  We present an accurate and simple analytical model for the computation of the
reflection amplitude and phase of Reflecting Intelligent Surfaces. The model is
based on a transmissionline circuit representation of the RIS which takes into
account the physics behind the structure including the effect of all relevant
geometrical and electrical parameters. The proposed representation of the RIS
allows to take into account the effect of incidence angle, the mutual coupling
among elements, the effect of the interaction of the periodic surface with the
RIS ground plane. It is shown that, by using the proposed approach, it is
possible to maximize the power received by a user in a RIS-assisted link
without recurring to onerous electromagnetic simulations. The proposed model
aims at filling the gap in the design of RIS assisted communications algorithms
that are usually disconnected from physical implementation issues and realistic
performance of these surfaces.
