Simulation and Measurement of Out-of-Band Resonances for the FDM Readout of a TES Bolometer

With applications in cosmology, infrared astronomy and CMB survey, frequency-division multiplexing (FDM) proved to be a viable readout for transition-edge sensors (TES). We investigate the occurrence of out-of-band resonances (OBR) which could constrain the bandwidth of the FDM readout of TES bolometers. The study includes SPICE modeling of the entire setup including the cryogenic harness, LC filters, Superconducting Quantum Interference Device (SQUID) and room-temperature amplifier. Simulation results show that the long harness (for flight model) could cause multiple reflections that generate repetitive spikes in the spectrum. Peaks of the OBR are mainly due to the parasitic capacitances at the input of SQUID. Implementing a low-pass RC circuit (snubber) at the input of the SQUID dampened the OBR. As a result, the first peak only appears around 20 MHz which is a safe margin for the 1 MHz-3.8 MHz FDM in use in the prototype readout. Using a spectrum analyzer and broadband LNAs,we also measured the OBR for the prototype FDM readout in the lab up to 500 MHz. The measurement was conducted at temperatures of 50 mK and 4 K and for various biasing of the DC SQUID. It turns out that OBR are more intense at 50 mK and are caused by the harness impedance mismatch rather than the SQUID. Simulation codes and supporting materials are available at https://github.com/githubamin/LT-Spice-Simulation-of-FDM-readout.