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Superconducting microwave resonators are reliable circuits widely used fordetection and as test devices for material research. A reliable determinationof their external and internal quality factors is crucial for many modernapplications, which either require fast measurements or operate in the singlephoton regime with small signal to noise ratios. Here, we use the circle fittechnique with diameter correction and provide a step by step guide forimplementing an algorithm for robust fitting and calibration of complexresonator scattering data in the presence of noise. The speedup and robustnessof the analysis are achieved by employing an algebraic rather than an iterativefit technique for the resonance circle.

Efficient and robust analysis of complex scattering data under noise in microwave resonators