Using Split-Ring Resonators to Measure Complex Permittivity and Permeability

Abstract

This paper describes how to measure the complex permittivity and permeability of materials using split-ring resonators. High-Q split-ring resonators, which can be modelled as LRC circuits, are easy to fabricate and can be used to measure electromagnetic material properties at frequencies that span approximately 10 MHz to 2 GHz. If the resonator is submerged in a liquid/suspension, its resonant frequency and quality factor will be be modified from the in-air values by factors that depend on the relative permittivity and permeability of the liquid/suspension. General expressions for the resonator’s frequency response are derived. Unlike an LRC circuit, the resonator’s response is not strictly Lorentzian. However, a wide variety of cases for which the response is approximately Lorentzian are explored. For each of these cases it is demonstrated that the real and imaginary components of the relative permittivity and permeability can be extracted from the in-air and in-liquid/suspension resonant frequencies and quality factors.