Theory of aperture aerials based on the properties of entire functions of the exponential type

Abstract

Based upon the theory of entire functions of the exponential type familiar in mathematics, and assuming separable illumination functions, several problems concerning aerial systems are discussed. It is shown that radiation patterns which can be achieved with finite aperture dimensions belong to theW ₁ class of functions. The construction of any arbitrary radiation pattern is reduced to a problem of approximations. The specified radiation pattern is represented as the limit of the series ofW ₁ functions convergent in the mean. It is further shown that an increase in the gain to above the classical level is of necessity associated with an increase in quality. A lower limit of quality at a given gain is determined. Finally, solutions of problems of approximation encountered in practical aerial design are presented.

Резюме

На основе Теории показательных функций, разработанной в математике, предполагая отделяющиеся функции освещенности, авторы обсуждают следующие проблемы антенны: необходимое и достаточное условия реализуемости характеристики направления, приближение характеристик любого направления, нижняя граница добротности при заданном выигрыше, далее различные задачи приближения.