Applications of Potential Theory to the Design of Linear Arrays

Abstract

The polynomial formulation of the linear array problem introduced by Schelkunoff is studied from the point of view of potential theory. An electrical analogy results which is not only very helpful in qualitative thinking about the problem, but which also makes possible the construction of an analog computer for the synthesis of arrays to produce a desired radiation pattern, and for the evaluation of existing arrays. Such a computer has been built, and tested on known patterns with remarkable success. Several theorems concerning the effect of the roots of the polynomial on the magnitude and phase of the space factor of an array are given. Some of the most important consequences of these are the lack of uniqueness in the array synthesis problem, and the evaluation of known methods of synthesis which consider only constant-phase patterns. A method of analysis is sketched which in principle does the same thing as the computer, and the difficulties in applying this are described. It is concluded that the computer would be preferable for a wide range of practical problems.