In this work both a theoretical study and experimental measurements are shown to describe the ENC (Equivalent Noise Charge) contribution of the parallel √ f noise of a chargesensitive pre-amplifier in a nuclear spectroscopic chain. Previous works have demonstrated that this noise is produced by the distributed capacitive coupling to bulk of the preamplifiers' highvalued feedback resistors, which give rise to a R-C structure known in literature as "diffusive line". The introduced noise is particularly evident when such devices are integrated in a chip using a polysilicon layer that has intrinsically high distributed capacitance to the chip's bulk. Different shaping amplifiers are taken into consideration (analog quasi-Gaussian, digital trapezoidal/triangular, CR-RC n ) and closed-form expressions of noise coefficients are given whenever possible.

In nuclear spectroscopy by definition a distorted signal from a saturated pre-amplifier cannot contain the correct energy information, being this one directly related to the signal amplitude. In this work we propose an innovative technique to exploit the charge-conservation principle to extract highresolution energy information from a deeply saturated chargesensitive pre-amplifier connected to semiconductor detectors. The previously described "Fast-Reset" technique enables to reconstruct the energy information from a saturated preamplifier collecting the charge on the input node with a current generator and performing a time-over-threshold measurement. However it requires an off-line post processing of the acquired data. The proposed circuit, instead, requires no post processing thanks to a peculiar Time-to-Amplitude converter that integrates a baseline rejection circuit. In this way an extension of the pre-amplifier spectroscopic energy range of a factor 20 or more is possible, with the generation of a signal whose shape is optimized for direct acquisition with a pulse-height analyzer and no additional filtering.

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