BEEME UNIT III.ppt

Electrical Measurements

1. UNIT III
ELECTRICAL MEASUREMENTS
BASIC ELECTRICAL,
ELECTRONICS AND
MEASUREMENT ENGINEERING

2. CLASSIFICATION OF
INSTRUMENTS
Electrical measuring instruments are mainly
classified as:
1. Indicating Instruments
2. Recording Instruments
3. Integrating Instruments
1. Indicating Instruments
Theseinstrumentsmakeuseofadialandpointer
forshowingorindicatingmagnitudeofunknown
quantity.
Examplesofthisinstrumentsareammeter,
voltmeter,wattmeteretc.

3. 2. Recording Instruments
Theseinstrumentsgiveacontinuousrecordofthegiven
electricalquantity
Theexamplesarevarioustypesofrecorders.Insuch
recordinginstruments,thereadingsarerecordedby
drawingthegraph.Thepointerofsuchinstrumentsis
providedwithamarker
3. Integrating Instruments
Integrating Instruments are those instruments which
totalize the events over a specified period of time. The
output of such instruments is the product of time and an
electrical quantity.
For example, a house energy meter , Unit of energy is
kwhr.

4. BASIC PRINCIPLE OF INDICATING
INSTRUMENTS
Three types of operating forces
i) Deflecting force
ii) Controlling force and
iii) Damping force
i) Deflecting Torque/Force
Thedeflectingtorque’svalueisdependentuponthe
electricalsignaltobemeasured;thistorque/forcehelpsin
rotatingtheinstrumentmovementfromitszeroposition.
Thesystemproducingthedeflectingtorqueiscalledthe
deflectingsystem.

5. ii) Controlling Torque/Force
Theactofthistorque/forceisoppositetothedeflecting
torque/force.
Whenthedeflectingandcontrollingtorquesareequalin
magnitudethenthemovementwillbeindefinitepositionor
inequilibrium.
Spiralspringsorgravityisusuallygiventoproducethe
controllingtorque.
Thesystemwhichproducesthecontrollingtorqueiscalled
thecontrollingsystem.
iii) Damping Torque/Force
Whenadeflectionforceisappliedtothemovingsystem,
itsdeflectsanditshouldcometorestatapositionwhere
thedeflectingforceisbalancedbythecontrollingforce.
Themovingsystemcannotimmediatelysettleatitsfinal
positionbutovershootorswingsaheadofit.Soinorderto
bringthepointertorestwithinshorttime,dampingsystem

6. Controlling System
Itisthesystemthatprovidesaforceequaland
oppositetothedeflectingforce.Controllingforcesare
appliedintwoways.
i)SpringControl(usedinmoderninstruments)
ii)GravityControl(notproperlyused)
i) Spring Control
A spring attached to the moving system produces a
controlling torque. The requirements for spring are
1. They should be non-magnetic.
2. They should be free from mechanical fatigue.
3. They should have a small resistance, where springs are
used to lead the current into moving system.

7. Flat spiral spring A and B as shown in figure.

8. ii) Gravity Control
Figureshowsthegravitycontrol,inwhichtwoweights,
balanceweightandcontrolweightareattachedtothe
spindleofthemovingsystem.
Thebalanceweightisusedtobalancetheweightofthe
pointer.Thecontrollingtorqueisproducedbycontrol
weight.
Thecontrollingtorqueisproportionaltothesineofthe
angledeflection'θ'

9. Damping System
Dampingsystemisprovidedinordertobringthepointer
torestwithinshorttime.
Thequicknesswithwhichthemovingsystemsettlesto
thefinalsteadyposition
Whenthemovingsystemoscillatesaboutfinalsteady
positionwithadecreasingamplitudeandtakessome
timetocometorest,thentheinstrumentissaidtobe
underdamping.
Whenthemovingsystemmovesrapidlybutsmoothlyto
itsfinalsteadyposition,thentheinstrumentissaidtobe
criticallydampedordeadbeat.
Whentheinstrumentisoverdamped,themoving
systemmovesslowlytoitsfinalsteadypositionina
lethargicfashion.

10. Generally, underdamped system is preferred for any
instrument.
Various methods used for producing damping torque
are,
i) Air friction damping
ii) Fluid friction damping and
iii) Eddy current damping

11. i) Air Friction damping
Theairfrictiondampingsystemwhichconsistsofa
lightaluminiumpistonattachedtothemovingsystem
(i.e.,pointer).
Thepistonmovesinafixedairchamberwhichis
closedatoneend.
Theclearancebetweenthepistonandchamberwall
isuniformthroughoutthechamberanditisvery
small.
Whenthereisoscillationsinthepointer,thepistonwill
moveinsidetheairchamber.

12. ii) Fluid Friction Damping
Astheviscosityofoilisgreaterthanair,thedamping
forceofthistypeofdampingthegreaterthanairfriction
damping.
Thediscisdippedintotheoilpotanditiscompletely
submergedinoil.Whenthemovingsystemmoves,the
discmovesinoilandwhichalwaysopposesthemotion.

13. iii) Eddy Current Damping
The eddy current damping which is the most effective
way to provide damping. It is based on Faraday's law
and Lenz's Law.
Whenaconductormovesinamagneticfield,itcutsthe
magneticfieldandhenceemfisinduced.Thisinduced
emfopposesthecausesproducingit,thusopposing
themotionofthemovingsystem.

14. Inthismethod,analuminiumdiscisconnectedtothe
spindlewhichisinturnconnectedtothepointer.
Apartofthealuminiumdiscisinsertedintothedamping
magnetwhichisapermanentmagnet.
Whenthepointeroscillates,thealuminiumdiscrotates
whichinturncutsthemagneticfieldofthedamping
magnet.
So,anemfisinducedinthedisc.Asthediscisaclosed
path,eddycurrentflowsthroughthediscwhich
opposesthecauseproducingiti.e.,thepointer
oscillation,thushuntingthepointeroscillation.

15. MOVING IRON INSTRUMENTS
There are two types
Moving iron attraction type instruments
Moving iron repulsion type instruments
Moving iron attraction type instruments
ItconsistoffixedcoilCandmovingironpieceD.
Thecoilisflatandhasanarrowslotlikeopening.
Themovingironisaflatdiscorasectoreccentrically
mountedonthespindle.
Thespindleissupportedbetweenthejewelbearings.
Thespindlecarriesapointerwhichmovesovera
graduatedscale.

16. Following consequences happens
Current in coil→ produce magnetic field → attract disc →
pointer moves → so measure current.
Tc provide by spring
Td provide as air friction damping

17. Moving iron repulsion type
instruments
Two vanes inside the coil, one is fixed and other is
movable
When the current flows in the coil, both the vanes are
magnetised with like polarities induced on the same
side.
Both vanes gets magnetized and get repulsive each
other. So pointer moves
It has two types
Radial vane type
Coaxial vane type

18. 1. Radial Vane Repulsion Type Instrument
Thetwovanesareradialstripsofiron.Thefixedvaneis
attachedtothecoil.
Themovablevaneisattachedtothespindleand
suspendedintheinductionfieldofthecoil.
Eventhoughthecurrentthroughthecoilisalternating,
thereisalwaysrepulsionbetweenthelikepolesofthe
fixedandthemovablevane.Hencethedeflectionofthe
pointerisalwaysinthesamedirection.

19. 2. Co-axial Vane Repulsion Type Instrument
In this type of instrument, the fixed and moving vanes are
sections of co axial cylinders

20. Thecontrollingtorqueisprovidedbysprings.
Thedampingtorqueisprovidedbyairfriction
damping.
Eddycurrentdampingcannotbeusedinmovingiron
typeinstruments,becauseintroductionofpermanent
magnetrequiredforeddycurrentdampingwould
distorttheoperatingmagneticfieldofMIinstruments
whichisveryweak.
MovingIrontypeofinstrumentscanbeusedforboth
ACandDCmeasurements

21. Torque Equation of Moving Iron
Instruments
The energy stored in the coil in the form of magnetic
field = (1/2)LI
2
.
As soon as the current changes to (I+dI), deflection in
the pointer becomes dƟ resulting into change in
inductance of coil from L to (L+dL).
Let this deflection in pointer is due to deflection torque
T
d.
Mechanical work done = T
d. dƟ ………………..(1)
Energy stored in Coil = (1/2)(L+dL)(I+dI)
2
Change in stored energy of coil = Final Stored Energy –
Initial Stored Energy

22. = (1/2)(L+dL)(I+dI)
2
–(1/2)LI
2
= (1/2)[ (L+dL)(I+dI)
2
–I
2
L]
= (1/2)[ (L+dL)(I
2
+2IdI+(dI)
2
–I
2
L]
= (1/2)[ LI
2
+2LIdI+L(dI)
2
+ dL.I
2
+2IdI.dL+dL.(dI)
2
–I
2
L]
Neglecting second order and higher terms of differential
quantities
i.e. L(dI)
2
, 2IdI.dL and dL . (dI)
2
= (1/2)[ 2LIdI+dL.I
2
]
= LIdI +(1/2)dL.I
2
……………………(2)
We can write as, e = d(LI) / dt
= IdL/dt + LdI/dt
But electrical energy supplied by the source = eIdt
= (IdL + LdI)
. I
= I
2
dL + LIdI

23. Accordingtolawofconservationofenergy,this
electricalenergysuppliedbythesourceisconverted
intostoredenergyinthecoilandmechanicalworkdone
fordeflectionofneedleofMovingIronInstruments.
I
2
dL + LIdI = Change in stored energy + Work done
⇒I
2
dL + LIdI = LIdI +(1/2)dL . I
2
+ T
d. dƟ
⇒T
d. dƟ = (1/2)dL.I
2
⇒T
d= (1/2)I
2
(dL/dƟ)
Thus deflecting torque in Moving iron Instruments is
given as
T
d= (1/2)I
2
(dL/dƟ)
In moving iron instruments, the controlling torque is
provided by spring. Controlling torque due to spring is
given as
T
c= KƟ in N-m

24. In equilibrium state,
Deflecting Torque = Controlling Torque
⇒T
d= T
c
⇒(1/2)I
2
(dL/dƟ) = KƟ
⇒Ɵ = (1/2)(I
2
/K)(dL/dƟ)
Ɵ α I
2
Thedeflectiontorqueisunidirectionalwhatevermay
bethepolarityofthecurrent.
Hence,theMIinstrumentscanbeusedforbothAC
andDC.

25. Errors in Moving Iron
Instruments
1. Errors with both A.C and D.C work:
(a) Hysteresis error.
(b) Stray magnetic field error.
(c) Temperature error.
(d) Friction error.
2. Errors with A.C work only:
(e) Frequency error.
(f) Error due to reactance of the instrument coil.
(g) Error due to eddy current.
(h) Error due to waveform.

26. Advantages of Moving iron
Instruments
UsedforthemeasurementofACandDCquantities.
Thesetypesofinstrumentshavehighvalueoftorqueto
weightratio.Duetothiserrorbecauseoffrictionisquite
low.
Itisverycheapduetosimpleconstruction.
Thereisnomovingpartintheinstrumentwhichcarries
current.
Theseinstrumentscanbedesignedtoprovideprecision
andindustrialgradeaccuracy.Awelldesignedmoving
ironinstrumentshaveaerroroflessthan2%orlessfor
DC.ForAC,theaccuracyoftheinstrumentmaybeof
theorderof0.2to0.3%at50Hz.
Notdamagedevenunderseveroverloadconditions.

27. Disadvantages of Moving Iron
Instruments
These instruments suffer from error due to hysteresis,
frequency change and stray losses.
Thescale of moving iron instrumentis not uniform.
Accurate readings are not possible at lower range.
If it is used at 50 Hz, calibration must also be done at
the same frequency i.e. 50 Hz.
Moving Iron Instruments are suitable for low frequency
application. Moving iron instruments are not suitable for
frequency above 125 Hz.
The reading of the instrument is affected by
temperature variation.

28. PERMANENT MAGNET MOVING
COIL (PMMC) INSTRUMENTS
The permanent magnet moving coil instrument is the
most accurate type for d.c. measurements.
Basic Principle
Theactionoftheseinstrumentsisbasedonthemotoring
principle.
Whenacurrentcarryingcoilisplacedinthemagneticfield
producedbypermanentmagnet,thecoilexperiencesa
forcedandmoves.
Asthecoilismovingandthemagnetispermanent,the
instrumentiscalledpermanentmagnetmovingcoil
instrument.
ThebasicprincipleiscalledD'Arsonvalprinciple.

29. Construction of PMMC
Instruments

30. Themovingcoiliseitherrectangularorcircularin
shape.
Thecontrollingtorqueisprovidedbythemethodof
springcontrolwiththehelpoftwophosphorbronzehair
springs.
Thedampingtorqueisprovidedbythemovementofthe
aluminiumformerinthemagneticfieldproducedbythe
permanentmagnet.
The scale markings of the basic d.c. PMMC instruments
are usually linearly spaced

31. Torque Equation for PMMC
The deflecting torque is given by,
T
d= NBAI
T
d= GI
Where, G = NBA = constant
The controlling torque is provided by the springs
 T
c= KØ
For the final steady state position,
T
d= T
c
ThereforeGI = KØ
Ø = (G/K)I or I = (K/G) Ø
Ø α I

32. Errors in PMMC Instrument
Errors due to permanent magnets
Error may appear in PMMC Instrument due to the
aging of the spring.
Change in the resistance of the moving coil with
the temperature

33. Advantages of Permanent Magnet
Moving Coil Instruments
The scale is uniformly divided
Power consumption is also very low
A high torque to weight ratio. So operating current
is small.
The sensitivity is high
It has high accuracy
Instrument is free from hysteresis error
Extension of instrument range is possible
Not affected by external magnetic field called
stray magnetic fields.

34. Disadvantages of Permanent
Magnet Moving Coil Instruments
These instruments cannot measure AC quantities.
The cost of these instruments is high
Ageing of permanent magnet and the control springs
introduces the errors.
The friction due to jewel-pivot suspension.

35. ELECTRODYNAMOMETER
WATTMETER
Fixed coil
Current Coil (C.C), which is connected in series with the
load and it carries the current through the load.
Moving coil
Across the load and it carries the current proportional to
the voltage across the load.
Pressure Coil (or) P.C.

36. Fixed Coil
Carry the load current of the circuit.
Generally they are divided into two halves but connected
in series.
The fixed coils are wound with heavy wire with less
number of turns
The maximum current range of wattmeter is 20A
Moving Coil
Themovingcoilisgenerallyattachedtothespindlewhich
isconnectedtothepointer.
Itismadeofthinwirebuthasmorenumberofturns
Aseriesresistorisusedinthevoltagecircuitinorderto
limitthecurrenttoasmallvalueintheorderof100mA.
Thevoltageratingofthewattmeterislimitedto600V.
ControlTorque-Controltorqueisprovidedbysprings
Damping-Air friction damping is used

37. Errors in electrodynamometer type
wattmeter
Error due to pressure coil inductance
Error due to pressure coil capacitance.
Error due to the effect of manual inductance.
Error due to wrong connection of current coil and
pressure coil.
Eddy current error.
Stray magnetic field error.
Error caused by vibration of moving system.
Temperature error.

38. INDUCTION TYPE ENERGY
METER
Energymetersisanintegratinginstrumentwhich
measuresquantityofelectricity.
Thesemetersrecordtheenergyinkilo-watt-hours
(kWh).
Energymeterisaninstrumentusedtomeasureenergy
whichisthetotalpowerconsumedoveraspecific
intervaloftime.
UnitofenergyiskWhorJoules.
Energy = Power x Time

39. Basic Principle
The operation of the induction type energy meter is based
on the passage of alternating current through two coils
Magnetic field which interacts with a aluminium disc
supported near the coils and make the disc rotates.
The current coil carries the line current and develops
magnetic field. This magnetic field is in phase with the
line current.
The pressure coil is highly inductive, hence the current
through it lags behind the supply voltage by 90̊.
Due to this, a rotating field develops which interacts with
the disc to rotate.

40. Construction Details
i) Driving System ii) Moving System
iii) Braking System iv) Registering System

41. i) Driving System
Thecoilofoneoftheelectromagnets,calledcurrent
coil,isexcitedbyloadcurrentwhichproducesflux.This
iscalledasaseriesmagnet.
Thecoilofanotherelectromagnetisconnectedacross
thesupplyanditcarriescurrentproportionaltosupply
voltage.Thecoiliscalledpressurecoil.Thisiscalled
shuntmagnet.
Thefluxproducedbytheshuntmagnetisboughtinexact
quadraturewithsupplyvoltage
ii)MovingSystem
MovingSystemconsistsofanaluminiumdisc
Themovingsystemisconnectedtoahardenedsteel
pivotwhichisscrewedtothefootoftheshaft.
ThePivotissupportedbyajewelbearing.Inthistypeof
energymeter,asthereisnocontrollingtorque

42. iii) Braking System
The braking system consists of a permanent magnet
positioned near the edge of the aluminium disc.
The aluminium disc moves in the field of this magnet and
this provides a braking torque.
iv) Registering System / Counting System
Thefunctionofaregisteringorcountingmechanismisto
recordcontinuouslyanumberwhichisproportionaltothe
revolutionsmadebythemovingsystem.

43. Operation
The C.C carries the load current. It produces the magnetic
fields in phase with the line current.
The P.C carries current proportional to the supply voltage.
The magnetic field due to pressure coil lags approximately
90̊ behind the supply voltage
Themagneticfieldduetocurrentcoildevelopseddy
currentinthealuminiumdiscwhichreactwithmagnetic
fieldduetothepressurecoil.
Thusatorqueisdevelopedinthediscthenitrotates.
Thebrakingmagnetproducesmechanismsothatthe
electricalenergyconsumedinthecircuitisdirectlygivenin
KWh(KiloWatthour)

44. Advantages of induction type energy meters
The construction is simple and strong.
It is cheap in cost.
It has high torque to weight ratio, so frictional errors are
less and we can get accurate reading.
It has more accuracy.
It requires less maintenance.
Disadvantages of induction type energy meters
The main disadvantage is that it can be used only for a.c.
circuits.
The creeping can cause error.
Lack of symmetry in magnetic circuit may cause errors.

45. INTRODUCTION TO
TRANSDUCERS
Atransducerisasensingdevice,itconvertsphysical
phenomenonintoelectrical,pneumaticorhydraulic
outputsignal.
Mostlyusedefinitioninelectricalinstrumentationfield
is,transducerisadevice,whichconvertsphysical
quantityintoelectricalquantity.
BasicRequirementsofTransducer
1.Ruggedness
2.Linearity
3.Repeatability
4.Highoutputsignalquality
5.Highreliabilityandstability
6.Gooddynamicresponse
7.Nohysteresis
8.Residualreformation

46. CLASSIFICATION OF
TRANSDUCERS
Classification based on transduction principle
used
Classifiedasresistive,inductive,capacitivedepending
uponhowtheyconvertinputquantityresistance,
inductance,andcapacitancerespectively.
Primary and Secondary transducers
Primary
Transducers senses the input physical quantity directly and
convert directly into electrical quantity output.
Secondary
Input signal is sensed by other some detector or sensor and then
its output is given to transducer in other form then the transducer
converts the secondary signalinto electrical.

47. Active and Passive transducers
Active
Converts physical quantity into electrical quantity directly
So it is called self generating type transducers.
Passive
Inthistransducertheelectricalparametersresistance,inductance,
andcapacitancechangeswithchangeininputsignalarecalled
passivetransducers.
AnalogandDigitaltransducers
Analog transducers:
Output of analog transducer is continuous function of time.
Digital transducers:
Output of this type transducer is pulses or discrete form

48. Transducers and Inverse transducers
Transducers:
Transducer is a device, which converts input
physical quantity into output electrical quantity.
Inverse transducers:
Inverse transducer is a device, which converts
Input electrical quantity and output physical
quantity.

49. Capacitive transducer
The principle based on capacitance of a parallel
plate capacitor
C=εA/d= εoεrA/d
The change capacitance caused by
Change in overlapping area
Change in distance “d” between the plates
Change in dielectric constant
These are changes due to changing the force,
displacement and pressure
The change in capacitance causes change in
dielectric constant. Also measure the liquid level

50. Capacitance transducer –By
variation of overlapping area of
plates
C αA, capacitance changes linearly with change
in area of plates

51. The area changes linearly with the displacement
and also the capacitance
Char are linear. But initially non linearity due to
edge effects
Parallel plate capacitor, the capacitance is
C= εA/d= (εXW/d)* F
X= length of overlapping portion of plates in m
W= width of overlapping portion of plates in m
Sensitivity as
Cylindrical capacitor whose over lapping area is
varied by varying length of over lapping portion of
cylinder
Cylindrical transducer as shown

52. Capacitance as
S=const. Then relationship between capacitance
and displacement is linear
Fig shows two plate capacitor

53. Angular displacement to measured is applied
movable plate
The angular displacement changes the effective
area between area of plate and thus changes the
capacitance

54. Capacitive transducers-By variation
of distance between the plates
C α(1/d), used to measure linear displacement

55. Here one plate fixed and other plate moving
Moving plates moving away from or towards the
fixed plate as per displacement under
measurement, so capacitance decreases or
increases
Capacitance measured by AC bridges circuit, so
displacement of moving plate is determined
Curve is non linear. Sensitivity is high for initial
portion of curve

56. Capacitive transducer-
Differential arrangement
To achieve linear char, differential arrangement as
shown

57. It have three plates,
P1, P2→ Fixed plate
M → Movable plate
So two capacitor with differential o/p
M-midway between P1 & P2
AC voltage E applied between P1 & P2
C1=C2, E1=E2=E/2 (i.e) exactly midway between
2 plates

60. Advantages of capacitive
transducers
Have very high i/p impedance, so min loading
effect
Have good freq response. This response as high
as 50KHz and very useful for dynamic studies
Not affect by stray mag fields
High sensitivity, higher resolution
Force requirement of capacitive transducer is
very small and require small power to operate
them

61. Disadvantages of capacitive
transducers
Very high o/p impedance. So complicated
measuring circuit
Stray capacitance including that cables etc in
parallel with o/p impedance of transducer also
causes error and introduces non linearity
The cable connecting the transducer to the
measuring point is also a source of error. The
cable may br source of loading resulting in loss of
sensitivity. Also loading makes the low freq
response error
The instrumentation circuitry used with these
transducer is very complex

62. Application of capacitive
transducers
Use to measure both linear and angular
displacement
Use to measure force and pressure. Here first
convert displacement causes change of
capacitance
Able to measure pressure directly in all those
cases in which permittivity of a medium changes
with pressure, such as in case of benzene
permittivity vary by 0.5%, in pressure range of 1 to
1000 times the atm pressure
Use to measure humidity. Since the permittivity of
gases varies with variation in humidity. Though the
variation in capacitance due to variation in
humidity is quite small but is detectable
Commonly used in conjunction with mechanical

63. Capacitor microphone
Most commonly used as studio
Thin electrically conductive diaphragm is
suspended over back plate forming a flexible
capacitor
One plate is diaphragm, it mounted not touching.
Other plate is back plate
Battery connected to both plates, which produces
electrical potential or change between them
Sound wave exit the diaphragm. Distant between
plate change the capacitance, due to change the
voltage
This is excellent choice for mixing vocals, acoustic
guitar, piane, sound effect.

65. Inductive transducer
Either self generating or passive type
Self generating type utilize basic generator
principle
An inductive transducer is a device that convert
physical motion into a change in inductance
The principle used as
No of turns
Geometric configuration
Permeability of magnetic material or magnetic
circuit

66. Transducer based on principle of change
in self inductance with no of turns
o/p changes w.r.to no of turns
Measure displacement of linear and angular
movement as shown
Here no of turns changes, inductance changes,
then o/p changes

67. Transducer working on principle of change in
self inductance with change in permeability
Inductive transducer on principle of variation of
permeability causing change in self inductance as
shown
Iron core surrounded by winding. Here
permeability changes, then L-changes
Iron move out of winding, permeability↓, then L↓
in coil. Source to measure displacement

68. Variable reluctance inductance
transducer
Use to measure linear displacement
Hence length of magnetic path varies with the
displacement and reluctance of magnetic circuit
changes causing in self inductance of the coil

69. Linear Variable Differential
Transformer (LVDT)
Construction
It is widely used inductive transducer to translate
linear motion into electrical signal
LVDT is differential transducer consist of one
primary (P) and two secondary (S1 & S2). Both
wound on non magnetic material
S1 & S2 have equal no of turns and identical placed
on either side of pri winding
Displacement to be measure is applied to arm
attached to the soft iron core
In order to overcome the problem of eddy current
losses in the core, nickel-iron alloy is used as core
material and is slotted longitudinally

70. Construction as shown

71. Working
Primary winding voltage range as 5-25V and freq
as 50Hz-20kHz
Primary winding exited AC current source, so
produces AC mag field which induces AC voltages
Es1-o/p voltage of S1
Es2-o/p voltage of S2
Both S1 & S2 are in series opposing.
Differential o/p voltage = Eo=Es1-Es2

73. Case (i): When the core is at its normal (NULL)
position
Core is normal null position
Both sec. have equal flux linkages (i.e) Es1=Es2
So Eo=Es1-Es2=0
Case (ii): The core is moved to the left of the NULL
position
Core moved left of NULL position (i.e) at A
Flux linkages more in S1 and less in S2
So Es1>Es2, Eo= Es1-Es2
Eo=+ve which is in phase wih o/p
Case (iii): The core is moved to the right of the null
position
Core move right of NULL position (i.e) at B
Flux linkages less in S1 and more in S2
So Es2>Es1, Eo=Es2-Es1

74. Eo α(movement of core) (i.e) linear motion
Eo↓ or Eo↑ depends on direction of motion
o/p of one secondary increases and other
secondary decreases. So which use to measure
displacement
Variation of Eo w.r.to displacement of core as
shown. For small displacement only linear char.
Small changes
At ‘O’ position of core, Eo not equal to zero due to
have some residual magnetism (i.e) 1% of Emax
Residual voltage due to mag unbalance or
electrical unbalance
Due to harmonics & saturation of iron core
contribute residual voltage. Also due to stray mag
field.

75. Advantages of LVDT
Upto 5mm, it have linear displacement
High sensitivity, range as 10mV/mm –40mV/mm
Give high o/p. No need of amplification
Use freq upto 20kHz, more reliable
Have low hysterisis, hence repeatability is
excellent under all condition
Rugged construction, vibration without any
adverse effect
Power consume < 1W, small weight
Stable and easy maintanance

76. Disadvantages of LVDT
Require large displacement of o/p
Sensitive with stray mag field
Performance affected by vibration
Receiving instrument select to operate AC signal
or a demodulator network must be used if a DC
o/p is required
The dynamic response is limited mechanically by
mass of the core and electrically by freq of applied
voltage. The freq of the carrier should be at least
10 times the highest freq component to be
measured
Performance is affected with temperature

77. Application of LVDT
LVDT use to measure
Displacement
Force
Weight
Pressure
Position

78. STRAIN GAUGES
Piezo resistive Effect
Ifametalconductorisstretchedorcompressed,its
resistancechangesonaccountofthefactthatbothlength
anddiameterofconductorchange.
Alsothereisachangeinthevalueofresistivityofthe
conductorwhenitisstrainedandthispropertyiscalled
piezoresistiveeffect.
Uses of strain gauges
Used for measurement of strain and associated stress in
experimental stress analysis.
Many detectors and transducers notably the load cells,
torque meters, pressure gauges, temperature sensors,
accelerometers and flow meters, employ strain gauges as
secondary transducers.

79. Classification of Strain gauges
Wire strain gauge
Foil strain gauge
Thin film strain gauge
Semiconductor strain gauge

80. 1. Wire strain gauges
It is small size, min leakage, employ high temp
It has two types
Unbounded resistance wire strain gauge
Bonded resistance wire strain gauge
Unbounded resistance wire strain gauge
It consist of wire stretched between 2-point of insulating
medium (i.e) air
Dia=25µm
Wire have high tension. So that no sag & no vibration
Load applied, resistance changes, unbalances the bridges.
So V0 changes, V0 αstrain, displacement ≈ 50µm

82. Bonded resistance wire strain gauge
The schematic as shown
Dia of wire≈25µm
Loop as back and forth
The grid of fine wire is cemented on a carriers which
may be a thin sheet of paper, backelite or teflon
Wire converted on the top with thin material, so not
damaged mechanically
Spreading of wire permits uniform distribution of
stress

83. 2. Foil strain gauge
It is extension of resistance wire strain gauge
Metal & alloys use for foil. Nichrome, constantant
use for wire
It have high dissipation capacity. So use high temp
gauge. It have better bonding due to larger area
Advantage as fabricate to larger scale, any shape.
Etched foil gauge construction consist of first
bonding layer of strain sensitive material to a thin
sheet of paper of paper or bakelite
Etched foil strain gauge made thinner than
comparable wire units. More flexible. So it placed
remote & restricted places and curved placed.

85. 3. Thin film strain gauges
This can be produced by depositing a thin layer of
metal alloy an elastic metal specimen by means of
vacuum deposition
This technique, relatively new and extensively
used to produces a strain gauge that is
molecularly bondes to the specimen under test
and so the drawback of epoxy adhesive bond are
eliminated
Thin technique is most widely used for transducer
application such as in disphragm type pressure
gauges.

86. 4. Semiconductor strain gauge
It have high sensitivity have gauge factor
It required high value of gauge factor. It is 50 time
higher then wire strain
Resistance change w.r.to applied strain
Semiconductor used as germanium & silicon
The schematic as shown

87. Consist of strain material and leads placed in
protective box. Thickness of wafer 0.05mm used
Bonded on suitable insulating subsrate, such as
teflon
For making contact use gold leads
For soldering leads use cadmium material
It have both +ve and –ve gauge factor for p and n-
type silicon respectevely

88. Advantages of semiconductor
strain gauges
Measure very small strain as well as 0.01 micron.
Also high gauge factor between -100 and +150
Manufacturing very small size range of 0.7-7mm
use to measure high localized strain
Chemically inert and low sensitivity
Have excellent hysteresis char.
Disadvantages
Sensitive to change w.r.to temp, more expensive
Poor linearity char

89. Hall effect

90. Ic flows downwards in semiconductor pellet which
placed in magnetic field perpendicular to pellet
surface, an VHcreated in pellet in direction
perpendicular in both Ic and magnetic field. This
process called as hall effect.
Electromagnetic force act on charged particle
according to F.L.H.R, the charged particle are
biasing to left side of semiconductor pellet.
The magnitude of emf VH, which is called the hall
voltage
VH=1/d(BIcRH)
RH= hall constant
B=flux density
D=thickness of semiconductor
Semiconductor device which are made use in
detecting magnetic field called “hall element or hall

91. Conceptual Diagram of Hall
Effect Transducer
(15)(15)

92. AconstantcurrentrunsthroughaconductiveHallstrip
insidethesensor.
Thediagramshowsarotatingmagnetplacednearthe
Hallsensor.
Thealternatingfieldfromthisrotatingmagnetwill
causeanalternatingHallvoltagetobegenerated
acrosstheHallstrip.
Thisalternatingvoltagewaveformisfedintothedigital
circuitry.Thisdigitalcircuitryconvertsalternating
voltagewaveformintosquarewaveformi.e.,digital
signal(ONorOFF)/+5VDCor0VDC).
Sensorsareavailablewithaverityofoutputvoltages
andpolarities.Ifthesensorisplacedinthesouth
magneticpole,thesensoristurnedONandremains
ON,afterthesouthpoleisremoved.
Now,ifthesensorisplacedinnorthmagneticpole,the

93. Advantages
Can operate high speed than mechanical points
Operating frequency as 100KHz
Measure wide range of magnetic fields
Stable, reliable, long lasting
High resolution and small size
Disadvantages
Very low o/p drive capability
Difficult to operate in strong external magnetic field
Less accurate
Application
BLDC motor, Proximity detector, Speed sensor
(motor control)
Vending machine, Shaft position sensor, valve
position detector

94. Piezoelectric transducer
Piezoelectric material is one which an electric
potential appears across certain surfaces of a
crystal surfaces of a crystal if the dimension of the
crystal are changed by the application of
mechanical force. This potential produced by
displacement of changes.
The effect is reversible also, varying potential
applied to proper axis of crystal, it will changes the
dimension of crystal thereby deform it. This
phenomenon is known as piezoelectric effect
Piezo is greek word meaning force or pressure.
Element exhibiting piezoelectric quantity are called
electro resistive elements

96. Material for piezoelectric transducer
Common used material as rochelle salt,
ammonium, dihydrogen phosphate, quartz and
ceramics made with barium titanate, dipotassium ,
lithum sulphate
The piezoelectric effect can be made to respond to
mechanical deformation of material in many
different modes. These modes are
Thickness expansion
Transverse expansion
Thickness shear
Face shear
Mechanical deformation generates a charge and
this charge appears as voltage across electrodes

97. A tensile force produce a voltage of one polarity while a
compressive force produces a voltage of opposite
polarity
A crystal between a solid base and the force summing
member. An extremely applied force, entering the
transducer through its pressure, applies pressure to top
of crystal. This produces a voltage across the crystal
proportional to the magnitude of applied pressure.
Magnitude and polarity of induced surface charges
proportional to mag and direction of force
Q=F*d
d= crystal charge sensitivity in coulombs per newton and is
constant for a given crystal cut
F= force in newton
The Voltage sensitivity g = E
0/tP or g=ε/P ...........
here ε = E
0/t

98. Modes of operation of
piezoelectric crystal
The different modes as
Thickness shear
Face shear
Thickness expansion
Transverse expansion

100. Advantages of piezoelectric transducer
Small size, light weight, rugged construction
It has self generating type and no need of external
power
o/p is quite large
Very good high freq response. Range as 1Hz to
20KHz. Natural frequency as 50KHz
Disadvantages of piezoelectric transducer
Eo affect with temp variation of crystal
Use for dynamic measurement only
Application of piezoelectric transducer
Use to measure of force, pressure, temp
Employ high freq accelerometer