Precision temperature sensing and electronic acquisition discussions have been occurring since the beginning of modern industrialization. Over the years, an enormous amount has been written to explain temperature sensor characteristics. This is coupled with other writings that elaborate on the appropriate circuits to reliably transform the temperature sensor output signal into a useful, electrical form. It would make sense that this market has matured to the point where further discussions would just belabor the subject. Seemingly, all of the concepts surrounding these sensors and electronics are all too well understood.

This is far from being true. The subject of temperature sensing is kept alive with innovations in sensor manufacturing and enhancements to sensor interfaces. So to say, "Enough is enough" may be a little premature in light of the continuing improvements to the sensors and circuit design and, consequently, the changing scene prompts a re-visit to the basics of temperature sensing.

Temperature sensing is the most common of the sensing technologies. This statement is easily explained once the details of other sensing technologies are explored: Pressure, force, flow, level, chemical/gas, humidity, position and proximity changes produce temperature-related errors if gone unmonitored. For instance, pressure and force are typically sensed with resistive elements in a Wheatstone bridge configuration. The temperature-induced errors from the elements of these bridges can exceed, or 'swamp out,' the real signal from the sensor. Many flow and level sensors depend on the known density of a liquid or gas and one variable that affects the density of these materials is temperature. Needless to say, the mastery of temperature sensing is one of the key elements in making a successful sensing system.

So Many Temperature Sensors!

The temperature sensors that are most likely to be used are the thermocouple, resistive temperature device (RTD), Thermistor, and most recently the integrated-silicon-based sensors. There are other temperature-sensing technologies out there but, for now, they are beyond the scope of this discussion.

Each of these sensor technologies cater to specific temperature ranges and environmental conditions. Beyond the challenge of designing the proper signal-conditioning electronics, the actual sensor could make or break the circuit's effectiveness and the sensor's temperature range, ruggedness, and sensitivity are just a few characteristics that are used to determine whether or not the sensor will work in the application.

The Versatile, Inexpensive Thermocouple

When you think thermocouple, think extended temperature ranges (up to 1800 ýC), low cost, and durability. The thermocouple is constructed with two wires, of dissimilar metals, soldered together at one end with the solder bead placed in physical contact with the temperature measurement point. As a consequence a voltage can be measured between the two wires at the unsoldered ends which changes as function of temperature. The thermocouple does not require any voltage or current excitation and, as a matter of fact, any attempt to provide either type of excitation will simply introduce errors into the system.

In principle a thermocouple can be made from any two metals and thermocouples are easier to construct than one would initially think; I have inadvertently built thermocouples into my precision circuits and I have found that a likely place for an unwanted thermocouple is between the input pin of an ultra-low voltage offset operational amplifier and the copper traces on the board. If the circuit design is not done carefully, a significant temperature drift problem can be created.

Good, reliable thermocouple construction is a little harder to implement than the non-deliberate example above. In practice, standard combinations of metals have been accepted as legitimate, intentional thermocouples because of their desirable qualities in terms of linearity and their larger voltage deltas versus temperature. These common thermocouple types are E, J, T, K, N, S, and R (summarized in the table below.)

Thermo-couple type	Conductors	Temperature range (ýF)	Standard limits of error	Seeback Coefficient
E	Chromel, Constantan	32 to 600 632 to 1600	ý3 ýF, ý0.5%	62 ýV/ýC
J	Iron, Constantan	32 to 530, 530 to 1400	ý4 ýF, ý0.75%	51 ýV/ýC
T	Copper, Constantan	-150 to -75, -75 to +200, 200 to 700	ý1.5 ýF, ý2%	40 ýV/ýC
K	Chromel, Alumel	32 to 530, 530 to 2300	ý4 ýF, ý0.75%	40 ýV/ýC
N	Nicrosil, Nisil	32 to 530, 530 to 2300	ý4 ýF, ý0.75%	38 ýV/ýC
S	Platinum(10%Rhodium), Platinum	32 to 1000, 1000 to 2700	ý5 ýF, ý0.75%	7 ýV/ýC
R	Platinum(13%Rhodium), Platinum	32 to 1000, 1000 to 2700	ý5 ýF, ý0.75%	7 ýV/ýC

At the time of shipment, the thermocouple's performance is usually guaranteed by the vendor in accordance with NIST 175 standards (adopted by American Society for Testing and Materials, ASTM.) These standards define the temperature behavior of the thermocouple as well as the quality of the material used. The size of the bead of the thermocouple is typically 5 times the wire diameter; this is relatively small and, consequently, the response time of the thermocouple is fast. The wide temperature ranges of the sensor makes it exclusively appropriate for many hostile sensing environments.

Thermocouple Error Analysis

So much for the good news. Now for the not so good news. The signal conditioning circuit for the thermocouple requires an additional temperature sensor to provide an absolute temperature measurement which can be easily done with an RTD, Thermistor, or IC sensor. Another problem with the thermocouple is its linearity. If precision is the objective, thermocouples require a considerable amount of linearization, usually done with a look-up table in the processor. The look-up table for the full temperature range of the Type K thermocouple is an 11 x 14 sized matrix.

This solves the linearity problems of the thermocouple, but these types of temperature sensors also have a very low output signal, so low that the signal-conditioning circuitry needs a considerable amount of gain. Since the output signals of the thermocouple are so low, special care should be taken to prevent EM signals from being coupled into this two-wire system.

Although thermocouples are usually selected because for the wide temperature range, ruggedness and price, accuracy and good linearity are hard to achieve for precision systems. If higher accuracy is required, other temperature sensors should be used.

Absolutely an Alternative: The RTD

Although the RTD (resistance temperature detector) has a limited temperature range, it does an excellent job in the accuracy and linearity departments. So good, that the low-end applications don't require any hardware or software correction techniques. On the other hand, the element technologies of the RTD are constantly improving and if you need a high quality, accurate temperature measurement, the selection of the RTD element can become critical. The RTD is a resistive element constructed from metals such as platinum, nickel or copper. Each of the different metals exhibit their own predictable changes in resistance with temperature and the temperature coefficient of resistance is large enough to produce measurable changes:

RTD Detector Material	Thermal Response (at 0 ýC)	Typical Material Resistivity (0 ýC)
Platinum	0.00385 W/ýC (IEC 751)	9.81 E-6 W-cm
Nickel	0.00672 W/ýC	5.91 E-6 W-cm
Copper	0.00427 W/ýC	1.53 E-6 W-cm

Platinum RTDs (PRTD) are the most accurate and reliable of the three types. The platinum material is less susceptible to environmental contamination, where copper is prone to corrosion, which causes long term stability problems. Nickel RTDs tolerate environmental conditions fairly well, but, they are limited to smaller temperature ranges.

The PRTD has nearly linear thermal response, good chemical inertness and is easy to manufacture in the form of small-diameter wires or films. The resistivity of the platinum is higher than the other metals, making the physical size of the element smaller and the thermal response better, often faster than silicon-based temperature sensors.

The absolute, 0 ýC value of the element is available in a wide range of resistances. The standard resistance of a platinum RTD is 100 W. They are also available as 50, 100, 200, 500 1000 or 2000-W elements. In most applications, linearization is not required. The table below (from OMEGA references) shows the temperature versus resistance of a 100-W platinum RTD. The accuracy of the PRTD over its temperature range is also shown in terms of dýC from ideal:

Temperature (ýC)	Typical Absolute Resistive Value (W)	Deviation in W	Deviation in ýC
-200	23.0	ý0.56	ý1.3
-100	61.5	ý0.32	ý0.8
0	100.0	ý0.12	ý0.3
100	138.5	ý0.30	ý0.8
200	177.0	ý0.48	ý1.3
300	215.5	ý0.64	ý1.8
400	254.0	ý0.79	ý2.3
500	292.5	ý0.93	ý2.8
600	331.0	ý1.06	ý3.3
700	369.5	ý1.17	ý3.8
800	408.0	ý1.28	ý4.3

If high accuracy is required software corrections can be implemented with linearization formulas or look-up tables. Of the temperature sensors that are discussed here, the RTD is the most linear with only two coefficients in the linearization equation, Rt = R0(1 + At + Bt²), for temperatures 0 ýC to 859 ýC, where Rt is the resistance of the RTD at measurement temperature, t is the measurement temperature, R0 is the magnitude of the RTD at 0 ýC, and A and B are calibration coefficients derived from experimentation.

These equations are easily solved after a few iterations making it possible to resolve to ý0.01 ýdeg C of accuracy.

RTD Error Analysis

Beyond the initial element errors in the table above, there are other sources of error that affect the accuracy of the RTD. Defects into the mechanical integrity of the part caused by bending the wires, shock due to rough handling, constriction of the packaging that leads to stress during thermal expansion, and vibration can have a long term effect on the repeatability of the sensor.

Another source of error with the RTD element is self-heating. Since the RTD is a resistive element, a current excitation is needed to convert its resistance to a voltage. It would seem desirable to have a high excitation in an attempt to keep the resultant voltage above the system noise levels but the down side to this design approach is that the element will self-heat as a result of the combination of higher resistance and a high-level current. The heat generated by this combination artificially increases the resistance of the RTD.

A second source of thermal error comes from the lead-wire resistance change with temperature. RTDs are available in 2-wire, 3-wire and 4-wire configurations. The 2-wire configuration is by far the least expensive but the current that is used to excite the RTD element also flows through the wires. The affects of the wire resistance change with temperature can become a critical issue. For example, if the lead wire is constructed of 5-gauge copper that is 50-m long (with a wire resistance of 1.028 W/km), the contribution of both wires increases the RTD resistance by 0.1028 W which translates into a temperature measurement error of 0.26 ýC. Circuits can be configured to effectively use the 3-wire and 4-wire configuration to remove the error contribution of the lead wires completely.

Get the Great Accuracy of the Thermistor

If accuracy is a high priority, the Thermistor should be the temperature sensor of choice. Thermistors are available in two varieties, NTC and PTC. The NTC (negative temperature coefficient) Thermistor is constructed of ceramics composed of oxides of transition metals (manganese, cobalt, copper, and nickel). With a current excitation the NTC has a negative temperature coefficient that is very repeatable and fairly linear.

These temperature-dependent semiconductor resistors operate over a range for -200 ýC to 1000 ýC. Combined with the proper packaging, they have a continuous change of resistance over temperature. This resistive change versus temperature is relatively larger than the RTD (~2,500 to one) and, consequently, the Thermistor is systematically more sensitive.

The Thermistor is less linear than the RTD in that it requires a 3^rd-order polynomial for precise temperature corrections, with the equation: ln Rt = B0 + B1/t + B2/t² + B3/t³, where Bx are the material constants of the Thermistor and t is the measurement temperature.

This linearization formula can resolve to a total measurement uncertainty of ý0.005 ýC. However, it is tedious when implemented in the processing unit and look-up tables can be generated to serve the same purpose with slightly less accuracy.

Wire resistance is not a problem with Thermistors because the average room temperature resistance of most devices is above 5000 W. On the other hand, thermal heating is more of a problem. This is due to the combination of a large resistor and the Thermistor's negative thermal coefficient. Take, for instance, a Thermistor with a package thermal resistance of 10 ýC/W (assumes a bead diameter of 14 mils), a nominal resistance of 10 kW, and an excitation current of 5 mA. The artificial increase in temperature (d ýC) as a result of self heating is 2.5 ýC.

With temperature changes of this nature, the measurement is obviously inaccurate. To complicate this thermal effect further, the thermal heating of the Thermistor decreases the Thermistor resistance (instead of the increase seen with the RTD). Since the Thermistor has a negative resistive coefficient, the overheating effect reverses as the Thermistor resistance becomes less than the voltage across the Thermistor divided by the excitation current. This phenomenum is not easily overcome with software calibration and should be avoided.

The PTC Thermistor has a positive temperature coefficient and is constructed from barium titanate. Its sensitivity is considerably higher than that of the NTC Thermistor and should be used when a specific temperature range is of interest (-25 to 150 ýC.) Over the lower portion of the resistance versus temperature curve the Thermistor resistance if fairly constant. At higher temperatures the material passes through a threshold (between 80 ýC and 140 ýC, dependent on chemical composition of the ceramic) where the resistance versus temperature characteristics change dramatically. At this point, increases in temperature cause a rise in the PTC's resistance and the PTC resistive/temperature characteristics become very steep.

A second type of PTC Thermistor is known as the Sillistor. This device is constructed of a thermally-sensitive silicon material and also has a positive temperature coefficient (-60 ýC to 150 ýC) that is linear over the entire operating range.

Don't Fight Integrated Circuit Temperature Drifts, Exploit Them

One of the challenges an IC designer has is to minimize the effects of the temperature drift of the basic forward-voltage diode. On the other hand, the IC temperature sensor designer is in the business of exploiting the linear temperature behavior of the same diode. The near room temperature response of the simple diode is approximately 2.2 mV/ýC. The first temperature-sensitive silicon on the market was a diode back in the 1980s. Recently, IC designers have integrated this basic building block into devices that have wider voltage output ranges or even N-bit digital outputs.