chapter3 chapter3 chapter3 chapter3 chapter3 chapter3 chapter3 chapter3 chapter3 chapter3 chapter3 chapter3 chapter3 chapter3 chapter3

1. 3 - Temperature Sensors
1. Thermoresistive sensors
2. Thermoelectric sensors
3. PN junction temperature sensors
4. Optical and acoustic temperature sensors
5. Thermo-mechanical sensors and actuators

2. A bit of history
 Temperature measurements and
thermometers
 1600 - thermometers (water expansion, mercury)
 1650 - first attempts at temperature scales (Boyle)
 1700 - “standard” temperature scales (Magelotti,
Renaldini, Newton) - did not catch
 1708 - Farenheit scale (180 div.)
 1742 - Celsius scale
 1848 - Kelvin scale (based on Carnot’s
thermodynamic work)
 1927 - IPTS - International Practical Temperature
Scale

3. More history - sensors
 Temperature sensors are the oldest
 1821 - Seebeck effect (Thomas Johann Seebeck)
 1826 - first sensor - a thermocouple - based on the
Seebeck effect (Antoine Cesar Becquerel)
 1834 - Peltier effect (Charles Athanase Peltier).
 First peltier cell built in 1960’s
 Used for cooling and heating
 1821 - discovery of temperature dependence of
conductivity (Sir Humphrey Davey)
 1771 - William Siemens builds the first resistive sensor
made of platinum

4. Temperature sensors -
general
 Temperature sensors are deceptively simple
 Thermocouples - any two dissimilar materials,
welded together at one end and connected to a
micro-voltmeter
 Peltier cell - any thermocouple connected to a dc
source
 Resistive sensor - a length of a conductor
connected to an ohmmeter
• More:
 Some temperature sensors can act as actuators as well
 Can be used to measure other quantities
(electromagnetic radiation, air speed, flow, etc.)
• Some newer sensors are semiconductor based

5. Temperature sensors - types
 Thermoelectric sensors
 Thermocouples and thermopiles
 Peltier cells (used as actuators but can be used as sensors)
 Thermoresistive sensors and actuators
 Conductor based sensors and actuators (RTDs)
 Semiconductor based sensors - thermistors, diodes
 Semiconductor junction sensors
 Others
 Based on secondary effects (speed of sound, phase of light)
 Indirect sensing (infrared thermometers - chapter4)
 Expansion of metals, bimetals

6. Thermal actuators
 A whole class of thermal actuators
 Bimetal actuators
 Expansion actuators
 Thermal displays
 Sometimes sensing and actuation is
combined in a single device

7. Thermoresistive sensors
 Two basic types:
 Resistive Temperature Detector (RTD)
 Metal wire
 Thin film
 Silicon based
 Thermistors (Thermal Resistor)
 NTC (Negative Temperature Coefficient)
 PTC (Positive Temperature Coefficient)

8. Thermoresistive effect
 Conductivity
depends on
temperature
 Conductors and
semiconductors
 Resistance is
measured, all other
parameters must
stay constant.
R = L
S

9. Thermoresistive effect (cont.)
 Resistance of a length
of wire
 Conductivity is:
 Resistance as a
function of
temperature:
 a - Temperature
Coefficient of
Resistance (TCR) [C]
R = L
S
 = 0
1 + a T  T0
R T = L
0S
1 + a T  T0

10. Thermoresistive effect (cont.)
 T is the temperature [C ]
 0 is the conductivity of the conductor
at the reference temperature T0.
 T0 is usually given at 20C but may be
given at other temperatures as
necessary.
 a - Temperature Coefficient of
Resistance (TCR) [C] given at T0

11. Example
 Copper: 0=5.9x107 S/m, a=0.0039 C
at T0=20C. Wire of cross-sectional area:
0.1 mm2, length L=1m,
 Change in resistance of 6.61x10 /C
and a base resistance of 0.017  at 20C
 Change of 0.38% per C .

12. Example (cont.)
 Conclusions from this example:
 Change in resistance is measurable
 Base resistance must be large - long and
or thin conductors or both
 Other materials may be used

13. Temperature Coefficient of
Resistance

14. Other considerations
 Tension or strain on the wires affect
resistance
 Tensioning a conductor, changes its length
and cross-sectional area (constant volume)
 has exactly the same effect on resistance as a
change in temperature.
 increase in strain on the conductor increases the
resistance of the conductor (strain gauge)
 Resistance should be relatively large (25
and up)

15. Construction - wire RTD
 A spool of wire (length)
 Similar to heating elements
 Uniform wire
 Chemically and dimensionally stable in the sensing range
 Made thin (<0.1mm) for high resistance
 Spool is supported by a glass (pyrex) or mica support
 Similar to the way the heating element in a hair drier is
supported
 Keeps strain at a minimum and allows thermal expansion
 Smaller sensors may not have an internal support.
 Enclosed in a glass, ceramic or metal enclosure
 Length is from a few cm, to about 50cm

16. Glass encapsulated RTDs

17. Construction (cont.)
 Materials:
 Platinum - used for precision applications
 Chemically stable at high temperatures
 Resists oxidation
 Can be made into thin wires of high chemical purity
 Resists corrosion
 Can withstand severe environmental conditions.
 Useful to about 800 C and down to below –250C.
 Very sensitive to strain
 Sensitive to chemical contaminants
 Wire length needed is long (high conductivity)

18. Construction (cont.)
 Materials:
 Nickel and Copper
 Less expensive
 Reduced temperature range (copper only works up to
about 300C)
 Can be made into thin wires of high chemical purity
 Wire length needed is long (high conductivity)
 Copper is not suitable for corrosive environments
(unless properly protected)
 At higher temperatures evaporation increases
resistance

19. This is unrelated to the course
- just a curiosity

20. This is unrelated to the course
- just a curiosity - close-up

21. Thin Film RTDs
 Thin film sensors: produced by depositing a
thin layer of a suitable material (platinum or
its alloys) on a thermally stable, electrically
non-conducting, thermally conducting
ceramic
 Etched to form a long strip (in a meander
fashion).
 Eq. (3.1) applies but much higher resistance
sensors are possible.
 Small and relatively inexpensive
 Often the choice in modern sensors
especially when the very high precision of
Platinum wire sensors is not needed.

22. Tnin film RTDs - (cont.)
 Two types of thin film RTDs from different
manufacturers
 Dimensions are typical - some are much
larger

23. Some parameters
 Temperature range: -250 C to 700 C
 Resistances: typically 100 (higher available)
 Sizes: from a few mm to a few cm
 Compatibility: glass, ceramic encapsulation
 Available in ready made probes
 Accuracy: ±0.01 C to ±0.05 C
 Calibration: usually not necessary beyond
manufacturing

24. Self heat in RTDs
 RTDs are subject to errors due to rise in their
temperature produced by the heat generated
in them by the current used to measure their
resistance
 Wire wound or thin film
 Power dissipated: Pd=I2R ( I is the current
(RMS) and R the resistance of the sensor)
 Self heat depends on size and environment
 Given as temperature rise per unit power
(C/mW)
 Or: power needed to raise temperature (mW/ C)

25. Self heat in RTDs (cont.)
 Errors are of the order of 0.01C/mW to
10C/mW (100mW/C to 0.1mW/C)
 Given in air and in water
 In water values are lower (opposite if mW/C used)
 Self heat depends on size and environment
 Lower in large elements, higher in small elements
 Important to lower the current as much as possible

26. Response time in RTDs
 Response time
 Provided as part of data sheet
 Given in air or in water or both, moving or stagnant
 Given as 90%, 50% (or other) of steady state
 Generally slow
 Wire RTDs are slower
 Typical values
 0.5 sec in water to 100 sec in moving air

27. Silicon Resistive Sensors
 Conduction in semiconductors
 Valence electrons
 Bound to atoms in outer layers (most electrons in pure
semiconductors)
 Can be removed through heat (band gap energy)
 When removed they become conducting electrons (conduction
band)
 A pair is always released - electron and hole
 Conductivity of semiconductors is
temperature dependent
 Conductivity increases with temperature
 Limited to a relatively small temperature range

28. Silicon Resistive Sensors (cont.)
 Pure silicon:
 NTC device - negative temperature
coefficient
 Resistance decreases with temperature
 Resistance in pure silicon is extremely high
 Need to add impurities to increase carrier density
 N type silicon - add arsenic (As) or antimony (Sb)
 Behavior changes:
 Resistance increases up to a given temperature
(PTC)
 Resistance decreases after that (NTC)
 PTC up to about 200 C

29. Resistance of silicon resistive
sensor

30. Resistance of silicon resistive
sensor - specific device

31. Silicon resistive sensors
 Silicon resistive sensors are somewhat
nonlinear and offer sensitivities of the order
0.5-0.7 %/C.
 Can operate in a limited range of
temperatures like most semiconductors
devices based on silicon
 Maximum range is between –55C to
+150C.
 Typical range: - 45C to +85C or 0C to
+80C
 Resistance: typically 1k at 25 C.
 Can be calibrated in any temperature scale
 Made as a small chip with two electrodes and
encapsulated in epoxy, metal cans etc.

32. Thermistors
 Thermistor: Thermal resistor
 Became available: early 1960’s
 Based on oxides of semiconductors
 High temperature coefficients
 NTC
 High resistances (typically)

33. Thermistors (cont.)
 Transfer function:
 a [] and  [K] are constants
 R(T): resistance of the device
 T: temperature in K
 Relation is nonlinear but:
 Only mildly nonlinear ( is small)
 Approximate transfer function
R T = ae/T

34. Construction
 Beads
 Chips
 Deposition on substrate

35. Epoxy encapsulated bead
thermistors

36. Thermistors - properties
 Most are NTC devices
 Some are PTC devices
 PTC are made from special materials
 Not as common
 Advantageous when runaway
temperatures are possible

37. Thermistors - properties
 Self heating errors as in RTDs but:
 Usually lower because resistance is higher
 Current very low (R high)
 Typical values: 0.01C/mW in water to 1C/mW in air
 Wide range of resistances up to a few M
 Can be used in self heating mode
 To raise its temperature to a fixed value
 As a reference temperature in measuring flow
 Repeatability and accuracy:
 0.1% or 0.25C for good thermistors

38. Thermistors - properties
 Temperature range:
  50 C to about 600 C
 Ratings and properties vary along the range
 Linearity
 Very linear for narrow range applications
 Slightly nonlinear for wide temperature ranges
 Available in a wide range of sizes, shapes and also
as probes of various dimensions and shapes
 Some inexpensive thermistors have poor
repeatability - these must be calibrated before use.

39. Thermoelectric sensors
 Among the oldest sensors (over 150 years)
 Some of the most useful and most common
 Passive sensors: they generate electrical
emfs (voltages) directly
 Measure the voltage directly.
 Very small voltages - difficult to measure
 Often must be amplified before interfacing
 Can be influenced by noise

40. Thermoelectric sensors (cont.)
 Simple, rugged and inexpensive
 Can operate on almost the entire range of
temperature from near absolute zero to about
2700C.
 No other sensor technology can match even
a fraction of this range.
 Can be produced by anyone with minimum
skill
 Can be made at the sensing site if necessary

41. Thermoelectric sensors (cont.)
 Only one fundamental device: the
thermocouple
 There are variations in construction/materials
 Metal thermocouples
 Thermopiles - multiple thermocouples in series
 Semiconductor thermocouples and thermopiles
 Peltier cells - special semiconductor thermopiles
used as actuators (to heat or cool)

42. Thermoelectric effect
 The Seebeck effect (1821)
 Seebeck effect is the sum of two other effects
 The Peltier effect
 The Thomson effect
 The Peltier effect: heat generated or absorbed at the
junction of two dissimilar materials when an emf
exists across the junction due to the current produced
by this emf in the junction.
 By connecting an external emf across the junction
 By the emf generated by the junction itself.
 A current must flow through the junction.
 Applications in cooling and heating
 Discovered in 1834

43. Thermoelectric effect (cont.)
 The Thomson effect (1892): a current
carrying wire if unevenly heated along
its length will either absorb or radiate
heat depending on the direction of
current in the wire (from hot to cold or
from cold to hot).
 Discovered in 1892 by William Thomson
(Lord Kelvin).

44. Thermoelectric effect (cont.)
 The Seebeck effect: an emf produced
across the junction of two dissimilar
conducting materials connected together.
 The sum of the Peltier and the Thomson
effects
 The first to be discovered and used (1821)
 The basis of all thermoelectric sensors
 Peltier effect is used in Thermoelectric
Generators (TEG) devices

45. The Seebeck effect
 If both ends of the two conductors are
connected and a temperature difference is
maintained between the two junctions, a
thermoelectric current will flow through the
closed circuit (generation mode)

46. The Seebeck effect
 If the circuit is opened an emf will appear
across the open circuit (sensing mode). It is
this emf that is measured in a thermocouple
sensor.

47. Themocouple - analysis
 Conductors a, b
homogeneous
 Junctions at
temperatures T2 and
T1
 On junctions 1 and
2:
 Total emf:
emfA = aA T2  T1 emfB = aB T2  T1
emfT = emfA  emfB = aA  aB T2  T1 = aAB T2  T1

48. Thermocouple - analysis
 aA and aB are the absolute Seebeck
coefficients given in V/C and are
properties of the materials A, B
 aAB=aAaB is the relative Seebeck
coefficient of the material combination A
and B, given in V/C
 The relative Seebeck coefficients are
normally used.

49. Absolute Seebeck coefficients

50. Thermocouples - standard
types
Table 3.4. Thermo couples (standard types and others) and some of their properties
Materials Sensitivity
[V/C]
at 25C.
Standard
Type
designa tion
Temperature
range [C]
Notes
Copper/Constantan 40.9 T 270 to 600 Cu/60%Cu40%Ni
Iron/Constantan 51.7 J 270 to
1000
Fe/60%Cu40%Ni
Chromel/Alumel 40.6 K 270 to
1300
90%Ni10%Cr/55%Cu45%Ni
Chromel/Constantan 60.9 E 200 to
1000
90%Ni10%Cr/60%Cu40%Ni
Platinum(10%)/Rhodium-Platinum 6.0 S  to 1450 Pt/90%Pt10%Rh
Platinum(13%)/Rhodium-Platinum 6.0 R  to 1600 Pt/87%Pt13%Rh
Silver/Paladium 10 200 to 600
Constantan/Tung sten 42.1 0 to 800
Silicon/Aluminum 446 40 to 150
Carbon/Sili con Carbide 170 0 to 2000
Note: sensitivity is the relative Seebeck coefficient.

51. Seebeck coefficients - notes:
 Seebeck coefficients are rather small –
 From a few microvolts to a few millivolts per
degree Centigrade.
 Output can be measured directly
 Output is often amplified before interfacing to
processors
 Induced emfs due to external sources cause noise
 Thermocouples can be used as thermometers
 More often however the signal will be used to take
some action (turn on or off a furnace, detect pilot
flame before turning on the gas, etc.)

52. Thermoelectric laws:
 Three laws govern operation of
thermocouples:
 Law 1. A thermoelectric current cannot
be established in a homogeneous circuit
by heat alone.
 This law establishes the need for junctions
of dissimilar materials since a single
conductor is not sufficient.

53. Thermoelectric laws:
Law 2. The algebraic sum of the thermoelectric
forces in a circuit composed of any number
and combination of dissimilar materials is
zero if all junctions are at uniform
temperatures.
 Additional materials may be connected in the
thermoelectric circuit without affecting the output
of the circuit as long as any junctions added to the
circuit are kept at the same temperature.
 voltages are additive so that multiple junctions
may be connected in series to increase the output.

54. Thermoelectric laws:
 Law 3. If two junctions at temperatures T1
and T2 produce Seebeck voltageV2 and
temperatures T2 and T3 produce voltage V1,
then temperatures T1 and T3 produce
V3=V1+V2.
 This law establishes methods of calibration of
thermocouples.

55. Thermocouples: connection
 Based on the thermoelectric laws:
 Usually connected in pairs
 One junction for sensing
 One junction for reference
 Reference temperature can be lower or higher than sensing
temperature

56. Thermocouples (cont.)
 Any connection in the circuit between
dissimilar materials adds an emf due to that
junction.
 Any pair of junctions at identical temperatures
may be added without changing the output.
 Junctions 3 and 4 are identical (one between
material b and c and one between material c and
b and their temperature is the same. No net emf
due to this pair
 Junctions (5) and (6) also produce zero field

57. Thermocouples (cont.)
• Each connection adds two junctions.
• The strategy in sensing is:
 For any junction that is not sensed or is not a reference
junction:
• Either each pair of junctions between dissimilar materials
are held at the same temperature (any temperature) or:
• Junctions must be between identical materials.
• Also: use unbroken wires leading from the sensor to the
reference junction or to the measuring instrument.
• If splicing is necessary to extend the length, identical wires
must be used to avoid additional emfs.

58. Connection without reference
 The connection to a voltmeter creates two junctions
 Both are kept at temperature T1
 Net emf due to these junctions is zero
 Net emf sensed is that due to junction (2)
 This is commonly the method used

59. Reference junctions
 Reference junctions must be at
constant, known temperatures.
Examples:
 Water-ice bath (0C)
 Boiling water (100C)
 Any other temperature if measured
 A separate, non-thermocouple sensor
 The output compensated based on this
temperature from Seebeck coefficients

60. Thermocouples - practical
considerations
 Choice of materials for thermocouples.
Materials affect:
 The output emf,
 Temperature range
 Resistance of the thermocouple.
 Selection of materials is done with the aid of
three tables:
 Thermoelectric series table
 Seebeck coefficients of standard types
 Thermoelectric reference table

61. Thermoelectric series tables
 Each material in the table is
thermoelectrically negative with respect
to all materials above it and positive
with respect to all materials below it.
 The farther from each other a pair is,
the larger the emf output that will be
produced.
 Tables are arranged by temperature
ranges

62. Thermoelectric series table
Table 3.5 The thermoelectric series: selected elements and alloys at selected temperatures
100C 500C 900C
Antimony Chromel Chromel
Chromel Copper Silver
Iron Silver Gold
Nichrome Gold Iron
Copper Iron 90%Pt-10Rh
Silver 90%Pt-10Rh Platinum
90%Pt-10Rh Platinum Cobalt
Platinum Cobalt Alumel
Cobalt Alumel Nickel
Alumel Nickel Constantan
Nickel Constantan
Constantan

63. Seebeck coefficients tables
 Seebeck coefficients of materials with
reference to Platinum 67
 Given for various thermocouple types
 The first material in each type (E, J, K,
R, S and T) is positive, the second
negative.

64. Seebeck coefficient tables

65. Seebeck coefficients tables
 The Seebeck emf with reference to Platinum
is given for the base elements of
thermocouples with respect to Platinum 67.
 Example, J type thermocouples use Iron and
Constantan.
 Column JP lists the Seebeck emf for Iron with respect to
Platinum
 Column JN lists the emfs for Constantan.
 Adding the two together gives the corresponding value for
the J type thermocouple in Table 3.5. JP and JN values at
0C in table 3.3 : 17.9+32.5=50.4 V/C gives the entry in
the J column at 0 C in Table 3.5.

66. Seebeck coefficients by type

67. Thermoelectric reference table
 List the transfer function of each type of
thermocouple as an nth order polynomial, in a
range of temperatures.
 Ensure accurate representation of the
thermocouple’s output and can be used by
the controller to accurately represent the
temperature sensed by the thermocouple.
 An example of how these tables represent
the transfer function is shown next

68. Thermoelectric reference table
(cont.)

69. Thermoelectric reference table
 Table entry for type E thermocouples.
 Second column is the exact representation of the
output emf (voltage) in V as a 9th order polynomial.
 The third column shows the inverse relation and
gives the temperature based on the emf of the
thermocouple within a specified error – in this case
±0.1C.
 The latter can be used by the controller to display
temperature or take action

70. Standard thermocouples - properties

71. Thermocouple (exposed
junction)

72. Thermocouple (flexible, to be
cemented to surface)

73. Thermocouple (protected
junction)

74. Semiconductor thermocouples
 Semiconductors have highest Seebeck
coefficients
 Typical values are about 1mV/C
 Junctions between n or p type
semiconductors with a metal (aluminum) are
most common
 Smaller temperature ranges (usually –55 C
to about 150C.
 Some materials - up to 225C
 Newer devices - up to about 800C

75. Semiconductor
thermocouples: operation
 Pure semiconductor: electrons in valence/covalence
bonds
 Few electrons are available for conduction
 Adding heat moves them across the energy gap into
the conduction band
 To increase number of electrons - need to dope the
material

76. Semiconductor
thermocouples: operation
 Doping
 Add impurities - various materials
 Increases availability of electrons (n-type)
or holes (p-type)
 Increases the Seebeck coefficient
 Silicon has 4 valent electrons
 Add impurity with 5 electrons to create n
type silicon
 Add impurity with 3 electrons to create p
type silicon

77. Semiconductor
thermocouples: operation
 P type silicon junction (on aluminum)
 Aluminum is deposited on an intrinsic layer of
silicon
 The silicon is doped with materials from the IIIrd
group in the periodic table
 materials such as Boron (B), Aluminum (Al),
Galium (Ga), Indium (In) and Thalium (Tl)
 N type silicon junction (on aluminum)
 The silicon is doped with materials from the Vth
group in the periodic table
 materials such as Phosphorus (P), Arsenic (As),
Antimony (Sb) and Bismuth (Bi)

78. Periodic table -
semiconductors

79. Thermopile
 n thermocouples in
series electrically
 In parallel thermally
 Output is n times the
output of a single
thermocouple

80. Thermopiles (cont.)
 Used to increase output
 Sometimes done with metal
thermocouples
 Example: pilot flame detector: 750 mV
at temperature difference of about
120C. about 100 metal thermocouples.

81. Semiconductor thermopiles
 Each thermocouple has higher output
than metal based devices
 A few thermocouples in series can
produce relatively high voltage
 Used to produce thermoelectric
generators.
 Outputs upwards of 15V are available
 Known as Peltier cells

82. Peltier cells
 Made of crystalline semiconductor materials
such as bismuth telluride (Bi2Te3) (n-p
junctions)
 Peltier Cells are often used for cooling and
heating in dual purpose refrigerators,
 Can also be used as sensors and can have
output voltages of a few volts (any voltage
can be achieved)
 Also used as power generators for small
remote installations

83. Peltier cells (cont.)
 Junctions are sandwiched between two
ceramic plates
 Standard sizes are 15, 31, 63, 127 and 255
junctions
 May be connected in series or parallel,
electrically and/or thermally.
 Maximum temperature difference of about
100C
 Maximum operating temperatures of about
225C
 Also used as power generators for small
remote installations

84. Some thermopiles (Peltier
TEGs)

85. Details of the TEG
construction

86. P-N Junction temperature
sensors
 A junction between a p and an n-doped
semiconductor
 Usually silicon (also germanium,
galium-arsenide, etc.)
 This is a simple diode
 Forward biased

87. P-N junction sensor (cont.)
 Construction of the sensor

88. P-N junction sensor (cont.)
 Forward current is temperature dependent
 Any semiconductor diode will work
 Usually the voltage across the diode is sensed

89. P-N junction sensor (cont.)
 Forward current through
diode
 Voltage across diode
 I0 - saturation current
 Eg - band gap energy
 q - charge of electron
 k - Boltzman’s constant
 C - a temp. independent
constant
 T - temperature (K)
I = I0eqV/2 kT
Vf =
Eg
q  2kT
q ln C
I

90. P-N junction sensor (cont.)
 If C and I are constant, Vf is linear with
temperature
 Diode is an NTC device
 Sensitivity: 1-10mV/C (current dependent)

91. P-N junction - operation
parameters
 Forward biased with a current source
 10-100A typically (low currents -
higher sensitivity)
 Maximum range (silicon) –55 to 150C
 Accuracy: ±0.1 C typical
 Self heating error: 0.5 mW/C
 Packaging: as a diode or as a transistor
(with additional circuitry)

92. The LM35 sensor

93. Other temperature sensors
 Optical
 Acoustical
 Thermomechanical sensors
 Thermomecahnical actuators

94. Optical temperature sensors
 Noncontact
 Conversion of optical radiation into heat
 Most useful in infrared temperature sensing
 Relies on quantum effects - discussed in the
following chapter
 Other sensors rely on phase difference in
propagation
 Light propagates through a silicon optical fiber
 Index of refraction is temperature sensitive
 Phase of detected light is a measure of temperature

95. Acoustical temperature sensor
 Speed of sound is
temperature dependent
 Measure the time it
takes to travel through
the heated medium
 Most sensors use
ultrasonic sensors for
this purpose.
vs = 331.5 T
273.15
m
s

96. Acoustical temperature sensor

97. Acoustical temperature sensor

98. Thermo-mechanical sensors
 Changes of physical properties due to temperature
 Length
 Volume
 Pressure, etc.
 Expansion of gasses and fluids (thermometers)
 Expansion of conductors (thermometers,
thermostats)
 Many have a direct reading (graduation, dials)
 Some activate switches directly (thermostats)
 Examples:

99. Gas expansion temperature
sensor
 Rise in temperature expands the gas
 Diaphragm pushes on a “sensor” (strain
gauge, potentiometer) or even a switch
 The sensor’s output is graduated in
temperature

100. Thermo-pneumatic sensor
 Called a Golay cell
 Gas expands in a flexible cell
 Motion moves a mirror and deflects light
 Extremely sensitive device

101. Thermal expansion of metals
 All metals expand
with temperature
 Volume stays
constant - length
changes
 Each metal has a
coefficient of linear
expansion a.
 a is usually given at
T1, temperatures in
C.
l2 = l1 1 + a T2  T1 m

102. Coefficients of linear
expansion

103. Thermal expansion of metals
 Coefficients of linear expansion are
small
 They are however measurable
 Can be used to directly operate a lever
to indicate temperature
 Can be used to rotate a shaft
 In most cases the bimetal configuration
is used
 Serve as sensors and as actuators

104. Example: direct dial indication
 Metal bar expands as temperature increases
 Dial arrow moves to the left as temperature rises
 Very small motion
 The dial can be replaced to a pressure sensor or a
strain gauge

105. Bimetal sensors
 Two metal strips welded together
 Each metal strip has different coefficient of
expansion
 As they expand, the two strips bend. This
motion can then be used to:
 move a dial
 actuate a sensor (pressure sensor for example)
 rotate a potentiometer
 close a switch

106. Bimetal sensors (cont.)
 To extend motion, the bimetal strip is bent
into a coil. The dial rotates as the coil
expands/contracts

107. Bimetal sensors (cont.)
 Displacement for the
bar bimetal:
 r - radius of
curvature
 T2 - sensed
temperature
 T1 - reference
temperature
(horizontal position)
 t - thickness of
bimetal bar
r = 2t
3 au  al T2  T1
d = r 1  cos 180L
r
m

108. Bimetal switch (example)
 Typical uses: flashers in cars, thermostats)
 Operation
 Left side is fixed
 Right side moves down when heated
 Cooling reverses the operation

109. Bimetal coil thermometer

110. Bimetal switch (car flasher)