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MEASURING TEMPERATURES USING THERMISTORS

by Jonathan Valvano

Start ý Alternative Transducers ý Resistance vs. Temperature Calibration ý Dissipation Constant ý Low-Cost Embedded Temperature Measurement ý High-Precision Temperature Measurement ý Sources and PDF

DISSIPATION CONSTANT

When electrical power is delivered to a thermistor, its temperature will rise. When using the thermistor to measure temperature, the temperature rise caused by self-heating represents a measurement error. The dissipation constant (D) is defined as:

where q is the applied electrical power to the thermistor and dT is the resulting temperature rise in the thermistor as a result of self-heating.

Typically, you use equation 7 to determine the maximum allowable power that can be applied to the thermistor. For example, if the desired temperature resolution is D T, then design the interface so that the power is less than D T ý D. It is important to take into account the thermal environment around the thermistor when considering errors caused by self-heating. The dissipation constant for the typical thermistor is:

in still air and

in still water.

ACCURATE TEMPERATURE MEASUREMENT

In this article, I present three thermistor-based temperature-measuring systems. In the first system, accuracy is of prime importance, and the system is built around an IBM-compatible PC. The objective of this system is to measure temperature in the range of 25ýC to 50ýC with a resolution (D T) of 0.01ýC. The frequencies of interest range from 0 to 0.1 Hz.

You begin designing by choosing a thermistor. I chose a Thermometrics P60DA102N thermistor because of its small size and rugged construction. In this interface, I employ a constant current source to convert thermistor resistance to voltage (see Figure 4). Given the dissipation constant of:

and a temperature resolution of 0.01ýC, the electrical power (q = I² ý R) must be kept below 0.025 mW. For a constant current source, the power increases with resistance. So, the maximum power occurs when the resistance is largest. Therefore, the current must be less than:

which is 0.15 mA. Adding a little bit of safety, I designed a 0.1-mA precision constant-current source.

Figure 4ýHere is an analog circuit that interfaces a thermistor to an ADC. As the thermistor resistance varies from 464 to 1101 ohms, the output voltage varies from ý5 to 5 V. The output voltage is connected to the PCL711 ADC input.

I use OP27 precision op-amps because of their low noise and low offset voltage. Because of negative feedback, the negative terminal of the first op-amp is at virtual ground. Therefore, the current through the resistor (R₁) is 0.1 mA. This makes the intermediate voltage (V₁) equal to ý0.1 mA ý R_T.

The second stage op-amp circuit provides the gain and offset so the output voltage matches the full-scale ý5- to 5-V range of the ADC. The ratio determines the gain, and the offset is determined by . This second stage could easily be adjusted for other temperature ranges, thermistor parameters, and ADC ranges.

The capacitor on the feedback creates a single-pole 10-Hz low-pass filter. I chose this capacitor value so 60-Hz noise would be removed. To select the correct number of ADC bits, multiply the sensitivity of the instrument by the desired temperature resolution. For an NTC thermistor, the worst cases are at higher temperatures. Using Table 3, I calculated the sensitivity at 50ýC to be:

Because a temperature resolution of 0.01ýC is desired, the ADC voltage resolution must be £ 0.0025 V. I chose the PCL711 12-bit ý5-V ADC because it has a resolution of:

The last column in Table 3 shows N, which is the resulting ADC digital sample from the 12-bit ý5-V ADC.

Because the analog circuit and ADC perform a linear translation from resistance to ADC digital output, the software uses a linear function to calculate thermistor resistance from the ADC sample. Let m and b be two calibration coefficients:

For this particular circuit, m is 0.16276 ohms and b is 781.25 ohms. Equation 4 is then used to calculate temperature.

The key to accurate temperature measurements is careful calibration. The advantage of this approach (the linear translation from resistance to ADC sample) is that the entire instrument (transducer, cables, analog circuits, and ADC) can be calibrated together.

First, I calibrated the resistance measuring circuit. The m and b coefficients can be empirically determined by inserting precision resistors in place of the thermistor and measuring ADC sample (N). Next, I calibrated the T versus R_T response. Rather than use a precision ohmmeter, I used the instrument itself to calculate the thermistor resistance. In other words, I measured the ADC sample (N), then calculated the thermistor resistance using equation 14.

The C++ program, part of which is shown in Listing 1, was compiled with Borland C 5 and runs on an IBM-compatible PC in DOS mode. I added a timeout feature to the ADC software interface so the program would not crash if the ADC board is missing or broken. The sample function calculates thermistor resistance and temperature.

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