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Because of their lower resistivities, gold and silver are rarely used as RTD elements. Tungsten has a relatively high resistivity, but is reserved for very high temperature applications because it is extremely brittle and difficult to work.
Copper is used occasionally as an RTD element. Its low resistivity forces the element to be longer than a platinum element, but its linearity and very low cost make it an economical alternative. Its upper temperature limit is only about 120ºC.
The most common RTD’s are made of either platinum, nickel, or nickel alloys. The economical nickel derivative wires are used over a limited temperature range. They are quite non-linear and tend to drift with time. For measurement integrity, platinum is the obvious choice.
The common values of resistance for a platinum RTD range from 10 ohms for the bird-cage model to several thousand ohms for the film RTD. The single most common value is 100 ohms at 0ºC. The DIN 43760 standard temperature coefficient of platinum wire is α = .00385. For a 100 ohm wire, this corresponds to + 0.385 ohms/ºC at 0ºC. This value for α is actually the average slope from 0ºC to 100ºC. The more chemically pure platinum wire used in platinum resistance standards has an α of +.00392 ohms/ohm/ºC.
Both the slope and the absolute value are small numbers, especially when we consider the fact that the measurement wires leading to the sensor may be several ohms or even tens of ohms. A small lead impedance can contribute a significant error to our temperature measurement.
A ten ohm lead impedance implies 10/.385 ≈ 26ºC error in measurement. Even the temperature coefficient of the lead wire can contribute a measurable error. The classical method of avoiding this problem has been the use of a bridge.
The bridge output voltage is an indirect indication of the RTD resistance. The bridge requires four connection wires, an external source, and three resistors that have a zero temperature coefficient. To avoid subjecting the three bridge-completion resistors to the same temperature as the RTD, the RTD is separated from the bridge by a pair of extension wires:
These extension wires recreate the problem that we had initially: The impedance of the extension wires affects the temperature reading. This effect can be minimized by using a three-wire bridge configuration:
If wires A and B are perfectly matched in length, their impedance effects will cancel because each is in an opposite leg of the bridge. The third wire, C, acts as a sense lead and carries no current.
The Wheatstone bridge shown in Figure 41 creates a non-linear relationship between resistance change and bridge output voltage change. This compounds the already non-linear temperature-resistance characteristic of the RTD by requiring an additional equation to convert bridge output voltage to equivalent RTD impedance.
4-Wire Ohms - The technique of using a current source along with a remotely sensed digital voltmeter alleviates many problems associated with the bridge.
The output voltage read by the dvm is directly portional to RTD resistance, so only one conversion equation is necessary. The three bridge-completion resistors are replaced by one reference resistor. The digital voltmeter measures only the voltage dropped across the RTD and is insensitive to the length of the lead wires.
The one disadvantage of using 4-wire ohms is that we need one more extension wire than the 3-wire bridge. This is a small price to pay if we are at all concerned with the accuracy of the temperature measurement.
3-Wire Bridge Measurement Errors
If we know VS and VO, we can find Rg and then solve for temperature. The unbalance voltage Vo of a bridge built with R1 = R2 is:
If Rg = R3, VO= 0 and the bridge is balanced. This can be done manually, but if we don’t want to do a manual bridge balance, we can just solve for Rg in terms of VO:
This expression assumes the lead resistance is zero. If Rg is located some distance from the bridge in a 3-wire configuration, the lead resistance RL will appear in series with both Rg and R3:
Again we solve for Rg:
The error term will be small if Vo is small, i.e., the bridge is close to balance. This circuit works well with devices like strain gauges, which change resistance value by only a few percent, but an RTD changes resistance dramatically with temperature. Assume the RTD resistance is 200 ohms and the bridge is designed for 100 ohms:
Since we don’t know the value of RL, we must use equation (a), so we get:
The correct answer is of course 200 ohms. That’s a temperature error of about 2.5ºC.
Unless you can actually measure the resistance of RL or balance the bridge, the basic 3-wire technique is not an accurate method for measuring absolute temperature with an RTD. A better approach is to use a 4-wire technique.
Resistance to Temperature Conversion
The RTD is a more linear device than the thermocouple, but it still requires curve-fitting. The Callendar-Van Dusen equation has been used for years to approximate the RTD curve:
The exact values for coefficients α , β, and δ are determined by testing the RTD at four temperatures and solving the resultant equations. This familiar equation was replaced in 1968 by a 20th order polynomial in order to provide a more accurate curve fit. The plot of this equation shows the RTD to be a more linear device than the thermocouple.