handbook of modern sensors

References 251
Fig. 6.17. Calculated and experimental
amplitudes of output signals in a PIR detector.
There are several conclusions which can be drawn from Eq. (6.20). The first
part of the equation (the first ratio) characterizes a detector and the rest relates to an
object. The pyroelectric current i is directly proportional to the temperature difference
(thermal contrast) between the object and its surroundings. It is also proportional to
the surface area of the object which faces the detector. A contribution of the ambient
temperature T a is not as strong as it might appear from its third power. The ambient
temperature must be entered in Kelvin; hence, its variations become relatively small
with respect to the scale. The thinner the sensing element, the more sensitive is the
detector. The lens area also directly affects signal magnitude. On the other hand,
pyroelectric current does not depend on the sensor’s area as long as the lens focuses
the entire image on a sensing element.
To evaluate Eq. (6.20) further, let us calculate the voltage across the bias resistor.
That voltage can be used as an indication of motion. We select a pyroelectric PVDF
film sensor with typical properties: P = 25 µC/K m 2 , c = 2.4 × 10 6 J/m 3 K, h = 25
µm, lens area a = 1cm 2 , γ = 0.6, and the bias resistor R = 10 9 (1 G). We will
assume that the object’s surface temperature is 27 ◦ C and the surface area b = 0.1 m2.
The ambient temperature t a = 20 ◦ C. The output voltage is calculated from Eq. (6.20)
as a function of distance L from the detector to the object and is shown in Fig. 6.17.
A graph for Fig. 6.17 was calculated under the assumption that the optical system
provides a sharp image at all distances and that the image is no larger that the sensing
element area. In practice, this is not always true, especially at shorter distances,
where the image is not only out of focus but also may overlap the out-of-phase parts
of a symmetrical sensor. The reduction in the signal amplitude at shorter distances
becomes apparent: The voltage does not go as high as in the calculated curve.
References
1. Blumenkrantz, S. Personal and Organizational Security Handbook. Government
Data Publications, Washington, DC, 1989.
2. Ryser, P. and Pfister, G. Optical fire and security technology: Sensor principles
and detection intelligence. In: Transducers’91. International conference on Solid-