Features of defining the scattering matrix of non-linear microwave devices using X-parameters

Abstract

We propose a theoretical analysis of method for determining scattering parameters of frequency converters by measuring X-parameters with non-linear vector network analyzer (NVNA). Analysis uses flow graphs theory. Diagrams of NVNA calibration and their equivalent flow graphs in X-parameters system are presented. Expressions are obtained for uncertainties of determining complex transmittion coefficients of frequency converters under test by NVNA, calibrated by a comb generator standard. The analysis showed that the process of defining components of X-matrix of non-linear device under test using a comb generator is equal to the process of defining components of S-matrix of non-linear device under test using a reference mixer or frequency converter. Therefore in this type of measurements it is possible to determine only relative scattering parameters of frequency converter under test and in this case a comb generator becomes a new type of standard, that is much more broadband and universal. Consequently by using the studied calibration procedure it is impossible to define true phase response and group delay of frequency converter under test if true phase response and group delay of comb generator are unknown.