  In this article, we develop analytical-numerical models for reconfigurable
reflecting metasurfaces formed by chessboard-patterned arrays of metallic
patches. These patch arrays are loaded with varactor diodes in order to enable
surface impedance and reflection phase control. Two types of analytical models
are considered. The first model based on the effective medium approach is used
to predict the metasurface reflectivity. The second model is the Bloch wave
dispersion model for the same structure understood as a two-dimensional
transmission line metamaterial. The latter model is used to study ways to
suppress parasitic resonances in finite-size beamforming metasurfaces. We
validate the developed analytical models with full-wave numerical simulations.
Finally, we outline a design of the metasurface control network with capacitive
memory that may allow for independent programming of individual unit cells of
the beamforming metasurface.
