A Recursive Algorithm to Improve the Sampling Rate of Microwave SQUID Multiplexed Readout for Fast Microcalorimeter Signals

Abstract The Microwave SQUID Multiplexer ($\mu$MUX) is a critical readout technology for large-scale Superconducting Transition-Edge Sensor (TES) array. It is considered as a promising readout system for both bolometer and calorimeter applications of large-scale TES array. It has been employed in several Cosmic Microwave Background (CMB) experiments, in which the TESes are used as bolometers. However, in the field of calorimeter applications of TESes, such as X-ray detection, the $\mu$MUX system has not been widely used. The main reason is the slew rate of calorimeter pulse signal is much faster than that of bolometer, which will increase the difficulties of data processing in $\mu$MUX electronics. In a typical microwave SQUID Multiplexed readout scheme, the sampling rate is determined by the frequency of the flux-ramp modulation. For CMB experiment, the frequency of the flux-ramp is usually set to about $\mathcal{O}$(10~kHz). However, for X-ray detection, it is necessary to improve the frequency of flux-ramp to about 1~MHz. It is a challenge to implement the high speed data processing with current $\mu$MUX electronics.%The $\mu$Mux readout algorithm is a crucial component.Currently, the implementation of the $\mu$Mux readout algorithm is complex, and the sampling rate for each TES is low, only reaching kHz.We propose a recursive algorithm to reconstruct the fast TES signals with high sampling rate in case of no hardware changes. This algorithm is simple enough to implement in real time data collection. %In this paper, we describe and demonstrate this technique with a reasonable simulation model of $\mu$MUX. The simulation results shows that the recovered sampling rate can break through the frequency limitation of the flux ramp, reaching up to analog-to-digital converter (ADC) sampling rate. The non-linearity is lower to 0.25\% in full dynamic range.