## 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)

R_{0} : resistance at absolute temperature T_{0}(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 (T_{0}, R_{0}), (T_{1}, R_{1}), (T_{2}, R_{2}), and (T_{3}, R_{3}).

With equation 3, B_{1}, B_{2} and B_{3}, can be determined from the resistance values for T_{0}, T_{1}, T_{2}, T_{3} 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= CT^{2} + 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