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Arrays of transition-edge sensors (TES) with applications from X-ray to FIR-to-mm astronomy can be read out efficiently using frequency domain multiplexing (FDM) readout with baseband feedback. The calibration of the TES/FDM systems is critical in assessing/improving their performance but the calibration is less straightforward than for TES detectors operated under DC bias. We have designed and tested a calibration method based on Johnson noise measurements, assuming good knowledge of the LC filter inductance and temperature. With the calibrated Johnson noise source at the input of our readout, we are able to measure both the open-loop and closed-loop behavior of the system. We applied this method to an 88-pixel TES bolometer array under dark conditions. Our new calibration successfully yields useful instrumental properties including TES normal resistances, feedback impedances, IV curves, power plateaus, and dark NEP. Notably, the resulting saturation power does not appear to depend on the resonance frequency, a desirable feature absent in our previous calibrations, suggesting that our noise-based calibration is robust. This calibration method can be applied to future TES arrays.
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