In this paper, a new measurement method is proposed to estimate the complex permittivity for each layer in a multi-layer dielectric material using a Ku-band rectangular waveguide WR62. The Sij-parameters at the reference planes in the rectangular waveguide loaded by a multi-layer material sample are measured as a function of frequency using the E8634A Network Analyzer. Also, by applying the two dimensional finite difference in time domain (2D-FDTD), the expressions for these parameters as a function of complex permittivity of each layer are calculated. The Nelder-Mead algorithm is then used to estimate the complex permittivity of each layer by matching the measured and calculated Sij-parameters. This method has been validated by estimating, at the Ku-band, the complex permittivity of each layer of three bi-layer and one tri-layer dielectric materials. A comparison of estimated values of the complex permittivity obtained from multi-layer measurements and mono-layer measurements is presented.
Lahcen Ait Benali,
Angel Mediavilla Sanchez,
"2D-FDTD Method to Estimate the Complex Permittivity of a Multilayer Dielectric Materials at Ku-Band Frequencies," Progress In Electromagnetics Research M,
Vol. 91, 155-164, 2020. doi:10.2528/PIERM20020102
2. Chakravarty, S. and R. Mittra, "Application of the micro-genetic algorithm to the design of spatial filters with frequency-selective surfaces embedded in dielectric media," IEEE Trans. Electromagn. Compat., Vol. 44, No. 2, 338-346, 2002.
3. Deshpande, M. D. and K. Dudley, Estimation of Complex Permittivity of Composite Multilayer Material at Microwave Frequency Using Waveguide Measurements, 212-398, NASA Langley Res, 2003. doi:10.1109/19.32194
4. Ghodgaonkar, D. K., V. V. Varadan, and V. K. Varadan, "A freespace method for measurement of dielectric constants and loss tangents at microwave frequencies," IEEE Trans. Instrum. Meas., Vol. 38, 789-793, 1989. doi:10.1109/TMTT.1983.1131471
5. Ligthart, L. P., "A fast computational technique for accurate permittivity determination using transmission line methods," IEEE Transactions on Microwave Theory and Techniques, Vol. 31, No. 3, 249-254, 1983. doi:10.1109/TIM.1970.4313932
6. Nicholson, A. M. and G. F. Ross, "Measurement of the intrinsic properties of materials by time domain techniques," IEEE Trans. Instrum. Meas., Vol. 19, 377-382, 1970. doi:10.2528/PIER09062501
7. Hasar, U. C., "Permittivity measurement of thin dielectric materials from reflection-only measurements using one-port vector network analyzers," Progress In Electromagnetics Research, Vol. 95, 365-380, 2009. doi:10.2528/PIER10060805
8. Hasar, U. C., "Unique permittivity determination of low-loss dielectric materials from transmission measurements at microwave frequencies," Progress In Electromagnetics Research, Vol. 107, 31-46, 2010.
9. Baker-Jarvis, J., Transmission/Reflection and Short-Circuit Line Permittivity Measurements, 1-5, National Institute of Standards and Technology, Boulder, Colorado, 1990.
10. Elmajid, H., J. Terhzaz, H. Ammor, M. Chaıbi, and A. Mediavilla, "A new method to determine the complex permittivity and complex permeability of dielectric materials at X-band frequencies," IJMOT, Vol. 10, No. 1, 2015.
11. Terhzaz, J., H. Ammor, A. Assir, and A. Mamouni, Application of the FDTD Method to Determine Complex Permittivity of Dielectric Materials at Microwave Frequencies Using a Rectangular Waveguide, Vol. 49, No. 8, Wiley, 2007.
12. Optimization Toolbox User’s Guide, The MathWorks, Version 9.2, 2017.
13. Nelder, J. and R. Mead, "A simplex method for function minimization," Computer SXSX Journal, Vol. 7, 1965.
14. Ait Benali, L., A. Tribak, J. Terhzaz, and A. Mediavilla Sanchez, "Complex permittivity estimation for each layer in a BI-layer dielectric material at Ku-band frequencies," Progress In Electromagnetics Research M, Vol. 70, 109-116, 2018.