handbook of modern sensors

62 3 Physical Principles of Sensing
Tungsten
Fig. 3.17. Specific resistivity of tungsten as a function of temperature.
3.5.2 Temperature Sensitivity
The conductivity of a material changes with temperature, t, and in a relatively narrow
range, it may be expressed by α, which is temperature coefficient of resistance (TCR):
ρ = ρ 0 [1 + α(t − t 0 )] (3.55)
where ρ 0 is resistivity at the reference temperature t 0 (commonly either 0 ◦ Cor25 ◦ C).
In a broader range, resistivity is a nonlinear function of temperature.
For nonprecision applications over a broad temperature range, the resistivity of
tungsten, as shown in Fig. 3.17 may be modeled by a best-fit straight line with α =
0.0058 C −1 . However, this number will not be accurate at lower temperatures. For
instance, near 25 ◦ C the slope of ρ is about 20% smaller: α = 0.0045 C −1 . When better
accuracy is required, formula (3.55) should not be employed. Instead, higher-order
polynomials may be useful for modeling the resistivity. For instance, over a broader
temperature range, tungsten resistivity may be found from the second-order equation
ρ = 4.45 + 0.0269t + 1.914 × 10 −6 t 2 , (3.56)
where t is the temperature (in ◦ C) and ρ is in m.
Metals have positive temperature coefficients (PTCs) α, whereas many semiconductors
and oxides have negative temperature coefficients of resistance (NTCs). It is
usually desirable to have very low TCRs in resistors used in electronic circuits. On
the other hand, a strong temperature coefficient of resistivity allows us to fabricate a
temperature sensor, known as a thermistor (a contraction of the words thermal and