Effective Height, Receiving Area, and Receiving Efficiency of Infinite Planar Phased Array Elements

For infinite planar phased array elements, a vector effective height is determined and the receiving area and receiving efficiency are found in terms of transmitting performance descriptors. The vector effective height allows the open-circuit received voltage to be expressed as an inner product with the incident electric field, as is for an isolated antenna. Generalizing a previously known expression, the effective area is expressed in terms of polarization mismatch, radiation efficiency, impedance mismatch, and the projected unit cell area, together with the element Floquet directivity introduced in this study that quantifies the unidirectional or bidirectional nature of radiation. An element's total receiving efficiency is defined and its expression is inspected for maximizing the received power.