The planar metal particles, consisting of a multi-turn spirals, are studied with the aim of using them to realize high impedance surfaces or as an elementary cell to create an artificial material. These spirals present a resonant behaviour in a certain frequency band. To obtain miniature devices, a compromise between the surface and the efficiency of the resonance must be found. The compactness of the particles can be increased by using s spirals. However, the accuracy on resonant frequency of existing models is not sufficient for our applications. We present a simple analytical model that determines the resonant frequency from the geometric dimensions of the approximated model. This model is verified by electromagnetic simulations and by measurements.
1. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 65, No. 18, 3966-3969, October 2000.
2. Smith, D. R. and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett., Vol. 85, 2933-2936, October 2000.
3. Caloz, C., A. Sanada, and T. Itoh, "A novel composite right-/left-handed coupled-line directional coupler with arbitrary coupling level and broad bandwidth," IEEE Transactions on Microwave Theory and Techniques, Vol. 52, No. 3, 980-992, March 2004. doi:10.1109/TMTT.2004.823579
4. Martin, F., F. Falcone, J. Bonache, R. Marquès, and M. Sorolla, "Split ring resonator based left handed coplanar waveguide," Appl. Phys. Lett., Vol. 83, 4652-4654, December 2003. doi:10.1063/1.1631392
5. Kurter, C., J. Abrahams, and S. M. Anlage, "Miniaturized superconducting metamaterials for radio frequencies," Appl. Phys. Lett., Vol. 96, 253504, 2010. doi:10.1063/1.3456524
6. Syms, R. R. A., I. R. Young, and L. Solymar, "Low-loss magneto-inductive waveguides," J. Phys. D: Appl. Phys., Vol. 39, 3945, 2006. doi:10.1088/0022-3727/39/18/004
7. Baena, J. D., R. Marquès, and F. Médina, "Artificial magnetic metamaterial design by using spiral resonators," Physical review B, Vol. 69, 014402, 2004. doi:10.1103/PhysRevB.69.014402
8. Beattie, M. W. and L. T. Pileggi, Inductance 101: Modeling and extraction design automation, Proceedings of Design Automation Conference, 323-328, 2001 (on-chip interconnect).
9. Grover, F. W., Inductance Calculations, Dover Publications, INC, Mineola, New York, 1962.
10. Bahl, I. and P. Bhartia, Microwave Solid State Circuit Design, Wiley, New York, 1988.