Method for characterization of multilayer substrates with complementary split-ring resonators.

Abstract

This paper presents a methodology based on the use of multiple complementary split ring resonators (CSRRs) in square form to obtain the relative permittivity of individual layers of a multilayer dielectric sample. The sensor uses CSRRs with different maximum penetration depths to analyze various sections of the sample. The methodology uses the resonant frequency change, which depends on the maximum measurable thickness of the resonator and dielectric permittivity of the sample. Various design parameters affecting the maximum measurable thickness, such as slot width and resonator size, were analyzed. Subsequently, a sensor consisting of two resonators at 2.4 and 7.4 GHz with maximum penetration depths of 5.3 and 3.0 mm, respectively, was designed to measure a two-layer sample. Each layer has a thickness of 3.0 mm. The sensor was tested satisfactorily with four commercial dielectric substrates, which were stacked into 16 different combinations. The results show great accuracy in the characterization of dielectric constant with an error smaller than 0.2% for the first layer and smaller than 9.4% for the second layer. The proposed method works correctly for materials that offer constant permittivities in the lower microwave region (<8 GHz).