Comparative Evaluation of Uncertainty Transformation for Measuring Complex-Valued Quantities

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.