Synthesis of coupled transmission lines

In this paper an important property of the time responses of coupled transmission lines is proven. Based on this property coupled transmission lines are synthesized from the given near-end and far-end time-domain responses. The inductance matrix L and capacitance matrix C of uniformly coupled lossless lines can be obtained from the responses without any approximation. As for uniform lossy lines, the impedance matrix (LC)/sup -0.5/L and the modified resistance matrix (LC)/sup -0.5/R are obtained by the characteristics method, and in the special case that LC=CL, the L, C, and R matrices can be derived. An equivalent time-domain model is developed by the generalized characteristics method for nonuniformly coupled lossless and lossy lines from the given near-end responses. Several synthesis examples are given to highlight the contributions of this paper.