Some considerations related to the evaluation of measurement uncertainty for complex-valued quantities in radio frequency measurements

Abstract

Several issues are discussed that relate to the evaluation of measurement uncertainty for complex-valued quantities in radio frequency measurements. In situations where there is information about the magnitude of a complex quantity, but not phase, uniform distributions in the form of a disc or a ring may be appropriate representations for the uncertainty. Variance–covariance matrices for these distributions are given for use in bivariate uncertainty calculations. The situation in which an uncertainty statement is provided in polar coordinates is also discussed. Such uncertainty statements need to be transformed into the real–imaginary coordinate system for the preferred method of uncertainty calculation. A simple transformation procedure is described together with a method to assess its accuracy.

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