Thursday, December 10, 2015

2 x 2-element Sloper Yagi for 40 Meters

I wanted one last kick at sloper arrays as an alternative gain antenna for 40 meters. Right up front I'll state that I have no intention of building this antenna, even though it has several attractive attributes. I'm putting it here for general interest, and for the lessons it can teach us.

For myself, it is a way to close this chapter of wire arrays before I explore more conventional rotatable yagis. Although my initial foray into slopers was not positive that is not a general indictment against this class of antennas. There are real possibilities here for a reasonably simple wire antenna with gain on 40.

Before describing the antenna it will help to review objectives. I had several in mind.
Array elevation pattern, not including wire ohmic loss
  • Gain that is competitive with wire yagis. I described several in this blog, all of which seem to be quite popular. The 2-element switchable yagi with inverted vee elements is perhaps the one most comparable to the one in this article. It is also one of the most popular articles, ever, in this blog.
  • Low interaction with the supporting tower. Common tower heights are in the range of 15 to 20 meters which, with or without a tri-band yagi as a capacity hat, are highly prone to coupling with a nearby vertically-polarized 40 meter antenna.
  • Low interaction with a tri-band yagi at the top of the supporting tower. Here the greatest risk is with 15 meters, the third harmonic of 7 MHz. The yagi can couple to the 40 meter wire antenna, damaging gain and F/B performance.
  • It should be switchable. Fixed wire antennas benefit from reversible switching more than those that are rotatable. From my location that is especially beneficial in contests since the reverse direction of Europe is the US midwest and southwest.
What we'll discover is that my objectives are only partially met. There are things to be learned from the exercise, and that makes the present antenna worth discussing. Follow along and see if you agree.

Model and performance

I built the model in EZNEC by stages. First I made a single 2-element sloper. Its geometry is designed to make it switchable. This is accomplished by making the elements equal length, with switchable loads and feed lines. I won't be saying much about the switching details (loads and coax harnesses) since this isn't an antenna I would choose to build. The slopers are set 45° to the ground (and tower). Sloper spacing is 6 meters (0.15λ), which is a good choice for a 2-element yagi with the parasite tuned as a reflector.

Second, I added a mirror image of the sloper yagi, with the upper ends offset laterally. The same 45° sloper angle is used, which also serves to orient the two sloper arrays at 90° to each other. The purpose is to minimize mutual impedance between the sloper yagis, allowing them to operate independently and add in the far field. The lateral spacing between the yagis is a compromise between performance and construction difficulty.

To test interactions I placed a 21 meter tall tower in the centre of the array, and a 3-element 15 meter yagi on top. The sloper wires have a maximum height of 20 meters. On a shorter tower some care is needed to keep the lower ends of the sloper out of harm's way, plus there will be some performance impact.

The azimuth pattern of a single sloper yagi is compared to that of the full 2x2 array. The pattern of a single sloper is skewed to one side. The full array is symmetric. The gain is modest, however (not shown) the 2x2 array has greatly reduced high angle radiation. It seems that the bulk of the horizontally polarized field is cancelled due to the relative orientation of the two yagis.

The gain of the full array averages 4.5 dbi and varies little from 7.0 to 7.3 MHz. It peaks at 4.82 dbi at 7.05 MHz. F/B peaks 200 kHz higher. Gain is net of copper wire losses (-0.3 db with 12 AWG) and with EZNEC medium ground (-3 db). SWR bandwidth is narrow and I found it difficult to tame. The SWR dip can be moved to a higher frequency but no improvement in SWR bandwidth can be expected with a passive matching network -- no better than 150 kHz 2:1 SWR). Since the antenna otherwise performs moderately well across the band a tuner can be used, keeping in mind that a poor choice of coax will result in loss due to the high SWR.

Ground loss vs. net gain

All vertically-polarized antennas are susceptible to high ground loss. In the near field this can be ameliorated by radials or a metal ground screen. The latter is rarely used in practice. If the tower is shunt loaded on 80 or 160 meters, the radials will also reduce loss for the 40 meter sloper array.

It is a common error to believe that just because a vertical-polarized antenna is resonant or can be matched without radials that ground loss is avoided. Take care not to fall into this trap. The loss mostly comes from being close to ground, which is usually not the case for horizontal antenna. Other than seawater, ground is almost always unavoidably lossy, so you want to keep the intense near field of the antenna out of the ground, whether by distance, radials (also used to resonate some antennas) or a metal ground screen.

Vertical losses in the far field cannot be controlled, except perhaps by moving to a QTH with a more favourable topography. The idea is that the loss is more than compensated by the increase in low elevation angle radiation intensity, in comparison to a horizontal antenna at a modest height.

If you compare the 10° gain to that of other 40 meters antennas I've discussed in the past you'll see that the sloper array compares favourably. You should expect that the gain change with height will be similar to the other vertically-polarized antennas in that survey. That is, it won't change much. In a congested urban or suburban environment you should expect a vertically-polarized antenna close to ground would perform worse than shown in the models. This is due to various environmental interactions, including that the ground is almost certainly worse than EZNEC's "medium" ground.


Aside from environmental factors (which I won't model) there are two important interactions to consider with the sloper array: tower and rotatable yagi. In the case of the tower we are concerned with its effect on the sloper array. In the case of the rotatable yagi for the higher HF bands we are concerned with the sloper's effect on that yagi.

However, if the tower plus yagi is used as a low band vertical there will be some coupling with the sloper array that can alter the vertical's impedance. I've seen this in my own installation. The high HF bands yagi is in general too small to noticably affect the sloper array, or any lower band antenna. Although I feel it necessary to mention these cases I will say nothing more about them here.

A tower that is ~20 meters tall is likely to resonate on 40 meters, seeing that it is close to a half wavelength. Even if the tower is not resonant on 40 meters, either due to its unencumbered length or when top loaded by a rotatable yagi, it is long enough and close enough to have a substantial mutual impedance with the sloper array. By placing the tower at the exact centre of the sloper array and with those 45° angles I hoped to minimize the net current on the tower. I was only partially successful. You can get a sense of this by looking at the current plot at the beginning of this article.

Despite the amount of current on the tower the performance impact is small. The loads in the sloper can be tuned to compensate, though that is not without the expense of time and inconvenience. This is one reason I am not mentioning the specific load values I used in the model; every installation will be unique, being very sensitive to the specific interactions encountered.

Of greater concern is that the interaction is sensitive to tower height and loading of the rotatable yagi. Small changes here can have undesirable results on the sloper array's performance, especially the F/B and the already finicky matching. This is a situation where it would make sense to detune the tower. However that may not be a viable option if the tower is used as a vertical on 80 or 160.

To model the impact of the sloper array on a multi-band yagi for some or all the bands from 20 to 10 meters I placed a 3-element 15 meter yagi at the top of the tower, with the elements aligned with the direction of the sloper wires. This is the worst case scenario since the slopers resonate on 15 meters. The yagi is initially placed 1 meter above the top of the sloper wires. The pattern is then compared with the sloper array absent.

The elevation plot reveals the impact of the interaction. The greatest impact is on gain, with the loss of about -2.5 db. I was surprised not to see a larger effect on the rear lobes (F/B).

When I increased the separation to 3 meters the interaction almost completely vanished. That is not a difficult requirement to meet in practice. While it may be tempting to get the slopers as high as the tower will allow, the benefit on 40 is slim and the negative impact on 15 is large.

Boom construction

The 6 meter long boom must not be resonant on the higher HF bands to avoid destructive interactions with a yagi at the top of the tower. It must also be strong enough to allow trussing to compensate for the tension placed on the 4 slopers. Tension may need to be moderately high so that the coax to each sloper centre and the relay box don't cause excess sag.

The other challenge is that the sloper upper ends are laterally offset 2 meters from the boom. An even greater offset is desirable, and 2 meters is the minimum recommended. Smaller offsets impact performance and tuning due to the upper ends of the slopers coupling to each other.

A possible approach is a 2 meter (6') long aluminum tube with same length ABS, PVC or fibreglass tubes projecting out each end. The boom would be mounted 1 meter below the top of the tower, allowing the tie point of the truss to be 1 meter above the boom, which is minimum recommended for robustness. From the ends of the boom have 3 meters of rope to each sloper end insulator. With the interior 45° angle, this places the sloper tops 2 meters below the boom and 3 meters below the yagi at the top of the tower. The lateral offset will be 2 meters from the boom.

If the target height is 20 meters this will require a 23 meter tower height. If the tower is shorter it is still better to have the sloper heights lower in order to maintain a healthy separation from the yagi.

Faraday rotation

In an earlier article I discussed the impact of Faraday rotation on inverted vees, or really any linearly polarized antenna. This is the ionospheric phenomenon responsible for much of the periodic fading of signals on HF. Those nulls can be quite deep. Even though they might only last seconds it can turn solid copy into temporary loss of signal. It applies on both receive and transmit.

The sloper array is unusual in that it less vulnerable to Faraday rotation. Take another look at the EZNEC view of the array up above. Each sloper yagi has a polarity 90° from that of the other. There will be no signal null anywhere in the 360° of polarity rotation. This has advantages for both rag chewing and DXing.

Of course there is a downside. The array gain is reduced somewhat because the polarities of the sloper yagis are not in phase. Also, off the broadside direction the polarity is more variable, and since the array is fixed there is no way to point the array to compensate.

Notwithstanding these negatives it is an advantage. I would not choose to build this antenna for this specific feature, but it is nice to have if it is built for other reasons.


If you've gotten this far you can see that this antenna model has taught us a few lessons. I don't believe it is worth building since there are alternative wire gain antennas for 40 meters that are easier to build and deliver better overall performance. This is the advantage of computer modelling: that you can explore antenna designs from the comfort of your shack.

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