handbook of modern sensors

476 16 Temperature Sensors
Upon waiting sufficiently long to reach a steady-state level T S , the rate of change
in Eq. (16.34) becomes equal to zero (dT S /dt = 0); then, the rate of heat loss is equal
to supplied power:
δ(T S − T a ) = δT = V T i. (16.36)
If by selecting a low supply voltage and high resistances, the current i is made very low,
the temperature rise T can be made negligibly small, and self-heating is virtually
eliminated. Then, from Eq. (16.34),
dT S
dt
=− δ C (T S − T a ). (16.37)
The solution of this differential equation yields an exponential function [Eq. (16.8)],
which means that the sensor responds to the change in environmental temperature
with time constant τ T . Because the time constant depends on the sensor’s coupling to
the surroundings, it is usually specified for certain conditions; for instance, τ T = 1s
at 25 ◦ C in still air or 0.1 s at 25 ◦ C in stirred water. It should be kept in mind that the
above analysis represents a simplified model of the heat flows. In reality, a thermistor
response has a somewhat nonexponential shape.
All thermistor applications require the use of one of three basic characteristics:
1. The resistance versus temperature characteristic of the NTC thermistor is shown
in Fig. 16.12. In most of the applications based on this characteristic, the selfheating
effect is undesirable. Thus, the nominal resistance R T0 of the thermistor
should be selected high and its coupling to the object should be maximized (increase
in δ). The characteristic is primarily used for sensing and measuring temperature.
Typical applications are contact electronic thermometers, thermostats,
and thermal breakers.
2. The current versus time (or resistance versus time) as shown in Fig. 16.10B.
3. The voltage versus current characteristic is important for applications where the
self-heating effect is employed, or otherwise cannot be neglected. The powersupply-loss
balance is governed by Eq. (16.36). If variations in δ are small (which
is often the case) and the resistance versus temperature characteristic is known,
then Eq. (16.36) can be solved for the static voltage versus current characteristic.
That characteristic is usually plotted on log-log coordinates, where lines of
constant resistance have a slope of +1 and lines of constant power have slope of
−1 (Fig. 16.11).
At very low currents (left side of Fig. 16.11), the power dissipated by the thermistor
is negligibly small and the characteristic is tangential to a line of constant resistance
of the thermistor at a specified temperature. Thus, the thermistor behaves as a simple
resistor; that is, the voltage drop V T is proportional to current i.
As the current increases, the self-heating increases as well. This results in a decrease
in the resistance of the thermistor. Because the resistance of the thermistor
is no longer constant, the characteristics start to depart from the straight line. The
slope of the characteristic (dV T /di), which is the resistance, drops with the increase
in current. The current increase leads to a further resistance drop which, in turn,