Recent Advances in the Modeling of Transmission Lines Loaded with Split Ring Resonators

This paper reviews the recent advances in the modeling of transmission lines loaded with split ring resonators (SRRs). It is well known that these artificial lines can exhibit a negative effective permeability in a narrow band above the SRR fundamental resonance, providing stopband functionality. By introducing shunt inductive elements to the line, the stopband can be switched to a pass band with left-handed (LH) wave propagation. For the design of microwave circuits based on these artificial lines, accurate circuit models are necessary. The former circuit model of SRR-loaded lines was presented more than one decade ago and is valid under restrictive conditions. This paper presents the progress achieved in the modeling of these artificial lines during the last years. The analysis, restricted to coplanar waveguide (CPW) transmission lines loaded only with SRRs (negative permeability transmission lines), includes the effects of SRR orientation, the coupling between adjacent resonators, and the coupling between the two SRRs constituting the unit cell. The proposed circuit models are validated through electromagnetic simulation and experimental data. It is also pointed out that the analysis can be easily extended to negative permittivity transmission lines based on complementary split ring resonators (CSRRs).