Friday, February 13, 2015

2-element Parasitic Ground Plane for 40 Meters

As the solar cycle declines my attention to the low bands increases. This means I have an increased interest in vertical antennas, even though "serious" low-band antennas are impractical on my suburban property. So I instead plan and model in the hope that one day I can start building large antennas.

Experimenting with 40 meters is in some respects easier than doing so on 80 and 160. Antennas are easier to successfully model and prototype at the shorter wavelengths, and then compared to existing antennas. Antennas that work out can then be scaled to the longer wavelengths with predictable results. There are also some things you can do that may be too mechanically challenging on lower bands. The antenna in this article is one of those.

Concept antenna, not a final design

Please keep in mind that this is purely a concept antenna. It is perhaps worthy of prototyping but should not be seriously considered without further work. I did not aim to fully optimize the design. My intention is to play with it to see it if has good DX performance with regard to gain, F/B and match. As we will see there are design aspects that require more work before committing to construction.

Another motivation is to see what can be accomplished with a relatively simple vertical array in comparison to well-tuned, switchable 4-square antennas that many big guns use on 80 and 160. Although this design is for 40 the antenna can be scaled, with some construction effort and expense.

My concern with the 4-square and similar directive arrays is the intricacy of the feed and switching networks. This invites the potential for failure when one or more elements is affected by weather (e.g. snow and ice) or a component drifts in value or fails. That is why 4-squares often have a "dump" resistor and a warning system. The design lacks a degree of robustness.

This is not meant to demean recent efforts at optimum phasing and power division, which can be very impressive. Designs such as those you'll find in chapter 11 of ON4UN's fifth edition of Low-band DXing are so bizarre because the elements are often so closely spaced that mutual coupling dominates. To my mind it is better to use judo rather than brute strength to tackle the problem. That is, to accept mutual coupling as a design partner rather than having to coerce it to behave in a prescribed manner. I try to do that in this article.

Copy and spin

There are many ways to make a parasitic array. You can even do it with λ/4 monopoles with ground planes, if you're careful. Consider the simple 4-radial ground plane mentioned near the end of my recent article on vertical modelling experiments. It is broadband, with low-angle radiation (good for DX), and is a good match to 50 Ω coax.

I proceed in the usual fashion of making a parasitic (reflector) array by copying a resonant single-element antenna and offsetting the copy in the desired direction. To avoid tangling the radials, which are about as long as the inter-element spacing, I spin the radials of one element by 45°.

With the elements mounted 10 meters above ground they a maximum height of about 20 meters. The bases can be light-duty television towers or masts made from aluminum or steel. I prefer the former so that the feed point is easily accessible for assembly and maintenance. Guying is necessary but there is no need for concrete. The radials can do double duty as guys, if you use something stronger than aluminum or pure copper wire.

With a bit of open space this should be an inexpensive and not too challenging antenna to construct. The minimum required area is 500 m² (25 x 20 meters). Even though mounted above ground it is recommended that there be no other structures within 1λ (40 meters) radius, and even farther from towers or other large conductors.

It's a Moxon!

Okay, it doesn't look like a typical (or even atypical) Moxon but it does have the same attributes. The reason is those radials: the way they intermingle causes near critical coupling between elements. Even with the relatively wide spacing between monopoles of 10 meters (close to 0.25λ) those radials keep the coupling high.

You can see this most clearly in the radial currents. Rather than the current in each of the 4 radials being ¼ that of the monopole it varies a lot, depending on the radial's position. One implication is that the parasite must be configured as a reflector. Well, you can try to make it a director but you'll find that task quite difficult unless you can find a way to reduce the coupling.

In the driven element (wires 6 to 10 in the current plot above) the radial currents are 6% and 43% that of the monopole in the rearward and forward radials, respectively. In the reflector (wires 1 to 5) the radial currents are 53%, 34% and 40% that in the monopole in the forward, rearward and side radials, respectively. These values are at 7.1 MHz, near where gain is maximum. No only are the radial currents unequal their sum only equals the monopole current in driven element. The sum far exceeds the monopole current in the reflector element.

The current in the reflector monopole ranges from 60% to 70% that of the driven element across the band. This is typical of a Moxon and higher than in a conventional 2-element parasitic array. As we'll see, gain, F/B and SWR vary less than a 2-element yagi across the entire 40 meters band.

Tuning for optimum performance

Performance is sensitive to element separation (equivalent to boom length in a conventional yagi or Moxon rectangle) and radial arrangement. The thing I found annoying is that although gain would vary a lot when these are adjusted a little, the feed point impedance (and thus SWR) and F/B were far more stable. It's annoying because the latter two are far easier to measure, and would simplify the tuning of this array.

In the model I settled on monopoles 9.95 meters tall and made from 25 mm (1") aluminum tubing. This is an approximation to a real antenna that would use telescoping, tapered tubes. The monopoles are 10 meters apart with bases 10 meters (~λ/4) above medium ground. The radials are 16 AWG aluminum wire, such as the often used (and inexpensive) aluminum fence wire. All radials are 10.525 meters long and slope downward 30°.

I²R loss in the aluminum monopoles and radials is around -0.1 db. The pattern plots are with zero loss conductors, including for the reference single ground plane. The performance chart below includes the loss. Ground loss is calculated by EZNEC to be about -5 db over medium ground.

Considering how peculiar an antenna this is its performance is quite good. Not only is it 5 db better than a single ground plane at 7.1 MHz (comparison in the elevation plot above) the gain varies little up through 7.2 MHz. The F/B, while not exceptional, is adequate to my needs. The SWR is particularly nice, staying below 2 across the band.

Compared to various single element and 2-element antennas the 10° elevation gain is very good. For example, it equals an inverted vee (broadside) 25 meters high and even a 2-element yagi up 15 meters. If you don't have a high tower but do have some open land this could be an attractive antenna choice. Don't expect this performance on a suburban lot since vertically-polarized antennas can under-perform the models.

As I stated at the beginning, I did not really design this antenna with the objective of putting in on 40 meters. If I eventually have higher towers there are superior alternatives. This experiment is about getting a handle on antennas for 80 and 160 where, often, towers cannot be high enough to make a horizontal antenna competitive. When scaled to 80 meters the the required towers for comparable horizontal antennas must be twice as high. Scaled verticals for 80 lose relatively little gain at low height (though half as high in wavelengths) but may suffer from additional ground loss and environmental interaction.

Although the monopoles are the same height the reflector element has a base loading coil. It is a very small coil with an inductance of 0.4 μH. Although small this value is critical. Even if only 0.1 μH higher or lower the SWR and gain will noticably suffer. F/B is less sensitive to inductance changes. Small changes to the radials will affect the required value of this coil since their length and position affect mutual coupling between elements.

To give an idea of the dimensions involved, a suitable 0.4 μH coil would be 5 turns with a length and diameter of 1" (2.5 cm). The equivalent shorted 300 Ω open wire stub would be 16" (40 cm) long at 7.1 MHz. The stub is easier to tune (with a sliding shorting bar) but will be exposed to the weather which can alter its reactance.

Direction switching

It is always helpful in a fixed element array to be able to change the direction of the beam. This antenna is amenable to such an arrangement, though with some stringent construction and tuning criteria. This, too, is typical of Moxon (critically-coupled) arrays.

The switching method I describe here has significant differences to the one I used for the various styles of 40 meter wire yagis I described over a year ago. I am assuming that the support masts for the elements allow convenient access to the feed points which are 10 meters above ground. This is why I recommend light duty television towers for the supports.

The switching system requires 2 plastic enclosures, 3 DPDT relays, 2 loading coils, DC switching circuitry and 50 Ω coax for the transmission line and running between the element feed points. One element will be connected through to the transmission line while the other will be isolated from the transmission line and a coil connected between monopole and radials. Relay DC power can be run by separate cable or on the transmission line. In the latter case a DC cable is still needed between the 2 enclosures at the bases of the monopoles.

The recommended arrangement has the transmission line terminate at the enclosure at the base of one of the monopoles. Make it the one closest to the shack to keep the total length of coaxial cable to a minimum. The length of coax between that enclosure and the one at the base of the other monopole is non-critical, except that it must (of course) be at least 10 meters long, the element separation. That section of coax will be fully isolated on both ends when the second element is a reflector. Similarly the transmission line will be fully isolated from the first element when it is a reflector. The outer conductor of the both lengths of coax must not be connected together or to the radials, except when connecting to the driven element. This is why the enclosure cannot be metal. Metal will also alter the coil's inductance if it is inside the enclosure.

One relay selects the element to connect both conductors of the transmission line. The other two relays switch each element between the coax feed and the loading coil. The coil provides the inductance to configure that element as a reflector. A shorted stub can be used in lieu of the coil. Obviously when one element is connected to the transmission line it becomes the driven element and the other is a reflector. The normally-off position of the relays should point the array in the most important or commonly used direction.

The transmission line outer conductor will act as a radial when the first element is driven. To avoid asymmetry and mistuning in that direction it is best to run the transmission line along one of the radials and choke it where the radial terminates, making them the same electrical length and at the same potential. A coax coil choke can be used if tuned to be effective on 40 meters. There should also be a choke where the coax enters the second enclosure to ensure it also does not become a radial when the second element is driven.

The two supporting masts and the isolated connecting coax are λ/4 long and so should not interact with the array. The supporting masts should be isolated from ground to make them non-resonant.


It is possible in many vertical arrays to create a feed arrangement (power division and phase) to convert an end fire array to broadside. The idea is that it's often more convenient to come up with an elaborate feed than put up more elements, whether two independent 2-element arrays or a 4-square. With the antenna described in this article this is not possible.

Pattern flexibility requires that the factors under one's control (phase, power division, element tuning) are sufficient to sculpt the desired result. With a near-critically coupled antenna like this one the mutual coupling tends to make any effort in that pursuit moot: the mutual coupling dominates. Coupling can be reduced by moving the elements farther apart, but that would negate the parasitic benefits of the array. More elements can be added, but that too has significant costs.

The best that can be achieved is an omnidirectional pattern by splitting the feed in the centre and running equal lengths of coax to both elements. The resulting feed point impedance is 15 Ω, which would require a 3:1 unun. In the broadside configuration here is less than 1 db of gain in comparison to a single ground plane.

I believe it is better to leave the array as is and use another antenna, even just an inverted vee, to fill the holes in the array's end fire pattern.

Next steps

This is an experimental design that I do not recommend be built by anyone. Because if you do you'll have to deal with its various idiosyncrasies either in your own modelling effort or (literally) in the field.

Before I would undertake construction of this antenna I would model variations in radial deployment to modify coupling in a way that preserves the array's best attributes while making it less sensitive to minor variations in tuning. Another thing I'd like is to find an easily-measured quantity that correlates well with antenna performance. For example, in the various 2-element switchable 40 meter antennas I've discussed in the past this metric was the frequency of maximum F/B.

Of course all of this modelling and planning is contingent on having the space to build it. That is tentatively in my long term plans, although for the present I can only design, plan and model. It's time well spent.


  1. Hi Ron, your modelling is very interesting: My wish-plan is a 3 el. wire yagi for 7 Mhz.
    Could you make available your Eznec file ?

    1. Send me an email and I'll send you the EZNEC model you want.

  2. Hi Ron. I had plans to build a 3x 1/4 GP linear array as pseudo vertical yagi for 40 meters band. MMANA modeling shown good results using clasic verticals on ground and 4 radials for each one but you stated that radials coupling is somehow unpredictable. If your model is using elevated radials, what can you tell about not elevated ones?I can send you mma file if interested. Regards, Gabriel yo8rxp

    1. Hi Gabriel, it's been a while so I don't remember these models very well. However I did look at ground radials for a similar antenna in an article that came shortly after:
      In this case it should be more obvious that radial crossings do introduce couplings that alter radial currents. But overall it appears to have only a minor impact on the efficiency and pattern.

      I used crossing radials in the 80 meter vertical yagi that I built. Detail on that can be found in the following article:
      I can measure no detrimental impact of crossing radials, and having so many radials also serves to smooth out asymmetries. Sorry I do not have MMANA so I can't use those model files, but it isn't really necessary. 73 Ron VE3VN

  3. Hi Ron and thanks for response.I still have doubts about building a 2 elements 1/4 phased array versus 2 elements parasitic vertical delta loop already tested.
    My main problem using delta loops close to ground (6.6 feet) and apex at 30 feet is that the proximity to ground makes it unstable and impedance varying from pure 50 ohms down to 25 ohms when ground is saturated with water yet keeping same F/B ratio 20 dB give or take, and also concerned about ground losses too.
    But as modelling shown, ground losses occur in radial system too and since MMANA software is not that good predicting gain at low heights, I cannot tell if a 2 elements vertical is better than 2 elements delta loop in real world.
    So, to conclude I would go for CQ WW this year using same old delta loop system and probably next spring will give a try for 2 verticals.
    I really appreciate your work as you were my inspiration source for 3 elements inverted Vee flip yagi which works like a charm but instead of gamma I have chosen 1:2.25 balun.
    73's and good luck !
    Gabriel yo8rxp

  4. From: KE4LJH, December 18th and 19th 2021, I set up a two element 40m parasitic array with what I feel are results very close to what your modeling predicted for forward gain and front to back ratio. The driven element design frequency was 7.150 mHz. The reflector element length was designed for 100 kHz below the driven element frequency, 7.050 mHz. Both elements were supported by two telescoping fiberglass push up poles from Spyder Beam, the 12 meter pole. Element spacing is 4/y or thirty three feet between elements. The driven element and the reflector element both had 35-1/8 wave ground radials. The reflector element ground radials were spread out over a 180 degree arch behind the reflector so the driven element radials were not crossed. The ground radials were measured to 16 feet, not quarter wave ground radials, but the equivalent lengths of 16 quarter wave radials. I had space restrictions for the ground radials and this did not seem to matter. The antenna seemed more interested in the amount of copper under the elements. Four wavelengths of ground radials under each element, just 1/8th wave long, 16 feet each element. The radials were made from 22 gauge insulated hookup wire. The inexpensive stuff I found on a spool that someone had thrown away.
    I did not do any software modeling. I began calling CQ on the grey line in the evening both nights and had a pile up into Europe, "Stacked and Racked" for two solid hours. This was from south Florida. I very clearly had a front to back ratio that was decent. The U.S. stations calling from behind the reflector could be heard but their signals were way down enabling me to hear the Europe stations answering. I could tell I clearly had receive gain worth noting, as I could tell a difference when I had just one vertical element without a reflector on previous portable set ups from the same location at other times.
    For those considering a two element parasitic array for forty meters, The set up was as simple as I described. I would encourage you to just set up your own 40 parasitic array for 40 meters. I was told repeatedly that I had a S9+40 over nine signal report, not from all stations but those directly in the beam width path. This simple setup exceeded my expectations. I was very pleased and hope to set up the same portable two element 40 meter array this next weekend. New Years weekend January 2022. If you build this one, They will come....


All comments are moderated, and should appear within one day of submission.