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Temperature SensorsWhat is the best sensor to measure temperature?

There is no such thing… depends on the temperature range,the accuracy needed, the environment, the cost, etc.

We have looked at RTDs, which have their electricalresistance vary with temperature. We then studied how tomeasure resistance.

NOTE: While we talked about measuring resistance in thecontext of thermometry, the tips we used are general, andapply to measuring resistance for other reasons too. We willrevisit this later today and in future lectures.

Thermistors• Solid-state semiconductor device

– Positive temperature coefficient (PTC) devicesincreases resistance with temperature increase

– Negative temperature coefficient (NTC) devicesdecreases resistance with temperature increase

• Relationship between R and T is non-linear,but has a very steep slope– Increases the sensitivity of the device– Resistance change of 3%/°C– Limits range of operation

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ThermistorsNon-linear resistance vs. temperature means:

•High sensitivity

•Reproducibility not as good as Pt RTD

•Calibration important, and must be done at severalpoints.

•Resistance can be chosen: Ω to MΩ

•Temperature range small, but can be chosen inrange of interest

Devices can be tiny - therefore fast response time. Muchcheaper than Pt RTDs.

Chemical stability not as good… long term drift due tothermal cycling.

Thermistor vs RTD

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Thermistors

Thermistor Functional Form

• Relationship between R and T given bythe Steinhart-Hart equation

RT - resistance at temperature Ta, b, c, d - constants given by device

manufacturerT - temperature in K

!

1

T= a + bln R

T( ) + c ln RT( )

2

+ d ln RT( )

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4

Higher resistance makes lead wire effects negligible.Self-heating problem identical to RTDs - best to stilluse a bridge.

Cryogenic SensorCernox ® from Lakeshore

Each device must be calibrated foraccurate use, but general form is similar, so a 1-pt calibration often used

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Temperature Ranges

Temperature (Kelvin)

MeasuringTemperature

1mK 10mK 100mK 1K 10K 100K 1000K 10000K

4.2K 77K 0oC100oC

4He

N2

194K

CO

2

H2 O

Magnetic Thermometry

RuO2 Resistance

Pt Resistance

Thermistor

Copper-Constantan

Thermocouples

IronConstantan

Chromel-Alumel

Tungsten-Rhenium

Infrared

PyrometryMelting Curve

Spectroscopy

Thermocouples

Two dissimilar metals in contact generate a potentialdifference between junctions at different temperatures

+V -V

Seebeck Effect

Relies on the correlation between the electric potentialand thermal gradient.

The size of the effect, and reproducibility has lead toestablished pairs of metals.

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Standard Thermocouples

Need to keep a “referencejunction” at a knowntemperature. Tables for0ºC (see Omega catalog!).

Electronic compensationcan be used if thereference junction isn’t at0ºC.

Thermocouples•Work over a wide range of temperature

•No self-heating

•mV output, but reasonable sensitivity (ΔV/ ΔT large).

•Use the “Thermocouple Laws”:

•Thermal emf unaffected by temperature elsewhere in thecircuit if the two metals are homogeneous

•A third homogeneous metal inserted in the circuit doesn’taffect emf [this is the voltmeter].

•Cheap! Rugged!

•Can be small for fast response.

•Good linearity, but not particularly accurate.

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Sealedsheath

Groundedto sheath

Exposed

• Isolated from sheath+ Wires well protected- Slow response time (75 sec)

• Grounded to sheath+ Wires well protected+ Reasonable response time (40 sec)

• Exposed+ Fast response time (2 sec)- Wires exposed to damage

(physical/chemical)

Thermocouples

-200 - 350 0°C55% Cu45% Ni

100% CuT

0 - 1450 0°C100% Pt90% Pt10% RhS

0 - 1450 0°C100% Pt87% Pt13% RhR

0 - 1250 0°C95.5% Ni

4.4% Si84.4% Ni14.2% Cr

1.4% SiN

0 - 1250 0°C95% Ni5% other

90% Ni10% CrK

0 - 750 0°C55% Cu45% Ni

99.5% FeJ

0 - 900 0°C55% Cu45% Ni

90% Ni10% CrE

870 - 1700 0°C93.9% Pt6.1% Rh

70.4% Pt29.6% RhB

TemperatureRange

Negative LegMetal

Positive LegMetalStandard Type

*Modified from Temperature Sensors, The Watlow Educational Series Book Four

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Seebeck EffectThe emf generated by the Seebeck effect can be present inRTDs and thermistors too! This is an unwanted effect thatwould look like a different temperature.

rsIrL

rL

R Vrin

rL

rL

emf

Avoid it by reversing current: emf doesn’t change, but IRdoes. We can do this with positive and negative DC currents, or use an AC signal.

Cryogenic AC ResistanceBridge

At low temperature, the self-heatingeffect is even more pronounced, soALL these techniques are used, plusmany more.

P=V2/R =10-8/103

=10-11 W

ΔR/R=.1/103 =10-4

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Junction SemiconductorSensors

Silicon transistors configured in a circuit that hasmeasurable and predictable I-V. Different configurationspossible.

Benefits:

•Cheap

•Integrated with other silicon circuits (for memory,communication, amplification, processing, etc.)

Disadvantages

•Needs power, not rugged, not standardized, limitedtemperature range

AD590 IC TemperatureSensor

Operating Principle: Transistor’s current in saturation dependson

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Optical ThermometryHot bodies radiateelectromagnetic energydepending on theirtemperature.

M=energy emitted perunit frequency.

The surface of thematerial matters:emissivity of a materialε<1, and can depend ontemperature.

Infrared Photometry

The intensity of the radiationincreases with increasingtemperature:

I = σ ε(T4-T04)

For most accessibletemperatures, the radiation is inthe infrared region.

Use an infrared light detector (discussed later in the class),measure the light intensity, infer the temperature.

Advantages: Non-contact, quick, thermal contact not a problem

σ = 5.67 × 10−8 J s-1 m-2 K-4

Stefan-Boltzmann constant

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Infrared PhotometryI = σ ε(T4-T0

4)

ε is the emissivity - a number between 0 and 1 whichdefines how close to a “black body” (perfect emitter)the material is. No material is perfect, and surfacechanges result in changes to the emissivity.

The “grey body” approximation sets ε as a constantfor all wavelengths.

Accurate measurements of ε are difficult, and arelikely to change. Thus accuracy of infraredphotometry is limited by the knowledge of theemissivity.

Ratio PyrometryMeasure the infrared intensity at two different wavelengths,take the ratio.

As long as ε doesn’t vary significantly withwavelength, the ratio has a simpledependence on temperature. Measuringat two narrow wavelengths difficult.

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Pyrometry

For still higher temperatures, the thermal emission will be in thevisible regime.

Measuring the colour of the light,or more precisely the spectrum,will allow the temperature to beknown.

One simple way to measuretemperature is to compare twospectra - Disappearing filamentoptical pyrometer.

Disappearing Filament OpticalPyrometer

Look at background image whilelooking at a tungsten filament. Putpower into the filament until it appearsto glow the same colour as thebackground. Using the knownproperties of the filament, itstemperature can be found, and thetemperature of the background objectis the same.

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Measurement & UncertaintiesAnytime you make a measurement, you should quote anuncertainty on that measurement. This uncertainty tells thereader how confident you are in the number and takes intoaccount two effects:

Statistical uncertainty: due to the random nature of someprocesses, we expect there to be variation in the measuredvalues. For example: nuclear decay is a perfectly randomevent, so counting the number of decays in a given time willhave some variation.

Statistical uncertainties happen whenever randomness isinherent:

- Nuclear decay-quantum processes-sampling of a larger ensemble

Measurement and UncertaintiesSystematic Uncertainties:“Systematic Uncertainty: This is the degree to which ameasured value differs from the 'true' value because of errorsinherent in the measurement. This may be due to an incorrectscale, a wrong calibration or an erroneous assumption. Ininstrumentation, changes in the original calibration of aninstrument over time, or if the instrument is used underabnormal conditions are major sources of systematic error.Systematic errors are generally not statistical in nature andmay be corrected by measurement of a standard.”

From textbook

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Measurement and Uncertainties

These definitions are rather narrow, and exclude lots of othererrors:

•Limited precision of a measurement device

•Uncontrolled variation of extraneous variables (eg. biology)

•Variation in amplifier output which affects measured values

•Difficulty in making a measurement

These fluctuations may or may not be strictly “random” orstatistical in nature. Often we will use statistics to study theseeffects - which may or may not be strictly true. Much of thiscourse focuses on designing instruments or experimentswhich minimize these effects.

Example of Uncertainties

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Uncertainties

Physics 252 (or other statistics class) dealt with the randomuncertainties present in all measurements, and harnessedthe power of statistics to deal with them.

- Much of this is reviewed in chapter 1 ofSayer & Mansingh.

Physics 352 builds on this. How can we use physics,instrumentation and electronics to reduce and understandthese uncertainties? We will still need to understandstatistics, since this is the way these random fluctuationsare characterized, but we will go beyond that to study whythe fluctuations occur…

Next few lectures: NOISE