Monte Carlo Method to Uncertainty Evaluation of The Relative Dielectric Constant and Loss Tangent Measured by Split-Cavity Resonator Technique

Abstract

According to the mathematical model of the split-cylinder resonator method, it is impossible to establish a simple equation between the intermediate variables and the relative dielectric constant or the loss tangent. Instead, the measured relative dielectric constant and the loss tangent must be calculated numerically by iterative programming. When evaluating uncertainty according to the Guide to the Expression of Uncertainty in Measurement (GUM), it is impossible to obtain the sensitivity coefficient of each intermediate. Therefore, the reliability of uncertainty evaluation is greatly reduced. ISO/TS15530 states that the most effective method for estimating uncertainty is computer simulation, and more specifically, a Monte Carlo simulation. In this study, Three typical samples with different relative dielectric constant and loss tangent were measured, respectively. The probability density function of each intermediate variable was given, according to which the Monte Carlo simulations were performed by MATLAB programming. Moreover, some of the simulation results are compared with those of the previous literature, and the results show that the measurement uncertainty evaluated by the GUM method was slightly larger, indicating that it was a little bit conservative to assume that each intermediate variable is completely uncorrelated in the GUM method.