Radiation patterns for aperture antennas with non-linear phase distributions

Two dimensional antenna patterns have been determined for several aperture distributions having symmetrical amplitude and non-linear phase by a method of calculation employing automatic punch-card machines to perform numerical integrations. These patterns have been arranged in sets which permit one to predict the pattern characteristics expected from a given aperture phase distribution. The method of calculation used here permits direct evaluation of the pattern integral with negligible error for any phase and amplitude distributions. The results presented extend previous work to the cases of quadratic and cubic phase distributions combined in various proportions together with uniform, tapered, and cosine amplitude distributions. Phase patterns, which permit determination of the effective aperture phase center, are presented as well as the magnitude patterns.