Superconducting microwave resonators are reliable circuits widely used for detection and as test devices for material research. A reliable determination of their external and internal quality factors is crucial for many modern applications, which either require fast measurements or operate in the single photon regime with small signal to noise ratios. Here, we use the circle fit technique with diameter correction and provide a step by step guide for implementing an algorithm for robust fitting and calibration of complex resonator scattering data in the presence of noise. The speedup and robustness of the analysis are achieved by employing an algebraic rather than an iterative fit technique for the resonance circle.

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Josephson junction arrays could be competitive candidates for radiation sources in the frequency range from 0.5 to 1.5 THz. This is the range where compact solid-state continuous wave sources are most lacking. We investigated the millimeter-wave radiation from arrays of high-temperature superconductor bicrystal Josephson junctions embedded in a quasi-optical resonator. The novel approach of utilizing the intrinsic resonance modes of the substrate to improve the impedance coupling between the series array of discrete Josephson junctions and the quasi-optical resonator was investigated by experiments and electromagnetic field simulations. Radiation from the arrays containing up to 536 junctions was detected at about 80 GHz and liquid nitrogen temperature using a low-noise receiver. The detected maximum radiation power of the arrays was about 50 pW and the peak voltage agreed exactly with the Josephson current-voltage relation.