DA & Control

# In Search of a Low-Cost Temperature Sensor: Part 2

December 1, 2005 By: Ed Ramsden Sensors

Last month we explored the possibility of using voltage drop across a silicon small-signal diode as a temperature sensor. Although this property varies vs. temperature in a consistent manner, it has two significant drawbacks: unit-to-unit variation and a very small output signal. Now let's consider another contender for the crown of cheap temperature sensor—the thermistor.

 Ed Ramsden

A thermistor is a resistor designed so that its resistance varies as a well-defined function of temperature. While all resistors have temperature-dependent resistance, thermistors differ from your garden-variety resistors in two ways. The first is the degree to which a thermistor's resistance varies over temperature. A typical resistor will have a maximum specified temperature coefficient (TC) in the 10–100 ppm/°range, meaning that it will change in value by a maximum of 0.001%–0.01% for a 1° change in case temperature. A typical thermistor, on the other hand, can have a TC on the order of 40,000 ppm/°C, or a whopping 4% change in resistance for every °C change in temperature. With this kind of sensitivity, you can readily detect temperature changes on the order of a thousandth of a degree (or even smaller) with the appropriate measurement circuitry.

 Figure 1. Thermistor Resistance vs. Temperature

The second difference is that a thermistor's TC is a specified value that can be expected to fall within specified tolerance limits for each and every device of a given model. Thermistors with unit-to-unit consistencies within 1°C are easy to find.

 Figure 2.

The downside of using a thermistor is its highly nonlinear resistance vs. temperature response, approximating an inverse exponential function (see Figure 1). This unit has a nominal resistance value of 10 kΩ at 25°C, and varies from 330 kΩ at –40°C down to 200 Ω at 150°C, a range of 1650:1. Such a huge dynamic range in output resistance can make measurement difficult. It requires some kind of logarithmic correction scheme, or a very wide dynamic range (1650/4% = 41,250:1 – 16 bits resolution!) to get 1° resolution across the whole –40° to 150° range. Although the sensor may be a bargain, the signal processing behind it certainly won't be.

 Figure 3. Bridge Response vs. Temperature

If you're interested in measuring temperature over a limited range, however, it's often possible to perform a "good enough" linearization by adding some very inexpensive circuitry. One way is to incorporate the thermistor into a Wheatstone bridge (see Figure 2), but this arrangement provides an essentially linear output voltage in response only to small changes in resistance. For large changes, a bridge's output voltage is quite nonlinear. The relationship between output voltage and the resistance of a single variable leg is given by:

Sometimes, as Mr. Spock would say, random chance operates in your favor (i.e., you get lucky). The Wheatstone bridge's nonlinearity is just such a case, at least when applied to thermistor linearization. You can obtain a more-or-less linear output voltage from a Wheatstone bridge/thermistor combination over a 40°–50°C range. To take advantage of this trick, er, technique, you must pick the other bridge resistors to match the thermistor's resistance in the middle of the range you want to measure. For example, if your span is 50°–120°C, you would use 1 kΩ reference resistors in the bridge because the thermistor is ~1 kΩ at the 85°C midpoint. Figure 3 shows some voltage responses you can expect from the thermistor in Figure 2 in 1, 10, and 100 kΩ bridge configurations. Note that in addition to getting a decently linear response over selected 40°–50° spans, the output voltage swing is pretty respectable, running 40% of the bridge bias voltage. This makes it a simple matter to interface this circuit to other circuitry downstream.

Ed Ramsden, B.S.E.E., a member of the Sensors Editorial Advisory Board, designs sensors for the heavy-truck industry in Portland , OR; eramsden@questex.com

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