Beam Efficiency and Gain Optimization of Antenna Arrays With Nonuniform Spacings

Abstract

A distribution of current across the elements corresponding to the optimum condition is given as a solution of the characteristic equation Ba = λ Ca where B and C are matrices whose elements depend on the type of sources and their spacings. The value “a” is a column matrix whose elements define the array excitation. The beam efficiency or gain of a nonunifonnly spaced array is increased over that of a uniformly spaced array. To find the element positions, one first finds the direction, known as the direction of steepest descent, of maximum change in the largest characteristic value; the direction is given as grad λ, where the partial derivatives are taken with respect to the element positions. By proceeding in the direction of steepest descent, one will arrive at the point located in the element position space that represents the optimum spacings. Perturbation methods are also used to show how the beam efficiency or gain is increased by nonunifonnly spacing the elements.