ON THE EFFICIENCY AND GAIN OF ANTENNAS

The fundamental limits of the gain and efficiency of an antenna are explored. These are very important quantities for e.g., superdirective arrays. The antenna is in this paper confined in a sphere and all of the currents are assumed to run in a material with a given conductivity. It is shown that one can find the current distribution in the sphere that optimizes the gain, given the frequency and the radius of the sphere. The results indicate the distribution of antenna elements in an antenna array in order to maximize gain, or efficiency. The analysis is based on the expansion of the electromagnetic fields in terms of vector spherical harmonics. Explicit expressions for the limits of gain and efficiency, and the corresponding current densities, are derived for different types of antennas.