History

During the same year that Seebeck discovered thermoelectricity, Humphrey Davy (1778-1829) would announce that metal resistivity had a clear dependance on temperature. Fifty years later, William Seamens used platinum in a resistance thermometer. This favourable choice standardized all future resistance thermometers with platinum being the key element for high precision temperature measurement. The Platinum Resistance Temperature Detector or PRTD is now used to measure from the triple point of hydrogen (-259,34°C) to the freezing point of silver (961,78°C). Platinum is particularly convenient for this type of temperature range, as it maintains an excellent stability which will hardly alter after repeat use.

In 1932, C.H. Meyers proposed construction of a Platinum Resistance Temperature Detector (RTD) composed of a platinum wire wrapped around a mica support core inside a glass tube. This type of construction minimizes the wire tension and maximizes resistance. Even thought it is a very stable assembly the thermal contact between the platinum and the measurement point is weak and a diminished temperature response time is the result. Due to the structure's fragility, this type of RTD is used mainly in laboratories today.

Another labaratory tool replaced Meyer's concept. This "bird cage" element (Figure 1) was proposed by Evans and Burns. Resistance constraints provoked by time and temperature were reduced to a minimum and this style RTD became the labaratory norm. However, due to it's fragile nature and sensitivity to vibrations, it was not suitable for industrial applications.

More solidly constructed RTDs are shown in figures 2, 3, and 4. A bifilament platinum wire is wound on a ceramic or glass core. This winding reduces magnetic induction and noise. Once the wire is wound on the core, the assembly is sealed by molten glass. As long as the dilation coefficient of the platinum wire and ceramic core are not exactly the same, the platinum wire's dilation will result in a resistance change, sometimes consequenting in a permanent change of the wire's resistance. Versions exist of RTDs that offer a compromise between the "bird cage" and the sealed spiral wound styles. This approach employs a rolled spiral of platinum wire wound on a ceramic cylinder and maintained by a

Modern fabrication techniques use a platinum or other metallic film deposited on a ceramic substrate that has been water jet cut, laser cut, and sealed. This film RTD offers a substantial savings in assembly time and high resistance for it's size. Due to advanced technological fabrication, these devices are very small and have high thermal conductivity allowing a quick temperature change response time.

Film RTDs are less stable than wire filament wound RTDs but have a smaller size advantage, lower production time advantage, and are user friendly. These advantages have made this style RTD very popular and widely used.

Metals

All metals produce a postive change in resistance for a positive change in temperature. This is the principal function of an RTD. System error is greatly reduced when the nominal value of the RTD resistance is high; this implies that a metallic wire has a high resistivity.

Due to their low resistivity, gold and silver are rearely used as RTD elements. Tungsten has a relatively high resistivity but is mainly used in applications that require an extremely high temperature measurement although the wire is very fragile and RTD construction difficult. Copper is used as an alternative to the popular platinum due to it's linearity and more economical pricing. It's low resistivity requires a longer length of wire than a standard platinum RTD and is limited to temperature measurement up to approx. 120°C. The most common RTDs are constructed with platinum, nickel, ar a nickel alloy blend. Nickel alloy wires are economical but are limited to a specific temperature range, are not linear, and have tendancy to drift over time. For precise temperature measurement, platinum is the obvious choice.

Temperature coefficient

The standard temperature coefficient DIN 43760 of platinum wire is: α = 0.00385. For a resistance of 100 ohms at 0°C, this corrsponds to + 0,385 ohm per °C which is the average curve from 0°C to 100°C. There exists a large variety of RTD's that have different coeffcients and ohm values at 0°C. However, the most common RTD is that with the above example, PT100, with a coeffficent of 0.00385 and an ohm value of 0°C at 100 ohms. This is what the following pages' calculations and explanations will be based on.

Resistance Measurement

Wheatstone Bridge

3 Wires Bridge

To avoid subjecting the 3 resistors to the same temperature of the RTD, we sperate them from the bridge with a

These wires recreate the problem that we have seen before: the resistance of the wires affects the temperature reading. This effect can be reduced to a minimum by employing the configuration of a 3 wires bridge (Figure 8). If wires A and B are the same length, their resistance effect will be annulled due to the fact that both are on an opposite side of the bridge. The third wire, C, is the measuring wire where there is no circulating current.

The Wheatstone bridge represented in Figure 8 creates a non linear relation between the resistance change and the change in tension in the bridge. This will require an additional equation to convert the tension measurement of the bridge into an RTD equivalent resistance.

4 Wires Measurement

The three resitances of the bridge are replaced by a resitance of reference permitting to know, with precision, the generated current (Figure 9). The inconvenience is that it requires an additional wire than the 3 wire bridge. It is a small price to pay in order to obtain exact resitance measurements.

Even though it has excellent precision, the 4 wire resistance measurement, like all other measurements, will always be affected by errors and the results will be to try and minimize these errors by taking all the necessary precautions.

Possible Errors and Precautions

The RTD is susceptible to three types of errors:

• The inherannt tolerances to resitance of the RTD itself,
• The gradient in temperature between the thermometer and the measuring point,
• The faults and errors in that are present in the extension connection between the sensor and the measurement instrument.

Some sources of error are electrical and others are the result of the mecanical construction of the RTD. Potential source errors include the interchangeability and conformity: The conformity indicates the quantity that the RTD is permitted to deviate from the standard curve. Two conformity components: one tolerance to the reference temperature, normally 0°C, and one tolerance on the slope. These possible gaps are defined by known standards. For example, the norme DIN 43760 class B, requires the calibration from 0,12Ω (0.3°C) at 0°C, but permits the curve to move away from the nominal 0,00385 by ±0.000012 Ω/Ω/°C. This can result in a difference of 0.8°C at 100° C, 1.3°C at 200°C, and up to 3.8°C at 700° C. It is therefore important to know with precision, the average tolerances used.

Self Heating

The RTD is a passive sensor, it requires the passage of a measurement current to produce a useful signal. This current heats the element and raises it's temperature. Errors will result if the sensor does not absorb the additional heat.

Self Heating is expressed in mW/°C, which is the power in milliwatts (1000.RI²) which raises the internal temperatureof the sensor by 1°C. The higher the mW/°C, the less the phenomen is important. For example, suppose a measurement current of 5 mA in a PT100 sensor in a 100°C ambient temperature. The specifications indicate 50mW/°C in water displaces at 1m/sec. The quantity of heat produced is: 1000 mW * (0,005 A) * (18,5) = 3,5 mW; the self heating error is (3,5 mW) / (50 mW/°C) = 0.07°C.

Modern measuring practices use very low currents, 100µA and sometimes lower. This practice, if used in the above example, would give an elevated temperature error of only (0.00138 mW)/(50 mW/°C) = 0,000027°C, which is negligable.

The resulting error is inversely proportional to the capacity of the sensor to evacuate the additional heat. This depends on materials, construction, and environment of the sensor. The worst case for this product is there is a high resistance value in a small bodied construction. RTD film, with a small surface area to absorb the heat, is an example. Self heating depends equally on where the sensor is immersed. The error in non-moving air can be 100 higher than that of running water.

Response Time

A time constant indicates the responce of an RTD to change in temperature. A common expression is the time it takes a sensor to reach 63,2% of the temperature grade of moving water. The response time depends on the mass of the sensor and the rate of thermal transfer between the external surface of the element and the environment in which it is immersed. A small time constant reduces errors in systems that are subject to rapid temperature changes.

Temperature Calculations

Callendar-Van-Dusen (CVD) Equation

The relationship between the temperature and ohmic value of RTD's were calculated by Callendar, and later on, refined by Van Dusen; this is why the equation is named Callendar-Van Dusen.

With RT = resistance at T°C, R0 = resistance at 0°C, α = temperature coefficient at 0°C in Ω/Ω/°C, δ = linearisation coefficient, β = second coefficient of linearisation for negatives temperature values (β = 0 for T > 0°C).

This equation has been transformed in order to be used easily with the coefficients A, B and C given by the standard DIN 43760 (IEC 751) and the component technicals specifications with the following conversions:

With the following conversions :

These three values represent the three principal specifications for RTD's.

1. 0,003850 Ω/Ω/°C: Standard DIN 43760, IEC 751, named Europeen Industrial Standard.
2. 0,003926 Ω/Ω/°C: Require pur platinum (99,999%), named U.S. Industrial Standard.
3. 0,3911 Ω/Ω/°C: Often named U.S. Industrial Standard.

The Callendar-Van Dusen equation permits a good linearity of RTD's, ±0.01°C between -100°C and +100°C but the error increases rapidly with high temperatures. Furthermore, this equation calculates the resistance with temperature change; which is the opposite of the most current uses : Temperature with resistance change.

To convert the resistance value of the RTD to temperature, we are obliged to use a quad equation to the 2nd degree, which is, in sort, the reciprocal of the Callendar-Van Dusen equation, but iniquely for temperatures superior to 0°C.

For temperatures inferior to 0 C, the Callendar-Van Dusen equation is too complex to reslove and the the use of successive approximations is necessary:

The following table propose calculated values with the Callendar-Van Dusen equation.

We can see that the gaps of the Callendar-Van Dusen equation are limited and are found around 0,05% and 0,1% for higher temperatures.

Advantages and Disadvantages

The major advantages that an RTD has over Thermocouples are: Stability, Precision, and Repeatability. The disadvantages are the price and response time. The following table explains in more detail.

Stability is the ability of a sensor to measure temperature with precision for a given length of time.

Repeatability characteristics of a temperature sensor represents the ability of the sensor to keep the same physical behaviour for any give temperature even though it has been used and exposed to different temperatures. In other words, it's ability to conserve it's stability even after many heating and cooling cycles.

Precision and Tolerances (Compared to Thermocouples)

Download our bilingual document in Excel format.