Modeling the analog response of passive infrared sensor

Passive infrared (PIR) sensors are sensitive to infrared (IR) rays and are mostly used for motion detection. In this paper we propose a mathematical model that enables better understanding of the analog response of the PIR sensor, the Fresnel lens, and the associated electronic circuitry. The proposed model relates the sensor's analog output waveform to the width of sensing element, and speed of movement and distance of the subject from the PIR sensor. Experiments were performed to capture the sensor's analog output waveform corresponding to the subject's movement through the sensor's field of view (FoV) at different distances, and the relationship of the sensor's peak-to-peak output voltage with distance and speed of the subject. The simulation results are shown to match reasonably well with the experimental results.