In-depth analysis of reciprocal periodic structures of transmission lines

An in-depth analysis of lossless reciprocal periodic structures of transmission lines (TLs) is presented. Interestingly, it is found that periodic structures can provide both non-negative (NNCR) and negative characteristic resistances (NCR). In addition, the magnitude of the voltage reflection coefficient associated with an equivalent model of periodic structures terminated with passive loads can be less than or equal to unity for the NNCR case, and can exceed unity and even approach infinity for the NCR case. However, associated powers are still conserved for both cases. Furthermore, an alternative derivation based on short- and open-circuited terminations for determining characteristic impedances and propagation constant of equivalent TLs is also introduced. An example of finite periodic TL structures, providing both NNCR and NCR cases, with varying the number of unit cells is also given. In addition, implementation and measurement are set up to verify theoretical and simulated results. It is found that these results are reasonably in good agreement.