Driving Arbitrarily Spaced Verticals on 160 Meters

This time of year most of my activity is on 6 meters. It is the peak of sporadic E season, and that means DX and fun times. That is not my sole activity, and there are multiple projects to be worked on. One that is suited to the summer weather while I wait for the DX paths to open on 6 meters is computer modelling of antennas. It is an activity that is easy to fit in anytime since all it requires is a computer.

One of my challenges is to improve my 160 meter signal, and that involves gain over a single vertical such as my current antenna: a shunt-fed 40 meter tower. There are several possibilities open to me and a few I've previously discussed for the blog. These have largely involved parasitic arrays of various types. They can be simple to home brew and are friendly to experimentation, which I like.

Ground loss is higher for a parasitic array than a driven array because they are close spaced, resulting in a low radiation resistance, and therefore greater loss for an equivalent radial system. Consider my 80 meter vertical yagi and how it compares to the 4-square. It takes less space but is less directive and tends toward inefficiency due to ground loss. But I had lots of fun experimenting with it, and will continue to do so as I strive for higher efficiency.

My two big towers constantly tempt me to try something similar on 160. The 60 meter separation works well for a 3-element yagi, by shunt feeding the towers to tune them as parasitic elements and a wire driven element hung from a rope catenary between the towers. The towers are big enough that they already affect any 160 meter antenna in the vicinity so it makes sense to put them to use.

Unfortunately there are several difficulties with this antenna:

• The radials have to be removed during the summer during haying season. An efficient radial system for a 3-element 160 meter yagi involves a lot of wire, and that means a lot of work to lay them down each fall and to roll them up again in the spring.
• A yagi has just 2 switchable directions, which are roughly northeast and southwest. Those are the most important ones, so it is tempting despite the limitation. The yagi would need an omni-directional mode by using the driven element alone.

I have therefore started to consider driven arrays. The 60 meter distance between the towers is pretty good for that, although not ideal. My challenge is to design a directive array using the two arbitrarily spaced towers in a driven array that is superior to the vertical yagi option. If it can be made to work well there are several advantages over a yagi:

• The higher radiation resistance and one less element (2 vs. 3) allows equal efficiency with significantly fewer radials.
• Impedance matching and direction switching can be done at one location, not at each tower.
• Gain can be had in 4 directions rather than just two. Omni-directional is also possible.

With that introduction let's dive into the two types of 2-element driven arrays. I will then explore what is possible with my towers, with both shunt-fed and not at an ideal separation as a driven array.

The are two important parameters in a 2-element driven array: separation (D) and relative phase. The latter can be achieved in a variety of ways, the simplest of which is adjusting the lengths of coax from the common source (La - Lb). Since the feed point impedance is unlikely to be 50 Ω, a matching network (N) may be required. 

Elaborate power division isn't necessary in a 2-element array. D is sufficiently large to minimize mutual impedance between elements so that driving the elements in parallel works very well. The minimum D would be ¼λ, which is also the typical element spacing in a 4-square antenna.

Extensive detail about the design of driven arrays can be found in ON4UN's Low-Band DXing, and if these antennas intrigue you, that is where you'll learn all you need. My discussion is narrowly focussed on my particular needs, to best exploit my towers. As we'll see, compromises are necessary when you don't build the driven array from scratch.

End-fire and broadside arrays

2-element driven arrays of these two types. An ideal end-fire is unidirectional to either the left or right per the diagram above; that is, on an extended line between the verticals. In my case, these are roughly northeast and southwest, the two directions of greatest utility for my primary interest: contests.

In ideal end-fire array D is ¼λ and La - Lb = ±90° (left or right). D can be smaller with appropriate choice of La and Lb, however driving the array is more challenging due to increased mutual impedance and the criticality of dimensions. D should not be too much larger or the array will sprout unwanted side lobes.

In an ideal broadside array D is ½λ and La = Lb. The pattern is bidirectional. There are similar concerns regarding smaller and larger values for D, but usually of greater negative impact since, in addition to side lobes, arbitrary choices for D tend to circularize the pattern. However, there will still be gain.

The azimuth plots above show ideal 2-element end-fire and broadside array over perfect ground. The broadside array has more gain since the lobes are narrower, despite there being two of them. At right you can see the sprouting of unwanted lobes for an end-fire with a D of ¾λ and a broadside with a D of 1λ. At other large values of D the arrays are not really end-fire or broadside due to those large side lobes.

For proper operation, D for the end-fire and broadside arrays should be odd multiples of ¼λ and ½λ, respectively. However, there will be additional lobes for multiples greater than 1. Intermediate values of D can be compensated for by adjusting the phasing with suitably calculated values for La and Lb. We'll come to this later since it is the focus of this article.

The gain is around 3 to 4 db better than a vertical, over perfect ground; the gain difference is smaller over real ground. Decreasing D for the end-fire configuration can add up to 1 db of gain over the expected 3 db due to mutual coupling, which lowers the radiation resistance and therefore the field intensity due to the higher current. Of course ground loss will increase over real ground and a radial system, so in practice less of that additional gain can be realized.

Geometry of the end-fire array requires adjustment of the phase and spacing to optimize gain and F/B for a specific elevation angle. The reason is that as the elevation angle increases the effective value of D decreases. Rather than go into detail I'll again refer you to ON4UN's book, where this and more is described in detail. 

It matters since gain of a ground-mounted ¼λ vertical at 0° elevation is always very poor due to the phase reversal at grazing angles over real ground. It is therefore worthwhile to optimize the antenna for a higher elevation angle, typically 20° for DX performance on 160 meters.

The 3D plot at right is for an end-fire array optimized for cancellation at 0° elevation over perfect ground. You can see how F/.B decreases as the angle increases. The same is true off the sides of the broadside array.

Arbitrary D: Gain or directivity

Although quite simple, a 2-element driven array competes well in gain versus more elaborate parasitic and multi-element driven arrays such as 4-squares. What you give up is directivity. There is only so much that can be accomplished with 2 elements. For those like me with a set of directional receive antennas, that is not a problem. My priority in a transmit antenna is gain.

The ideal element spacings for end-fire and broadside arrays optimize both gain and directivity. Since D is ¼λ for end-fire and ½λ for broadside it is not possible to optimize a 2-element driven array for both. However, we can do pretty well with a non-optimal D. 

I am fortunate that my two big tower are 60 meters apart, since that is approximately ⅜λ, or midway between the two optimums. For those with verticals with lesser or greater D, the techniques I will discuss are applicable, although the results may not always be as good.

With a non-optimal D we can optimize gain or directivity, but not both. The plot at right illustrates this for the end-fire (unidirectional, cardioid pattern) by varying the feed point phase shift from 60° through 130° (90° is the primary pattern).

Ground is EZNEC medium, using MININEC ground to simulate a fairly poor radial system with an equivalent resistance of 10Ω. The radial system may be better than this, but this affects efficiency and feed point impedance, and not the antenna pattern.

The larger D requires a phase shift greater than 90° for maximum gain and a smaller phase shift for maximum F/B. This is at an elevation angle of 22° for medium ground. Notice that the "ideal" 90° phase shift is not suitable for medium ground and a D of 60 meters.

For real ground the peak of the main lobe is always substantially above the horizon so it makes good sense to phase the elements so that peak gain occurs above the horizon. In this case, 22°. Targetting a lower elevation angle should only be attempted with taller verticals or better ground, otherwise performance will suffer.

Notice that among this range of element phase differences the gain varies by 2 db and the F/B variation is profound. As expected for the non-optimal spacing the gain is poor when F/B is excellent and vice versa. One curiosity is that for the high F/B cases the main lobe is "two-headed", with twin gain peaks ±40° off the main axis. 

As the phase difference is further reduced the pattern gradually transforms into that of a broadside array. Again, this is what we expect and want. The next plot with smaller phase shifts shows our options for the broadside configuration of the array.

Broadside gain is barely affected with a phase difference of up to 30°. The side nulls are greatly softened with the non-optimal spacing, with little to distinguish them. There is no compelling reason to use anything other than in-phase (0°) feeds for broadside.

Gain is substantially lower than a broadside array with an optimal D of ½λ. It is lowered enough that th 1 db gain difference that favoured the broadside configuration for ideally spaced verticals now favours the end-fire array by about the same amount. Radiation that is "wasted" off the sides is not available to contribute to gain in the broadside directions.

For reference, the 22° elevation angle gain for a single, omni-directional vertical is almost exactly 1 dbi. Thus, for our D of 60 meters the broadside gain is 2.2 db (bidirectional) and the end-fire gain is 3.3 db. Although this may not seem like a lot, on 160 meters it will provide a substantial competitive edge. It is especially attractive due to its simplicity in comparison to a K3LR 3-element wire yagi, like my 80 meter array (about 4 dbi gain) and a 4-square (about 5 dbi gain). Radial requirements for similar efficiency are lower than for either of those larger and more complex antennas.

Feeding the array

To simplify the model, I directly specified the element phasing with sources for each of the two verticals. This is easy to do in EZNEC as follows:

For a real antenna the verticals are connected to a common feed point by coax. Coax has loss that is low enough at 1.8 MHz that it can be ignored. However, coax has another important effect that cannot be ignored since the mutual impedance between the two verticals changes the 50 Ω feed point impedance of each vertical. The complex impedance at the feed point varies with the length of the coax.

The individual vertical impedances are not 50 Ω so their parallel impedance is not 25 Ω. It is possible to adjust the gamma matches of each shunt-fed tower (or other vertical of your choice) to be 50 Ω or some other impedance that will present an impedance at the feed point that is "easy" to work with. That is not as easy as it seems since the feed point impedance is different when the phase is changed, as it must be to support both end-fire and broadside configurations. 

Out of curiosity I played with the model and successfully achieved an excellent match for the end-fire configurations. This is only useful if you only use the array as a reversible end-fire array, with no broadside or omni-directional modes. However, it's a cumbersome process that I do not recommend. The more sensible method is a switchable impedance transformation network at the feed point.

With the elements 60 meters apart the minimum coax to each vertical is 30 meters. I happen to have two ~40 meter lengths of RG213 and two ~40 meter lengths of LDF4 available, and I will likely choose from those should I build this antenna. I would run the coax over ground in the fall and roll them up in the spring for haying season, just as I do for the radials.

The patterns of the 3 combinations of end-fire (2 directions) and broadside (bidirectional) provide good compass coverage without bothering with feeding one of the verticals as an omni-directional antenna. I will therefore proceed to design matching for just those. To use one of the verticals alone is only a 50 Ω match if the other is detuned. I prefer to avoid the additional complexity.

In the model the 40 meter lengths of RG213 are joined in parallel at the feed point. An extra length of RG213 delays the signal (negative phase) of one end-fire element. For the 3 modes -- end-fire left, end-fire right and broadside -- the phasing (delay) line is switched into the right element, into the left element, or out, respectively. A separate control cable can be used for switching or two different DC signals (+12 and -12 VDC, for example) can be placed on the feed line using Bias-T circuits at both ends.

The length of the delay line is easy to calculate. To simplify for repeated experimentation I calculated the length of RG213 for a -10° phase shift. This is 1/36 of λ, which is 163.83 meters at 1.830 MHz. Adjusting for the 0.66 velocity factor the length is almost exactly 3 meters. It is then very easy to mentally multiply by 9 to find that a -90° phasing shift is 27 meters of RG213.

The plot at right is for a -120° phase shift which, as we saw earlier, is close to maximizing gain for verticals separated by 60 meters. For these electrically tall shunt-fed towers the gain is about 3 db versus a single tower. The gain is about 2 db for the broadside configuration.

Although there were no surprises replacing ordinary λ/4 verticals with my tall shunt-fed towers, the validation is necessary so that we can proceed to inspect the impedances.

Due to the small magnitude of the mutual impedance, the parallel impedance in both end-fire and broadside is not too far from half the impedance of each shunt-fed tower alone. However, since it is far from 50 Ω it must be dealt with.

The R component of the impedance is roughly half, which itself is a concern since this is a fairly high Q antenna where the 2:1 SWR bandwidth of each vertical is about 75 kHz. In end-fire and broadside configurations the residual X is mostly negative and positive, respectively, but not large in comparison to R. A relatively small X is a hint that matching will not be difficult.

Below are the model's SWR curves for end-fire and broadside, followed by an L-network for the end-fire case that optimizes the match at 1.830 MHz.

It is interesting that the bandwidth of the driven array is better than that of a single vertical. With an L-network tuned for broadside the result is similar. I experimented with the L-network design using TLW and came up with one that is easy to switch by only needing to switch taps on the series coil and using a fixed shunt capacitor midway between 1500 pf and 1800 pf calculated for each configuration.

I will not describe the network since its design is very sensitive to the design of the verticals and the lengths of the coax from the feed point to each vertical. Using TLW or a similar tool it is not difficult to design a switchable matching network based on field measurements after the array is built. For coax which can withstand the voltage associated with the uncorrected SWR, the matching could be done in the shack with an ATU or other device. The mismatched loss of any suitable coax is very low at 1.8 MHz.

Where I go from here

Although summer is not prime top band season it is a good time to play with antenna models in air conditioned comfort. I do not know whether I will build this antenna, and it is not a high priority for this year. It is good to have several options in hand when the time does come. 

Hopefully this design will spur some readers to explore similar possibilities for a high-performance 160 meter antennas. I like its good -- but not great -- performance and its simplicity. Most hams don't have the land or the resources to put up multiple towers and recruit them for use on top band, so I consider myself fortunate. Of course I moved here several years ago to make antennas such as this possible.