RTD Sensors - Platinum Resistance Thermometer (RTD, PRT, Pt100 Sensors)

RTD Sensor, Pt100 Resistance Thermometer Working Principles

The resistance that an electrical conductor exhibits to the flow of an electric current is related to its temperature, essentially because of electron scattering effects and atomic lattice vibrations. The basis of this theory is that free electrons travel through the metal as plane waves modified by a function having the periodicity of the crystal lattice. The only little snag here is that impurities and what are termed lattice defects can also result in scattering, giving resistance variations. Fortunately, this effect is largely temperature-independent, so does not pose too much of a problem.

In fact, the concept of detecting temperature using resistance is considerably easier to work with in practice than is thermocouple thermometry. Firstly, the measurement is absolute, so no reference junction or cold junction compensation is required. Secondly, straightforward copper wires can be used between the sensor and your instrumentation since there are no special requirements in this respect.

The first recorded proposal to use the temperature dependence of resistance for sensing was made in the 1860’s by Sir William Siemens, and thermometers based on the effect were manufactured for a while from about 1870. However, although he used platinum (the most widely used material in RTD sensor types today), the interpolation formulae derived were inadequate. Also, instability was a problem due mainly to his construction methods - harnessing a refractory former inside an iron tube, resulting in differential expansion and platinum strain and contamination problems. Callendar took up the reins in 1887, but it was not until 1899 that the difficulties were ironed out and the use of platinum resistance thermometers was established.

It is now accepted that as long as the temperature relationship with resistance is predictable, smooth and stable, the phenomenon can indeed be used for temperature measurement. But for this to be true, the resistance effects due to impurities must be small - as is the case with some of the pure metals whose resistance is almost entirely dependent on temperature. However, since in thermometry almost entirely is not good enough, the impurity-related resistance must also be (for all practical purposes) constant such that it can be ignored. This means that physical and chemical composition must be kept constant.

An important requirement for accurate resistance thermometry is that the sensing element must be pure. It must also be (and remain) in an annealed condition, via suitable heat treatment of the materials such that it is not inclined to change physically. Then again, it must be kept in an environment protected from contamination so that chemical changes are indeed obviated.

Meanwhile, another challenge for the manufacturer is to support the fine, pure wire adequately, while imposing minimum strains due to differential expansion between the wire and its surroundings or former - even though the sensors may be attached to operating plant, with all the rigours of this characteristically arduous environment. Depending upon the accuracy you are after, the relationship governing platinum resistance thermometer output against temperature follows the quadratic equation:

RTD Sensor Resistance / Temperature Calculations

R_t /R₀ = 1 + At + Bt²
(above 0°C this second order approach is more than adequate) or R_t /R₀ = 1 + A^t + Bt² + Ct³ (t-100)
(below 0°C, if you are looking for higher accuracy of representation, the third order provides it).

Therefore:

t = (1/α)(R_t - R₀)/R₀ + δ(t/100)(t/100 -1)

Where: Rt is the thermometer resistance at temperature t; R₀ is the thermometer resistance at 0°C; and t is the temperature in °C. A, B and C are constants (coefficients) determined by calibration. In the IEC 60751 industrial RTD standard, A is 3.90802 x 10^-3; B is -5.802 x 10^-7; and C is -4.2735 x 10^-12. Incidentally, since even this three term representation is imperfect, the ITS-90 scale introduces a further reference function with a set of deviation equations for use over the full practical temperature range above 0°C (a 20 term polynomial).

The a coefficient, (R₁₀₀ - R₀)/100 . R₀, essentially defines purity and state of anneal of the platinum, and is basically the mean temperature coefficient of resistance between 0 and 100°C (the mean slope of the resistance vs temperature curve in that region).

Meanwhile, δ is the coefficient describing the departure from linearity in the same range. It depends upon the thermal expansion and the density of states curve near the Fermi energy. In fact, both quantities depend upon the purity of the platinum wire. For high purity platinum in a fully annealed state the a coefficient is between 3.925x10^-3/°C and 3.928x10^-3/°C.

For commercially produced platinum resistance thermometers, standard tables of resistance versus temperature have been produced based on an R value of 100 ohms at 0°C and a fundamental interval (R₁₀₀ - R₀) of 38.5 ohms (α coefficient of 3.85x10^-3/°C) using pure platinum doped with another metal (see Part 2, Section 6). The tables are available in IEC 60751, tolerance classes A and B.

Platinum Resistance Thermometers

Firstly, being a noble metal, it has a wide and unreactive temperature range. Secondly, its resistivity is more than six times that of copper. Thirdly, it has a reasonable, simple and well understood resistance vs temperature relationship. Finally, it can be obtained in a very pure form, and drawn into fine wires or strips very reproducibly, making the production of interchangeable detectors relatively easy.

Although platinum is not cheap, only very small amounts are needed for resistance thermometer construction its expense is therefore not a significant factor in calculating the overall cost. On the down side, it is contaminated by a number of materials, particularly when heated, so support and sheath materials have to be chosen carefully. Furthermore, heat treatment of the material is particularly important in view of the presence of vacancy defects which are present at all temperatures unless annealed out.

RTD (Resistance Thermometer Detector)
The industry-wide acronym for resistance thermometer detector is widely used to describe the RTD sensor which is a device comprising a resistive element (usually Pt100) which relies on the inherent change in resistance with temperature of the wire or material in the sensing element.

Resistance Thermometer
An instrument or system incorporating a length of wire or film having predictable resistance vs temperature characteristics, forming a temperature sensor. Measurement of the resistance of the device yields its temperature.

PRT
Platinum Resistance Thermometer

Pt100
A generic term usually used to describe a Pt100 Sensor. It reallty refers to the resistance of the element at 0ºC (100 ohms) and the material it is made from (Platinum).

RTD Element
The sensing part of an RTD sensor. Usually a suspended wire wound coil of Platinum wire within a ceramic cylinder or a Platinum film deposited on a substrate. Can be Pt100, Pt1000 or Cu.

Fundamental Interval
The Fundamental Interval is the value of resistance change in the element over the temperature 0 to 100ºC which is usually 38.5ohms for a Pt100 element to IEC 60751.

Alpha Value (coefficient)
Linked to Fundamental Interval, the alpha value represents the change in resistance per ºC step (over the range 0 to 100ºC) for a resistance element. The industry standard is IEC 60751 Pt100, where the α coefficient is 3.85x10^-3/°C.