Modeling and Analysis of Maximum Multiplexing Number with Crosstalk Suppression under Electrical Crosstalk Constraint for Frequency Domain Multiplexing Readout of Transition Edge Sensor Arrays between 1-100 MHz

Abstract The 1-100 MHz frequency band remains relatively unexplored for Frequency Division Multiplexing (FDM) readout of TransitionEdge Sensor (TES) arrays, despite its potential to increase channel counts beyond the traditionally used 1-5 MHz range. Thisgap, however, is becoming increasingly addressable with advancements in the fabrication of high-resonance-frequency LCresonators and wide-band Superconducting Quantum Interference Devices (SQUIDs). It still partly stems from understudiedcrosstalk challenges in this higher-frequency regime, where mutual inductance, SQUID input inductance, and carrier leakageeffects tend to be more pronounced, which may limit the feasibility of high-multiplexing systems.In this work, we aim to addressthis less explored area by modeling crosstalk between the 1-100 MHz range under a lumped-parameter framework, with afocus on static crosstalk (ECTstatic)—a metric that has received less attention in lower-frequency studies. To mitigate mutualinductance, we propose a chessboard pixel arrangement that maximizes frequency differences between adjacent channels.Leveraging the 1-100 MHz bandwidth with a 0.1 MHz channel spacing, this configuration can suppress crosstalk by up to 59.4dB.Our simulations show that with this layout and through dynamic carrier frequency design, reducing mutual inductance to 3nH enables 186 channels under a 1% ECTstatic constraint when the SQUID input inductance is 1 nH; this count increases to 299channels when the input inductance is reduced to 0.5 nH. Relaxing the threshold to 3.2% or 10% further expands the channelcounts—for instance, reaching 612 or 2067 channels with 1 nH input inductance, respectively.This study preliminarily exploresthe crosstalk characteristics of 1-100 MHz FDM for TES arrays, offering a framework for low-crosstalk, high-channel-countreadout systems and highlighting key trade-offs in this relatively unexplored frequency range.