This article presents an exact formulation for dual-band composite right/left handed (CRLH) transmission line (TL) design. Because of using an approximation, the previously introduced formulation for design of such TLs is not exact. Furthermore, 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, transmission matrices of the CRLH-TL 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 CRLH-TL are obtained. In this derivation no approximation is used, and hence the final formulation, independent of the structure homogeneity, is exact.

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