4 - Sensors and Transducers

8/2/2019 4 - Sensors and Transducers

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ME21 43 / ME21 43 E Sensor s and

Transducers

Chui Chee Kong, PhDMechanical Engineering

NUS

1. Introduction1.1 Sensor Classification

1.2 Transducer1.3 Resistive Sensors1.4 Potentiometer

2. Temperature-Sensing Devices2.1 Resistive Temperature Detector (RTD)

2.2 Thermistors2.3 Radiative Temperature Sensing2.4 Thermocouples

3. Strain Gauges3.1 Gauge Factor3.2 Bridge Circuit Arrangement

3.3 Possible Arrangement of Strain Gauges4. Electromagnetic Flow Meter5. Signal Conditioning

5.1 Wheatstone Bridge - Measurement of Resistance6. Smart Sensors7. Selection of Sensors

Reference:

Mechatronics System Design by D Shetty and R. A. Kolk. PWS Publishing

Company. 1997


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1 . I n t r o d u ct i o n

Sensors transform real-world data into electrical signals. It provides a

mechanism for collecting different information about a particular process.

Definition. A sensor is defined as a device that produces an output signalfor the purpose of sensing of a physical phenomenon.

Sensors are also referred to as transducers. A transducer is a device thatconverts a signal from one physical form to a corresponding signal that

has a different physical form. In a transducer, the quantities at the inputlevel and the output level are different. Typical input signal could be

electrical, mechanical, thermal or optical.

The extent to which sensors and transducers are used is dependent uponthe level of automation and the complexity of the control system.


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1 .1 Sensor Classi f icat ion

Selection of a suitable sensor is important in the design of a mechatronic

system. In addition to the objective of measurement, application,precision and environment of usage, we also need to consider subject of

the measurement, dynamic range, cost, delivery time and ease ofmaintenance. Comparison with other sensors is usually required to justifythe use of a specific sensor for an application.

Sensors can be classified into two categories: Analog sensors and Digitalsensors. Analog is a term used to convey the meaning of a continuous,uninterrupted, unbroken series of events. Analog sensor is also known ascontinuous sensor. Continuous sensors provide information overcontinuous range of operation of the process. They are commonly used in

continuous control applications, where the process is being regulatedbased on continuously sensed attribute data. They are usually based on

electrical, optical and acoustical technologies. Digital refers to a sequenceof discrete events. Each event is a separate from the previous and thenext event. Digital sensors are also known as discrete event, or on/offsensors. These sensors typically only give knowledge of two states basedon the condition being sensed. They are usually based on mechanical,

electrical or optical technology.

Another form of classification: Active sensors and Passive sensors, isbased on power supply. In an active sensor, most of the output is

produced from a separate power source. In a passive sensor, the outputis produced from the input parameters. Passive sensors are also known as

self-generating sensors. They produce an electrical signal in response toan external stimulus.

Sensors have also been classified based on the subject of measurement.These subjects include acoustic, biological, chemical, electric, magnetic,

mechanical, optical, radiation, thermal and other.

There are many sensing types including capacitive, electromagnetic,inductive, magnetostrictive, photoconductive, photovoltaic, piezoelectric,potentiometric, reluctive, resistive, strain gage and thermoelectric.Electromagnetic, magnetostrictive, photovoltaic, piezoelectric, and

thermoelectric sensing methods are often used in passive sensors. Theydo not require external power supply since they could draw their energyfrom the process they are measuring. Examples are thermocouples, solar

panels, and tachometers.


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1.2 Tran sdu cer

A transducer is an element or device used to convert information from

one form to another. A spring is an example of a transducer. When acertain force is applied to a spring, it stretches, and the force information

is translated to displacement information. Different quantities of forceproduce differential movements that are a measure of the force. Thedisplacement y is proportional to force F, which can be expressed as

F= ky

where F= applied force, y=deflection and k=constant.

For converting temperature information into an electromotive force, a

thermocouple is used as a transducer.

Motion transducers are used for the measurement of mechanicalquantities including force, pressure, displacement, flow rate andtemperature. A transducer may measure one phenomenon in order tomeasure another variable. The primary transducer senses the preliminarydata and converts them into another form, which is then converted into

some usable form by a secondary transducer. It is common to havecombination of transducer elements in a measurement system.

A potentiometer is a displacement transducer that uses the variable

resistance transduction principle, i.e. the principle of change in resistanceof a material in the sensor.


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1 .3 Resis t ive Sensor s

A resistive sensor is a transducer or electromechanical device that

converts a mechanical change such as displacement into an electricalsignal that can be monitored after conditioning.

Definition. Resistive sensor is a sensor based on changes of electricresistance of an element due to the change of the particular quantity tobe measured in according to the theory of resistivity.

The simplest resistive sensor is the potentiometer which is based upon

physical length. Other resistive sensors include resistive temperaturedetectors (RTDs) and thermistors which are based upon change in

temperature. The strain gages based upon strain is another example ofresistive sensor. Resistive sensors are often combined with Wheatstone

bridges.

Examples ofPotentiometer

Examples ofRTDs


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1 .4 Po t en t i om et e r

Definition. A potentiometer is a transducer in which a rotation or

displacement is converted into a potential difference.

A potentiometer can be manufactured with a rotary or linearpotentiometer. As shown in the figure below, the displacement of thewiper of a potentiometer causes the output potential difference obtainedbetween one end of the resistance and the slider. This device convertslinear or angular motion into changing resistance, which may beconverted directly to a voltage or current signal. The position of the slideralong the resistance element determines the magnitude of the electricalpotential. The voltage across the wiper of the linear potentiometer is

proportional to the displacement. Voltage across the wiper of the linearpotentiometer is measured in terms of the displacement, d, and is given

by the relationship:

V=E(d/L).

E is the voltage across the potentiometer and L is the full scale

displacement of the potentiometer. Note that the resistance of thepotentiometer is not included in the equation.


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2 . Tem pera t u r e -Sensing Dev ices

Temperature is an important engineering variable. Its measurement has

been based on change in various material properties including electricalresistance, contact voltage between two dissimilar metals, and changes in

radiated energy.


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2 .1 Resist i ve Tem pera t u r e

Detec tor ( RTD)

Resistance temperature detectors, RTDs, are used to measure

temperatures ranging from very cold to approximately 600 degree C.These transducers are sensitive, stable and do not need special circuitry.They are manufactured using materials such as Platinum, Cu, Ni, andtungsten, which all have high positive temperature coefficients ofresistance. Platinum is the most common metal used with very highstability and wide operating range between -220 degree C to 750 degreeC.

A RTD is a length of wire whose resistance is a function of temperature. It

is temperature detector that depends on the variation in resistance ofmetal. The design consists of a wire that is wound in the shape of a coil to

achieve small size and improve thermal conductivity. In many cases, thecoil is protected from the environment by a protecting tube. Thisenclosure inevitably increases response time, but it is essential whenRTDs are used in hostile environment.

Resistance relationships of most metals over a wide range of temperatureare given by quadratic equations. A quadratic approximation to the R-T

curve is a more accurate representation of the resistance variation over aspan of temperatures. It includes both a linear term and a term that

varies as the square of the temperature:

R = R0 ( 1 + a (T T0) + (T T0)2

+ )

where R0 is the resistance at absolute temperature T0, and a and arematerial constants that depend on the purity of the material used. T0 isthe reference temperature.

Over a small temperature range of 0 to 100 degree C, the linearrelationship is

RT = R0 ( 1 + a (T T0)),

where a is the temperature coefficient of resistivity. Typical values of a forthree materials are Cu = 0.0043 per degree C, Pt = 0.0039 per degree Cand Ni = 0.0068 per degree C.


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The disadvantages of RTD include (1) the typically relatively large andhence not suitable in small volume enclosures, (2) somewhat slowresponse, and (3) expensive. The advantages are: (1) very highsensitivity (10 times that of thermocouples), (2) high repeatability and

accuracy (especially for platinum).

RTD made of platinum is often used as temperature standards because ofits stability and accuracy (0.005 degree C). 100O platinum probe(Pt100) is one of the most common sensors.


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2 .2 The r m ist o r s

A thermistor is a temperature transducer whose operation relies on the

principle of change in semiconductor resistance with change intemperature. Its name came from thermally sensitive resistor. The

particular semiconductor materials used in a thermistor vary widely toaccommodate temperate range, sensitivity, resistance ranges and otherfactors. The characteristics are dependent on the behavior ofsemiconductor resistance versus temperature. An in increase intemperature will decrease electrical resistance by improving conductanceof a semiconductor. The semiconductor becomes a better conductor ofcurrent as its temperature is increased. This behavior is opposite that of a

metal. Note that the change in semiconductor resistance is highlynonlinear.

Individual thermistor curves are approximated by the nonlinear equation:

1/T = A + B ln R + C (ln R)3.

T is the temperature in kelvins; R is the resistance of thermistor and A, B,C are curve-fitting constants. The temperature range measured with a

typical thermistor is between --250 degree C and 650 degree C.

Since the thermistor is a bulk semiconductor, it can be fabricated in manyforms, and can be made to be as small as a bead with about 0.1 mm in

diameter. The multiple forms enable it to be used for differentapplications.

The high sensitivity of the thermistor is one of its significant advantages.The high sensitivity is due to its large change in resistance - changes in

resistance of 10% per degree C are not uncommon. Since a thermistorexhibits a large change in resistance with respect to temperature, there

are many possible circuits that can be used for their measurement. Abridge circuit with null detection is most frequently used.

The response time of a thermistor depends primarily on the quality andquantity of the material present. It can be used in hostile environmentwith shocks and vibrations.

Compared to RTD, thermistor is less accurate and less stable. The highlynonlinear response of the material can be a disadvantage. The self

heating effect also limits the precision of measurement.


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2 .3 Rad iat i ve Tem pera tu re

Sensing

Bodies at any temperature emit radiation and absorb radiation from other

bodies. A body at a temperature greater than 0 K radiate electromagneticenergy in an amount that depends on its temperature and physicalproperties.

A sensor for thermal radiation typically does not make contact with thesurface to be measured. The radiation emitted by an object isproportional to the fourth power of its temperature:

W = s T4

where W is the flux of energy radiated from an ideal surface and s is the

Stefan-Boltzmann constant. Commerical radiation thermometers, orradiometers, vary in their complexity and accuracy.


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2 .4 The rm ocoup les

Thermocouples are temperature sensors based on contact voltage

between different metals.

When two conductors of dissimilar materials are joined to form a circuit,the following effect is observed:

Seebeck effect:

When the two junctions are at different temperatures, q1 and q2, smallemfs, e1 and e2, are produced at the junctions, and the algebraic sum ofthese causes a current.

Peltier effect:

When two dissimilar conductors that are joined together have a currentpassed through them, the temperature at the junction changes as heat isabsorbed or generated.

The Peltier effect is the inverse of the Seebeck effect.

Another effect, Thomson effect, predicts that in addition to the Peltier

emf, another emf occurs in each material of a thermocouple as a result ofthe longitudinal temperature gradient between its ends when it forms partof a conductor.

When a thermocouple is used to measure an unknown temperature, thetemperature of the thermo-junction, called the reference junction, mustbe known and maintained at constant temperature.

Following figure shows a typical thermocouple circuit using a chromelconstantan thermocouple, a reference junction, and a potentiometric

circuit to monitor the output voltage. Calibration of the thermocouple isperformed by knowing the relationship between the output emf and the

temperature of the measuring junction.


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The resultant emf of a particular transducer may be increased bymultiplying the number of hot and reference junctions. If there are threemeasuring junctions, then the emf is enhanced appropriately. If thethermocouples in this arrangement are at different temperatures, then

the resultant emf is a measure of the mean value.


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3 . St r a in Gaug es

Different situation in an automated manufacturing environment has

different sensing requirements. Assembly tasks and automated handlingtasks require controlled operations such as grasping, turning, inserting,

aligning, orienting and screwing. The object may have to be movedthrough space avoiding obstacles.

Electrical resistance strain gauges are widely used to measure strains dueto force or torque. When a force is applied to a structure, it undergoesdeformation. The gauge, which is bonded to the structure, is deformed bystrain. The electrical resistance changes accordingly in a nearly linearfashion.

Earlier strain gauges were manufactured from metal filaments. Currentstrain gauges are manufactured from constantan foil, a copper-nickel

alloy, or single crystal semiconductor materials. There are two types ofstrain gauges: unbonded and bonded.

Unbonded Strain Gauges

In an unbonded strain gauge, a resistance wire is stressed between twoframes. The first frame is called the fixed frame, and the second frame

the moving frame. The wires are connected such that the input motion ofone frame stretches one set of wires and compresses another set of

wires. For a particular stress input, the winding experiences wither anincrease or decrease in stress, resulting in a change in resistance. The

output is connected to a wheatstone bridge for measurement. Themeasurement of motions can be as small as a few microns.

Bonded Strain Gauges

The bonded strain gauges have a backing material that aids the bonding

process to a surface used to measure strain. The gauges are made ofmetallic or semiconductor materials in the form of a wire gauge or thinmetal foil. When the gauges are bonded to the surface, they undergo thesame strain as the member surface. The coefficient of thermal expansion

of the backing material should match that of the wire. It is usually madepart of a wheatstone bridge so that the change in resistance due to straincan be either measured or used to produce an output that can be

recorded or displayed. The bonded strain gauge can be used to measurestrain as low as a fraction of a micron.


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A bonded strain gauge made of nichrome (Ni: 80%, Cr: 20%) which has astrain gauge factor = 2.5, resistance = 100 ohms, and temperaturecoefficient of resistivity per degree C = 0.1 x 10^-3^ is suitable forapplications with temperature less than 1200 degree C. For high

temperature application, a bonded strain gauge made of platinum (gaugefactor = 4.8, resistance = 50 ohms, temperature coefficient of resistivity

per degree C = 4 x 10^-3^) could be used. For large strainmeasurement, a bonded strain gauge made of silicon (gauge factor = -

100 to +150, resistance = 200 ohms, temperature coefficient ofresistivity per degree C = 90,000) could be used.

A strain gauge should have the following desired properties for precisemeasurement:

1. A high gauge factor, which increases its sensitivity and causes alarge change in resistance for a particular strain.

2. High resistance of the strain gauge, which minimizes the effect ofresistance variation in the signal processing circuitry. The gaugecharacteristics should be chosen such that the variation inresistance is a linear function of strain.

3. Low temperature coefficient and absence of the hysteresis effect.


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3 .1 Gaug e Fact or

Gauge Factor, also referred to as strain gauge factor or sensitivity factor,

is typically associated with strain gauge. This value is usually provided bythe manufacturer of the strain gauge.

Definition. Gauge factor is defined as the ratio of unit change in resistanceto unit change in length.

Suppose that a specimen is subjected to tension, causing an increase in

length, its longitudinal dimension will increase and its lateral dimensionwill decrease. If a resistance gauge made of this conducting material is

subjected to a positive strain, its length increases while its cross sectionalarea decreases. Since the resistance of the conductor depends on its

length, cross sectional area, and specific resistivity, the change in strain isdue to the change in dimension or specific resistivity.

For a circular wire of length L, cross sectional area A, and diameter D, theresistance of the wire before straining is

Equation (1):

The wire is subjected to tension that causes the strain. Tension increaseslength and reduces the diameter, which in turn reduces the crosssectional area.

Let the stress applied to the strain gauge be s in N/m2,

L = change in length of wire,

A = change in area of cross section,

D = change in diameter,

= resistivity,

= Poissons ratio, and

Strain, e = L/L.


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In order to find how R depends on the material physical quantities,Equation (1) is differentiated with respect to applied stress s:

Equation (2):

Dividing Equation (2) throughout by Equation (1) yields

Equation (3):The change in resistance is due to the unit change in length and the unit

change in area.

Since A=pD2/4, we have

Equation (4):

Equation (5):Equation (5) can be written as

Equation (6):

Poisson ratio is defined as:

Equation (7):

Equation (8):

And for small variations, this relationship can be written as

Equation (9):


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The gauge factor, Gf, is defined as the ratio of unit change in resistance tounit change in length.

Equation (10):Guage factor can also be expressed as:

Equation (11):

The change in resistivity occurs because of the piezoresistive effect, whichis explained as an electrical resistance change that occurs when the

material is mechanically deformed. In some cases the effect is a source oferror. If the change in resistivity or piezoresistive effect of the material is

neglected, the gauge factor becomes

Gf= 1 + 2.

The gauge factor gives an idea of the strain sensitivity of the gauge interms of the change in resistance per unit strain. The gauge factor formetal can vary from 2 to 6, and for semiconductor, it can vary from 40 to

200.


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3 .2 B r i dge Ci r cu i t A r r angem en t

The Wheatstone bridge circuit is the device used to measure the small

change in resistance that results in most strain gauge applications. Thechange in resistance can be either measured or provided as an output to

be displayed or further processed by a computer. Following figure showsan arrangement of a bridge circuit.

In the balanced bridge arrangement, strain gauge resistance, R1, formsone arm (or leg) of the Wheatstone bridge, and the remaining arms haveresistances R2, R3, and R4. Between the points A and C of the bridge thereis a power supply; between points B and D there is a precision

galvanometer. For zero current to flow through the galvanometer, thepoints B and D must be at the same potential. The bridge is excited by

the DC source with voltage V, and Rg is the resistance in thegalvanometer.


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The condition of balance is

R1/R4 = R2/R3.

If R1 changes due to strain, the bridge, which is initially in balancedcondition, becomes unbalanced. This may be balanced by changing R4 (or

R2). This change can be measured and used to indicate the change in R1,and hence, the strain.


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Calculating the Offset (or output voltage)

With reference to the following figure, G is used to compare potentials ofpoints B and D. The potential difference between points B and D is V =

VD - VB. If all the resistance values (R1, R2, R3 and R4) in the bridge circuitare the same, then the voltage is the same at points B and D, ?V will bezero, and the bridge is balanced.

Let us consider R1 as the strain gauge. If R1 is strained, its resistancevalue changes, and the bridge becomes unbalanced, causing a nonzero

V. The bridge can be brought back to a balanced condition if any otherresistance value is adjusted. The adjusted value of the any resisternecessary to force V to zero will be equal to the strained value of thestrain gauge.

The currents flowing through the bridge arms are computed as follows:

Current through ABC, I1 = V/(R1 + R4)

Current through ADC, I2 = V/(R2 + R3)

The voltage drop across R3 is I2R3, and the voltage drop across R4 is I1R4.The voltage offset is given by

V=VD VB = R3V/(R2+R3) R4V/(R1 + R4).


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3 .3 Possib le Ar r angem ent o f

St r a in Gaug es

There can be many different bridge circuit arrangements of the strain

gauges. When more than one arm of the bridge circuit contains straintransducers and the resistances of these transducers changes, the bridgeoutput is due to the combined effect of these changes. More than onestrain gauge, if suitably arranged, can lead to a higher signal environmentfactor and a larger change in output voltage for a given strain. In manyexperimental situations, there are areas of tension and compression inthe same object with strain similar but with opposite sign. In such

situations care must be taken in arranging strain gauges in such a waythat the adjacent arms of the bridge have strains of opposite nature.

In Figure A, R1 measures changes due to axial tensile strain.

Figure A. Possible arrangement of strain gauge to measure P

In Figure B, strain gauge R1 is bonded to the elastic member to measureaxial tensile strain. R1 changes because of axial tensile strain. R2measures changes due to transverse compressive strain.

Figure B. Possible arrangement of strain gauge to measure P


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In Figure C, both R1 and R3 are subjected to axial tensile strain of sameamount, and R1 and R3 form opposite arms of the bridge. This causes asignal enhancement factor of 2.

Figure C. Possible arrangement of gauges to measure tension

In Figure D, R1 has tensile strain and R2 has compressive strain; R3 hastensile strain and R4 has compressive strain. Strain gauges R1, R2, R3 and

R4 are bonded at the root of the cantilevers, where the bending stressesare at maximum.

Figure D. Cantilever deflection measurement


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In Figure E, four active gauges are used with R2 and R4 arranged at rightangles to R1 and R3 to produce a signal enhancement factor of 2(1 + v),where v denotes Poissons ratio.

Figure E. Alternative arrangements

In Figure F, the strain gauges are arranged in such a way that R1 and R3measure axial strains whereas R2 and R4 measure the circumferential

strains, which have strain of the opposite nature.

Figure F. Hollow cylinder, axial loading


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4 . Elect r om agne t i c Flow Met e r

The operating principle of electromagnetic flow meter is based on the

voltage that is generated in an electrically conducting fluid as it movesthrough a magnetic field. This method is useful for measuring flow of

conducting liquids that may have abrasive materials and are not suited forother measurement methods. It cannot be used for electricallynonconducting fluids like gases but produces satisfactory results for low-conductivity fluids like water. For monitoring corrosive fluids, solid-contaminated liquids, paper pulp, detergents, cement slurries and greasyliquids, the electromagnetic flow meters could be used.

In electromagnetic flow sensing, a pair of electrodes is inserted on theopposite sides of a non-conducting and non-magnetic pipe that carries the

liquid. The pipe is surrounded by an electromagnet, which produces themagnetic field. The voltage is induced across the electrodes. The

magnitude of emf is proportional to the rate at which the fleld lines arecut. With a constant magnetic field, the magnitude of voltage across theelectrodes is proportional to the velocity.

The induced voltage, e, is given by the Faradays Law:

e = Blv,

where B is the magnetic flux density, l is the length of the conductor

which is the pipe diameter and v is the velocity of the conductor.


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5. Sign a l Con d i t ion ing

The output signal from sensor of a measurement system has generallybeen processed in some way to make it suitable for next stage of the

operation.

Signal conditioning can involve protection to prevent damage to the nextelement in a system, getting a signal into the form, getting the level of asignal right, reducing noise, manipulating a signal to perhaps make it

linear.

Commonly used signal conditioning elements are operational amplifierswhich are high-gain DC amplifiers with gains of the order of 100 000 or

more.

Protection against perhaps a high voltage or current can involve the useof resistors and fuses, Zener diodes can be used to protect against wrongpolarity and high voltages.

Filters can be used to remove a particular band of frequencies from asignal and permit others to be transmitted.

The Wheatstone bridge can be used to convert an electrical resistance

change to a voltage change. Wheatstone bridge is an efficient method formeasurement of resistance.


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5 .1 Wh eat st one Br idg e -

Measur em ent o f Resist ance

About 1843, Sir Charles Wheatstone designed a circuit called a bridge

circuit which is an accurate method for measuring resistance. In thefigure below, X is the unknown resistance, and P, Q, R are resistors.Suppose that R is adjusted until the galvanometer G between A and Cshows no deflection balance condition. In this case the current Ig in Gis zero.

At balance, since no current flows through the galvanometer, the points Aand C must be at the same potential. Therefore,

VAB = VCB and VAD = VCD,

So VAB/VAD = VCB/VCD.

Since Ig = 0, P and R carry the same current, I1, and X and Q carry the

same current I2, therefore

VAB/VAD = I1P/I1R = P/R and VCB/VCD = I2Q/I2X = Q/X.

Hence, P/R = Q/X.

So X = (Q/P)R.


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The significance of Wheatstone bridge or bridge circuit is its ability toindirectly measure physical phenomenon such force, pressure,

temperature etc., by measuring the unknown resistance. It has beenwidely used for signal conditioning in strain gauge which is an example of

resistive sensors.

Following figure illustrates a typical configuration of bridge circuit fortemperature readings in terms of voltage. In this configuration, athermistor has been installed as one leg (or arm) of a bridge circuit. Athermistor is a semiconductor device whose resistance changes withtemperature. When a constant voltage is applied to the circuit, the heatsource causes the thermistor resistance to change, creating a potentialdifference between points A and C proportional to temperature. This

potential difference is known as offset voltage or output voltage.


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6 . Sm ar t Sensor s

A sensor can combine with its signal conditioning, for example

Wheatstone bridge, in one package. However, this integrated sensor stillrequires further data processing. It is possible to have the sensor and

signal conditioning combined with a microprocessor in the same package.This arrangement is termed a smart sensor.

A smart sensor is able to have intelligent functions including the ability tocompensate for random errors, to adapt to change in the environment,self-calibration and self-diagnosis of faults.

IEEE 1451 is the standard for smart sensors. A sensor conforms to thisstandard can be used in a plug-and-play manner, holding and

communicating data in a standard way.


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7 . Se lect ion o f Sensor s

There are a number of factors to be considered in selecting a sensor for a

particular application:

1. The nature of the measurement required, for example, the variableto be measured, its nominal value, the range of its values, theaccuracy required, the required speed of measurement, thereliability required, environmental conditions under which themeasurement is to be made.

2. The nature of the output required from the sensor. This determinesthe signal conditioning requirements in order to give suitable outputsignals from the measurement.

3. Identify and then Compare the various possible sensors taking intoaccount factors such as the sensing range, accuracy, speed ofresponse, reliability, maintainability, life, power supply requirement,

ruggedness, availability and cost.

The non-engineering factors - availability and cost, are very importantconsiderations in practice.

Reference: Mechatronics (4th Edition) by W Bolton, Pearson Prentice Hall,2008.

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4 - Sensors and Transducers