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Thermistor Linearizer

There are many methods for linearizing an NTC thermistor and scaling the result for input to an ADC. Here is a practical circuit that linearizes the thermistor temperature curve and produces an output which is proportional to the temperature in volts. The voltage output allows it to be measured with a DMM or any voltage input data logger.

Figure 1 - Thermistor Linearizer

The linearization circuit is given in Figure 1. The circuit consists of a voltage divider which includes the thermistor and an inverting opamp with the non-inverting input set to a fixed reference voltage. The analysis of the circuit is as follows:

Since the opamp non-inverting input is at a reference voltage, the typical gain formula will not suffice. It is necessary to derive the overall gain using superposition. Setting the non-inverting input at zero volts, the gain is simply R3/R2. Shorting the input resistor R2 to ground and applying a source at the non-inverting input yields the non-inverting gain 1+(R3/R2). Combining the two yields the overall gain with a given Vref.

Figure 2 - Vout equation

To find the input voltage it is necessary to find the Thevenin equivalent voltage and input resistance. First the voltage divider R1/Rth is calculated. Next the parallel value of R1 and Rth are found and added to the input resistance R2. We now have V-thevenin and R-thevenin.

Since the endpoint thermistor resistance is used to find the range of the circuit, the unknowns are the feedback resistor R3 and Vref. Since we have R-thevenin and the gain is determined by R4/R-thevenin we can let G = R4/R-thevenin and solve for G in terms of Vin, Vout and Vref, yielding the following:

Figure 3 - Gain function

We now have two values for G, one at the lower and one at the upper temp, G-low and G-high. Using Excel solver, we find a minimum difference between G-low and G-high while adjusting Vref and targeting an equal R3 value for low and high. When a solution is found, the temperatures coorelate well to the output voltage. The best fit will be for narrow ranges as opposed to wider ones. Also, picking a thermistor that is optimal for the range will yield acceptable results.