A simple analytic technique for the design of linear apertures generating piece-wise polynomial shaped beams

A simple technique for the synthesis of shaped beams defined by piecewise polynomial expressions is proposed. The technique, derived generalizing an algorithm previously introduced by Ksienski, provides a continuous linear tapering in analytical format. The technique can be used to preliminary assess the fundamental parameters of a shaped pattern i.e. the ripple within the beam, the slope at the end of the shaped region, and the sidelobe level. The obtained tapering can be used as an excellent starting point in a full wave numerical analysis where additional requirements and contributions, like the mutual coupling, can be rigorously evaluated. Several examples are presented to prove the simplicity and the effectiveness of the technique.