Digital Active Nulling for Frequency-Multiplexed Bolometer Readout: Performance and Latency

We consider the stability and performance of a discrete-time control loop used as a dynamic nuller in the presence of a relatively large time delay in its feedback path. Controllers of this form occur in mm-wave telescopes using frequency-multiplexed Transition Edge Sensor (TES) bolometers. In this application, negative feedback is needed to linearize a Superconducting Quantum Interference Device (SQUID) used as an amplifier. $M$ such feedback loops are frequency-multiplexed through a SQUID at distinct narrowband frequencies in the MHz region. Loop latencies stem from the use of polyphase filter bank (PFB) up- and down-converters and have grown significantly as the detector count in these experiments increases. As expected, latency places constraints on the overall gain $K$ for which the loop is stable. However, latency also creates spectral peaks at stable gains in the spectral response of the closed loop. Near these peaks, the feedback loop amplifies (rather than suppresses) input signals at its summing junction, rendering it unsuitable for nulling over a range of stable gains. We establish a critical gain $K_C$ above which this amplifying or "anti-nulling" behaviour emerges, and find that $K_C$ is approximately a factor of 3.8 below the gain at which the system becomes unstable. Finally, we describe an alteration to the loop tuning algorithm that selects an appropriate (stable, effective for nulling) loop gain without sensitivity to variations in analog gains due to component tolerances.