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

A transition-edge-sensor (TES) microcalorimeter's shunt resistor (R (sh)) 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 R (sh) and G that give the same decay time-constant (tau (crit)). 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 R (sh) and G, is just as important as tau (crit). Here, we present a set of calculations to select the optimal values of R (sh) and G, given a linear TES model and count-rate and energy-resolution requirements. Lower G and lower R (sh) make multiplexing easier. Our calculations also determine the allowed combination of SQUID-readout noise (S (I broken vertical bar) ) and multiplexer row-period (t (row)) and row-count (N (rows)). Recent improvements to S (I broken vertical bar) and t (row) 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 N (rows)=16.