A Transformation Technique to Produce Almost Rotationally Symmetric Hexagonal Array Patterns

Abstract

In this paper, a transformation technique for designing hexagonal antenna arrays that produce almost Φ-symmetric patterns is presented. Under the transformation, the hexagonal array factor is represented by a single-variable polynomial. Since every Φcut in the hexagonal array pattern tracks the shape of the polynomial, the resulting array pattern is almost a figure of rotation. When the polynomial is chosen to be a Chebyshev polynomial, a hexagonal array with a Dolph/Chebyshev pattern is obtained. Also, with a known linear array current distribution which is in general complex and symmetric, the hexagonal array can be made to produce a flat-topped main beam with specified ring side lobe levels. A novel expression that computes the hexagonal array current distribution from the complex polynomial coefficients is derived.