Temperature Sensors/Transducers

By Dr. B.P. Nayak

Body Temperature Measurement

Where to Measure Noninvasive Sites for Tc Measurements

Oral: Temperature in this region is usually, but not always, close to core temperature because of the large regional arterial blood flow from a branch of the carotid artery. However, this measurement may be substantially affected by the following factors: •The skin on the head or face being cooler than the rest of the body •Exposure to cold air •Rapid or irregular mouth breathing patterns, especially in athletes or crying •children, that may increase local evaporation thus lowering the temperature •Ingestion of hot or cold beverages •Recent smoking •Neurological compromise making compliance difficult, e.g., by heat illness •Differences in the temperature in different parts of the mouth cavity

Where to Measure

Axilla: Measuring temperature at the axilla (‚armpit‛) is slower than oral temperature measurement, as it takes longer to reach equilibrium. Ear (Tympanic membrane): The tympanic membrane receives blood from branches of the internal carotid artery. ICA in turn supplies to the thermoregulatory center in the hypothalamic region of the brain, and is close to core temperature. Body Surface: Skin temperature is normally measured by thermistors placed on the skin, covered by a layer of insulation and secured in place by tape. This body surface temperature does not reflect Tc (core temp.), but only the temperature of the skin.

Where to Measure Invasive Sites for Tc Measurements

Rectum: Rectum contains a high density of blood vessels with a large blood flow from the core. It is accurate and convenient location for measuring core temperature. In particular, the rectum is the most widely used location for physiological and clinical studies of heat illnesses (especially in babies and children). However, the response time for determining rectal temperatures is slower. Esophagus: A small thermistor or thermocouple attached to a thin insulated wire can be swallowed so that it remains in place within the esophagus. This deep body location is close to the heart and aorta. Measurements at this location respond rapidly to changes in core temperature. Difficulty of insertion and requires skill.

Where to measure

Pulmonary Artery: A large vessel containing blood with low oxygen content extending from the right ventricle to the lungs. Reaching PA is an invasive procedure carrying significant medical risk. A long, flexible catheter (narrow tube) containing a tiny thermistor is to place the later into the pulmonary artery. Most accurate indicator of core temperature with least response time

Heat Equilibrium in

Biological System

Body Temperature Under neutral environmental conditions of an ambient temperature of 28 to 30oC and 40 to 60% relative humidity, Tc of approximately 37oC in a resting, healthy nude subject is regarded as normal body temperature.

Factors affecting: Skin temperature of a nude resting human is largely determined by the •environmental temperature, •relative humidity, •wind speed, •intensity of solar radiation, •atmospheric pressure, •metabolic rate and •skin blood flow.

Expression of Heat

During exercise at room temperature: Body temperature rises flow of warm blood from the core to the extremities increases Surface temperature rises Skin dissipates heat by radiation, conduction, convection and the evaporation of sweat. At cold ambient temperatures at rest: Blood flow to the skin is reduced heat loss from the core is minimized skin temperature falls. Circadian Rhythm: Even at rest and under constant environmental conditions, body temperature rises and falls about 0.5oC from a mean of approximately 37.0oC in a circadian cycle,

HOT: Sweating COLD: Shivering

Temperature Regulation

Heat Balance Equation

S= M-W-E-Q (M±W-E-Q)

S= Rate of heat storage of human body (W/m2) M= Metabolic rate of human body (W/m2) W= Mechanical work done by human body (W/m2) E= Rate of total evaporative loss due to respiration/skin (W/m2) Q= Total rate of heat loss from skin (W/m2)

Continued….

Metabolic Rate (M): Degree of muscle activities Environment Body size Mechanical Work (W): Positive: Work done by the body that restores energy Negative: Work done by the body that utilizes energy

J.Maxwell Donelana, Rodger Krama and Arthur D. Kuob; Simultaneous positive and negative external mechanical work in human walking; Journal of Biomechanics 35 (2002) 117–124

Continued….

Evaporative Heat Loss (E): 1. Respired vapor loss (Eres): Latent respiration heat loss (Erel) Convective or sensible respiration heat loss (Erec) 2. Evaporative heat loss from skin surface (Esk) Evaporative Heat Loss by skin diffusion (Edif) Heat loss due to regulatory sweating (Ersw)

E= Eres +Esk

= Erel + Erec + Edif + Ersw

Continued….

Dry Heat Exchange: Heat exchange b/w human body and environment by radiative heat transfer Effect of Clothing: A. Thermal insulation: Addition of thermal resistance affects heat transfer b/w human body and environment (1 Clo= 0.155 m2K/w) B. Evaporative Resistance: Measure of moisture permeability that affects latent heat transfer from skin through clothing layer and affects Esk

Heat Equivalent Circuit

Heat Form of energy of a body as an effect of their molecular motion (Q)

CHARGE

Heat Flux Transport of thermal energy (dQ/dT)

CURRENT

Temperature The degree of heat in a body as measured on a defined scale (T)

VOLTAGE

Heat Capacity The amount of heat to increase the temperature of a body by one unit (Q = CΔT)

CAPACISTANCE

Specific Heat Heat capacity per unit mass (Cs = C/m)

Thermistors A thermistor is a type of resistor with resistance varying according to its temperature. Principle:

ΔR = f (ΔT)----working p/p ΔT = f (ΔR)----recording p/p

Thermistors are widely used as temperature sensors, self-resetting overcurrent protectors, and self-regulating heating elements. Thermistors differ from resistance temperature detectors (RTDs) in that the material used in a thermistor is generally a ceramic or polymer, while RTDs use pure metals.

Thermistor: Mathematical Derivation

OVER NARROW RANGE TEMPERATURE Assuming, as a first-order approximation, that the relationship between resistance and temperature is linear, then:

ΔR = kΔT

Where, ΔR = change in resistance, ΔT = change in temperature

k = first-order temperature coefficient of resistance Thermistors can be classified into two types depending on the sign of k. A. PTC: If k is positive: device is called a positive temperature coefficient

(PTC) thermistor, or posistor. B. NTC: If k is negative: device is called a negative temperature coefficient

(NTC) thermistor.

What is a Resistor ?

Thermistors OVER WIDE RANGE TEMPERATURE

(A) For PTCs: The Steinhart-Hart equation is used: However the third order approximation gives best result, thus widely used the ‚squared‛ term is neglected due to approximation to zero Where, x, y and z are called the Steinhart-Hart constants that are specific for the thermistor and never a material property. T is the temperature in Kelvin and R is the resistance in Ohm. To give resistance as a function of temperature, the above can be rearranged into: Where, and

1/T = x + y . (ln R) + p . (ln R)2 + z . (ln R)3+……………+ p . (ln R)n

1/T = x + y . (ln R) + z . (ln R)3

R = e (β - α/2)1/3 - (β + α/2)1/3

α = (x- 1/T) / z β = sqr [(y/3z)3 + α2/4]

Thermistors

(B) For NTCs: NTC thermistors can also be characterised with the B parameter equation, which is essentially the Steinhart Hart equation with z=0. Where, the temperatures are in Kelvin and Ro is resistance at To= 25oC or 298.15oK and B= material constant Rearranging above equation: temperature can be expressed as where The linear form of B-parameter equation is On plotting ln R against T we will get a line, the slope of which gives the value of B.

1/T = 1/To + 1/B . ln (R/Ro)

r = Ro . e -B/To) T = B/ ln (R/r)

ln R = B/T + ln r

Sensitivity, Resolution and Error of NTCs Only NTCs are used for proportional temperature sensors PTCs are used as ‚switching‛ devices The sensitivity of NTCs: The fractional change in R per unit change in external temperature Where, B= Material constant (3000-5000 o K) Higher the value of B of a NTC, higher the sensitivity High sensitivity of a thermistor leads to: Large output signal More accuracy More resolution ( )

S = = [- B / T2 ]

R0 . S

R / R

T

Continued….. S = ΔR / ΔT = - B /T2

Steinhart-Hart equation introduces errors < 0.1°C over a temperature range of -30°C to +125°C < 0.01°C between -20°C to +50°C.

PTC: Construction Most PTC thermistors are of the "switching" type => their resistance rises suddenly at a certain critical temperature. Crystalline PTCs The devices are made of a doped polycrystalline ceramic containing barium titanate (BaTiO3). Principle: The dielectric constant of this ferroelectric material varies with temperature. Polymer PTCs This consists of a slice of plastic with carbon grains embedded in it. Principle: Carbon grain distance affected by the temperature Example: Polyfuse", "Polyswitch" and "Multiswitch". Like the BaTiO3 thermistor, this device has a highly nonlinear resistance /temperature response It is used for switching, not for proportional temperature measurement. Silistor A thermally sensitive silicon resistor. Silistors are similarly constructed and operate on the same principles as other thermistors, but employ silicon as the semiconductive component material.

NTC: Fabrication Principle Principle: Raising the temperature of a semiconductor increases the number of electrons able to move about and carry charge => It promotes them into the conduction band. The more charge carriers that are available, the more current a material can conduct. This is described in the formula: I = electric current (ampere) n = density of charge carriers (count/m³) A = cross-sectional area of the material (m²) v = velocity of charge carriers (m/s) e = charge of an electron (1.602 × 10-19 coulombs)

NTC: Fabrication

Solid state sintering Liquid state sintering

NTC: Fabrication-1

■ 2 or more metal oxides are powdered into fine granules ■Powder is dried and fried under high temperature ■The heated powder is passed through a chamber of high pressure and the outlet is attached to a pressing apparatus ■Pressed chips of metal oxides are cut into different shapes and are attached to lead wires by application of heat

NTC: Fabrication

■A dollop of slurry made of metal oxides and a binder is dropped onto platinum alloy wires; ■The slurry forms ellipsoid shapes; ■Metals are heated so that they shrink onto wires to form an excellent electrical contact; ■The wires are cut into shapes depending upon the use of device ■Thermistor is usually coated with glass and/ or another coating material to seal the thermistor and provide some strain relief

NTC: Fabrication-2

NTC: Recording

Thermistor is placed in one arm of a Wheatstone Bridge Other arms contain fixed resistors After appropriate mathematical derivation, the following equation is obtained The value of RT* is converted to temperature using tables that lists T as a function of RT* for the specific thermistor used

Eo

RT R2

R4 R3

Ei

RT* = RT [{1+ (2 ΔEo / Ei)} / {(1- (2 ΔEo / Ei)} ]

NTC Linearization Circuit

NTC Advantage?

High sensitivity Small size

Ruggedness Fast response times

Low cost

Disadvantage? Non linear relationship

Limited temperature range, typically -100 ~ 150 °C

Sensitivity low at higher temperature

Summary

‚Self heating‛ in thermistors is a misnomer Thermistors are passive devices and thus cannot heat themselves. It is the external circuit that supplies the energy that causes the heating. "Resistive heating" is a more accurate term. When a current flows through a thermistor, it will generate heat which will raise the temperature of the thermistor above that of its environment. If the thermistor is being used to measure the temperature of the environment, this electrical heating may introduce a significant error if a correction is not made. The resistive heating can be minimized by proper design of circuit and careful use of lead wires

Thermocouples

Based on:

Thermoelectric effect or Seebeck effect By attaching/coupling two metals/metal alloys with different conductivity, a thermocouple is designed Thermocouples measure the temperature difference between two points, NOT absolute temperature. A thermocouple can produce current, which means it can be used to drive some processes directly, without the need for extra circuitry and power sources.

Basic Working Principle

The principle of operation is on the Seebeck effect.

A temperature gradient along a conductor creates an EMF.

If two conductors of different materials are joined at one point, an EMF is

created between the open ends which is dependent upon the temperature of

the junction.

As T1 increases, so does V. The EMF also depends on the temperature of the

open ends T2.

The junction is placed in the process, the other end is in iced water at 0C. This is called the reference junction.

Thermoelectric series Seebeck's thermoelectric series:

• The position of a metal in this series, as Seebeck himself observed, is dependent upon the temperature and also somewhat upon its purity.

• When a circuit is formed of two metals in the series, the thermal electromotive force (emf) is greater the farther the metals are apart in the series.

• Also, the direction of the current, at the hot junction, is from the metal occurring earlier in the series to the metal occurring later in it.

bismuth (Bi), nickel (Ni), cobalt (Co), palladium (Pd), platinum (Pt), copper (Cu), manganese (Mn), mercury (Hg), lead (Pb), tin (Sn), gold (Au), silver (Ag), zinc (Zn), cadmium (Cd), iron (Fe), antimony (Sb), tellurium (Te).

Mathematical Derivation The relationship between the temperature difference and the output voltage of a thermocouple is nonlinear and is approximated by polynomial: Where, T= Change in external temperature E= Voltage produced across the couple The coefficients an are given for ‘n’ from zero to between five and nine.

0

Nn

n

n

T a E

2 2

0 1 1 2 2 1 2 1 2( ) ( ) ........ ( )n n

nE T T T T T T

2 2

0 1 1 2 2 1 2( ) ( )E T T T T

0 1 1 2( )E T T

Where, T1 and T2 = Temperatures at junctions Eo= Voltage produced across the couple α1 = αa - αb

Operation TCs cause an electric current to

flow in the attached circuit when

subjected to changes in temperature.

Current produced is dependent on

1. ΔT between the measurement and

reference junction;

2. Characteristics of the two metals

used; and

3. Characteristics of the attached

circuit.

Figure 1

TC material and connecting wire are

same metal, Eo= 0

Figure 2

TC material and connecting wire are

same metal, Eo= EA-EB= αAB (T1-T2)

Operation

ETC Tx

Tc Tv

αa

αb

αc

αc

Tx = unknown temperature. Tc = temperature at the voltmeter connector (assumed the same for both wires). Tv = internal temperature of all the voltmeter circuit elements. αa = Seebeck coefficient of thermocouple wire material .a.. αa = Seebeck coefficient of thermocouple wire material .b. αc = Seebeck coefficient of the wiring used in the voltage measuring circuit. ETC= thermocouple open circuit voltage with a high impedance circuit to minimize loop current.

ETC = αa (Tx-Tc)+ αb (Tc-Tx)----Fig 1

Fabrication

Theoretically: any pair of dissimilar materials can be used as a thermocouple. In practice: Only few materials have found applications for temperature measurement. The choice of materials is influenced by • sensitivity, • stability in calibration, • inertness in the operating atmosphere and • reproducibility (i.e. the thermocouple can be replaced by a similar

one without any recalibration).

How to Choose !!!

Fabrication

The leads of the thermocouple are encased in a

rigid metal sheath.

The measuring junction is located at the

bottom of the thermocouple housing.

Magnesium oxide surrounds the thermocouple

wires

It prevents vibration that could damage the

fine wires

It enhances heat transfer

between the measuring junction and the

medium surrounding the thermocouple.

Cold Junction Compensation

Method-1 Keeping cold junction at fixed temperature Problem: Not convenient for most directly connected indicating and control instruments. Only used at laboratory set-up

Tx

Tc Tv

αa

αb

αc

αc

ETC

Ti

αb

ETC = αa (Tx-Tc)+ αb (Tc-Ti)+ αb(Ti-Tx)---Fig 2

Cold Junction Compensation Method-3: An alternative is to use a thermostatically controlled constant temperature oven. Reference junction = Ambient temperature A fixed voltage must be added to the voltage generated by the thermocouple, to obtain the actual temperature. Since ambient temperature varies as 25 ± 15 0C, offset of the op-amp is adjusted to give/add a constant voltage corresponding to range (10-40 0C)

Cold Junction Compensation Method-2: Incorporation into their circuits an artificial cold junction using some other thermally sensitive device (a thermistor/RTD) It measures the temperature of the reference junction at the instrument and helps its deduction from probe temperature Caution: with special care being taken to minimize any temperature gradient between terminals.

• Here a thermistor, or a RTD is used to measure the ambient temperature and compensate the error through a bridge circuit.

• The bridge circuit is balanced at 0oC. • When the ambient temperature goes above 0oC, the emf generated in the

thermocouple is reduced; at the same time bridge unbalanced voltage is added to it in order to maintain the overall voltage at the same value.

Cold Junction Compensation

Method-4: Adding a device that can perform cold junction compensation by computation. It can translate device voltages to temperatures by either of two methods. 1. Approximate using polynomial interpolation and shown on display 2. Using look-up tables

Law of intermediate metals Importance: This law is also important in the construction of thermocouple junctions. It is acceptable to make a thermocouple junction by soldering the two metals together as the solder will not affect the reading.

Law of Intermediate Metals simply states that a third metal may be inserted into dissimilar metals of a thermocouple system without affecting the system if the junctions with the third metal are kept isothermal (i.e. at the same temperature).

Law of intermediate temperature

The e.m.f. of a thermocouple with junctions at two different temperatures T1and T2 is equal to the sum of the e.m.f. for any number of successive steps into which the given range may be divided. The output voltage V will be that of an Fe-C couple at temperature T, regardless of the external heat source applied to either measurement lead.

Types

Advantages

Simple and rugged installation helps remote T measurement with

proper lead wire arrangements

Highly stable and robust

Low cost

A thermocouple is capable of measuring a wider temperature

range than an RTD

Disadvantages

If the thermocouple is located some distance away from the measuring device, expensive extension grade thermocouple wires or compensating

cables have to be used.

Thermocouples can’t be used in areas where high radiation fields are present (for example, in the reactor vault).

Slower in response than RTDs

RTDs If the temperature versus resistance relationship is linear over a specific temperature range (limited), then an approximation of the relationship can be used as:

α= material temperature coefficient of resistivity (depends on material and purity) RTDs require a small current to be passed through in order to determine the resistance. Care should also be taken: To avoid any strains on the resistance thermometer in its application. To minimize the lead wire resistance To minimize resistive heating by RTD material

RTDs There are 3 common RTDs Pt-RTD Ni-RTD Cu-RTD Platinum is the most common RTD material. Platinum has a predictable (linear over a wide range) and reproducible (stable to within 0.005°C) electrical resistance to temperature relationship. The final design (or choice) of RTD measuring device depends on the acceptable level of uncertainty in the final measurement.

RTDs

Over a wide range of temperature:

RT=R0(1+ αt + βt2) To prevent this polynomial function, Calender and Griffith proposed:

RT=R0(1+ ctpt) Where, c= mean temp. coefficient of resistance over t= 0 and 100oC

tpt = Pt-specific temp. at to C

Construction

Important points: • The resistance wire is often put in a stainless steel well for protection

against mechanical hazards.

• This is also useful from the point of view of maintenance, since a defective sensor can be replaced by a good one while the plant is in operation.

• Heat conducting but electrical insulating materials is placed in between the well and the resistance material.

• The resistance wire should be carefully wound over insulating material so that no strain is developed due to length expansion of the wire.

Construction

RTD elements nearly always require insulated leads At low temperatures (< 250°C ) polymer insulators are common. At > 250°C, glass fiber or ceramic are used. The measuring point and usually most of the leads are housed in a protection sleeve (often a metal alloy which is inert) Selecting and designing protection sheaths is more crucial than sensors since this layer must withstand chemical or physical attack .

RTDs: Recording This current causes self heating of the RTD. This ‚loading error‛ may cause a significant temperature change in the sensor. To minimize loading errors, bridge circuits are used to measure the resistance of RTDs. Wheatstone bridge is the most common.

The simplest resistance thermometer configuration uses two wires. It is only used when high accuracy is not required Using this configuration , up to 100 meters of cable can be used.

Lead Wire Correction In order to minimize the effects of the lead resistances a three wire configuration can be used. The lead resistances are kept on two adjoining arms of bridge so that they cancel each other (provided the lead resistances are same) This configuration allows for up to 600 meters of cable.

R2/R3=R1/RT R2/R3= R1+a/RT+c If R2=R3, RT= R1+a- b If a=b, then lead resistance can be cancelled

b does not contribute to any error at balanced conditions because no current flows through the galvanometers, G (Vb).

a

b

c

Lead Wire Correction The four wire resistance thermometer configuration even further increases the accuracy and reliability of the resistance being measured. In the diagram below a standard two terminal RTD is used with another pair of wires to form an additional loop that cancels out the lead resistance.

We can use one or two bridges

Lead Wire Correction A better alternative configuration is four-wire Kelvin connection. It uses less wire has least error due to resistance. In this four wire measurement the resistance error due to lead wire resistance is zero.

Pyrometers

Optical Pyrometers: |Compares the color of visible light given off by the object with that of an electrically heated wire | The wire can be preset to a certain temperature | The wire can be manually adjusted to compare the two objects

Manual

Automatic

Pyrometers

Design-1: | The operator adjusts the power to the filament, changing its color, until it matches the color of the target. | The temperature of the target is measured based upon power being used by the internal filament. Design-2: | It maintains a constant current to the filament and changes the brightness of the target by means of a rotatable energy-absorbing optical wedge. | The object temperature is related to the amount of energy absorbed by the wedge, which is a function of its annular position.

The operator sights the pyrometer on target. At the same time one can see the image of an internal lamp filament in the eyepiece.

Variable current

Constant current

Pyrometers | These instruments use an electrical radiation detector, rather than the human eye. | It operates by comparing the amount of radiation emitted by the target with that emitted by an internally controlled reference source. | The instrument output is proportional to the difference in radiation between the target and the reference. | A chopper, driven by a motor, is used to alternately expose the detector to incoming radiation and reference radiation.

| The figure shows a schematic of an automatic optical pyrometer with a dichroic mirror | Radiant energy passes through the lens into the mirror, which reflects infrared radiation to the detector, but allows visible light to pass through to an adjustable eyepiece. | The calibrate flap is solenoid-operated from the amplifier, and when actuated, cuts off the radiation coming through the lens, and focuses the calibrate lamp on to the detector..

Pyrometers

Latency for flag to fall in path Latency for flag to move away from path current flow due to reference radiation

Current flow due to target radiation

Pyrometers Radiation Pyrometers: | It has two components 1. an optical system and 2. detector. | Optical system focuses the thermal radiation (IR/ Visible light) onto the detector (a thermocouple). | Output signal of the detector (Temperature T) is related to the thermal radiation or irradiance j* of the target object through the Stefan– Boltzmann law.

The law is as follows: σ= Stefan-Boltzmann constant (constant of proportionality) ε= emissivity of object

Pyrometers

Source Detector

L [W/(m².sr)] E [W/(m²)] x sr

Irradiance (E / j*) Power incident on a surface

(watt /square metre or W·m−2 )

Radiance (L) Power /unit solid angle /unit projected source area (watt /steradian /square metre or W·sr−1·m−2 )

Calculate how many solid angles of the source the incident surface corresponds

IR Probes A new and popular method for measuring body temperature at home and in many clinics is the aural thermometer that measures temperature from the tympanic membrane or tympanic canal. Why? |Within the ear, infrared (IR) radiation is emitted from all surfaces, at frequencies dependent on local temperature. |An IR probe can be placed inside the ear canal can evaluate radiation to measure inner ear temperature. |One branch of the internal carotid artery supplies blood to the thermoregulatory center in the hypothalamus region of the brain, while another branch supplies the tympanic membrane. | Because a high proportion of blood flow from the heart goes to the brain, the temperature of the brain is close to the temperature of the heart and core.

IR Probes | A disposable otoscope probe is placed into the patient’s ear. | This probe consists of a flaring cylinder with a highly polished interior surface. | It collects IR radiation from the direction in which it is aimed, and only that radiation strikes the transducer | The field of view ‚seen‛ by the transducer depends on both its distance from the target surface and viewing angle. | Conventional wave-guides in commercial use have conical fields of view of 45o around their axes. | The radius of the field of view for such a waveguide is equal to its distance from the target.

IR Probes Advantage: | Measurement is cost-effective, | Non-invasive | Convenient compared to other methods. | IR thermometers operate very rapidly, typically in less than 5 sec, because they simply record radiation; they do not have to absorb heat from a tissue that requires time for adequate heat transfer to the transducer. Disadvantage: | Despite its use in certain sports activities the aural thermometer is usually not considered accurate enough for most research. | These thermometers typically have a viewing angle that is too wide, resulting in a field of view that is too large to measure exclusively temperature of the tympanic membrane. Readings are generally lower than the actual temperature of the tympanic membrane and lower than Tc.