UNIT-I: TRANSDUCERS AND PRIMARY SENSING ELEMENTS
Introduction:
The transducer can be defined as a device which is used for converting one form of energy into
another form. In general, transducers deal with different energy types such as electrical energy,
mechanical energy, chemical energy, light energy, electromagnetic energy, thermal energy, acoustic
energy, and so on. For example, consider mic (mic of telephone or mobile phone or audio set mic)
we use in our day-to-day life converts the audio signals into electrical signals and then amplifies it
into the desired range Then, it converts the electrical signals into audio signals at the output of the
speakers or loudspeaker.
The fluorescent bulbs used for lighting, converts the electrical energy into light energy. The mic,
speaker, and fluorescent bulb can be considered as transducers. Similarly, there are different types
of transducers used in practical applications.
Transducers are often employed at the boundaries of automation, measurement, and control
systems, where electrical signals are converted to and from other physical quantities (energy, force,
torque, light, motion, position, etc.). The process of converting one form of energy to another is
known as transduction
Principle of a Transducer
A transducer normally measures the physical quantity of interest indirectly through its effect on one
of the transducer’s parameters. Typically this change is then converted into an electrical signal, e.g.
voltage or current which provide a measure for the quantity of interest.
Difference between Sensor and Transducer
Sensor
An element which is used to sense the changes in one parameter to produce a change in other
parameter at the o/p is known as sensor
Transducer
An element of the instrument which completely modifies (change) the i/p parameter exists in one
form to other form is known as transducer. The parameter subject to the changed may be in any
form such as Electrical, physical or mechanical etc depends on the application.
So a transducer which converts a non-electrical quantity into analog electrical signal may be
considered as consisting of two parts
These two parts are
i)
Sensing element, and
ii)
Transduction element
1. Sensing or Detector Element
A detector or a sensing element is that part of a transducer which responds to a physical
phenomenon or a change in a physical phenomenon.
2. Transduction Element
A transduction element transforms the output of a sensing element to an electrical output.
Energy type
Measurand
- Parameter to be measured]
Mechanica
l/
Physical
Electrical
Length, Area ,Volume Force ,Acceleration
,Pressure
Torque, Mass, Flow etc.
Charge, Current,
Voltage
Inductance
Dielectric
Constant
Frequency
Chemical
Concentration
Composition
Power, Resistance
,Capacitance
Thermal
Reaction Rate, pH
Value Oxidation Rate
etc.
Temperature, Heat flow etc..
Radiant
Transmittance, Reflectance, Absorbance, Radiant Flux
Magnetic
Magnetic flux density, Field strength, Permeability
Polarization
Classification of Transducers / Sensors
Transducers and Sensors widely used in Commercial applications are usually classified based on
the following parameters.
1) Energy generating capability
2) Hierarchy of Conversion
3) Transduction Principle
4) Technology
5) Industrial Application
6) Property
7) Cost & Accuracy (Rarely Classified)
The parameters mostly preferred for the classification are Material and Technology and application
1. Classification based on Energy generating capability
Active and Passive Transducers
Active Transducer
These transducers do not need any external source of power for their operation. Therefore they are
also called as self generating type transducers. The active transducer is self generating devices
which operate under the energy conversion principle. As the output of active transducers we get an
equivalent electrical output signal e.g. temperature or strain to electric potential, without any
external source of energy being used
Passive Transducers
These transducers need external source of power for their operation. So they are not self generating
type transducers. A DC power supply or an audio frequency generator is used as an external power
source. These transducers produce the output signal in the form of variation in electrical parameter
like resistance, capacitance or inductance.
Examples – Thermistor, Potentiometer type transducer
2. Classification based on Hierarchy of Conversion
Primary and Secondary Transducers: Primary transducers are transducers which convert a
physical quantity into another form. But the secondary transducers convert the output signal from
the primary transducer into a usable output (i.e. an electrical signal).
For eg., the Bourdon tube converts the input pressure into a displacement, as primary transducer
and the LVDT converts this displacement into an analogous voltage, as secondary transducer.
Fig. Measurement of pressure using Bourdon tube and LVDT
3. Classification based on Transduction principle
Based on the transduction phenomenon transducers are classified as,

Resistive transducer

Capacitive transducer

Inductive transducer

Photoelectric transducer

Photovoltaic transducer
4. Classification based on industrial application
Sensor or Transducers
Industrial use
Non- Industrial use
Process control Automation
Aircraft
Navigation
Automobile
Medical
Instrumentation
Consumer
Electronics
5. Classification based on technology
Sensor or Transducers
MEMS CMOS BIO Proximity Magnetic (Hall Effect) IR based Motion based Temperature
detection
based
6. Classification based on property
Sensor or Transducers
Flow rate
Level Control
Temperature
Pressure
Image
Chemical
Gas
Radiation
Advantages of Electrical Transducers / Sensors
1. Most accurate O/P is guaranteed
2. Fast Response time
3. Suitable for wide Range of measurement
4. Good shelf life
5. Ease of installation and maintains
6. Greater Reliability
Characteristics of sensors / Transducers
Static characteristics=> gives the characteristic when the sensor is idle
CharacteristicsDynamic characteristic => Gives the characteristic when the sensor is active
Static Characteristics of Sensors / Transducer
Following are some of the important static characteristics related to the sensors under idle condition
1. Accuracy
2.Precision
3.Resolution
4. Minimum Detectable Signal (MDS)
5.Threshold
6. Sensitivity
7.Selectivity
8. Non Linearity
9. Hysteresis
10 . O/P Impedance
11. Isolation and Grounding
Accuracy
The value very close to the standard value.
Precision
Degree of reproducibility / Repeated standard measurement
Resolution
By giving a small change in input how the sensor is reproduce to make the change in output
resolution is similar to sensitivity
Minimum Detectable signal
A minimum detectable signal is a signal at the input of a system whose power produces a signal-tonoise ratio of m at the output.
Threshold
It is a operating voltage minimum voltage which operate a signal
Selectivity
It should not be select undesirable value. It will measure only the desirable value
Non-Linearity
It is the relationship between output voltage and output current which are non linear to each other
Hysteresis
Hysteresis refers the percentage of variation in the magnetic field strength of a sensor or transducer
for the given value of magnetic induction (B) or flux. When magnetic flux (B) is increased
gradually the magnetic field strength initially increases and then decreases slowly and reaching the
origin level.
O/P Impedance
The O/p impedance of the sensor or transducer shall be made equivalent to the I/P impedance of the
device with which it is interfaced.
Isolation and Grounding
Necessary to protect the sensor against Electrical, Mechanical, Electromagnetic, Thermal over load.
Application Device Interface
Dynamic characteristics of Sensors / Transducer
When a sensor or transducer is activated its performance is measured by evaluating the following
characteristics.
1. Frequency Response
2. Transfer Function
3. Impulse Response.
Frequency response
The frequency response gives the faithful operation of sensor under a specified range of
frequencies.
Under the specified range of frequencies the gain obtained from the device is
measured and plotted. It is a very important characteristic to be tested.
Transfer function
Transfer function refers the changes in the o/p [y(+)] for a step change in the i/p [x (+)]. The input
x(t) is changed a little because of the application of external factor if any which influence the i/p
Impulse Response
The performance of a transducer or sensor under the influence of signal impulses result abruptly in
the measuring stage is known as impulse response e.g: Over voltage, under voltage, Ripple current,
Power factor ratio The Sensor or transducer proved to be stable under impulse conditions is said to
be a noise reliable one.
Factors influencing the choice of a Sensor / Transducer
The sensor or transducer for a particular application is selected only based on the following criteria
1. Physical quantity to be measured: Depending on the type of physical quantity weather
electrical quantity or non electrical quantity measured the most suitable transducer is selected
2. Principle of the sensor/ Transducer : The principle of a transducer mostly suits for particular
application.
3. Accuracy: It must have high degree of accuracy and repeatability.
4. Sensitivity: It must be highly sensitive to desired signal and insensitive to unwanted signal.
5. Operating range: The transducer selected must cover a wide operating range
6. Transient and Frequency Response:
The transducer should meet desired time
domain specifications like peak overshoot, rise time, settling time and small dynamic
error. It should ideally have a flat frequency response curve. In practice, however,
there will be cutoff frequencies and higher cut off frequency should he high in order
to have a wide bandwidth.
7. Loading effects: The transducer should have a high input impedance and low output impedance
to avoid loading effects.
8. Environmental compatibility: It should be assured that the transducer selected to
work
under
specified
environmental
conditions
maintains
its
input/
output
relationship and does not break down. For example, the transducer should remain
operable
under
environments,
its
temperature
should
be
range.
It
able
to
should
be
able
withstand
to
work
pressures
in
corrosive
and
shocks
and other interactions
9. Stability over the time period: The stability of a transducer is its ability to give the same output
when used to measure a constant input over a period of time. Ideal transducers should have higher
stability
10. Other electrical aspects such as wattage, cable length required etc.
UNIT-II: Linear Displacement Transducers
Linear Transducer
It is a kind of transducer whose o/p remains linear all times with respect to the i/p some of the
commonly used linear transducer are;
1. Resistive Potentiometers
2. LVDT
3. Strain Gauge
4. Capacitive Transducers
5. Piezo electric Transducers
6. Hall effect transducers
7. Digital transducers ect…
All the above mentioned transducers shows linearity in their o/p with respect to their i/p
Resistive Potentiometers
Resistive transducers usually produces o/p voltage when the depending on the changes in the i/p
resistance when the resistance changes at the i/p some of the worthful resistance transducers are
resistive pot, LVDT,RTD, Thermistor, Anemometer Piezo resistor etc.
Resistive potentiometer is most widely used type of transducer / sensor because fo its simplicity in
construction and cost.
On a insulted for mad up of Nickel alloy material turns of copper wire are wounded. Hence most of
the times. It is referred as Resistive Potentiometer. A movable Jockey or Key is provided as one
side of the windings so as to select the required number of turns wires ( Winding) . Based on the
number of turns selected the o/p voltage will be determined becomes we know that
R= Pl /A
Whose r= Resistance of the copper wire turns selected
E= Overall length of the wire
P= specific resistivity
A= Area of cross section.
If ‘n’ number of turning are selected then the changes on the o/p voltage can be calculatedas
AV= V/n
Fig
Advantages
1. Larger O/P
2. More Sensitivity]
3. Easy of construction
4. Cheap Cost Draw backs
1. Less Resolution
2. Power Accuracy
3. Not with stands for more mechanical vibrations
4. Less stability in the O/p temperature
Types of Resistive Potentiometers
1. Translator type [Moving type]
2. Rotational type
3. Helipot
All the 3 types of potentiometer have the same advantages and disadvantages. Heli pot type is
rarely used in industrial applications. Other two types of potentiometers are widely used in
commercial applications.
Capacitive Manometer [Capacitive Transducer]
The capacitive transducer or sensor is nothing but the capacitor with variable capacitance. The
capacitive transducer comprises of two parallel metal plates that are separated by the material such
as air, which is called as the dielectric material. In the typical capacitor the distance between the
two plates is fixed, but in variable capacitance transducers the distance between the two plates is
variable.
In the instruments using capacitance transducers the value of the capacitance changes due to change
in the value of the input quantity that is to be measured. This change in capacitance can be
measured easily and it is calibrated against the input quantity, thus the value if the input quantity
can be measured directly.
Capacitance of the Capacitive Transducers
The capacitance C between the two plates of capacitive transducers is given by:
Capacitance [ C ] = KA/ d
Where K = Dielectric constant
A= Area of the Plates
d= distance between the plates
It is clear from the above formula that capacitance of the capacitive transducer depends on the area
of the plates and the distance between the plates. The capacitance of the capacitive transducer also
changes with the dielectric constant of the dielectric material used in it.
Thus the capacitance of the variable capacitance transducer can change with the change of the
dielectric material, change in the area of the plates and the distance between the plates. Depending
on the parameter that changes for the capacitive transducers, they are of three types as mentioned
below.
1) Changing Dielectric Constant type of Capacitive Transducers
In these capacitive transducer the dielectric material between the two plates changes, due to which
the capacitance of the transducer also changes. When the input quantity to be measured changes the
value of the dielectric constant also changes so the capacitance of the instrument changes. This
capacitance, calibrated against the input quantity, directly gives the value of the quantity to be
measured. This principle is used for measurement of level in the hydrogen container, where the
change in level of hydrogen between the two plates results in change of the dielectric constant of
the capacitance transducer. Apart from level, this principle can also be used for measurement of
humidity and moisture content of the air.
2) Changing Area of the Plates of Capacitive Transducers
The capacitance of the variable capacitance transducer also changes with the area of the two plates.
This principle is used in the torquemeter, used for measurement of the torque on the shaft. This
comprises of the sleeve that has teeth cut axially and the matching shaft that has similar teeth at its
periphery.
3) Changing Distance between the Plates of Capacitive Transducers
In these capacitive transducers the distance between the plates is variable, while the area of the
plates and the dielectric constant remain constant. This is the most commonly used type of variable
capacitance transducer. For measurement of the displacement of the object, one plate of the
capacitance transducer is kept fixed, while the other is connected to the object. When the object
moves, the plate of the capacitance transducer also moves, this results in change in distance
between the two plates and the change in the capacitance. The changed capacitance is measured
easily and it calibrated against the input quantity, which is displacement. This principle can also be
used to measure pressure, velocity, acceleration etc.
Capacitive pressure transducer
A capacitance sensor operates by measuring the change in electrical capacitance that results from
the movement of a sensing diaphragm relative to some fixed capacitance electrodes (Figure 4-6).
The higher the process vacuum, the farther it will pull the measuring diaphragm away from the
fixed capacitance plates. In some designs, the diaphragm is allowed to move. In others, a variable
dc voltage is applied to keep the sensor's Wheatstone bridge in a balanced condition. The amount of
voltage required is directly related to the pressure.
Figure :Capacitance Vacuum Manometer
The great advantage of a capacitance gauge is its ability to detect extremely small diaphragm
movements. Accuracy is typically 0.25 to 0.5% of reading. Thin diaphragms can measure down to
10-5 torr, while thicker diaphragms can measure in the low vacuum to atmospheric range.
To cover a wide vacuum range, one can connect two or more capacitance sensing heads into a
multi-range package. The capacitance diaphragm gauge is widely used in the semiconductor
industry. They are also favored because of their high accuracy and immunity to contamination
Advantages :

The capacitance manometer is a device which directly measures pressure and thus its
readings are totally independent!

The response time is almost instantaneous

Gauges with capacitive sensing and electronic readouts provide highly sensitive and
repeatable measurements.

Capacitive manometers are immune to contamination.
Application area:
Capacitance manometers are often used to accurately measure pressure in process reactors, and
are often used in feedback control loops.
Piezoelectric Transducer
A piezoelectric crystal transducer/sensor is an active sensor and it does not need the help of an
external power as it is self-generating. It is important to know the basics of a piezoelectric quartz
crystal and piezoelectric effect before going into details about the transducer.
Piezoelectric Quartz Crystal
A quartz crystal is a piezoelectric material that can generate a voltage proportional to the stress
applied upon it. For the application, a natural quartz crystal has to be cut in the shape of a thin plate
of rectangular or oval shape of uniform thickness. Each crystal has three sets of axes – Optical
axes, three electrical axes OX1, OX2, and OX3 with 120 degree with each other, and three
mechanical axes OY1,OY2 and OY3 also at 120 degree with each other. The mechanical axes will
be at right angles to the electrical axes. Some of the parameters that decide the nature of the crystal
for the application are

Angle at which the wafer is cut from natural quartz crystal

Plate thickness

Dimension of the plate

Means of mounting
Piezoelectric Effect
The X-Y axis of a piezoelectric crystal and its cutting technique is shown in the figure below.
X-Y Axes of a Piezoelectric Crystal
The direction, perpendicular to the largest face, is the cut axis referred to.
If an electric stress is applied in the directions of an electric axis (X-axis), a mechanical strain is
produced in the direction of the Y-axis, which is perpendicular to the relevant X-axis. Similarly, if a
mechanical strain is given along the Y-axis, electrical charges will be produced on the faces of the
crystal, perpendicular to the X-axis which is at right angles to the Y-axis.
Some of the materials that inherit piezo-electric effect are quartz crystal, Rochelle salt, barium
titanate, and so on. The main advantages of these crystals are that they have high mechanical and
thermal state capability, capability of withstanding high order of strain, low leakage, and good
frequency response, and so on.A piezoelectric transducer may be operated in one of the several
modes as shown in the figure below.
Piezoelectric Crystal
Piezoelectric Transducer
The main principle of a piezoelectric transducer is that a force, when applied on the quartz crystal,
produces electric charges on the crystal surface. The charge thus produced can be called as
piezoelectricity. Piezo electricity can be defined as the electrical polarization produced by
mechanical strain on certain class of crystals. The rate of charge produced will be proportional to
the rate of change of force applied as input. As the charge produced is very small, a charge
amplifier is needed so as to produce an output voltage big enough to be measured. The device is
also known to be mechanically stiff. For example, if a force of 15 kiloN is given to the transducer, it
may only deflect to a maximum of 0.002mm. But the output response may be as high as
100KiloHz.This proves that the device is best applicable for dynamic measurement.
The figure shows a conventional piezoelectric transducer with a piezoelectric crystal inserted
between a solid base and the force summing member. If a force is applied on the pressure port, the
same force will fall on the force summing member. Thus a potential difference will be generated on
the crystal due to its property. The voltage produced will be proportional to the magnitude of the
applied force.
Piezoelectric Transducer can measure pressure in the same way a force or an acceleration can be
measured. For low pressure measurement, possible vibration of the amount should be compensated
for. The pressure measuring quartz disc stack faces the pressure through a diaphragm and on the
other side of this stack, the compensating mass followed by a compensating quartz.
Applications
1. Due to its excellent frequency response, it is normally used as an accelerometer, where the
output is in the order of (1-30) mV per gravity of acceleration.
2. The device is usually designed for use as a pre-tensional bolt so that both tensional and
compression force measurements can be made.
3. Can be used for measuring force, pressure and displacement in terms of voltage.
Advantages
1. Very high frequency response.
2. Self generating, so no need of external source.
3. Simple to use as they have small dimensions and large measuring range.
4. Barium titanate and quartz can be made in any desired shape and form. It also has a large
dielectric constant. The crystal axis is selectable by orienting the direction of orientation.
Disadvantages
1. It is not suitable for measurement in static condition.
2. Since the device operates with the small electric charge, they need high impedance cable for
electrical interface.
3. The output may vary according to the temperature variation of the crystal.
4. The relative humidity rises above 85% or falls below 35%, its output will be affected. If so,
it has to be coated with wax or polymer material.
Linear Variable Differential Transformer (LVDT)
LVDT stands for Linear Variable Differential Transformer. Like other inductive transducers, this
transducer is also used for converting a linear motion into an electrical signal. The basic
construction of an LVDT is explained and shown in the figure below.
Construction
LVDT Construction
The device consists of a primary winding (P) and two secondary windings named S1 and S2. Both
of them are wound on one cylindrical former, side by side, and they have equal number of turns.
Their arrangement is such that they maintain symmetry with either side of the primary winding (P).
A movable soft iron core is placed parallel to the axis of the cylindrical former. An arm is
connected to the other end of the soft iron core and it moves according to the displacement
produced.
Working
As shown in the figure above, an ac voltage with a frequency between (50-400) Hz is supplied to
the primary winding. Thus, two voltages VS1 and VS2 are obtained at the two secondary windings
S1 and S2 respectively. The output voltage will be the difference between the two voltages (VS1VS2) as they are combined in series. Let us consider three different positions of the soft iron core
inside the former.

Null Position – This is also called the central position as the soft iron core will remain in the
exact center of the former. Thus the linking magnetic flux produced in the two secondary
windings will be equal. The voltage induced because of them will also be equal. Thus the
resulting voltage VS1-VS2 = 0.

Right of Null Position – In this position, the linking flux at the winding S2 has a value
more than the linking flux at the winding S1. Thus, the resulting voltage VS1-VS2 will be in
phase with VS2.

Left of Null Position – In this position, the linking flux at the winding S2 has a value less
than the linking flux at the winding S1. Thus, the resulting voltage VS1-VS2 will be in
phase with VS1.
From the working it is clear that the difference in voltage, VS1-VS2 will depend on the right or left
shift of the core from the null position. Also, the resulting voltage is in phase with the primary
winding voltage for the change of the arm in one direction, and is 180 degrees out of phase for the
change of the arm position in the other direction.
The magnitude and displacement can be easily calculated or plotted by calculating the magnitude
and phase of the resulting voltage.
Difference output Voltage Vs Displacement Curve
The graph above shows the plot between the resulting voltage or voltage difference and
displacement. The graph clearly shows that a linear function is obtained between the output voltage
and core movement from the null position within a limited range of 4 millimeter.
The displacement can be calculated from the magnitude of the output voltage. The output voltage is
also displayed on a CRO or stored in a recorder.
Advantages
1. Maintains a linear relationship between the voltage difference output and displacement from each
position of the core for a displacement of about 4 millimeter.
2. Produces a high resolution of more than 10 millimeter.
3.Produces a high sensitivity of more than 40 volts/millimeter.
4. Small in size and weighs less. It is rugged in design and can also be assigned easily.
5. Produces low hysteresis and thus has easy repeatability.
Disadvantages
1. The whole circuit is to be shielded as the accuracy can be affetced by external magnetic field.
2. The displacement may produce vibrations which may affect the performance of the device.
3. Produces output with less power.
4. The efficiency of the device is easily affected by temperature. An increase in temperature causes
a phase shift. This can be decreased to a certain extent by placing a capacitor across either one of
the secondary windings.
5. A demodulator will be needed to obtain a d.c output.
Applications of LVDT
Acting as a secondary transducer it can be used as a device to measure force, weight and
pressure etc. The force measurement can be done by using a load cell as the primary
transducer while fluid pressure can be measured by using Bourdon tube which acts as
primary
transducer.
The
force
or
the
pressure
is
converted
into
a
voltage.
In these applications the high sensitivity of LVDTs is a major attraction.
Strain Gauge
Strain Gauge is a passive transducer that converts a mechanical elongation or displacement
produced due to a force into its corresponding change in resistance R, inductance L, or capacitance
C. A strain gauge is basically used to measure the strain in a work piece. If a metal piece is
subjected to a tensile stress, the metal length will increase and thus will increase the electrical
resistance of the material. Similarly, if the metal is subjected to compressive stress, the length will
decrease, but the breadth will increase. This will also change the electrical resistance of the
conductor. If both these stresses are limited within its elastic limit (the maximum limit beyond
which the body fails to regain its elasticity), the metal conductor can be used to measure the amount
of force given to produce the stress, through its change in resistance.
Strain Gauge Transducer
The device finds its wide application as a strain gauge transducer/sensor as it is very accurate in
measuring the change in displacement occurred and converting it into its corresponding value of
resistance, inductance or capacitance. It must be noted that the metal conductor which is subjected
to an unknown force should be of finite length.
Types:Strain gauge transducers are broadly classified into two. They are
1. Electrical Resistance Type Strain Gauge
In an electrical resistance strain gauge, the device consists of a thin wire placed on a flexible paper
tissue and is attached to a variety of materials to measure the strain of the material. In application,
the strain gauge will be attached to a structural member with the help of special cement. The gauge
position will be in such a manner that the gauge wires are aligned across the direction of the strain
to be measured. The wire used for the purpose will have a diameter between 0.009 to 0.0025
centimeters. When a force is applied on the wire, there occurs a strain (consider tensile, within the
elastic limit) that increases the length and decreases its area. Thus, the resistance of the wire
changes. This change in resistance is proportional to the strain and is measured using a Wheatstone
bridge.
A simple Wheatstone bridge circuit is shown in the figure below. It can be set in three different
ways such as – full bridge, half bridge or quarter bridge. A full bridge will have all four of its
gauges active. The half bridge will have two of its gauges active and thus uses two precise value
resistors. The quarter bridge will have only one gauge and the rest of the resistors will be precise in
value.
Wheatstone Bridge
The wire strain gauge can be further divided into two. They are bonded and unbonded strain gauge.
As shown in the figure below, an unbounded strain gauge has a resistance wire stretched between
two frames. The rigid pins of the two frames are insulated. When the wire is stretched due to an
applied force, there occurs a relative motion between the two frames and thus a strain is produced,
causing a change in resistance value. This change of resistance value will be equal to the strain
input.
Unbonded Strain Gauge
A bonded strain gauge will be either a wire type or a foil type as shown in the figure below. It is
connected to a paper or a thick plastic film support. The measuring leads are soldered or welded to
the gauge wire. The bonded strain gauge with the paper backing is connected to the elastic member
whose strain is to be measured.
Bonded Type Strain Gauges
According to the strain to be measured, the gauges can be classified as the following.

Uniaxial/Wire Strain Gauge
The figure of such a strain gauge is shown above. It mostly uses long and narrow sensing elements
so as to maximize the length of the strain sensing material in the desired direction. Gauge length is
chosen according to the strain to be calculated.
Gauge Configurations
Biaxial Strain Gauges
When the measurement of strain is to be done in two directions (mostly at right angles), this method
is used. The basic structure for this is the two element 90 planar rosette or the 90 planar
shear/stacked foil rosette. The gauges are wired in a Wheatstone bridge circuit to provide maximum
output. For stress analysis, the axial and transfers elements have different resistances which can be
selected that the combined output is proportional to the stress while the output of the axial element
alone is proportional to the strain. The figure is given below.

Three Element Rosettes
It is divided into two types – three element 60delta rosette strain gauge and three element 45planar
rectangular rosette. They are used in applications where both the magnitude and direction of the
applied strains are to be found out. Both the figures are shown below. The 60 rosette is used when
the direction of the principal strain is unknown. The 45 rosette is used to determine a high angular
resolution, and when the principal strains are known.
2. Semiconductor Strain Gauge
This is the most commonly used strain gauge as a sensor, although the bonded type may also be
used in stress analysis purposes. The bonded type is usually made in wafers of about 0.02
centimeters in thickness with length and resistance values nearly equal to the wire gauge. It uses
either germanium or silicon base materials to be made available in both n-type or p-type. The ptype gauges have a positive gauge factor while the n-type gauges have a negative gauge factor.
Temperature dependence of gauge factor is governed by the resistivity of the material. The large
value of the gauge factor in semiconductor gauges is attributed to the piezoresistance effect in such
materials.
Variable Inductance Type Strain Gauge
The basic arrangement of a variable inductance strain gauge is shown below. This type of strain
gauge is very sensitive and can be used to measure small changes in length – as small as 1 millionth
of an inch. Thus, it is highly applicable as a displacement transducer. The member whose strain is
to be measured is connected to one end of a moveable iron armature. The long part of the armature
is placed between the two cores with wires coiled in between. If the strain produced makes the
armature move towards the left core (core 1), it increases the inductance of the left hand coil, that is,
coil 1 and decreases the inductance of coil 2. These two coils produce the impedance Z1 and Z2 in
the bridge circuit. This produces an output voltage E, which is proportional to the input
displacement and hence proportional to the strain. This type of strain gauge is more accurate and
sensitive than a resistive strain gauge. But, it is difficult to install the device as it is bulky and
complex in construction.
Photo Multiplier Tube
The photo multiplier tube consists of an evacuated glass envelope containing a photo cathode, an
anode and several additional electrodes, termed Dynodes, each at a higher voltage, than the
previous dynode.
Figure 13.32 illustrates the principle of the photo multiplier. Electrons emitted by the cathode are
attracted to the first dynode. Here a phenomenon known as secondary emission takes place.
When electrons moving at a high velocity strike an appropriate material, the material emits a greater
number of electrons than it was struck with.
In this device, the high velocity is achieved by the use of a high voltage between the anode and the
cathode. The electrons emitted by the first dynode are then attracted to the second dynode, where
the same action takes place again. Each dynode is at a higher voltage, in order to achieve the
requisite electron velocity each time. Hence, secondary emission, and a resulting electron
multiplication, occurs at each step, with an overall increase in electron flow that may be very great.
Amplification of the original current by much as 105 — 109 is common. Luminons sensitivities
range from lA per lumen or less, to over 2000 A per lumen. Typical anode current ratings range
from a minimum of 100 μA to a maximum of 1 mA.
The extreme luminous sensitivity possible with these devices is such that for a sensitivity of 100 A
per lumen, only 10-5 lumen is needed to produce 1 mA of output current.
Magnetic fields affect the photo multiplier because some electrons may be deflected from their
normal path between stages and therefore never reach a dynode or anode. Hence, the gain falls. To
minimise this effect μ-metal magnetic shields are often placed around the photo multiplier tube.
Hall Effect Transducers
The material used in the manufacture of Hall effect devices is a ptype or an ntype semiconductor.
Typical examples are indium arsenide, indium arsenide phosphide, and doped silicon. Figure shows
a section of a pdoped semiconductor subjected to a magnetic field Bz in the z direction and an
electric field Ex in the x direction. A current Ix flows in the x direction.The holes move in the x
direction across the magnetic fieldand experience an upward magnetic force, which results in the
accumulation of holes on the top surface and electrons on the bottom face, as indicated in Fig.
Figure Hall - effect device.
An electric field Ey, known as the Hall field, is set up as a consequence, and this is known as the
Hall effect.The corresponding Hall voltage VH=Eyt. Since there is no flow of current in the y
direction, the magnetic force equilibrates with the electric force that is exerted on the holes, and as
a result the Hall voltage can be expressed as,
Figure Hall -effect displacement transducer.
Figure shows the HET being used to measure small displacements. If the displacement brings
magnet 1 close to the transducer, the output voltage will be increasingly positive, and it will be
increasingly negative if magnet 2 moves closer to the HET.The magneto resistance effect is closely
associated with Hall effect transducers.33
If the length of the device in Fig. is made much shorter than its width h, the Hall voltage can be
almost short circuited. As a consequence, the charge carriers move at t he Hall angle to the x
direction. The increase in path length causes an increase in resistance of the device, and this is
known as the geometrical magneto resistance effect.33 Transducers for measuring angular velocity
of ferrous gear wheels have been developed based on this effect