TES-based bolometer and microcalorimeter arrays with thousands of pixels are under development for several space-based and ground-based applications. A linear detector response and low levels of cross talk facilitate the calibration of the instruments. In an effort to improve the properties of TES-based detectors, fixing the TES resistance in a resistance-locked loop (RLL) under optical loading has recently been proposed. Earlier theoretical work on this mode of operation has shown that the detector speed, linearity and dynamic range should improve with respect to voltage biased operation. This paper presents an experimental demonstration of multiplexed readout in this mode of operation in a TES-based detector array with noise equivalent power values (NEP) of $3.5cdot 10^{-19} $W/$sqrt{mathrm{Hz}}$. The measured noise and dynamic properties of the detector in the RLL will be compared with the earlier modelling work. Furthermore, the practical implementation routes for future FDM systems for the readout of bolometer and microcalorimeter arrays will be discussed.
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