Two-Element Sloper Array for 40 Meters

This article follows on from a previous one on the challenges I face squeezing a DX-friendly antenna for 40 onto my 14 meters high tower. I have to accomplish this without deleterious interactions with other antennas, particularly the tri-band yagi.

If you refer back to that earlier article one of the antennas that has my interest in the sloper. Or in this case a loaded sloper since I have to shorten the length to under 17 meters to fit in my yard and not have it so horizontal that it interacts with the yagi and 40 meters inverted vee. The inductor-loaded sloper I designed in EZNEC is 16.8 meters long and symmetrical: fed in the centre and with coils midway along each leg.

At a target 10° elevation angle this sloper is 1.6 db better than the inverted vee. It is also uni-directional due to its slope and the parasitic action of the tower plus yagi.

Parameters

Sloper arrays are not new though they do not seem to have ever become popular. I suspect this may be in part because the benefits have at times been overstated. In my present challenging situation I decided to give them a look. I found it easy enough to do so since I already have a full interaction model with one loaded sloper; cloning and then positioning the second sloper in EZNEC is easy.

After cloning the original sloper I set up sources on both elements. These will be replaced by a suitable feed system once the design is complete. I then adjusted the following array parameters, at each step inspecting the gain, directivity and match.

• Angle between the slopers
• Angle between the slopers and the tower
• Separation between the sloper top ends and the tower
• Phase offset between the slopers
• Position of feed and loading coil(s)

Symmetry was maintained between the slopers and tower. Constraints of the parameters were set to ensure that the antenna would be safe to walk under and avoid tower clutter.

Design process and result

The antenna that I ended up with has an angle between slopers of 90°, angle to the tower of 45°, 0° phase offset between sources and 3 meters between tower and each sloper top end (top ends are 6 meters apart). Each sloper is 16.84 meters long (insulated 12 AWG), fed in the centre, and has one 10.5 μH coil (estimated ESR 0.5 Ω) 75% down the wire. I cannot guarantee that this is the absolute best design but if not it should be close to the best.

I used an equivalent series resistance (ESR) of 0.5 Ω for the loading coils. Even if made larger the effect is remains small since the absolute loss is a fraction of a decibel.

The currents are shown in the view above right. The current in the slopers is equal. Current on the tower is about half the magnitude of that in the slopers, along with related current in the yagi (top hat). A smaller current is induced on the 80 meters half sloper.

When compared to the sloper from the previous article the gain in the forward direction is better by 1.5 db (see left plot above). Since the single sloper is 1.6 db better than the inverted vee at 10° elevation the sloper array is 1.0 dbi, which is 3.1 db better. This will make a difference on DX paths along the main lobe.

Notice that the F/B is worse on the 2-element sloper. This is not as odd as it might seem. The reverse directions of the two slopers are different. Therefore their reverse nulls do not coincide; they quite effectively fill each other's respective nulls.

When compared to other antennas including loops and arrays that I've dealt with before, it is better than all single-element antenna candidates, other than the chevron loop which is equal in gain, and also bidirectional. Loop arrays and wire yagis do better, though not by a large amount. At an apex height of 14 meters the best of the lot, a full-sized 2-element wire yagi, is almost 3 db better. I estimate that the gain from a rotatable shortened yagi such as the Cushcraft XM240 would be 2 db better than the sloper array at this height (all measured at 10° elevation angle).

However we do have to keep in mind that an antenna like the sloper array has much of its current at lower heights that a rotatable yagi, which in most places gave have greater loss in the environment. At lower heights radiation is more likely to have to pass through houses and buildings that are rich in wiring and other metal. In other words, the sloper array and other wire antennas will likely perform less favourably in comparison to that yagi.

Match

Feeding this antenna is quite easy. Since the two source model had a system impedance of 145 Ω and the required phase shift is zero all I needed was to run a 90 Ω (e.g. RG-62) λ/4 transformer from each sloper to a common point, where 50 Ω coax is attached. If RG-62 or equivalent is unavailable 70 Ω coax can be used if an SWR between 2 and 3 is acceptable. You might want to try this anyway since environmental effects could lower the array impedance such that 70 Ω transformers will work better than in the model.

After you marvel at the broadband coverage in the above SWR chart you might want to ask how it is possible that a 2-element array can possibly achieve this. For example, every yagi has a much narrower bandwidth. Let's look at why the SWR is so good.

Additive vs. subtractive arrays

There are basically two types of directive arrays used at HF, as characterized by their dominant mode of operation: subtractive or additive. Both ultimately create their pattern by the phase and magnitude relationship among array elements. It is typical that both modes are present in the majority of antennas, although one is usually dominant.

• Subtractive: Mutual (near-field) coupling among array elements dominates. The yagi is of this type.
• Additive: Far-field superposition from array elements dominates. A 4-square array is of this type, as is the sloper array discussed in this article.

A yagi is an almost wholly subtractive array since all but one element is excited by the near field. Of course the far field pattern is ultimately additive, but that is determined by the coupling. An additive array can exhibit coupling, but the sources (phase and amplitude) at each element are mostly responsible for determining the pattern.

As Roy Lewallen W7EL showed years ago you still need to consider the coupling in a close-spaced array (one with even lightly-coupled elements). The laws of physics are always in force whether or not you choose to pay attention. EZNEC and similar tools help us to avoid errors of omission.

With regard to the match, the mutual coupling in a subtractive array is responsible for the lower bandwidth and lower radiation resistance. You can, if you like, consider that it is caused by the field cancellation in most directions; that is, subtraction. Since conservation of energy must be observed there must also be above-unity gain in some directions (net of any increased loss due to that higher ohmic heating of the antenna).

In an additive array there is less cancellation of the near field, allowing the far-field addition of the elements to determine the pattern. Since coupling is low there is less reduction of bandwidth (system Q). This is how the sloper array can have an SWR curve similar to that of a single element antenna, and do so without a complex matching network.

Tower erasure

The sloper array has both additive and subtractive features. There is some near-field coupling between the two sloper element, and a stronger coupling with the tower. The tower's resonance and placement give it the characteristics of a parasitic reflector. As to how big this latter effect is can be shown by removing the tower from the array. This is easy to do in software so let's do that.

Gain falls by 0.6 to 0.7 db, the main lobe narrows and F/B is poor. Or, if you prefer, the array is moderately omnidirectional. The effect of the tower as a parasitic reflector is not large although it is significant and, in this instance, beneficial.

Without the lower resonant frequency of the reflector (tower) pulling down system resonance the same sloper array configuration resonates 100 kHz higher: 7.225 MHz rather than 7.125 MHz. This is easily compensated for by lengthening the elements.

Conclusion

This little experiment is illustrative of what to watch for when designing an array of this type. It is helpful, and even mandatory to model the tower so that the array can be properly assessed and then modified if necessary.

Will I build this antenna? Maybe. My current thought is to build a single loaded sloper and see how it performs. If the modelled performance is confirmed and there is sufficient time before the snow flies I may give it a shot. It's simple enough to not require too much time. My only major concern is the multitude of wires hanging off the tower, all of which will have to terminate near the common property line with one of my neighbours.

The adventurous may want to consider putting up 4 of these slopers and, with a switch box, feed pairs of adjacent slopers for a switchable beam to each quadrant. It won't compare to a full-size yagi but it could be a good performer, and one that doesn't require a rotator and heavy-duty tower. If your tower is few meters taller than mine you can even forgo the loading coils.

Squeezing In a 40 Meters DX Antenna

Multi-band Inverted Vee on 40 meters

As my new (used) tri-band yagi is slowly coming into shape on my backyard lawn I am giving some thought to what I will do for a DX antenna on 40 meters. I currently have 40 meters coverage with my multi-band inverted vee but that is more oriented to North American (short) paths due to its high-angle radiation. While it has served to work a variety of DX, including S01WS, a few more decibels at low angles would prove helpful for DX and DX contests.

The inverted vee has a bidirectional broadside gain of -2.1 dbi at 10°. For an apex height of 14 meters and legs that go off at different vertical and horizontal angles this is not bad. The F/S is about -4 dbi, so it is roughly omnidirectional. The broadside directions favour Europe and the US southwest.

Any wire antenna that goes on the new tower can go higher than 14 meters. However there is more space around the tower to string wires than there is at the house-bracketed mast. Trees and a yard width of 15 meters are constraints.

To provide a basis for comparison I am reproducing at right the main chart from an earlier article on low-angle performance of a variety of wire antennas for 40 meters, plotted against apex height. (That article is the third most popular one that I've published on this blog.) For this exercise we only need to concern ourselves with the plotted gain at about 14 meters apex height.

On this chart the gain of my multi-band inverted vee falls between the lowest two lines, which are a dipole and inverted vee. This is likely due to one of its legs being more horizontal than the plotted reference inverted vee design. Other than that, no surprises.

I spent some time on this blog last winter playing with models for various oddly-shaped loops and 2-element loop and dipole arrays. Unfortunately almost all are incompatible with my existing setup due to interactions with the yagi, tower and the inverted vee. I will have to be more creative if I am to achieve my objective. To be specific here are the major problems I am encountering:

• Tower is resonant on 40 meters: Actually it resonates below the band but even so the coupling to a vertically-polarized antenna is severe. Whether I like it or not the tower must be included in the antenna design. Detuning the tower on 40 is not an option since that would compromise operation of the 80 meters half-sloper antenna. There are also the cables running down the tower will also couple unless extensively broken up with chokes.
• Wire angles: From initial modelling work I am restricting the angle between low-band wires and the tower to a maximum of 45°. Beyond this and modelled interactions with the tri-band yagi become noticable and often detrimental. This excludes from consideration inverted vee yagis and all loops other than the delta loop.

I'll briefly run through the most obvious candidates I assessed with EZNEC and my interaction model.

Loaded sloper

Since a sloper is a dipole it must be λ/2 long, which on 40 meters is about 21 meters. On a 14 meters high tower this requires an angle greater than 45° to fit. This exceeds my yagi interaction criteria. I therefore tightened the angle, kept the bottom about 1 or 2 meters above ground and added loading coils. If built the bottom would need to be supported by a pole at the property line.

Antenna length is 16.5 meters (insulated 12 AWG) with 6.3 μH coils midway along each half. It runs parallel to the 80 meters half sloper but is offset 2 meters (probably with a non-conductive pole sticking out from the tower) and drops at a sharper angle.

The typical sloper is modestly directional in the direction the wire points. There is a further effect from the strongly-coupled tower. I expected a small boost in gain due to this since the tower will act as poorly-tuned and non-parallel parasitic reflector. You can see that there is some induced current on the tower in the above plot.

The main lobe is very broad combined with a deep null in the back. The 10° gain in the forward direction is quite good, better than a delta loop and about equal to a narrow diamond loop. This has potential since my most productive path is toward Europe. The inverted vee would fill the gaps in the sloper's coverage.

SWR is broadband and a good match to 50 Ω coax. I have this one cut to favour CW but it can be shortened so as to cover the entire band.

Delta loop

I used a delta loop with a 17 meters high apex hanging from a 19 meters high tower in my 1980's era station. It was positioned close to the tower and strongly coupled to the tower. It performed well, but not as well as the 2-element wire yagi that replaced it. I had no ability to model the delta loop back then and I had no other 40 meters antenna up at the same time for comparison. The question I want to answer: how much does the tower affect the delta loop's performance?

The delta loop has to be squashed a bit to keep the bottom wire above head height for safety (2.5 meters above ground in this model). The feed point should still be placed λ/4 down from the apex along one leg to achieve the best low-angle performance and to be omnidirectional. I put the delta loop into the interaction model alongside the yagi and 80 meters half sloper and measured its performance at several different distances from the tower. As shown above the delta loop is 1 meter behind the tower (opposite the 80 meters half sloper).

The current on the yagi boom and elements is due to tower coupling. Otherwise there is little interaction with other antennas. The yagi shows no interaction on 20, 15 or 10 meters. The sharp downward angle of the delta loop legs is responsible for that positive outcome.

The elevation plots show that the tower has some effect as a parasitic reflector. Since the delta loop is behind the tower (with respect to my desired direction) this is a negative outcome. There is gain over a standalone delta loop in the other direction. The elevation patterns are for the delta loop 3 meters and 1 meter from the tower, on the left and right respectively. The antennas are otherwise omnidirectional. Due to NEC2 issues with the large-diameter tower the pattern for 1 meter separation is exaggerated by 0.35 db. Towards Europe the gain is worse than the inverted vee.

Resonance shifts from 7.1 MHz to 7.2 MHz when moved from 1 meter to 3 meters separation. With a 90 Ω λ/4 transformer the SWR is below 2 across the entire band.

Of course the result is better when the delta loop is placed on the other side of the tower. However this requires running the 80 meters half sloper inside the delta loop and places the delta loop adjacent to the 40 meters inverted vee (not yet included in the interaction model). There is also a tree in the way. This makes placing the delta loop in the best position quite difficult. That's unfortunate since its 10° gain of -0.25 dbi in the desired northeast direction is 1 db better than a standalone delta loop, and 2 db better than the inverted vee.

Tower vertical

Tower resonance as a vertical dipole is difficult to characterize. Assuming it is ungrounded and not affected by the various cables running along its length it appears to fall somewhere between 6  and 6.5 MHz. At least as far as EZNEC can calculate. This figure is unreliable, and therefore any assessment of it as a 40 meters vertical dipole is unreliable. I decided to try anyway.

The impedance is high, getting higher the lower down the tower it is fed. A matching network is mandatory. Its azimuth is omnidirectional, unencumbered by any apparent coupling to the 80 meters half-sloper wire. The yagi is an effective capacity hat since it is at a high impedance point.

Gain is poor. It calculates to -1.3 dbi. This is slightly worse than a standalone delta loop at an apex height of 14 meters and not much better than the existing inverted vee. Since it is omnidirectional it could be considered better overall. However with all the unconsidered side-effects from the cable runs and environment the modelled performance likely cannot be achieved. There will be additional loss in the matching network.

Boom dipole

An uncommon but potentially useful method of making a high dipole is to load the boom of a rotatable yagi, with the yagi elements acting as capacity hats. There are no wires hanging off the tower to clutter the yard or cause problematic interaction. A tunable omega match is needed to transform the impedance to 50 Ω. It has come up many times in the amateur literature and most recently in the October 2014 issue of QST. A good online description of the antenna (but without pictures) is provided by N4KG.

When all is said and done you still are dealing with a short dipole. A full-size 3-element 20 meters (or tri-band) yagi has a 7.3 meters (24') boom, which is only 0.17λ, or about ⅓ the resonant length. Obviously the longer the boom the better. The yagi I am about to put up has a short 4.1 meters (14') boom.

No matter how good and loss-free the matching network this dipole will have poor gain. For the 7.3 meters boom you should expect about -1 dbd. The power isn't lost, it just goes into broadening the pattern. Its only performance advantage is that it is rotatable, so the gain can be directed where you want it.

This is insufficient to motivate me to take the trouble to build such an antenna. This would necessarily include extending the 0.1λ boom with narrow-diameter tubing.

Next steps


Of the available choices the loaded sloper seems most attractive with regard to interactions, physical design and fit with my environment. However that does not make it a great antenna, perhaps just a good one.

Before I proceed there are a couple of promising variations on the sloper I will explore in a future article. I have several weeks to make a final decision since I cannot put up more wire antennas until the yagi is raised: they would only get in the way when lifting the yagi.

"Not in log"

In late March I decided to try operating a SSB contest using QRP and my wire antennas. The contest was CQ WPX. In my report on the contest I made a variety of observations regarding why SSB, and SSB contests in particular, can be so difficult.

QSO rates and totals are worse than in CW contests because the challenge to get the other station to copy puny signals is much greater. I half joked in my article that operators who failed to properly copy my call or exchange before rushing onward to the next contact would be the ones to suffer.

Let's face it, in every QSO my signal was difficult to copy. Many operators didn't let that delay them. They simply logged whatever they imagined my exchange was just so they could move on and work the next station. They will be penalized during log checking. It is better to say "sorry, no QSO, try again later" as good operators did. That works out better for both of us.

Well the log checking is now done and the results are published. It turns out I spoke too soon. The joke, it turns out, was also on me.

I did well enough to win Canada in the QRP single-operator all-bands (SOAB) category, but my score was reduced by errors more than I expected. The error rate was 2.9%, as compared to an error rate of 0.8% in last year's CQ WW CW contest. The score reduction is worse since in WPX contests most contacts are new multipliers. The error summary is below, directly copied from the LCR (log check report) I was sent. There are 454 claimed QSOs.

    2.9% Error Rate based on claimed and final qso counts
       0 (0.0%) duplicates (without penalty)
       3 (0.7%) calls copied incorrectly
       5 (1.1%) exchanges copied incorrectly
       5 (1.1%) not in log
       0 (0.0%) calls unique to this log only (not removed)

Perhaps half of the errors were due to my own sloppiness. These are mostly typos (e.g. transposition of letters and numbers) and failure to pay close attention (e.g. copying serial number 166 as 116). These errors can be improved with practice and concentration. My contest operating skills have degraded over 20 years of disuse. It didn't help that I was overly casual in my approach to a contest in which I didn't expect to do well. Those require no further discussion here.

The errors in the dreaded category "not in log" are the ones I want to delve into. What causes them and what can be done about them? Based on my recollection of those calls (LCR lists QSO info, which allows me to go back and look) and other behaviours I observed I can offer some tentative answers.

Operating QRP means that 95% to 99% of my contacts are S & P (search and pounce). That is, I scan the bands for stations that are sitting on one frequency and running QSOs. Calling CQ in a contest nets few results for a station like mine. QSOs rates are modest at best since time must be spent scanning the band for new stations and then having to waiting for an opportunity to call. Agility is required. It can also be quite fatiguing.

The primary objective of the running station is to achieve a high rate, which is typically measured as QSOs/hour. Super-stations with an attractive call sign in the early hours of a SSB contest can exceed rates of 250 QSOs/hour. For them time is of the essence. They are motivated to spend as little time as possible acquiring each QSO.

More so than in a CW contest my SNR (signal-to-noise ratio) at the other end of the QSO is poor. The other station often has to work hard to copy my call and exchange. This is something I remember well when I used to be in that position. However a big signal is not well-correlated with ability. Poor operators can grow impatient with weak callers, despite needing those points, which leads to sloppy practices.

The best contest operators will recognize when they need to move on and scratch the QSO. They will do so by saying something like "sorry, no QSO, please try later". Others scratch the QSO in less-desirable ways. They might say "73, QRZ?" or simply proceed to call CQ again. But they fail to actively confirm the QSO with you, such as by saying "got it, thanks, QRZ?"

There are operators that behave the same whether they logged the contact or not. So there is no definitive way to be sure that you ought to log the QSO. If they scratched the QSO and you log it they suffer no penalty but you do. First, you get that dreaded not in log error, and you then pass them over when you hear them later, possibly under better conditions.

While it may feel good to rail against the poor operating practices of others it is of no utility since we cannot control how they act. It is only our own behaviour we can control. If there is to be a solution it will have to come from the QRP operator himself/herself.

Here are a few suggestions that can help to lower the number of not in log errors for the QRP contester. They are not foolproof, but I have had some success with them.

1. Don't push it in the early hours: The first 12 hours are the worst. Every station you hear is a new contact and the super-stations are running at high rates. Competition and QRM are fierce. If you call a station and are obviously being received poorly, even despite no other callers you can hear, just QSY. Do not waste time their time or yours. Trust me, you'll run across them later when the QRM is lighter and they are more desperate for the points you mean to them.
2. Listen to the start of their next QSO: In contests with serial numbers, like CQ WPX, it can be worthwhile to stick around for 15 seconds after the end of a questionable QSO. The running station often has another QSO immediately after yours. If the serial number is not incremented you know that your QSO was not logged.
3. Listen to the end of their next QSO: Obviously this takes a little longer. Listen whether the close of that next (and hopefully good) QSO is more definitive. If it is you ought to be suspicious. Log the QSO but make a side note, and proceed to the next point below.
4. Deliberately dupe them: Later, when the opportunity is better, call the stations on your suspect list again. If they say "sorry, QSO before" then all is good. However if they work you then you'll know your suspicion was well founded. It's a rare contest nowadays where you are penalized for dupes. This may seem an underhanded trick to pull but I believe it is justified considering the (alleged) poor operating practices of some and the fact that rates for those running stations are much lower late in the contest. You aren't inconveniencing them all that much.

As operators of small contest stations we need all the help we can get. When it comes to not in log errors the larger stations have a distinct advantage over you. When they S & P they are unlikely to face anywhere near the same degree of difficulty being accurately copied.

When a larger station is running there is no risk to them of a not in log error. After all, their callers obviously copy them and, by the fact of their action alone, callers are ready, willing and able to log the QSO. You should see the obviousness of this every time you S & P a QSO; they are already in your log, duped and multiplier-checked, before you make your call to them.

Contesting with a small station can be fun but challenging. Those challenges are often quite different from what others face. Therefore the strategies must be different. It can be very rewarding to see those strategies bear fruit in your results when properly put into practice. Including a reduction or even elimination of not in log errors.

80 Meters Loaded Half-sloper

A half-sloper for 80 meters was listed in my antenna plans for the new tower. I have had good luck with half slopers for 80 in the past, so perhaps one cut down to fit a 14 meters tall tower can also do well. I don't know the provenance of this antenna but it was already popular in the 1980s with hams who needed decent DX performance that works in a small lot with the typical modest-height tower and tri-bander.

When I put up a half-sloper in 1985 it was on a whim. It was easy to build and I had no other good ideas a good 80 meters DX antenna. Since then I have been intrigued by this class of antenna since, to my surprise at the time, it worked very well indeed. All it needed was coax to the top of my 19 meter tall tower and a wire sharply angled downward to...somewhere. The "somewhere" was a challenge since I discovered that antenna impedance and resonant frequency were very sensitive to wire placement and length. I had to deal with interactions since it strongly coupled to the unshielded rotator cable running down the tower.

Once I had it working it worked great, netting close to 200 countries on 80 meters and it made for quick work in the pile-ups. Of course the Collins 30S1 helped.

When ELNEC arrived I tried to build a model of the antenna. This was difficult since MININEC ground didn't deal especially well for antennas close to ground. The need to add in my stacked yagis to the model added more complexity. With so many segments on a 20 MHz 386 PC (early 90s state-of-the-art) some runs took 30 minutes.

In the end I managed to squeeze results out of ELNEC that resembled what I saw and measured on the actual antenna. Later, after upgrading to NEC2-based EZNEC, I discovered that my model was nonsense. Shortly afterward I left the hobby and did not pursue the matter further. Twenty years later it is time to give this antenna another look.

Objectives

Even when it works well this antenna does not truly measure up to the best single-element 80 meters antennas currently in use. It is a compromise antenna, so our objectives must be realistic. Here are mine:

• Vertically polarized, with the bulk of the antenna current high up rather than close to the ground. The idea is to get good DX performance with modest near-field ground loss and no radials.
• Fit comfortably on the tower and within the property, without encumbering other yard uses and without deleterious interactions with the tri-band yagi and other wire antennas.
• Develop a good antenna model so that the antenna can be better understood, optimized, experimented with, and effectively compared to alternatives.

Model

The interaction model I recently developed is also a pre-requisite for modelling this antenna. The tower and yagi, and even cables, are an inevitable part of the half-sloper antenna. That is why the half-sloper is the first wire antenna I added to the interaction model.

Although this is not a full size half-sloper due to the height of the tower my hope is that the modelled characteristics are indicative of a non-loaded version. If I have time I will play with various tower heights. But for now my focus is on what I can use, and that means sticking with my tower and environment.

Here are some of the things I hoped to learn:

• Contribution of the yagi to antenna tuning and performance
• Effect of inductively loaded wire
• Varying the angle between wire and tower
• Directionality and polarization
• Alternative source placement

To begin the modelling process I inserted a 17.5 μH coil 60% of the way down the wire. The inductance is not critical, so I chose that of a suitable coil I had on hand. The wire is 12 AWG insulated wire 18.5 meters long making an angle of about 45° angle with the tower.  The wire end is 1 meter above ground, which is not ideal (safety hazard) but acceptable at this stage in the design. The SWR is above 2 due to a feed point impedance of 22 Ω at resonance.

Variations on the above modelling parameters will be explored in the article, and possibly in future articles.

Note: This antenna is a good example of how to drive NEC2 crazy. With the source near a multi-wire junction (tower, wire and mast) and with very different diameters strange things can occur. W7EL warns about this in the EZNEC manual and provides suggestions on evaluating and correcting calculation errors that result in erroneous antenna gain (loss). In this case a slight shift in source placement made a difference of 4 db! I have corrected for this in the model.

Yagi contribution and interaction

Since the yagi is part of the half sloper that is not considered an interaction. The concern is that the half-sloper wire will interfere with yagi performance on 20, 15 or 10 meters. So let's look at that first.

The result isn't surprising to me since I've noted in the past that even wires that cross the aperture of a yagi at a sharp angle have little induced current. That is true here as well. The worst case I found was on 10 meters with the yagi elements pointing in the same direction as the sloping wire. As the plot at right graphically demonstrates there is little current induced on the wire even in this case. So far so good.

However there is current there even though its magnitude is small. That can still be a problem since the high F/B of the yagi is predicated on the precise phase and magnitude relationship among the yagi elements, which can be disturbed by induced currents elsewhere. For example a 20 db F/B ratio is a 99% power reduction. Gain is also be affected, though to a much lesser degree.

As it turns out the pattern is affected only slightly. The F/B is not so much degraded as having the frequency of peak F/B shifted a small amount. Some pattern asymmetry is introduced (seen more on 20 and 15 in this particular instance), but it is small enough that I judge it to be entirely inconsequential. The gain reduction on 10 meters is < 0.1 db, and is lower yet on the other two bands.

The yagi contribution to the behaviour of the half sloper is different from what I expected. On reflection I see that my expectation was unreasonable. Let's look at that now.

There are currents on the yagi elements and boom as we expected to find. After all, one side of the transmission line is connected to them and the tower. The current plot is taken at 3.550 MHz, the frequency where I tuned the antenna to resonance. Notice that the current on the yagi is significant but not large.

In retrospect this makes sense. The effect of capacity hat placement increases from a small value near the centre of a dipole (or dipole variant) to a far larger value as it approaches the element end. That is, its effect increases where the impedance and voltage are high. A coil is the opposite, with its effect greatest where current is highest.

I tested this in the model by doing what is quite difficult in a real antenna system: I disconnected the yagi from the mast, leaving it free-floating in space above the tower. When I did this the resonant frequency of the half sloper rose from 3.550 MHz to 3.650 MHz. This isn't much. The feed point impedance also rose a small amount, from 22 Ω to 34 Ω, for this particular arrangement of wire and coil (more on this later).

The difference should be larger for a larger yagi (e.g. TH6), a longer mast or a stack of yagis. Even so, the effect of the yagi is less than I had believed.

Pattern

Once I had a functional model and began plotting the antenna patterns I got a few surprises. By that I mean my recollection of my 1980's half-sloper performance showed distinct differences compared to the present model. I believe that the new model steers closer to the truth.

I've focussed on the pattern at 10° elevation since DX is more of a challenge than short path for a small antenna on 80 meters. The antenna is clearly directional in the direction the wire points. However this is only true at low angles. At higher angles the azimuth pattern is less directional. At 10° the gain is -5.85 dbi, with a F/B of -4 db and F/S of -5 db.

Radiation off the ends at low angles is vertical, and is largely horizontal off the sides and in all directions at high radiation angles. This is an interesting mix in that it has radiation components that favour both DX and short path. It is however a compromise antenna, doing neither especially well.

I plan to point the antenna to Europe since it the most productive DX path for this locale and is short enough of a path that QRP has a chance. The forward gain of about -6 dbi may seem poor but for a simple antenna of this type on 80 it is actually quite good in comparison to alternatives. A large ground plane would lower the overall system loss but would contribute little to the far field gain at low radiation angles.

From my past experience I would have expected the DX performance to be better and the short path performance to be worse. That's the problem of only having one antenna for a band: there is little opportunity to quantitatively assess performance. This is where modelling can help if you are unable or unwilling to spend time and money experimenting with real antennas. In fact, it can help you direct your efforts in more fruitful directions.

Inductor placement

The placement of the inductor matters. The closer to the "centre" of the antenna it is placed the greater it will lower the resonant frequency. While that may seem attractive there is a cost: inductor loss. Current is highest at the centre and therefore the loss due to the ESR (equivalent series resistance) of the coil increases. But place it too far towards the far end of the wire and its effect is greatly reduced.

At the initial coil position 60% out along the wire the loss is about -0.1 db, assuming an ESR of 0.5 Ω for my junk box 17.5 μH coil. Loss increases to -0.2 db with the coil 40% out along the wire. I consider this negligible. Just be careful of losses if you are tempted to move the coil further inward or use a higher inductance in an effort to shorten the length of wire needed.

The other impacts are feed point impedance and SWR bandwidth. As you move the coil inward the impedance drops and the SWR bandwidth decreases. Again, the range of 40% to 60% out along the wire is a reasonable placement to balance the pros and cons.

If the wire can be lengthened it may be possible to eliminate the coil entirely even with a relatively short 14.1 meters tall tower. The wire will have to go out form the tower more horizontally. This requires more yard space and increases yagi interaction with the half sloper wire on the high bands. Another alternative is linear (capacitive end loading) of the wire element instead of a coil.

Matching

With a loaded element and a 45° angle between wire and tower this antenna is not a good match to 50 Ω coax. Its impedance at resonance is 22 Ω and, when matched, the SWR 2:1 bandwidth is 90 kHz. The feed point is near the electrical center of the antenna, in a 1 meter long wire extending horizontally from the top of the tower to the top end of the sloping, inductively-loaded wire.

I can live with the narrow bandwidth since with QRP my interest is primarily CW. A good match from 3.5 to 3.6 MHz meets my needs for both DX and contests. SSB QRP on 80 meters is not to my taste.

There are several ways to match the antenna at the feed point, and not with an in-shack tuner and the transmission line losses that can entail.

• Quarter-wave transformer: If the model proves accurate in a real system (unlikely for this peculiar, highly-interacting antenna) the transformer characteristic impedance must be 32 Ω. You can get close to this with parallel runs of RG-59 or RG-11 (or RG-6).
• Move the feed point: Impedance rises as the feed point moves towards the end of a doublet (of which this antenna is an example). Since the feed cannot easily be inserted into the tower leg of the antenna it would have to be moved further out on the wire element. Since the impedance changes slowly near the centre the feed point has to be moved quite far out to get a 50 Ω match. A current choke (or balun) would provide some protection from imbalance.
• Gamma or omega match: One way to accomplish this is to run the coax out a suitable distance and parallel to the tower and use the outer conductor of the coax as the arm to short to the tower at a lower height. Variable capacitors can be inserted to assist with tuning.

The downside is that despite the model this is an unpredictable antenna with regards to environmental interactions. Therefore there is no certainty which of these techniques might work best, if at all. On the other hand you may get a good match by doing nothing other than plugging in the coax. I've found that this will sometimes work. I suggest putting up the antenna and measuring the feed point impedance, and only then decide how to proceed with the match.

Wire angle and direction

In the section above on inductor placement I mentioned that the wire can be tilted upward. In the model I tilted the wire upward by 30°, so that the angle between tower and wire is 75°. This is getting close to horizontal. If the wire were made fully horizontal you would have a loaded inverted-L. But let's stick with the intermediate step and see what happens.

There is now a deleterious interaction with the tri-bander when its elements point in the same direction as the wire. However, in this particular case with the inductor-loaded wire the only significant affect is on 15 meters due to the induced current on the half sloper wire. The azimuth pattern widens and gain is reduced by -1 db or more. Impact on the 20 and 10 meters is small enough to be ignored. Because the yagi feed system is imperfect in the interaction model I did not attempt to measure the impact on SWR. However there must be a change.

On 80 meters there are also interesting changes. First, the SWR improves to better than 1.5 at resonance. This is expected since the tower and wire are approximately equivalent to an inverted vee (actually, so is an inverted-L), and the feed point impedance of such an antenna increases with increasing interior angle. The resonant frequency also declines, in this case by 50 kHz.

Before you become tempted to do this there is more to be dealt with than tri-bander interaction. The pattern is also affected. While system loss improved from -6.2 db to -3.8 db that recovered power primarily goes to high-angle radiation. That isn't good for DX. At 10° elevation the gain degraded by -2 db. This should not be surprising since by raising the wire it becomes more horizontal.

With a more acute angle the antenna match becomes a challenge but it is a better DX antenna and yagi interactions are negligible. The more the antenna resembles an inverted-L the better the match, and the worse the yagi interactions and DX performance.

Comparison to an inverted-vee

The simplest alternative to this antenna is a loaded inverted-vee with leg configuration similar to that of the half-sloper wire element. Mutual coupling with the yagi is small and, if symmetrically positioned, negligible with the tower.

Without going into model details here is a summary of my findings:

• Radiation at 10° elevation is -1 dbi worse in comparison to the loaded half sloper, but is more omnidirectional. Low-angle gain is highest in the end-fire direction, the same as the half sloper.
• Impedance at resonance is 40 Ω, which is a good match to 50 Ω coax.  SWR bandwidth is about the same as the half-sloper.

This is a favourable comparison. You get some benefits at the cost of another leg and coil. These benefits include: match; omnidirectionality; more predictable match; and better match.

Of course there are far better antennas for 80 meters than either a half sloper or inverted-vee. But these are not compatible with a suburban lot and limited height. For example, I recently visited a super-station with a full-sized, steerable 4-square vertical array in a wide-open field and lots (lots!) of radials. Very impressive, but impossible for me.

Conclusions

It should be clear from this analysis that there is nothing particularly special about the half-sloper antenna. It is similar to an inverted-vee or inverted-L antenna, but is oddly structured, with an acute interior angle and unpredictable relationship to ground. That is, it really doesn't belong in a distinct antenna category.

Yet the antenna has advantages:

• Easily turns the tower into "half" a low-band antenna, eliminating wire(s) and yagi interactions.
• Decent DX and short-path performance, allowing a small station to do reasonably well on 80 meters.
• Modest system losses without the need for an artificial ground plane.

Among the disadvantages:

• Unpredictable match means that time may need to be spent adjusting wire placement for best performance.It could be aggravating to find that the perfect spot for the wire is where the kids will run right into it.
• A matching network (e.g. gamma or omega match) may be desirable to avoid the need for a tuner and transmission line (coax) loss. 
• Narrow SWR bandwith means this one antenna can only cover one 80 meters band segment. That implies the need for a tuner (remote or in the shack) or more than one wire if you want to operate the full band. In my case, if I ever feel to need to operate an SSB contest on 80 I can simply place a junction near the end of the wire and open it to move resonance up to 3.8 MHz.
• The antenna has directivity so you'll have to choose which direction matters most to your operating objectives or, as already said, you'll have to add one or more wires.

My options are limited by space and antenna interactions. I will most likely build this antenna. When I do and I have some experience with it I'll report back. If I don't like it I can opt to convert it to an inverted-vee. But that could interfere with my plans for a vertically-polarized wire antenna for 40. There are further alternatives I have yet to explore.