Characterization and modeling of left-handed microstrip lines with application to loop antennas

This study investigates in detail the left-handed (LH) properties of the two-layer microstrip line, periodically loaded with broadside-coupled split ring resonators (BC-SRRs) and vias. The mechanism of the left-handed microstrip line (LHML), which includes the diamagnetic response, the backward-wave propagation and the proportionality of the guided wavelength on frequency, is discussed in terms of the field and current distributions and the dispersion diagram. To examine the resonance of the BC-SRR, both the full-wave eigenmode analysis and the closed-form formula based on the quasistatic approach are developed. The effects of the BC-SRR shape on the resonant frequency are evaluated. To facilitate the computer-aided-design (CAD) applications of the LHML, the equivalent-circuit model, which comprises the three-conductor coupled microstrip line for the coupling section, the series LC for the BC-SRR, and the shunt inductance for the via, is established. Good agreement among the results of the full-wave simulation, equivalent-circuit model, published data, and measurement supports the usefulness of the proposed modeling methodology and also validates the analytical expressions. The application of the LHML in the microstrip rectangular loop antenna fed by the conductor-backed coplanar waveguide-to-conductor-backed coplanar stripline (CBCPW-to-CBCPS) transition is presented to highlight the unique features of the LHML. Compared with the conventional loop antenna, the LHML-loaded loop antenna achieves a 50% area reduction and the 52% of main beam steering.