Download Temperature Measurement Overview ...................................................... 1

RIGOL
Application Notes
Temperature Measurement Techniques
Apr. 2014
RIGOL Technologies, Inc.
Note: this application notes is for RIGOL M300 Series Data Acquisition/Switch System and
DM3068/DM3058/DM3058E Series Digital Multimeter. Wherein, DM3058/DM3058E Series Digital
Multimeter only supports TC.
RIGOL
Contents
Temperature Measurement Overview ...................................................... 1
Thermocouple .......................................................................................... 1
Thermocouple Overview............................................................................ 1
Voltage-Temperature Conversion ................................................................ 5
Noise Rejection during Thermocouple Measurements ................................... 7
Common Mode Noise Generated by Ground Loops ................................ 7
Common Mode Noise Generated by Power Lines ................................... 8
Normal Mode Noise ............................................................................ 8
Electrostatic Noise.............................................................................. 9
Sources of Error in Thermocouple Measurements ........................................ 9
Reference Junction Error .................................................................... 9
Decalibration Error ............................................................................10
Shunt Impedance .............................................................................10
Galvanic action .................................................................................11
Thermal shunting..............................................................................11
Calculation Error ...............................................................................11
RTD ........................................................................................................ 12
RTD Overview .........................................................................................12
Relationship between Temperature and Resistance .....................................13
To Measure the Resistance of the RTD.......................................................14
Thermistor ............................................................................................. 16
Thermistor Overview ...............................................................................16
Relationship between Temperature and Resistance .....................................16
Advantage and Disadvantage....................................................................17
Summary ............................................................................................... 18
Temperature Measurement Techniques Application Notes
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Temperature Measurement Overview
A temperature is a numerical measure of hot or cold. The basic unit of temperature
in the International System of Units (SI) is the kelvin. It has the symbol K. For
everyday applications, it is often convenient to use the Celsius scale, in
which 0℃ corresponds very closely to the freezing point of water and 100℃ is
its boiling point at sea level. Because liquid droplets commonly exist in clouds at
sub-zero temperatures, 0℃ is better defined as the melting point of ice. In this scale
a temperature difference of 1 degree Celsius is the same as a 1 kelvin increment, but
the scale is offset by the temperature at which ice melts (273.15 K). In the United
States, the Fahrenheit scale is widely used. On this scale the freezing point of water
corresponds to 32℉ and the boiling point to 212℉. The Rankine scale ( ° R ), still
used in fields of chemical engineering in the U.S., is an absolute scale based on the
Fahrenheit increment. We can denote the relationship among the four units using the
following equations.
°C= 5 / 9(° F − 32)
° F= 9 / 5°C + 32
K =°C + 273.15
° R =°F + 459.67
Usually, a temperature transducer, either resistance or voltage measurement
converted to an equivalent temperature by software conversion routines, may be
used to measure the temperature. The most common temperature transducers are
the thermocouple, the RTD and the thermistor. This document is intended to explain
the fundamentals of the common temperature measurement transducers.
Thermocouple
Thermocouple Overview
A thermocouple is a temperature-measuring device made by two different wires. It
converts temperature to voltage. In 1821, Thomas Seebeck discovered that when
two wires composed of dissimilar metals are joined, a voltage is generated. The
voltage is a function of the junction temperature and the types of metals in the
thermocouple wire. Since the temperature characteristics of many dissimilar metals
are well known, a conversion from the voltage generated to the temperature of the
junction can be made. The commonly used thermocouples are listed in the table
below.
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Table 1 Thermocouple Types
Type
B
J
K
T
E
N
R
S
Temperature
Range
Probe Accuracy
250℃-1820℃
±0.5℃
-210℃-1200℃
-200℃-1370℃
-200℃-400℃
-200℃-1000℃
-200℃-1300℃
±1.1℃-2.2℃
±1.1℃-2.2℃
±0.5℃-1℃
±1℃-1.7℃
±1.1℃-2.2℃
Rhodium
-50℃-1760℃
±0.6℃-1.5℃
Platinum
-50℃-1760℃
±0.6℃-1.5℃
Pos (+) Lead
Neg (-) Lead
Platinum30% Rhodium
Iron
Nickel-Chromium
Copper
Nickel-Chromium
Nicrosil
Platinum
-13% Rhodium
Platinum
-10% Rhodium
Platinum60% Rhodium
Constantan
Nickel-Aluminum
Constantan
Constantan
Nisil
Firstly, a set-up similar to that shown in Figure 1 is used to measure the unknown
temperature. After making voltage measurements, they determine the unknown
temperature using a thermocouple look-up table.
Voltmeter
Cu
V
Cu
J2
J3
Alloy 1
Alloy 2
Alloy 2
J4
J1
Unknown
Temperature
Reference
Temperature
0℃
Ice Bath
Figure 1
A thermocouple consists of two wires of dissimilar metals joined at one end (named
as “hot junction”). This "hot junction" is used to measure an unknown temperature,
while the "reference (cold) junction" and measurement hardware comprise the rest
of the system. Although many metal combinations exhibit the Seebeck effect, a
limited number have been established as industry standards because of their
predictable output characteristics over a wide temperature range. The measured
EMF is related to the difference in temperature between the hot and cold junctions
(J1 and J4), and the types of metals used to construct the thermocouple. The result
can be expressed by the following equation:
=
V α (Tunknown − TREF )
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Temperature Measurement Techniques Application Notes
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Wherein, α is the Seebeck coefficient. This coefficient in highly non-linear, and
varies for different types of thermocouples. It can be found in thermocouple
references (usually in a table of voltage versus temperature), but modern electronic
instruments and software generally automate the conversion of voltage to
temperature, so the user needn't bother with α .
Modern thermocouple measurement instruments do not use the ice bath and
corresponding reference thermocouple shown in Figure 1. This eliminates the need
for a potentially large number of input channels for the references, not to mention
the hassle of dealing with ice. Historically, the purpose of the ice bath was to force
the reference junction to a known temperature (0℃), but any reference temperature
can be compensated for, as long as we can measure it.
In Figure 1, it is obvious that connecting the thermocouple to a voltmeter input
introduces more metal junctions into the circuit (J2, J3), both of which can generate
additional thermal EMFs. Ideally, these terminals will be at the same temperature to
eliminate additional error voltages, but this can be assured by mounting them to an
"isothermal block" as shown in Figure 2. The isothermal block offers sufficient mass
to withstand minor fluctuations in ambient temperature and maintain the attached
terminals at the same temperature. This block can be integrated directly into the
measurement hardware.
Cu
J2
Alloy 2
+
V
-
J1
Cu
J3
Unknown
Temperature
Alloy 2
Alloy 1
Isothermal Block
J4
Reference
Temperature
0℃
Ice Bath
Figure 2
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Cu
Alloy 2
J2
+
V
-
J1
Cu
J3
Unknown
Temperature
Alloy 2
J4
Alloy 1
Reference Temperature
Isothermal Block
Figure 3
In Figure 3, the reference junction (J4) is moved into the isothermal block. At this
point, the instrument terminals and the reference junction are now at the same
temperature. This temperature can be read with a sensor that does not require a
reference junction, such as a thermistor or semiconductor temperature sensor.
Cu
J2
Alloy 2
+
V
-
J1
Cu
Unknown
Temperature
J3
Alloy 1
Reference Temperature
Isothermal Block
Figure 4
Based on the Law of Intermediate Metals [1], we eliminate the wire between
junctions J3 and J4. By removing this wire, we achieve the input circuit commonly
used for modern thermocouple instrument inputs, as shown in Figure 4.
Typically, multiple thermocouple inputs are populated on one isothermal block, and
one temperature sensor is used as the reference for all measurements. This
minimizes the cost of adding a reference sensor for every channel.
Note [1]: According to the Thermocouple Law of Intermediate Metals, inserting any type of wire
into a thermocouple circuit has no effect on the output as long as both ends of that wire are the
same temperature, or isothermal.
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Temperature Measurement Techniques Application Notes
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Voltage-Temperature Conversion
After acquiring the reference temperature ( TREF ), the following task is to read the
digital voltmeter and convert the voltage reading ( V ) to a temperature.
Because the temperature-versus-voltage relationship of a thermocouple is not linear,
the Seebeck coefficient ( α ) is not a constant and varies with the temperature and
the type of the thermocouple. For example, the Seebeck coefficient vs. temperature
of the K type thermocouple is shown in the figure below.
Figure 5
The NIST Thermocouple Tables list all the coefficients of the common types of
thermocouples. We could store these look-up table values in a computer and then
consulting the temperature corresponding to the voltmeter reading, but they would
consume an inordinate amount of memory. A more viable approach is to approximate
the table values using a power series polynomial. The general form for all except
type K thermocouple is:
n
V = ∑ ci (t90 )i
i =0
For type K thermocouples above 0℃, there is an additional term to account for a
magnetic ordering effect:
=
V
n
∑ c (t
i =0
i
90
)i + a0 e a1 (t90 − a2 )
Wherein,
V is the voltmeter reading in mV.
t90 is the temperature in ℃.
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ci are the polynomial coefficients unique to each thermocouple which has been
given in the NIST ITS-90 Thermocouple Database (an example for type E is listed
below).
e is the natural logarithm constant.
a0 is a constant and equal to 0.118597600000×100.
a1 is a constant and equal to -0.118343200000×10-3.
a2 is a constant and equal to 0.126968600000×103.
Table 2 Type E Thermocouple Coefficients
-270℃ to 0℃
Coefficient
0
0℃ to 1000℃
c0
0.000000000000x10
0.000000000000x100
c1
0.586655087080x10-1
0.586655087100x10-1
c2
0.454109771240x10-4
0.450322755820x10-4
c3
-0.779980486860x10-6
0.289084072120x10-7
c4
-0.258001608430x10-7
-0.330568966520x10-9
c5
-0.594525830570x10-9
0.650244032700x10-12
c6
-0.932140586670x10-11
-0.191974955040x10-15
c7
-0.102876055340x10-12
-0.125366004970x10-17
c8
-0.803701236210x10-15
0.214892175690x10-20
c9
-0.439794973910x10-17
-0.143880417820x10-23
c10
-0.164147763550x10-19
0.359608994810x10-27
c11
-0.396736195160x10-22
c12
-0.558273287210x10-25
c13
-0.346578420130x10-28
The following approximate inverse function is usually used in modern thermocouple
measurement instruments.
t90 = d 0 + d1V + d 2V 2 + ... + d nV n
Wherein,
t90 is the temperature in ℃.
V is the voltmeter reading in mV.
di are the inverse polynomial coefficients unique to each thermocouple which has
been given in the NIST ITS-90 Thermocouple Database (an example for type E is
listed below).
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Temperature Measurement Techniques Application Notes
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Table 3 Type E Thermocouple Inverse Coefficients
-200℃ to 0℃
Voltage Range:
-8.825 mV to 0 mV
0℃ to 1000℃
0 mV to 76.373 mV
d0
0.0000000x100
0.0000000x100
d1
1.6977288x101
1.7057035x101
d2
-4.3514970x10-1
-2.3301759x10-1
d3
-1.5859697x10-1
6.5435585x10-3
d4
-9.2502871x10-2
-7.3562749x10-5
d5
-2.6084314x10-2
-1.7896001x10-6
d6
-4.1360199x10-3
8.4036165x10-8
d7
-3.4034030x10-4
-1.3735879x10-9
d8
-1.1564890x10-5
1.0629823x10-11
-0.01℃ to 0.03℃
-3.2447087x10-14
-0.02℃ to 0.02℃
d9
Error Range:
Noise Rejection during Thermocouple Measurements
There are many sources of noise that can affect thermocouple measurements. The
most common sources of noise are:
1.
2.
3.
Ground loops, which generate common mode noise
Electromagnetic fields, which generate normal mode noise
Rotating equipment, which generate electrostatic noise
Common Mode Noise Generated by Ground Loops
Common mode noise creates an unwanted voltage that is present on both leads of
the thermocouple.
Typically, common mode noise is caused by a ground loop that is created when a
system has a potential difference between two grounds. Because the tip of a
thermocouple is a bare wire junction, it is at risk of creating a ground loop. If the tip
is grounded at the point where it is measuring temperature, and that ground is at a
different potential from the ground at the measuring end of the thermocouple, a
ground loop is formed and current will flow.
The best way to avoid a ground loop is to avoid grounding the tip of the
thermocouple, and use isolated thermocouples when necessary. Common mode
errors are also reduced by using a DMM with high impedance to ground.
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Common Mode Noise Generated by Power Lines
Common mode noise is also generated by sources such as power lines and electrical
motors. The noise is coupled to the unshielded thermocouple wires through
distributed capacitance. As the induced current flows to ground through the internal
DMM, voltage errors are generated along the distributed resistance of the
thermocouple wire. Adding a shield to the thermocouple wire will shunt the common
mode noise to earth ground and preserve the measurement, as shown in Figure 6.
Power Line
Distributed
Capacitance
HI
J1
Distributed
Resistance
WITHOUT SHIELD
LO
DVM
Power Line
HI
J1
LO
WITH SHIELD
DVM
Figure 6
Normal Mode Noise
Normal mode noise creates a current that flows in the same direction as the
measurement current. This type of noise is typically caused by large AC current
sources, such as AC power lines, that create a magnetic field. In turn, the magnetic
field creates a current in the measurement path. High-current devices include motors,
lights, and power mains. Normal mode noise is typically at line frequency of 50/60 Hz.
The normal mode error current is proportional to the strength of the field, the size of
the loop, and the orientation of the loop to the field.
To reduce the field strength interfering with the measurement, it is better to run
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Temperature Measurement Techniques Application Notes
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more wire and avoid the field than run the thermocouple wire through the field.




Minimize the size of the measurement loop. Use twisted-pair cabling, which
leaves little room between the cables. It’s like making a smaller receiving
antenna.
Run the measurement wires perpendicular to high-current wires, and change
the orientation to the field. Never run thermocouples in parallel with power lines
or other noisy signals.
Reduce normal mode currents with a filter. A relatively simple filter can reduce
the normal mode noise on a DC signal by several orders of magnitude.
Use an integrating A/D. Normal mode noise is typically the same frequency as
the line frequency, which is also described as a power line cycle or PLC. An
integrating A/D will return the average voltage during the integration period. If
you integrate over the same period as the line frequency or PLC, the average
value of the normal mode noise will be zero.
Electrostatic Noise
Electrostatic noise is coupled into the measurement path via stray capacitance.
Electrostatic noise is caused by rotating equipment; it generates an AC current that is
capacitance-coupled into the measurement path. Stray capacitance can couple
electrostatic noise through the tip of a thermocouple.
To combat electrostatic noise, use shielded wiring. Also, using a DMM with high
impedance to ground will help. When using a shield to prevent electrostatic noise
coupling, only ground one end of the shield to avoid creating a ground loop.
Sources of Error in Thermocouple Measurements
Reference Junction Error
1.
Soldering Introduces a Third Metal into the Junction
A thermocouple is typically formed by welding or soldering two wires together to
make the junction. Soldering introduces a third metal into the junction. Provided
that both sides of the thermocouple are at the same temperature, the third
metal has little effect.
Commercial thermocouples are welded using a capacitive-discharge technique.
This technique is used to prevent overheating of the thermocouple wire near the
junction and to prevent the diffusion of the welding gas and atmosphere into the
thermocouple wire.
2.
Poor junction connection
A poor weld or bad solder connection can also cause errors in a thermocouple
measurement.
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Open thermocouple junctions can be detected by checking the resistance of the
thermocouple. A resistance measurement of more than 5 kΩ typically indicates a
defective thermocouple. The modern measurement instrument may contain a
built-in, automatic thermocouple check feature. If you enable this feature, the
instrument measures the channel resistance after each thermocouple
measurement to ensure a proper connection.
Decalibration Error
Decalibration refers to that the thermocouple wire no longer conforms to the NIST
polynomial within specified limits due to some reasons. Those reasons may include:
 A bad thermocouple whose quality is not guaranteed or an incorrect type of
thermocouple is used.
 Atmospheric particles can actually diffuse into the metal. These changes in the
wire alloy introduce small voltage changes in the measurement. Diffusion is
caused by exposure to high temperatures along the wire or by physical stress to
the wire such as stretching or vibration.
Temperature errors due to diffusion are hard to detect since the thermocouple will
still respond to temperature changes and give nearly correct results. The diffusion
effects are usually detected as a drift in the temperature measurements.
Replacing a thermocouple which exhibits a diffusion error may not correct the
problem. The extension wire and connections are all subject to diffusion. Examine
the entire measurement path for signs of temperature extremes or physical stress. If
possible, keep the temperature gradient across the extension wire to a minimum.
Shunt Impedance
The insulation used for thermocouple wire and extension wire can be degraded by
high temperatures or corrosive atmospheres. These breakdowns appear as a
resistance in parallel with the thermocouple junction. This is especially apparent in
systems using a small gauge wire where the series resistance of the wire is high.
Open
HI
J1
LO
DVM
Figure 7
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Galvanic action
The dyes used in some thermocouple insulation will form an electrolyte in the
presence of water. This creates a galvanic action, with a resultant output hundreds of
times greater than the Seebeck effect. Precautions should be taken to shield the
thermocouple wires from all harsh atmospheres and liquids.
Thermal shunting
No thermocouple can be made without mass. Since it takes energy to heat any mass,
the thermocouple will slightly alter the temperature it was meant to measure. If the
mass to be measured is small, the thermocouple must naturally be small. But a
thermocouple made with small wire is far more susceptible to the problems of
contamination, annealing, strain, and shunt impedance. To minimize these effects,
thermocouple extension wire can be used.
Extension wire is commercially available wire primarily intended to cover long
distances between the measuring thermocouple and the voltmeter. Extension wire is
made of metals having Seebeck coefficients very similar to a particular thermocouple
type. It is generally larger in size so that its series resistance does not become a
factor when traversing long distances. It can also be pulled more readily through
conduit than very small thermocouple wire. It generally is specified over a much
lower temperature range than premium-grade thermocouple wire. In addition to
offering a practical size advantage, extension wire is less expensive than standard
thermocouple wire. This is especially true in the case of platinum-based
thermocouples.
Calculation Error
An error is inherent in the way a thermocouple voltage is converted to a temperature.
These calculation errors are typically very small compared to the errors of the
thermocouple, wiring connections, and reference junction.
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RTD
RTD Overview
An RTD (Resistance Temperature Detector) is a resistance thermometer, whose
electrical resistance varies according to its temperature in a precisely known way. We
usually measure the resistance of the RTD and then calculate the equivalent
temperature using multimeter.
The common RTD is made of 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.
PT100, PT500 and PT1000 are the common platinum RTDs. The most common
platinum RTD is designed by the following three methods, see the figure below.
Thin film RTD
Wire Wound RTD
Helical RTD
Figure 8
1． Thin film RTD
This design have a sensing element that is formed by depositing a very thin layer
of resistive material, normally platinum, on a ceramic substrate; This layer is
usually just 10 to 100 angstroms (1 to 10 nanometers) thick. This film is then
coated with an epoxy or glass that helps protect the deposited film and also acts
as a strain relief for the external lead-wires. Disadvantages of this type are that
they are not as stable as their wire wound or coiled counterparts. They can only
be used over a limited temperature range due to the different expansion rates of
the substrate and resistive deposited giving a "strain gauge" effect that can be
seen in the resistive temperature coefficient. These elements work with
temperatures to 300℃ without further packaging but can operate up to 500℃
when suitably encapsulated in glass or ceramic.
2． Wire Wound RTD
This design can have greater accuracy, especially for wide temperature ranges.
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Temperature Measurement Techniques Application Notes
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The coil diameter provides a compromise between mechanical stability and
allowing expansion of the wire to minimize strain and consequential drift. The
sensing wire is wrapped around an insulating mandrel or core. The winding core
can be round or flat, but must be an electrical insulator. The coefficient of
thermal expansion of the winding core material is matched to the sensing wire
to minimize any mechanical strain. This strain on the element wire will result in a
thermal measurement error. The sensing wire is connected to a larger wire,
usually referred to as the element lead or wire. This wire is selected to be
compatible with the sensing wire so that the combination does not generate an
emf that would distort the thermal measurement. These elements work with
temperatures to 660℃.
3． Helical RTD
This design has largely replaced wire-wound elements in industry. This design
has a wire coil which can expand freely over temperature, held in place by some
mechanical support which lets the coil keep its shape. This “strain free” design
allows the sensing wire to expand and contract free of influence from other
materials; in this respect it is similar to the SPRT, the primary standard upon
which ITS-90 is based, while providing the durability necessary for industrial use.
The basis of the sensing element is a small coil of platinum sensing wire. This
coil resembles a filament in an incandescent light bulb. The housing or mandrel
is a hard fired ceramic oxide tube with equally spaced bores that run transverse
to the axes. The coil is inserted in the bores of the mandrel and then packed
with a very finely ground ceramic powder. This permits the sensing wire to move
while still remaining in good thermal contact with the process. These Elements
works with temperatures to 850℃.
Relationship between Temperature and Resistance
The relationship between the temperature and the electrical resistance is usually
non-linear and described by a higher order polynomial:
R(t ) = R0 (1 + At + Bt 2 + Ct 3 + ...)
Wherein, R0 is the nominal resistance at a specified temperature. The number of
higher order terms considered is a function of the required accuracy of measurement.
The coefficients A, B and C etc. depend on the conductor material and basically
define the temperature-resistance relationship.
Platinum RTDs are available with alternative R0 values, for example 10, 25 and 100
Ohms. A working form of resistance thermometer sensor is defined in IEC and DIN
specifications and this forms the basis of most industrial and laboratory electrical
thermometers. The platinum sensing resistor, PT100 to IEC 751 is dominant in
Temperature Measurement Techniques Application Notes
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Europe and in many other parts of the world. Its advantages include chemical
stability, relative ease of manufacture, the availability of wire in a highly pure form
and excellent reproducibility of its electrical characteristic. The result is a truly
interchangeable sensing resistor which is widely commercially available at a
reasonable cost.
This specification includes the standard variation of resistance with temperature, the
nominal value with the corresponding reference temperature, and the permitted
tolerances. The specified temperature range extends from –200℃ to 961.78℃. The
series of reference values is split into two parts: -200℃ to 0 and 0 to 961.78℃.
The first temperature range is covered by a third-order polynomial:
R(t ) = R0 [1 + At + Bt 2 + C (t − 100 oC )t 3 ]
For the range from 0℃ to 850℃, there is a second-order polynomial:
R(t ) = R0 (1 + At + Bt 2 )
The coefficients are as follows:
=
A 3.9083 ×10−3 (o C −1 )
B=
−5.7750 ×10−7 (o C −2 )
C=
−4.1830 ×10−12 (o C −4 )
The value R0 is referred to as nominal value or nominal resistance and is the
resistance at 0℃. According to IEC 751 the nominal value is defined as 100.00Ω, and
this is referred to as a PT100 resistor.
An additional parameter defined by the standard specification is the mean
temperature coefficient between 0℃ and 100℃ and the typical values may be
0.00385, 0.00389, 0.00391 or 0.00392. It represents the mean resistance change
referred to the nominal resistance at 0℃:
Alpha =
R100 − R0
R0 ×100 oC
Wherein, R100 is the resistance when the temperature is 100℃.
To Measure the Resistance of the RTD
An RTD is a passive measurement device; therefore, you must supply it with an
excitation current and then read the voltage across its terminals. You can then easily
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Temperature Measurement Techniques Application Notes
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transform this reading to temperature with a simple algorithm. To avoid self-heating,
which is caused by current flowing through the RTD, minimize this excitation current
as much as possible. The easiest way to take a temperature reading with an RTD is
using the 2-wire method, see the figure below.
→i
+
R
V
RTD
R
-
R=Lead Resistance
Figure 9
Using the 2-wire method, the two wires that provide the RTD with its excitation
current and the two wires across which the RTD voltage is measured are the same.
The inaccuracy using this method is that if the lead resistance in the wires is high, the
voltage measured V, is significantly higher than the voltage that is present across the
RTD itself. To get a more accurate measurement, use the 4-wire method, see the
figure below.
RTD
+
→i=0
V
→i=0
-
Figure 10
The 4-wire method has the advantage of not being affected by the lead resistances
because they are on a high impedance path going through the device that is
performing the voltage measurement; therefore, you get a much more accurate
measurement of the voltage across the RTD.
Temperature Measurement Techniques Application Notes
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Thermistor
Thermistor Overview
A thermistor is a piece of semiconductor made from metal oxides, pressed into a
small bead, disk, wafer, or other shape, heated at high temperatures, and coated
with epoxy or glass. It is a type of resistor whose resistance varies significantly with
temperature, more so than in standard resistors. It differs from the RTD in that the
material used in a thermistor is generally semiconductor (ceramic or polymer), while
the RTD uses pure metals. The temperature response is also different; the RTD is
useful over larger temperature ranges, while thermistor typically achieves a higher
precision within a limited temperature range, typically -90℃ to 130℃.
Figure 11
Relationship between Temperature and Resistance
Assuming, as a first-order approximation, that the relationship between resistance
and temperature is linear, then:
∆R = k ∆T
Wherein, ∆R denotes the change in resistance, ∆T denotes the change in
temperature and k denotes the first-order temperature coefficient of resistance.
Thermistors can be classified into two types, depending on the sign of k . If k is
positive, the resistance increases with increasing temperature, and the device is
called a positive temperature coefficient (PTC) thermistor, or posistor. If k is
negative, the resistance decreases with increasing temperature, and the device is
called a negative temperature coefficient (NTC) thermistor. Resistors that are not
thermistors are designed to have a k as close to zero as possible, so that their
resistance remains nearly constant over a wide temperature range.
In practice, the linear approximation (above) works only over a small temperature
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Temperature Measurement Techniques Application Notes
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range. For accurate temperature measurements, the resistance/temperature curve
of the device must be described in more detail. The Steinhart–Hart equation is a
widely used third-order approximation:
1
=
a + b ln( R) + c ln( R )3
T
Wherein, a , b and c are called the Steinhart–Hart parameters, and must be
specified for each device. T is the temperature in K and R is the resistance in Ω
(the value of R of common thermistor may be 2.2kΩ, 3kΩ, 5kΩ, 10kΩ or 30kΩ).
a , b and c are found by selecting three data points on the published data curve
and solving the three simultaneous equations. When the data points are chosen to
span no more than 100℃ within the nominal center of the thermistor’s temperature
range, this equation approaches a rather remarkable ±0.02℃ curve fit.
Advantage and Disadvantage
The high resistivity of the thermistor affords it a distinct measurement advantage.
The four-wire resistance measurement may not be required as it is with RTD’s. For
example, a common thermistor value is 5000Ω at 25℃. With a typical TC of 4%/℃, a
measurement lead resistance of 10Ω produces only 0.05℃ error. This error is a factor
of 500 times less than the equivalent RTD error.
Because they are semiconductors, thermistors are more susceptible to permanent
decalibration at high temperatures than are RTD’s or thermocouples. The use of
thermistors is generally limited to a few hundred degrees Celsius, and manufacturers
warn that extended exposures even well below maximum operating limits will cause
the thermistor to drift out of its specified tolerance.
Thermistors can be made very small which means they will respond quickly to
temperature changes. It also means that their small thermal mass makes them
especially susceptible to self-heating errors. Thermistors are a good deal more fragile
than RTD’s or thermocouples and they must be carefully mounted to avoid crushing
or bond separation.
Temperature Measurement Techniques Application Notes
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Summary
If you want to make reliable temperature measurements, firstly, you need to
carefully select the right temperature sensor for your application. Understanding the
advantages and disadvantages of temperature sensors will help you take the proper
precautions when you set up a test. Thermocouples, thermistors and resistance
temperature detectors (RTDs) are the most common temperature sensors used in
electronic test. This section gives a summary to compare the advantages and
disadvantages for these popular temperature sensors.
Table 4 Three common temperature transducers
Advantages
Thermocouple
 Self-powered
 Simple
 Rugged
 Inexpensive
 Wide variety of physical forms
 Wide temperature range
RTD
 Most stable
 Most accurate
 More linear than thermocouple
Thermistor
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 High output
 Fast
 Two-wire resistance
measurement
Disadvantages
 Non-linear
 Low voltage
 Reference required
 Least stable
 Least sensitive










Expensive
Slow
Current source required
Small resistance change
Four-wire measurement
Non-linear
Limited temperature range
Fragile
Current source required
Self-heating
Temperature Measurement Techniques Application Notes