Equivalent-circuit models for the design of metamaterials based on artificial magnetic inclusions

Filiberto Bilotti*, Alessandro Toscano, Lucio Vegni, Koray Aydin, Kamil Boratay Alici, Ekmel Ozbay

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

191 Scopus citations


In this paper, we derive quasi-static equivalent-circuit models for the analysis and design of different types of artificial magnetic resonators i.e., the multiple split-ring resonator, spiral resonator, and labyrinth resonator which represent popular inclusions to synthesize artificial materials and metamaterials with anomalous values of the permeability in the microwave and millimeter-wave frequency ranges. The proposed models, derived in terms of $RLC$ equivalent circuits, represent an extension of the models presented in a recent publication. In particular, the extended models take into account the presence of a dielectric substrate hosting the metallic inclusions and the losses due to the finite conductivity of the conductors and the finite resistivity of the dielectrics. Exploiting these circuit models, it is possible to accurately predict not only the resonant frequency of the individual inclusions, but also their quality factor and the relative permeability of metamaterial samples made by given arrangements of such inclusions. Finally, the three models have been tested against full-wave simulations and measurements, showing a good accuracy. This result opens the door to a quick and accurate design of the artificial magnetic inclusions to fabricate real-life metamaterial samples with anomalous values of the permeability.

Original languageEnglish (US)
Pages (from-to)2865-2873
Number of pages9
JournalIEEE Transactions on Microwave Theory and Techniques
Issue number12
StatePublished - Dec 2007


  • Artificial magnetic inclusions
  • Labyrinth resonators
  • Metamaterials
  • Miniaturization
  • Multiple split-ring resonators
  • Split-ring resonators

ASJC Scopus subject areas

  • Radiation
  • Condensed Matter Physics
  • Electrical and Electronic Engineering


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