Revising the equivalent circuit models of resonant-type metamaterial transmission lines

In this work, it is shown that the previously reported and accepted equivalent circuit models of resonant type left-handed lines, either loaded with split ring resonators (SRRs), or with complementary split ring resonators (CSRRs), need a revision in order to properly account for the different elements of the structures and to accurately describe their behavior. The main relevant conclusion and novelty of this paper is that the already existing models are formally correct, but some of the reactive parameters do not have the physical interpretation given so far. However, these parameters are related to the parameters of the improved models, which are proposed and exhaustively analyzed here for the first time. A comparative analysis of SRR and CSRR-loaded lines, to the light of these new models, is also included. The results of this work are of interest for the design of CSRR- and SRR-based microwave circuits.