Optimal Synthesis Of Circular Apertures Based On Ludwig Distributions

Ludwig distributions are a generalization of circular Taylor distributions that generate radiation patterns with wide-angle side lobe levels decaying faster than for Taylor patterns. In this paper we show that by means of an appropriate optimization technique the zeros of Ludwig patterns can be perturbed so as to improve or modify pattern and/or aperture distribution characteristics without altering the wide-angle decay behavior. The examples presented include footprint patterns, pencil beam patterns with individually controlled side lobe heights, footprint beams generated by real excitations, and pencil beam patterns with aperture distributions that are smoother than the original Ludwig distribution.