Shaped Circularly Symmetric Dual Reflector Antennas by Combining Local Conventional Dual Reflector Systems

This paper presents a geometrical optics (GO) shaping method for circularly symmetric dual reflector antennas. The method is a one step procedure obtaining a local dual reflector system including both reflector surfaces and caustic simultaneously, such that a given feed power is transformed through a corresponding local reflector system into a desired aperture distribution. A shaped reflector system consists of an electrically small section of distinctive local reflector surfaces and its own caustic. Each caustic location varies and explains how the power is redistributed through the shaped reflector system. Each local reflector system is found iteratively with a previously known local dual reflector system. Several nonlinear algebraic equations are formulated based on GO principals and geometrical properties of a dual reflector system. The method reduces the solution to one simple non-differential equation with one unknown in order to find a local dual reflector system. Physical Optics (PO) analysis is used to verify the solution.