Systematic Obtaining of Foster’s Equivalent Circuits for Symmetric Frequency Selective Surfaces

This work presents an eigenvalue problem to identify the characteristic resonances of a 2-D periodic distribution of planar metallic symmetric patches (stopband-like frequency selective surface) operating within the nondiffraction frequency regime. The eigenvalues of such problems provide the resonance frequencies in that range, whereas the eigenfunctions are a natural basis to expand a general solution under oblique illumination conditions. These basis functions are advantageously used to implement an efficient method of moment (MoM) computer code that leads to small size impedance matrices. It is also shown how the solution of this MoM problem naturally yields a canonical Foster-like equivalent circuit. A systematic method to determine accurate values of the capacitive and inductive components for such an equivalent circuit is proposed. The accuracy of the results obtained using this methodology is demonstrated by means of a systematic comparison with results computed using an
ad hoc
in-house MoM software.