Uncertainty estimation in complex permittivity measurements by shielded dielectric resonator technique using the Monte Carlo method

Abstract

In this paper, we estimate the uncertainty in complex permittivity measurements performed in a shielded dielectric resonator, by using the Monte Carlo Method. We selected this approach since the theoretical expressions required to interpret the experimental results are highly non-linear. Furthermore the resonant frequency of the system and its quality factor are highly correlated. Thus we propose a model for the measurement process which considers the major sources of uncertainty previously reported in published experimental results. The proposed model combined with the Monte Carlo method was used to propagate the probability distributions of each uncertainty contribution, obtaining a) the approximate probability density function for the measured complex permittivity, and b) the estimated expanded uncertainty for the mode TE011. The results show that this procedure leads to small uncertainty intervals for the real part of the dielectric permittivity, while it is not very reliable in the loss tangent measurement. Additionally, for each input quantity, we calculated the standard deviation in the experimental results produced independently by each uncertainty contribution.