The Front-End electronics for the liquid Argon instrumentation of the LEGEND-200 experiment

In this paper we provide a detailed technical description of the Front-End electronics for the liquid Argon instrumentation of the LEGEND-200 experiment, searching for the very rare, hypothetical neutrinoless double $\beta$ decay process at the Italian Laboratori Nazionali del Gran Sasso. The design stems from the need to read out the silicon photo-multiplier response to the scintillation light in the liquid Argon with excellent single-photon resolution. The Front End is required to be placed far from the detectors to meet the experiment's radio-purity constraints, which represented a challenge for a high signal-to-noise ratio. We address how this could be achieved in a stable way. The system was installed in July 2021 and has been commissioned with the rest of LEGEND-200, proving we could attain a very low overall level of electrical noise, of 200 $\mu$V on average