Equivalent Circuit Modeling for Reflectarrays Using Floquet Modal Expansion

The starting point in the design of reflectarray antennas is the derivation of the so-called S-curve, which maps changes in unit cell design parameters to the phase of the scattered field from the cell. In general, full-wave simulations are used to derive this curve, though recently a number of analytical techniques have emerged based on equivalent circuit models (ECMs). However, most ECMs are cumbersome to employ, either because they are too specialized or they depend on extraction of component values from supplementary simulations. This paper presents a fully analytical method for predicting the S-curve from dipole-like reflectarray elements based on an ECM derived from a Floquet modal expansion of a planar dipole. The model does not need supplementary simulations that can be used to predict the co-polarized reflection coefficient from a variety of fixed and reconfigurable reflectarray elements. The model is validated against full-wave simulations for several reflectarray element types, including fixed patches, varactor-loaded patches, and patches on tunable substrates, and is shown to be accurate. As such, it could become a highly useful design tool for quickly deriving the S-curve of reflectarray elements during the initial design stages of reflectarrays.