A Pulse Generator with Poisson-Exponential Distribution for Emulation of Radioactive Decay Events

Abstract

We present an FPGA-synthesizable version of a pseudo-random pulse generator that can be used to emulate radioactive source activity. It is intended for debugging real-time digital pulse processing applications, beyond the capabilities of periodic generators. The proposed module delivers a discrete random sequence that follows the Poisson inter-arrival distribution. Operation is based on a barrel-shifted maximal-length linear feedback shift register, operating as uniform random number generator, followed by an implementation of the Bernoulli trial to emulate exponential inter-arrival times. Due to its simple design, it can operate at high clock frequencies, providing a minimum time between events of two FPGA clock cycles operating at full-speed. A small footprint Verilog module is proposed for embedding in digital processors. Attainable performance and required resources are calculated. Additionally, it is shown how digital output pulses can be width-modulated to generate, with minimum conditioning, the analog signals present in a spectroscopy detection chain.