An Overview of Equivalent Circuit Modeling Techniques of Frequency Selective Surfaces and Metasurfaces

TLDR

Circuit analysis of frequency selective surfaces is reviewed to highlight the range of validity of different models and their advantages in terms of simplicity and physical insight. The circuit approach represents FSSs with series or shunt inductances and capacitances, but becomes fully analytical only for dense, non‑resonant periodic surfaces; as the lattice period grows relative to the wavelength or the element becomes resonant, a fully analytical circuital approach fails, especially with thin substrates. Analytical modeling of dense non‑resonant FSS arrays is achieved by computing inductance and capacitance values via homogenization theory, while simple circuit approaches can still be used by pre‑processing lumped parameters, adding extra elements to capture high‑order Floquet harmonics, and employing a multi‑mode formulation to model nonlinear responses in the grating‑lobe region when the current profile remains stable. The results are accurate up to the resonant frequency region of the element.

Abstract

Circuit analysis of frequency selective surfaces is reviewed with the aim to underline range of validity of different models and their advantages in terms of simplicity and physical insight. The circuit approach is based on an equivalent representation of the FSSs with series or shunt connections of inductances and capacitances. Dense non-resonant periodic surfaces (i.e.: grid or patch arrays) can be analyzed analytically by computing the values of inductors or capacitors via the homogenization theory. As the lattice period increases with respect to the operating wavelength or the element shape becomes resonant, a fully analytical circuital approach fails, in particular, in the presence of thin substrates. However, simple circuit approaches can still be employed by deriving lumped parameters values via a quick pre-processing and then generalizing them. The results are accurate up to the resonant frequency region of the element. By including an additional lumped element it is possible, taking into account the effect of the first high order Floquet harmonic. The multi-mode formulation is also able to catch the highly nonlinear response of FSS screens in the grating lobe region provided that the current profile of the element does not change significantly.