Mumbai University > Electronics and Telecommunication > Sem 5 > RF Modeling and Antennas

Marks: 5M

Year: Dec 2014

The variations of the radiation characteristics (pattern, radiation resistance, directivity) of infinitesimal vertical and horizontal linear elements were examined when they were placed above plane perfect electric conductors. From this analysis we came to know that although ideal electric conductors (σ =∞) are not realizable, their effects can be used as guidelines for good conductors (σ>>ωε, where ε is the permittivity of the medium). One obstacle that is not an ideal conductor, and it is always present in any antenna system, is the ground (earth). In addition, the earth is not a plane surface. To simplify the analysis, however, the earth will initially be assumed to be flat. For pattern analysis, this is a very good engineering approximation provided the radius of the earth is large compared to the wavelength and the observation angles are greater than about $57.3/(ka)^{1/3}$ degrees from grazing (a is the earth radius) . Usually these angles are greater than about 3◦.In general, the characteristics of an antenna at low (LF) and medium (MF) frequencies are profoundly influenced by the lossy earth. This is particularly evident in the input resistance. When the antenna is located at a height that is small compared to the skin depth of the conducting earth, the input resistance may even be greater than its free-space values. This leads to antennas with very low efficiencies. Improvements in the efficiency can be obtained by placing radial wires or metallic disks on the ground.

The analytical procedures that are introduced to examine the ground effects are based on the geometrical optics models. The image (virtual) source is again placed a distance h below the interface to account for the reflection. However, for each polarization non unity reflection coefficients are introduced which, in general, will be a function of the angles of incidence and the constitutive parameters of the two media. Although plane wave reflection coefficients are used, even though spherical waves are radiated by the source, the error is small for conducting media. The spherical nature of the wave front begins to dominate the reflection phenomenon at grazing angles (i.e., as the point of reflection approaches the horizon). If the height (h) of the antenna above the interface is much less than the skin depth $δ [δ = \sqrt{2 / (ωμσ)}]$ of the ground, the image depth h below the interface should be increased by a complex distance δ(1 − j). The geometrical optics formulations are valid provided the sources are located inside the lossless medium. When the sources are placed within the ground, the formulations should include possible surface-wave contributions. Exact boundary-value solutions, based on Sommerfeld integral formulations, are available. Concept of Ground effect is shown in figure below.