Generalized Coupled-Mode Approach of Metamaterial Coupled-Line Couplers: Coupling Theory, Phenomenological Explanation, and Experimental Demonstration

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Abstract
A generalized coupled-mode approach of metamaterial coupled-line couplers is presented. This approach is an extension of the traditional coupled-mode theory (CMT) to the cases of arbitrary types of conventional or metamaterial couplers with lines represented by the most general composite right/left-handed (CRLH) transmission line models. The proposed approach is completely rigorous and applicable to any type of coupler, symmetric or asymmetric, conventional or metamaterial. The CRLH generalized CMT is thoroughly derived and closed-form results for both the complex propagation constants and scattering parameters are provided. Simplified formulas based on a quasi-TEM approximation (exact in the perfectly TEM limit) are derived for contra-directional couplers, which are the most common types in microwaves. The phenomenology of both symmetric CRLH-CRLH and asymmetric conventional CRLH metamaterial coupled-line couplers is completely explained from the proposed approach. The theoretical predictions and phenomenological explanations are validated by experimental demonstration, accompanied by ideal circuit simulation, for the case of a symmetric conventional coupler, a symmetric CRLH coupler, and an asymmetric conventional CRLH coupler

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