Stacking Scenarios for the New Tower: 15 and 20 M

As I grind my way towards completion of my stacks of 5 element yagis for 15 and 20 meters it is time to decide what goes where. The objective is to maximize performance, when used as a stack and when used individually. The major decisions on placement: height and separation.

There is also the matter of interactions with yagis for the other bands and with the guy wires. For the present exercise I will ignore those interactions since the way I broke up the guys to be non-resonant and with sufficient yagi separation the pattern impact will be small.

In addition to electrical considerations there are physical constraints:

• The yagis atop the tower cannot be separated by more than 3 meters (10') to keep mast stress within reason. Similarly the smaller yagi for 15 meters will go at the top of the mast and the 20 meter yagi at the bottom of the mast.
• Lower yagis must be above a guy set, but not too far above to avoid tangling with the guys further up. The constraint is tighter if those yagis are rotatable rather than fixed. At least t his year they will be fixed towards Europe.

When completed the tower for these antennas will stand approximately 133' tall (40.5 meters) and the mast will rise another 10' (43.5 meters). Guy stations are nominally at 30', 65', 100' and 135', however due to section overlap the heights are more like 28', 61', 93' and 128'.

To recap the yagi dimensions:

• 15 meters: 5 elements on a 32' boom (10 meters). This antenna has low SWR across the full band and has been optimized for best gain while having a good match and F/B. Design details can be found in an earlier article.
• 20 meters: 5 elements on a 40' boom (12 meters). This antenna is a minor optimization of the yagi having the same dimension in recent versions of the ARRL Antenna Book.

Modeling is done with EZNEC. I use dual sources for in-phase stacking rather than phasing harnesses to make the modelling exercise easier. This does not materially affect the pattern but does affect the impedance, and the latter is not the focus of this article. SDC (stepped diameter correction) is used for all elements per my tapering schedule. Construction detail will appear in a future article.

If you're new to stacking you may want to review my article on the basics of stacking. There are of course many other resources on the topic of stacking around the internet and in the amateur literature.

20 Meters

I'll look at 20 meters first since the stack is more constrained; that is, there are fewer viable options for placement of the yagis. The upper yagi is at the bottom of the mast, which I waffled on with regard to the precise height, as you can see in the plot traces. The 2' (0.6 m) different is negligible. The lower yagi is in the vicinity of guy stations, ideally slightly above as discussed earlier.

Height of the upper yagi is ~2λ. Height of the lower yagi is at either 1λ or 1.35λ. The modest difference in height of the lower yagi has a significant impact on the stack behaviour.

The respective separations are 41' (12.5 m or 0.6λ) and 67' (20.5 m or 1λ). The first is equal to the boom length, usually considered the minimum separation for good performance; this is discussed in more detail below. The second is well separated at the cost of placing the lower yagi relatively close to ground (1λ).

The lowest lobe of the upper yagi is 7°, and 11° or 15° for the lower yagi. Lowest lobe of the stack is 8° and 9°, respectively.

Gain of the stack and individual yagis varies by less than 0.4 db for the two scenarios. This is indicative of low interaction, and that is confirmed in the EZNEC model. Although not confirmed in this exercise the low interaction (mutual impedance) between yagis promises low pattern distortion when they are pointed in different directions.

Stacking gain over the individual yagis varies from 1.5 to 2.5 db, which is quite good for 20 meters at these heights. The nominal 3 db stacking gain is just that: nominal. There are many variables that determine this performance metric.

Notice that the patterns of the lower yagis differs quite a bit due to their different height, and this affects the pattern of their respective stacks.

• Vertical radiation is higher for the lower yagi at 92' since that is the only position that is not a multiple of λ/2.
• Inter-lobe nulls coincide more closely when the stack separation is smaller, as expected. Better elevation angle diversity is achieved with greater separation. That is desirable for paths with an elevation angle close to a null so that we can avoid dead spots. 
• The major lobe of the lower yagi is significantly higher at the lower height. This, too, is desirable for path diversity. When fixed to Europe with its wide range of probable elevation angles the lower yagi becomes more useful.
• High angle minor lobes are attenuated with the lower yagi at 1λ height.

The choice for 20 meters is quite easy. The lower yagi will go directly above the second guy station. When (if) the lower yagi becomes rotatable it will also perform well on paths to Africa, Caribbean and North America.

15 Meters

With the upper yagi at the top of the mast and the shorter wavelength it is easier to achieve low interaction between yagis on 15 meters in comparison to 20 meters. The shorter boom length is also helpful in this respect.

The maximum height possible for the lower yagi is below 120', otherwise the elements get dangerously close to the top guys. I therefore chose this height for the first test case since while not physically practical it highlights a too small stack height of 20' (6 m or 0.42λ), which is less than the boom length.

In the second case the lower yagi is at the more practical height of 100', a little above the second highest guy station. This maximizes the distance from the outermost elements to the upper guys. The stack height is 40' (12m or 0.85λ). This is much better spacing.

When modelled the difference in performance is readily apparent. As with the 20 meter stack the greater stack height there is better distribution of the elevation nulls, reduced high angle radiation and greater stack gain.

If I had a tower dedicated to each band I could exploit the height to add a third yagi to the stack. This is not practical in my case where 15 and 20 meter yagis present since optimum and equal spacing would have yagis tangling with the guys or parked too close to a yagi for the adjacent band. A friend of mine who does manage to have a 15 meter 3 stack shared with 20 meters uses a taller tower than mine.

My next test case was to move the lower yagi even lower, though not too close to the lower 20 meter yagi at approximately 68'. The chosen height of 80' is, like 120', risky since it places the outermost elements close to the next highest set of guys.

The result is a mixed bag. Rearward lobes are small but there is an increase in radiation at high angles. Differences in gain of the stack and individual yagis compared to 100' are negligible at less than 0.3 db.

My tentative choice is to place the lower yagi at 100' or a little lower to increase distance to the upper guys while not getting too cozy with the set of guys immediately below.

Other antennas on or near the tower

Interactions limit further use of the tower. I plan to use my TH6 and TH7, possibly stacked, at lower heights for short paths such as the US and Caribbean. There is no good place for these tri-band yagis on the tower that would not impact performance due to interactions with at least the lower 20 meter yagi in the stacks. The tri-band yagis will therefore go on the other big tower, well below the 40 meter and 10 meter yagis.

I would like to leave open the possibility of a wire 40 meter yagi pointed at Europe, strung on a catenary between the big towers. With 5 elements the wire yagi would be 30 meters longs, which is about half the distance between the towers. Interaction with 20 meter yagis should be managable. Impacts on the performance of the 15 meter yagis could be more severe. The same is true of the tri-band yagis which are, of course, resonant on 15 meters.

I am looking at alternative placements of the wire yagi to best advantage. There is modelling work to be done.

Vertical antennas for 160 meters are less concerning due to the polarization difference. However the T-top of my current 160 meter antenna will require a close look to confirm that it will not causing any problems with the yagis on both towers.

Yagi separation vs. boom length

There exists a rule of thumb that two yagis in a stack should not be closer together than the yagis' boom length (for identical yagis). This is good guidance even if it obscures the reason for why it is a useful rule. Without delving into excruciating detail we can dig a little deeper for some insight.

But first let's review how a stack develops gain. For two identical yagis fed in phase, in free space and far enough apart that the mutual impedance is negligible, the stacking gain is exactly 3 db. This fact alone is a curiosity since we are dividing the power so that each yagi get half of it and the yagis' far field patterns sum in the far field. Fortunately I wrote an article on how this is possible if it seems paradoxical.

In the real world the yagis interact with real ground and there will always be some mutual impedance between the yagis. The closer together the greater the mutual impedance since the various elements will have near field coupling to those in the other yagi.

It is possible to have stacking gain greater than 3 db with carefully engineered close spacing. However this is only advisable if the yagis always point in the same direction, whether fixed or rotatable. Otherwise when one of them is turned the high mutual impedance will distort the patterns of both yagis. In general it is a poor idea.

Ground reflections for the two yagis place their lobes and nulls at different elevation angles which affects stacking gain. By closely spacing the yagis the lobes, especially the lowest main lobes, will reinforce each other and give close to the theoretical but nominal 3 db gain. This is at the price of a reduced ability to sidestep elevation angle nulls since these, too, will coincide, as we saw in the discussion earlier in the article.

With the preliminaries out of the way let's return to yagi separation and coupling. Yagi gain increases with boom length. Gain comes from a narrowing of the main lobe. As the lobe narrows the mutual impedance to a vertically separated identical yagi decreases. This is due to field cancellation away from the main lobe, directions which would intersect elements of the other yagi. Note that for this purpose we are primarily concerned with the free space elevation pattern (shown on the right).

However the lobe narrowing happens in concert with a longer boom length. Therefore the angle of, say, the -6 db point is lower but will still interact with the outermost elements of the other yagi because they are further out. The relationship is not exactly proportional but close enough that the rule of thumb is justified: increase the separation as the boom length increases to achieve approximately the same amount of element coupling (interaction).

Keep in mind this is a minimum distance not an optimum distance. When you allow the yagis to point in different directions more separation reduces pattern distortion. This is usually a better choice than trying for maximum stack gain.


Refinement

I have ample time before winter to refine the stacking arrangements. This can be done in parallel with the construction and tuning of the four yagis. Although I had hoped to be further along by now I am getting closer. It's been a learning experience, one with unexpected stumbling blocks.

You can see from the picture of aluminum shavings (the dark patches are steel) filling most of a 5 gallon pail that I have not been idle! Construction of the yagis is a story unto itself and will be covered in future articles.