An accurate macro-cell-method for extracting dispersion characteristics of 1D reciprocal microwave structures with finite periodicity

Abstract

A novel macro-cell-method (MCM) has been proposed, which is capable of accurately extracting the dispersion characteristics of 1D reciprocal microwave structures with finite periodicity. In practice a single macro-cell consists of multiple periodic unit cells, therefore the electromagnetic coupling effects among unit cells can be rigorously considered. The eigen transfer factors ξN and 1/ξN corresponding to the forward and backward Bloch waves can be calculated in terms of the Bloch theory. Imposing complex logarithmic operation to ξN, the attenuation constant α can be univocally determined, while multiple integer branches exist in the solution of the phase shift constant β due to the multiroots property of the complex logarithm function. The rational integer branch is uniquely selected by comparing β from the MCM with that extracted from the unwrapping-method (UPM), regarding β from the UPM as the approximate value. Compared to the conventional eigenmode-method, UPM and single-cell-method, the MCM has no requirements to the coupling intensity among unit cells comprising finitely periodic structures, and with such good generality and accuracy, the MCM can be an effective tool for characterizing 1D reciprocal finitely periodic structures, facilitating their wide applications in microwave engineering.