Propagation of Linear Uncertainties through Multiline Thru-Reflect-Line Calibration

This study proposes a linear approach for propagating uncertainties in the multiline thru-reflect-line (TRL) calibration method for vector network analyzers (VNAs). The multiline TRL formulation we are proposing applies the law of uncertainty propagation as outlined in the ISO Guide to the Expression of Uncertainty in Measurement (GUM) to both measurement and model uncertainties. In addition, we conducted a Monte Carlo (MC) analysis using a combination of measured and synthetic data to model various uncertainties, such as measurement noise, reflect asymmetry, line mismatch, and line length offset. The results of our linear uncertainty formulation demonstrate agreement with the MC analysis and provide a more efficient means of assessing the uncertainty budget of the multiline TRL calibration.