n this article we suggest that the coupling to ground and adjacent objects sets the gain and the bandwidth of compact antennas, mounted in practical environments, predominantly. The ground absorption does not depend much on the size of the small antenna, but it affects the Q factor which, in turn, limits the gain and enhances the bandwidth. For this reason, many compact antenna installations work better than the limitations of the CHU formula for small-antenna Q might indicate.

antenneX readers will now be familiar with many of the arguments about the theoretical limitations to the performance of compact antennas, brought about by their small size and consequently low radiation resistance. See for example antenneX Archive VI, article number 66, for February, 2001, “Radiation impedances of wire and rod antennas” by D. J. Jefferies.

In the present article we discuss the effects on the gain and the bandwidth of compact antennas brought about by interactions with the ground. Many compact antennas are limited in overall height. This means that they have to be mounted very close to the ground or to other absorbing and scattering objects, in order for the advantages of the compact design to be exploited. Under such circumstances, radiation absorption by the ground is greatly enhanced. This has positive effects on the bandwidth and tuneability of the antennas, although it reduces their gain.

Now for some theory. The radiation resistance of the antenna we call Rrad, and the loss resistance of the antenna structure we call Rloss. Power is absorbed from the near field region by the ground close to the antenna. For an r.m.s. antenna current I amps, we call this absorbed power Pground = I^2 Rground. The quantity Rground appears as a component of the driving point impedance of the tuned compact antenna.

Thus, the total power absorbed by the antenna from the feed is, for r.m.s. feed current I amps,

I^2[Rrad + Rloss + Rground]

Prad = I^2[Rrad]

Rrad/[Rrad+Rloss+Rground]

10 log[10](Rrad/{Rrad +  Rloss + Rground})

Formulas on their own need interpretation with real numbers. If we assume that the Rrad of 0.2 Ohms is equal to the Rloss at an antenna length of 1/30 wavelength (see the article cited above), then the maximum possible gain of this short antenna in free space will be 1.8dBi (appropriate to a short dipole in the azimuth plane), minus 3dB for the loss due to the resistance of the metal parts of the antenna. There will also be additional loss in a practical installation, for we cannot feed a 0.4-Ohm antenna effectively from sensible transmission lines without some kind of matching network, which is necessarily lossy and must be regarded as an integral part of the antenna itself.

Before considering ground loss, therefore, a short antenna is bound to have gain less than –1.2 dBi, and perhaps quite a bit less than this after taking into account the extra losses of the matching network.

Placing the antenna above a perfect ground gives up to 3 dB of extra gain due to the ground reflections, but alters the Rrad at the antenna terminals. But in this article we want to consider what might be the effects of a lossy ground.

Looking again at the factor {Rrad + Rloss + Rground}, we see that the effects of the ground resistance Rground are proportionally more if the other two terms are small. We recall that Rrad reduces as the length gets shorter, going down by a factor of 4 each time we halve the length. Thus, ground loss, which would not be very significant for a half wave dipole with Rrad = 72 Ohms, will become dominant for a short antenna for which Rrad is only a few tenths of an Ohm. Thus, the thesis of this article is that ground effects dominate the gain and the bandwidth of compact antennas.

If we assume there is (for sake of argument) 3 dB of extra ground loss for a quarter wave monopole (36 Ohms) over an imperfect ground, then clearly the terminal resistance due to Rground also has a component of 36 Ohms. Now we attempt to make the antenna shorter, and see what happens to the gain.

TABLE 1

We see that the ground absorption of power greatly reduces the gain of the monopole. However, it is in the character of the trade-off that there is an upside to this problem. We recall that the CHU formula for the limit to the intrinsic Q of a small antenna, due to radiation damping alone, is

Q >= [lambda/(2 pi a)] + [lambda /(2 pi a)]^3

TABLE 2

TABLE 3

Thus we see that the compact antenna structures favoured by antenneX readers are not compromised in terms of the Q factor by the amount that the CHU formula suggests.

For other kinds of short and compact antenna which couple less strongly to the ground, the loaded Q figures will be larger than this and the gain reduction will be smaller. We can get an idea of what will happen by running a NEC simulation for the antenna structure above an imperfect ground, at various heights from the ground.

Dan Handelsman has provided the following figures for a certain class of compact antenna that he is developing at 7 MHz. These are simulation figures above a real ground. His unloaded gain will have been about 2 dBi, so from these figures we may estimate the Q factor at about 80 for the smallest antenna, providing 86 kHz of useful bandwidth at 7MHz. The measured bandwidths are smaller.

TABLE 4

The lesson we learn from this exercise is that compact antennas will work over a sensible bandwidth if mounted in a real environment containing lossy adjacent ground and scattering obstacles. The price to be paid is gain, but that is of secondary importance for many communication scenarios where the establishment of a link out of a confined site is desired. –30-

Dr. David J. Jefferies School of Electronics and Physical Sciences University of Surrey Guildford GU2 7XH Surrey, England D.Jefferies email Click Here for the Authors' Biography

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