Study of Sallen–Key digital filters in nuclear pulse signal processing

The Sallen–Key filter (S–K) is widely used in nuclear pulse signal processing because of its simple working principle and good performance. Related research has only reviewed the recursive numerical model of digital S–K using idealized parameters. The use of digital S–K thus has limitations under these circumstances. This paper comprehensively deduces a recursive numerical model of digital S–K and discusses the effects of resistance and capacitance on the filter quality factor, cutoff frequency and amplitude–frequency response. The numerical recursive function, transfer function and amplitude–frequency response are analyzed using different parameters. From a comparative analysis of the shaper in a simulation and an actual nuclear signal, an optimal parameter selection principle is obtained. Using different forming parameters, the energy resolution and pulse counting rate of the 55\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{55}$$\end{document}Fe energy spectrum are compared and analyzed based on a Si-PIN detector. Capacitance has a stronger influence on the Gaussian shape, whereas the influence of resistance is stronger on the shaping amplitude.