A general closed-form solution to multi-port scattering parameter calculations

Measurements using error terms to describe the imperfections of test equipment have been used for a long time, and there are many methods utilized to model the error terms. In all these methods, after having determined the error terms on the basis of calibration measurements, the s-parameters of the device-under-test (DUT) are computed from the measured s-parameters by an appropriate algorithm. One problem that arises in this context is that the methods used for calculating the s-parameters, while widely known for the one- and two-port case, appear to not be generally available for the multi-port situation. This paper addresses this situation by deriving a simple method which allows for calculating the s-parameters of a multi-port DUT from the measured s-parameters, using the error terms obtained in the calibration step. The method generates exact, closed-form solutions, and is applicable to all error models in use today.