The Care and Feeding of Thermocouples
AST Conference Presentation, October 1999
By: Richard D. Smith, P.E.
The purpose of this document is to give the reader a better understanding of how and why thermocouples work. In so doing, it will help to identify and resolve the most common forms of thermocouple measurement and set-up errors. This includes common and potentially destructive ground looping, and misapplication and placement of thermocouples on the DUT (Device Under Test).
Thermocouples work on the Seebeck effect (1821). Mr T. J. Seebeck found that if you take two dissimilar metals and form a closed loop, if one junction is kept at a different temperature than the other junction, a small current exists in the loop. This current is related to the temperature difference between the two junctions. It is a common misconception that the thermocouple voltage is caused only by the temperature at the measuring junction. If one junction is kept at a known temperature, the temperature of the other junction can be determined from the amount of voltage produced. As the temperature difference increases, the current in the closed loop increases. The thermocouple voltage, although very predictable for a given thermocouple type, is non-linear. The change in junction voltage as a function of junction temperature is:
D V = a * D t
where 'a' is the Seebeck coefficient.
The Seebeck coefficient (a) depends on the two different metals used, and the temperature. In general, a is smaller at lower temperatures and increases as the temperature increases. Depending on the metals used, this coefficient can vary as much as a factor of two (2) over the useful operating range of the thermocouple. The tabulated published values for any given thermocouple type are always referenced to 0°C, i.e., the other junction (measuring junction) is at 0°C. The National Bureau of Standards accepted thermocouple approximation method is defined as wire behavior following a specific nth order polynomial for the appropriate thermocouple type. The coefficients for the type-T model are listed at the end of this paper.
The Law of Homogeneous Circuits says simply that if the thermocouple conductors are homogeneous, they are unaffected by intermediate temperatures. This is why the length and routing of the thermocouple wire (within reason and with some restrictions) can be set up not to effect the temperature measurement. This is also why you must use thermocouple extension wire, not regular wire, for long thermocouple runs.
The Law of Intermediate Metals says that if there is a third metal introduced into the thermocouple circuit, it will not adversely effect the reading if and only if the two junctions of the third metal are at the exact same temperature. Remember that the Seebeck effect requires that the junctions be at different temperatures to induce a current. If the two connecting junctions of the third metal are not exactly at the same temperature, non-linear errors will occur from this second thermocouple. If, for example, you solder (Tin-Lead) the leads of the thermocouple and the two metals touch only through the solder, as long as the soldered section is all at the same temperature, the solder will have no effect. If, however, the soldered area is relatively lengthy and in a high thermal gradient area where the temperature changes rapidly with very small distances, temperature readings will be significantly effected by this second thermocouple.
NOTE: The connection point of the thermocouple wire to the measuring instrument is another thermocouple and must be accounted for in the final measurement.
Although any two dissimilar metals will form a thermocouple, the idea behind the "standard" thermocouple types is to have a large, stable, well defined Seebeck coefficient (a). The standard error associated only with the standard thermocouple wire is from ± 0.8°C to ± 4.4°C. (There are also other sources of error which will be discussed later.) There are several types of thermocouples with well defined properties, all of which are designated with a single letter. The standard types are: J, K, T, E, R, S, and B. Their components and properties are in the following table:
|
T/C Type |
B |
E |
J |
K |
R |
S |
T |
|
+ Material |
Pt / Rh(30%) |
Ni / Cr |
Ni / Cr |
Fe |
Pt / Rh(13%) |
Pt / Rh(10%) |
Cu |
|
- Material |
Pt / Rh(6%) |
Ni / Cr |
Cu / Ni |
Ni / Al |
Pt |
Pt |
Cu / Ni(45%) |
|
+ color |
Grey |
Purple |
White |
Yellow |
Black |
Black |
Blue |
|
- color |
Red |
Red |
Red |
Red |
Red |
Red |
Red |
|
Lowest Temp |
+50C |
-200C |
0C |
-200C |
0C |
0C |
-200C |
|
Highest Temp |
+1700C |
+900C |
+750C |
+1250C |
+1450C |
+1450C |
+350C |
|
Minimum Standard Error |
±4.4C |
±1.7C |
±2.2C |
±2.2C |
±1.4C |
±1.4C |
±0.8C |
Since the environmental chambers typically run from about -100
°C to +200°C, the obvious choice is type-T (Copper and Constantan). This gives the largest span over the desired operating range, with the least inherent minimum error.All thermocouples generate very small voltages. The voltage generated at the hot junction ranges from a low of –3.379 mili-volts at -100°C to +9.288 mili-volts at 200°C. This means that the entire span of 300°C represents only 12.667 mili-volts total, or 0.012667 volts. Keep in mind that a standard fluorescent light can produce more than twice as much voltage noise as this full scale voltage. Even a small induced voltage in the thermocouple lead will have a significant impact on the "temperature" measured.
All thermocouple systems have "cold junction compensation". This is required because the terminal connection points of the thermocouple wire also form thermocouples, i.e., two dissimilar metals. With type-T thermocouples, the Copper to Copper terminal strip connection has no effect, but the Constantan to Copper terminal strip connection is another thermocouple junction. This extra junction must be backed out of the voltage reading at the Copper side of the connection point. This is done by automatically measuring the temperature at the terminal strip, or cold junction, and applying the appropriate compensation to the voltage reading.
The measured voltage out of the op amp is actually (V1-V2) when what is desired is V1 only. By measuring the temperature at the terminal strip, V2 is known and can be added back to the measurement.
III. Measuring Junction- how to make a thermocouple
The measuring junction is the point at which the Constantan and Copper metals touch. Making a thermocouple is fairly easy and requires minimal tools. Ideally, this end point is as small as possible. In practice, the ends are twisted together and soldered, after being cleaned with Alcohol. If the end is soldered, caution must be exerted to ensure that the Constantan and Copper are in direct contact. The twisting should be of sufficient length to make sure that the poor solderability of the Constantan does not form an incomplete or mechanically unsound connection. The temperature measuring point is effectively at the last twist where the wires separate, not from the end of the wire. If the twisting is too long, the temperature location actually measured may not be physically where the desired measuring point at the end of the wire is located. It will be a combination of the conducted thermal energy from the point of contact and the ambient in the area of the twist separation.
Soldering, or silver soldering the thermocouple limits the useful upper temperature because of the re-liquefaction of the solder. If higher temperatures than the melting point of the solder used are needed, then welding should be considered. Welding a thermocouple is not a trivial process. Because of the different materials, the wires melt at different temperatures. Over heating can easily degrade the wire. If a torch welder is used, the welding gas and the atmosphere in which the thermocouple was welded can diffuse into the thermocouple metal, changing its characteristics.
IV. Induced Voltages
If the reference junction is soldered to a point on a part such that there is electrical contact with a non-ground DUT (Device Under Test) conductor, the thermocouple must be electrically isolated from the device onto which it is soldered. If this is not true, ground loops and short circuits can occur. The point at which the thermocouple is soldered is grounded through the thermocouple system. If this point is even slightly above ground potential, the ground loop current will severely distort the temperature reading. Excessive ground loop currents can destroy both the DUT and the temperature measuring system. Most labs are set up as a common ground non-isolated system. Soldering the thermocouple to any DUT point except a ground is not a good thing since the thermocouple is referenced to ground.
If Multiple thermocouples are soldered to multiple ground points of a DUT, all the grounds must be electrically connected to each other. If not, they will be connected to each other through the thermocouple system, which again is not a good thing.
All ground connections should be of sufficient ampacity to guarantee that there is no difference in the ground voltage from any ground point to any other ground point regardless of the IR losses through the ground connections. If the grounding conductors are too small, the IR losses through the ground path will cause the "connected" points to be at different voltages. If thermocouples are then connected to these points, sufficient current will flow through the thermocouples to normalize these voltages.
Soldering to ground should also be avoided because multiple grounding points beg for ground loops. We use either a fine coating of SuperGlue (Cyanoacrylate Ester like Eastman #910 or Loctote #495), or Kapton tape (like Permacel #60-232), to electrically insulate the thermocouple. We use SuperGlue, high temperature glass cloth electrical tape (like Scotch #27), and / or epoxy to hold the thermocouples to the DUT. If epoxy is used, the upper temperature limit will be limited by the epoxy chosen because epoxy is inherently flammable.
V. Susceptibility to EMI/RFI and Interference
Remember that the voltage levels due to temperature are very small, and a small change can make a big difference to the temperature reported by the system.
Thermocouples should never be run with any other control wiring, especially any type of AC line. All thermocouples can be run together in the same conduit, and should be run in their own conduit or wire way. Any varying magnetic field (even DC switching on and off) is picked up by the thermocouple wire from the transformer effect. The common wire run is effectively an air core transformer. The longer the wire run, the better the air core transformer. This is not good. If thermocouple wires must cross power wires (which is not a good idea), cross at 90
Very electrically noisy environments can be tamed with shielded thermocouple wire. If shielded thermocouple wire is used, ground the shield only at one end. If both ends are grounded it will form a potential ground loop.
If the thermocouples are used on or near an RF source, ferrite torroids must be used on the thermocouples to prevent the RF energy from traveling up the thermocouple wire and causing a voltage bias at the terminal strip. Torroids are used at both the hot junction end (to prevent the initial injection) and at the terminal strip end (to eliminate radiated noise reception). They must be placed at less than one half the wave length of the noise source from the ends, to effectively block the RF energy. Practically, if you put the torroid less than 1-1/2 inches from the ends you will be covered up to 1.9GHz. If the system is to be cycled over any temperature range more than about 15
°C above or below room temperature, care must be used in the selection of the torroid because the magnetic properties of the torroid are temperature dependant. I have found a torroid that, although physically large, has the necessary thermal magnetic characteristics for high frequency that will allow it to be used inside a chamber: Feronics # 11-282-PIn highly reactive and / or corrosive atmospheres, especially at elevated temperatures, protection for the thermocouple may be required. As mentioned earlier, the properties of the thermocouple wire, and thus the accuracy, can be changed significantly by chemical reactions. If you wish to operate in this type of environment and maintain the thermocouple accuracy, a thermowell must be used to isolate the thermocouple from the environment. A thermowell is basically a stainless steal (or sometimes brass) housing that is placed between the thermocouple and the environment. The thermowell isolates the harsh environment from the thermocouple, but is also slows down the thermocouple response time significantly. Thermowells have large thermal inertia compared to the bead end of a thermocouple. Typical response times from inside a thermowell usually increase by a factor of ten or more. It is not uncommon for reaction times from a thermowelled thermocouple to be measured in seconds. Obviously, in a rapidly changing system the thermowell will cause system instability and overshoot / undershoot.
The insulation of the thermocouple wires also has a significant bearing on the system accuracy in a harsh environment. Even if the wire itself is unaffected, if the insulation is degraded to a point that there are virtual junctions (from capacitive coupling, etc.), the system accuracy is severely damaged. See Shunt Impedance below.
There are numerous sources of errors in a temperature measurement system. If the system is installed correctly, the normal error sources are the thermocouple wire errors, the thermocouple extension wire errors, the amplifier prior to the A/D (Analog to Digital) converter, the A/D converter itself, and the software to convert the number to a temperature.
Thermocouple Wire
The normal type-T thermocouple wire has a tolerance that is temperature range dependant. Obviously, the tighter the tolerance the more expensive the wire. Also note that the wire is only required to be checked by the manufacturer for calibration at +200
|
Temperature Range |
Standard Grade |
Premium Grade |
|
-200 to 0 °C |
± 1 °C or ± 1.5% |
N/A |
|
0 to 350 °C |
± 1 °C or ± 0.75% |
± 0.5 °C or ± 0.4% |
Note that the percentage is relative to the temperature being measured, not the entire range. The allowed error is which ever error of the two specifications is greater. At +200
°C, for example, the error due only from the wire, on standard grade thermocouple wire, would be ± 3°C because 1.5% of 200 is 3, and 3°C is bigger than 1°C.Thermocouple Extension Wire
The normal type-TX thermocouple extension wire has a tolerance that is not temperature range dependant because the allowed range of ambient variation is far more restricted. Extension wire is not intended to be used to make a thermocouple, and should not be subjected to large temperature swings. The following table illustrates the typical range of tolerances available for type-TX thermocouple wire. Obviously, this is manufacturer dependant.
|
Temperature Range |
Standard Grade |
Premium Grade |
|
-60 to 100 °C |
± 1 °C or ± 1.5% |
± 0.5 °C or ± 0.75% |
Note that the percentage is relative to the temperature being measured, not the entire range. The allowed error is which ever error of the two specifications is greater.
Amplifier Error
Amplifier error is very hardware dependant. Typical values for relatively common hardware are in the range of from 0.01% to 0.5% of the reading, depending on the gain setting, cost of the hardware, the manufacturer, etc. Non-linearity errors are on the magnitude of 0.0005% to 0.02%, again depending on the gain setting, cost of the hardware, the manufacturer, etc. These errors are independent of drift, which is a stability error. The thermal drift errors are generally in the range of from ± 25 ppm/
°C to ± 500 ppm/°C, so variations in the temperature of the measuring system will also greatly effect absolute accuracy.A/D Converter Error
The Analog to Digital converter error is specified in bits because the resolution is a function of the number of bits from zero to full scale. Typical errors are ± 1.5 bits. An 8 bit A/D has 8 bits resolution so the error is ± (1.5 / 256) or 0.6% of full scale. The cost of an A/D goes up exponentially with the number of bits resolution. The typical temperature measuring system A/D is generally 12 bits for accuracy reasons and cost effectiveness. A typical 12 bit A/D has an accuracy of ± (1.5 / 4096) or 0.04% of full scale. Note that this error is relative to full scale, not the reading. If total full scale hardware span is 500
°C, for example, then the error due to the 12 bit A/D is ± 0.2°C.Software Error
All math calculations done by a computer have an associated round-off error. This error is a function of the software language used, the floating point hardware or software available, and the requested precision of the programmer. If done correctly, the error due to software is relatively negligible, on the order of 0.05% of the reading or less, and need not be considered.
Statistically, not all the errors will normally add in the same direction, but for a worst case analysis, all errors should be added together. In practice, this is generally the way it works anyway. If we assume that the measuring computer is held at a constant temperature, standard tolerance parts are used, and that there are no installation errors, the expected accuracy will be between 3% and 5% of the reading. This can be lowered if the system uses premium parts and it is calibrated all the way to the thermocouple, however, it isn't practical to expect much better than about 1.2% to 1.5% of the reading. A reading of 100
°C is at best ± 1.5°C, and is normally about ± 4°C, and it doesn't matter how many decimal places are displayed on the digital meter.There are generally only two delays in the system. These are the conversion time of the measuring system, and the thermal inertia of the thermocouple. As a practical matter, the conversion time of the electronics (typically 3 microseconds) is such a small factor of the total reaction time, that it is generally not considered. The smaller the thermocouple, the faster it reacts to changes. Also note that the smaller the thermocouple wire, the more susceptible it becomes to physical damage. Use of a thermowell for thermocouple protection slows the response significantly. In general, typical response times without a thermowell range from 50 milliseconds (0.05 seconds) to 200 milliseconds (0.2 seconds). A thermowell can slow response up to as much as 30 seconds, or as little as 1-1/2 seconds, depending on the physical setup.
The initial installation is far more important than most people realize. If the insulation of the thermocouple wire is cut or chafed on the sharp edge of a conduit, or the wire is cold formed because of physical abuse, the system accuracy will never reach its full potential. In all likelihood, it will also significantly degrade with time. If the thermocouples are installed in a very electrically noisy environment, or run with other control wiring, the readings will not be accurate of consistent. If too small a gauge thermocouple wire or extension wire is used, the noise susceptibility will be so great that the readings may be unusable.
General Rules of Thumb
There are two types of wire: solid and stranded. The thermocouple itself should be solid wire (so that there is only one controlled junction), however, the extension wire is easier to run if it is stranded. Stranded wire is far more flexible and easier to work with during installation. Note that the maximum allowable operating temperature goes down as the wire gauge goes up, i.e., as the wire gets smaller, the upper temperature limit lowers. See the wire size table below.
The resistance of the thermocouple run is the sum of the thermocouple resistance plus the resistance of the extension wire. Generally, the thermocouple wire is smaller than the extension wire so that the system response time is minimized. The length of the thermocouple is usually just sufficient to bring the wire out of the harsh environment. From this point, thermocouple extension wire is used if the length is over a few feet. The following table gives the approximate worst case resistance per foot of wire of various gauge type-T thermocouple and type-TX thermocouple extension wires at 20
|
AWG Size |
Maximum allowable operating temperature ( °C) |
Approximate W (ohms) per foot of wire |
|
6 |
--- |
0.006 |
|
8 |
--- |
0.010 |
|
10 |
--- |
0.015 |
|
12 |
--- |
0.023 |
|
14 |
--- |
0.037 |
|
16 |
320 |
0.059 |
|
AWG Size |
Maximum allowable operating temperature ( °C) |
Approximate W (ohms) per foot of wire |
|
18 |
260 |
0.095 |
|
20 |
260 |
0.149 |
|
24 |
205 |
0.376 |
|
26 |
205 |
0.602 |
|
30 |
150 |
1.522 |
|
32 |
140 |
2.379 |
|
34 |
130 |
3.830 |
There are everything from ultra high temperature mineral insulation to cheap type TW insulation available. For environmental chambers, generally a Teflon type insulation for the actual thermocouple works well, and a standard PVC insulation on the extension wire is cost effective. If the thermocouple is used near the heat of cold source (for chamber plenum temperature control) Teflon will not be sufficient and a high temperature glass braid type insulation or a high temperature mineral type insulation should be used. Note that this plenum thermocouple will be subjected to both very high and very low temperatures and will be subjected to extreme thermal shock.
De-calibration occurs when you unintentionally alter the physical makeup of the thermocouple wire such that it no longer conforms to the NBS polynomial within the specified limits. De-calibration can occur from torch welding, diffusion of atmospheric particles into the metal caused by corrosive and reactive atmospheres and / or extreme heats, high temperature annealing, or by cold-working the metal. Cold working most often occurs as the thermocouple wire is handled or pulled through an unfriendly conduit. Annealing can occur within a section of wire that undergoes a large temperature gradient - the annealed section is no longer homogeneous. This error is insidious because it appears that the thermocouple is working when in reality the errors are significant.
Abuse, age, and thermal cycling can take their toll on the thermocouple wire insulation. Insulation resistance also decreases exponentially with increasing temperature. If the insulation degrades sufficiently from either thermal cycling, physical abuse, age, or damage from installation, there will be a point at which the insulation is insufficient to prevent a virtual junction. This virtual junction, or in some cases actual junction if one wire shorts out, will have a major effect of the reported voltage of the thermocouple. The reported voltage will be related to the average of these two junctions. The major problem is that the other thermocouple wire is what ever the wire is shorting or shunting to, and the properties of that junction are unknown. The smaller the gauge of the thermocouple wire (larger resistance) the more susceptible the thermocouple is to shunt impedance problems. Cuts in the insulation from improper installation or physical abuse can give intermittent shunt impedance's that are virtually impossible to find, and are totally independent of wire size. Any time a thermocouple is in a high wind stream and is allowed to move, the point at which it enters the chamber or the last tie down point is subject to insulation chafing.
The dyes used in some thermocouple insulation will form an electrolyte in the presence of water. Two dissimilar metals (thermocouple) in the presence of an electrolyte creates an effective battery that produces voltages several orders of magnitude greater than that of the Seebeck effect. This error will be a function of the humidity and / or water exposure, and will simply go away when things dry out. If this is suspected as a problem simply wet the thermocouple and see what happens.
Most calibrations consist of only removing the thermocouple and attaching a precision thermocouple simulator to the thermocouple input. This is required to calibrate the amplifier and analog to digital converter while removing any error due to the thermocouple wire. This is the absolute minimum required calibration. While these errors account for the majority of the system errors, any errors due to the thermocouple and thermocouple extension wire are ignored.
The thermocouple wire itself can be a significant source of measurement error. The standard manufacturers calibration points for type-T thermocouple wire are 93.3
Most thermocouple boards come with a filtering optional jumper. Basically the filtering consists of a resistor-capacitor filter on the input. This capacitor looks like a short circuit to rapidly changing signals while the resistor limits the current. This R-C combination effectively filters out rapidly changing signals that are generally due to noise. The time constant of the R-C network, or the time required to charge the capacitor through the resistor, determines the lowest frequency effected. If the system is a high speed system, however, this filtering can significantly slow down the change response time.
Two separate thermocouples can be paralleled for redundancy. Both thermocouples are attached to the same input of the measuring instrument. The two thermocouple tips should be located as close as physically possible to each other because the voltage seen at the sensing end will be the average of both thermocouples. They should not be electrically connected to each other. The routing of the thermocouples back to the measuring instrument is not a factor so the two thermocouples can be routed differently with different lengths of thermocouple extension wire. If one of the thermocouples opens up, the second thermocouple becomes the only thermocouple in the system. Paralleling thermocouples gives a simple form of redundancy, however, when one of the thermocouples opens up it is almost undetectable. The standard open circuit techniques will not work because the circuit is not open: the second thermocouple is still functional. If the two thermocouples are not periodically independently checked for continuity, the redundancy could be lost without the operator being aware of a problem. In critical applications where redundancy is required, the impedance as seen from the instrument end could be monitored for both short circuit and open circuit detection, however, this is very expensive and complicated because of the required isolation and relatively low impedance's involved. (See Short Circuit Detection below.) If open circuit protection is the only requirement, open circuit protection is by far the easiest failure to detect. (See Open Circuit Detection below.)
When only one of the thermocouple leads grounds out, the junction formed is a second thermocouple in the system. The grounding point is chassis ground, which is usually referenced to the zero voltage reference in the thermocouple data collection system. This is the other end of the loop. If the shorted lead is the ground reference, ground loops usually result. If the lead is the source lead then the behavior is also indeterminate because of the new ill defined thermocouple junction. The combination of the two junctions is what is reported at the monitoring end of the wire. In any case, this type of fault is difficult to detect with hardware because it is not either an open or short circuit. This type of fault, however, is usually not very subtle. An intelligent system that recognizes unreasonable temperatures or temperature changes can protect against this type of fault.
Open circuit protection is by far the easiest to implement. Most thermocouple interface cards have a jumper that allows for this detection. Normally, a relatively high impedance pull up resistor is used on the plus lead such that if the circuit is opened, the input voltage is pulled up to the supply rail. This is easy to detect in software because the temperature is at the absolute upper limit of the hardware, well beyond the upper limit of the system. It does, however, require that the software or system firmware recognize this situation as an open circuit.
Short circuit protection is very difficult. The point at which the short between the two thermocouple leads occurs now becomes the temperature sensing point, however, the thermocouple "appears" to function normally. If the short circuit is sufficiently removed form the active controlled area such that it will not respond to temperature changes, the short could result in thermal runaway (if it is the control thermocouple that has become shorted). The only way to detect the short is to measure the thermocouple impedance while it is running. The larger the wire gauge, and-or the closer the short is to the desired sensing point, the more difficult the short is to detect. The difference in impedance could be as low as 0.001 ohms or less. The measurement circuit must also not disturb or distort the small thermocouple currents in the wire. The best way to protect against shorted thermocouples is to use armored thermocouple wire in the area where damage can occur. The operator should always secure and prevent the thermocouple wires from moving around in the high velocity air streams inside the environmental chamber. A stable unmoving thermocouple is far less likely to short out.
If electrical isolation is required to prevent ground looping, there are several methods to electrically isolate the temperature measurement thermocouples and still mechanically and thermally couple the thermocouples to the DUT.
Isolated thermocouple system: a system that has each thermocouple electrically isolated from everything else including other thermocouples of the same system.
Pros:
Cons:
Partially Isolated thermocouple system: a system that has each thermocouple electrically isolated from the DUT but electrically connected to other thermocouples of the same system through a high impedance ground.
Pros:
Cons:
Isolator modules
Pros:
Cons:
Kapton tape
Pros:
Cons:
Super Glue
Pros:
Cons:
High Temperature Glass Cloth Electrical Tape
Pros:
Cons:
If everything in the system is operating correctly, and the ambient temperature of the wire and measuring system is at exactly the same temperature as previously run, the repeatability will be within the expected error of the system. (See Overall Error Magnitudes above.) Radical changes in ambient, especially near the measuring instrument, can significantly increase this error. If the thermocouple measuring system is not periodically calibrated, the natural drift of the electronics will increase this error. The drift rate is a function of the instrument and is usually unpredictable without a calibration history.
All thermocouples are assumed attached to the DUT, and therefore have the thermal inertia of the DUT area of attachment. If the thermocouple is used simply to monitor temperature, the physical placement in not critical. If the thermocouple is the chamber control thermocouple, the physical placement is extremely important. The chamber controller can only respond to the temperature changes it "sees" through this thermocouple. If the thermocouple has too much thermal inertia, low thermal inertia sections of the DUT could over heat. If the control thermocouple has too little thermal inertia, the heavy sections of the DUT will not be sufficiently heated. Simply changing the position of the control thermocouple will have a very significant effect on the performance of any environmental chamber.
If a thermocouple is completely embedded and enclosed in the DUT (such as epoxied in a hole), the thermal coefficients of expansion of the materials used must be considered. For type-T thermocouples, the largest coefficient of thermal expansion for 20
For those of us who have no life, the following formula is the NBS polynomial mathematical relationship (model) between temperature and voltage for a type-T thermocouple.
t=c0 + c1E + c2E2+ c3E3+ c4E4+ c5E5+….+ cnEn
Where t is temperature in
°C and E is the thermoelectric voltage in micro-volts. As n increases, the accuracy of the polynomial improves. As a point of reference, n=9 gives approximately ± 1°C on the conversion error of a type-K thermocouple. Larger values of n give smaller conversion errors. With type-T thermocouples, the coefficients for temperatures from -200°C to 0°C are different than from 0°C to +350°C. This is because the operational properties of the thermocouple below zero (7th order polynomial) are different than they are above zero (6th order polynomial). The coefficients are as follows:|
Temperature Range |
-200°C to 0°C |
0°C to +350°C |
|
Voltage Range |
-5,603 to 0m V |
0 to 20,872m V |
|
C0 |
0.000000 |
0.000000 |
|
C1 |
2.5929192e-2 |
2.592800e-2 |
|
C2 |
-2.1316967e-7 |
-7.602961e-7 |
|
C3 |
7.9018692e-10 |
4.637791e-11 |
|
C4 |
4.2527777e-13 |
-2.165394e-15 |
|
C5 |
1.3304473e-16 |
6.048144e-20 |
|
C6 |
2.0241446e-20 |
-7.293422e-25 |
|
C7 |
1.2668171e-24 |
------------ |
|
Error |
+0.04 to -0.02 °C |
+0.03 to -0.03 °C |
For those of us who read the footnotes, the Seebeck coefficient for type-T thermocouples at 20°C, in m V/°C, is approximately 40.