### Moving Reference Planes of Unit Cells of Reciprocal Lossy Periodic Transmission-Line Structures

#### Abstract

An analysis of moving reference planes of unit cells of reciprocal lossy periodic transmission-line (TL) structures (RLSPTLSs) by using the equivalent bi- characteristic-impedance transmission line (BCITL) model is presented. Applying the BCITL theory, only the equivalent BCITL parameters (characteristic impedances for wave propagating in forward and reverse directions and associated complex propagation constant) are of interest. In the analysis, an arbitrary infinite RLSPTLS is firstly considered by shifting a reference position of unit cells along TLs. Then, a semi-infinite terminated RLSPTLS is subsequently investigated in term of associated load reflection coefficients. It is found that the equivalent BCITL characteristic impedances of the original and shifted unit cells, as well as the associated load reflection coefficients of both unit cells, are mathematically related by the bilinear transformation. However, the equivalent BCITL complex propagation constant remains unchanged. Numerical results are provided to show the validity of the proposed technique.

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