Comparative Evaluation of Uncertainty Transformation for Measuring Complex-Valued Quantities

Abstract

This paper presents a comparative study on practical evaluation of measurement uncertainty for complex-valued RF and microwave quantities in polar coordinate. The measurement uncertainty is first evaluated in rectangular coordinate to avoid the biased effect, and then transformed into the desired polar coordinate. In this work, uncertainty coordinate transformation from rectangular coordinate to polar coordinate is focused and performed in two ways; the law of propagation of uncertainty and the coordinate rotation. Their performances are compared through practical evaluations and simulations, and found to be highly consistent when the uncertainty region is distant from the origin of a complex plane.

Practical evaluation of phase uncertainty in scattering parameter measurements

“…Law of Propagation of Uncertainty in [2] and Coordinate Rotation [5] have found to be possible solutions for uncertainty transformation. As a continuation of [7], in this paper we will compare their performances for evaluating phase uncertainty from practical S-parameter measurements.…”