Abstract
In this paper, a flexible and a modular approach to design complementary split-ring resonator (CSRR) metamaterials is presented which is further applied for a planar antenna miniaturization. The design task is treated as an optimization problem and one of the well-known computational techniques, particle swarm optimization (PSO) is employed to identify the design dimensions of planar CSRR structure followed by a C-band antenna miniaturization. Two trained neural networks (NNs) make use of machine learning (ML) approach to reduce the design time. The proposed procedure is easy to implement and can be further employed to design similar or other distinct metamaterial structures.











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The datasets generated during and/or analyzed during the current study are not publicly available due to organizational restrictions but are available from the corresponding author on a reasonable request after approval from authorities.
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References
Kula, J. S., Psychoudakis, D., Liao, W.-J., Chen, C.-C., Volakis, J. L., & Halloran, J. W. (2006). Patch-antenna miniaturization using recently available ceramic substrates. IEEE Antennas and Propagation Magazine, 48, 13–20.
Waterhouse, R. B., Targonski, S. D., & Kokotoff, D. M. (1998). Design and performance of small printed antennas. IEEE Transactions on Antennas and Propagation, 46, 1629–1633.
Wong, H., Luk, K.-M., Chan, C. H., Xue, Q., So, K. K., & Lai, H. W. (2012). Small antennas in wireless communications. Proceedings of the IEEE, 100, 2109–2121.
Huang, J. (2001). Miniaturized UHF microstrip antenna for a Mars mission. In Antennas and propagation society international symposium (Vol. 4, pp. 486–489). IEEE.
Chair, R., Luk, K. M., & Lee, K. F. (2000). Miniature multi-layer shorted patch antenna. Electronics Letters, 36, 3–4.
Behdad, N., & Sarabandi, K. (2004). Bandwidth enhancement and further size reduction of a class of miniaturized slot antennas. IEEE Transactions on Antennas and Propagation, 52(8), 1928–1935.
Lee, Y., & Hao, Y. (2008). Characterization of microstrip patch antennas on metamaterial substrates loaded with complimentary split ring resonators. Microwave and Optical Technology Letters, 50(8), 2131–2135.
Ochetan, A. B., & Lojewski, G. (2010) Metamaterial leaky-wave and resonant type antennas. In Electronics and telecommunications (ISETC), 2010 9th international symposium on, Timisoara (pp. 57–60).
Marbet, O. E., Aznabet, M., Falcone, F., Rmili, H., Floch, J. M., Drissi, M., & Essaaidi, M. (2013). A compact split ring resonator antenna for wireless communication system. Progress in Electromagnetic Research Letters, 3, 201–207.
Queipo, N. V., Haftka, R. T., Shyy, W., Goel, T., Vaidyanathan, R., & Tucker, P. K. (2005). Surrogate-based analysis and optimization. Progress in Aerospace Sciences, 41, 1–28.
Gorissen, D., Couckuyt, I., Demeester, P., Dhaene, T., & Crombecq, K. (July 2010). A surrogate modeling and adaptive sampling toolbox for computer based design. Journal of Machine Learning Research, 11, 2051–2055.
Pham, T.-Q., Kamusella, A., Neubert, H. (2011). Auto-extraction of modelica code from finite element analysis or measurement data. In 8th International Modelica Conference, 20–22 March 2011 in Dresden.
Soller, D. R., et al. (2001). Progress report on the national geologic map database, phase 3: An online database of map information digital mapping techniques '01—Workshop proceedings U.S. Geological Survey Open-File Report 01-223.
Garitselov, O., Mohanty, S., & Kougianos, E. (2012). A comparative study of metamodels for fast and accurate simulation of nano-CMOS circuits archived 23 September 2015 at the Wayback machine. IEEE Transactions on Semiconductor Manufacturing (TSM), 25(1), 26–36.
Nelson, M. F. (2014). Experimental and simulation studies of the population genetics, drought tolerance, and vegetative growth of Phalarisarundinacea (Doctoral Dissertation). University of Minnesota.
Gustafsson, L., & Sternad, M. (2010). Consistent micro, macro, and state-based population modelling. Mathematical Biosciences., 225(2), 94–107.
Bandler, J. W., Cheng, Q. S., Nikolova, N. K., & Ismail, M. A. (Jan. 2004). Implicit space mapping optimization exploiting preassigned parameters. IEEE Transactions on Microwave Theory and Techniques, 52(1), 378–385.
Bandler, J. W., Cheng, Q., Dakroury, S. A., Mohamed, A. S., Bakr, M. H., Madsen, K., & Sondergaard, J. (2004). Space mapping: the state of the art. IEEE Transactions on Microwave Theory and Techniques, 52(1), 337–361.
Zhang, Q. J., & Gupta, K. C. (2000). Neural network for RF and microwave design. Artech House.
Christodoulou, C., & Georgiopolous, M. (2001). Application of neural networks in electromagnetics. Artech House.
Haykin, S. (1994). Neural networks: a comprehensive foundation. IEEE Press/IEEE Computer Socity Press.
Robinson, J., & Rahamat-Sammi, Y. (2004). Particle swarm optimization in electromagnetic. IEEE Transactions on Antennas and propagation, 52(2), 397–407.
Xu, S., & Rahamat-Sammi, Y. (2007). Boundary condition in particle swarm optimization revisited. IEEE Transaction on Antenna and Propagation, 55(3), 760–765.
Parsopoulos, K. E., & Varhatis, M. N. (2002). Recent approaches to global optimization problems through particle swarm optimization. International Journal on Natural Computing, 1(2–3), 235–306.
Smith, D. R., & Schultz, S. (2002). Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients. Physical Review Letters, 65, 195104-1-195104–5.
Chen, X., Grzegorczyk, T. M., Bae-Ian, W., Pacheco, J., & Kong, J. A. (2004). Robust method to retrieve the constitutive effective parameters of metamaterials. Physical Review Letters, 70, 016680-1-016680–8.
Smith, D. R., Vier, D. C., Koshney, T., & Soukoulis, C. M. (2005). Electromagnetic parameter retrieval from inhomogeneous metamaterial. Physical Review Letters, 71, 033617–033621.
Ziolkowski, R. W. (2003). Design, fabrication, and testing of double negative metamaterials. IEEE Transactions on Antennas and Propagation, 51, 1516–1529.
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Pal, D., Singhal, R. & Bandyopadhyay, A.K. Parametric Optimization of Complementary Split-Ring Resonator Dimensions for Planar Antenna Size Miniaturization. Wireless Pers Commun 123, 1897–1911 (2022). https://doi.org/10.1007/s11277-021-09220-6
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DOI: https://doi.org/10.1007/s11277-021-09220-6