A Closed-form Expression for the Directivity of Planar Arrays with Arbitrary Topologies and Element Patterns

This work presents a new analytical (i.e., closed-form) solution to the directivity of a planar array with arbitrary topology. The derived method also makes use of a novel element pattern model which can take into account radial asymmetries in both θ and ϕ: a generic pattern suitable for a wide range of applications. The analytical method is validated by numerical integration using Simpson's 1/3
^rd
method. The analytical method enables fast topology optimization of phased array designs by avoiding time-consuming numerical integration.