Optimization of the TES-Bias Circuit for a Multiplexed Microcalorimeter Array

Abstract

A transition-edge-sensor (TES) microcalorimeter’s shunt resistor (Rsh) and thermal conductance to the cryogenic bath (G) are often considered to be interchangeable knobs with which to control detector speed. Indeed, for otherwise-identical TES-parameter models, there are many combinations of Rsh and G that give the same decay time-constant (τcrit). However, our previous work showed that with time- or code-division-multiplexed readout, the distribution of signal-to-noise ratio with frequency, which depends strongly on Rsh and G, is just as important as τcrit. Here, we present a set of calculations to select the optimal values of Rsh and G, given a linear TES model and count-rate and energy-resolution requirements. Lower G and lower Rsh make multiplexing easier. Our calculations also determine the allowed combination of SQUID-readout noise (SΦ) and multiplexer row-period (trow) and row-count (Nrows). Recent improvements to SΦ and trow in the NIST time-division-multiplexing architecture have allowed a NIST eight-pixel TES array to be read out with 2.70 eV (full-width at half-maximum) average energy resolution at 6 keV. The improvements make the X-ray Microcalorimeter Spectrometer co-proposed by NASA and NIST for ESA’s Athena X-ray observatory straightforwardly achievable, including engineering margin, with Nrows=16.