An Exact Formulation for Dual-Band Composite Right/Left-Handed Transmission Line Design

This article presents an exact formulation for dual-band composite right/left-handed transmission line design. Because of using an approximation, the previously introduced formulation for the design of such transmission lines is not exact. Furthermore, the accuracy of the previous formulation depends on the homogeneity of the structure; i.e., accurate results are obtained only if the phase shift of each cell is small. To derive the new formulation, the transmission matrices of the composite right/left-handed transmission line at two desired frequencies are set equal to the transmission matrices corresponding to the desired phase shifts and characteristic impedances. Using some mathematical calculations, closed-form relations for unknown parameters of composite right/left-handed transmission lines are obtained. In this derivation, no approximation is used, and hence, the final formulation, independent of the structure homogeneity, is exact.