Generic Antenna Patterns

There’s more to antennas than meet the eye. Every antenna type has its own typical performance. One can fathom antennas by their radiation pattern. This pattern can be divided into mainly two categories. And the radiation pattern is governed not only by the antenna proper but also by its orientation in space and presence of ground and what type of ground. These latter circumstances will be elaborated upon below. It will be apparent that any antenna will fall in one of a few more generic classes depending upon its polarisation.

1. Isotropic radiator

To fully understand the radiation pattern we will have to study the isotropic radiator and its connexion to the decibel unit.

Imagine a radiating source that radiates equally well in all directions; east, west, north, south and up and down. This is an isotropic radiator. Now place this source in free space, much like the sun in our solar system. Its “light” will then radiate in all directions and “illuminate” any object we arrange in its way. Close to the source we will experience a higher intensity of this radiation and farther way we will experience a lower intensity.

Since the radiation is isotropic the same intensity of radiation can be measured at particular distance from the source, no matter where we are, as long as we keep this exact distance. Specifically, along a sphere with the isotropic radiator at its centre we will experience the same intensity of radiation.

Now, if this source emits a power of one watt then, collecting every piece of energy from this source that is “sprayed” onto the sphere, will sum up to the emitted one watt, no matter at what distance we do this. For the sake of this argument, pick a distance, any distance, lets call it R. Then at that distance R, let the intensity of the received radiation on a little square be I. Putting together all intensities from all the squares around the sphere will add up to the emitted 1 watt. Viewing it this way is important in the future.

If the output power of the source is doubled, to two watts, we will at this same distance, R, experience a doubling of the received power, or 2I, in other words an increase in power of 3 decibels, 3 dB.

A 100 watt radiator gives then, of course, a hundred-fold increase in power received compared to the one-watter, or, to put it in decibel terms 10*log(100/1), circa 13 dB.

It is convenient to express the received power in decibels when comparing different antennas. But to compare values we must decide on a “norm”, a “zero” on the ruler. As decibels only express relations between these intensities it does not matter what exact power, in actual watts, is emitted from the isotropic source. We just have to stick to a value, call it 1 watt, 100 watts or equally well, I. This “zero” is then used as a reference, and any antenna that radiates the same energy in some direction is said to emit 0 dBi (i for isotropic) power.

A bad antenna with 100 watts into it, can, placed in the position of the isotropic radiator of 1 watt, be found to give the same intensity, i.e. 0 dBi. Then one must wonder where the other power disappeared? Probably it is emitted in another direction or – worse – is not emitted at all, or partly, transformed into heat. Ok, then heat is radiated, but that’s not the frequency we expected.

The purpose of many antennas is to squeeze this isotropic sphere into some other form. The volume of the sphere is constant, only its dimensions are changed. A bidirectional antenna squeezes the sphere into something of a tube, while a unidirectional antenna tries to redirect the bidirectional antennas back-lobe to the front, making the gain higher, and preferably the lobe smaller. The more one can press the sphere in one direction, the higher the gain. Accepting this one also realises that smaller lobe means higher gain in that direction.

2. Polarisation

Before getting our feet wet, we must partition our antennas in two groups, the vertically polarised ones and the horizontally polarised ones. This has to do with the antenna’s orientation and is – in our case – always referred to ground. A horizontally polarised antenna will propagate its waves much as we see waves in a pond, after dropping a stone into it. The waves bob up and down on their march in a direction away from where the stone plunged. For vertically polarised antenna it is harder to find a physical analogy as the waves in the pond would have to “bob” left-to-right on their way. Perhaps imagining the wiggling of the tail of a fish in the same pond will give the proper illusion?

While a dipole normally is erected horizontally, and thus emits horizontally polarised waves, there is nothing that prevent us from standing it on edge and emit vertically polarised waves. In fact in some instances that may be a good thing! But we start off the discussion with horizontal polarisation first, taking vertical polarisation later.

3. Horizontal Dipole (or any horizontally polarised antenna as we shall see)

An antenna in the shape of a half wave dipole will not emit equally well in all directions in free space. Specifically it cannot emit anything from its ends. It will, however, emit in a direction perpendicular to its wires. Since the dipole is symmetrical in that respect, the radiated pattern will be in the form of a doughnut with no hole in it with the dipole’s ends sticking out of said hole. If we compare the dipole’s pattern with the isotropic radiator we will find that the dipole’s radiation intensity is 1.64*I, in the maximum direction and reduced to nil in a direction perpendicular to that.

A dipole in free space will have a radiation pattern in the shape of a doughnut. In the diagrams above we see the dipole oriented in a east-west fashion. Maximum radiation is perpendicular to the antenna wires. Along the antenna there is no radiation, hence the “waist” in the left diagram. Seen from “east-west” the intensity is the same in all directions, as is illustrated by the rightmost diagram. (Due to symmetry only the upper half of the pattern is printed.)

In other words, the dipole has formed the isotropic sphere into a doughnut and squeezing the sphere that way the intensity will extend in some other direction. Something had to yield and in this case the doughnut “protrudes” out of the sphere, resulting in an antenna with a radiation pattern that gives a gain of 1.64 at best. Now, 10*log(1.64)=2.15, so the dipole is 2.15 dBi better in this maximum direction. In all other directions the dipole is worse than this. (Which may not be a bad thing if we can point the “deaf” ends of the pattern straight onto interfering sources.)

3.1 Real ground

Until now this discussion has been very idealised assuming free space and isotropic radiators. Of course there is no such thing as true free space, and no ideal isotropic radiator exist. So now we have to consider the effect of the earth, the ground, soil, under the antenna and its effect on the radiating pattern.

While no free space exist we can come close to free space if our antenna is placed more than 2 wavelengths above ground. This is easily done at higher frequencies, e.g. at 433 MHz (70 cm) a height of 1.40 metres is sufficient. When dealing with short wave frequencies then this is no longer easy. Specially not on the lower frequencies of 3.5 and 1.8 MHz, with wavelengths of 80 and 160 meters respectively. 2 wavelengths at 1.8 MHz is some 320 metres!

It is evident that the radiation pattern will be only above ground as ground losses and, as we shall soon see, reflections, eliminate any radiation on or below ground. In the figure below we see a dipole at a height of 2 wavelengths. In the left diagram we see the standing doughnut from above. In the rightmost diagram we have the ground as the horizontal part and the bulge above it is the radiation pattern above ground. We need to be fluent in deciphering this type of figures.

As we thus lower our antenna to more manageable heights, its pattern will be distorted. Why is this? If we follow one particular ray of emitted power we will understand why. Assume that the ray in question is emitted downwards. It will hit the ground below and reflect off it, much like rays of light reflects off a mirror. The reflection is controlled by the same law that govern optical light, so an incoming ray at a certain angle will be bounced off in the same angle but in the forward direction. The problem appears a while later when this ray mingles with the “direct” rays from the source. Since the ray is really a wave it will add to the other rays in some way. The end result is that the waves can “mingle” more or less, either constructively or destructively. A destructive mingle destroys the radiation in that direction, while a constructive mingle will amplify the radiation in that direction. The net result being that we have a distortion of the free space radiation pattern.

Keep in mind that the deformation of the radiation pattern is not necessarily a bad thing. It all depends on what you want the antenna for. Knowledge of these effects will help you decide for an antenna that is suitable to do the job you want it to.

From the figures below we ascertain that the dipole pattern’s distinctive properties are muddled more and more as we get closer to ground. The extreme case is at very low heights, tenths of wavelengths, when the doughnut shape is no longer recognisable at all. In this, and the following diagrams, we have left free space and have a ground below the antenna. A ground that will reflect the downward waves, bounce up again and mix to give more interesting radiation patterns.

2 wavelengths above ground.

1 wavelength above ground.

2/3 wavelength above ground.

1/2 wavelength above ground.

1/4 wavelength above ground.

We do however observe one major feature: The gain in the maximum direction is always more than the 2.15 dBi quoted above! This is another effect of the ground reflection, the “constructive mingle” gives us a circa 5 dB extra gain. A most welcome effect of any horizontally polarised antenna.

We analyse the diagrams one by one: Starting off with the 2 wl one, we have only a small deformation of its free space pattern. Even at 1 wl we can conclude that the antenna performance is likely not to differ from the free space case. But as we go lower the thin “waist” will gradually fill out and be more and more blunt. At low heights the pattern is almost entirely circular – in all directions. The pattern has deteriorated into an oblong ball with maximum radiation straight into zenith. We conclude, that to have reasonable directivity, a dipole must be at least half a wavelength up – and preferably more.

If we look at the elevation angle we find that an angle of circa 40 degrees is within reach, but only at a height of about half a wavelength. Below that height the directivity in this plane disappears and the dipole is more and more a “cloud warmer”.

To reiterate, for horizontally polarised antennas we have the following results:

  • to have directivity the antenna must be at least half a wavelength above ground level,
  • for really low angles of radiation the antenna must be at least half a wavelength above ground level,
  • if we cannot position the antenna above half a wavelength above ground it will more or less only radiate straight up.

The above, combined with ionospheric propagation, then teach us:

  • For DX we need a low angle of radiation ==> Put the antenna as high as possible. There is some directivity, its pattern is an oblong.
  • For short distances, we must have a high angle of radiation ==> Put the antenna low above ground – or in some instances even on it! Its pattern is omnidirectional. This is the case for NVIS, Near Vertical Incidence Sky-wave-propagation, frequently used for short range HF communications.

To sum up: It is not easy to get an angle of radiation below circa 30 degrees with a horizontally polarised antenna at short wave frequencies and anyhow it is likely to radiate more or less equally well all around the compass. But we get a useful extra 5 dB gain absolutely for free!

3.2 Extending the results to other antennas

These results hold for any type of antenna that is horizontally polarised, for example any type of dipole, be it a G5RV, W3DZZ or a 135-feet doublet to name a few. Even yagis, quads, moxons etc. that are horizontally polarised – as virtually all of them are – succumb to these results.

4. Vertical dipole (or any vertically polarised antenna as we shall see)

A vertically oriented dipole antenna will – in free space – radiate perpendicular to the antenna wire, to form a lying doughnut. This is exactly the same pattern as the horizontal dipole, only tilted 90 degrees. Still no radiation takes place off its ends, so this antenna will not radiate straight up or straight below. Its angle of radiation is typically 0 degrees.

Due to the polarisation of the waves, they cannot now reflect in the same manner as the horizontally polarised waves did, and specifically we cannot benefit from ground reflections, there is no radiation pointing downwards! We miss out the extra circa 5 dB gain. Vertically polarised antennas have another benefit though, that in some circumstances clearly outweighs this drawback, and in fact, makes the vertical antenna a very good antenna: Its low radiation angle!

A vertically oriented dipole at a height of 1/2 wavelengths (lowest leg-end at that height). The radiation angle is much lower than for the horizontal dipole, at the cost of a 5 dB decrease of gain.

At higher frequencies vertical polarisation is used successfully in mountainous areas as the radiation is not bounced off into space but rather penetrates valleys sideways, and stays in the valleys, bouncing left and right! For frequencies where the ionosphere is used for reflecting the waves in space the polarisation is not kept after the reflection. When received at ground the polarisation will be a bit vertical and a bit horizontal, so even if one would expect that a vertical antenna at the transmitter would require a vertical antenna at the receiver, this is not so in practice. If the ionosphere and ground reflections are eliminated (shudder!) one would however require the same polarisation at both ends of the communication link.

As we lower the antenna close to ground the doughnut shape is distorted in a way that forces the donut away from the ground. The take-off angle is thus not 0 anymore, but some small positive angle, typically about 20 degrees for average ground conditions, even if the antenna is placed only a metre or so above ground level!

The key to this behaviour is the kind of reflection that actually takes place even for vertically polarised antennas. As we put the antenna close to ground some of its radiation (the one coming from its outer parts, close to the ends) is directed to ground, but only at a very small angle. The rays will hit the ground a long distance away. Now something quite odd happens: Below a certain angle the rays do not just reflect off the ground surface to mingle constructively with the direct portions of the radiation, but at a certain distance from the antenna the phase of the waves is changed 180 degrees too! All rays that are reflected further away from this reflection point will experience this phase change.

So, close rays will not change phase but reflect and mingle constructively. And further away rays will change phase by 180 degrees and mingle destructively. This resulting pattern can be seen in the figure below. Note how the “underside” of the radiation pattern is free from radiation – this is the effect of the destructive interference.

The same vertical dipole now mounted less than one meter above ground level. There is now only one side-lobe, lesser gain but still a very low take-off angle. No radiation is exactly along the ground. This is due to the destructive interference mentioned in the text but also due to absorption of rays in the ground.

4.1 Soil conductivity

Soil conductivity has not much effect on the radiation pattern of horizontally polarised antennas as can be seen in the comparison below, where a half-wave dipole is simulated at 1/2 wavelength AGL for “normal” and “very” conductive soil:

Effect on ground conductivity for horizontally polarised antennas is small. The diagrams show horizontal a dipole at 1/2 wavelength above normal ground and salt water respectively. It is unlikely one would notice any difference at all under practical circumstances between the two.

For vertically polarised antennas the picture is different though. Depending on the soil conductivity we get varying take-off angles: Poor conductivity results in a larger take-off angle and good conductivity results in a low one. One cannot really change the soil conductivity much, even though rain will make the ground a bit more conducting. Experiments show that watering the ground and/or laying out large sheets of wire net will improve the conductivity in this context but unfortunately the area required is in the order of several wavelengths so this is not practical.

Given the chance we can however let a vertically polarised antenna have a lower or higher take-off angle by erecting it on a good soil or bad soil, that is one with high conductivity or low conductivity. Sandy soils or rocky dry soils are worst since the have very low conductivity, resulting in higher angles, while wetlands and marshes have relatively high conductivity and will thus yield a low take-off angle.

The best conductivity for our DX-purposes is not soil at all, but salt water! The ions in the salt water give a very high conductivity indeed. While “average ground” has a conductivity of circa 5 mS (S=Siemens, 1/ohm) salt water has as high as 80 000 mS! This makes the take-off angle very, very low, only a few degrees. The radiation runs along the water straight into the horizon, it cannot be better for long distance communication. And it clearly outperforms the take-off angles achievable with even the best horizontally polarised antennas. Note also how the obtained gain is increased substantially!

Vertically polarised antenna (actually a vertical dipole) 1/2 wavelength above very conductive ground, as would be experienced above saltwater. Note the increase in gain (>6dB extra) and the extremelylow take off angle. The take-off angle doesn’t get any lower than this!

Same vertical dipole at 1 m above a very conductive ground.

4.2 Height above ground level

As can be imagined from the discussion above it is beneficial for the take-off angle to have the vertical antenna close to the ground. Unfortunately this is not quite true. Ground losses, which can be thought of as being resistive in nature, must be avoided. These losses increase as we get closer to ground, but are really wrecking our purposes only if we erect the antenna very close to ground. If we can isolate the lower part of our antenna by lifting it a few metres (1-3) or so above ground, the ground losses diminish and are of no practical importance to us.

Elevating the antenna above ground will of course also have an effect on its radiation pattern. From the reasons mentioned above it is clear that a position close, but not too close to ground will be satisfactory. Increasing the height will spread the radiation into larger lobes.

If this is good or bad is good point for discussion: Is it better to have one low take-off higher gain lobe or a broader lobe with lower gain? It is up to you to decide. For pure DX, and we are talking extreme DX here, the lower take off angle is to be preferred.

Apparently most man made noise is vertically polarised at a close distance. A vertical is generally regarded as a noisy antenna. Whether this is a problem or not depends on the amount of local noise in the first place. I can’t say that I have ever been troubled by the alleged extra noise.

5. Absorption

One final note of importance. Now that we know what to expect from different polarisations, we must make sure that the radiated power is not unduly hindered before hitting the ionosphere.

It is tempting to use high trees as supports for our antennas. Specially for vertical antennas it seems appropriate to, more or less, tack the wire to the tree. The antenna is invisible this way but unfortunately the sap in the trunk will absorb some of the emitted energy. So try to keep a distance of a few meters between the antenna and the trunk.

In the same vein, erecting vertically polarised antennas in a forest is bound to cause problems, as much energy is absorbed in the trees! The trees act as vertically polarised receivers and will absorb energy. Using horizontal polarisation in this situation is not equally detrimental but the trees will absorb some of the energy in this case too.

In general, one should try to place the antenna clear of any disturbing object, specially metallic ones and ones that have an extension in the polarisation used. The area around the antenna, up to a distance of several wavelengths, has most influence on the antenna’s performance. Mountains etc. at longer distances do not degrade performance substantially.

6. Other antennas

To drive home the results of the discussion above, here are some diagrams of other antennas. From the diagrams you should have no problems to ascertain whether polarisation is vertical or horizontal in each case:

First out is the half-square. Over normal ground, salt water, and the two combined in the same diagram for comparison.

Then there is the half-square beam, 1/4 wavelength over normal ground, salt water and the two put together for comparison.

To show what to expect from different heights of the half-square beam here are: (normal ground first, then very conductive)

1 meter AGL…

…1/2 wavelength AGL…

…and 1 wavelength AGL.

A XQ-beam, 2 element delta and a HSQB in the same picture, all at 14 MHz. Normal ground and saltwater:

The inner and outer lobes are the HSQB at 1 meter AGL with normal or salty ground. The lobes in the middle are for the XQ-beam and the 2 element delta. The QX has a small advantage, but not to the HSQB. The HSQB is vertically and the others are horizontally polarised.

And finally a normal quarter wave vertical over salt water at various heights above ground, 0, 1/4, 1/2 and 1 wavelength. They are displayed in yellow, black, red and green in increasing order.

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2 Responses to Generic Antenna Patterns

  1. Riley Barnes says:

    One of the outstanding pieces i have seen this week.

  2. Pingback: Antenna Information

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