On the expression of measurement uncertainty for complex quantities with unknown phase

摘要

Simple expressions are obtained for the measurement uncertainty of complex quantities when no information about phase is available. Three different cases are considered: a known magnitude, an upper bound on the magnitude and an estimate of the magnitude with an associated uncertainty. An expression is also given for the uncertainty of a product when there is no information about the phase of the factors. These results are applied to simple examples of power, attenuation and impedance measurements. The performance of uncertainty calculations is checked by observing the coverage of uncertainty statements achieved under simulated measurement conditions.