A Novel Equivalent Circuit Model for the Design and Analysis of Square Loop Metamaterials

A comprehensive understanding of the fundamental resonance property of metamaterials is critical to their design. In this regard, the equivalent circuit model has gained traction due to its simplicity and accuracy. It is also frequently deduced as a correlation between the electromagnetic response of metamaterial elements and their physical dimensions. Valuable insights can be obtained regarding the interaction between waves and metamaterials, as well as potential optimizations or modifications for particular applications. There are noteworthy reports on the equivalent circuit analysis of the square-loop metamaterial; Marcuvitz and its improvements attempt to characterize the square loop's resonance with a closed-form expression, but the model has numerous limitations of validity and is a compound function of the geometrical parameters, which complicates intuition and optimization. The coupled transmission line theory necessitates proximity and adjacency to neighboring square loops. Moreover, the equivalent circuit model that is produced is exceedingly intricate.This paper proposes a novel lumped-element equivalent circuit model to precisely characterize the resonance of square-loop metamaterials. The model is based on long-wave-thin-wire intuition that presumes identical behavior for a square loop of cylindrical conductors and a square loop of conducting strips with similar geometrical configurations. This assumption was verified using the finite element method (FEM) in HFSS. The modified quasi-TEM approximation procedure was used to derive the square loop's equivalent capacitance. Prototypes have been fabricated and measured.