Analyzing uncertainty matrices associated with multiple S-parameter measurements

This paper presents a detailed analysis of uncertainty matrices (i.e. measurement covariance matrices) associated with multiple complex-valued microwave scattering (S-) parameter measurements. The analysis is based on forming combinations of (2 × 2) sub-matrices from selected elements in the uncertainty matrix and using these sub-matrices to define uncertainty ellipses in two-dimensional measurement planes. These uncertainty ellipses can be used to assess the quality, accuracy and validity of the measurements. A simple example is given using measurements made on a waveguide mismatched line section at frequencies from 75 GHz to 110 GHz. The analysis is also useful when multiple S-parameter measurements are used as input quantities for measurement models used to determine other measurement quantities (i.e. as output quantities).