volume | PIER Journals

Abstract

This paper presents an evaluation of measurement uncertainty for complex-valued quantities in microwave applications, mainly focusing on the non-linear transformation of measurement uncertainty from rectangular coordinate to polar coordinate. Based on the law of propagation of uncertainty in matrix form, general expressions of the covariance matrix for the magnitude and phase uncertainties in polar coordinate have been derived, and several different application scenarios have been analyzed and evaluated with numerical simulations. This is followed by some recommendations on the coordinate transformations in practical microwave measurements.

1. Shan, Y., L. Oberto, Y. S. Meng, H. Neo, L. Brunetti, and M. Sellone, "Scattering parameter measurement comparison between NMC and INRIM on vector network analyzer using WR15 and WR10 connectors," CPEM 2012 Digest, 96-97, Washington DC, USA, 2012. Google Scholar

2. Meng, Y. S., Y. Shan, and H. Neo, "Development of a waveguide microwave power sensor calibration system at NMC," APEMC 2012 Proceedings, 745-748, Singapore, 2012. Google Scholar

3. Meng, Y. S., Y. Shan, and H. Neo, "Evaluation of complex measurement uncertainty in polar coordinate for equivalent source reflection coefficient," CPEM 2012 Digest, 116-117, Washington DC, USA, 2012. Google Scholar

4. Shan, Y. and X. Cui, "RF and microwave power sensor calibration by direct comparison transfer," Modern Metrology Concerns, Chapter 7, 175-200, ISBN: 978-953-51-0584-8, 2012. Google Scholar

5. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, OIML, , Evaluation of measurement data --- Guide to the expression of uncertainty in measurement, JCGM 100:2008 (GUM 1995 with Minor Corrections), BIPM Joint Committee for Guides in Metrology, 2008.

6. Wang, Z., W. Che, and L. Zhou, "Uncertainty analysis of the rational function model used in the complex permittivity measurement of biological tissues using PMCT probes within a wide microwave frequency band," Progress In Electromagnetics Research, Vol. 90, 137-150, 2009.
doi:10.2528/PIER09010403 Google Scholar

7. Azpurua, M. A., C. Tremola, and E. Paez, "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. Google Scholar

8. Haarscher, A., P. De Doncker, and D. Lautru, "Uncertainty propagation and sensitivity analysis in ray-tracing simulations," Progress In Electromagnetics Research M, Vol. 21, 149-161, 2011.
doi:10.2528/PIERM11090103 Google Scholar

9. Paez, E., M. A. Azpurua, C. Tremola, and R. C. Callarotti, "Uncertainty estimation in complex permittivity measurements by shielded dielectric resonator technique using the monte carlo method," Progress In Electromagnetics Research B, Vol. 41, 101-119, 2012. Google Scholar

10. Ridler, N. M. and M. J. Salter, "An approach to the treatment of uncertainty in complex S-parameter measurements," Metrologia, Vol. 39, No. 3, 295-302, 2002.
doi:10.1088/0026-1394/39/3/6 Google Scholar

11. Hall, B. D., Notes on complex measurement uncertainty --- Part 1, Tech. Rep. 2483, Industrial Research Ltd., New Zealand, 2010.

12. Hall, B. D., "Calculating measurement uncertainty for complex-valued quantities," Measurement Science and Technology, Vol. 14, No. 3, 368-375, 2003.
doi:10.1088/0957-0233/14/3/316 Google Scholar

13. Hall, B. D., "Some considerations related to the evaluation of measurement uncertainty for complex-valued quantities in radio frequency measurements," Metrologia, Vol. 44, No. 6, L62-L67, 2007.
doi:10.1088/0026-1394/44/6/N04 Google Scholar

14. Hall, B. D., "On the propagation of uncertainty in complex-valued quantities," Metrologia, Vol. 41, No. 3, 173-177, 2004.
doi:10.1088/0026-1394/41/3/010 Google Scholar

15. Ridler, N. M. and J. C. Medley, An uncertainty budget for VHF and UHF reflectometers, NPL Rep. DES 120, National Physical Laboratory, UK, 1992.

16. R Development Core Team, , R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, 2009, http://www.r-project.org/.

Dr. Yu Song Meng

Dr. Yueyan Shan