mesh penetrates the ground, which will therefore donate some of its dielectric attributes to the ground plane. The specific numbers are not critical, which I tested with a range of values for these ground characteristics, so don't worry too much if you disagree with my numerical choices.

I should point out that a set of radials under the antenna is not equivalent to the mesh described above. I tested several of these antenna with a ground plane made up of a small number of short and long radials. It takes a lot of these non-resonant radials before an appreciable effect is seen. Unless you are committed to laying 100 or more of these on or in the ground (as done by AM broadcasters and some 160 meters enthusiasts) it won't help much. It takes a lot of metal to make an effective ground plane.

I then ran the model through EZNEC, measuring the loss, and the gain and elevation angle of peak far-field radiation, varying the ground plane radius from 0 meters (no ground plane) out to 100 meters (2.5λ). Here is a plot of the results.

As you can see the loss is acutely dependent on the extent of the metal ground plane, improving from -5.9 db to -1.0 db. The affect of the local ground on the antenna's net efficiency is plain to see.

The elevation angle where the broadside lobe peaks gets lower -- better for DX -- as the ground plane grows. A bump centred at a radius of 10 meters might be surprising but is easily explained, as I'll do further along in this article.

The plotted gain is for the elevation angle peak radiation not the 10° I've used in the analyses until now. I made this choice to give a sense of how the pattern shape changes with the increasing ground plane radius. The gain at 10° is also increasing but is not plotted. At a radius of 85 meters (coincidentally, 2λ) the peak is at 10°, and the gain is far superior to even the previously modelled 2-element yagis up 15 meters. Unfortunately this requires several acres of property, all covered with metal mesh! It's cheaper and easier to put up a dipole or yagi on a taller tower.

Let's look at the mechanics of how these performance figures are generated. It has much to do with the construction of the far-field gain.

The far field is the vector sum of the sky wave and ground-reflected wave. If the reflected wave does not undergo a phase shift, at low angles the two waves (with the same final elevation angle) have approximately the same phase and reinforce each other. As you may know there is an angle, the Brewster angle, determined by ground characteristics, below which the reflected wave is phase-inverted. When this happens the two cancel. That is why antennas, vertical and horizontal, always fail as the elevation angle approaches 0°.

The elevation angle where the lobe peaks also drops as ground conductance rises. If you can't pave the planet in metal your next best choice is an island in the ocean. That's why so may DXpeditions to islands, such as the recent FT5ZM operation, can have unbelievably great signals even on the low bands. With just 10 watts and a delta loop I was able to work them on 40 meters.

When the ground reflection at a particular angle is off the metal ground plane the loss and phase shift are small. You can see this effect in the adjacent elevation far-field plot. In this instance the ground plane radius is 85 meters, which is where the space wave from the top of the delta loop at 10° is reflected.

Notice the sharp drop in gain below 10°. Those involve reflections from the beyond the metal ground plane.

As hinted above this also explains the elevation angle bump at a radius of 10 meters. With no ground plane (radius of 0) the ground is consistently medium and behaves as we have come to expect. As the ground plane is extended outward the first low-loss reflection is at a steep incident angle from the bottom of the antenna. As the radius continues to be extended the lower incidence angle reflections from more of the antenna are off the ground plane. At 85 meters the entire antenna can illuminate the ground plane at a downward angle of 10°. It's straight-forward geometry.

I suppose one possible recommendation is to measure off 85 meters from your antenna in the direction that matters most for your DXing activity. Determine which neighbour that is, knock on their door and ask if you can pave their yard with chicken wire. For free! People like free stuff.

To close off let's pretend that we are the ones on an island DXpedition with a delta loop. We edit the model by reversing the two grounds, with the inner one becoming a medium ground (or worse if the island is rocky) while the outer one is seawater. I put the antenna in the centre of a circular island that is 200 meters across (100 meters radius) and 5 meters above sea level.

As you can see the elevation plot is noticably odd. There is an excellent but narrow peak at 2° elevation but with a node at 10° and lots of radiation at high angles where the poor island ground comes into play. Loss is also substantial, not much different from not having the ocean there at all; the shore is too far from the antenna to counter most of the ground loss.

A simple vertical would likely do better since it would not have as much high-angle radiation as the delta loop. The loss, however, is not so easily defeated. Unless you buy the island and pave it with metal.

Height & Gain: 40 Meters Wire Antenna Summary

For those who have followed along I have written a number of articles over the past several weeks on one and two-element wire antennas for 40 meters. My objectives are particularly aimed at DX (low angle) performance and a single support for the antenna apex. Some of these antennas were only intended as references -- the dipole and inverted vee -- for the purpose of comparison.

[The TL;DR version of this long article is to just read the chart below. I at least want the long version to document my observations for future use. Others might not.]

This article is an opportunity to distill a few performance aspects of all these antennas in one place. The result is one (very) busy chart plus several discussion points. To introduce the chart I will make a few points, most of which have appeared earlier.

• The elevation angle selected for comparison is 10°. This is the median value of measured elevation angles for medium to long path lengths at 7 MHz, which range from 0° to 20°. The peak gain is almost always higher than 10° but that is of no interest to me. The vast majority of antenna articles I've read focus on the peak gain at whatever elevation angle it occurs, but that is often not indicative of DX performance on the low bands where antennas are, for most hams, at low heights.
• Ground, topography and "obstacles" in the environment of the antenna can have a strong effect. On this I had to compromise if the comparison is to have any meaning. I therefore assume a medium, real ground, as modelled in EZNEC, which is approximately what many suburban hams will have. I also assume that the ground is flat out to the horizon and that there are no obstacles that would shadow or couple to the antenna. This includes a tower or metal support for the antenna that might be resonant on 40 meters. In the real world where we all live these interactions are inevitably present. As a general rule, the lower the antenna the greater the interactions. Interactions are more than not reduce antenna performance, especially for arrays with two or more elements.
• The loops and loop arrays are all fed for vertical polarization. When fed for horizontal polarization their DX performance (gain on the chart) would be substantially worse.
• The interior apex angle of the inverted vees, narrow diamond loop and chevron loop is 120°. The explanation for this choice is in the articles of the associated antenna articles. In general, a smaller interior apex angle for these antennas result in one or more of reduced bandwidth (higher Q), lower gain at 10° elevation, and reduced F/B (for the 2-element antennas).
• The gain shown in the chart for the 2-element antennas is at the frequency where it is maximum. It will be lower at other frequencies. You'll need to read the individual antenna articles for how the gain varies with frequency. 
• All wires in the model are 12 AWG insulated copper, except for the chevron which uses thicker 10 AWG. Choice of wire affects element length and resistive loss. After decades of playing with antennas I have come to prefer insulated wires to keep corrosion at bay. This not only makes adjustments easier in the future (no sanding/cleaning) but also avoids resistive loss due to oxidation.
• Links to the antenna articles: 2-element yagi with wire dipoles; 2-element yagi with inverted vees; 2-element yagi with diamond vees; delta loop; chevron loop; diamond loops; 2-element delta loop and 2-element narrow diamond loop.

Yes, it's a busy chart, but it isn't too difficult to unpack if you note that the dipole and inverted vee start from the bottom left and are roughly parallel, and the three 2-element yagis (dipole elements, inverted vee elements and diamond vee elements) start at the centre left and are also mostly parallel. All the loops and loop arrays cease to increase in gain as the height increases.

There are a few conclusions to be taken from this chart, which I'll list. Just keep in mind that there are a number of factors that could reduce the performance you might see in actual practice.

Gain Performance

If you must have gain, at any height, you should put up a wire yagi. While it may seem an expensive waste, a rotatable 2-element short yagi only 15 meters high will do very well. As you turn down the element ends, as you must with a fixed (or switchable) wire yagi, make the angle as shallow as possible. Alternatively, or below about 18 meters, a 2-element narrow diamond loop array will give about the same gain and superior F/B. But first test for tower resonance which would impact performance.

If you want to keep it simple and use a single element a vertically-polarized loop is the superior choice at heights below 18 meters. The choice of loop configuration is determined by how much F/S and low-SWR bandwidth you can live with, suitable tie-down points and interactions with the tower, a high-bands yagi above the loop and the local environment. The chevron loop offers the best gain but requires the greatest amount of compromise. The delta loop offers the best omnidirectionality but with unexceptional gain.

Copper Losses

Voltage Divider

Wire antennas are made from conductors that are narrower than found in the typical rotatable yagi made from aluminum alloy tubes. This results in resistive (I²R) losses that are higher than in the rotatable yagis despite copper being a better conductor than aluminum. Aluminum oxide, which readily coats the surfaces of yagi elements is a good enough conductor to not change this relationship.

Oxidized bare copper wires (cuprous oxide) have higher resistance, and therefore loss. The impact on low HF is usually not a large concern since the oxidation doesn't usually penetrate too deep and the skin depth is greater. Stranded bare copper is worse than solid bare wire since there is more surface area that will oxidize. I use stranded copper wire in most of my antennas, but I use insulated wire to avoid corrosion. There is dielectric loss in the plastic insulation, but it is small at low frequencies.

The resistive losses in the single-element wire antennas is typically no worse than -0.1 db, and so can be considered of no significance. The chevron loop losses are more significant, though still no more than -0.5 db, due to its low radiation resistance. The conductor resistance is in series with the radiation resistance, so as with any voltage divider circuit the lower the radiation resistance the greater the current and therefore the power dissipated in the conductor resistance.

In the 2-element wire antennas the impact of resistive losses is more pronounced since the radiation resistance is lower. This results in greater current flow and thus greater loss in the conductor resistance. This is not a large effect but is still significant. The typical loss figure for the 2-element antennas in this article is -0.3 db.

W8JI has a description of radiation resistance, height and loss you should consider reading if you'd like to learn more on this important topic. It also applies to the next topic.

Element Length vs. Gain

I think everyone knows that the free-space broadside gain of a λ/2 dipole is ~2.1 dbi. When the length is shorter the gain declines. One way to understand this is to imagine a dipole getting shorter and shorter until it becomes a point source. A point source is an isotropic radiator with a gain of 0 dbi. That we cannot actually build this antenna is unimportant. It is enough to understand that as an antenna element is shortened the gain declines.

It is important to understand that this loss of gain for short antenna elements is not due to losses. What actually happens is that the pattern broadens such that less power goes toward the broadside direction. However it is also true that short antennas have lower impedances which require matching networks, and those matching networks can introduce noticable loss.

The 2-element wire yagis that I modelled have elements that are shorter than λ/2. I did note this at the time as an advantage since it allows the antenna to fit a smaller space. The reason the elements are shorter (0.41λ) is due to the inductive loading of the ladder line running from each element to the switch box. In comparison to a wire yagi with full λ/2 elements the gain of these switchable yagis is -0.3 db.

Thus we have -0.3 db due to I²R loss and -0.3 db due to element shortening, which sums to -0.6 db. The gain of a full-size 2-element rotatable yagi would therefore be 0.6 db greater than that for the 2-element wire dipole yagi on the chart.

It is interesting to briefly look at how these figures compare to the expected gain from a short rotatable yagi such as those made by Cushcraft and Force 12. The I²R losses are largely eliminated but the even shorter elements (~0.32λ and ~0.28λ, respectively) increase that gain reduction by about another 0.1 to 0.2 db, plus a small loss due to the loading coils. So if you were to put up one of these small commercial yagis you would see a gain (at the frequency it peaks) indistinguishable from the modelled 2-element wire dipole yagi (top line in the chart above) and only 0.6 db worse than a 2-element full-size rotatable yagi.

The 2-element loop arrays I modelled have not been through the "shortening" process to make them switchable. When I get around to doing so expect that the gain will be similarly reduced from that shown in the chart above.

Antenna Height and Tuning

You should expect that the impedance and resonant frequency of all the single-element antennas will change with height above ground. The rate of change is greatest at the lowest height. Loops and inverted vees are particularly sensitive to height since for a given apex height they get closest to the ground.

Proximity to buildings wires (and other conductors) and utility wires will result in interactions that will skew the antenna pattern and shift resonance and impedance from the modelled values. Since these interactions are difficult to predict some tuning is required once the antenna is installed. These interactions are typically greatest when the antenna is low and the other conductors are within either broadside lobe.

Tuning of 2-element yagis and loop arrays is less sensitive to height. Once the 40 meter beam's lowest point is higher than about 8 meters the impedance and resonant frequency hardly shift at all with further increase of height. The same applies to the frequencies of maximum gain and F/B. While this is a topic all its own I can summarize the reason for this useful attribute, one that applies to all yagis, quads and similar beam antennas.

As the gain of an antenna rises the solid angle of the main lobe(s) covers a smaller area of the far field. That is, the antenna "sees" less of the ground and other conductors that are not within the free-space lobe(s). With a F/B or F/S over 10 db anything behind or beside the antenna, respectively, farther than ~λ/4 is pretty much invisible to the antenna, and therefore does not appreciably interact. The same is true of the ground, though more so for the yagis than the higher-beam width loop arrays.

This is why yagi manufacturers can confidently state the exact dimensions of their antennas regardless of where it is to be installed. Further tuning just isn't required. This is especially true of the higher bands where the distance to ground and other conductors is farther in terms of wavelength.