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Temperature sensors
1.
2.
3.
4.
5.
Introduction, temp. scales
Thermoresistive sensors
2.1 Resistance temperature detectors (RTD)
2.2 Thermistors
Thermoelectric sensors
Semiconductor p/n junction sensors
Optical temperature detectors
5.1. Pyrometers
5.2. Fiber optic detectors
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Introduction
From historical point of view the most widely used phenomenon for temperature
sensing was expansion (mercury thermometers).
At present one uses detectors with electrical signal at the output.
Temperature detectors can be classified basing of several criteria.
From the point of view of generated power we have:
• generation-type sensors (eg. thermoelectric)
• parametric-type (eg. resistance R(T), magnetic μ(T), dielectric ε(T))
From the point of view of other criterion we have:
• contact-type sensors (eg. thermoresistors)
• noncontact sensors (eg. pyrometers)
In practice we expect that temp. sensors will be:
• accurate (for a given temp. range)
• reliable (important in process control)
• inexpensive (in consumer applications)
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Growing perspectives of temperature sensors:
• expansion of layer technologies and micromachining
• increased application of fiber optic sensors
• increased role of microprocessors and sensors with digital output.
Temperature scales
• Celsius scale (1742)
Based on two equilibrium points of water: freezing (00C) and boiling (1000C)
• Thermodynamic scale
Based on the Carnot engine
T = Ttr · Q/Qtr Q – heat absorbed from the source of temp.T
Qtr – heat discharged to the source of temp.
Ttr= 273.16 K
• International Temperature Scale 1990 (ITS90)
Based on thermodynamic scale which is conneted with Celsius scale as follows:
t(oC) = T(K) – 273,15 then 1oC = 1K.
There are introduced 17 fixed points (phase equilibrium points) with defined
temperatures, interpolation formulae between the fixed points and 4 standard
thermometers for temperature measurements. For example between the triple point of
equilibrium hydrogen (13.8033K) and the freezing point of silver (961.78 0C) T90 is
defined by means of platinum resistance thermometer.
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Thermoresistive sensors
Thermoresistive sensors can be divided into metallic - type, called RTD (resistance
temperature detectors) and semiconductor - type known as thermistors.
Metallic temperature detectors (RTDs)
The resistance of metallic snsors in a narrow temp. range can be given as a linear
dependence:
R(t) = Ro[1 + α(t - to)]
α – temp. coefficient of resistance TCR
Ro – resistance at to (mostly 0oC or 25oC)
In a wider temp. range higher order polynomials should be used.
For example for platinum the good approximation in a range fom 00C to 8500C
is a second order polynomial (PN-EN 60751 in accordance with ITS90):
R(Ω) = Ro(1 + 39,083·10-4 T – 5,775 ·10-7 T2)
Ro – resistance at 00 C
T – temp. in Kelvin scale
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RTDs, cont.
The requirements for metallic thermoresistors are as follows:
• high sensitivity, i.e. high α
• linearity (constant α )
• miniaturization (high resistivity ρ)
• chemical inertness and long-term stability
Metal
Al
Ag
Au
Cu
Ni
Pd
Pt
Ta
W
Zn
Resistivity ρ [μΩcm] at
20oC
2,65
1,6
2,24
1,67
6,84
10,5
10,6
12,4
5,6
5,9
TCR α [1/oC]
0,0039
0,0061
0,0034
0,0039
0,0069
0,0037
0,0039
0,0038
0,0045
0,0042
Resistivities and TCR for selected metals
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Platinum resistance thermometers
Platinum is the most popular material for resistance thermometers.
Pure Pt is obtained in a form of wires with a diameter lower than 0.05mm, what is
necessary to obtain the required magnitude of a thermometer resistance.
A lot of possibilities give thin and thick film technologies, which reduces the sensor
fabrication costs.
Typical Pt sensor is known as Pt100 (100 Ω at 0oC).
Relative resistance of a platinum wire given as: R100/Ro = 1 + α Δt
is a measure of TCR and depends on wire purity.
For a very pure Pt wire one obtains:
in a precise thermometry one uses:
R100/Ro = 1,3927
R100/Ro = 1,3910
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Platinum resistance thermometers
In USA SAMA standard for Pt α value specifies :
In Eurpe the standard for Pt thermometers in
technical applications (DIN 43760, IEC 751) is:
R100/Ro = 1,3925
R100/Ro = 1,3850
IEC standard defines additionally two classes of precision for Pt thermometers:
A for the range -200 do 650oC (more rigorous)
possible error [oC]: ±(0,15 + 0,002|t|)
B for the range -200 do 850oC
possible error [oC]: ±(0,3 + 0,005|t|).
Typical dimensions of Pt wire thrmometers:
3,2 x 10 mm dla 100 Ω, 500 Ω, 1000 Ω
2 x 10 mm dla 100 Ω, 500 Ω, 1000 Ω
2 x 2,5 mm dla 100 Ω
1 x 5 mm
dla 100 Ω
Outside view of Pt wire thermometers
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Thin film Pt sensors
Thin film of Pt is deposited on the ceramic
substrate and the resistance corrected for the
required magnitude.
Laser cut thin film of
platinum with bonded lead
wires (view of a sensor
without covering protective
layers).
Ready for use thin film Pt thermometer
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Semiconductor resistance temperature sensors
(thermistors)
Thermistors are mostly obtained as sintered oxides, sulfides and selenides of
elements such as Co, Mn, Ti, Fe, Ni, Cu, Al, fabricated in a form of bars, droplets,
discs and also thick films.
Thermistors can be divided into two groups:
NTC (negative temperature coefficient)
PTC (positive temperature coefficient).
Characteristics of NTC and PTC thermistors
as compared to metallic RTD
thermoresistors.
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NTC thermistors
Conventional oxide resistors have a negative TCR and their resistance as a function of
temperature can be written with a good approximation as:
RT = A exp [β/ T]
Constant A depends on sample dimensions, β is a material constant which determines
the sensitivity (β = 3000 – 4500K).
Introducing the reference resistance Rref at a reference temp. Tref = 25oC, one obtains
RT = Rref exp [β(1/T – 1/Tref)]
The values of Rref vary in a range: 500Ω – 10MΩ.
In a wide temp. range the sensitivity is better characterised by TCR:
α = 1/RT · dRT/dT = - β/T2
The values of α are ca. 6 – 10 times higher than those for metals but decrease quickly
with temperature.
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Measurements of thermoresistors resistance
U out  IR 
Uz R
R  RT
for R T / R  1
U out  U z (1 
RT
)
R
Compensation of leads
resistance (in this case 1 and 3)
1,2,3 – identical thermoresistor leads
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Thermoelectric sensors
For this kind of sensors the generated thermo EMF is based on the Seebeck effect.
Seebeck effect (1821)
In a circuit consisting of two conductors A and B, which junctions have temperatures
+ ΔT and T, the thermoelectric voltage is generated and a thermoelectric current is
flowing.
A(+) – metal A positive
in respect to B
For a given conductor the absolute Seebeck coefficient is defined as:
a
dV
dT
and connects the generated electric field Ea with temperature gradient
Ea  a T
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T
Thermocouples
As the thermocurrent flows in a circuit consisting of at least two different conductors, the
differential Seebeck coefficient is introduced
a AB  a B  a A
and accordingly
dVAB  a ABdT
For the small temperature change we can then write
VAB  a AB ( T  T0 )
If temperature T0 of the reference junction is known then from the measurement of
thermovoltage V the temperature T of a measurement junction can be determined
(thermocouple).
In practice we do not use α which is temperature dependent but in calculation of a
thermovoltage for a given thrmocouple we exploit the tabulated values.
Example:
Calculate the thermovoltage for Au-Pd thermocouple in the case t0 = 00C, t = 2000C:
given thermovoltage for a junction Au-Pt: +1,84 mV
given thermovoltage for a junction Pd-Pt : - 1,23 mV
Calculated thermovoltage for Au-Pd thermocouple: 1,84 – (-1,23)= 3,07 mV
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Thermocouples
Thermocouples widely used are standardised. They are manufactured from alloy materials
with compositions which are often restricted by the producer.
Designation (ANSI)
Materials
E
Chromel/Constantan
J
Fe/Constantan
K
Chromel/Alumel, known also as NiCr/NiAl
T
Cu/Constantan
R
Pt/Pt-13%Rh
S
Pt/Pt-10%Rh
B
Pt-6%Rh/Pt-30%Rh
Properties of K-type thermocouple:
• 1-st thermoelectrode NiCr (+), composition: 85% Ni, 12% Cr and other elements in
small quantities
• 2-nd thermoelectrode NiAl (-), composition: 95% Ni, 2% Al, 2% Mn, 1% Si,
• nearly linear thermometric characteristics,
• resistant to oxidizing atmosphere, at elevated temperatures sensitive to reducing
atmosphere,
• working temp. range from – 2700C to 11500C, average sensitivity 41 μV/K.
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Thermocouples
Typical thermocouples are manufactured in insulation.
With the help of micromachining technology the thermocouples are manufactured on
membranes. The small heat capacity and good thermal isolation enable the registration of
infrared radiation spectra.
In the solution shown in the figure
the cold junction is placed in the
area of a good heat conductivity.
The hot junction is placed in a central
part of a membrane with low thermal
conductivity.
Additionaly the hot junction is placed
under the IR absober. Serial connection
of thermocouples, called the thermopile,
enhances the sensitivity.
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Measurements with the help of thermoelements
The basic measurement circuit
of a thermocouple.
Reference junction temperature variation
introduces the measurement error.
In a reference temp. 00C one measures εt.
In a reference temp. tr one measures εa= εt - εr
Compensation of reference temperature variation
1.
The reference junction is put at a distance from the heat source with the help of
compensation leads
PX, NX - the leads with thermoelectrical properties identical with those of thermoelements
(for PtRh-Pt one uses alloys of copper and nikel).
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Compensation of reference temperature variation, cont.
2. One uses a thermostat stabilising the reference temp., eg. 500C .
Traditionally a reference ice bath was used to maintain 00C, which presents some
limitations for the practical uses.
3. Automatic correction of the influence of reference temperature variation
The reference temp. increases from t0 to t1 .
Response of a thermometer:
Rt = R0 [1 + α (t1 – t0)]
Response of a thermocouple:
Δε = k (t1 – t0)
Compensation condition: Δε = - UN
The compensation condition is fulfilled
if Uz = 4k/α
4. Actual temperature is calculated by a microprocessor as:
t = td + C tr
td , tr– measured temp., C – thermocouple constant
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Pyrometers
This kind of thermometers is used for distant (noncontact) measurements of temperature.
It is based on the analysis of thermal radiation emitted by the objects.
Monochromatic pyrometers are used as standard thermometers from the freezing temp. of
silver (961,780C).
Classification of pyrometers:
• total radiation pyrometers (wide bandwidth)
• monochromatic pyrometers
• two-color pyrometers
• multicolor pyrometers
Basic laws of thermal radiation
• Planck’s law
Radiation flux density, i.e. power of radiation per unit of area and unit of wavelength
(Wm-2µm-1) is equal:
λ- wavelength, c1,c2 – radiation constants
c1 
   5 c2 / T
ελ –monochromatic emissivity of a source
 (e
1)
(for a blackbody equal 1)
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Pyrometers, cont.
• Stefan-Boltzmann law
Radiation is absorbed by the detector in a limited range of wavelength. Integration of the
Planck’s formula vs. wavelength gives a power per unit of area which is emitted by the object
with temperature T
σ = 5.67x10-8 W/m2K4
ε - emissivity, depending on
the surface condition and temperature
Above formulae, called S-B law, is a base of the wide
band pyrometry.
In the analysis of radiation exchange between
an object and a sensor the radiation reflected
and emitted by the sensor must be taken into
account. This leads to the dependence:
b    T 4
  s  ( T 4  Ts4 )
εS, TS – emissivity and temp.
of a sensor
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Two color pyrometer
The analysis of radiation flux density Φλ as a function of source emissivity ε indicates, that
for neighbour wavelength one can write
x 0.4 x 0.7 x 1


y 0.4 y 0.7 y 1
Therefore measurement of a
signal in two neighbour
narrow spectral ranges
elliminates the necessity of
determination the source
emissivity ε.
This is a base of the so called
two color pyrometry.
Emission spectrum for the source at temperature of
600oC and for three different emissivities ε
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Pyrometers construction
Two color pyrometer
For this purpose photonic detectors
(photovoltaic or photoconductive) are
developed,
λ1, λ2 – determine narrow bands placed in
a neighbourhood.
Wide band pyrometer
Thermal detectors are used (bolometers or
thermopiles).
Wide band entrance window is necessary.
Four colour pyrometers were developed for uses where the emissivity is very low
and not stable during processing. Four color pyrometers measure the radiation
intensity simultaneously in four different spectral areas and they are able to
adapt and make a correction of the emissivity setting.
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p/n junction as temperature sensor
Semiconductor p/n junction (of eg. diode connected transistor) is polarized in a forward
direction.
I = IS [exp(qUBE/kT) – 1]
for qUBE >> kT
UBE = (kT/q) ln (I/IS) = f(T)
for I = const one obtains quite good linearity
in a range from - 500C to + 1500C
For silicon bipolar transistors the sensitivity is equal
∂ UBE/ ∂ T ≈ - 2,25 mV/K for T=300 K and I=10 μA
However the saturation current IS depends weakly on temperature which gives the
nonlineatity error. This error is quite small and in many cases no linearity correction is
required.
Better linearity one obtains in a differential configuration.
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p/n junction as temperature sensor, cont.
Voltage drops at the junctions powered from constant current sources are equal
U F1 
kT I F 1
ln
q
I S1
UF2 
kT I F 2
ln
q
IS2
The differential voltage is equal
U  UF1  UF 2 
kT
I
I
kT
I
J
A
ln( F1  S 2 ) 
ln( F1  S 2  e 2 )
q
IF 2 IS1
q
IF 2 JS1 Ae1
For a given technology of transistors one can
assume that emitter current densities are equal
JS1 = JS2.
Labelling the emitters cross-sections ratio as r = AS2/AS1
one obtains
U 
kT
I
ln( F 1  r )
q
IF2
For IF1 = IF2 and r = 4 one gets: U  kT ln 4  120V  T [ K ]
q
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Junction as temperature sensor, integrated circuit
The circuit in the figure illustrates the practical solution of the described differential
method employing semiconductor p/n junctions.
This system is often manufactured as integrated
ciruit in a silicon substrate in monolithic sensors
requiring temperature compensation
(eg. in micromechined membrane
of pressure sensors).
Transistors Q3 i Q4 form the so called current
mirror which secures the equality of currents
IC1 = IC2= I
Drop of voltage VT on resistor R is equal
I R k

V  V V
 T   ln r T
T
be1 be2
2
q

and then is proportional to the absolute temperature.
The sensors of this type are called PTAT (proportional–to-absolute-temperature)
sensors.
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Optical temperature sensors
Fiber optic detector
With the increse of temperature,
semiconductor absorption
edge shifts to the longer wavelengths
and the transmitted light intensity
decreases.
Emission spectrum of the source
diode is also shown.
Light intensity decreases
after passing the
seniconductor.
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