volume | PIER Journals

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.

1. Kukharchik, P. D., V. M. Serdyuk, and J. A. Titovitsky, "Diffraction of hybrid modes in a cylindrical cavity resonator by a transverse circular slot with a plane anisotropic dielectric layer," Progress In Electromagnetics Research B, Vol. 3, 73-94, 2008.
doi:10.2528/PIERB07112502

2. Wang, J., S. Qu, H. Ma, J. Hu, Y. Yang, and X. Wu, "A dielectric resonator-based route to left-handed metamaterials," Progress In Electromagnetics Research B, Vol. 13, 133-150, 2009.
doi:10.2528/PIERB09011103

3. Zhou, Y., E. Li, G. Guo, Y. Gao, and T. Yang, "Broadband complex permittivity measurement of low loss materials over large temperature ranges by stripline resonator cavity using segmentation calculation method," Progress In Electromagnetics Research B, Vol. 113, 143-160, 2011.

4. Chen, L. F., C. K. Ong, C. P. Neo, V. V. Varadan, and V. K. Varadan, Microwave Electronics Measurement and Materials Characterization, John Wiley & Sons, 2004.
doi:10.1002/0470020466

5. Krupka, J., "Frequency domain complex permittivity measurements at microwave frequencies," Measurement Science and Technology, Vol. 17, 55-70, 2006.
doi:10.1088/0957-0233/17/6/R01

6. Yeh, Y.-S., J.-T. Lue, and Z.-R. Zheng, "Measurement of the dielectric constant of metallic nanoparticles embedded in a paraffin rod at microwave frequencies," IEEE Transaction on Microwave Theory and Techniques, Vol. 53, No. 5, 2005.

7. Collin, R. E., "Field theory of guided waves," IEEE Antennas and Propagation Society, 1960.

8. Liu, J., C. Chen, H. Lue, and J. Lue, "A new method developed in measuring the dielectric constants of metallic nanoparticles by a microwave double-cavity dielectric resonator," IEEE Microwave and Wireless Components Letters, Vol. 13, 181-183, 2003.
doi:10.1109/LMWC.2003.811668

9. Dester, G. D., E. J. Rothwell, M. J. Havrilla, and M. W. Hyde, "Error analysis of a two-layer method for the electromagnetic characterization of conductor-backed absorbing material using an open-ended waveguide probe," Progress In Electromagnetics Research B, Vol. 26, 1-21, 2010.
doi:10.2528/PIERB10080506

10. Krupka, J., A. P. Gregory, O. C. Rochard, R. N. Clarke, B. Riddle, and J. Baker-Jarvis, "Uncertainty of complex permittivity measurements by split-post dielectric resonator technique," Journal of the European Ceramic Society, Vol. 21, 2673-2676, 2001.
doi:10.1016/S0955-2219(01)00343-0

11. Joint Committee for Guides in Metrology Evaluation of Measurement Data Guide to the Expression of Uncertainty in Measurement, 1st Ed., BIPM, Sèvres-France, 2008, Available at: http://www.bipm.org/en/publications/guides/gum.html, http://www.bipm.org/en/publications/guides/gum.html..

12. Joint Committee for Guides in Metrology Evaluation of Measurement Data Supplement 1 to the Guide to the Expression of Uncertainty in Measurement Propagation of Distributions Using a Monte Carlo Method, 1st Ed., BIPM, Sèvres-France, 2008, Available at: http://www.bipm.org/en/publications/guides/gum.html, http://www.bipm.org/en/publications/guides/gum.html..

13. Azpúrua, M. A., C. Tremola, and E. Páez, "Comparison of the gum and monte carlo methods for the uncertainty estimation in electromagnetic compatibility testing," Progress In Electromagnetics Research B, Vol. 34, 125-144, 2011.

14. Koch, K. R., "Evaluation of uncertainties in measurements by Monte-Carlo simulations with an application for laserscanning," Journal of Applied Geodesy, Vol. 2, 67-77, 2008.
doi:10.1515/JAG.2008.008

15. Jing, H., M.-F. Huang, Y.-R. Zhong, B. Kuang, and X.-Q. Jiang, "Estimation of the measurement uncertainty based on quasi monte-carlo method in optical measurement," Proceedings of the International Society for Optical Engineering, 2007.

16. Khu, S. T. and M. G. Werner, "Reduction of Monte-Carlo simulation runs for uncertainty estimation in hydrological modelling," Hydrology and Earth System Sciences, Vol. 7, No. 5, 680-690, 2003.
doi:10.5194/hess-7-680-2003

17. Andræ, A. S. G., P. MÄuler, J. Anderson, and J. Liu, "Uncertainty estimation by monte carlo simulation applied to life cycle inventory of cordless phones and microscale metallization processes," IEEE Transactions on Electronics Packaging Manufacturing, Vol. 27, No. 4, 233-245, 2004.
doi:10.1109/TEPM.2004.843163

18. Schuëller, G. I., "On the treatment of uncertainties in structural mechanics and analysis," Journal Computers and Structures, Vol. 85, No. 5-6, 235-243, 2007.
doi:10.1016/j.compstruc.2006.10.009

19. Paez, E., C. Tremola, and M. Azpúrua, "A proposed method for quantifying uncertainty in RF immunity testing due to eut presence," Progress In Electromagnetics Research B, Vol. 29, 175-190, 2011.
doi:10.2528/PIERB11020802

20. Stratton, J. A., Electromagnetic Theory, McGraw-Hill Book Company, Inc., 1941.

21. Pozar, D. M., Microwave Engineer, John Wiley & Sons, 2005.

22. Willink, R., "On using the Monte Carlo method to calculate uncertainty intervals," Metrologia, Vol. 43, L39-L42, 2006.
doi:10.1088/0026-1394/43/6/N02

Prof. Eduardo Paez

Dr. Marco A. Azpurua

Mrs. Ciro Tremola

Dr. Roberto Cesare Callarotti