An analytical expression for the kinetic inductance of the superconducting coplanar waveguide is given using the conformal mapping technique. This expression is shown to be in good agreement with experimental results obtained from the temperature dependence of the resonant frequency of the NbN coplanar waveguide resonators, especially in the case of a film thickness smaller than the magnetic penetration depth. It is also shown that the magnetic penetration depth of the superconducting thin films can be evaluated by this method.

In this letter, we report some superconducting properties and normal-state resistivities of single-crystal NbN films prepared by a reactive rf-magnetron sputtering method. It was found that the prepared single-crystal NbN films have Tc’s above 16 K, normal-state resistivities in the range from 12.2 to 14.3 μΩ cm (at 20 K), and magnetic penetration depths in the range from 93 to 100 nm (at 4.2 K). From a temperature dependence of the upper critical magnetic field for a single-crystal NbN film, the zero-temperature Ginzburg–Landau coherence length ξGL(0) for the film was calculated to be 6.9 nm.

Effects of a damping resistance on noise characteristics of a dc SQUID are studied theoretically, where the damping resistance is in shunt with a loop inductance of the SQUID. An analytical expression for the energy resolution of the SQUID is obtained, with which the relation between the damping resistance and the energy resolution is studied in detail. It is shown that an optimum value of the damping resistance exists, which is determined by the tradeoff between the improvement of the transfer function and the additional noise due to the damping resistance. Optimum values of the damping resistance are about twice the shunt resistance of the SQUID and vary slightly with SQUID modulation parameter β. For optimum damping, the energy resolution is improved, compared with the case without the damping resistance. This means that the SQUID with large β can be used without significant degradation of the performance, i.e., the previous restriction of β=1 can be loosened. The analytical results agree quantitatively with numerical ones.

We report very-low-noise, fast-response, middle-scale multiplexing in a microwave superconducting quantum interference device multiplexer (MW-Mux) as a transition-edge sensor (TES) readout. Our MW-Mux is able to read 40 channels with 500 kHz sampling and has a low readout noise of 0.9 μΦ0/Hz (where Φ0 is the magnetic flux quantum), equivalent to 9 pA/Hz. By contrast, a multiplexer of less than 10 pixels with 500 kHz sampling and ∼2 μΦ0/Hz readout noise has so far been reported in the literature. Owing to the 500 kHz sampling, our MW-Mux exhibits a fast response to detect a TES pulse with a rise time around 12 μs. We demonstrated simultaneous readout of 38 pixels from an array of x-ray TES microcalorimeters. The measured full-width values at half-maximum spectral resolution ranged from 2.79 to 4.56 eV, with a median value of 3.30 eV at 5.9 keV, including a ∼10% contribution of readout noise, i.e., 0.9–1.7 eV.

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