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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.
The voltage across R12 will follow the supply voltage (V
dd
) according to the relationship
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
------------------------- =