handbook of modern sensors

64 3 Physical Principles of Sensing
Fig. 3.18. Resistance–temperature characteristics for two thermistors and Pt RTD (R 0 = 1k);
thermistors are calibrated at t 0 = 25 ◦ CandRTDat0 ◦ C.
Thermistors possess nonlinear temperature–resistance characteristics (Fig. 3.18),
which are generally approximated by one of several different equations. The most
popular of them is the exponential form
R t = R t0 e β(1/T−1/To) , (3.59)
where T 0 is the calibrating temperature in kelvin, R t0 is the resistance at the calibrating
temperature, and β is a material’s characteristic temperature. All temperatures and β
are in kelvin. Commonly, β ranges between 3000 and 5000 K, and for a relatively narrow
temperature range, it can be considered temperature independent, which makes
Eq. (3.59) a reasonably good approximation. When a higher accuracy is required, a
polynomial approximation is generally employed. Figure 3.18 shows the resistance–
temperature dependence of thermistors having β = 3000 and 4000K and that for the
platinum RTD. The temperature characteristic of platinum is substantially less sensitive
and more linear with a positive slope, whereas thermistors are nonlinear with a
high sensitivity and a negative slope.
Traditionally, thermistors are specified at temperature of t 0 = 25 ◦ C(T 0 = 298.15 ◦ K),
whereas RTDs are specified at t 0 = 0 ◦ C(T 0 = 273.15 ◦ K).
3.5.3 Strain Sensitivity
Usually, electrical resistance changes when the material is mechanically deformed.
This is called the piezoresistive effect. In some cases, the effect is a source of error. On