Wednesday, January 28, 2015

Exploring Verticals with a 4-radial Ground Plane Model

Vertical antennas is a subject that currently interests me since I feel the pain of a poorly-performing antenna for 80 meters. It is noteworthy now that I'm running 100 watts in the DX pile-ups. For example, I quickly cut through the pile-ups to work C5X on 40 meters and above yet ran head first into a brick wall on 80. It isn't all bad since I have had a few notable DX successes on 80 with the loaded half sloper, and I did even better years ago with a full-sized half sloper. They will do if nothing better is available.

The EZNEC (NEC2 engine) modelled loss of my present antenna over medium ground is about -6 db. This understates the reality since the ground in my yard is worse than that, and there are many housing-related long conductors in the antenna's near field. I am, in effect, dialling down my recently-acquired 100 watt rig to QRP. What it does when I operate with my KX3 is dreadful to contemplate. Yet that's how I currently operate on 80: very, very poorly. I had similarly poor results with my experimental and vertically-polarized loaded sloper on 40.

Verticals are nice but radials and interactions with obstructions are a problem in suburbia. I have therefore avoided them over the years even though I know how well than can perform on the low bands. Software modelling of verticals is tricky due to their strong interaction with ground, regardless of the number of radials or high-conductance ground screen. Horizontally-polarized antenna are more predictable.

Motivation: use my tower as a ground-mounted vertical

To address the problem it is helpful to step back and consider what radials do and don't do in various antennas. If I want to load my tower as a monopole on 80 it would be helpful to choose the length and number of radials that minimize the loss without creating a backyard tangle of wires. However, first let me place this in context by presenting my thoughts on how I might utilize my tower on 80.

The first thing is to determine the electrical length of the tower. It is loaded by a tri-band yagi 15 meters above ground, which is the very top of the structure. ON4UN presented a simple formula for estimating this important datum in his book Low-band DXing. (Note: I am using the 1987 version which may have since updated this item.)

Using that formula the electrical length of my tower plus tri-band yagi is 100° at 3.6 MHz, or about 10% longer than λ/4. I then added 4 radials to my EZNEC model of the tower and yagi. ON4UN's formula was surprisingly accurate, with the antenna resonating at 3.3 MHz. Since the feed point resistance was a good match to 50 Ω I only needed to add a series capacitor of 900 pf to get a good match that can cover the entire band (500 kHz).

That sounds good, if it were only that simple. First, this feed requires that the tower be electrically isolated from ground so that the radials only need connect to the coax -- use the braid for the radial connection so that the coax outer surface can serve as a radial, if it isn't buried, and it's choked before entering the house.

While my tower is sitting on a wood platform and the guys are isolated with insulators there will still be conduction from tower to ground. The wood base is not a high-quality dielectric, especially when wet, and it has 1 m² contact area with the soil. Last, the half sloper must be removed, strapped to the tower or isolated or it becomes an active part of the vertical, and not in a good way. All the other coax and rotator cable will also affect performance unless radically reconfigured. Thus a more reliable approach to feeding the tower is to connect the radials to the tower and build an omega match. It is then also easier to adjust the match.

The modelled ground loss is -5 db and the radiation at 10° elevation is -2 dbi. The loss is 1 db better and the low angle gain is 3.5 db better than the loaded half sloper. Thus 1 db of increased low angle gain comes from the lower loss and the other 2.5 db from excising the excess high angle radiation of the half sloper.

Both models push NEC2 far enough that the reported ground losses are inaccurate. When adjusted in the manner recommended by W7EL the relative difference in loss (and gain) is lower by ~0.7 db. So the adjusted losses are comparable, though the vertical still excels at low elevation angles. However questions remain regarding loss in the model.

When modelled over poor ground (as in my case) the (adjusted) losses are -7.2 and -8 db for the half sloper and vertical, respectively. If this seems surprising note that the average current height is higher on the half sloper, and therefore is less negatively impacted by ground. You can easily add radials to the vertical for lower loss, but not for the half sloper.

The loss in both antennas perversely contributes to their excellent SWR since ground is a broadband resistor in series with the radiation resistance. I mentioned this very thing when I commented on the unexpectedly good match of the loaded half sloper, which the model did not fully anticipate. My especially poor ground (not medium) is likely to blame.

Despite the uncertainties this approach may be worth an experiment this winter, if I have the time. Direct A-B comparison with the half sloper is not possible due to the previously mentioned requirement of putting it out of the way. I recently found a large roll of 22 AWG insulated wire lurking deep in my junk box which can serve for radial experiments. After 20 years of inactivity I am frequently surprised at all the gems I am discovering I already own. I don't remember half the stuff I keep finding.

Basic model: 40 meters ground plane with 4 horizontal radials

Now that you see my motivation I will switch over to a simpler model to demonstrate a few attributes of verticals and how they affect performance. By performance I mean efficiency: getting as close to 0 db ground loss as possible. With 4 or more radials, a monopole height near to λ/4 and no obstacles in the near field the far field pattern will be omnidirectional with a single low-angle lobe. That is, the pattern is unaffected by antenna height, radial number and length, ground quality or match.

I am using a model for 40 meters since it is easier to visualize. Lots of hams use ground planes on 40, but on 80 almost all verticals are ground mounted with surface or buried radials: the mechanical requirements of a raised base on 80 are considerable. The 4-radial ground plane is perhaps the simplest of the breed since 4 is the minimum number of radials to achieve an omnidirectional azimuth pattern. It's a good place to start the exploration of radials and verticals.

A further reason is to enable a comparison to the extensive data in a 2-part QEX magazine article by N6LF: part 1; part 2. My simpler treatment of the subject is intended to narrowly focus on a few aspects of these antennas' relationship to ground, especially as it relates to my particular needs and interests.

Questions to be considered:
  • How does height of the antenna above ground affect radial behaviour?
  • How long should the radials be?
  • How much does the impedance change with radial configuration and height?
  • How much does the ground loss change with radial configuration and height?
A commonly-held tenet of radials is that when above ground (a ground plane vertical) they and the monopole should be λ/4 long. For a ground-mounted vertical the rule is that radial length is less critical and can be non-resonant, sometimes shorter and other times longer than λ/4, or even a mix of lengths. There is truth to these practices even if it is not immediately obvious why. This is where models come in handy.

In NEC2 (the engine use by EZNEC and EZNEC+) radials cannot be placed on or in the ground. That requires NEC4 (available with EZNEC Pro), which is expensive. However as W7EL recommends it is possible to model surface radials by lifting the antenna slightly above ground, by at least 0.001λ. In my models I make this distance 10 cm on 80 and 5 cm on 40, slightly above the minimum. This seems to work pretty well.

Free space

To start I will place the antenna in free space to discover its properties in the absence of ground effects. That will be our baseline for comparison. To be resonant at 7.1 MHz in free space the wires are zero loss 16 AWG bare wire, with each radial and the monopole 10.525 meters long. While not fully realistic it is a good place to start since we avoid several confounding variables. Feed point impedance is 22.2 Ω.

Notice anything odd about the free space elevation pattern at right? Despite its asymmetric structure the ground plane radiates equally above and below the plane of the radials. The radiation from the radials cancels so that there is no net horizontally-polarized radiation in the far field. All of the far-field pattern comes from the λ/4 monopole. At this point it should be clear that the radials are not behaving in the manner that many hams would guess or expect. Keep this in mind since we'll later see how this impacts performance.

Performance vs. height above ground

Now let's bring ground into the picture. I'll start by placing it 10 meters above medium ground and lower it down to ground from there, measuring change in resonance, feed resistance, loss and low-angle radiation. I did the plot in a manner that might look odd since I scaled some variables to improve presentation on a single chart.

At 10 meters height the resonant frequency is already shifting upward, until is dives sharply lower as the ground is approached. The feed resistance at resonance gradually increases as the antenna drops lower. Loss is surprisingly stable, remaining in a tight 1 db range.

The antenna's interaction with ground is interesting, and perhaps not what many would expect. An increasing proportion of the near field is penetrating the ground as the height is lowered. Go back and look at the free space elevation pattern as we review a few points.
  • The velocity factor of the radials declines as ground is approached, pulling resonance to a lower frequency. Each radial is like an insulated wire where the thick, lossy ground is the insulator. The ground parameters -- conductivity and dielectric constant -- determine the effect. Every part of the antenna, radials and monopole, has its own contribution to the near field, and it is strong within λ/4. Much of the energy associated with the radials and monopole is flowing in the ground, not on the conductors.
  • Feed point resistance steadily increases as ground is approached. This is likely due to the series resistance of the ground coming increasingly into play.
  • Ground loss is not much different over this range of heights. Indeed it only starts to substantially drop as the antenna is raised to unrealistic heights. The "ripple" is partly due to NEC2 inaccuracy at the lowest heights, though I did adjust the values using techniques suggested by W7EL. A confounding effect is from the monopole's ground interaction and affect on the far field pattern. I did not attempt to determine how much each factor contributes to the loss.
  • Low-angle radiation shows a remarkable change with height. Higher is better. I don't often see this discussed in other articles about this type of antenna..
7.1 MHz 4-radial ground plane at 0 and 10 meters height
A ground plane antenna that is well above ground level is notable as a good DX performer. Not only does it get above at least some obstructions (houses, etc.) it has good low-angle radiation. That performance does not come from lower ground loss (as should be clear from the chart above), but from the far field pattern change due to ground reflections.

Look again at the free space pattern above and then the adjacent elevation pattern. Like a horizontal antenna a vertical antenna benefits from being higher. This holds true whether it is a ground plane or a "no-radial" vertical dipole.

What radials do

Not all radials are alike. There was a time when I (like many) was confused by some verticals requiring different length radials than others. For some the radials must be λ/4, with a λ/4 vertical monopole. Other styles of vertical can have non-resonant radials that can be shorter or longer than λ/4, yet still with a λ/4 vertical monopole. What is going on here? Can both be right?

Let's hear it from W7EL, as stated in his EZNEC user manual:
The effect of radials and other buried ground systems is widely misunderstood. In a typical quarter wavelength high vertical antenna, the ground has two distinct and somewhat independent effects. One is that the current flowing into the base of the antenna is matched by an equal current flowing from the ground to the other feedline conductor. This current flows through the ground and incurs loss in the process. The primary purpose of a buried ground system is to reduce this loss by increasing the conductivity of the ground near the antenna. The effect of a poor ground system is to reduce the antenna efficiency. This reduces the strength of the radiated field, but doesn't change the antenna pattern.
The other purpose of ground (as he goes on to describe) is as a reflector to form the far-field pattern. Since that is not done with radials I will skip over that for now to briefly consider the near field, under and near the antenna.

Both the radials and the ground provide a return path to the feed point (generator). However for the ground to do so there must be a direct ground connection of some sort, such as a ground rod or metal stubs in concrete (Ufer ground). In effect the radials and ground act as a set of parallel conductors, where the radials are low resistance and the ground is high resistance. As more of the return path is via the radials the lower the ground loss in the near field. Longer radials can capture more of the near field at the cost of often undesired effects on loss and pattern, due to the radials becoming self resonant.

Pounding a ground rod into the ground does provide a return path in the absence of radials. However even with good quality (high conductivity) soil all you`re doing is building a high quality connector to a big resistor. Other than dipping a ground wire into salt water radials always provide the least lossy return path.

When the antenna base is above ground you should only use radials, and not make a direct ground connection. The wire from the antenna base to the ground connection has a radiation resistance and will degrade antenna behaviour.

Radial length sensitivity analysis

If you've ever researched or experimented with verticals you'll likely know that there is a great deal of flexibility in their permitted length. That is, the antenna doesn't change much until the radials are shortened or lengthened by more than you might expect. Let's look at this behaviour in the case of the model 4-radial ground plane for 40 meters with its equal length radials and monopole.

What I did was to vary the radial lengths by 2% and measure the change in resonant frequency, and I did so at base heights from 0 to 10 meters. Then I did the same for the monopole. The idea is to numerically discover the derivative (rate of change, from calculus) of frequency with respect to length, for this particular scenario, and thus tuning behaviour of radials and the monopole. The derivative will be different (not a constant) at other base values, though we don't need to deal with that right now.

I usually would present a chart at this point but that isn't necessary. The rates are constant (within modelling precision) within the chosen height range of 0 to 10 meters. For a 2% change in length the resonant frequency changes by 0.4% and 1.6% for the radial length and monopole length, respectively. If they had contributed equally both values would be ~1%.

This tells us that there is no need to fuss over the radial lengths, within reason. Conversely the monopole is more sensitive to length change than expected. Therefore a reasonable tuning procedure would be to cut the radials first and then adjust the monopole length to resonance. If you shorten the radials a lot you would compensate by lengthening the monopole ¼ as much. Just keep in mind that this only addresses resonance, since large changes in radial length impact ground loss (longer is usually better). But when approaching an electrical λ/2 (watch that ground dielectric constant) can cause significant misbehaviour. See the N6LF references given above.

That is for 4 radials, which is a reasonable number for a ground plane mounted above ground. Mounted on the ground and with more radials the situation is different. I won't get into that, or at least not in this article. My modelling experiments so far make me suspect that NEC2 is misreporting ground loss for large numbers of radials even though I have not (yet) found any obvious error in my approach. However I do feel safe in stating that for more radials their length can be shorter without significant additional loss, though probably not less than λ/8.

As one final exercise on this topic, let's assume the above rates of change are linear -- that isn't really true but is good enough for a first-order estimate. Then the 3% lowering of the resonant frequency at 0 meters height is equivalent to a velocity factor of 0.85; that is, radials lying on the ground. There are experimental results out there that measure self-resonance of surface radials in the 0.4λ to 0.45λ interval so this appears to be consistent. Another way of saying this is that λ/4 surface radials would have to be cut to a physical length of about ~0.2λ. Off the ground by more than ~0.1λ the velocity factor is close to 1, so the electrical and physical lengths are equal.


I earlier showed how the ground-mounted vertical can be directly fed by coax. The typical feed resistance at resonance is 30 to 35 Ω, or higher with ground loss added in, which is a good match to 50 Ω. On 80 meters you can have low SWR across most of the band, and certainly correctable with a typical transceiver ATU. The modelled 4-radial vertical made from my tower and yagi has a feed point resistance of 34 Ω.

If you are loading a tower plus yagi (as I would be) the direct feed method would most times require a series adjustable reactance (coil or capacitor) to bring resonance where you want it. For more flexibility an omega match is recommended. If the tower is grounded, or even if anchored in concrete (see Ufer ground) you should connect the radials to the tower and use an omega match.

When independently constructed and mounted above ground a ground plane antenna is easier to match. With the several radials sloping downward (and often doubling as guy wires) the feed point resistance can be very close to 50 Ω. This is useful to know. If nothing else, the common lore regarding feed point resistance of various vertical antenna styles is correct.

Conclusions and next steps

For a brief foray into the wide world of vertical antennas I am learning quite a lot. Although preliminary there are a few conclusions I would hazard to make. I also have some ideas on where I need to go from here.
  • Rather than run a large number of radials to reduce ground loss it can be easier to improve low-angle DX performance the same amount (1 to 3 db) by raising the vertical`s base. This can also reduce interference from and interaction with nearby conductive obstacles. The near field on the low band extends quite far.
  • An omega match, while not always required, is worth the trouble to ease adjustment of the vertical`s resonance and impedance. Turning a knob is easier than trimming 32 radials or moving a yagi up or down a tower!
  • On 40 meters you can probably get equal or better low-angle performance by using the monopole as a support for an inverted vee. Compare the gain charted above to other antennas for 40. Even so many do use verticals in 4-square 40 meter arrays to achieve 5 to 6 db of broadband gain. However on 80 and 160 it is usually easier to get good low-angle performance and array gain from λ/4 verticals than from a horizontally-polarized antenna. It`s often too difficult to get a horizontal antenna up high enough for it to be the superior choice.
What I can do next is uncertain. For the next several weeks I am too busy with other things to construct an experimental 80 meters vertical out of my tower and yagi. The colder than typical weather we`re experiencing this winter is also dampening my enthusiasm. Perhaps I`ll do it in the early spring. Unfortunately this means I`m stuck with a poor antenna for 80 in the coming contests.

Regardless of what I physically build, I do plan to explore software models of verticals using more radials of various lengths to gain additional insight into lowering ground loss and increasing low-angle performance. The literature is clear that more and shorter radials can work well. Shorter radials would be a great advantage in my yard which is 15 meters wide and where the tower is set back 15 meters from the house.

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