Linearize thermistors with new formula

Mark Bieger

EDN

I often have to get a reasonably accurate temperature measurement for a laser, transistor, or printed circuit board. I usually use a thermistor for my temperature sensor because they are inexpensive. However, the thermistor’s nonlinear resistance characteristic makes accurate temperature conversion complex. To minimize this difficulty, I often linearize the thermistor’s resistance characteristic by placing the thermistor within a resistor divider. This linearized response is simpler to convert to a temperature value than the thermistor’s raw response. To obtain an optimum level of linearity, I have derived a pair of formulas that are useful in determining component values (RS and RP) for this common linearization circuit.

Figure 1 shows the thermistor linearization circuit that I am addressing in this Design Idea. The temperature of the thermistor is linearly related to the output voltage (approximately).

Linearize thermistors with new formula
Figure 1. Two-resistor thermistor linearization circuit.

The design process begins by picking a temperature, which I call the inflection temperature TI, at which we want the flattest possible transfer function (VOUT/VIN). My design task is to compute values for RS and RP given TI and the resistor ratio

at TI.

Three parameters, R0, β, and TREF, are often used with Eq. 1 to model the thermistor’s resistance versus temperature characteristic

  (1)

I determine RS and RP by setting the second derivative of VOUT/VIN in Figure 1 to 0 at temperature TI. After much algebra, I obtained the two formulas shown in Eq. 2.

  (2)

Not all ratios are possible with passive components – ratios less than

result in negative RP values.

Figure 2 shows a graph of the linearized thermistor voltage transfer function for a common thermistor.

Linearize thermistors with new formula
Figure 2. Graph of the linearized thermistor transfer function.

I have put together an Excel spreadsheet and a Mathcad worksheet that models this data, downloadable below.

ZIP archive of spreadsheet & worksheet (please use "Save as" and remove the dummy .txt extension before saving)

EDN

You may have to register before you can post comments and get full access to forum.
EMS supplier