Characterization and modelling of a microstrip line loaded with complementary split-ring resonators (CSRRs) and its application to highpass filters

A method to characterize and model a microstrip line coupled with complementary split-ring resonators (CSRRs) is investigated. The detailed parameter extraction approach based on three characteristic frequencies is presented. Good agreement between the results of the equivalent circuit model and the full wave simulations supports the effectiveness of the proposed modelling methodology. In particular, it is found that the shunt capacitance in the equivalent circuit has a negative value which appears to contradict the general physical perception. The physical rationality of the problem is discussed and justified. It is found that the negative capacitance is a natural part required to approximate more closely the distributed nature of the CSRR-loaded microstrip line and the whole equivalent circuit still satisfies Foster's reactance theorem. To extract the effective permittivity of the CSRR-loaded microstrip, the dielectric window concept and the effective medium theory are both applied. Both their results show the negative permittivity at the vicinity of the resonance. Finally, the application of the CSRRs in microstip highpass filters is presented to highlight the unique features of the CSRRs and the validity of their equivalent circuit descriptions. Compared with conventional structures, the proposed highpass filters not only have via free structure but also exhibit extremely steep out-of-band rejection. This may lead to useful applications.