Simple Calculation Method for Conformal Beam-Scanning Array Pattern

In this paper, we discuss a simple beam-scanning calculation method for conformal array with arbitrary shaped surface. In order to scan a beam of array antenna with the curved surface, it is necessary to calculate optical path-length from each antenna element to an aperture plane, so called `equi-phase front', which is perpendicular to scanning beam direction. Furthermore, normal vectors and polarized direction of each element are needed. For these calculation, we propose a new algorithm which can calculate the path-length (driving phase input to each element) by employing the direction-cosine relation between the beam direction and each element. Using this direction-cosine, the path-length can be easily and generally obtained for arbitrary shaped conformal array. Furthermore, if the shape of array surface is expressed by polynomial equation, normal vector and polarized direction of element antenna can be analytically determined. Polarization loss of the element and shadowing procedure, which depend on beam direction, can also be calculated. Taking these relations into consideration, we show radiation patterns for polynomial curved surface array with curved rectangular patch element by using array-factor.