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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

RESISTANCE VS. TEMPERATURE CALIBRATION

The basic temperature-dependent mechanism is the population of charge carriers into a conduction band. If the temperature is expressed in degrees Celsius, the NTC thermistor resistance is:

The basic idea of a thermistor-based thermometer is to measure the thermistor resistance and then calculate temperature using an equation that relates temperature as a function of resistance. You can rewrite equation 1, solving for T (in degrees Celsius) in terms of R (in ohms). I replaced the two thermistor parameters (R₀ and b ) in equation 1 with two other calibration parameters, H₀ and H₁.

You need to perform a resistance temperature calibration to determine the coefficients H₀ and H₁. Because each thermistor is different, the calibration experiment is an important step when temperature accuracy is desired. On the other hand, if relative temperature is more important than accuracy, you could skip the calibration and simply use the coefficients given by the manufacturer.

I placed a Thermometrics P60DA102N NTC thermistor next to a reference temperature probe and placed the two in a water bath. I measured the thermistor resistance with my instrument and measured the true temperature with the reference thermometer. Table 2 shows a temperature calibration for this thermistor. I performed a linear regression of:

versus ln(R) to obtain the calibration coefficients, H₀ = 1.3091Eý03 and H₁ = 2.9175Eý04. The average error was 0.017ýC.

For small temperature ranges or in systems where accuracy is secondary, this approach is sufficient. In systems that demand better accuracy, I use this three-term equation:

Although there is no fundamental theory to support it, I have found that equation 4 produces excellent results for a wide range of thermistor types.

The least squared fit of this same data in equation 4 gives an average error of only 0.002ýC. For this thermistor, H₀ = 1.38077Eý3, H₁ = 2.75309Eý4, and H₃ = 1.27290Eý7.

LINEARIZATION

Because the microcomputer (even without a floating-point processor) is capable of calculating these nonlinear equations, thermistors can easily be used for accurate temperature measurements. Sometimes, however, it is convenient to use a linear transducer.

For small temperature ranges, a simple resistor network can be used to create a more linear resistance versus temperature response. In particular, a fixed resistor placed in parallel with the thermistor will reduce the sensitivity but increase the linearity of the combination. The parallel combination of a fixed resistor and a thermistor will flatten and straighten resistance versus temperature response. Let R_T be the thermistor resistance, R_p be the fixed parallel shunt resistor, and R_n be the network resistance:

T_m is the midpoint temperature in Kelvin, and R_m is the thermistor resistance at that temperature. To maximize the linearity of equation 5, R_p will be chosen such that:

where b (from equation 1) is expressed in Kelvin. For the temperature range 25ýC to 50ýC, T_m is 311ýK, b is 3428ýK, and R_m is 697 ohms. Using these values in equation 5 yields an R_p of 483 ohms.

In Figure 3, you can see that the 483-ohm parallel shunt resistor decreases the sensitivity but improves the linearity. The decrease in sensitivity means a larger gain in the analog amplifier is required, which will make the system more susceptible to noise. On the other hand, you can also see that without linearization, the system is more sensitive (higher R versus T slope) to temperature at low temperatures. This means the instrument will work better for low temperatures than for high temperatures. For small temperature ranges, this disparity is not a problem, but for large temperature ranges, consider using a linearized system.

Figure 3ýHere you can see the resistance temperature response of the P60DA thermistor (raw data) and the resistance temperature response of this thermistor in parallel with a fixed 483-ohm resistor.

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