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Type-B uncertainty for unknown phase

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

B D Hall

Metrologia, 2011, 48, 324-332

Abstract

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.

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

B D Hall

Metrologia, 2011, 44, L62-L67

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 disk 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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