Partial and indirect non-reciprocal S-parameter measurement for (m + n)-port fixture with DUT

A partial and an indirect measurement method for estimating the S-parameter of an (m + n)-port fixture and of an n-port device under test (DUT) are presented, respectively. Our model is extended to cases where the fixture and DUT are non-reciprocal, and the number m of measurement ports is less than the number n of DUT connection ports. In addition to the S-parameter between the measurement ports, the remaining diagonal elements and the product of symmetric off-diagonal elements regarding the S-parameter of the fixture and DUT are obtained. The advantage of our estimation method is that the S-parameter can be estimated by solving simultaneous linear equations and second-order algebraic equations without directly solving nonlinear equations. The proposed method can be applied to systems such as IC packages that have difficult ports to connect measuring instruments to, or cases in which circuit grounds are not common.