handbook of modern sensors

16.1 Thermoresistive Sensors 469
Fig. 16.6. Value of β changes with temperature.
where A and B are constants. The evaluation of this equation shows that the 3 rd and
4 th summands are very small as compared with the first two and for many practical
cases can be removed. After elimination of two last terms, a model for the material
constant can be represented as linear function of temperature:
β = A 1 + BT (16.23)
Considering β as a linear function of temperature, the simple model can be refined
to improve its fidelity. Because β is no longer a constant, for practical purposes its
linear function should be defined through at least one fixed point at some temperature
T b and a slope γ . Then, Eq. (16.23) can be written as
β = β b [1 + γ (T − T b )] , (16.24)
where β b is attributed to the temperature T b . The coefficient γ is the normalized
change (a slope) in β per degree Celsius:
( )
βx 1
γ = − 1 , (16.25)
β y T c − T a
where β x and β y are two material characteristic temperatures at two T a and T c characterizing
temperatures 4 To determine γ , three characterizing temperature points are
required (T a , T b and T c ), however, the value of γ does not need to be characterized
for each individual thermistor. The value of γ depends on the thermistor material
4 Note that β and T are in Kelvin. When temperature is indicated as t, the scale is in Celsius.