Analysis on sampling bounds for digital spectrometers

In this paper, the impact of random arrival time on the amplitude resolution is analyzed for digital spectrometers. The improvement performance of amplitude estimation is also analyzed by using timing techniques. This effect relies on the sampling frequency f_s and the characteristics of analog section and digital filters. The equivalent noise charge ENC_a and baseline V_BL caused by this effect is derived for digital filters. For the digital trapezoidal filter using a charge sensitive preamplifier and a simple CR-RC circuit as analog section, the minimum f_s is required to be 7/tau to make ENC_a / Q_in lower than 10^-3, i.e. ENC_a is only 6.25 electrons with 1 fC detector charge. The Cramer-Rao Limited Bounds (CRLB) for estimating arrival time and amplitude synchronously is also calculated. This work will provide a selection criterion for choosing f_s, analog prefilter and timing method to reduce the influence of random arrival time.