Yagi Elevation Angle Nulls: Tilt & Fill

A common source of ideas for this blog is other hams. When a recurring question came up recently I thought that it would make for an interesting article. The question is: can you fill in those elevation angle nulls in a yagi pattern by tilting the antenna up? The short answer: no.

More interesting is why it is true since it can teach us about how antenna patterns are what they are. In this article I'll dig a little deeper and discuss its implications, including how to go about filling those nulls. I believe it is worth the effort since you can be held back in the achievement of your operating goals if you ignore pattern nulls.

Yagi tilt in free space

Ground is responsible for the existence of elevation nulls. Before we go into that we should have an understanding of a yagi's free space pattern where ground plays no role. Only then should we bring ground into the picture.

I am using EZNEC to do the models and pattern generation. I am use its features to easily rotate antennas and to compare patterns by overlaying them on one plot. Since I have 6 meters on my mind these days I returned to my optimized A50-6 model to provide the examples. It has enough gain that the main lobe is not too narrow nor too wide, helpful in illuminating the current topic.

In free space the main lobe (looking forward along the boom) is a bulb shape. With no ground reference the 15° tilt has no effect on the pattern. Of course the same is true for any amount of tilt, for any direction or boom rotation. Just as for astronauts in space there is no up or down.

Ground reflection

The pattern of a horizontally polarized antenna over ground is the sum (interference pattern) of the sky wave and the ground reflection. The relative phase and amplitude of the two determines the flux in every direction. Since we cannot transmit a signal into the ground we can safely ignore the half sphere of the pattern below a plane tangent to the ground. EZNEC automatically trims it.

We can now return to a comparison of the two antenna patterns. Because height affects how the ground reflections sums with the sky wave I am using the actual height of my antenna, which is 24 meters (80'). I've made the elevation plot large and used a 1° step size so that detail can be seen.

There are a few features of the pattern comparison that stand out. First, gain of the tilted yagi decreases at low elevation and increases at high elevation. This should not be a surprise. The antennas have equal gain at 35°. The second and perhaps most important feature is that the elevation angles of the nulls are identical. All that has changed is the depth of the nulls, which are shallower for the tilted yagi. The third and equally important feature is that the nulls of the tilted yagi are increasingly shallow at high angles.

To understand what's going on we need to refer back to the free space patterns. Gain is equal for equal positive and negative elevation angle deviations from 0° elevation due to pattern symmetry. Therefore when ground is parallel to the yagi ground reflections are therefore of similar amplitude for equal positive and negative angles. Reflection gain (nominally 6 db) and null depth depends on ground quality which determines reflection loss and, at low elevation angles, reflection phase shift.

Maximum gain and maximum null depth occur when the amplitude of the reflected wave is equal to the sky wave. Lobe peaks are at elevation angles where the phase difference is 0° and nulls occur where the difference is 180°. The higher the antenna is above ground, as measured in wavelengths, the greater the number of minor lobes and nulls. The 0° null is due to phase reversal of reflections at low incidence angles over imperfect ground.

Tilting the antenna does not affect behaviour of ground reflections. What does change is the amplitude of the reflections. Since the yagi main lobe is no longer symmetric with respect to 0° elevation the sky wave and ground reflection amplitudes are no longer equal for equal positive and negative elevation angles. For the modest 15° tilt being examined the inequality is greatest at high elevation angles.

Suffice to say this is not what we want. Tilting a yagi upward not only doesn't fill the nulls, except at the less useful high elevation angles, the gain at low angles is reduced.

Terrain

This analysis assumes flat, uniform ground. Complex terrain introduces complex ground reflections that shift the positions of the lobes and nulls, and their heights and depths, respectively. However, tilt still has no particular advantage since the lobe and null elevation angles remain as they are. Ray tracing tools such as HFTA can provide insight into how the terrain affects the elevation pattern.

Ground quality determines the amplitude of reflections, including the elevation angle below which reflections are phase reversed. The latter is why gain is zero at 0° elevation. For horizontal yagis like yagis the reflection amplitudes even over poor ground are reliably strong. Not so for vertically polarized antennas, but we're restricting this discussion to horizontal yagis.

Stacking

A common technique for increasing gain is to stack two or more yagis. Power is split among the antennas with phase set to achieve the operating objective. In almost all cases the yagis are fed in phase.

Another desirable characteristic of stacks is to move or reduce elevation pattern nulls. This is done by taking advantage of the different heights of the yagis (not applicable to side-by-side yagis). The lobes and nulls are different for each yagi alone and when two or more yagis are used. We'll keep it simple by restricting the discussion to two yagis in a vertical stack.

I've kept the first yagi at 24 meters height and added an identical one at 18 meters height, which is 1λ separation, the same as the boom length. Equal separation and boom length usually works well, and in any case we are interested in the general pattern rather than maximum forward gain.

Green is the upper yagi, red is the lower yagi and black is the stack (BIP: both in phase). Stack gain is as expected at about 3 db. The higher yagi has more minor lobes due to the greater height. For the lowest inter-lobe null (marked) the difference among the three is only very small at a little over 1°. The difference increases at higher angles. Unfortunately that first null is pretty stable for all configurations of the stack, so our objective is not met since the lowest null is the most critical for DXing.

The reason for the lack of movement of the lowest null is that the ratio of yagi heights is only 1.3. Small height ratios are typical at VHF and above, while at HF larger differences are the norm. The small ratio is good for gain but not for moving nulls. If this is important at VHF it is desirable to have a second antenna at a lower height. For example, to work single hop E_s at high angles and DX at low angles, as covered in a previous article.

Space

Now then, what about antennas that must tilt upward to target satellites and the Moon? I rarely hear talk about the effects of ground reflections in these communications modes, yet they can be important in some situations.

If you point a high horizontal yagi well above the horizon there is no problem. Ground reflections are negligible because the main lobe has a narrow beam width and little radiation is directed towards the ground. However there are ground reflections for moderate and low gain yagis that enter the picture for satellite passes less than ~30° above the horizon.

Circular and vertical polarization are immune from deep nulls. But many small satellite antennas are linearly polarized, especially those that are hand held. Hand held horizontal yagis are actually less of a problem on low passes because they are close to the ground and the nulls are at higher elevation angles.

So, not a big problem overall. When a null is encountered it tends to be a transitory phenomenon (the satellite is in motion) that may be mistaken for bad aim or incorrect polarization. By the time you adjust the antenna the satellite would have already moved out of the null.

Anyway...

Tilt seems a simple solution to dealing with nulls. Like many simple solutions to difficult problems it does not work. Besides which it isn't easy to accomplish. Do you really want to spec the mechanical design of an elevation rotator for a long boom 20 meter yagi? Leave those elevation rotators where they do something useful: satellite and space communication.