Temperature Dependence of Relative Permittivity: A Measurement Technique Using Split Ring Resonators

Authors: Sreedevi P. Chakyar, Jolly Andrews, V. P. Joseph

Abstract:

A compact method for measuring the relative permittivity of a dielectric material at different temperatures using a single circular Split Ring Resonator (SRR) metamaterial unit working as a test probe is presented in this paper. The dielectric constant of a material is dependent upon its temperature and the LC resonance of the SRR depends on its dielectric environment. Hence, the temperature of the dielectric material in contact with the resonator influences its resonant frequency. A single SRR placed between transmitting and receiving probes connected to a Vector Network Analyser (VNA) is used as a test probe. The dependence of temperature between 30 ^oC and 60 ^oC on resonant frequency of SRR is analysed. Relative permittivities ‘ε’ of test samples for different temperatures are extracted from a calibration graph drawn between the relative permittivity of samples of known dielectric constant and their corresponding resonant frequencies. This method is found to be an easy and efficient technique for analysing the temperature dependent permittivity of different materials.

Keywords: Metamaterials, negative permeability, permittivity measurement techniques, split ring resonators, temperature dependent dielectric constant.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1124965

References:

[1] E. Havinga, ``The temperature dependence of dielectric constants,'' Journal of Physics and Chemistry of Solids, vol. 18, no. 23, pp. 253 - 255, 1961. (Online). Available: http://www.sciencedirect.com/science/ article/pii/002236976190169X
[2] Z.Y. Cheng, R. S. Katiyar, X.Yao, and A.S. Bhalla, ``Temperature dependence of the dielectric constant of relaxor ferroelectrics,'' Phys. Rev. B, vol. 57, pp. 8166 - 8177, Apr 1998. (Online). Available: http://link.aps.org/doi/10.1103/PhysRevB.57.8166
[3] E. Li, Z. P. Nie, G. Guo, Q. Zhang, Z. Li, and F. He, ``Broadband measurements of dielectric properties of low-loss materials at high temperatures using circular cavity method,'' Progress In Electromagnetics Research, vol. 92, pp. 103--120, 2009.
[4] L. F. Chen, C. Ong, C. Neo, V. V. Varadan, and V. K. Varadan, Microwave electronics: measurement and materials characterization. John Wiley & Sons, 2004.
[5] D. L. Gershon, J. Calame, Y. Carmel, T. Antonsen Jr, and R. M. Hutcheon, ``Open-ended coaxial probe for high-temperature and broad-band dielectric measurements,'' IEEE Transactions on Microwave Theory and Techniques, vol. 47, no. 9, pp. 1640--1648, 1999.
[6] T. Shimizu and Y. Kobayashi, ``Millimeter wave measurements of temperature dependence of complex permittivity of gaas plates by a circular waveguide method,'' in Microwave Symposium Digest, 2001 IEEE MTT-S International, vol. 3. IEEE, 2001, pp. 2195--2198.
[7] J. B. Pendry, A. J. Holden, D. Robbins, and W. Stewart, ``Magnetism from conductors and enhanced nonlinear phenomena,'' IEEE Transactions on Microwave Theory and Techniques, vol. 47, no. 11, pp. 2075--2084, 1999.
[8] D. R. Smith, W. J. Padilla, D. Vier, S. C. Nemat-Nasser, and S. Schultz, ``Composite medium with simultaneously negative permeability and permittivity,'' Physical review letters, vol. 84, no. 18, p. 4184, 2000.
[9] S. Y. Chiam, R. Singh, W. Zhang, and A. A. Bettiol, ``Controlling metamaterial resonances via dielectric and aspect ratio effects,'' Applied Physics Letters, vol. 97, p. 191906, 2010.
[10] E. Ekmekci and G. Turhan-Sayan, ``Comparative investigation of resonance characteristics and electrical size of the double-sided srr, bc-srr and conventional srr type metamaterials for varying substrate parameters,'' Progress In Electromagnetics Research B, vol. 12, pp. 35--62, 2009.
[11] Z. Sheng and V. V. Varadan, ``Tuning the effective properties of metamaterials by changing the substrate properties,'' Journal of applied physics, vol. 101, no. 1, p. 014909, 2007.
[12] M. Boybay and O. M. Ramahi, ``Material characterization using complementary split-ring resonators,'' IEEE Transactions on Instrumentation and Measurement, vol. 61, no. 11, pp. 3039--3046, Nov 2012.
[13] K.S. Umadevi and V. P. Joseph, ``Experimental studies on the effect of substrate dielectric constant on the resonant frequency of split-ring resonator metamaterial structure,'' Journal of Science and Research, vol. 3132, p. 135, 2014.
[14] P.~M. Ragi, K.~S.~Umadevi, P.~Nees, J.~Jose, M.~Keerthy, and V.~P.~Joseph, ``Flexible split-ring resonator metamaterial structure at microwave frequencies,'' Microwave and Optical Technology Letters, vol. 54, no. 6, pp. 1415--1416, 2012.
[15] Z. Sheng and V. V. Varadan, ``Effect of substrate dielectric properties and tunable metamaterials,'' Antennas and Propagation Society International Symposium 2006, IEEE. IEEE, 2006, pp. 4497--4500.
[16] C. S. Lee and C. L. Yang, ``Thickness and permittivity measurement in multi-layered dielectric structures using complementary split-ring resonators,'' Sensors Journal, IEEE, vol. 14, no. 3, pp. 695--700, 2014.
[17] V. V. Varadan and L. Ji, ``Temperature dependence of resonances in metamaterials,'' IEEE Transactions on Microwave Theory and Techniques, vol. 58, no. 10, pp. 2673--2681, 2010.
[18] R. Singh, A. K. Azad, Q. Jia, A. J. Taylor, and H. T. Chen, ``Thermal tunability in terahertz metamaterials fabricated on strontium titanate single-crystal substrates,'' Optics letters, vol. 36, no. 7, pp. 1230--1232, 2011.
[19] I. M. Rusni, A. Ismail, A. R. H. Alhawari, M. N. Hamidon, and N. A. Yusof, ``An aligned-gap and centered-gap rectangular multiple split ring resonator for dielectric sensing applications,'' Sensors, vol. 14, no. 7, pp. 13,134—13, 148, 2014.
[20] K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, ``Investigation of magnetic resonances for different split-ring resonator parameters and designs,'' New journal of physics, vol. 7, no. 1, p. 168, 2005.
[21] K. T. Mathew, “Perturbation Theory”. John Wiley & Sons, Inc., 2005. (Online). Available: http://dx.doi.org/10.1002/0471654507.eme309