13.505 ELECTRONIC INSTRUMENTATION (E) MODULE II

Prepared by: Muhammedali Shafeeque K

+91 9746755046

kshafeeq007@gmail.com

onlinemas.weebly.com

Reference:

A.K. Sawhney, A course in Electrical and Electronics Measurements and Instrumentation, Dhanpat

Rai and sons

Kalsi H. S., Electronic Instrumentation, Tata McGraw Hill, 2012.

TRANSDUCERS

The electrical signal may be a current or a voltage or a frequency and production of these signals

is based upon, resistive, capacitive, inductive effects etc. The first stage of a measurement system

may simply be called a transducer stage instead of detector transducer stage by redefining a

transducer.

A transducer, in general form, may be defined as a device which converts energy from one form

to another. However this definition has to be restricted, many a time especially in the field of

electrical instrumentation. Keeping this restriction in view, transducer may be defined as a

device which converts a physical quantity or a physical condition into an electrical signal.

Another name for a transducer is pick up.

Primary arid Secondary Transducers

Primary Transducers: These are detectors which sense a physical phenomenon. According to our

latest definition of transducers which says that a transducer converts a physical phenomenon to

an electrical output. The transducer which falls in this category is thermocouple. The

thermocouple's hot junction senses the radiant heat energy and directly converts it into an analo-

gous electrical output which is a voltage.

Secondary Transducer: The physical phenomenon is first sensed by a detector and in many

situations it is converted into an analogous output. This analogous output is then converted into

electrical signal by a secondary transducer. An example of a use of secondary transducer is the

LVDT along with a Bourdon tube is used for measurement of pressure.

Infra-red Pyrometers

Infra-red pyrometers are partial or selective radiation pyrometers. Infrared energy is invisible to

the human eye, but can be felt. There is a proportional increase in infra-red energy as the

temperature of the surface radiating body increases. Above temperatures of approximately

550°C, a surface starts to radiate visible light energy and simultaneously there is a

proportional increase in the infra-red energy. This proportions increase in infra-red energy with

surface energy makes infra-red pyrometry possible combining a suitable detector, electronic

circuitry, and means of indication and/or control. The infra-red spectrum ranges from 0.22

micrometer to 17 micrometer and the commonly used portion is 2 to 7 micrometer. Some

manufacturers use only 5 to 7 micrometer portion of the range for the purposes of pyrometers.

Infra-red principles using vacuum thermocouples, thermopiles and bolometers have been

successfully employed in infra-red spectrometers as well as in total radiation pyrometers.

Various types of photo-electric transducers are most commonly used for Infrared transducers.

The most successful transducer used for industrial applications is photovoltaic cell cell. The cell

used in radiation pyrometers, in fact, responds to wavelengths in infra-red region rather than to

visible light, and may be used to measure temperatures down to above 400 degC.

An outstanding feature of the pyrometers based on photovoltaic cells is their high speed of

response. The time to reach 98% of full response to a step input is of the order of 1ms as

compared with several seconds for a total radiation pyrometer.

The infra-red radiation is focused on to a photo-voltaic cell and therefore it is necessary to insure

that the cell does not become overheated. The cone of radiation passing ultimately to the photo

cell is defined by the area of 1 first diaphragm. The protective window is made of thin glass and

serves to protect the cell and filter from physical damage. The filter is used in the range of

1000°C to 1200°C in order reduce the infra-red radiation passed to the photo cell. This helps in

preventing the photo cell from getting overheated.

All infra-red systems depend upon the transmission of the infra-red radiant energy being emitted

by a heated body to a detector in the measuring system through surroundings. There is no direct

contact with the surface whose temperature is being measured. The sensor heat| is focused on the

object whose temperature is being measured and/or controlled. The infra-re energy falling on the

detector either changes the detector resistance in proportion to temperate as in the case of a

thermistor, or generates an emf in the detector, such as a thermopile. The change in resistance or

generated emf is then indicated on a meter or a digital display or is used to operate a controller

for the process.

Optical Pyrometers

The radiations from a heated body at high temperatures fall within the visible region of the

electromagnetic spectrum. For a given wavelength in the visible region the energy radiated is

greater at higher temperatures. Within the visible region a given wavelength has a fixed colour

and the energy of radiation is interpreted as intensity or brightness. Therefore if we measure

brightness of the light of a given colour emitted by a hot source, we can have an indication of

temperature. This is the principle on which an optial pyrometer works.

In an optical pyrometer the wavelength of radiation accepted is restricted by means of a colour

filter and the brightness is measured by comparison with a standard lamp.

Disappearing Filament Optical Pyrometer: The most common type of optical pyrometer is the

"Disappearing Filament Pyrometer". The schematic diagram of this pyrometer is shown in Fig.

An image of the radiating source is produced by a lens and made to coincide with the filament of

an electric lamp. The current through the lamp filament is made variable so that lamp intensity

can be adjusted. The filament is viewed through an eye piece and a filter. The current through

filament is adjusted until the filament and the image are of equal brightness.

When the brightness of image produced by the source and brightness produced by the filament

are equal, the outline of the filament disappears as shown in Fig. (c).

However, if the temperature of the filament is higher than that required for the equality of

brightness, it (filament) becomes too bright as shown in Fig. (a). On the other hand, the

temperature of filament is lower, it becomes dark as shown in Fig..

Since the intensity of light of any wavelength depends upon the temperature of 1 radiating body

and the temperature of filament depends upon the current flowing through 1 lamp, the instrument

may be directly calibrated in terms of the filament current. However filament current depends

upon the resistance of the filament, therefore modern pyrometer are calibrated in terms of

resistance of filament circuit.

The range of temperature which can be measured by instruments of this type is governed by the

maximum allowable temperature of the lamp which is of the order of 1400°C. The range can be

extended by using an absorption type screen near objective lens. Thus a known fraction of

radiant energy enters the pyrometer for comparison. The range can be extended to 30C by

adopting this technique.

The optical pyrometer is widely used for accurate measurement of temperature of furnaces

molten metals and other heated materials.

MEASUREMENT OF FLOW

There are a number of devices for sensing the rate of fluid flow. They mainly operate with the

principle of placing an obstruction in the path of fluid causing a change in fluid press which is

dependent upon the rate of flow. Thus by measuring the difference in pressure before and after

the obstruction by means of a differential pressure sensor, the rate of flow may a determined.

They are, in fact, mechanical means of measuring rate of liquid flow. The examples of these flow

meters are : Orifice plate, venturi tube and Rotameter. Some of these method have been

explained in previous chapter. These are indirect means of measuring fluid flow However, there

are some direct methods of measuring fluid flow which are described below. These methods

employ electrical means directly.

Electromagnetic Flow meters

Electromagnetic flow meters are particularly suitable for the flow measurements of slurries,

sludge and any electrically conducting liquid.

A schematic diagram of an electromagnetic flowmeter is shown in Fig. It consists basically of a

pair of insulated electrodes buried flush in the opposite sides of a non-conducting, non-

magnetic pipe carrying the liquid whose flow is to be measured. The pipe is surrounded by an

electromagnet which produces a magnetic field. The arrangement is analogous to a conductor

moving across a magnetic field. Therefore, voltage is induced across the electrodes. This voltage

is given by : E = Blv volt where B = flux x density; Wb/m2, / = length of conductor = diameter of

pipe; m, and v = velocity of conductor (flow); m/s

Thus, assuming a constant magnetic field, the magnitude of the voltage appearing across the

electrodes will be directly proportional to velocity.

Non-conducting pipe has to be used as the output voltage gets short circuited if metallic pipes are

used. This is true when liquids of low conductivity are being measured. But when liquids of high

conductivity are measured the short circuiting has no effect. Stainless steel pipes can then be

used. The voltages produced are small specially at low flow rates. Therefore, the meter relies

greatly on a high gain amplifier to convert the induced voltage into a usable form.

Advantages :

(i) The electromagnetic flowmeters may be manufactured to measure flow in pipes of any size

provided powerful magnetic field can be produced.

(ii) The major advantage from a fluid handling point of view is that with the electromagnetic

flow meter there is no obstruction to flow that may cause pressure drops.

{Hi) The output (voltage) is linearly rated to the input (flow rate).

(iv) The output is unaffected by changes is characteristics of liquid such as viscosity, pressure,

and temperature.

Ultrasonic Flow Transducer

Basically an ultrasonic transducer for flow rate consists of two piezoelectric crystals in the liquid

or gas separated by a distance. One of crystal acts as a transmitter and the other as a receiver.

The transmitter emits an ultrasonic pulse which is received at the receiver a time Δt later. The

transit time in the direction of flow is,

𝛥𝑡1 =𝑑

𝑐 − 𝑣

where

d = distance between transmitter and receiver ; m,

c = velocity of sound propagation in medium ; m/s,

v = linear velocity of flow ; m/s.

When the signal is travelling in the opposite direction against the flow

𝛥𝑡2 =𝑑

𝑐 + 𝑣

Similarly, a sinusoidal signal of frequency f Hz travelling in the flow direction has a phase shift

of:

𝛥𝛷1 =𝑑

𝑐 − 𝑣

and that travelling against the direction of flow has a phase shift of:

𝛥𝛷2 =𝑑

𝑐 + 𝑣

Velocity can, therefore, be determined by either measuring the transit time or the phase

shift.Figure shows a system which can be used external to the pipe carrying the liquid. T and R

are respectively transmitting and receiving crystals. They are either pressed to the exterior of

pipe or are immersed in the liquid so that the signal is transmitted through the liquid.

MEASUREMENT OF DISPLACEMENT

Gray Code encoders

The shaded areas are made of conducting material and the unshaded areas are made of non-

conducting materials. Brushes are placed on the transducer which act as sliding contacts. The

circuit of sliding contacts, which come, in contact with conducting areas are completed and the

circuits of others which make contacts with insulated area are not completed. Thus the encoder

gives out a digital read out which is an indication of position and hence the encoder determines

the displacement.

In Fig., the read-out lamps are only shown for an explanatory function. The voltage on the four

lamps-lines could be sent to a digital computer directly. If a visual read-out were desired, these

four voltages would be applied to a binary-to-decimal conversion module and then read out

decimally on a display.

While the code pattern of Fig. 1.136 is most convenient for explaining how motion is represented

in the familiar natural binary system, many commercial encoders use a different code patterns

such as Gray code in order to avoid errors resulting from small misalignment which occur in

practical applications. For example, (Fig. 1.137) at the midpoint of binary scale, if the shaded

area of 22 bit were displaced slightly to the left, instead of going from 0111(7) to 1000(8), the

count would go from 0111(7) to 0011(3). The Gray code shown in the same diagram does not

suffer from this problem since only one bit changes at each transition in the case of Gray code.

Since the Gray code output may not be compatible with the read-out device, converssion from

Gray code to natural binary system (or vice versa) may be necessary. This is accomplish by

using standard logic gates as shown in Fig. 1.138.

Gray code is used for over coming the inherent disadvantages of a natural binary code. In a

natural binary code, a change of decimal number by one may result in a change of number of

bits. In the example quoted above, the transition from natural number to 7 to 8, would need a

change in all four bits as number 7 is represented by 0111 and number 8 by 1000. Thus, an

error of one bit in a large digital number, in practice, will result in large error when the

binarynumber is converted to decimal number. In the case of digital transducers, an increment of

:his order, would result in large errors when the result is reflected back into the decimal system.

In case of Gray code, in which case the change in one value to the next is by one bit ony. For

example, the change in Talue from 7 to 8 (in decimal system) is 0100 (corresponding to 7) to

1100 (corresponding to a value of 8). Thus there is a change in one bit only. Therefore, the use of

Gray system greatly reduces the errors.

LINEAR VARIABLE DIFFERENTIAL TRANSFORMER (LVDT) The most widely used inductive transducer to translate the linear motion into electrical signals is

the linear variable differential transformer (LVDT).

The basic construction of LVDT is shown in Fig. The transformer consists of a single

primary winding P and two secondary windings S1 and S2 wound on a cylindrical former.The

secondary windings have equal number of turns and are identically placed on either side of the

primary winding. The primary winding is connected to an alternating current source. A movable

soft iron core is placed inside the former. The displacement to be measured is applied to the

arm attached to the soft iron core. In practice the core is made of high permeability, nickel iron

which is hydrogen annealed. This gives low harmonics, low null voltage and a high sensitivity.

The is slotted longitudinally to reduce eddy current losses. The assembly is placed in a stainless

steel housing.

As the core is moved in one direction from the null position, the differential voltage the

difference of the two secondary voltages, will increase while maintaining an in-phase

relationship with the voltage from the input source. In the other direction from the null position

the differential voltage will also increase, but will be 180° out of phase with the voltage : the

source. By comparing the magnitude and phase of the output (differential) voltage that of the

source, the amount and direction of the movement of the core and hence displacement may be

determined.

The amount of output voltage may be measured to determine the displacement. The output signal

may also be applied to a recorder or to a controller that can restore the moving system to its

normal position.

The output voltage of an LVDT is a linear function of core displacement within a limited range

of motion, say, about 5 mm from the null position. Fig. 1.64 shows the variation of output

voltage against displacement for various positions of core. The curve is practically linear for

small displacements (upto about 5 mm as mentioned above). Beyond this range of displacement,

the curve starts to deviate from a straight line.

Fig. shows the variation of output voltage versus displacement for various positions of core. The

curve is practically linear for a limited range of displacement from the null position.

MEASUREMENT OF FORCE & PRESSURE:

Resistive Transducers. The electrical strain gauges attached to a diaphragm as shown in Fig

may be used for measurement of pressure.

The output of these strain gauges is a function of the local strain, which, in turn, is a function of

the diaphragm deflection and the differential pressure. The deflection generally follows a linear

variation with differential pressure P = P2 - P1. (when the deflection is less than one third of the

diaphragm thickness.)

One of the disadvantages of the method is the small physical area is required for mounting the

strain gauges. Change in resistance of strain gauges on account of application of pressure is

calibrated in terms of the differential pressure. Gauges of this type are made in sizes having a

lower range of: 100 kN/m-square to 3 MN/m-square to an upper range of; 100 kN/m-square to

100 MN/m-square

Inductive Transducers. Inductive transducers have been successfully used secondary

transducers along with a diaphragm for measurement of pressure. Fig shows an arrangement

which uses two coils ; an upper and a lower cod winch form the two arms of an a.c. bridge. The

coils have equal number of turns. The other two arms of the bridge are for-by two equal

resistances each of value R.

The diaphragm is symmetrically placed with respect to the coils and so when P1 = P2, the

reluctances of the paths of magnetic flux for both the coils are equal and hence the inductances of

the coils are equal.

Now initial self-inductance = N2/R0 where N = number of turns, and R0 = initial reluctance of

flux path. Under this condition the bridge is balanced and the output, e0, of the bridge is zero.

Suppose P2 is greater than P1 and therefore the differential pressure P = P2- P1, deflects die

diaphragm upwards through a distance d. For small displacements of diaphragm, the reluctance

of the flux path of the upper coil is R1 = R0 + K (D - d) and that of the lower coil is R2 = R() +

K(D + d).

Hence, the inductance of the upper coil L1 =N2/R1 and that of lower coil is L2 =N

2/R2.

The bridge becomes unbalanced and the approximate value of output voltage is given by :

𝑒0 = 1

2−

𝐿2

𝐿1 + 𝐿2 𝑒𝑖

Since D and ei are constant, the output voltage is directly proportional to replacement d, of the

diaphragm.( L1, L2 depends on d)

Displacement d, is directly proportional to differential pressure P = P2-P1. Hence the output

voltage e0 may be calibrated in terms of the differential pressure P.

LVDT. The LVDT is used as a secondary transducer for measurement of pressure with Bellows

or Bourdon tube acting as the primary transducer i.e., as a force summing device. The two

arrangements are shown in Figs respectively. The pressure is converted into displacement which

is sensed by the LVDT and transduced into a voltage.

PIEZOELECTRIC TRANSDUCERS (Pressure and force measurement)

A piezoelectric material is one in which an electric potential appears across certain surfaces of a

crystal if the dimensions of the crystal are changed by the application of a mechanical force. This

potential is produced by the displacement of charges. The effect is reversible, i.e., conversely, if

a varying potential is applied to the proper axis of the crystal, it will change the dimensions of

the crystal thereby deforming it. This effect is known as piezoelectric effect. Elements exhibiting

piezoelectric qualities are called as electro-resistive elements.

Common piezo-electric materials include Rochelle salts, ammonium dihydrogen phosphate,

lithium sulphate, dipotassium tartarate, potassium dihydrogen phosphate, quartz and ceramics A

and B. Except for quartz and ceramics A and B, the rest are man-made crystals grown from

aqueous solutions under carefully controlled conditions. The ceramic materials are

polycrystalline in nature. They are, basically, made of barium titanate. They do not have piezo-

electric properties in their original state but these properties are produced by special polarizing

treatment.

The materials that exhibit a significant and useful piezo-electric effect are divided into two

categories : (i) Natural group and (ii) Synthetic group.

Quartz and Rochelle salt belong to natural group while materials like lithium sulphate, ethylene

diamine tartarate belong to the synthetic group.

The piezoelectric effect can be made to respond to (or cause) mechanical deformations of the

material in many different modes. The modes can be : thickness expansion, transverse expansion,

thickness shear and face shear. The mode of motion effected depends on the shape of the body

relative to the crystal axis and location of the electrodes.

A piezo-electric element used for converting mechanical motion to electrical signals may be

thought as charge generator and a capacitor. Mechanical deformation generates a charge and this

charge appears as a voltage across the electrodes. The voltage is E = Q/C.

The piezo-electric effect is direction sensitive. A tensile force produces a voltage of one polarity

while a compressive force produces a voltage of opposite polarity.

A piezo-electric crystal is shown in Fig..

The magnitude and polarity of the induced surface charges are proportional to the magnitude and

direction of the applied force F. The polarity of induced charges depends upon the direction of

applied force.

Charge, Q = d x F coulomb

where

d = charge sensitivity of the crystal ; C/N : (it is constant for a given crystal)

F = applied force, N,

The force F causes a change in thickness of the crystal.

𝐹 =𝐴𝐸

𝑡𝛥 𝑡

Where

A = area of crystal ; m2,

t = thickness of crystal ; m,

E = Young's modulus, N/m2.

Young's modulus,

𝐸 =𝑆𝑡𝑟𝑒𝑠𝑠

𝑆𝑡𝑟𝑖𝑛=

𝐹

𝐴 .

1

𝛥𝑡/𝑡=

𝐹𝑡

𝐴∆𝑡

So,

Q=dAE(𝛥𝑡/𝑡)

Due to this charge voltage induced is

Voltage, E0 = Q/CP

where

Cp = capacitance between electrodes ; F.

Again, Capacitance between electrodes Cp =𝜀𝐴/𝑡

So,

𝐸0 =𝑄

𝐶𝑝=

𝑑𝑡

𝜀𝐴𝐹

(Expression for force measurement)

Also, pressure, P=F/A

So,

𝐸0 =𝑄

𝐶𝑝=

𝑑𝑡

𝜀𝑃

(Expression for pressure measurement)

Voltage sensitivity, 𝑔 =𝐸0

𝑡𝑃=

𝑑

𝜀

Modes of Operation of Piezo-electric Crystals

The piezo-electric crystals are used in many modes. These modes are :

STRAIN GAUGES If a metal conductor is stretched or compressed, its resistance changes on account of the fact that

both length and diameter of conductor change. Also there is a change in the value of resistivity of

the conductor when it is strained and this property is called piezoresistive effect. Therefore,

resistance strain gauges are also known as piezoresistive gauges. The strain gauges are used for

measurement of strain and associated stress in experimental stress analysis. Secondly, many

other detectors and transducers, notably the load cells, torque meters, diaphragm type pressure

gauges, temperature sensors, accelerometers and flow meters, employ strain gauges as secondary

transducers.

Theory of Strain Gauges The change in the value of resistance by straining the gauge may be partly explained by the

normal dimensional behaviour of elastic material. If a strip of elastic material is subjected to

tension, as shown in Fig. 1.29 or in other words positively strained, its longitudinal dimension

will increase while there will be a reduction in the lateral dimension. So when a gauge is

subjected to a positive strain, its length increases while its area of cross-section decreases as

shown in Fig. 1.29. Since the resistance of a conductor is proportional to its length and inversely

proportional to its area of cross-section, the resistance of the gauge increases with positive strain.

The change in the value resistance of strained conductor is more than what can be accounted for

an increase in resistance due to dimensional changes. The extra change in the value of resistance

is attributed to a change in the value of resistivity of a conductor when strained. This property, as

described earlier, is known as peizoresistive effect.

Let us consider a strain gauge made of circular wire. The wire has the dimensions : length = L,

area = A, diameter = D before being strained. The material of the wire has a resistivity p.

.

So,

Resistance of unstrained gauge R = pL/A.

Let a tensile stress s be applied to the wire. This produces a positive strain causing the length to

increase and area to decrease as shown in Fig. 1.29 Thus when the wire is strained there are

changes in its dimensions. Let ΔL = change in length, ΔA = change in area, ΔD = change in

diameter and ΔR = change in resistance.

Change in resistance,R with respect to change in stress,s:

From, R = pL/A. 𝑑𝑅

𝑑𝑠=

𝜌

𝐴

𝜕𝐿

𝜕𝑆−

𝜌𝐿

𝐴2

𝜕𝐴

𝜕𝑆+

𝐿

𝐴

𝜕𝜌

𝜕𝑆

Dividing throughtout by R = pL/A 1

𝑅

𝑑𝑅

𝑑𝑠=

1

𝐿

𝜕𝐿

𝜕𝑆−

1

𝐴

𝜕𝐴

𝜕𝑆+

1

𝜌

𝜕𝜌

𝜕𝑆

But, A=π/4D2

So, 𝜕𝐴

𝜕𝑆= 2

𝜋

4𝐷

𝜕𝐷

𝜕𝑆

Dividing throughout by A=π/4D2

1

𝐴

𝜕𝐴

𝜕𝑆=

2

𝐷

𝜕𝐷

𝜕𝑆

Hence, 1

𝑅

𝑑𝑅

𝑑𝑠=

1

𝐿

𝜕𝐿

𝜕𝑆−

2

𝐷

𝜕𝐷

𝜕𝑆+

1

𝜌

𝜕𝜌

𝜕𝑆

Now, Poisson’s ratio 𝜗 =𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑛

𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑛𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑛=

−𝜕𝐷

𝐷𝜕𝐿

𝐿

Or, −𝜕𝐷

𝐷=

𝜕𝐿

𝐿𝜗

Hence, 1

𝑅

𝑑𝑅

𝑑𝑠=

1

𝐿

𝜕𝐿

𝜕𝑆+

2

𝐿

𝜕𝐿

𝜕𝑆𝜗 +

1

𝜌

𝜕𝜌

𝜕𝑆

For small variations, ∆𝑅

𝑅=

∆𝐿

𝐿+ 2𝜗

∆𝐿

𝐿+

𝜕𝜌

𝜌

Gauge factor=𝐺𝑓 =∆𝑅/𝑅

∆𝐿/𝐿= 1 + 2𝜗 +

𝜕𝜌

𝜌

∆𝐿/𝐿

Strain=∈=∆𝐿

𝐿

So, 𝐺𝑓 =∆𝑅/𝑅

∆𝐿/𝐿= 1 + 2𝜗 +

𝜕𝜌

𝜌

∈

𝐺𝑓 =

∆𝑅𝑅∆𝐿𝐿

= 1 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑐𝑕𝑎𝑛𝑔𝑒 𝑑𝑢𝑒 𝑡𝑜 𝑙𝑒𝑛𝑔𝑡𝑕

+ 2𝜗 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑐𝑕𝑎𝑛𝑔𝑒 𝑑𝑢𝑒 𝑡𝑜 𝐴𝑟𝑒𝑎

+

𝜕𝜌𝜌

∈ (𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑐𝑕𝑎𝑛𝑔𝑒 𝑑𝑢𝑒 𝑡𝑜 𝑝𝑖𝑒𝑧𝑜𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑒 𝑒𝑓𝑓𝑒𝑐𝑡)

Unbonded Metal Strain Gauges

An unbonded metal strain gauge is shown in Fig.. This gauge consists of a wire stretched

between two points in an insulating medium such as air. The wires may be made of various

copper nickel, chrome nickel or nickel iron alloys. They are about 0.003 mm in diameter, have a

gauge factor of 2 to 4 and sustain a force of 2 mN. The length of wire is 25 mm or less.

In Fig. , the flexture element is connected via a rod to a diaphragm which is used for sensing of

pressure. The wires are tensioned to avoid buckling when they experience a compressive force.

The unbonded metal wire gauges, used almost exclusively in transducer applications, employ

preloaded resistance wires connected in a wheatstone bridge as shown in Fig.. At initial preload,

the strains and resistances of the four arms are nominally equal, with the result the output voltage

of the bridge, e0 = 0. Application of pressure produces a small displacement which is about 0.004

mm (full scale), the displacement increases tension in two wires and decreases it in the other two,

thereby increase the resistance of two wires which are in tension and decreasing the resistance of

the remaining two wires. This causes an unbalance of the bridge producing an output voltage

which is proportional to the input displacement and hence to the applied pressure.

Electric resistance of each arm is 120 ohm. to 1000ohm, the input voltage to the bridge is 5 to 10

V, and the full scale output of the bridge is typically about 20 mV to 50 mV.

Bonded Wire Strain Gauges:

The bonded metal-wire strian gauges are used for both stress analysis and for construction of

transducers.

A resistance wire strain gauge consists of a grid of fine resistance wire of about 0.025 mm in

diameter or less. The grid is cemented to carrier (base) which may be a thin sheet of paper, a thin

sheet of bakelite or a sheet of teflon. The wire is covered on top with a thin sheet of material so

as to prevent it from any mechanical damage. The spreading of wire permits a uniform

distribution of stress over the grid.

The carrier is bonded with an adhesive material to the specimen under study. This permits a good

transfer of strain from carrier to grid of wires. The wires cannot buckle as they are embedded in a

matrix of cement and hence faithfully follow both the tensile and compressive strains of the

specimen. Since, the materials and the wire sizes used for bonded wire strain gauges are the same

as used for unbonded wire strain gauges, the gauge factors and resistances for both are

comparable.

The size of the strain gauges varies with application. They can be as small as 3 mm by 3 mm

square. Usually they are larger but seldom more than 25 mm long and 12.5 mm wide.

For excellent and reproducible results, it is desirable that the resistance wire strain gauges should

have the following characteristics :

(i) The strain gauge should have a high value of gauge factor Gf. A high value of gauge factor

indicates a large change in resistance for a particular strain resulting in high sensitivity.

(ii The resistance of the strain gauge should be as high as possible since this minimizes flie

effects of undesirable variations of resistance in the measurement circuit. Although undesirable,

but necessary, are the resistance of connecting leads and terminals, etc. Typical resistances of

strain gauges are 120 ohm, 350ohm. and 1000ohm. Although a high resistance value of strain

gauges is desirable from the point of view of swamping out the effects of variations of resistance

in other parts of the bridge circuit in which they are invariably used but it results in lower

sensitivity.

MEASUREMENT OF TEMPERATURE

THERMISTORS

Thermistors follow the principle of decrease in resistance with increasing temperature. The

material used in thermistor is generally a semiconductor material such as a sintered metal oxide

(mixtures of metal oxides, chromium, cobalt, iron, manganese and nickel) or doped

polycrystalline ceramic containing barium titanate (BaTiO3) and other compounds. As the

temperature of semiconductor material increases the number of electrons able to move about

increases which results in more current in the material and reduced resistance. Thermistors are

rugged and small in dimensions. They exhibit nonlinear response characteristics. Thermistors are

available in the form of a bead (pressed disc), probe or chip. Figure 2.5.4 shows the construction

of a bead type thermistor. It has a small bead of dimension from 0.5 mm to 5 mm coated with

ceramic or glass material. The bead is connected to an electric circuit through two leads. To

protect from the environment, the leads are contained in a stainless steel tube.

Applications of Thermistors

• To monitor the coolant temperature and/or oil temperature inside the engine

• To monitor the temperature of an incubator

• Thermistors are used in modern digital thermostats

• To monitor the temperature of battery packs while charging

• To monitor temperature of hot ends of 3D printers

• To maintain correct temperature in the food handling and processing industry equipments

• To control the operations of consumer appliances such as toasters, coffee makers, refrigerators,

freezers, hair dryers, etc.

THERMOCOUPLES

A pair of two dissimilar metals that are in physical contact with each other form a thermocouple.

These metals may be twisted, screwed, peened, clamped or welded together. The most

commonly used method for fabricating is to weld the metals together.

Thermocouples do not use bare conductors except in applications where atmospheric conditions

permit their use. These conditions obtain when temperatures to be measured are low and the

atmosphere is non-corrosive. Industrial thermocouples employ protective sheathing surrounding

the junction and a portion of the extension leads. The leads and the junction are internally

insulated from the sheath, using various potting compounds, ceramic beads or oxides. The type

of insulation used depends upon the process being monitored. The different types of protective

sheaths are shown in Fig.

.

Thermocouples are normally not installed in pipelines vessels or other pieces of equipment

directly. They are usually placed inside protective wells so that they may be easily removed

laced without interruption or shutdown of the plant. Protecting wells are made of stainless steel

and some other special alloy materials. They are normally 12.5 mm to 25 mm in diameter.

The use of protective wells slows down the response appreciably as they increase the mass

thermocouples. However, in applications, where response time is the primary consideration.,bare

or thin sheathed thermocouples are used.

Theory of Thermocouple:

A pair of two dissimilar metals that are in physical contact with each other form a thermocouple.

Cold Junction Compenstion:

Temperature should be measured with the cold junction at 0°C or 32°F. When a thermocouple or

its extension wires are connected to the terminals of a device like a thermocouple transmitter the

cold junction is at the room temperature T1°C. If both temperatures of the hot and the cold

junctions are above 0°C, the device receives a lower emf than when the cold junction

temperature is 0°C. In order to measure the temperature accurately, we need to add the emf value

which corresponds to T1 to the measured emf. To add this emf is called cold junction

compensation.

The figures show the temperature-emf curve (not to scale) and a temperature measuring setup

with a thermocouple and a millivolt meter. Assume the cold and the hot junctions are at T1°C

and T2°C, respectively. According to the temperature-emf table of the standard, the

thermocouple generates emf of E1 mV at the temperature T1 and E2 mV at T2. The millivolt

meter receives the potential difference, E2 - E1 which corresponds to T2 - T1. In order to obtain

T2, we need to add E1 to the potential difference, E2 - E1 for elimination of E1.

A more accurate method for reference junction temperature compensation is shown in fig..

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 0 deg C. When the ambient

temperature goes above 0degC, 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.

As referred to Fig., the cold junction compensation is normally kept along with the signal

conditioning circuits, away from the measuring point. This may require use of long

thermocouple wires to the compensation circuit. In order to reduce the length of costly

thermocouple wires (platinum in some case) low-cost compensating wires are normally used in

between the thermocouple and the compensation circuit. These wires are so selected that their

temperature emf characteristics match closely to those of the thermocouple wires around the

ambient temperature.

Signal Conditioning Circuit

A high input impedance amplifier permits the use of large valued input resistors and retains

signal accuracy. This is very useful for protecting both the amplifier and cold junction

compensator in thermocouple applications as the sense element can often be inadvertently

connected to destructive voltage potentials. The 1MΩ resistors protect the circuit up to ±350V

with no phase reversal to amplifier output. The 1pA maximum IBIAS of the LTC6081 translates

to a miniscule 0.05°C temperature error with the 1MΩ input protection resistor. The ±90μV

offset over the entire operating temperature range ensures a less than 2°C temperature offset. The

LTC6081 is a high performance dual op amps combining excellent noise, offset drift, CMRR,

PSRR and input bias current specifications. They perform in a variety of topologies without

compromising performance. LTC6081 is available in 8-lead MSOP and 10-lead DFN packages.

BIMETALLIC THERMOMETERS

Bimetallic thermometers are extensively used in process industries for local temperature

measurements. These thermometers use two fundamental principles :

(i) all metals expand or contract with change in temperature and,

(ii) the temperature coefficient of expansion is not the same for all metals and therefore their

rates of expansion or contraction are different. The difference in thermal expansion rates is used

to produce deflections proportional to temperature changes.

A bimetallic thermometer consists of a bimetallic strip which is constructed by bonding together

two thin strips of two different metals such that they cannot move relative to each other. Since all

metals try to change their physical dimensions at different rates when subjected to same change

in temperature, these two metallic strips change their lengths at different rates. The differential

change of expansion of two metals results in bending of the bimetallic strip with change in

temperature.

Figure shows a bimetallic strip in the form of a straight cantilever beam. With one end fixed, the

temperature changes cause the free end to deflect.

The range over which a linear relationship exists between deflection and temperature depends

upon the combination of metals used for the bimetallic strip.

The deflection of the free end is directly proportional to the temperature change and square of the

length of strip, and inversely proportional to the thickness throughout the linear port of

deflection-temperature characteristics.

Figure shows a bimetallic strip made up of two metals A and B, having differ thermal expansion

co-efficients, bonded together at a temperature T1. A change Temperature, (T2 - T1), causes a

differential expansion of the strip and if the motion is unstrained, the strip deflects into a uniform

circular arc. The radius of arc is given by :

It is clear from Fig. that the bimetallic strip bends towards the side whose metal has a lower

thermal expansion co-efficient when there is increase in temperature and reverse happens when

there is decrease in temperature.

In most practical applications, the metals and their dimensions are so chosen that their noduli of

elasticity and thickness are equal i.e., EB = EA or n = 1 and tA = tA = tB or m =1.

Therefore, deflection,

Resistance Thermometers (RTD)

The resistance of a conductor changes when its temperature is changed. This property is utilized

for measurement of temperature.

The variation of resistance R with temperature T(°K) can be represented by the following

relationship for most of the metals as :

R = R0(1 + α1T + α2T 2 +......+ αnT

n + ...)

where R0 = resistance at temperature T= 0 and α1 α2…are constants.

The resistance thermometer uses the change in electrical resistance of conductor to determine the

temperature.

The resistivity of metals showed a marked dependence on temperature was discovered by Sir

Humphry Davy. A few years later Sir William Siemens preferred the use of platinum as an

element in the resistance thermometer. His choice proved most propitious, as platinum is used to

this day as the primary element in all high accuracy resistance thermometers. In fact, the

platinum resistance temperature detector (PRTD) is used today as an interpolation standard from

oxygen point (- 182.96°C) to antimony point (630.74°C)

Platinum is especially suited for this purpose, as it can withstand high temperatures while

maintaining excellent stability. As a nobel metal, it shows limited susceptibility to

contamination. All metals produce a positive change in resistance with temperature. This, of

course, is the main function of an RTD. The system error is minimized when the nominal value

of RTD is large. This implies a metal with a high value of resistivity should be used for RTDs.

The lower is the resistivity of the metal, the more material we will have to use.

The requirements of a conductor material to be used in RTDs are :

(i) The change in resistance of material per unit change in temperature should be as large as

possible.

(ii) The material should have a high value of resistivity so that minimum volume of material is

used for the construction of RTD.

2 lead RTD

2-wire construction is the least accurate of the 3 types since there is no way of eliminating the

lead wire resistance from the sensor measurement. 2-wire RTD’s are mostly used with short lead

wires or where close accuracy is not required.

Measured resistance is not accurate as lead resistance R1 and R2 are included.

3 lead RTD

3-wire construction is most commonly used in industrial applications where the third wire

provides a method for removing the average lead wire resistance from the sensor measurement.

When long distances exist between the sensor and measurement/control instrument, significant

savings can be made in using a three wire cable instead of a four-wire cable.

The 3 wire circuit works by measuring the resistance between lead 1 & lead 2 (R1+R2+ Rb) and

subtracting the resistance between lead 2 & lead 3 (R2+ R3) which leaves just the resistance of

the RTD bulb (Rb). This method assumes that wires 1,2 & 3 are all the same resistance

4 lead RTD

4-wire construction is used primarily in the laboratory where close accuracy is required. In a 4

wire RTD the actual resistance of the lead wires can be determined and removed from the sensor

measurement.

The 4-wire circuit is a true 4-wire bridge, which works by using wires 1 & 4 to power the circuit

and wires 2 & 3 to read. This true bridge method will compensate for any differences in lead

wire resistances.