UM0277

Thermal sensor linearization

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Appendix A

Thermal sensor linearization

An NTC thermistor is a thermal resistor whose value decreases when its temperature

increases. The thermal law is exponential, as presented in Equation 1.

Equation 1

To achieve a simple voltage sensor, it is better to linearize the temperature response using a

constant resistor (R12) added in series with the NTC. A voltage divider is then achieved.

below:

Equation 2

To make the relationship of Equation 2 to vary linearly, it's enough to ensure that the second

order derivative will be zero. Equation 3 gives the R12 value to ensure this condition.

Equation 3

To linearize the voltage response of a M2020 5 k NTC thermistor from EPCOS, between -20

and +5 °C, a 30 kOhm resistor should be chosen for R12.

In this temperature range, Vs varies according to Equation 4, for a 5 V supply:

Equation 4

Figure 14 gives the variation of Vs and the linear value given by Equation 4 (Vl), versus the

temperature sensed by the NTC thermistor.

Rc T

() Ro

B

1

T

---

1

To

-------

–

⎝⎠

⎛⎞

•

=

Vs

Rc T

()

Rc T

() R12

+

----------------------------------

Vdd

•

=

R12

2

d

dT

-------Rc T

()

⎝⎠

⎛⎞

2

•

d

2

dT

2

----------Rc T

()

-----------------------------------------

Rc T

()

–

=

Vl T

()

T

51.84

+

16.1943

-------------------------

=