I. Introduction
The ring resonator has been used in determining guided wavelength (, equivalent circuits for discontinuities [1], and relative ( and effective ( dielectric constant [2]. Compared with the linear resonator, the ring resonator does not suffer from open-ended effects and can be used to give more accurate measurements [3]. In recent work [4], the electrical conductivity has been characterized using a half-wavelength line resonator. In this paper, we used the ring resonator in asymmetric coplanar configuration [asymmetric coplanar waveguide (ACPW)] for characterizing the effective electrical conductivity of composite conductors. The composite conductors to be characterized have been developed to replace gold, used as a coating conductor in microwave and automotive connectors [5]. The material under test has to be deposited on only one side of dielectric substrate. The thickness of the layer should be set between 2 and . In the literature, little work has been done on the characterization of the effective electrical conductivity of conductor materials [6], [7]. In this paper, our characterization method uses the relationship between the quality factor ( of a ring resonator and associated losses ( which depend, with other parameters, on the electrical conductivity of the metal that forms the resonator. Analytical approximations for the conductor, dielectric, and radiation losses of ACPWs, which are developed in [8] and presented in Section II, are applied to the case of an asymmetric coplanar ring resonator with one ground plane. Comparisons between the theoretical, numerical, and measured -factors for several ring resonators realized by four known conductors, such as silver (Ag), copper (Cu), gold (Au), and tin (Sn), are carried out to verify this application.