Accurate circuit analysis of resonant-type left handed transmission lines with inter-resonator coupling

In this paper, a circuit model for the description of left handed transmission lines based on complementary split rings resonators (CSRRs) is proposed. As compared to previous models, coupling between adjacent resonators is included in the present work. The conditions that make this coupling significant are discussed. Specifically, it will be shown that it is barely present when circular CSRRs are used to implement the left handed transmission line. However, if the line is loaded with rectangular CSRRs separated by a small distance, inter-resonator coupling is important and it significantly influences the electromagnetic behavior of the structures. It will be also shown that under low or moderate coupling, it is possible to describe the structures by means of a simplified model with modified parameters. Several prototype devices with different CSRR topologies and coupling levels have been fabricated to illustrate the phenomenology associated with these structures and the accuracy of their model descriptions. The results of this work can be of interest for the design of planar microwave circuits based on CSRR left handed lines.