Effects of Different Spectroscopic Filtering Techniques on the Noise Produced by Charge-Sensitive Pre-amplifiers with Feedback Resistors Characterized by High Distributed Capacitance

Integrated polysilicon resistors are characterized by a distributed capacitance to bulk which makes them deviate from their ideal theoretical model, especially at high frequency. This difference manifests itself both in terms of impedance and generated noise. Specifically, when using these resistors as feedback discharge devices of charge-sensitive pre-amplifiers, this capacitive coupling turns the thermal white current noise into a non-white one. This noise can be well represented by the sum of two non-correlated components: the first is a white one and the second has a power spectral density proportional to the square root of the frequency. In previous works closed-form calculations have been presented which exhaustively describe impedance and noise power spectrum of such devices. In this work the effects of different types of signal shaping on the contribution to the ENC value of such non-white noise are described. The study includes the most common spectroscopy shaping filters: CR-RCn, quasi-Gaussian and trapezoidal ones and has never been discussed in literature before. All the presented calculations are expressed completely in closed form and without approximation.