On The Co-polarized Hannan's Limit for Circularly Polarized Arrays

Embedded element efficiency (EEE), which characterizes the gain utilization of elements in large planar arrays, has a fundamental upper bound known as Hannan's limit. This limit was originally derived for linearly polarized arrays. In this Letter, we extend Hannan's limit to circularly polarized (CP) arrays, accounting for the amplitude and phase constraints required to generate CP waves. Inherent amplitude and phase errors in feed networks, along with mutual coupling among array elements, are analyzed. Both factors constrain the achievable EEE bound. A compensation method of the amplitude and phase errors is proposed to approach the extended Hannan's limit. Findings of this Letter can assist the optimization of CP arrays in a limited space, which is critical for satellite navigation and communication applications.