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Temperature Measurement
Priyatmadi
Temperature Concept
• Temperature is a useful measure of the thermodynamic
state of an object or system. It is a macroscopic
description of the aggregate amount of microscopic
kinetic energy in a material. If two bodies are at the
same temperature, they are in thermodynamic
equilibrium with each other; if they were connected to
each other, there is no net flow of heat from one to the
other.
• Interestingly, temperature is not a measure of the unit
thermodynamic energy of a body; unit masses of
differing materials can require differing amounts of
energy to be added or removed to change their
temperature by a given amount. Identical temperature of
two bodies merely implies there would be no transfer of
heat between the two, regardless of the actual energy
stored as heat in each body.
Temperature Concept
• The International Temperature Scale of 1990
(ITS-90) is the current standard for temperature
measurement, defining the Kelvin temperature
scale. The standard is based on phase transition
points of various pure substances, with the Kelvin
degree defined as 1/273.16 the absolute
temperature of the triple point of water. Examples
of a few other key points defined in this scale are
listed in Table 1.
Temperature Concept
TABLE 1
K
C
Substance
State
13.8033
-259.3467
Hydrogen
Triple-point
83.8058
-189.3442
Argon
Triple-point
243.3156
-38.8344
Mercury
Triple-point
273.16
0.01
Water
Triple-point
429.7485
156.5985
Indium
Freezing Point
692.677
419.527
Zinc
Freezing Point
1234.93
961.78
Silver
Freezing Point
Temperature Concept
• The reason for defining the temperature scale
on the basis of freezing and triple points is that
these events can be readily reproduced to a
high degree of repeatability.
• This means that there need not be a standard
kilogram of temperature locked in a vault
somewhere.
• To measure temperatures between reference
points, you have to resort to less fundamental
devices, calibrating them to the known points
and interpolating between those calibration
points.
Mechanical Temperature
Measurement
• As the temperature of a material changes, the material
expands or contracts. While thermal expansion can be a
nuisance to mechanical designers, it is the physical
property that underlies the operation of many
thermometers.
• The constant-volume gas thermometer (CVGT) depends
on the pressure-volume-temperature relationship of an
ideal gas:
PV = kT
(1)
• Equation 1 implies that you can measure the expansion
of a gas at constant pressure to measure temperature.
When using the less-than-ideal gases available in the
real world, however, keeping the volume constant and
measuring the pressure provides better results.
Mechanical Temperature
Measurement
Mechanical Temperature
Measurement
• Liquids also expand when heated, and
because they (unlike most gases) are
visible, they can be used in simple and
easy-to-read thermometers. Colored
alcohol and mercury are popular
working liquids.
• Because the coefficient of volumetric
expansion for most liquids is small, a
large reservoir bulb of working liquid is
required for thermal expansion to
move a small amount of fluid up a
significant length of capillary tube.
Mechanical Temperature
Measurement
• Bimetal thermostats are also
based on the thermal
expansion of metals.
• By bonding two metals with
dissimilar coefficients of
thermal expansion, you obtain
a strip that flexes in response
to temperature change.
• This principle is used
extensively in thermostats,
where flexure beyond a certain
point causes a pair of switch
contacts to open or close.
resistance temperature detector (RTD)
• While techniques based on thermal expansion provide
useful measurements, they lack the ability to directly
transduce temperature into a continuous electrical
signal. This limits their application in automated
monitoring and control functions. Fortunately, there are
many measurement techniques that do represent
temperature as an electrical quantity.
• Electrical resistance can also be used to determine
temperature.
• The resistance of many metals (e.g., iron, copper, and
aluminum) increases at about 0.3%/°C over a wide
temperature range.
• To obtain a significant amount of resistance (e.g., 100 ),
the metal (in the form of fine wire) is either wound on a
core or patterned as a thin film on a substrate. The
resulting device is known as a resistance temperature
detector (RTD).
resistance temperature detector (RTD)
• While RTDs can be made of nearly any metal,
platinum is the metal of choice.
• Platinum is highly corrosion resistant and stable
over a wide temperature range, and it can be
refined to levels of high purity, making for
consistent sensors.
• ITS-90 specifies the platinum RTD as the means
of measuring temperatures between physical
reference points ranging from the triple point of
hydrogen (13.8033 K) to the freezing point of
silver (961.78 K).
resistance temperature detector (RTD)
Thermistor
• For those of us with more pedestrian measurement
requirements—and smaller budgets—thermistors offer
another type of temperature-to-resistance transducer.
• These devices are made from various nonmetallic
conductors (e.g., metal oxides and silicon) and offer the
advantage of much higher thermal coefficients of
resistance compared to RTD.
• Thermistors come in two basic flavors: negative
temperature coefficient (NTC) and positive temperature
coefficient (PTC). The resistance of an NTC thermistor
drops with increasing temperature, while that of a PTC
device rises.
Thermistor
• One of the advantages provided by a thermistor over a
metal RTD is that the sensitivity ( R/ T) of a thermistor
can be an order of magnitude greater than that of the
RTD. NTC thermistors with sensitivities of –4%/ °C are
not uncommon. Such high sensitivities make it possible
to easily measure temperature changes on the order of
hundredths of a degree.
• Because an NTC thermistor has a highly nonlinear
response, it’s often characterized by a measure called β
, which is used to describe an exponential fit of
resistance over a given temperature range.
Thermistor
• For a thermistor, β is calculated:
where:
T1 and T0 = two reference temperatures in K
RT1 and RT0 = the resistances at T1 and T0
The resulting value of b can then be used to estimate RT for a given T:
Thermistor
• Conversely, if you know the resistance, the estimated
temperature can be obtained by:
To make their customers’ lives easier, thermistor
manufacturers often provide detailed tables of
resistance vs. temperature for their devices,
reducing the need for complex calculations,
especially when high degrees of accuracy are not required.
Thermistor
• Although you can measure the resistance of an RTD or
thermistor with an ohmmeter, it’s often more convenient
to convert the resistance into a proportional voltage.
• The circuit shown in next figure will bias a thermistor or
RTD with a constant current and deliver an output
voltage proportional to temperature. Because a
thermistor or RTD must be powered up to be read,
excessive bias current can lead to self-heating effects.
• While reducing the bias current will minimize self-heating
errors, it will also minimize the available output voltage
signal.
Thermistor
Thermistor
Thermocouples
• Another popular temperature sensor is
thermocouples, which consists of two dissimilar
metals bonded to each other, typically by welding.
The bimetallic junction develops a small voltage
that varies with temperature.
• The principal advantages of thermocouples are
that they are inexpensive (you can get
thermocouple wire pair in rolls to make your own,
often for <$0.50/ft.).
• It provides moderately accurate and consistent
measurements, and operate over a wide
temperature range (from <0°C to >1000°C).
Thermocouples
A classic thermocouple (A) must
have a reference or cold junction.
A modern systems (B) use an
additional temperature sensor to
simulate the effects of a cold
junction.
Thermocouples
• Their principal disadvantage is that they produce small output
voltages. For example, a Type J thermocouple (iron/constantan)
produces only about 50 µV/°C. The problem with a voltage of this
magnitude is not that it is too small to accurately process; the real
issue is that it is comparable to the voltages developed at the
parasitic thermocouple junctions formed where the thermocouple
wire is connected to the measuring instrument. To accurately
measure temperature at the junction of interest, you must
compensate for the effects of these parasitic cold junctions.
• The classical solution is to make an additional reference junction
and place it in a 0°C ice bath. A more usual approach, however, is to
measure the temperature of the parasitic junctions and use the
reading as a correction factor in the primary measurement.
P-N Junctions
• Semiconductor devices can also be used to measure
temperature. At a constant current bias, the voltage drop
across a silicon P-N diode junction shows roughly a –2
mV/ °C temperature coefficient.
• Because the P-N junction is the basic building block of
diodes, transistors, and ICs, temperature sensing can be
incorporated in many devices at low cost. This technique
is used in the onboard temperature sensors of
microprocessors (e.g., Intel’s Pentium) and for the
thermal-shutdown circuits of power-supply chips.
• Next shows how a 1N914 diode can be used as an
inexpensive (<$0.05) temperature probe.
P-N Junctions
When a silicon diode is biased
with a constant current (A),
the voltage drop across it
varies with temperature
at the rate of about –2 mV/°C
(B).
P-N Junctions
• inexpensive and sometimes even free
• P-N junction thermometers can provide a fair
degree of accuracy. But they’re more often useful
for coarse, inexpensive measurements.
• The room-temperature output voltage is about 600
mV, and even then the voltage varies both from unit
to unit and with bias current.
• Sensitivity also varies.
Temperature-Dependent Sources
• Although most analog circuits are intended
to operate with minimal dependence on
ambient temperature, the circuit shown in
the next figure provides a current output
that is nearly linear with respect to
absolute temperature.
• For this reason, the circuit is called a
proportional-to-absolute temperature
(PTAT) current source.
Temperature-Dependent Sources
• The proportional-toabsolute temperature
current source is a circuit
that has bias currents that
vary as a linear function
of absolute temperature.
The circuit is the basis for
most precision
semiconductor
temperature sensors.
Temperature-Dependent Sources
• The PNP transistors (Q1, Q2) form a current mirror that
maintains I1 = I2. Because I2 is split four ways among
Q4a-Q4d, the bias current in each of the transistors is
1/4 what it is in Q3.
• Q3 and Q4a-Q4d, however, are all identical devices
and have similar characteristics. In addition, because
they all live on the same silicon die, they are all at the
same temperature.
• Under these conditions, the difference in base-emitter
voltage between Q3 and any of the Q4s is given by:
Temperature-Dependent Sources
where:
k = Boltzmann’s constant (1.38 3 10–23 J/K)
q = the charge on an electron (1.6 3 10–19C)
T = absolute temperature in K
• Because the current being fed into the Q4s is split evenly
among them, the ratio of IQ4a to IQ3 is 1/4. Because the base
voltages of Q3 and the Q4s are the same, the resultant Vbe
appears across R1, where it causes I2 to be:
Temperature-Dependent Sources
• Notice that other than the value of R1 and T, everything
else is either a fundamental constant (k, q) or an integer
ratio (1/4).
• The resulting current I2 (and also I1) will be proportional
to temperature.
• In theory, the stability of the thermometer is solely
dependent on the stability of R1 and how well you can
match transistors.
• In practice, there are other factors that can affect its
performance, but the circuit (with suitable modifications)
remains one of the fundamental building blocks for solidstate temperature sensors.
• A commercial example of a temperature sensor using
the PTAT principle is Analog Devices’ AD590.
Temperature-Dependent Sources
A commercial
proportional-to-absolute
temperature sensor, such as
Analog Devices’ AD590,
can be used as a precision
temperature measurement
system with the addition of
a single precision resistor.
Radiation Sensing
• Sometimes you need to measure an object’s
temperature without making physical contact with it. This
situation is especially common when the object in
question is very hot (e.g., molten metal in a steel
foundry). Noncontact temperature sensing is also useful
when temperature measurements must be made quickly
on a series of objects, such as items moving down an
assembly line. Radiation sensing is one way to measure
temperature remotely.
• You can infer the temperature of an object by the amount
and wavelength of the electromagnetic radiation emitted
by the object.
• Although this is obvious for very hot objects that
are incandescent (at temperatures >1000°C), it
is also true for any object with a temperature
greater than absolute zero.
• A very cold object will, of course, radiate much
less energy than a hot one; total radiation per
unit area is proportional to the fourth power of
temperature:
R = k T4
• The radiation emanating from a warm object is
theoretically distributed over a wide (infinite) bandwidth,
ranging from radio waves through gamma rays and
beyond. Developing effective radiation detectors to cover
such a wide range of wavelengths (picometers to
kilometers) would be a difficult, if not impossible, task.
• Fortunately, the radiation is not uniformly distributed
across all wavelengths but has well-defined emission
peaks.
• For temperatures of common interest (e.g., from 0°C to a
few thousand °C), these peaks fall mainly in the IR to
visible light ranges—meaning optical techniques can be
used to construct detectors.
• Hot objects emit IR
and visible radiation
as a function of their
surface temperature.
As an object gets
hotter, not only does
it radiate more, but
the peak
wavelengths it emits
get shorter.
• There are two types of IR detectors in
common use:
– thermal detectors
– quantum detectors.
• A schematic view of one type of thermal
detector, a thermopile, is shown in the next
Figure.
• A thermopile radiation
sensor develops a
voltage output in
response to incoming
radiation. The device is a
series connection of
many thermocouple
junctions arranged so that
incoming radiation heats
a group of detecting
junctions while not
heating a group of
reference junctions.
• In this device, a series of thermocouple junctions are
slightly heated by incoming radiation, generating a small
voltage. By wiring a large number of junctions in a
series, the resultant voltage is multiplied by the number
of junctions, enabling detection of small temperature
changes. To maximize absorption, the ac tive area is
often coated with black paint or a similar material.
• Because any radiation absorbed by the device is
converted to heat, this type of detector does not
discriminate between radiation of different wavelengths.
For this reason, an optical filter is often used to exclude
radiation at unwanted wavelengths.
• Quantum detectors do not rely on the conversion of
incoming radiation to heat, but convert incoming photons
directly into an electrical signal.
• When photons in a particular range of wavelengths are
absorbed by the detector, they create free electron-hole
pairs, which can be detected as electrical current.
• Because the energies of IR photons are significantly
lower than those of visible-light photons, exotic lowband-gap semiconductors (e.g., indium-antimonide or
mercury-cadmium-telluride) must be used to implement
this type of detector.
• A quantum IR detector
is constructed from a
piece of low-bandgap
semiconductor. When
an incoming IR photon
is absorbed by the
material, it produces an
electron-hole pair that
can then temporarily
conduct an electric
current.
• Quantum detectors provide several advantages over
thermal detectors.
• They can provide high sensitivity for long-wavelength
radiation (10 µm), making them useful for lowtemperature (<0°C) measurements.
• They are also fast. Because they directly detect photons,
as opposed to their cumulative thermal effects, they can
provide response time on the order of microseconds.
• On the other hand, because the energies of the incoming
photons are close to room-temperature thermal
energies, quantum sensors must be cooled to cryogenic
temperatures to provide maximum sensitivity.
• The next figure shows how a radiation detector
can be used to measure temperature.
• An enclosure is provided around the detector to
limit its field of view to an appropriately sized
target area.
• Depending on the application, additional optics
may be provided to increase the amount of
radiation gathered or better define the target
area.
• The raw signal from the transducer is then
amplified and linearized through either analog
circuitry or a look-up table to provide a
temperature output.
In addition to an IR sensor, an optical thermometer requires
circuitry to linearize the output and correct the signal
for variations in target emissivity.
• Because the primary measurement is of radiation
intensity, there are several conditions that can cause
measurement error. The first is when the target does not
fill the detector’s field of view. A target that fills only half
the detector’s field appears to be colder than one at the
same temperature that does fill the field of view.
• Another source of error is absorption of radiation
between the target and the detector. Absorption-induced
errors have numerous causes. Viewing windows can
attenuate transmitted radiation and can become dirty.
Some “invisible” gases, such as water vapor and carbon
dioxide, strongly absorb IR radiation at certain
wavelengths.
• Different targets emit radiation at different rates
depending on composition and surface characteristics.
• A measure of how well a given surface radiates is called
emissivity.
• The maximum rate of emission is obtained by a
hypothetical surface called a black-body radiator, which
has an emissivity of 1.
• All other targets have an emissivity ranging between 0
and 1.
• Practical radiation thermometers have adjustable gains
to account for both changes in target emissivity and
absorption errors.
• One way of reducing the effect of absorption and
emissivity variation is to measure the color of the
radiation emanating from the target. A white-hot object
doesn’t merely emit more radiation than a red-hot one;
the hotter object emits a larger fraction of its radiation at
shorter wavelengths.
• By measuring the ratio of radiation intensity at two
different wavelengths, you can achieve a temperature
reading that is largely independent of variations in
radiation transmission or target emissivity. This is the
basis for the two-color radiation thermometer, where the
colors of interest may be deep in the IR range. Although
a two-color radiation thermometer is not foolproof, it
does provide measurements that are less susceptible to
target variation and signal corruption than those provided
by measuring total radiance.
The Best Method for the Job
• Because temperature is important in such
a wide range of applications, many
different measurement techniques have
been developed to meet widely varying
technical and economic requirements.
• With a solid understanding of how each
method works, you can more easily
choose the one best suited to your
application.