Simplified method for measurements and calculations of coupling coefficients and Q0 factor of high-temperature superconducting dielectric resonators

To accurately determine the surface resistance of high-temperature superconducting films, multifrequency measurements of S₂₁, S ₁₁, and S₂₂ 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 (Q₀) factor, which require measurements of S₁₁ and S₂₂ at the lowest temperature only. For all other temperatures, only S₂₁ measurements are needed. The method has been shown to give sufficiently accurate Q₀ values and, hence, the surface resistance of superconducting samples, as compared to results obtained from S₂₁, S₁₁, and S₂₂ measurements using the transmission-mode Q factor technique. The presented method has been tested under different coupling coefficients and frequencies