Analyzing Uncertainty Matrices Associated with Multiple S-parameter Measurements

TL;DR

This paper introduces a method to analyze and visualize the uncertainty in multiple S-parameter measurements using covariance matrices and uncertainty ellipses, enhancing measurement quality assessment.

Contribution

It provides a novel approach to evaluate measurement uncertainty through sub-matrix analysis and uncertainty ellipses, applicable to complex microwave S-parameters.

Findings

Uncertainty ellipses effectively visualize measurement accuracy.

Method applied to waveguide measurements from 75 GHz to 110 GHz.

Analysis aids in validating measurement quality and input-output measurement models.

Abstract

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 X 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).