Analysis of reciprocal lossy periodic transmission-line structures using bi-characteristic-impedance transmission lines and Meta-Smith charts

This paper presents an analysis of reciprocal lossy periodic structures of transmission lines (TLs) by using the bi-characteristic-impedance TLs (BCITLs). It is found that the reciprocal lossy periodic TL structures (RLSPTLSs) can provide both non-negative (NNCR) and negative characteristic resistances (NCR) with proper complex propagation constants. In addition, an alternative approach based on short- and open-circuited terminations for determining characteristic impedances and complex propagation constant of equivalent BCITLs is also discussed. Interestingly, it is found that both NNCR and corresponding NCR cases always exist at the same frequency with proper complex propagation constants. An example of finite RLSPTLSs, providing both NNCR and NCR cases, is also given. Furthermore, graphical solutions for both NNCR and NCR cases are plotted on the Meta-Smith chart (MSC) for BCITLs. It is found that the MSC for both NNCR and NCR cases provide the same input impedance as expected.