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 TE 011 . 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.

Measurable Dielectric Permittivity Range for TE and TM Modes in a Shielded Dielectric Resonator

“…Those portions represent regions of less sensitivity of the permittivity regarding the frequency measurement. This region is not a recommendable region to measure properties due to higher expected uncertainty associated to the measurement according results given in [19] and [20]. However the method shown in this article to determine the usable range of a given cavity can be used to avoid those regions of higher associated uncertainty, simply changing the diameter of the dielectric rod and hence the position in the curve of the expected permittivity under measurement.…”

“…Solving for B and C in (18), substituting it in (19) and (20), and then dividing side by side these two expressions, we can obtain the following relation, ( )…”

Optimization for Brain Activity Monitoring With Near Infrared Light in a Four-Layered Model of the Human Head

“…It is a very versatile method in solving numerical computing problems [13][14][15]. The principles of the Monte Carlo algorithm based on the variance reduction technique have already been described in [16].…”

Measurement Uncertainty of Complex-Valued Microwave Quantities

“…Analysis and evaluation of the uncertainty in a measurement is very important as it can itemize those known sources of errors and also quantify their combined influence on the best estimates [5][6][7][8][9]. In Singapore, National Metrology Centre (NMC) of the Agency for Science, Technology and Research (A*STAR) serves as the custodian of the national standards.…”