1. Background Information
Monitoring temperature is a widespread and common engineering task. Whether in a laboratory or factory, performing accurate, high-resolution, temperature measurements can be difficult and expensive. Most commonly, a simple thermocouple is used along with a data acquisition device and some kind of signal conditioning hardware, like the NI SCXI platform. This type of data acquistion system provides fast sample rates and high channel counts. For applications that require high-accuracy and high-resolution, you should consider using a digital multimeter, such as the new NI PXI-4071 7½-Digit FlexDMM,with the high-channel multiplexing capabilities of an NI PXI Switch module. This whitepaper will explain how to implement this high performance temperature measurement system utilizing both thermocouples and Resistive Temperature Devices (RTDs).
With the complexity of such systems it can become difficult understanding system accuracy, resolution, and rate of most temperature measurement solutions. Every temperature measurement application has different performance requirements and it is important to know exactly what errors exist in your system and how your resolution is being affected by noise. Even more useful is the ability to customize your measurement settings to tune your system to your specific accuracy, resolution, and sampling rate needs.
Therefore, this document will provide an in-depth explanation on calculating the accuracy, resolution, and reading rate for these systems. In the process, this document will provide clarity into what errors are most significant, how to minimize those errors, and how to determine the most cost-effective solution.
System Accuracy: It is important here to distinguish between system accuracy and measurement accuracy. While many products on the market will claim extremely high measurement accuracy, this is often simply the accuracy, or amount of error, in the actual measurement device, in our case the digital multimeter or DAQ device. However, this specification often leaves out the error involved with other components of the system like the temperature sensor itself, the cold junction compensation (CJC) sensor, any cabling, SCXI hardware, or Switch hardware. It is important to know how to calculate the actual system accuracy, which is a combination of all these errors, so you can determine the true tolerance on your final temperature reading.
System Resolution: This is the smallest detectable change in temperature that a system can detect. For example, the NI 4071 FlexDMM has the capability of returning a 1 uV resolution in the 10V range. This is equivalent to 7½ digits of resolution, but is dependent on a completely noiseless signal. Similar to system accuracy, the system resolution, or effective resolution, will depend on the level of noise and error in the signal due to the source, the cabling, and any other components in the system. This document will show you how to benchmark the effective resolution of your final temperature reading using an example VI.
System Reading Rate: The system reading rate is the number of total temperature measurements you can perform per second. This sampling rate therefore determines how quickly your system can react to a change in temperature. As a rule of thumb, there is always a tradeoff between sampling rate and accuracy and resolution. As you attempt to maximize the accuracy and resolution of your measurements by minimizing the amount of error in your system, you will inevitably reduce the reading rate. Even so, being able to benchmark your actual system reading rate is necessary to ensure that you are meeting your specific application requirements.
Sensor (Thermocouple vs. RTD)
The importance of the temperature sensors themselves in any thermal system is often overlooked. It is extremely important to understand the role of sensors in your system since and what error they may introduce into the system. We will therefore address the important differences between the two most common industrial temperature sensors, thermocouples and RTD’s. Your choice of sensor may play a large role in how cost effective the system becomes.
Thermocouples are by far the most widely used type of temperature sensor in industry. Extremely rugged, they can be used from sub-zero temperatures to temperatures over 4000 degrees Fahrenheit. A thermocouple takes advantage of the voltage induced between two different metals as they are heated. This document will not go into all the specifics on this topic. For more detail on how thermocouples and RTDs work, refer to whitepapers located in the online National Instruments Sensor Fundamentals Series.
It is important to keep in mind how thermocouples work. By connecting any thermocouple to a measurement device, you are in fact creating three dissimilar metal junctions in your circuit: the thermocouple junction itself, or hot junction, and the junctions between each lead and your measurement device, or cold junctions. These cold junctions produce their own thermoelectric voltages that are proportional to the temperature at your device terminals. A technology known as cold junction compensation (CJC) is therefore used to remove this unwanted effect. CJC essentially uses a direct-reading temperature sensor (usually a thermistor) to measure the cold-junction temperature, and then adds the appropriate value to the measured voltage to eliminate these ‘parasitic’ thermocouple effects.
Understanding how cold junction compensation works is important because the error introduced by your CJC sensor compounds any error already existent in your measurement. When calculating the system accuracy, you will see that this error can be significant and should be considered.
RTD’s on the other hand do not require a CJC sensor since there is no thermo-electric voltage produced at the leads. Accordingly, no additional error is introduced. In general, RTD’s are considered ‘precision’ temperature sensors. RTD’s are also typically more accurate than thermocouples and will maintain that accuracy over a longer period of time. The technology behind RTD’s is also discussed in further detail in the Sensor Fundamentals Series.
First and foremost, it is important to note that RTD’s are not subject to the cold junction effect, instead they are effected by a different error inducing problem called lead wire resistance. Lead wire error is most prominent when using a 2-wire RTD. When reading from a 2-wire RTD, you are actually measuring the resistance of the two connecting wires as well as the temperature sensitive resistor itself. Since RTD’s have such a low nominal resistance, the extra resistance in the lead wires can be significant and can easily cause measurement errors over 1%. The important difference with thermocouples here is that this lead wire effect can be removed without having to introduce another sensor that will add error to the system. Through the use of 3-wire or 4-wire RTD’s, hardware can measure the lead wire resistance and automatically remove it from the measurement for you. In essence, the lead wire effect can be removed for no effective cost in accuracy. How this is done exactly, along with schematics, is further detailed in the RTD example found on page 12 of this document.
There are several other application specific advantages and disadvantages between RTD’s and thermocouples which are summarized in the following table. It is important to take all of these into consideration before deciding on a specific temperature sensor.
|Thermocouple||· Simple and rugged
· Widest operating range
· Fastest response to temperature change
· No resistance lead wire problems
|· Least stable, least repeatable
· Low sensitivity to small temperature changes
· Lowest accuracy
· Requires CJC which introduces more error into the system
|RTD||· Most stable over time
· Most accurate
· Most repeatable
· Very resistant to corrosion/contamination
· No CJC required
|· Higher cost
· Slower response time
· Sensitive to vibration
· Decalibration if used beyond sensor’s temperature range
2. How-to Guide for Performing Temperature Measurements and Benchmarking Your System
The remainder of this document will explain how to set-up and program a digital multimeter and switch temperature measurement system using both a thermocouple and an RTD. You will also learn how to benchmark the system resolution, reading rate, and how to calculate the entire system accuracy. For all of our examples we will use an NI PXI-4071 FlexDMM and an NI PXI-2503 Switch along with an NI TB-2605 terminal block.
Figure 1. PXI-4071, PXI-2503 with TB-2605, and three RTD’s installed
in a PXI-1042 Chassis with a PXI-8187 embedded Controller.
We will also be examining and utilizing several example VI’s which are available for download along with this document in the NI Developer Zone.
3. Example 1: Thermocouple-Based System
For this example we selected a J-type thermocouple. J, K, T, and E-type thermocouples are the most commonly used in industry. Many online resources will guide you through the qualities and use-cases of each type. For example, the J-type thermocouple has an iron positive conductor, a copper-nickel alloy negative conductor, and an operating range of 0-750 degrees Celsius.
Using NI LabVIEW and the latest instrument driver software, you can quickly develop a digital multimeter and switch system to accurately measure thermocouples. The “Maximizing Thermocouple Accuracy.vi” has been created as a guide to help you get up and running quickly. In examining this VI, notice there are two main command threads, one to control the digital multimeter, and one to control the switch. You will also notice that no scan list was setup and that all the channel changes on the switch were performed manually. By manually connecting and disconnecting switch channels, error due to switch debounce and thermal EMF can be minimized. Since the example application is only measuring one thermocouple and it is more concerned with accuracy than reading rate, connecting and disconnecting each channel is not too cumbersome. The general programming flow for this program is documented in more detail on the block diagram of the VI.
Figure 2. Front Panel of Maximizing Thermocouple Accuracy.vi
Figure 3. Portion of the Block Diagram of Maximizing Thermocouple Accuracy.vi
Notice also in this example that the digital multimeter is configured to all the default settings for 7½ digit resolution. This will automatically enable Auto Zero, ADC calibration, set DC Noise Rejection to High-Order, and maximize the Aperture time. Since high levels of accuracy and resolution are the end goal, these settings are acceptable. However, using the assortment of powerful NI-DMM configuration VI’s, it is simple to customize and tweak these settings to achieve the desired balance of accuracy, resolution, and reading rate.
Benchmarking Thermocouple System Resolution
Unfortunately, configuring a digital multimeter to perform at 7½ digits of resolution does not ensure an effective resolution of the same precision. All measurement device specifications base their resolution numbers off a noise-free signal source. In the real world, cabling and electrical connections make noise-free signals extremely rare. Take as an extreme example, a 5V signal that has 1V of noise. Even if your measurement device reads a 1 uV change in the signal, we cannot conclude anything about the value of the original signal. Essentially, our effective resolution is stuck at 1V since the amount of noise masks any smaller changes in the signal. To help calculate the effective resolution of your system, you can now use the new “Resolution Benchmarking.vi”. This program will determine the effective resolution through statistical analysis on the acquired data.
The example below uses this VI to determine the effective resolution of the J-type thermocouple measurement system. Since this is a real world system acquiring actual data, the measurement error will include the noise due to the cabling, connections, switch, and any other source that might be missed in the theoretical-based accuracy calculations. In order to get the most realistic reading, the thermocouple must be hooked up to the digital multimeter through the switch. To do this, use the NI-Switch Soft Front Panel to manually connect your thermocouple to your digital multimeter. In the screenshot below, you can see the VI measuring the DC voltage from a J-type thermocouple in the 100 mV range, with high order DC Noise Rejection, and a desired resolution of 7½ digits.
Figure 4. Measuring the effective resolution of our thermocouple-based system
When trying to find the effective resolution of a system, it is important that the signal itself be as stable as possible. The VI works by statistically analyzing a series of measured points that “should” be the same value. From the amount of variation in the acquired data, the noise within the entire system can be calculated. To achieve this, the thermocouple was placed in a controllable temperature bath, which was held at 27.0. Another alternative is to use a thermocouple calibrator that outputs exact thermocouple voltages for any desired temperature. The statistical analysis is then performed off of the total set of points acquired during the entire program execution, so not only should the measured voltage remain as constant as possible, it is also important to acquire a large set of points to ensure accurate standard deviation calculations.
This example acquires 470 points, with the multimeter resolution set to 7½ digits and utilizes High-Order DC Noise Rejection. By keeping the thermocouple temperature as perfectly stable as possible, it is safe to conclude that any other variation in the signal is due to ambient noise in the system. As a result, the effective resolution of 5.56 digits seen in figure 4 was the maximum achievable resolution for the thermocouple system.
This does not limit, however, the possibility of changing the system. By better shielding the connections and cables, especially along the length of the thermocouple wire, you can reduce the noise being produced, thereby improving the maximum effective resolution. Decreasing cable length between system components can also help. Keep in mind that this example is simply using the default settings for Auto Zero, ADC Calibration, Aperture Time, and Number of Averages that correspond to the desired resolution indicated. It is possible to tweak your effective resolution by modifying these settings. To do so, simply add in the configuration VI’s necessary and you will be able to directly observe the effects of changing these settings. It is possible to increase the effective resolution by increasing the Number of Averages and Aperture Time, in Power Line Cycles. For more help on how to do this, examine the example “Achieving 7 Digits Resolution.vi” located in the packaged NI-DMM examples folder. On the other hand, to improve reading rate at a slight cost in resolution, changing the Auto Zero and ADC Calibration settings can often be effective.
Calculating Thermocouple System Accuracy
This system is composed of three independent sources of error: the digital multimeter, the switch, and the thermocouple. When calculating system accuracy, it is imperative to include all three components and combine their errors in the correct way. This can be done with the following mathematical formula for compound errors.
To calculate the error introduced by the digital multimeter, reference the DC Accuracy section of the specifications for your specific digital multimeter. More details on how to use the DC Accuracy Specifications chart can be found in the NI-DMM help file.
For this example, the calculation is done assuming:
· A stable 25 temperature to measure
· Use of a J-Type thermocouple
· A digital multimeter operating temperature of 23
· A calibration temperature of 23.8
· A configuration of the digital multimeter in the 100mV range
Using these assumptions; you can calculate the digital multimeter accuracy to be:
This value corresponds to the noise-free accuracy. It is the error introduced internally by the digital multimeter, not including uncertainties introduced by outside sources. Coming back to the “Resolution Benchmarking.vi” you can again measure the real-world noise in the signal and factor that into the accuracy calculations. Re-examine figure 4 and notice that along with measuring the effective resolution, this VI also measures the amount of noise error in parts per million (ppm) of range. This example recorded an additional error of 47.57 ppm of range due to noise. Adding this into the equation for EDMM we get
There are VIs included with Traditional DAQ can be helpful in converting voltages to temperatures and vice versa. These VIs are “Volts to Temperature.vi” and “Temperature to Volts.vi”. Using these VIs, you know that a J-type thermocouple measuring 25should output a 1.277 mV signal. Both of these VI’s are sub-VI’s of the “Convert Thermocouple Reading.vi” available in the Functions >> NI Measurements >> Data Acquisition >> Signal Conditioning palette of LabVIEW 7.1 and earlier. Since the digital multimeter range is known, we can simplify to the following.
Using the same conversion VI’s, you can calculate the error in to be
To calculate the error introduced by the Switch, you can break down in the following way.
where = error due to thermal EMF of the Switch
= error due to the CJC temperature sensor of the Switch Terminal Block
To calculate the error due to thermal EMF, use the following equation which can be found in the NI Switches Help File.
where T = temperature being measured, in
T+1 = T + 1
V = voltage that corresponds to T
V+1 = voltage that corresponds to T+1
= thermal EMF of the Switch
To find V and V+1 use the “Temperature to Volts.vi” or you can also use thermocouple reference tables. To find VEMF, refer to the Input Characteristics section of the specifications for your Switch.
In the example situation, you find
* It is important to note here for the NI PXI-2527 Switch, values for VEMF can be much higher, ranging up to 12 uV. To ensure a thermal EMF of only 2.5 uV, power down the latching relays of the NI PXI-2527 after every switching action. This is done using a property node and is shown in the thermocouple example, “Maximizing Thermocouple Accuracy.vi”.
To find the error due to the CJC sensor, refer to the Cold Junction Temperature Sensor section of the installation guide for your terminal block. In this example , the terminal block is operating in the 15 to 35 range, so:
You can now calculate the total error introduced by the switch to be
Of obvious interest at this point should be the fact that the largest source of error so far is the error due to the CJC sensor. As mentioned earlier, it is one of the limiting factors of using thermocouples.
Lastly, to calculate the error introduced by the thermocouple, refer to the specifications provided by the manufacturer of your specific sensor. For almost all manufacturers, two values will be given for thermocouple error: a temperature range or a percent of the measurement. The actual thermocouple error is the greater of these two values.
In this example, a standard grade J-type thermocouple is used to measure 25 °C. The error for a standard grade J-type thermocouple is ±2.2 °C or ±0.75% of the measurement temperature. Because ±0.75% of 25 °C (± 0.1875 °C) is less than ±2.2 °C, the error of a standard grade J-type thermocouple is ±2.2 °C.
Now that errors introduced by each of the three independent components of the system are known, you can combine them to find the total system accuracy. To do this, plug the error found in the digital multimeter, switch, and thermocouple into the original independent errors equation.
(for a 25measurement)
Benchmarking Thermocouple System Reading Rate
Unlike accuracy, the system reading rate is dependent on other components of the system. It is determined by the slowest, or most limiting, component. Since the goal of this document is to maximize accuracy and resolution, reading rate will be sacrificed, therefore making the digital multimeter the limiting factor in determining the system reading rate. You can therefore look solely at the measurement period of the digital multimeter when benchmarking. To do this, take advantage of simulation and the niDMM “Get Measurement Period” function. This function will benchmark your measurement period under any unique configuration, allowing you to experiment with modifying the default configurations for Auto Zero, ADC calibration, settling time, and aperture time, examining immediately their direct effects on sampling rate. For more detailed information on how to benchmark the reading rate of your digital multimeter, refer to the following NI Forum Post on Simulating and Benchmarking DMM’s.
After building and programming a temperature measurement system utilizing an NI-PXI 4071 FlexDMM, an NI PXI-2503 Switch, and a J-Type thermocouple, there are several important conclusions that can be made. First and foremost, the limiting effect of using a thermocouple as your temperature sensor has become quite evident. This is most obvious in our accuracy calculations. The relatively small errors introduced by the digital multimeter and switch, and respectively, become very small when combined with the error due to the thermocouple. In essence, the high-accuracy capabilities of the digital multimeter are not taken advantage of when using a thermocouple temperature sensor. Similarly, due to inherent signal noise, the maximum effective resolution for a thermocouple system is approximately 5½ digits. While steps can be taken to improve this value slightly, ambient noise in the system and thermocouple wire will always prevent effective resolutions approaching 7½ digits in which the PXI-4071 FlexDMM is capable of measuring. In conclusion, when implementing a DMM/Switch, high-accuracy, high-precision temperature measurement system, a thermocouple is an ineffective choice of sensor.
4. Example 2: RTD-Based System
Now that we have looked at the drawbacks of using thermocouples, it is important to look at other solutions that may take advantage of the low error and low noise characteristics of a switch and digital multimeter. The most common alternative to thermocouples is an RTD. The tools and techniques outlined in the previous section for benchmarking and analyzing the system accuracy, resolution, and reading rate can still be applied.
For this example, an industry standard, 3-wire Platinum RTD produced by Watlow will be used. While 4-wire RTD’s are the most accurate, 3-wire RTD’s are the most common and readily available. This presents a common, but slightly interesting problem. The NI PXI-4071, like most high-end digital multimeters, performs both 2-wire or 4-wire resistance measurements. So how do you perform a resistance measurement on a 3-wire RTD? You simply jumper the 4th wire connection to one of the other wire connections. While this sounds simple, it is important to understand how 4-wire resistance measurements are made so that you jumper the right two wires. Additionally, this ‘quick-fix’ is not as ideal as performing a 4-wire resistance measurement on a 4-wire RTD. Understanding why will let you explore some other options to improve the accuracy of a 3-wire RTD.
When performing any resistance measurement, a digital multimeter is required to perform two main functions. It needs to supply an excitation current, IEX, as well as measure the actual voltage drop, Vo, across the temperature sensitive resistor. When performing a 4-wire resistance measurement, these two functions are effectively independent. In doing so, the connection places the leads on a high impedance path through the measurement device, thereby removing the lead wire resistance. The following diagram illustrates a theoretical 4-wire setup.
Figure 5. Typical 4-wire resistance measurement
To use a 3-wire RTD in this configuration, you simply jumper the negative end of the current excitation connection to the negative end of the voltage measurement connection, essentially creating the following setup.
Figure 6. 4-wire resistance measurement of a 3-wire RTD
In doing so, you are able to eliminate any lead wire resistance due to RL1 and RL2. Unfortunately, some lead wire effect due to RL3 will still be encountered.
One way to manually remove the lead wire resistance due to RL3 and achieve the most accurate reading possible is to perform a separate 2-wire resistance measurement across the loop created by RL1 and RL2. Divide this resistance value by two and you get the approximate value of RL2. If we make the assumption that RL2 RL3, then you can subtract this value from every measurement, effectively eliminating all the lead wire resistance. If RL2 does in fact equal RL3, then it is possible to come very close to the accuracy of a 4-wire RTD.
Another common method to manually remove lead wire resistance requires only 2-wire resistance measurements and is often used with lower end digital multimeters that cannot perform 4-wire resistance measurements. To use this method, first read the 2-wire resistance across the loop created by RL1 and RL2. Now read the 2-wire resistance across the loop created by RL2, RT, and RL3. Making the same assumptions as before, that RL1 RL2 RL3, then subtract the first measurement, not-including RT, from the second measurement, with RT. You therefore end up with just the resistance of the RTD. It is important to reiterate that these methods are dependent on the validity of the assumptions, which can sometimes be incorrect depending on the manufacturer of your RTD. As a result, 4-wire resistance measurements on a 4-wire RTD will always be the most reliable and best solution.
The pin diagrams for your switch when in 4-wire mode can be found in the NI Switches Help document. To connect the 3-wire Platinum RTD through our PXI-2503 Switch to our PXI-4071 DMM, we made the following connections.
Note that the positive and negative pins for CH1A perform the current excitation, and the positive and negative pins for CH1B perform the voltage measurement. This is important because when you make your jumper connection you must connect one lead from the current excitation connection to the same sign lead from the voltage measurement connection. Therefore place a jumper wire between CH1A+ and CH1B+. Connecting CH1A+ to CH1A- or CH1B+ to CH1B- will cause a short that will prevent the digital multimeter from being able to measure the RTD itself. When creating this jumper wire, it is also a good idea to keep it as short as possible. If you’re jumper wire is too long, you can cancel out the lead wire resistance removed by introducing further lead wire resistance.
Programming the devices to control and measure an RTD is again extremely simple when utilizing LabVIEW and the latest driver software. To illustrate how to perform high-accuracy RTD temperature measurements, examine the new “Maximizing RTD Accuracy.vi”.
Figure 8. Front panel of “Maximizing RTD Accuracy.vi”
Figure 9. Block diagram of “Maximizing RTD Accuracy.vi”
This VI utilizes two main command threads, one for controlling the digital multimeter and one for controlling the Switch, which is very similar to the way the “Maximizing Thermocouple Accuracy.vi” works. Notice however, that this VI is significantly simpler and shorter than the VI needed to make accurate measurements on a thermocouple. This is largely due to the fact that no CJC sensor needs to be read. Therefore, only two manual switch connections are made and then the digital multimeter can continuously perform measurements without having to worry about error due to switch debounce or timing. In this example, manually removing the lead wire resistance due to RL3 is not being done. This is because the lead wire resistance due to RL3 was found to be negligible in this setup. Keep in mind that this is largely due to the short wire length between the RTD and Switch. Extending the length of these wires will increase RL3 and eventually require more steps to maintain a high level of accuracy.
* Note: The “Convert RTD Reading.vi” used in this example has been modified from the shipping VI found in the Functions >> NI Measurements >> Data Acquisition >> Signal Conditioning palette. It has been changed to take as an input, the actual RTD resistance value, as opposed to the voltage drop, Vo, and excitation current, IEX. This allows you to wire in directly the value from the 4-wire resistance measurement.
Benchmarking RTD System Resolution
Returning to the example program, “Resolution Benchmarking.vi”, you can again measure the effective resolution of the RTD-based system. In this case, configure the VI for a 4-wire resistance measurement, in the 1.00k Ohm range, with High-Order noise rejection, and a desired resolution of 7½ digits. Use a controllable temperature bath again at 27 to keep the temperature reading as stable as possible, and acquire approximately 400 points. As you can see in figure 10, the measurement system is able to achieve an effective resolution of 7.06 digits.
Figure 10. Measuring the effective resolution of our RTD-based system
Compared to the thermocouple-based system, this is a huge improvement in the effective resolution. This indicates that the signal from the RTD itself is inherently more stable (less noise) than the signal from the thermocouple. Still, the noise in the cabling, switch and electrical connections continues to exist, and you can see this slightly limiting the effective resolution. While you are still not achieving the full 7½ digit potential of the PXI-4071, unprecedented levels of effective resolution are achievable.
Calculating RTD System Accuracy
Once again, there are three independent errors introduced by the digital multimeter, the switch, and the RTD. To calculate accuracy, use the following equation.
Look again at the specifications document of your digital multimeter and now examine the Resistance (4-Wire and 2-Wire) accuracy table. When in the 1 k range, and within the 2 year calibration window, we find the base error introduced by the PXI-4071 digital multimeter to be:
From figure 9, you can see that the real world noise introduced by the system in ppm of range is so small that it is negligible. This is due to the much higher level or repeatability in RTD’s when compared to thermocouples. Using the “Convert RTD Reading.vi” found in the referenced example, a reading value of 110.564, and a range of 100 k, you can simplify the error caused by the digital multimeter to
When previously calculating the error due to our switch, the sum of the errors due to the CJC sensor and due to thermal EMF was used. With the RTD based system, you do not need to reference the CJC sensor of the Switch terminal block, so
To include the error due to thermal EMF in the switch, you need to first convert the resistance measurement into a voltage. To do this, you need the excitation current, or test current, being used in the 4-wire resistance measurement. For the 4071 this can be found on the Resistance (4-Wire and 2-Wire) accuracy table. Under the 1 k range, the 4071 uses a test current of 1mA.
*Note that there is a -10% to 0% tolerance on the test current value. For the purposes of this paper 1mA will be assumed correct. For a more accurate calculation use a separate DMM to measure the exact value of the excitation current.
With a measured resistance value of 110.564 and a current value of 1mA, you can use Ohm’s law, V = IR, to calculate the voltage drop, , being measured by the digital multimeter.
Referring to the Input Characteristics section of the specifications for the 2503 Switch, you will find that VEMF is 2 uV. You can therefore write including the error due to thermal EMF as
Using Ohm’s law again, calculate back into resistance values and you can calculate the error due to thermal EMF, in terms of resistance is actually
Using the “Convert RTD Reading.vi”, you find that:
Lastly, to calculate the error introduced by the RTD, refer to the specifications provided by the manufacturer of the RTD. Using Watlow’s Platinum RTD DIN Class A tolerance definition, it follows that
where t is the temperature being measured. From a 25measurement, you can quickly calculate that
Combining the three independent errors found in the digital multimeter, Switch, and RTD, you can compute the total system accuracy to be
Benchmarking RTD System Reading Rate
When performing high accuracy, high resolution measurements, the limiting factor in system reading rate will continue to be the measurement period of the digital multimeter. As explained above in the thermocouple system, the system reading rate can therefore be calculated using the niDMM “Get Measurement Period” function.
Keep in mind that by lowering the desired resolution, the measurement period is shortened, thereby allowing faster reading rates. Eventually, since RTD’s have a slower response time than thermocouples, they will start becoming the limiting factor in system reading rate. Remember that by increasing reading rate you are also sacrificing resolution and accuracy which negates the benefits of using an RTD.
The advantages to using an RTD in a DMM/Switch based temperature measurement system have been shown. A dramatic increase in actual system resolution and system accuracy clearly indicate the benefits of using an RTD over a thermocouple in any high-accuracy, high-precision system. This is demonstrated by a decrease in total error of and an increase in system resolution of over 1½ digits. Additionally, it is easier to program an RTD based system since it is not necessary to switch to, and measure a CJC sensor. In summary, despite the increase in price, when designing a high-accuracy, high-precision temperature measurement system, RTD’s are much more cost-effective than thermocouples, but are still easy to use, reliable, and durable.
5. Final Recommendations
When designing a temperature measurement system, it is absolutely necessary to know your desired performance characteristics. In situations demanding high accuracy and high resolution, this document has proven that it does not help to upgrade only one side of your system. Due to the nature of compounding errors, the capabilities of high end digital multimeters will be lost when used in conjunction with low-accuracy sensors like thermocouples. An RTD, along with other high-accuracy sensors not discussed in this paper, can be an acceptable replacement, preserving the high-accuracy levels of your digital multimeter and Switch. This is especially true when utilizing some of the unique features of the NI PXI-4071 like 4-wire resistance measurements and Offset Compensated Ohms (OCO). On the other hand, if you are designing your system for high reading rates, but lower levels of accuracy and resolution, thermocouples coupled with a DAQ and SCXI based system continue to present a very competitive solution. Once the principles, calculations, and factors behind system accuracy, system resolution, and system reading rate, are fully understood, designing a temperature measurement system with the desired performance and full knowledge of how the system will perform.
High Performance Modular Instruments
Measurement Fundamentals Tutorial Series
NI Temperature Measurement Solutions
National Instruments Digital Multimeters (DMMs) and LCR Meters
National Instruments Switches
Low-Level Measurement Resources