Determination of measurement uncertainty by a Monte Carlo method for an RF power sensor calibration system using a VNA

Abstract

This work proposes a systematic assessment of measuring type A uncertainty (caused by random errors) used in RF power sensor calibration. To reduce A type uncertainty, several successive measurements are repeated. The uncertainty arises from repeatability errors in connectors caused by changes in their electrical properties during repeated mating. The suitability of the METAS UncLib software was analysed and we concluded that software should be developed to take into account the shape of probability density function (PDF) using a Monte Carlo method (MCM), which was lacking in METAS UncLib. The self-developed software was then tested on an example taken from the literature and the superiority of the MCM over the analytical method (GUM) was confirmed. During the calibration of the RF sensor using a vector network analyzer (VNA), a series of repeated measurements were performed and, after applying our MCM software, it was found that the measurement uncertainties calculated by the MCM method were several times larger than those by the GUM. The reason for this was that the correlation between the measured input quantities was not taken into account. When this was done using a covariance matrix and assuming a normal PDF of the input quantities, the results obtained with the GUM and the MCM converged. Our main objective was to investigate the influence of the PDF shape of the input measurement samples on the measurement uncertainty. Taking more than a dozen measurements is too costly, on the other hand, the small sample size prevents a reliable determination of the PDF shape. Finally, to overcome this inconvenience, we have developed a special method that uses the histograms of standardized input data taken at all measurement frequencies under fixed conditions without disconnecting the connectors, to increasing the total number of results which were needed to create the PDF histograms of input quantities.