Finding Your Balance
Errors related to cable resistance imbalance in three-wire RTDs can be minimized.
Many sources of error exist in process applications, and they can impact the accuracy of a resistance temperature detector (RTD) measurement. The cable incorporated into the sensor can cause a significant error.
This article presents an analysis of cable resistance imbalance in three-wire RTDs, with emphasis on the errors that affect the accuracy of the temperature measurement. Guidance and techniques are given for minimizing the magnitude of these errors.
RTDs are temperature sensors that use the predictable change in electrical resistance of a material (typically, platinum) with changing temperature. To provide a practical temperature measuring instrument for process applications, it is necessary to attach extension leads to the platinum sensing element. If not properly selected for the application, the number and type of extension leads used can introduce significant errors into the temperature measurement (figure 1).
Two-Wire RTD. The two-lead-wire circuit has no mechanism to compensate for or eliminate the resistance of the lead wires from the resistance of the element. The two-lead wire design is only useful when the extension lead resistance is insignificant compared to the sensing element resistance. Two examples of this are applications where the leads are very short, or the sensing element resistance is large.
Three-Wire RTD. The three-wire configuration provides a compensation loop that can be used to subtract the lead wire resistance from the resistance measurement of the element loop, resulting in a value for just the element resistance. As will be shown, achieving an accurate measurement with this method is predicated on the resistance of each of the leads being exactly equal. Unfortunately, this is seldom the case, and steps must be taken in the design and application of a three-wire sensor to maintain the accuracy of the measurement.
Four-Wire RTD. The method that offers the highest accuracy temperature measurement is the true four-wire design. A sensor circuit with two wires on each side of the element allows for a measurement current to be passed across the element via two of the leads and a voltage measurement to be taken through the other two leads. The resistance then is calculated using Ohm’s law (V = IR or R = V/I). The impedance of the meter taking the voltage measurement is sufficiently high to prevent any current that is flowing through the leads from being used for the voltage measurement. The current flowing through the other two leads and the element is the same throughout the circuit. Measuring the voltage across the element and dividing it by the known current yields just the resistance of the element.
Unfortunately, it is not always practical or feasible to use the four-wire method. Instead, often the method selected is the three-wire method.
Three-Wire Measurement Theory
Essentially, to provide a three-wire temperature measurement, it is necessary to measure the resistance of the element loop and subtract the resistance of the compensation loop. As shown in figure 2, the resistance of the lead wires and element are in series, so:
RELEMENT Loop = RL2 + EELEMENT + RL3
RCOMP Loop = RL1 + RL2
RELEMENT Loop – RCOMP Loop = (RL2 + RELEMENT + RL3) – (RL1 + RL2)
RL1 = RL2 + RL3
Then, the lead resistances cancel out and
RELEMENT Loop – RCOMP Loop = RELEMENT
In practice, however, the theoretical assumption that
RL1 = RL2 = RL3
is rarely true. Within any set of wire, there is always some difference in these values. This imbalance results in the residual difference between the three values being included in the measurement of RELEMENT, resulting in an offset in the element resistance and, therefore, in the resulting temperature measured.
Typically, the sensor manufacturer will use one lead color for RL3 and another lead color for both RL1 and RL2. (In other words, RL1 and RL2 will be the same color.) If the resistance imbalance is large between RL1 and RL2, then depending on which way these seemingly interchangeable leads are connected to the readout in the field, a significant error can result in the temperature measurement.
Sources of Cable Resistance Imbalance
The resistance of a conductor (R) is based on the formula:
R = ρ x L/A
where ρ is resistivity, a constant for a particular material at a particular temperature (? ft). L is the length of the conductor (ft). A is the cross-sectional area of the conductor (ft2).
As the length increases or the diameter decreases, the resistance of the conductor increases.
To maintain flexibility, cables usually are manufactured from multiple drawn strands of thin wire that are twisted together to form a conductor of the correct diameter for the particular wire gauge size. The bare twisted strand conductor then is insulated. Several insulated conductors are twisted together to form the cable, then an insulating, protective jacket is applied over the twisted conductors.
Each these cable manufacturing steps involves de-reeling the wire, passing it through a series of tensioning pulleys through the process, and then spooling it back onto another reel before it goes to the next step. This processing of the wire, despite the best efforts of the cable manufacturers, causes the conductors to stretch. The stretching of the cable results in a reduction in cross-sectional area and an increase in cable resistance. From lot to lot, it is difficult to consistently control the stretching.
Typically, the conductors that make up the cable come from different production runs. Ultimately, when the different conductors are brought together to form the cable, they have slightly different cross-sectional areas although they are each still within the standard for the gauge size. These slight cross-sectional variations result in an imbalance in their resistances.
In addition, in the case of copper conductors, the copper typically is plated with silver or nickel to improve corrosion resistance. The overall resistance of the conductor is a function of the resistivity of the two materials and their corresponding cross-sectional areas. Unfortunately, thickness control in the plating process is difficult. Any variation in the thickness results in a variation in the cross-sectional area. When the resistivity of the plating material is high, this problem is exacerbated.
Nickel is a common plating material used for copper conductors and has a much higher resistivity than the copper. So, a variation in thickness of the nickel results in a larger variation in the resistivity of the conductor.
Another common plating material for copper is silver, which has a lower resistivity than nickel. Any variation in the thickness of the coating of the silver has much less of an effect on the conductor resistivity compared to what a similar variation in nickel plating would have. Silver plating is not a miracle cure for resistance, however. There are cost, corrosion and temperature constraints that have to be considered when selecting silver rather than nickel.
For applications where circuit resistance is not important to the function, the imbalance in the cable’s conductors is not significant enough to cause a problem. The ASTM standards only specify the cross-sectional area of the conductor and the plating thickness. Yet the variation allowed in the standards yields a range in wire resistance greater than the three-wire RTD compensation method can accept. Most cable manufacturers are able to do much better than what the ASTM standards dictate.
Methods to Mitigate Errors from Cable Imbalance
Steps can be taken to mitigate the problem of cable imbalance in a three-wire RTD. Typically, some compromise needs to be made in order to reduce the effect of cable imbalance. There are several options.
Switch from a Three-Wire Sensor to a True Four-Wire Sensor. A true four-wire measurement negates any effect of lead wire resistance; thus, it will always give a superior measurement. It is not always possible to switch to a four-wire configuration. Sometimes, due to space constraints in the probe, or because the existing control or meter infrastructure is configured for three-wire sensors, the option is not available.
Increase the Cable Gauge. For a three-wire measurement, the cable conductor gauge used should be as large as possible. The larger the cable gauge, the lower the resistance and the lower the imbalance in the conductors in the cable. Unfortunately, space constraints inside the RTD may not allow for a larger cable size in all applications. Even with a larger cable, there will be a cable length at which the possible cable resistance imbalance will result in the sensor being out of its accuracy tolerance.
Splice to a Large Cable Outside the RTD. If space constraints inside the RTD prevent users from incorporating a larger cable size, then a larger cable can be spliced to the small cable outside of the sensor. One drawback to this approach is that in the area of the splice, the cable will be stiffer and have a slightly larger diameter than either of the cables. This may make it difficult to pass the cable through conduit. Also, even with a larger cable gauge in the circuit, there is still a cable length at which the possible cable resistance imbalance will result in the sensor being out of its accuracy tolerance.
Resistance Trim the Cable and Fix the Length. The cable can be balanced by adding a compensation resistance to the appropriate conductors in the cable. Typically, the compensation resistance is added near the end of the cable to keep it away from process temperatures. To maintain the accuracy of the temperature sensor, it is important that the cable is not cut during installation as this will physically remove the compensation resistance and return the cable to its original unbalanced state.
Switch to a Silver-Plated Copper Cable. Switching from a nickel-plated copper to a silver-plated copper cable will allow for longer cable lengths. Unfortunately, silver has a lower temperature rating and does not do particularly well in moist environments.
In conclusion, a high accuracy temperature measurement requires a true four-wire sensor. When the application will not allow this, a three-wire sensor can be used, but the end user should be aware of how the accuracy is potentially being affected by the three-wire circuitry.
Some probe manufacturers do not address the issue of degradation of measurement accuracy with reduced cable gauges or longer cable lengths. However, the cable imbalance issue is always present. By taking into consideration the effects of cable imbalance at the time that a three-wire sensor is specified, and by carefully evaluating and selecting one of the techniques to reduce the effect of cable resistance imbalance, it is possible to produce a three-wire measurement probe that will provide a temperature measurement at the needed accuracy.