Uncertainty contributions from mismatch in microwave measurements

One of the important error contributions in measurements of microwave attenuation and power is caused by mismatch between the attenuator and neighbour components such as the microwave source and load. Unless vector measurements of the reflection coefficients involved are performed in the measurement process the mismatch will contribute to the uncertainty. Warner (1977) has derived a formula for the case where the magnitudes of the reflection coefficients involved are known, but the phases are unknown, i.e. are evenly distributed between 0 and 2π. This case results in the so-called U-distribution. New formulas have been derived for calculation of the uncertainty contribution from mismatch for cases where only maximum values of the reflection coefficient magnitudes are known (and the phases are unknown). In these latter cases the distribution functions for the mismatch errors, and thus the uncertainties, deviate significantly from the case treated by Warner. It is therefore important to use the appropriate distribution function for the actual case when estimating uncertainties due to mismatch. By doing so the estimated uncertainty is typically reduced by a factor of two