Bloch wave approach to the design of optimally matched non-effective medium composite right/left handed transmission lines

A simple method to design optimally matched composite right-/left-handed transmission lines (CRLH-TLs), based on the computation of the Bloch wave equivalent impedance of the corresponding unit cell circuit is presented. Although the matching of CRLH-TLs that can be considered as effective media is straightforward, it is shown that it is not the case for non-effective medium structures, which are also relevant realisations of this type of metamaterial in particular situations. Since the method does not rely on any assumptions on the parameters of the circuit, it is valid both for effective medium and non-effective medium CRLH-TLs. The reduction of the mismatch obtained with the proposed method also results in an improvement in the insertion loss and phase shift linearity in terms of S-parameters. Finally, we present some experimental validation of the benefits of the method by means of quartz-integrated CRLH-TLs realisations