Design and characterization of third-order Sallen-Key digital filter in nuclear signal processing

The Gaussian filter shaping circuit is widely used in the nuclear pulse signal processing due to its good performance in amplitude extraction and pulse counting. A third-order Sallen-Key (3rd S-K) filter shaping circuit is designed based on a RC integrator and a second-order Sallen-Key (2nd S-K) circuit. According to the digital 3rd S-K, the transfer functions is derived in the Laplacian domain, and the numerical recurrence model is analyzed and researched, the purpose is to obtain its transfer function and amplitude-frequency response curve in the z-domain. For the simulation and actual sampling of the nuclear signal, digital shaping processing is performed at different parameters, three parameters (d, SNR, δ) are defined to compare and analyze the amplitude extraction, noise suppression and symmetry of the digital shaping method, which shows that as the shaping parameters increases, the digital shaping output noise suppression performance is better, the SNR increased from 49.25 to 64.21, the waveform is more symmetrical, the δ reduced from 34.05 to 0.22. At the same parameters, it is compared and analyzed with CR-RC³ and 2nd S-K shaping methods, according to the digital Gaussian shaping results, the 3rd S-K digital shaping method has better pulse amplitude extraction(d = 36.06%), noise suppression performance (SNR = 64.21) and waveform symmetry (δ = 0.22). Under different shaping methods, the energy resolution and pulse counting rate of the Fe characteristic X-ray energy spectrum are compared based on a Si-PIN detector. The results show that the 3rd S-K digital shaping method has better energy resolution performance and comprehensive performance indicators, which can be further applied for digital shaping of nuclear pulse signals.