Investigation on the accuracy of equivalent electric models for mushroom structures

Planar distributed periodic structures more commonly known as mushroom structures which present a negative refractive index (NRI) in a very narrow frequency band, are usually studied using equivalent electric models under quasi-static approximation. The dispersion equations for different configurations can be established using Bloch theorem for 2D transmission lines (TL). This paper proposes a critical study concerning the validation of results obtained from these utilised dispersion equations through comparing them to those obtained using a full-wave method. An extraction method has been proposed to simulate the frequency dependent of each distributed element. These results show a frequency dependence different from that obtained from effective elements calculated using conventional analytical formulas for the effective material parameters of the unit cell.