Wednesday, September 24, 2014

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.


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.


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.


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.

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