Backward wave microstrip lines with complementary spiral resonators

Microstrip lines loaded with series gap discontinuities and compact metamaterial particles-complementary Archimedean spiral resonators-are investigated. The theory of periodic structures is applied for establishing the propagation characteristics of infinite lines from full-wave electromagnetic simulations. Thanks to their convoluted geometry, the spirals are very compact which makes the unit cell electrically small (e.g., 0.1 guided wavelength or even smaller). Then, the effective medium theory is applied to extract the effective permittivity and permeability of the periodic structure. By analyzing the effective medium parameters and phase constant, it is shown that the structure supports backward wave propagation and exhibits double negative parameters over a 19% bandwidth around its zero-reflection frequency. Moreover, a simple equivalent-circuit model of the unit cell is established. Finally, finite-length lines with one or two complementary spirals are investigated. It is shown by comparison with full-wave results that the circuit model almost perfectly describes the structure for all practically important frequencies. It is also shown that the inter-element coupling is negligible in the multi-spiral structures considered. Measured results for two prototypes are presented to verify the analyses.