Indirect Measurement Method for S-Parameters with a Recursive Procedure

A measurement method for the S-parameters of a multiport reciprocal circuit is reported where the majority of the ports are connected with some known loads and the remaining ports are directly measured by changing the load values to estimate the whole S-matrix. First, some of the ports to be connected with the known loads (indirect-measured ports) are terminated with loads to temporarily exclude them from the measurements so that the number of indirect-measured ports equals to that of direct-measured ports. Then, our previously proposed method for a circuit in which the majority of ports are directly measured is applied to estimate the partial S-matrix. Finally, the partial S-matrix is treated as if directly measured and the process is recursively repeated until no ports need to be excluded from the measurements. A numerical experiment with a simple PCB is shown to evaluate the validity and the robustness of this method.