volume | PIER Journals

Abstract

This paper investigates a new, simple, fast, and broadband procedure to extract the material intrinsic parameters through new mathematical modeling. It only uses the transmission coefficient of two identical lines. The method is based on the mathematical reformulation of the two transmission lines, taking into account the effects of discontinuities at the interface connecting the trapper and the connector, as well as the included S-parameters. These test cells have different lengths, so the sample under test (SUT) complex relative permittivity is determined after fixing the vacuum structure's electric length. At the same time, the mathematical formulation of the telecommunications equation, which links transmission and reflection coefficients, was used to determine the loss tangent parameter by combining the attenuation and phase coefficients. The correction of the electric length difference of the transmission coefficients resulting from the measurement of the vacuum-filled test cells is done using an affine function. The frequency is the variable parameter, and the slope (rate of variation) and the initial value (ordered at the origin) are computed according to the test cell used. On the one hand, the suggested principle has the advantage of extracting the relative permittivity of the sample under test beyond the limit set by the appearance of higher-order modes (propagated by considering the test fixture's transverse dimensions). On the other hand, the use of the reflection coefficient, although it improves the attenuation coefficient extraction, limits the characterization band of the loss tangent. A circular coaxial test fixture has been used in the 1-20 GHz frequency range to validate the proposed method with samples of various materials, including semolina, polenta, Q-Cell 5020 (ceramic powder), aquarium stone, distilled water, and phantom gel. The results are compared with those from the two transmission lines technique, as defined in its popular form.

1. Bouesse, Ghislain Fraidy and Franck Moukanda Mbango, "Probe with a metallic bowl termination to determine the electric material parameters from variable thicknesses," Engineering Research Express, Vol. 6, No. 1, 015314, 2024. Google Scholar

2. Canicattì, Eliana, Nunzia Fontana, Sami Barmada, and Agostino Monorchio, "Open-ended coaxial probe for effective reconstruction of biopsy-excised tissues' dielectric properties," Sensors, Vol. 24, No. 7, 2160, 2024.
doi:10.3390/s24072160 Google Scholar

3. Fan, Benhui, Frédéric Bosc, Yu Liu, Mathieu Le Feuvre, and Cyrille Fauchard, "Permittivity analysis of weathered concrete in a bridge based on open-ended probe and impedance measurements," Construction and Building Materials, Vol. 429, 136354, May 2024. Google Scholar

4. Diepolder, Adrian, Mario Mueh, Susanne Brandl, Philipp Hinz, Christian Waldschmidt, and Christian Damm, "A novel rotation-based standardless calibration and characterization technique for free-space measurements of dielectric material," IEEE Journal of Microwaves, Vol. 4, No. 1, 56-68, 2024. Google Scholar

5. Ali, Syed Zeeshan, Kamran Ahsan, Danish ul Khairi, Wadee Alhalabi, and Muhammad Shahid Anwar, "Advancements in FR4 dielectric analysis: Free space approach and measurement validation," PLoS One, Vol. 19, No. 9, e0305614, 2024. Google Scholar

6. Xue, Bing, "Characterizing complex permittivity of thin materials by free space transmission and reflection coefficients," IEEE Antennas and Wireless Propagation Letters, Vol. 23, No. 12, 4438-4442, 2024. Google Scholar

7. Moukanda Mbango, Franck, Ghislain Fraidy Bouesse, and Fabien Ndagijimana, "Extraction of the complex relative permittivity from the characteristic impedance of transmission line by resolving discontinuities," Electronics, Vol. 11, No. 23, 4035, 2022. Google Scholar

8. Yamaguchi, Takaaki, Naoto Yamamoto, Daichi Naito, Takeshi Takahashi, and Shogo Sakanaka, "Resonant cavity method based on RF measurement and simulation for measuring complex permittivity or permeability of RF absorbing materials," Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 1064, 169449, 2024. Google Scholar

9. Wang, Jingchen, Eng Gee Lim, Mark Paul Leach, Zhao Wang, and Ka Lok Man, "Open-ended coaxial cable selection for measurement of liquid dielectric properties via the reflection method," Mathematical Problems in Engineering, Vol. 2020, No. 1, 8942096, 2020. Google Scholar

10. Victoria, Jorge, Adrian Suarez, Pedro A. Martinez, Andrea Amaro, Antonio Alcarria, Jose Torres, Roberto Herraiz, Victor Solera, Víctor Martinez, and Raimundo Garcia-Olcina, "Advanced characterization of a hybrid shielding solution for reducing electromagnetic interferences at board level," Electronics, Vol. 13, No. 3, 598, 2024. Google Scholar

11. Costa, Filippo, Michele Borgese, Marco Degiorgi, and Agostino Monorchio, "Electromagnetic characterisation of materials by using transmission/reflection (T/R) devices," Electronics, Vol. 6, No. 4, 95, 2017. Google Scholar

12. Lara, L. A., D. L. Mancipe, Y. Pineda, J. J. Moreno, and G. Peña-Rodríguez, "Design and characterization of a magneto-dielectric composite in high frequency with aligned magnetite powders," Journal of Physics: Conference Series, Vol. 1386, No. 1, 012103, 2019.

13. Massamba, Omar Christian, Franck Moukanda Mbango, and Désiré Lilonga-Boyenga, "Four subbands from dual mismatched wideband bandpass filter for 5G/WAS/Wi-Fi/WiMAX/WLAN applications," International Journal of RF and Microwave Computer-Aided Engineering, Vol. 2023, No. 1, 4713995, 2023. Google Scholar

14. Moukala Mpele, Pierre, Franck Moukanda Mbango, and Dominic B. O. Konditi, "Comparative analysis of five planar monopole antennas for LTE/C-V2X/5G/WiMAX applications," Arabian Journal for Science and Engineering, Vol. 48, No. 5, 6841-6855, 2023. Google Scholar

15. Pikovsky, Arkady and Franco Bagnoli, "Dynamics of oscillator populations with disorder in the coupling phase shifts," New Journal of Physics, Vol. 26, No. 2, 023054, 2024. Google Scholar

16. Kombolias, Mary, Jan Obrzut, Michael T. Postek, Dianne L. Poster, and Yaw S. Obeng, "Method development for contactless resonant cavity dielectric spectroscopic studies of cellulosic paper," Journal of Visualized Experiments, No. 152, e59991, 2019. Google Scholar

17. Paul, Robert B., A. Ege Engin, and Jerry Aguirre, "Dielectric and underfill characterization using cavity resonators for millimeter-wave applications," IEEE Letters on Electromagnetic Compatibility Practice and Applications, Vol. 2, No. 3, 76-80, 2020. Google Scholar

18. Farhat, Iman, Lourdes Farrugia, Julian Bonello, Rafel Grima, Raffaele Persico, and Charles Sammut, "One-port coaxial line sample holder characterisation method of dielectric spectra," Sensors, Vol. 24, No. 17, 5573, 2024.
doi:10.3390/s24175573 Google Scholar

19. Zhang, Jianmin, Marina Koledintseva, Giulio Antonini, James Drewniak, Antonio Orlandi, and Konstantin Rozanov, "Planar transmission line method for characterization of printed circuit board dielectrics," Progress In Electromagnetics Research, Vol. 102, 267-286, 2010. Google Scholar

20. Moukanda Mbango, Franck, Ghislain Fraidy Bouesse, and Fabien Ndagijimana, "Material relative permittivity determination from the inhomogeneous transmission-line secondary parameters," IEEE Access, Vol. 10, 124595-124603, 2022. Google Scholar

21. García-García, J. I., D. Marín-Aragón, A. Sánchez-Loureiro, and A. Vigneron-Tenorio, "Some properties of affine C-semigroups," Results in Mathematics, Vol. 79, No. 2, 52, 2024. Google Scholar

22. Massamba, Omar C., Pierre Moukala Mpele, Franck Moukanda Mbango, and Desire Lilonga-Boyenga, "Tri-band bandpass filter using mixed short/open circuited stubs and Q-factor with controllable bandwidth for WAS, ISM, and 5G applications," Progress In Electromagnetics Research C, Vol. 119, 177-190, 2022.
doi:10.2528/PIERC22012713 Google Scholar

23. Andryieuski, Andrei, Svetlana M. Kuznetsova, Sergei V. Zhukovsky, Yuri S. Kivshar, and Andrei V. Lavrinenko, "Water: Promising opportunities for tunable all-dielectric electromagnetic metamaterials," Scientific Reports, Vol. 5, No. 1, 13535, 2015. Google Scholar

24. Park, Min-Seok, Jeahoon Cho, Soonyong Lee, Youngkun Kwon, and Kyung-Young Jung, "New measurement technique for complex permittivity in millimeter-wave band using simple rectangular waveguide adapters," Journal of Electromagnetic Engineering and Science, Vol. 22, No. 6, 616-621, 2022. Google Scholar

25. Moukanda Mbango, F., M. G. Lountala, E. J. D. M'Pemba, F. Ndagijimana, D. Lilonga-Boyenga, and B. M'Passi-Mabiala, "Comparison of materials characterization methods using one-port and two-port transmission line principles," Int. J. Eng. Appl., Vol. 9, No. 6, 370-381, 2021. Google Scholar

26. Zhang, Zhengpeng, Jianhua Liu, Xinyu Xie, Tianshuo Hu, and Shuhui Liu, "Data and model-driven 3D modeling method for transmission line LiDAR data," Journal of Spatial Science, Vol. 70, No. 2, 309-328, Dec. 2024. Google Scholar

27. Edwards, Terry C. and Michael B. Steer, Foundations for Microstrip Circuit Design, 4th Ed., 688, John Wiley & Sons, 2016.
doi:10.1002/9781118936160

28. Reynoso-Hernandez, J. A., "Unified method for determining the complex propagation constant of reflecting and nonreflecting transmission lines," IEEE Microwave and Wireless Components Letters, Vol. 13, No. 8, 351-353, 2003. Google Scholar

29. Ramos Somolinos, D., D. Ramos Somolinos, J. Cidrás Estévez, B. Plaza Gallardo, Carolina Peñafield Moravec, et al., "Novel electromagnetic characterization methods for new materials and structures in aerospace platforms," Materials, Vol. 15, No. 15, 5128, 2022. Google Scholar

30. Al-Nedawe, Basman M., Israa Hazem Ali, Ahmed Mohammed Ahmed, and Hamid M. Mahan, "Reflection and transmission coefficients measurements for polymer composites with a nano-PZT material using a non-resonant method," IOP Conference Series: Materials Science and Engineering, Vol. 1076, No. 1, 012065, 2021.

31. Kim, Sung and Jeffrey R. Guerrieri, "Low-loss complex permittivity and permeability determination in transmission/reflection measurements with time-domain smoothing," Progress In Electromagnetics Research M, Vol. 44, 69-79, 2015. Google Scholar

32. Xiong, Rui, Yuanhang Hu, Anqi Xia, Kama Huang, Liping Yan, and Qian Chen, "A high-temperature and wide-permittivity range measurement system based on ridge waveguide," Sensors, Vol. 25, No. 2, 541, 2025.
doi:10.3390/s25020541 Google Scholar

33. Meuel, Holger and Jörn Ostermann, "Analysis of affine motion-compensated prediction in video coding," IEEE Transactions on Image Processing, Vol. 29, 7359-7374, 2020. Google Scholar

34. Dubuc, Serge, "Non-differentiability and Hölder properties of self-affine functions," Expositiones Mathematicae, Vol. 36, No. 2, 119-142, 2018. Google Scholar

35. Sridhar, Sundaramoorthy and Qiang Li, "Multiphase constant on-time control with phase overlapping --- Part I: Small-signal model," IEEE Transactions on Power Electronics, Vol. 39, No. 6, 6703-6720, Jun. 2024. Google Scholar

36. Lin, Bin, Shi-Peng Li, Zhong-Chen Cao, Yunfei Zhang, and Xiang-Min Jiang, "Theoretical modeling and experimental analysis of single-grain scratching mechanism of fused quartz glass," Journal of Materials Processing Technology, Vol. 293, 117090, 2021. Google Scholar

37. M'Pemba, Josué Éric Delfort, Ghislain Fraidy Bouesse, Franck Moukanda Mbango, and Bernard M'Passi-Mabiala, "Probes in transmission with material variable thicknesses to extract the material complex relative permittivity in 1.7-3 GHz," Measurement: Sensors, Vol. 20-21, 100369, 2022. Google Scholar

38. Farcich, Nick J., Jaakko Salonen, and Peter M. Asbeck, "Single-length method used to determine the dielectric constant of polydimethylsiloxane," IEEE Transactions on Microwave Theory and Techniques, Vol. 56, No. 12, 2963-2971, 2008. Google Scholar

39. Bidgoli, Hossein Asilian, Nicola Schieda, and Carlos Rossa, "A simplified formulation of the reflection coefficient of an open-ended coaxial probe in multilayered media," IEEE Transactions on Microwave Theory and Techniques, Vol. 72, No. 11, 6485-6495, 2024. Google Scholar

40. Hasar, Ugur Cem, "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. Google Scholar

41. Kolb, J., Y. Minamitani, S. Xiao, X. Lu, M. Laroussi, R. P. Joshi, K. H. Schoenbach, E. Schamiloglu, and J. Gaudet, "The permittivity of water under high dielectric stress," 2005 IEEE Pulsed Power Conference, 1266-1269, Monterey, CA, USA, Jun. 2005.

42. Behzadi, G. and L. Fekri, "Electrical parameter and permittivity measurement of water samples using the capacitive sensor," International Journal of Water Resources and Environmental Sciences, Vol. 2, No. 3, 66-75, 2013. Google Scholar

Dr. Ghislain Fraidy Bouesse

Dr. Amour Elang Ghordanne Langa-Etotsou

Prof. Franck Moukanda Mbango