On the efficiency and gain of antennas

The fundamental limits of the gain and e±ciency of an
antenna are explored. These are very important quantities for, e.g.,
superdirective arrays. The antenna is in this paper con¯ned 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 ¯nd 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 e±ciency.
The analysis is based on the expansion of the electromagnetic ¯elds
in terms of vector spherical harmonics. Explicit expressions for the
limits of gain and e±ciency, and the corresponding current densities,
are derived for di®erent types of antennas.