Mathematics of 2r-port S-parameter Estimation by the r-port measurements

An estimation method of the 2r-port S-parameters for reciprocal circuits is presented. In this method, several known loads are connected to r ports in turn and reflection and transmission characteristics among the remaining r ports are measured. Therefore, there is no need to connect a network analyzer to the ports that are connected to the known loads. S-parameters are obtained by solving several linear equations and quadratic equations only. In addition, applying this method to estimate the S-parameters of an circuit model of an enclosure mounting an IC chip, validness of this method is confirmed.