Digital-sampling systems in high-resolution and wide dynamic-range energy measurements: Comparison with peak sensing ADCs

The use of fast digital sampling techniques in Nuclear Physics experiments as a replacement of the standard analog signal processing methods is discussed for applications needing high-resolution signal amplitude measurements. This is for example the case of a solid-state detector with a charge-sensitive preamplifier, processed using fast digital sampling methods. Under very general assumptions, an expression for the achievable resolution and dynamic range of the system is reported, valid for any detector/digitizer/digital-filter combination, taking into account the detector noise and the ADC properties, namely the Effective Number of Bits (ENOB) and the sampling frequency. The system properties are summarized using the parameter PSENOB, i.e. the “Peak-Sensing-Equivalent Number of Bits”. These results can be used to predict the attainable performances in various applications, possibly requiring a resolution/dynamic-range trade-off. Numerical examples for some representative cases in γγ-ray spectroscopy and charged particle experiments are reported, demonstrating that the equivalent performances of a 15 bit peak-sensing ADC are feasible with today-available sampling ADCs. For ease of presentation, other non-trivial effects as baseline- and non-linearity-related issues as well as experimental tests of the proposed approach are presented in a companion paper [L. Bardelli, G. Poggi, Digital sampling-systems in high-resolution and wide dynamic-range energy measurements: finite time window, baseline effects, and experimental tests, this issue].