  This study proposes a linear approach for propagating uncertainties in the
multiline thru-reflect-line (TRL) calibration method for vector network
analyzers. 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 analysis using a combination of
measured and synthetic data to model various uncertainties, such as additive
noise, reflect asymmetry, line mismatch, and line length offset. The results of
our linear uncertainty formulation demonstrate agreement with the Monte Carlo
method and provide a more efficient means of assessing the uncertainty budget
of the multiline TRL calibration.
