Theoretical Analysis of Moving Reference Planes Associated with Unit Cells of Nonreciprocal Lossy Periodic Transmission-Line Structures

Abstract

This paper presents a theoretical analysis of moving reference planes associated with unit cells of nonreciprocal lossy periodic transmission-line structures (NRLSPTLSs) by the equivalent bi-characteristic-impedance transmission line (BCITL) model. Applying the BCITL theory, only the equivalent BCITL parameters (characteristic impedances for waves propagating in forward and reverse directions and associated complex propagation constants) are of interest. An infinite NRLSPTLS is considered first by shifting a reference position of unit cells along TLs of interest. Then, a semi-infinite terminated NRLSPTLS is investigated in terms of associated load reflection coefficients. It is found that the equivalent BCITL characteristic impedances of the original and shifted unit cells are mathematically related by the bilinear transformation. In addition, the associated load reflection coefficients of both unit cells are mathematically related by the bilinear transformation. However, the equivalent BCITL complex propagation constants remain unchanged. Numerical results are provided to show the validity of the proposed theoretical analysis.