handbook of modern sensors

78 3 Physical Principles of Sensing
conduction. The bottom electrode may be given a heat-absorbing coating, such as
goldblack or organic paint. As a result of heat absorption, the bottom side becomes
warmer (the new temperature is T 1 ), which causes the bottom side of the material to
expand. The expansion leads to flexing of the sensor, which, in turn, produces stress
and a change in dipole orientation. Being piezoelectric, stressed material generates
electric charges of opposite polarities across the electrodes. Hence, we may regard
a secondary pyroelectricity as a sequence of events: a thermal radiation → a heat
absorption → a thermally induced stress → an electric charge.
The dipole moment, M, of the bulk pyroelectric sensor is
M = µAh, (3.72)
where µ is the dipole moment per unit volume, A is the sensor’s area, and h is the
thickness. The charge, Q a , which can be picked up by the electrodes, develops the
dipole moment across the material:
M must be equal to M 0 , so that
M 0 = Q a h. (3.73)
Q a = µA. (3.74)
As the temperature varies, the dipole moment also changes, resulting in an induced
charge.
Thermal absorption may be related to a dipole change, so that µ must be considered
as a function of both temperature, T a , and an incremental thermal energy, W,
absorbed by the material
Q a = Aµ(T a ,W). (3.75)
Figure 3.27 shows a pyroelectric detector (pyrosensor) connected to a resistor R b ,
which represents either the internal leakage resistance or a combined input resistance
of the interface circuit which is connected to the sensor. The equivalent electrical
circuit of the sensor is shown at the right. It consists of three components: (1) the
current source generating a heat induced current, i (remember that a current is a
movement of electric charges), (2) the sensor’s capacitance, C, and (3) the leakage
resistance, R b .
The output signal from the pyroelectric sensor can be taken in the form of either
charge (current) or voltage, depending on the application. Being a capacitor, the
pyroelectric device is discharged when connected to a resistor, R b . Electric current
Fig. 3.27. Pyroelectric sensor and its equivalent circuit.