NTC Thermistor Linearization Circuit Design

An NTC thermistor is one of the cheapest and most accurate ways to measure temperature, and its output is one of the least convenient. The resistance falls steeply and non linearly as the temperature rises, so the circuit and the firmware both have to work with a curve rather than with a scale factor.

The Shape of the Resistance Curve

A ten kiloohm thermistor at twenty five degrees might be thirty two kiloohms at zero degrees and four kiloohms at fifty degrees. Over a hundred degree span the resistance changes by a factor of twenty or more, and the sensitivity per degree falls as the temperature rises.

That shape has consequences for the interface. A simple voltage divider gives a large output change at low temperatures and a small one at high temperatures, so the resolution of the measurement is not uniform across the range. A converter with sixteen bits may give a resolution of a hundredth of a degree near zero and a quarter of a degree near a hundred.

The curve is smooth and repeatable, which is what makes the part useful. Two thermistors of the same type from the same batch track each other closely, and the curve is stable over years when the part is not operated at the extremes of its range.

beta Value and Its Limits

The beta value is a single number that describes the curve between two temperatures, usually twenty five and eighty five degrees. It is enough for an accuracy of a degree or so over a narrow range and it becomes progressively worse as the range widens.

The beta value itself changes with temperature, so a sensor specified with a tolerance of one percent on beta still has a curve error of several tenths of a degree at the ends of a wide range. The datasheet usually gives a table of resistance against temperature, and using the table is more accurate than using beta.

For the best accuracy the Steinhart-Hart equation with three coefficients fits the curve to within a few hundredths of a degree across a hundred degree span. The coefficients come from a calibration at three temperatures, which is practical in production with a stirred bath and a reference thermometer.

Linearization with resistors

linearization in hardware means adding fixed resistors so that the combination is closer to a straight line. A resistor in parallel with the thermistor compresses the high temperature end, and a resistor in series with the pair stretches the low temperature end.

The classic result is a pair of values, different for each thermistor curve, that give a nearly linear response over a limited span of about fifty degrees. Outside that span the error grows again, and the arrangement is a compromise rather than a cure.

Hardware linearization is worth it when the output goes to a simple display or a comparator with no processor to do the arithmetic. Where a microcontroller is present, the arithmetic is free and the resistor network only adds tolerance. The decision is about where the correction belongs, and the measurement chain thinking behind it is set out in our guide to mixed signal board design.

excitation current and Self Heating

The thermistor is a resistor, so it heats itself when current flows through it. A bead in still air has a dissipation constant of about one milliwatt per degree, which means that a hundred microwatts of dissipation raises its temperature by a tenth of a degree.

self heating is therefore a design constraint rather than a footnote. A divider with five volts across a ten kiloohm thermistor at twenty five degrees dissipates a quarter of a milliwatt and reads about a quarter of a degree high, and the error grows at low temperatures where the resistance is higher.

The current should be kept in the tens of microamps for a bead in still air, or the excitation should be pulsed with a low duty cycle. A higher current is acceptable in a stirred liquid, where the dissipation constant is much larger, and the datasheet distinguishes the two cases.

Wiring, Lead Resistance and Shielding

A bead thermistor on a metre of thin wire has a lead resistance of a few tenths of an ohm, which is negligible against ten kiloohms. The same thermistor in a probe with long leads and a low resistance type may see a lead resistance that is a real fraction of the reading.

A three wire or four wire connection removes that error, exactly as it does for a resistance thermometer. Where the thermistor is a low resistance type and the cable is long, the extra conductor is cheaper than the error.

Shielding matters more than the lead resistance in most installations. The measurement node is a high impedance point, and a cable running beside a mains conductor couples into it. A twisted pair with the screen earthed at the instrument end keeps most of the interference out.

ADC Interface and Reference

The divider output can be read directly by an analog to digital converter with a reference equal to the supply, which makes the measurement ratiometric and cancels the supply error. The converter must have a high enough input impedance that the divider is not loaded.

A converter with a low input impedance draws current from the divider and shifts the voltage. Where the thermistor resistance is comparable with the converter input resistance, a buffer amplifier is needed, and the amplifier offset then becomes part of the error.

Reading the divider against the supply rather than against a fixed reference is the usual choice for a thermistor, because the supply is the source of the excitation. The exception is a system with a precision reference available, in which case the divider can be fed from the reference.

Interchangeability and Tolerance

Thermistor tolerance is quoted at twenty five degrees and is often five percent of the resistance, which corresponds to about a quarter of a degree at that temperature and rather more at the ends of the range. Interchangeability is the tolerance between parts, and it is what limits a system assembled without calibration.

A producer that calibrates each unit removes the interchangeability error at the reference temperature and can then rely on the curve tolerance, which is smaller. Calibrating at two temperatures removes most of the curve error as well.

Where a batch is expected to be uniform, a single point calibration against a reference is enough. Where the parts come from different batches, a two point calibration is safer, and the extra minute on the production line is cheaper than a warranty return.

Verification and Drift

Verify the reading against a reference thermometer in a stirred bath at two or three temperatures, and record the values. A reading that is consistently offset points to a divider error, while a reading that is correct near the calibration points and wrong between them points to a curve problem.

Drift in service is rare for a thermistor that is not operated at its limits. The more common cause of a changing reading is moisture in the probe or a corroded junction, and both show up as a resistance that is higher than expected at all temperatures.

Ageing is specified as a small drift in resistance per year at a reference temperature, and a design that operates the part well inside its range can expect very little. The release checks that keep these sensor boards consistent from unit to unit are collected in our PCB design release checklist and the inspection points in judging PCB quality.

FAQ

Should I use beta or the Steinhart-Hart equation? Use beta for a narrow range and a rough reading. Use the three coefficient Steinhart-Hart fit when the range is wide or the accuracy requirement is better than half a degree.

Why does my thermistor read high? Self heating is the usual reason. Reduce the excitation current or pulse it, and check whether the part sits in still air.

Do I need a linearization resistor? Only if the output drives a simple display with no processor. With a microcontroller, fitting the curve in firmware costs nothing and avoids the resistor tolerance.