Simplified method for measurements and calculations of coupling coefficients and Qο factor of high-temperature superconducting dielectric resonators

To accurately determine the surface resistance of high-temperature superconducting films, multifrequency measurements of S-21, S-11, and S-22 and sophisticated data processing are required. As a result, surface resistance measurements and calculations for varying temperatures are very time consuming. In this paper, we introduce a simplified method for calculations of the unloaded Q (Q(o)) factor, which require measurements of S-11 and S-22 at the lowest temperature only. For all other temperatures, only S-21 measurements are needed. The method has been shown to give sufficiently accurate Q(o) values and, hence, the surface resistance of superconducting samples, as compared to results obtained from S-21, S-11, and S-22 measurements using the transmission-mode Q factor technique. The presented method has been tested under different coupling coefficients and frequencies.