UNIT-V

SENSORS AND TRANSDUCERS

2. Inductive Transducer:
The inductive electromechanical transducer is a device that
convert physical motion(position change) into a change in
Inductance.
It is mainly used for the measurement of displacement.
Transducer type work on one of the following principles
1.Variation of self inductance
2.Variation of mutual inductance
The displacement to be measured to cause variation in any of
Three variables.
1.Number of turns
2.Geometric configuration
3.Permeability of the magnetic material or magnetic circuits
When current is passed through the coil, the flux is
Ni

R
d N di N di
 X  2 X
dt R dt R dt
If the current varies very rapidly
d N di
 X
dt R dt
d
But emf induced in the coil is given by eN
dt
N di N 2 di
Therefore e  NX 
R dt R dt

e N2
Self inductance is given by L 
di R
dt
 Change in Self Inductance with Numbers of Turns

Air cored transducer for measurement of linear displacement.

Iron cored coil used for measurement of angular displacement
Transducer working on the principle of change in self
Inductance with change in permeability
It works on the principle of the variation of permeability
Causing a change in self inductance.
 It can be used to measure displacement.
Variable Reluctance type transducer
The displacement which is to be measured is applied to a
ferromagnetic target.
The reluctance of the magnetic path is determined by the size of
the air gap.
The inductance of the coil depends on the reluctance of the
magnetic circuits.
The self inductance of the coil is given by
N2
L
Rg
But reluctance of the air gap is given by
lg
Rg 
 0  Ag
where l g  length of the air gap
Ag  area of the flux path throu gh air
 0  permeabili ty
 2. Capacitive Transducer (Pressure):
The capacitance is given by C=KA/d
Where
K= the dielectric constant
A= the total area of the capacitor
surfaces
d = distance between two capacitive
surfaces
C=the reluctance capacitance
A variable plate area transducer is made up of a fixed plate called
stator and a movable plate is called the Rotor.
It is designed to measure pressure( in vacuum)
Enclosed in an airtight container is a metallic diaphragm which
moves to the left when pressure is applied to the chamber and to
the right when vacuum is applied.
The diaphragm is used as one plate of a variable capacitor.
The distance from the stationary plate to its left, as determined
by the pressure applied to the unit, determines the capacitance
between the two plates.
Changes in pressure may be easily detected by the variation of
capacity between a fixed plate and another plate free to move as the
pressure changes.
The basic capacity formula
K(n - 1)A
C  0.885 pf
t
where A  area of one side of one plate in cm 2
n  number of plates
t  thickness of dielectric in cm
K  dielectric constant
4. LINEAR VARIABLE DIFFERENTIAL TRANSDUCER(LVDT)
Advantages of LVDT:
1.Linearity: The output voltage of this transducer is linear for
displacements upto 5mm.
2.High output: It gives a high output.
3.High sensitivity: 40V/mm
4.Ruggedness: Tolerate a high degree of vibration and shock.
5.Less friction: There is no sliding contact
6.Low power consumption: consume less than 1W of power.
Disadvantages of LVDT:
1. Large displacement are required for appreciable differential
output.
2. They are sensitive to stray magnetic fields
3. Temperature also affects the transducer.
5.STRAIN GAUGES
It is passive transducer that uses the variation in electrical resistance
in wires to sense the strain produced by a force on the wires.
There is a change in the value of the resistivity of the conductor when
subjected to strain called piezo-resistive effect and resistance strain
gauges are called piezo-resistive gauges.
The resistance of gauge increases with positive strain.
Types of strain gauges:
1.Wire 2. Foil 3.Semiconductor strain
Resistance Wire Gauge
Unbonded Resistance Wire Strain Gauges
It consist of wire stretched between two points in an insulating
medium, such as air.
The wires are kept under tension so that there is no sag and no free
vibration.
Unbounded strain gauges are connected in a bridge circuit.
A displacement of the order of 50µm can be detected with these
strain guages.
 Bonded Resistance Wire Strain Gauges
l
R
A
As a result of strain, two physical
parameters are interest
1. The change in gauge resistance
2. The change in length

 The measurement of the sensitivity of a material to strain is called

gauge factor (GF). It is the ration of the change in resistance ΔR/R
to change in the length Δl/l.
 R / R
GF ( K )       (1)
l / l
since strain is defined as the change in length divided by the original length
σ  Δl/l
Eq (1) can be written as
R / R
K      (2)

The resistance of a conductor of uniform cross - section is
length
R
area
l
R 2
r
d d2
since r  r  2

2 4
l l
R      (3)
d2  2
 d
4 4
  specific resistance of the conductor
l  length of conductor
d  diameter of conductor
when the conductor is stressed , due to the strain, the length of the conductor is increased
by l and decreases by d in the diameter
 l  l  (l  l )
Rs   
 
(d - d) 2 (d 2 - 2dd  d 2 )
4 4
sin ce d is small, d 2 can be neglected
 (l  l )
Rs 

(d 2 - 2dd)
4
 (l  l ) l (1  l / l )
Rs      (4)
 2d  2 2d
d 2 (1  ) d (1  )
4 d 4 d
poisson ratio  is defined as the ratio of strain in the lateral direction to strain in the axial direction
d/d
        (5)
l / l
l
 d/d         (6)
l
substitute Eq (6) in eq(4), we have
l (1  l / l )
Rs 
l
( / 4)d 2 (1  2  )
l
Rationalis ing, we get
l
) (1  2 
l (1  l / l ) l
Rs 
l l
( / 4)d 2 (1  2  ) (1  2  )
l l
  l 
l  (1  l / l ) (1  2  )
l 
Rs   
( / 4)d 2  l l 
(1  2  ) (1  2  )
 l l 
 
l  1  2 l / l  l / l  2 l / l
2 2 
Rs   
( / 4)d 2  2 l
2

 (1  4  2
) 
l
l is small, we can neglect highe power of l
l
Rs  1  2l / l  l / l 
( / 4)d 2
l
Rs  1  (2  1)l / l 
( / 4)d 2
l l
Rs   (1  2 )l / l 
( / 4)d 2
( / 4)d 2
from Eq(3)
l
R
( / 4)d 2
Rs  R  R
l
Where R  (1  2 )l / l 
( / 4)d 2
The gauge factor wil l now be
R/R
K  1  2
l / l
6.PIEZO ELECTRICAL TRANSDUCER

Quartz, Rochelle salt and Barium titanate produce an emf when

they are placed under stress is called piezo electrical transducers.
Use in HF accelerometers.
The device needs no external power source and is self generating.
It cannot measure static conditions. The output voltage is also
affected by temperature variation of the crystal.
E=Q/Cp

coupling coefficient (K)

Mechanical energy converted to electrical energy
K
Applied mechanical energy
or
Mechanical energy converted to electrical energy
K
Applied electrical energy
Disadvantage:
The voltage will be generated as long as the pressure applied to the
piezo electric element changes.
7.TEMPERATURE TRANSDUCER
RTD , Thermocouples and Thermistors.
RTD and Thermistor are passive devices whose resistance changes
with temperature .It need an electrical supply to give a voltage output.
Thermocouples are active devices.
Resistance Thermometer:
The resistance of a conductor changes when its temperature is
changed.
Requirement of a conductor material to be used in these
thermometers
1. The change in resistance of material per unit change in
temperature must be large as possible.
2. The resistance of the material must have a continuous and stable
relationship with temperature.
 Temperature sensing element may be any material that exhibits a
relatively large resistance change with the change in temperature.
Platinum, Nickel and Copper are the metals used to measure
temperature.
The resistivity of platinum increase less rapidly at higher temperature.
The temperature range over which platinum has stability is 260˚C-
1100˚C.
When the sensing element is very near the bridge, and under balance
conditions R1 Rs

R2 R5
The sensing element away from the indicator R1 Rs  R3  R4

R2 R5
When Rs changes, the bridge balance is upset and the galvanometer
shows a deflection, which can give suitable temperature.
Advantages:
The measurement is very accurate.
They are best suited for remote sensing and indication.
The size of the resistive element may be about 6-12mm in diameter.
No necessity of temperature compensation.
Performance stability over longer periods of time.
Limitations:
High cost
Need for bridge and power source
Possibility of self heating
8.THERMOCOUPLE
Measurement of moderately high temperature.
Temperature measurement with thermocouple is based on the
seebeck efffect.
Each junction is a voltage source known as Peltier emf.
When two dissimilar conductors are joined, electrons will diffuse
across the junction from the conductor with higher electron density
and losing electrons acquire a positive voltage w.r.t other conductor
is called Peltier emf.
When the junction is heated a voltage is generated, this is known
as seebeck effect.
The junction of the wires of the thermocouple is called sensing
junction or hot junction and end of the wire is cold or reference
junction.
Type ‘E’ thermocuple units use chromel alloy as the positive
electrode and constant alloy as the negative electrode.
Type ‘S’ thermocuple produces the least output voltage but can be
used over greatest temperature range.
Type ‘T’ uses copper and constants.
Cold junction compensation (by placing reference junction in an ice
bath to keep it at a known temperature).
Thermocouples in series and parallel

Thermocouples must be protected from mechanical damage and

isolated from corrosive effect by using wells.
9.THERMISTOR
Thermistor (Thermally sensitive resistor) are non metallic resistors
made by mixtures of metallic oxides such as manganese, nickel,
cobalt, copper and uranium.
It is NTPC and non-linear device with better than 0.2% linearity
over the 0-100˚C.
The sensitivity is 3mV/˚C
The resistance of thermistors at room temperature decrease by 5%
for each 1˚C rise in temperature.
Disc, washer or rod forms thermistors produc greater power
dissipation.
Disc thermistor about 10mm in diameter,either self supporting or
mounted on a small plate used for temperature control having
resistance value of 1Ω to 1MΩ.
Washer themistors are like disc except a hole is formed in the
centre in order to make them suitable for mounting on a bolt.
Rod thermistors are extruded through dies to make long cylindrical
units of 1.25,2.75 and 4.25mm in diameter and 12.5-50mm long and
their resistance varies from 1-50kΩ.
Bed thermistors are smallest therimistors made in the form of
beads with diameter of 0.15mm with resistance ranges from 300Ω
to100MΩ.
10.DATA ACQUISITION AND CONVERSION
It consist of individual sensors with necessary signal conditioning ,
data conversion, data processing, multiplexing, data handling and
associate transmission, storage and display systems.
The important factors that decide the configuration and sub systems
of the DAS.
1.Accuracy and resolution
2.Number of channels to be monitored
3.Analog or digital signal
4.Single channel or multichannel
5.Sampling rate per channel
6.Cost
The various general configurations include the following
1.Single channel possibilities
(i). Direct conversion
(ii) Pre-amplification and direct conversion
(iii) Sample and hold, and conversion
(iv) Pre-amplification, signal conditioning
2.Multi channel possibilities
(i). Mutiplexing the outputs of single channel converters
(ii) Mutiplexing the outputs of sample-hold conversion
(ii) Mutiplexing the inputs of sample-hold conversion
(iii) Mutiplexing of low level data
Objecive of a DAS
It must acquire the necessary data, at correct speed and at the
correct time.
Use of all data efficiently to inform the operator about the sate of
the plant.
It must monitor the complete plant operation to maintain on-line
optimum and safe operation.
It must be able to collect, summarise and store data for diagnosis
of operation an record purpose.
It must be flexible and capable of being expanded for future
requirements.
It must be reliable, and not have a down time greater than 0.1%
Ratiometric Conversion

Logarithm Compression
ΔV=log (1.01)x1V
Single Channel DAS

A/D
Pre-amplification and Filtering
Multi-channel DAS
Multi-Channel Analog Multiplexed System
Multiplexing the outputs of sample/hold
Multiplexing after A/D conversion
Multiplexing Low Level Data
 Velocity Transducer
A velocity transducer/sensor consists of a moving coil
suspended in the magnetic field of a permanent magnet.
v=N(d∅//dt)
N ––Number of turns of the coil
d∅/dt –– Rate of change of
flux in the coil
Vibration Transducer
It requires that the equipment should withstand stated levels of
vibration.
Vibration measurements are frequently carried out on rotating and
reciprocating machinery for analysis, design and trouble shooting
purpose.
Vibration monitoring is carried out on power station turbines and
generators to give an early warning of machine conditions which may
lead to complete failure and destruction of the equipment.
Nature of Vibrations:
Vibration may be defined by its amplitude and frequency
For a sinusoidal vibration, the displacement is given by