Using uncertain complex numbers with VNA measurements

The uncertain complex number is a simple construct that can be used to achieve full uncertainty propagation in multi-step processing of measurement data. The entity encapsulates information about a measured complex quantity and propagates it through equations by using a few simple algorithms. Software can easily automate the operations involved. The paper shows how uncertain complex numbers can be used to implement calibration and data-processing routines for VNA measurements. An example is presented in which the uncertainties associated with a pair of reflection measurements are evaluated, as well as the uncertainties associated with the ratio and difference of these measurements. It is shown that, by using uncertain complex numbers, the variances associated with the ratio and difference results can be reduced by an order of magnitude, by correctly accounting for correlated errors associated with the VNA calibration.