Antennas, Images and Ground
By David J. Jefferies
D.Jefferies email

Introduction
antenneX readers are interested in frequencies from HF to microwave and beyond. This article treats interactions with the ground, and the representation of ground reflections by the "method of images".

Here, we discuss the intermediate frequency region where the antenna may be spaced above a ground by at least a quarter wavelength (40 metres at 160 metre band, 2.5 metres at 10 metre band) but by not more than several wavelengths. We show that, given a good ground, there will be significant gain enhancement in certain directions over that of the antenna alone (in free space, far from any obstacles). We shall discuss how the fields fall off with distance away from the antenna, showing that for reasonably close ranges there are two markedly different laws for horizontally polarised structures and for vertical antennas.

Images
Dan Handelsman, N2DT asked "how does an antenna couple to its image?". He viewed an image as a real second antenna placed at the location of the main antenna's reflection in the ground. Let us consider this for a moment. The main antenna induces currents in the real perfect plane ground. The electric fields from the real antenna must (by electromagnetic boundary conditions for a perfect conductor) meet the ground plane at right angles. There is a propagation time delay between what happens on the main antenna and its effects on the ground. Light travels approximately one foot a nanosecond (30 cm a nanosecond), and so the time delay to the "signal" represented by the currents in the ground plane from the energizing "signal" in the antenna is roughly the same number of nanoseconds as the average height of the antenna measured in feet.

If we now imagine taking the ground away, but requiring the field distributions just above the ground to remain unchanged, the E-fields pass straight through the plane where the ground was and just below the ground level are directed (away from, towards) the ground if just above the ground they had been directed (towards, away from) the surface.

We may consider these "image fields" to be due to an "image antenna" which has exactly the same structure as the main antenna, but is reflected "positive to negative". This image antenna is excited at the same instant in time as the main antenna. Thus there is a time delay from the currents in the image to the currents in the ground plane.

If this "image antenna" was a real structure, it would be excited by the fields from the main antenna after a time delay appropriated to twice the height of the main antenna above the ground plane. This would not give the same field distribution as the image scenario we have invoked, where there are identical currents in the main and image, and they are synchronous in time.

Of course, if we now analyse the far fields from the combination of main and image antennas, we have doubled the number of antenna elements contributing to the radiation, and therefore we have doubled the potential gain (an extra 3 dBi) in certain "boresight" directions in which all the fields add up in phase. For a discussion of array antenna basics, and the concept of "element pattern", "array pattern", and "pattern multiplication" to give "total pattern", the interested reader is referred to
DJJ's web page on array antennas

So the ground, if perfect, actually gets us more antenna directivity. Depending on the loss in the ground, this may or may not increase the gain, after allowing for the overall antenna efficiency.

Depending on the height above ground, and on the polarisation, the antenna radiation pattern will be modified and the boresight direction may be changed. For horizontally polarised structures such as Yagi-Uda arrays, the boresight take off angle for the combination of main and image antennas will be upwards, at an angle to the ground that decreases as the height above the ground increases.

SOME EXAMPLES
Dipoles above a perfectly conducting ground plane

Vertically polarised antennas
Consider the situation sketched diagrammatically here.... We have placed a vertically orientated dipole at a height h above a perfectly conducting infinite plane earth. If the earth were not there, the field pattern above the earth would be identical, and would be modelled by the sum of the fields from the source dipole and its image.

The image of the vertical dipole in the ground plane consists of a virtual dipole having the SAME current direction as the source dipole. This is because the electric fields from the source dipole meet the ground plane at right angles, and so the electric field on opposite sides of the plane would be in the same direction if we assumed the plane was not physically there, but the field distribution was entirely created by the source and its image.

We now see that we have a 2-element array antenna, with the source elements fed in phase. The element spacing is 2h and there is axial symmetry about a vertical axis. The general form of the radiation pattern of the array factor, in a vertical plane, for the assumed arbitrary special case of h = three wavelengths, is shown here.

Of course, for the full radiation pattern we must multiply the array pattern by the element pattern, so as there is an element pattern null in the direction "straight up" there will be no radiation straight up.

We see that there are numerous fringes caused by the interference pattern between the antenna and its image; these fringes will increase in number and decrease in width as we increase the height h .

On the surface of the ground plane the fields fall off as 1/distance from the antenna footprint, in the far field. Thus, unlike the horizontal polarisation case, the propagation (power density) loss is an inverse square law, until we consider other factors such as the curvature of the earth, and scattering from objects having vertical conducting surfaces.

Horizontally polarised antennas
If, however, the antenna above the ground plane is horizontally polarised, so:-

the image is reversed in polarity, since the tangential component (horizontal component) of electric field has to vanish on the conducting ground plane. The radiation pattern is then appropriate to elements spaced 2h and fed in anti-phase. The fields are zero on the ground plane, however far we go away from the sources.

There are still lobes in the vertical plane, which again narrow and increase in number as we increase the height h. However, the lobe maximum closest to the ground is at an angle to the horizontal, for which angle the differential phase delay between the radiation from the source and the image amounts to one half wavelength. We therefore expect the field strength in this direction again to decrease as 1/distance, and the radiated power density to decrease as 1/(distance^2).

Geometrical factors for both polarisations
There is a further factor in practical situations. We have pointed out that the fields on the ground plane are maximum (vertical polarisation) or null (horizontal polarisation). To receive a signal, the receiving antenna has to be placed at a height H above the ground plane. Let us consider the height H, (which for a vertically polarised quarter wave monopole cannot be less than an eighth of a wavelength). (In practice, the ground is obstructed and lossy, as well as being reactive, and often the receive antenna is spaced a number of wavelengths above the ground to get a clear line of sight to the transmitter.) The point at the centre of this antenna lies at an angle to the "ground zero" point which is on the ground plane between source and image. As we move the receiving antenna further away, this angle decreases proportionately. However, the fields and power densities only obey the power laws derived above providing the angle from the transmit antenna remains the same. It so happens that we nearly always find ourselves on the edge of a lobe, and the angle decrease moves us further towards the null as the range is increased. The power density and the fields in this scenario therefore may fall off faster than the amounts calculated above.

If there are lobes below the angle from "ground zero" to the receive antenna, we may also find that the signal strength can increase with distance, and oscillate up and down as we go further away from the transmitter. Ultimately, however, the received signal power will fall off faster than "inverse square" [1/r^2].

An observable "rule of thumb" is that the field strengths (for horizontally polarised antennas) fall off, for constant H, as 1/(distance^2) and the power density as 1/(distance^4). For the case of moderate values of h and H, a distance can be found where the power law dependence changes from inverse square to inverse quartic (in received signal power density vs distance). We observe that according to the commonly used Rayleigh distance criterion that we have to be further than about 2[(max dimension of antenna)^2]/(lambda) away from the antenna to be in the far field, so the far field region starts at a range 8(n^2)lambda for radiation of wavelength lambda and antenna height h = n(lambda).

Dr. David J. Jefferies
School of Electronic Engineering, Information Technology and Mathematics
University of Surrey
Guildford GU2 7XH
Surrey
England
Click Here for the Authors' Biography

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Last modified: December 27, 2003