handbook of modern sensors

438 14 Light Detectors
Some of the radiation power goes out of the element to the sensor’s housing, while
some come from the object (or goes to the object). What is essential is that the net
thermal flow (coductive+convective+radiative) always must come out of the sensor
(e.g., it must have a negative sign).
If the AFIR element is provided with a cooling element (e.g., a thermoelectric
device operating on Peltier effect 2 , T s may be maintained at or below ambient. However,
from practical standpoint, it is easier to warm the element up rather than to cool it
down. In the following, we discuss the AFIR sensors where the surface is warmed up
either by an additional heating element or due to a self-heating effect in a temperature
sensor [8,14–16].
Dynamically, the temperature T s of any thermal element, either active or passive,
in general terms may be described by the first-order differential equation
cm dT s
= P − P L − , (14.28)
dt
where P is the power supplied to the element from a power supply or an excitation
circuit (if any), P L is a nonradiative thermal loss which is attributed to thermal conduction
and convection, m and c are the sensor’s mass and specific heat, respectively,
and = η + b is the net radiative thermal flux. We select a positive sign for power
P when it is directed toward the element.
In the PIR detector, for instance, in the thermopile or pyroelectric, no external
power is supplied (P = 0), hence, the speed response depends only on the sensor’s
thermal capacity and heat loss and is characterized by a thermal time constant τ T .
In the AFIR element, after a warmup period, the control circuit forces the element’s
surface temperature T s to stay constant, which means
dT s
= 0, (14.29)
dt
and Eq. (14.28) becomes algebraic:
P = P L + . (14.30)
Contrary to PIR sensors, the AFIR detector acts as an “infinite” heat source. It follows
from the above that under idealized conditions, its response does not depend on
thermal mass and is not a function of time. If the control circuit is highly efficient,
because P L is constant at given ambient conditions, electronically supplied power
P should track changes in the radiated flux with high fidelity. A magnitude of
that power may be used as the sensor’s output signal. Equation (14.30) predicts that
an AFIR element, in theory, is a much faster device if compared with the PIR. The
efficiency of the AFIR detector is a function of both its design and the control circuit.
Nonradiative loss P L is a function of ambient temperature T a and a loss factor α s :
P L = α s (T s − T a ). (14.31)
To generate heat in theAFIR sensor, it may be provided with a heating element having
electrical resistance R. During the operation, electric power dissipated by the heating
element is a function of voltage V across that resistance:
2 See Section 3.9 of Chapter 3.