Equivalent Circuit Models for Metasurfaces Using Floquet Modal Expansion of Surface Current Distributions

This work presents a fully analytical method for obtaining equivalent circuit models (ECMs) that predict the magnitude and phase of scattering parameters for reflectarray (RA) and/or metasurface (MTS) unit cells. The proposed ECM is derived from a Floquet modal expansion of surface currents and does not rely on full-wave simulations. Analytical functions are used to represent the current distribution on the unit cell, and the proposed ECM is validated against full-wave simulations for several RA/MTS element types including loaded loops, dogbone and symmetric cross unit cells, and is shown to be accurate under normal and oblique incidence conditions, thus providing a fast and efficient design tool for deriving the scattering parameters of patch-like unit cells in the initial design process. As this approach allows for modeling unit cells loaded using lumped components such as varactor diodes, it can also be used to derive the dynamic response of tunable RA and MTS unit cells.