Analytical Beam Forming for Circularly Symmetric Conformal Apertures

In this paper, we present an analytical beam-forming approach capable of synthesizing differently shaped beams for circularly symmetric conformal apertures with axisymmetrical excitations. Closed form formulas of far-field radiation are mathematically derived in order to obtain rotationally symmetric radiation patterns for typical conformal apertures frequently used in satellite and flight vehicle applications, such as the cone-surfaced, truncated cone-surfaced, hybrid disc-cone and sphere-cone apertures. Based on these formulas, various shaped beams, including pencil, flat-topped and bimodal beams can be rapidly achieved by adjusting either the geometric parameters or the excitation distributions of the conformal apertures. The deterministic approach proposed in this paper provides an efficient method to synthesize specified beam shapes for the aforementioned conformal apertures. Collaborating with conventional optimization based beam forming approaches, the proposed approach can effectively shorten the time-consuming optimization in the beam forming of circularly symmetric conformal arrays, especially large conformal arrays.