volume | PIER Journals

Abstract

In this paper,a nondestructive technique for determining the complex permittivity and permeability of magnetic sheet materials using two flanged rectangular waveguides is presented. The technique extends existing single probe methods by its ability to simultaneously measure reflection and transmission coefficients imperative for extracting both permittivity and permeability over all frequencies. Using Love's Equivalence Principle,a system of coupled magnetic field integral equations (MFIEs) is formed. Evaluation of one of the two resulting spectral domain integrals via complex plane integration is discussed. The system,solv ed via the Method of Moments (MoM),yields theoretical values for the reflection and transmission coefficients. These values are compared to measured values and the error minimized using nonlinear least squares to find the complex permittivity and permeability of a material. Measurement results for two magnetic materials are presented and compared to traditional methods for the purpose of validating the new technique. The technique's sensitivity to uncertainties in material thickness and waveguide alignment is also examined.

1. Li, C. and K. Chen, "Determination of electromagnetic properties of materials using flanged open-ended coaxial probe — Full wave analysis," IEEE Trans. Instrum. Meas., Vol. 44, No. 1, 19-27, 1995.
doi:10.1109/19.368108 Google Scholar

2. Chang, C., K. Chen, and J. Qian, "Nondestructiv e determination of electromagnetic parameters of dielectric materials at X-band frequencies using a waveguide probe system," IEEE Trans. Instrum. Meas., Vol. 46, No. 5, 1084-1092, 1997.
doi:10.1109/19.676717 Google Scholar

3. 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.

4. Stewart, J. W. and M. J. Havrilla, "Electromagnetic characterization of a magnetic material using an open-ended waveguide probe and a rigorous full-wave multimode model," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 14, 2037-2052, 2006.
doi:10.1163/156939306779322693 Google Scholar

5. Olmi, R., R. Nesti, G. Pelosi, and C. Riminesi, "Impro vement of the permittivity measurement by a 3D full-wave analysis of a finite flanged coaxial probe," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 2, 217-232, 2004.
doi:10.1163/156939304323062103 Google Scholar

6. Bois, K. J., A. D. Benally, and R. Zoughi, "Multimo de solution for the reflection properties of an open-ended rectangular waveguide radiating into a dielectric half-space: the forward and inverse problems," IEEE Trans. Instrum. Meas., Vol. 48, No. 6, 1131-1140, 1999.
doi:10.1109/19.816127 Google Scholar

7. Mautz, J. R. and R. F. Harrington, "T ransmission from a rectangular waveguide into half-space through a rectangular aperture," IEEE Trans. Microwave TheoryT ech., Vol. MTT-26, No. 1, 44-45, 1978.
doi:10.1109/TMTT.1978.1129307 Google Scholar

8. Teodoridis, V., T. Sphicopoulos, and F. E. Gardiol, "The reflection from an open-ended rectangular waveguide terminated by a layered dielectric medium," IEEE Trans. Microwave Theory Tech., Vol. MTT-33, No. 5, 359-366, 1985.
doi:10.1109/TMTT.1985.1133006 Google Scholar

9. Encinar, J. A. and J. M. Rebollar, "Con vergence of numerical solutions of open-ended waveguide by modal analysis and hybrid modal-spectral techniques," IEEE Trans. Microwave Theory Tech., Vol. MTT-34, No. 7, 809-814, 1986.
doi:10.1109/TMTT.1986.1133445 Google Scholar

10. Popovic, D., et al. "Precision open-ended coaxial probes for in vivo and ex vivo dielectric spectroscopy of biological tissues at microwave frequencies," IEEE Trans. Microwave TheoryT ech., Vol. 53, No. 5, 1713-1722, 2005.
doi:10.1109/TMTT.2005.847111 Google Scholar

11. Bao, J., S. Lu, and W. D. Hurt, "Complex dielectric measurements and analysis of brain tissues in the radio and microwave frequencies," IEEE Trans. Microwave TheoryT ech., Vol. 45, No. 10, 1730-1741, 1997.
doi:10.1109/22.641720 Google Scholar

12. Mazlumi, F., S. Sadeghi, and R. Moini, "In teraction of rectangular open-ended waveguides with surface tilted long cracks in metals," IEEE Trans. Instrum. Meas., Vol. 55, No. 6, 2191-2197, 2006.
doi:10.1109/TIM.2006.884282 Google Scholar

13. Huber, C., H. Abiri, S. I. Ganchev, and R. Zoughi, "Mo deling of surface hairline-crack detection in metals under coatings using an open-ended rectangular waveguide," IEEE Trans. Microwave TheoryT ech., Vol. 45, No. 11, 2049-2057, 1997.
doi:10.1109/22.644234 Google Scholar

14. Yeh, C. and R. Zoughi, "A novel microwave method for detection of long surface cracks in metals," IEEE Trans. Instrum. Meas., Vol. 43, No. 5, 719-725, 1994.
doi:10.1109/19.328896 Google Scholar

15. Baker-Jarvis, J., M. D. Janezic, P . D. Domich, and R. G. Geyer, "Analysis of an open-ended coaxial probe with lift-off for nondestructive testing," IEEE Trans. Instrum. Meas., Vol. 43, No. 5, 711-718, 1994.
doi:10.1109/19.328897 Google Scholar

16. Wang, S., M. Niu, and D. Xu, "A frequency-varying method for simultaneous measurement of complex permittivity and permeability with an open-ended coaxial probe," IEEE Trans. Microwave Theory Tech., Vol. 46, No. 12, 2145-2147, 1998.
doi:10.1109/22.739296 Google Scholar

17. Maode, N., S. Yong, Y. Jinkui, F. Chenpeng, and X. Deming, "An improved open-ended waveguide measurement technique on parameters εr and μr of high-loss materials," IEEE Trans. Instrum. Meas., Vol. 47, No. 2, 476-481, 1999.
doi:10.1109/19.744194 Google Scholar

18. Chen, C.Z. Ma, T. Anada, and J. Hsu, "Further study on twothickness- method for simultaneous measurement of complex EM parametersbas ed on open-ended coaxial probe," 2005 European Microwave Conference, 4-6, 2005.

19. Tantot, O., M. Chatard-Moulin, and P. Guillon, "Measurement of complex permittivity and permeability and thickness of multilayered medium by an open-ended waveguide method," IEEE Trans. Instrum. Meas., Vol. 46, No. 2, 519-522, 1997.
doi:10.1109/19.571900 Google Scholar

20. Hyde, M. W. and M. J. Havrilla, "Measurement of complex permittivity and permeability using two flanged rectangular waveguides," 2007 International Microwave Symposium, 3-8, 2007.

21. Collin, R. E., FieldThe ory of GuidedWaves, 2nd edition, 1991.

22. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, IEEE Press, 1998.

23. Weir, W. B., "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proc. IEEE, Vol. 62, No. 1, 33-36, 1974.

24. Nicolson, A. M. and G. F. Ross, "Measurement of the intrinsic propertiesof materialsb y time-domain techniques," IEEE Trans. Instrum. Meas., Vol. IM-19, No. 4, 377-382, 1970. Google Scholar

25. Hanson, G. W. and A. B. Yakovlev, Operator Theory for Electromagnetics: An Introduction, Springer-Verlag, 2001.

26. Hanson, G. W., A. I. Nosich, and E. M. Kartchevski, "Green's function expansions in dyadic root functions for shielded layered waveguides," Progress In Electromagnetics Research, Vol. 39, 61-91, 2003.
doi:10.2528/PIER02082205 Google Scholar

27. Arfken, G. B. and H. J. Weber, Mathematical Methods for Physicists, 5th ed., 2001.

28. Agilent 8510C Network Analyzer Data Sheet, Agilent Technologies, Agilent Technologies, 2000., 2000.

Dr. Milo Hyde IV

Dr. Michael John Havrilla