Efficient Technique for the Cascade Connection of Multiple Two-Port Scattering Matrices

There are several practical applications in microwave engineering that require the cascade connection of multiple two-port scattering matrices. Many microwave devices are analyzed by segmenting the structure into small building blocks (steps, resonators, lines, etc.) that are characterized by means of the generalized scattering matrix. In order to obtain the reflection and transmission parameters of the entire structure, the scattering matrices of all the building blocks must be cascaded. Traditionally, the conversion of the scattering matrices to ABCD or T matrices has been used in order to perform the cascade connection. An alternative to this procedure is to perform a recursive connection by pairs of the scattering matrices. In this paper, we present a new technique for the efficient cascade connection of N monomodal or multimodal scattering matrices that reduces the computation time by 35% when compared to the cascading by pairs, and by 75% when compared with the use of ABCD matrices.