RTD Sensors / Platinum Resistance Thermometer (RTD, PRT, Pt100 Sensors, Pt1000)

Pt100 Sensor (Resistance Thermometer) Theory

The resistance value 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.

Resistance Thermometer History

The first recorded proposal to use the temperature dependence of resistance value 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 thermometry 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.

Resistance vs Temperature for a Platinum Resistance Thermometer

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:

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.

Commercial Resistance Thermometers

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. The tables are available in IEC 60751, tolerance class A or class B.

Platinum Resistance Thermometer Wiring Configuration Diagram

Pt100 sensors are available with a 2 wire, 3 wire or 4 wire wiring connection as shown below. For an explanation of pt 100 wiring configuration, please click here.