Thursday, March 19, 2015

Radial Topology Options: 2-element Parasitic Vertical Array for 80

In this article I want to look further at radial topology of vertical arrays for the low bands. In an earlier article I looked at the impacts of base height and radial arrangement of an above-ground mount for a 2-element vertical (ground plane) array on 40 meters, one that had 4 radials per element. That antenna performed well in the model, although I did note the potential pitfalls regarding the precise way in which the radials interlace, parasite tuning and the expectations for ground loss that may differ in the real world.

Although doing that model on 40 meters makes the antenna more mechanically friendly there are better alternatives for gain, directivity and low radiation angle on that band, such as a small yagi that is 20 or more meters high. So it was perhaps more of a modelling convenience than a desirable antenna project. On the other hand, hams without large towers and a disinterest in large yagis have used vertical arrays, including 4-squares, on 40 to good effect.

Dropping down to 80 meters and the situation is markedly different. Even among the big guns of the world a yagi is rare and raised vertical arrays are, while not rare, not common either. Ground-mounted vertical arrays are more typical, with the 4-square being pretty much the big-gun standard.

Standard element

The vertical element I will use here is a ground-mounted monopole tuned to resonance (X = 0) at 3.6 MHz over EZNEC medium ground (0.005, 13):
Top view of vertical; wire 1 is the vertical monopole
  • Monopole is 20.2 meters long and 50 mm diameter aluminum, fed at the bottommost wire segment. The chosen diameter is an average value assuming a tapering schedule for telescoping aluminum tubes.
  • Radials are 20 meters long, 16 AWG aluminum wire. This is commonly available and economical electric fence wire.
  • There are 16 radials. This quantity is a compromise among computation time, ground loss reduction and NEC2 model reliability.
  • Mounted at a height of 10 cm, which is just above the 0.001λ minimum W7EL recommends for reliable NEC2 emulation of radials lying on the ground.
  • Use of a common mode choke at the feed point and other places is assumed in order to remove the need to model common mode current on the outside of the transmission line. Burying the coax does not eliminate this requirement.
At resonance the antenna has a feed point resistance of 37.6 Ω with a broad SWR bandwidth that is a good match to 50 Ω coax. Its gain is -0.7 dbi at an elevation angle of 15°. This is pretty typical performance for a vertical of this type.

I have chosen 15° as the comparison standard for 80 meters since that is a median value for medium length DX paths, which are the most productive on this band. The longest paths can have angles well below 10°, though not always. Since low angles are the most difficult to attain and are needed to best DX results and high angles are easy with a second, horizontal antenna I choose suitably low angles as the standard of comparison in the majority of my models. In my many articles about 40 meters antennas I used 10°, and lower angles for progressively higher bands.

Adding a second element

I will continue with λ/4 element spacing, which on 80 meters places the identical second element at 21 meters distance. The optimum spacing may be different though, I expect, not by much. My interest here is to evaluate radial topologies. Optimization can be performed later, should one of these arrays be built.

The parasite will be a reflector element. As we'll see identical elements work well to achieve the desired effect in this configuration. Switching between either end-fire directions is straight-forward, being no more difficult than for the design I proposed for the 40 meters array.

With 21 meters spacing and 20 meter long radials the two radial systems overlap. We have a few strategies to deal with this:
  • Place one radial field above the other, allowing capacitive coupling between them. Doing so can require making the parasite a reflector since there is near-critical coupling between elements when the height separation is small.
  • Lay them in the same plane with electrical continuity where radials cross. This is sometimes done in 4-squares and similar arrays though there is limited benefit in extending radials further than the first crossing. It is usually better to use the extra wire to make a mesh ground plane at the monopole base to reduce near-field ground loss.
  • As above but terminate the radials at the first crossing.
I built models for the first and third cases, rejecting the second since it is mostly redundant to the third.

Overlapping, capacitance-coupled radials

The most critical parameter of a Moxon antenna is the distance between the turned-in ends of two elements. That is where the capacitive coupling is strongest since that is where voltage is highest.

Strong coupling drives the parasite current higher than in a conventional yagi. It also restricts the phase relationship between the elements such that above a critical level of coupling the parasite can only operate as a reflector element. This is why I commented in my earlier article on the 2-element ground plane model that it is sensitive to precise placement of the (interlaced) radials.

As I noted above when the second element is added to make a 2-element ground-mounted vertical array the radial systems must be vertically separated and the amount of separation is a critical parameter, as in any critically-coupled array. I modelled the array with a range of separations, each small enough that the vertical offset of the monopoles would not significantly alter the far-field pattern.

With a 10 cm (4") separation (driven element on the right is 20 cm above ground) I achieved the best performance. However I did not try to fully optimize the array: my aim is to generally characterize the array to decide on whether its merits motivate further investigation.

Wire currents at 3.6 MHz, 10 cm radial separation; reflector at left

To demonstrate radial/element coupling I have plotted the modelled currents on the array's top view. The driven element current is normalized at 1 A. The driven element is to the right (red) and the reflector is to the left (blue). Radial currents are roughly maximum about 2 meters out from the monopole: the ground's dielectric constant makes the 20 meter long radials electrical length slightly more than 0.25λ. Strong coupling is evident in the high current in the parasite monopole: 70% that of the driven element at 3.6 MHz. It only appreciably declines when the radial system separation grows to at least 30 cm (12").

Radial currents are not close to equal or sum to that of their respective monopoles. Currents are higher where a radial crosses another, and highest where the far end of a radial is close to another radial. Only where a radial stands clear is the current close to the theoretical 1/16 of the monopole current. It should be evident that radial placement is critical to antenna performance, as it was in the 2-element ground plane.

The forward gain at 3.6 MHz is  about 4 db more than the single element at an elevation angle of 15°. Relative gain of 4.2 db is maximum at 3.5 MHz, and slowly declines to 2.2 db at 3.8 MHz. F/B is poor, ranging from 8.4 db at 3.5 MHz to 9.7 db at 3.8 MHz, and reaching a maximum of 10.9 db at 3.7 MHz.

The SWR is surprisingly good, staying below 2 over most of the band of interest to DXers and contesters. Unlike conventional parasitic arrays the SWR bandwidth is excellent and a good 50 Ω match. The change in SWR with frequency is mostly due to the feed point resistance since the reactance changes more slowly.

Increasing the radial system separation to 20 cm leaves the SWR and F/B nearly unchanged. However the gain at 3.5 Mhz is 1 db lower and the frequency of maximum gain rises to 3.6 Mhz. Even a small change in radial coupling can have a significant effect.

For a simple antenna on which I spent so little time this is good performance. But it comes with some important catches:
  • Maintaining the required radial field separation is difficult. Not only is it mechanically challenging it is a safety hazard to have 20 meter long wires 10 cm above ground, whether for pets or wildlife that will inevitably wander into the area. The radials, if bare wire, must never touch any other.
  • Weather will alter radial coupling. Winters with snow and ice will almost certainly destroy the radial behaviour, and the structural integrity of the raised radials.
  • The antenna is very sensitive to changes in radial coupling. Those changes are usually for the worse.
The study of this radial topology has been interesting and instructive. Since it is not promising for an 80 meters vertical array it is time to move on to the second case.

Radials tied at the mid-point

Terminating and tying radials of adjacent verticals in an array is an old idea, and has been used in commercial broadcast arrays for years. It is also an obvious one, so that it is unsurprising that I independently thought of it before discovering it in the literature. In the amateur field you can read, for example, a discussion by the late W4RNL (Cebik).

There is some coupling in this array, mostly between radials whose ends are close together. However this is dominated by monopole coupling and direct connection of the radial systems. At first blush this would appear to be an array more suited to having all elements driven, with a power splitting and phasing system to achieve the desired result. Antennas such as 4-squares are of this type, though so are 2-element end-fire arrays such as described here.

Connected radial; reflector (blue), drive (red), connected pairs (black)

The radial currents (defined above) vary less than in the array with overlapping radials. First, the reflector current is 58% that of the driven element, which is lower than with overlapping radials though still more than in a conventional yagi. The sums of the radial current for each element are roughly equal to that of the monopole, approaching the ideal situation of a single element where radial currents are equal and sum to that of the monopole (assuming radials lengths near 0.025λ).

Radials that had been capacitance coupled are now directly connected: 16-21, 15-22, 14-23, 13-24 and 12-25. While the currents in these radial pairs are (necessarily) equal where they connect it may seem surprising that currents are quite different at their origins. Power is flowing between the elements, but with a 133° phase difference (at the radial origins). Current nodes occur on driven element side of the radial pairs, closer to the driven element where the current differential is greatest. On wire #23 the node is adjacent to the radial origin (driven element monopole junction).

Despite the relative lack of control over parasite current and phase this array has gain and F/B. However performance is not quite as good as the array with overlapping radials. Nevertheless this is a more realizable antenna since the radials can all be on or just below ground, and coupling requires less fine tuning.

Since the elevation pattern is indistinguishable from the one above I will instead show the azimuth pattern, which is also the same. The plot is at right.

Maximum gain is 2.82 dbi at 3.575 MHz and 15° elevation, which is 3.52 db better than a single vertical. At 3.5 MHz the relative gain is 3.2 db. Going higher, relative gain gradually declines to 2.9 db at 3.8 MHz. F/B is poor. Its maximum is 9.8 db at 3.8 MHz, and an especially bad 3.5 db at 3.5 MHz.

Although I have spoken against the importance of high F/B, particularly for the high bands in a small station with a single yagi, the situation is different on 80 and 160. The bigger problem here is QRN, not QRM. Directivity is needed to improve SNR enough to copy DX stations. If this antenna is built it ought to be supplemented with a low-noise receiving antenna such as a Beverage or compact, rotatable loop. Otherwise be prepare to not hear many stations that call you, especially if you run a kilowatt.

SWR is sufficiently broadband to allow no-tuner use from 3.5 MHz to 3.8 MHz. The above SWR plot is for equal height monopoles (identical elements). This worked well in the array with overlapping radials, though here the resonant frequency drops a little lower than is ideal. A 2,500 pf capacitor should be switched in series with the driven element to bring the SWR below 2 across this frequency range. The value isn't critical, 2,200 pf or 2,700 standard values can be used, but use a ceramic knob capacitor if possible to reduce loss (and potential failure when running a kilowatt).

My take on this antenna:
  • It has the makings of a good, simple, broadband switchable gain array without the burden of a power-splitting and phasing system. Even a commercial product to perform these tasks requires work to tune and match the elements and adjust array performance.
  • F/B is so bad that a high-directivity receiving antenna be seriously considered.
  • Altering the radial quantity and length will change array behaviour. Model first before adding radials to reduce ground loss, since wire lengths may need adjustment.
Again, this is an experimental model and not a design to be rushed into construction without further evaluation.

Disconnecting the common radials

As a final experiment in this phase of modelling 2-element parasitic vertical arrays I will take the previous design and disconnect the 5 radials pairs that are joined at the midpoint between elements. My aim is to see how much capacitive coupling can be achieved and whether it can be used to raise parasite current and thus hopefully improve F/B without the tribulations of overlapping radial systems.

I modified the connected radials model by disconnected the 5 pairs of connected radials and various the separation distance. The results were disappointing. Mutual coupling between elements was low, as evidenced by parasite current (reflector) only around 36% that of the driven element. Gain and F/B performance was, not surprisingly, poor. There was little benefit found by varying the separation distance; I tried values from 10 to 100 cm. More drastic measures would be needed to increase coupling, such as in the overlapping radial case.

The adjacent elevation plot is typical of the performance. Gain is only about 1 db better than a single vertical! F/B was typically below 6 db. Like the connected radials array, gain peaked at 3.5 MHz and F/B peaked at 3.8 MHz.

However SWR performance mimicked that of the connected radials array, being almost indistinguishable and so not worth showing the curve again. I also declined to mark up the antenna diagram with radial currents as it was not worth my time for this unpromising antenna.

One interesting difference was ground loss: it modelled from -1 to -1.5 db worse than the connected radials array. That is undoubtedly where some of the missing gain went. My guess (I didn't look at it more closely) is that the additional loss is due to a third of the radials being about half the length of the others.


Of these experimental models the only one that shows promise is the one with connected radials. It has good power flow between elements, accomplished with a robust physical design. I expect that it can deliver the modelled performance when built.

To get improved F/B from this array it would be necessary to feed both elements and use a power splitter/phasing system to architect the required electrical parameters in each element, in part by "taming" the mutual coupling to do our bidding. That system could also be used for direction switching. Designs are readily available, with perhaps the most comprehensive treatment found in ON4UN's Low-band DXing book (5th edition), chapter 11.

My approach would be to either build a 4-square or build the 2-element end-fire array described here. In the latter case, going with simplicity and maximum reliability rather than the best F/B performance. A simple, low-cost directional receive antenna would complement the parasitic array. That is, if you have the land.

It is possible to use elevated verticals to reduce ground loss and deal with any local topography and obstacles that impede the view of the horizon. While more challenging on 80 meters it is not necessary to raise the base 20 meters (λ/4) to get the benefits. Half that height can be effective, though probably no lower. There are ample resources on elevated radials, of which I'll point to two available on the internet: by VE2CV and another by N6LF. ON4UN's book also has many ideas in this regard.

But if you do so the antenna must be carefully modelled so that it can deliver the desired performance. You cannot simply lift the arrays discussed in the article and expect that they'll work.


  1. Curious to know if you have sample .nec files of this to peruse.

    Thanks & 73, Jim KK0U

  2. I probably have the .EZ files hidden deep in my archives. The article is an old one. They're pretty easy to create in EZNEC with its radial generation tool. If you really want me to hunt the EZNEC files send me a direct mail to my call sign at

    The 2-el vertical parasitic antenna was just an experiment. I built a 3-element 4-direction 80m vertical yagi a few years ago with overlapping radial fields. You can search for it on the blog if that interests you, Jim.

    73 Ron VE3VN


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