Stacking 20 Meter Yagis: 2 Long vs. 3 Short

Only a fraction of hams have stacked yagis. They are common in both VHF/UHF and HF big gun stations. There are still lessons about antennas to be learned for those who do not and will never deploy a stack. There is a question about stacks that I'd like to explore in this article that comes up from time to time. It may be of interest to those with and without stacks.

The question is this: which is better, 2 long boom yagis or 3 yagis with more modest boom lengths? I am going to focus my analysis on 20 meters since that is a band where long boom yagis are very large and expensive. Many contesters instead choose to stack three or more yagis with shorter booms. There are more of them in the stack but each is less difficult to build and raise.

There are advantages to using 3 smaller yagis:

• More pattern possibilities by selecting combinations of 2 of the 3 yagis
• It is easier to rotate the side mounted yagis, offering more directions with stacking gain
• The main azimuth lobe is wider, which can be a benefit for contesting
  

There are disadvantages as well. These are primarily narrower low SWR bandwidth and lower gain. Unless the ham has unlimited resources, the stacking of smaller yagis is a popular choice. 

It also helps that there are suitable yagis on the used market that can be purchased inexpensively and, where needful, optimized for gain, pattern and SWR. The Hy-Gain 204BA is a common choice. The optimized version of that antenna by N6TV is popular. Performance and construction details can be found in the ARRL Antenna Book.

I chose two long boom yagis for my 20 meter stack, and similarly for 15 and 10 meters, although those are smaller antennas. I kept the expense down by designing and building them myself, and I got a lot of satisfaction from the project. Most contesters would rather buy or modify so that they can get a big signal with minimum fuss. Not everybody has the same interests and priorities.

The breadth of this article is narrow in that the baseline for comparison is my antennas. I am most interested in alternatives to what I've built and the scope for future improvement. I will not do a broad comparison of various stack configurations. That said, lessons from this brief analysis have broader application.

The antennas

I will compare my 20 meter 5-element yagis on a 41' (12.7 m) boom to the N6TV 4-element yagi on a 26' (8.1 m) boom in the ARRL Antenna Book. Despite a 50% longer boom the gain of the 5-element yagi is not that much higher. Many big guns with 5-element yagis put them on a 48' boom for more gain. I chose an intermediate length boom as a compromise between performance and mechanical difficulty.

There are diminishing returns as the boom get longer. Keep in mind that the boom length, not the number of elements, is the determining factor for maximum gain. Elements are added to a long boom yagi to achieve the required level of mutual coupling for maximum performance.

The 4-element yagi is blue on the above charts. The gain difference ranges from 1.2 db at 14 MHz to 0.8 db at 14.350 MHz. The pattern comparison was done near the top of the band where the gain difference is small. Although the gain advantage for the 5-element yagi drops at the high end, the SWR remains very good while that of the smaller yagi rises to over 2. 

For a 5-element yagi on a 48' (14.6 m) boom the gain is higher by 0.5 db at 14 MHz and rises to 1 db at 14.35 MHz. At the time I designed my yagis I decided not to make the boom longer to keep the weight, cost and maintenance to within bounds that I was comfortable with. I will continue the analysis with my antennas since that is my primary interest. Tack on the extra gain if your interest is a 48' boom

These comparisons bring up a common point of contention: does 1 db make a difference? Yes, it does, though perhaps not in the way most think about it. Except for weak signals riding the noise level, you will benefit little from the difference on receive. It is different at the other end of the QSO. More stations will hear you because your signal is more competitive with their QRN and their QRM. You don't often notice that for daily operating, but it makes a difference in DX pile ups and during contests. A seemingly small signal improvement can improve contest scores.

Comparison of 2 × 5-element and 3 × 4-element stacks 

For model simplicity, the yagis are directly driven with a source placed at feed point of each driven element. There are no matching networks since there is no model penalty for an impedance mismatch and the patterns are unaffected. All yagis experience mutual coupling with the others, which is unavoidable and the reason that stack gain is not the 3 db that one might expect.

Now that we've set the baseline, let's move on to the comparisons. We know at the outset that stack gain is nominally 3 db. It can vary ±1 db or so due to yagi separation and height, and there may be effects of unequal power division when the impedances of the yagis are different. I think most will agree that 2 to 4 db does make a difference in on air results. In my experience the impact can be surprisingly large.

The heights of the 20 meter 5-element yagis are 140' (42.7 m) and 70' (21.3 m), which is approximately where I have them on my tower. I placed the upper and lower optimized 4-element yagis at the same heights and inserted a third midway at 105' (32.0 m). The one in the middle is approximately at the height of my lower 15 meter yagi. 

I believe that this a fair comparison. A third 5-element yagi does not easily "fit" because it's too close to the existing yagis. I exclude that case for now, but I will return to it later. Hence the comparison of my 5-element stack to a 3-stack comprised of the shorter 4-element yagis.

There are several interesting points that can be seen in the elevation plots:

• The gains of the full stacks are nearly equal.
• The 5-element yagi, as a stack and as individual antennas, have poor coverage of elevation angles between about 30° and 35°. There are no gaps with the 4-element yagis.
• Other than the full stack, the 5-element yagis are individually always better. That is perhaps most important for the upper yagi on long haul DX paths with the lowest elevation angles.

The 4-element stack does pretty well in the comparison. The azimuth pattern (see above) is broader and that can be an asset during contests where you want to reach the maximum number of stations while running. However, the beam width difference is small. Vertical stacking narrows the elevation lobes but not the azimuth lobes.

Although you need 3 yagis instead of 2, the mechanical advantages of the smaller 4-element yagis is enticing. I know many contesters that have gone that route. 

Additional combinations of the 4-element yagis

There are 3 combinations for the 4-element yagis (not including BOP -- both out of phase) that are not available with the 5-element yagis. Those are the three combinations of two yagis.

• Upper + Middle
• Middle + Lower
• Upper + Lower

We now have 7 total selection possibilities. The question is whether so many is beneficial. Compare these elevation plots with those above. The full 3-stack is the primary (black) trace.

It isn't surprising that the elevation pattern of the last combination -- upper + lower -- looks very similar to that of the 5-element stack. The only significant difference is that the gain is lower by about 1.3 db. That closely matches the difference between single 4-element and 5-element yagis.

The other combinations of two yagis are more interesting. Both do well in the lowest elevation angle lobe, with only a small difference in the elevation angle where they peak. The gains are down only by about 1 to 1.5 db from the full 3-stack. This is about what to expect in general between 2 vs 3 yagis in a stack; the difference between 1 and 2 yagis is of course approximately 3 db. There are diminishing returns. You'd need a fourth yagi to get close to 3 db more gain than a stack with 2 yagis.

Another advantage of the upper-middle and middle-lower combinations is that the middle elevations are well covered. The individual yagis in a stack of 4-element yagis achieve that as well (see above) but now we do it with increased gain. The high angle radiation is also reduced in comparison to the upper-lower combination. That may be useful if you don't have a separate low yagi or you wish to avoid BOP (both out of phase) configurations. The latter adds complexity to the stack switch. 

Challenges and benefits

The many combinations of a stack with three yagis add complexity on the tower and in the shack. There are 7 combinations compared to 3 with a two yagi stack, not counting BOP. At right is an example of a controller for a 3-stack system sold by Array Solutions.

Impedance matching is, perhaps surprisingly, less of a problem. There are several stack switches for three yagis that employ one network for feeding two or three of the yagis; the network is bypassed when selecting an individual yagi. 

A common solution is a TLT (transmission line transformer) wound on a large (2.4") ferrite toroid. There is a low insertion loss design whereby the transformation ratio is approximately 2.25. The net SWR isn't perfect but it is still pretty good for both cases. For a 50 + j0 Ω load, the SWR would be 1.1 for two yagis and 1.3 for three yagis. Since no yagi has a perfectly flat SWR, the mismatch due to the TLT may be dominated by antenna's SWR. That is, you might not notice it most of the time.

I could do the same with my home brew stack switches by altering transformation ratio of the L-network. It is also possible to switch a capacitor by relay to improve the match when selecting either two or three yagis. My stack switches are single band only while the TLT network is broadband, typically covering 40 to 10 meters. You need the latter for multi-band antennas such as tri-band yagis.

What I've learned

There are no big surprises in this analysis and comparison, nor did I expect any. The benefit comes from being able to put numbers to the scenarios rather than make broad assumptions. It was a useful exercise. I'll briefly list several of my thoughts from this modelling exercise:

• A stack of 4-element yagis works very well. The gain of a 3-stack compares favourably to my 2-stack of 5-element long boom yagis.
• There are more stacking options with 3 yagis. You can split the stack to point the rotatable yagis one direction and still have a 2-stack in another. Smaller yagis are far easier to rotate on a side mounted swing arm (or ring rotator) than my 5-element yagis.
• When the 4-element stack is split, typically the upper yagi would be used for a long haul path such as Asia while the middle and lower yagis can be pointed to Europe. The gain to Europe of this combination is about 1.5 to 2 db lower than the full 4-element stack. That can be a reasonable sacrifice during contests if done only occasionally. It is superior to the choices I now have.
• The many combinations that are possible with a 3-stack entail complexity. During a contest there is no time to play with all of the possibilities or to explain it to guest operators. There is also little advantage since the elevation angle and other propagation factors vary from one QSO to the next. They additional combinations may be have greater value for DXers.

One way to reduce the complexity of the stack is to permanently bond two of the 4-element yagis. If I were to do it, I would bond the middle and lower yagis. That entails bringing the transmission lines for those yagis to a common point at 0° phase shift (in phase) and feeding them in parallel with a network to transform 25 Ω to 50 Ω. Coax is run from there to the stack switch, also with a 0° phase shift, between the bottom pair and the upper yagi.

The stack switch can be same one as for a 2-stack since its operation is identical. When you select the "lower" yagi you are actually selecting a 2-stack.

I have no intention of replacing my 5-element yagis. They are excellent antennas that do wonders when stacked. However the stack only works towards Europe because the lower yagi is fixed. It would be nice to have another yagi in between so that there can a middle-lower 2-stack to Europe when the upper yagi is pointed elsewhere.

Possibilities

I do not want another 5-element 20 meter yagi on the tower for several reasons. It also fits poorly since the separation between yagis would be less than the boom length. That's a pretty good heuristic for spacing the yagis in a stack since it addresses the bulk of the mutual coupling issues. A side mounted 5-element yagi is difficult and expensive to rotate due to its weight and wind load. I won't even try.

This is what it looks like by the numbers. The gain of the three 5-element yagis is only about 0.6 db better than my existing two yagi stack. Even if that small boost is gain is acceptable, notice that the gain for the upper-lower combination (middle yagi not fed) is significantly reduced relative to my existing stack. Gain is compromised by interactions among the yagis -- they're too close together. The combinations of two yagis are, like the 4-element stack, equally useful, though gain is limited by those interactions.

There is another possibility: place a small yagi in the middle. The separation between yagis is greater than the small yagi's boom length though still less than the 5-element yagi boom length. Since the 4-element yagi is centred on the tower, the driven element is offset from that of its larger cousins. That can be compensated by a delay line to the middle yagi -- it is "ahead" of the others.

The  optimum delay line was found in the model to be 40°. That is larger than the expected 36° due to the 83" (211 cm) offset of the driven element. Mutual coupling is once again the culprit. The length of the delay line will also be sensitive to the matching network at the feed point, such as a gamma or beta match, since they will impose a different phase shift (reactance) compared to the larger yagis. To avoid model complexity, I included sources for each yagi without concern for impedance mismatches. You can do that in a model but not for a real antenna.

Even that doesn't help us. The gain of the 3-stack is almost exactly the same as my existing 2-stack of 5-element yagis. The degradation due to mutual coupling becomes very apparent when the middle 4-element yagi isn't fed. The currents induced on the inactive antenna elements isn't large but more than enough to disturb the stack's pattern. The currents can be inspected in the model.

Gain is about 1.5 db worse than if the 4-element yagi were not on the tower. The upper-middle and middle-lower combinations certainly have utility but for the reduced gain. The middle-lower combination can have higher gain when the upper yagi is rotated to a different direction.

If you are enamoured of the additional combinations made possible with a 3-stack, you must either use 4-element yagis or increase the tower height to achieve wider spacing of the 5-element yagis. A taller tower is not in my future!

This is useful information. While I have no serious plan to redo the 5-element 20 meter stack, the alternatives are worth pondering. If a 20 meter stack is in your future, detailed modelling should be done before planting a big tower. HFTA is another useful tool to optimize stack configurations for the local terrain before beginning construction.