Thermally sensitive resistors (thermistors) are used widely in laser diode and detector cooling applications because of their high sensitivity, small size, ruggedness, fast response times, and low cost. When used properly with a thermoelectric (TE) cooler and support circuitry, a common thermistor costing less than a dollar has enough sensitivity to stabilize the temperature of a laser diode to better than 0.001℃. The price of the thermistor’s high sensitivity is paid with non-linearity, a factor which makes their selection and use a bit more challenging than might be otherwise expected.

Thermistor Characteristics

Thermistors are generally two-terminal semiconductor devices that have an electrical resistance that varies non-linearly with temperature. The non-linearity of thermistors complicates their calibration and use.

In the past, design engineers often resorted to resistor-based linearizing networks which effectively converted resistance to temper-ature only over very narrow temperature ranges. Fortunately, microprocessors have greatly simplified this task with their ability to quickly calculate complex expressions. The R-T characteristics of most thermistors are accurately described by the Steinhart-Hart equation:

1/T = A + B*(Ln R) + C*(Ln R)³

In this relationship, T is the absolute temperature (in Kelvin) and A, B, and C are constants which can be determined from measured values of resistance and temperature. Assuming good calibration data is available, the Steinhart-Hart equation introduces errors of less than 0.1℃ over a temperature range of -30℃ to +125℃, and errors of less than 0.01℃ between -20℃ to +50℃.

Figure 1. Resistance-Temperature response curves for nine common thermistors.

Thermistor Families - Most thermistors have a negative temperature coefficient (NTC), which means resistance decreases with increasing temperature. The R-T characteristics of nine common NTC thermistors are shown in Figure 1. Each thermistor is labeled according to its nominal resistance at 25℃; commonly available thermistors range from 250 Ω to 100 kΩ.

Course resistance control is accomplished during the thermistor manufacturing process by using different metal oxides to form the semiconductor junction. Several different material combinations are used to arrive at the same nominal 25℃ resistance, and each combination leads to a slightly different R-T characteristic. This variety of available R-T characteristics often seems to complicate thermistor selection. However, as shown in Figure 2, the differences between thermistors of the same nominal resistance are relatively small.

Nominal Resistance -Generally, thermistors are operated at temperatures where they exhibit resistances of thousands of ohms. At these high resistances, simple two-wire resistance measurements work well using conventional digital multimeters, and the measurement circuitry of temperature controllers does not have to be overly complicated or precise for reliable temperature measurement.

Temperature Sensitivity -Thermistors achieve their highest sensitivity at low temperatures, where the resistance vs. temperature curve is steepest. This sensitivity drops rapidly as the temperature increases. For a typical 10 kΩ thermistor, the sensitivity varies as follows:

To understand practical thermistor selection trade-offs, consider the system block diagram shown in Figure 3. This figure shows a tem-perature sensing and display system like the one used here and other temperature controllers. Thermistor resistance is sensed by forcing a constant current, either 10 µA or 100 µA, through the thermistor and then measuring the voltage drop. The voltage is digitized and then input to the microprocessor, the resistance is calculated, and the Steinhart-Hart equation is used to calculate temperature.

The temperature controller uses a 23-bit A/D converter over a measurement range of 0 – 6V, resulting in an A/D input voltage resolution of about 0.7µV per step. Since the thermistor resistance is non-linear, the actual temperature measurement resolution is also non-linear. This non-linearity complicates the definition of the temperature measurement limits.

As the thermistor temperature increases, its resistance and sensitivity to temperature change also decrease. This means that the number of ohms per bit decreases and the number of degrees per A/D step increases. Figure 4 illustrates this relationship. The upper part of the figure shows the thermistor resistance and voltage input to the A/D, and is used to determine the low temperature limit of the system. The lower part of the figure shows the system measurement resolution in degrees C per A/D converter step, and is used to determine the upper temperature limit.

The display resolution of the temperature controller is 0.001℃. As long as a single A/D bit corresponds to a change of less than 0.001℃, the measurement resolution does not significantly impact the instrument application. The temperatures at which a single A/D step corresponds to a change of greater than 0.001℃ are as follows:

As the thermistor temperature decreases its resistance increases and, likewise, so does the voltage across it. The practical lower temperature limit is reached when the voltage exceeds the maximum input voltage of the A/D converter.  Typical low temperature measure-ment limits are:

Temperature Controller Using Typical 10 kΩ  Thermistor 

Figure 4. Measurement Resolution Change vs. Temperature

Conclusion

The type of thermistor you choose will depend primarily on the required operating temperature range. Thermistor R-T curves, like Figure 1, are usually supplied by the thermistor manufacturer, and provide a good guideline for thermistor selection.

The useful temperature range of a thermistor is shifted by varying the sensing current. The temperature ranges for the temperature controller, using a 10 kΩ thermistor, are shown by the horizontal bars in the center of Figure 4, and can be shifted dramatically by changing the sense current.

Figure 4 provides data for a typical 10kΩ thermistor, but the same approach can be used with other thermistors. From the figure you can see that 10 kΩ thermistors are generally a good choice for most laser diode cooling applications where high stability is required from just above room temperature to approximately -40℃.