2) Resistance - Temperature characteristics

The resistance and temperature characteristics of a thermistor can be approximated by equation 1.

 


R: resistance at absolute temperature T(K)
R0 : resistance at absolute temperature T0(K)
B: B value
※T(K)= t(˚C)+273.15


The B value for the thermistors is not fixed and it can vary by as much as 5K/˚C, depending on material composition, so equation 1 may yield different results from actual values if applied over a wide temperature range.


By taking the B value in equation 1 as a function of temperature as shown in equation 2, the difference with the actual value can be minimized.

 


C, D, and E are constants.
The B value distribution caused by manufacturing conditions will change the constant E, but will have no effect on constants C or D. This means, when taking into account the distribution of B value, it is enough to do it with the constant E only.


● Calculation for constants C, D, and E
Using equations 3~6, constants C, D, and E can be determined through four temperature and resistance value data points (T0, R0), (T1, R1), (T2, R2), and (T3, R3).
With equation 3, B1, B2 and B3, can be determined from the resistance values for T0, T1, T2, T3 and then substituted into the equations below:

 

 

● Example
Using the Resistance-Temperature chart, the resistances for the range of 10˚C ~ 30˚C for a thermistor with 5kΩ resistance and a B value of 50K at 25˚C.
● Process
1) Determine the constants C, D, and E from the Resistance-Temperature chart.

 

 

2) BT= CT2 + TD + E + 50, substitute the values into the equation and solve for BT


3) R= 5exp {BT (I/T-I/298.15)}, substitute the values into the equation and solve for R:
※T: 10 + 273.15 ~ 30 + 273.15

 

● Results of plotting the Resistance-Temperatures are in figure 1

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