  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.
