Optimum performance indices of aperture antennas with and without pattern constraints

The optimization of the following performance indices has been investigated for circular apertures: the efficiency eta, the spread of radiation power sigma-squared, and the ratio eta/sigma-squared. The investigation involves the evaluation of some new Bessel-function integrals. Limit values of the indices, aperture fields, and far fields are determined analytically for the unconstrained patterns. One new result is that the maximum value of eta/sigma-squared equals 1/8; this value is reached if the aperture illumination is 1 - r-squared. Computations are also performed for the case when pattern constraints are introduced; constraints can be applied to the main beam and/or the sidelobe peak levels.