Evaluation of Random Errors for Vector Network Analyzers Based on a Residual Model

The residual model is widely used to calculate the measurement uncertainty of vector network analyzers (VNAs). However, precisely evaluating the parameters within the residual model can be challenging. As a result, it often overestimates or underestimates measurement uncertainty compared to the VNA error model. In this article, we propose a new method for evaluating parameters such as drift, test port cable stability (CA), and connection repeatability (CO) within the residual model. The proposed method allows for precise measurement of each parameter and easily captures correlations not only between the real and imaginary parts but also between cross frequencies. We also analytically computed Jacobian matrices for uncertainty calculations of 1-port and 2-port device under tests (DUTs). These Jacobian matrices (or sensitivity coefficients) depend solely on the scattering parameter values of the DUT, making it easy to propagate uncertainty to the DUT. Finally, we demonstrate that each covariance of the residual model obtained using the proposed method can be reduced to 1.3% of its original size while retaining 99.99% of the variation through principal component analysis (PCAs).