chapter5-a-Magnetic and electromagnetic.ppt

Electric and magnetic
sensors and actuators
(chapter 5, Part A)

Introduction
 Broadest by far of all other classes
 In numbers and types of sensors
 In variety within each type.
 Reasons:
 Sensor exploits the electrical properties of materials
 Many electrical effects
 The requisite output is almost always electrical
 Some electrical/electromagnetic sensors not
discussed here:
 (Thermocouples, optical, ultrasonic sensors etc.)

Introduction
 Most actuators are either electrical or,
more commonly, magnetic.
 This is particularly true of actuators that
need to provide considerable power.
 We will limit ourselves here to the
following types of sensors and actuators:

Introduction
 Sensors and actuators based on electric/electrostatic
principles.
 include MEMS (micro-electro-mechanical sensors), which are
most often based on electrostatic forces
 capacitive sensors (proximity, distance, level, material
properties, humidity and other quantities such as force,
acceleration and pressure may be sensed) and related field
sensors.
 Magnetic sensors and actuators based on static and quasi-
static magnetic fields.
 motors and valves for actuation,
 magnetic field sensors (hall element sensors, inductive sensors
for position, displacement, proximity and others),
 magnetostrictive sensors and actuators and more.

Definitions
 Electric field: Force per unit charge
 exists in the presence of charges or charged bodies.
 electric field may be static when charges do not move or
move at constant velocity
 time dependent if charges accelerate and/or decelerate.
 Moving charges in conducting media or in space
cause currents
 Currents produce magnetic fields.
 Magnetic fields are either static – when currents are
constant (dc) or:
 Time dependent when currents vary in time.

Definitions (cont.)
 If currents vary in time: both an electric and a
related magnetic field are established.
 This is called the electromagnetic field.
 Electromagnetic field implies that both an electric and a
magnetic field exists.
 It is OK to call all electric and magnetic fields by that
name since, for example an electrostatic field may be
viewed as a time independent electromagnetic field with
zero magnetic field.
 All fields described by Maxwell’s equations - will not
be discussed here

Sensing strategies
 Anything that influences one of these quantities
may be sensed through the electromagnetic field.
 Electromagnetic actuators are based on one of
the two basic forces;
 the electric force (best understood as the attraction
between opposite polarity charges or repulsion between
like polarity charges)
 the magnetic force. The latter is the attraction of current
carrying conductors with currents in the same directions
or repulsion of current carrying conductors with currents
in opposite directions.

Electric Field – Capacitive
Sensors and Actuators
 Electric field sensors and actuators
 operate on the physical principles of the electric field
and its effects (capacitance, charge, stored energy)
 The primary type: capacitive device.
 Some sensors such as charge sensors are better
explained in terms of the electric field
 On the whole, discussion of capacitance and its use in
sensing and actuation covers most aspects necessary
for a thorough understanding of these types of sensors
without the need to study the intricacies of the electric
field behavior.

Capacitance
 Capacitance: the ratio between
charge and potential of a body
 Measured in coulombs/volt. This
unit is called the farad [F].
 Capacitance is only defined for
two conducting bodies, across
which the potential difference is
connected.
C =
Q
V
C
V

Capacitance (cont.)
 Body B is charged by the
battery to a positive
charge Q and body A to
an equal but negative
charge –Q.
 Any two conducting
bodies, regardless of size
and distance between
them have a capacitance.

Parallel plate capacitor
 Parallel plate capacitor:
 Assumes d is small,
 0 is the permittivity of vacuum,
 r the relative permittivity (dielectric
constant) of the medium between plates,
 S the area of the plates and
 d the distance between the plates.
 0 is a constant equal to 8.854x10
F/m
 r is the ratio between the permittivity of
the medium to that of free space.
 available as part of the electrical
properties of materials.
C =
ε
0
ε
r
S
d
F

Parallel plate capacitor (cont.)

Permittivities of dielectrics
Material εr Mat
er
ial ε r Material ε r
Quartz 3.8-5 Paper 3.0 Silica 3.8
GaAs 13 Bakelite 5.0 Quartz 3.8
Nylon 3.1 Glass 6.0 (4-7) Snow 3.8
Paraffin 3.2 Mica 6.0 Soil (dry) 2.8
Perspex 2.6 Water (distilled) 81 Wood (dry) 1.5-4
Polystyrene foam 1.05 Polyethylene 2.2 Silicon 11.8
Teflon 2.0 Polyvinyl Chloride 6.1 Ethyl alcohol 25
Ba Sr Titanate 10,000.0 Germanium 16 Amber 2.7
Air 1.0006 Glycerin 50 Plexiglas 3.4
Rubber 3.0 Nylon 3.5 Aluminum oxide 8.8

Capacitors - cont.
 Any of the quantities in Eq. (2) affect the
capacitance
 Changes in these can be sensed.
 A wide range of stimuli including
 displacement and anything else that can cause
displacement (pressure, force), proximity, permittivity
(for example in moisture sensors)
 a myriad of other effects are related to capacitance.

Capacitors - cont.
 Eq. (2) describes a very specific device
 Was obtained by assuming that the electric field
between the two plates does not leak (fringes)
outside the space between the plates.
 In the more general case, when d is not small, or:
 Plates are arranged in a different configuration
 we cannot calculate the capacitance directly
 but we can still write the following:
C = α ε
0
, ε
r
, S , 1/ d

Capacitive position, proximity
and displacement sensors
 Position and displacement can be sensed in
three fundamental ways:
 (1) By allowing a plate to move relative
to the other (figure a).
 A number of configurations are shown next:
 the sensor is made of a single plate while the second
plate is a conductor to which the distance (proximity)
is sensed.
 Requires connection to the sensed object

Position and displacement
sensing

Position sensing relative to a
fixed conductor
 A schematic position sensor is shown in below
 One plate is fixed while the other is pushed by the moving device.
 The position of the moving device causes a change in position of
the dielectric and this changes the capacitance. C
 Capacitance is inversely proportional to the motion and
 As long as the distances sensed are small, the output is linear.

Sensing by moving the dielectric
 (2) The plates remain fixed but the
dielectric moves in or out as in Figure b.
 Practical for some applications.
 For example, the dielectric may be connected to a float
which then senses the fluid level or
 It may be pushed by a device to sense end of travel or
position.
 Advantages: linearity, range of motion is rather large and
can equal the width of the capacitor.

Sensing by moving the whole
capacitor
 (3) by keeping the plates fixed as in Figure c
and sensing the distance to a surface.
 This is a more practical arrangement since the
sensor is self contained and requires no
mechanical contact to sense distance or
position.
 Most capacitive sensors are a variation of this
arrangement

Practical proximity sensors
 Typically, a hollow cylindrical conductor forms
one plate of the sensor as in Figure 5.7.
 The second plate of the sensor is a disk at the
lower opening of the cylinder.
 The whole structure may be enclosed with an
outer conducting shield or may be encased in a
cylindrical plastic enclosure. The capacitance of
the device is C0 based on dimensions, materials
and structure.

Structure of a practical proximity
sensor

Proximity sensors - cont.
 When any material is present, effective permittivity
seen by the sensor and capacitances increases -
indicates distance
 Senses distances to conducting or nonconducting
bodies of any shape but output is not linear.
 the smaller the sensed distance d, the larger the
sensitivity of the sensor.
 dimensions of the sensor makes a big difference in span
and sensitivity.
 large diameter sensors will have a larger span while small
diameter sensor will have a shorter span.

Proximity sensors - cont.
 Other methods:
 Example: Two fixed plates and one moving plate.
 When the plate is midway, its potential is zero
since C1=C2.
 As the plate moves up, its potential becomes positive.
 When it moves down it is negative.
 More linear than the previous sensors
 Motion must be small or the capacitances will be very
small and difficult to measure.

Other position, displacement,
proximity sensors:
 Rotary (angular) position sensors
 Linear displacement sensors:
 Integrated comb-like sensors
 Sideways sliding plates
 Plunger type sensors
 Others

Other configurations for linear
displacement sensors

Capacitive fluid level sensors
 Fluid level:
 may be sensed by any of the position or proximity
sensors discussed in the previous paragraph
 by sensing the position of the fluid surface directly
 or through a float which then can change the
capacitance of a linear capacitor or a rotary capacitor.
 There is however another method which is linear
but can have a very large range. The method is
shown next:

Co-axial fluid level sensor
 A coaxial capacitor is made of
two concentric cylinders
establishing a capacitance C0.
 Capacitance of a coaxial
capacitor of length L, inner
radius a and outer radius b is:
 If the fluid fills the capacitor to
a height h, capacitance is:
C
0
=
2 π ε
0
L
ln ( b / a )
F
C
0
=
2 π ε
0
ln ( b / a )
h ε
r
+ L − h F

Co-axial fluid level sensor
 Capacitance is linear with respect to h
from h=0 to h=L
 Capacitive fuel gages are of this type
but the idea can be used for any fluid
that is nonconductive such as oils.

Capacitive sensors - comments
 Simple and rugged sensors
 Useful in many other applications
(pressure, acoustic sensors, etc.)
 Capacitances are small and changes in
capacitance even smaller.
 Require special methods of transduction.
 Often part of LC oscillator (measure freq.)
 Others use an ac source (measure imped.)

Capacitive actuators
Capacitive actuation is simple:
 Potential is connected across the two
plates of a capacitor
 Plates acquire opposite charges.
 These charges attract each other based
on Coulomb’s law
 Force tends to pull the plates together.

 Mechanical motion of the
plates is possible -
constitutes actuation
 In a parallel plate capacitor
the force is:
 For other configurations: no
exact relation but:
 Same general behavior
F =
C V
2
d
=
ε
0
ε
r
S V
2
d
2

 Force developed is
proportional to:
 Capacitance:
 Distance between plates:
 Potential across plates
 Forces are typically small (
is very small)
F =
C V
2
d
=
ε
0
ε
r
S V
2
d
2

Basic capacitive actuator
An electrostatic actuator (electrostatic speaker)
Upper plate is attracted or repelled by lower, fixed
plate
Motion may be used for positioning or for voice
reproduction

Angular capacitive actuator
 Upper plate moves relative to lower plate
 Force proportional to position (capacitance
changes)
 Useful for small, low force motion.

Electrostatic actuators -
comments
 Motion is usually small (except
loudspeakers)
 Voltages are high
 Force is low
 Usually accurate and linear
 Very common in MEMs

Magnetic sensors and actuators
 Magnetic sensors and actuators are governed
by the magnetic field and its effects.
 The magnetic flux density is also called
magnetic induction. Therefore, these sensors
tend to be named inductive sensors.
 We will rely on inductance, magnetic circuits and
magnetic forces which can be explained, at least
qualitatively, without resorting to Maxwell’s
equations.

Magnetics - some theory
 Lets start with a permanent magnet.
 It exerts a force on another magnet through space.
 We can say that a “field” exists around the magnet
through which it interacts.
 This force field is in fact the magnetic field.
 The same can be observed by driving a current
through a coil
 Since the two fields are identical, their sources are
identical - currents generate magnetic fields

Equivalence between
permanent magnet and coil

 A magnet attracts or repels another magnet –
this gives us the first observable interaction in
the magnetic field –it also attracts a piece of
iron.
 It will not attract a piece of copper.
 Conclusion: there are different types of material
in terms of their magnetic properties.
 Magnetic properties are governed by the
permeability of the material,  [henry/meter]

 The strength of the magnetic field is usually
given by the magnetic flux density B [tesla]
 The magnetic flux density is also called
magnetic induction
 The magnetic field intensity H [ampere/meter].
 The relation between the two is simple:
B = μ
0
μ
r
H

 0=4x10
[H/m] is the permeability of vacuum
 r is the relative permeability of the medium in which
the relation holds,
 r is given as the ratio between the permeability of
the medium and that of vacuum
 A dimensionless quantity associated with each
material in nature.
 Permeabilities of some useful materials are given
next.

 Magnetic materials:
 Diamagnetic, r < 1
 Paramagnetic r > 1
 Ferromagnetic r >> 1 (iron-like)
 The latter are often the most useful materials when
working with magnetic fields.
 There are other types of magnetic materials (ferrites,
magnetic powders, magnetic fluids, magnetic glasses,
etc.)

Permeabilities of diamagentic
and paramagnetic materials
Material Relative Permeability Material Relative Permeability
Silver 0.999974 Air 1.00000036
Water 0.9999991 Aluminum 1.000021
Copper 0.999991 Palladium 1.0008
Mercury 0.999968 Platinum 1.00029
Lead 0.999983 Tungsten 1.000068
Gold 0.999998 Magnesium 1.00000693
Graphite (Carbon) 0.999956 Manganese 1.000125
Hydrogen 0.999999998 Oxygen 1.0000019

Permeabilities of ferromagnetic
materials
Material μr Material μr
Cobalt 250 Permalloy (78.5% Ni) 100,000
Nickel 600 Fe
3O4 (Magnetite) 100
Iron 6,000 Ferrites 5,000
Supermalloy (5% Mo, 79% Ni) 107 Mumetal (75% Ni, 5% Cu, 2% Cr) 100,000
Steel (0.9%C) 100 Permendur 5,000
Silicon Iron (4% Si) 7,000

Magnetics - some definitions
 Soft magnetic materials are those for which
magnetization is reversible
 Hard magnetic materials are materials which
retain magnetization and are therefore used for
production of permanent magnets
 Hysteresis - a property of ferromagnetic materials
best explained through the magnetization curve
 Nonlinear magnetization: permeability is field
dependent.

Soft magnetic materials - used
as magnetic cores
Material Relativepermeability(Max.) μr
Iron(0.2%impure) 9,000
Pure iron (0.05% impure) 2× 105
Silicon
iron(3%Si) 55,000
Permalloy 106
Superm-alloy
(5% Mo, 79% Ni) 107
Permendur 5,000
Nickel* 600

Hard magnetic materials - used
in permanent magnets
Material μr
Alnico (Aluminum-Nickel-Cobalt)
3-5
Ferrite (Barium-Iron) 1.1
Sm-Co (Sammarium-Cobalt) 1.05
Ne-Fe-B (Neodymium-Iron-Boron)
1.05

Magnetization curve and
permeability of ferromagnetic
materials

Currents, fields and flux
 Relation between current and magnetic
flux density.
 For a long straight wire carrying a
current I and placed in a medium of
permeability 0r. The magnitude of
the magnetic flux density is:
 r is the distance from the wire to the location
where the field is calculated
 the magnetic field is a vector and has a
direction (next) - field is perpendicular to I
B = μ
0
μ
r
I
2 π r

Relation between current and
magnetic field

General idea:
 In more practical configurations, the wire
may not be very long or it may be wound
in a coil but, nevertheless, the basic
relations hold: The larger the current
and/or the permeability, or the shorter the
distance between current and the location
where the magnetic field is needed, the
larger the magnetic field

Magnetic flux
 Flux is the integral of flux
density over an area S:
 If B is constant over an area
S and at an angle  to the
surface, flux is =BScos.
 Unit of flux is the weber [Wb]
 1 [Wb] = 1 [Tm2
]
 Flux relates to power and
energy in the magnetic field
Φ = B . d s
S
Wb

Force in the magnetic field
 Force in a magnetic field is
based on the fact that a
charge moving at a velocity v
in a magnetic field B
experience a force (called the
Lorentz force) given as:
 vB is the angle between the
direction of motion and the
direction of B
 F is perpendicular to both v and
B as shown (next).
F = qvBsin θ
vb
[N]

Relation between charge,
current and force in a magnetic
field

Forces on currents
 Charges (electrons) move in conductors
(current)
 Two wires carrying currents in opposite
directions exert forces on each other
 The forces the wires exert on each other are in
opposite direction and tend to separate the
wires.
 If the currents were in the same direction (or the
magnetic field reversed) the wires would attract.

Forces on currents
 For long parallel wires, the force for a length L of
the wire is: F = BIL
 For other configuration the relation is much more
complicated but force is proportional to B, I and L.
 A single wire carrying a current will be attracted or
repelled by a permanent magnet
 These principles are the basis for magnetic
actuation
 Forces can be very large since B, I and L can be
controlled and can be quite large.

Inductive sensors
Rely on two basic phenomena:
 Inductance of a coil and changes of inductance
due to a variety of effects (distance, materials,
dimensions, etc.)
 Induced currents in conducting materials.
 Inductance is a property of a magnetic device just
as capacitance is the property of an electric device
 Usually associated with coils and conductors
 Inductance can be made to respond (change) to
almost any physical property either directly or
indirectly

Inductance
 Defined as the ratio of flux and the
current that produced is:
 Inductance is independent of
current since  is current
dependent
 All magnetic devices have an
inductance but inductance is
most often associated with coils
L =
Φ
I
webber
ampere
or [ henry ]

Inductance
 Two types of inductance:
 1. Self inductance: the ratio of the flux produced by a
circuit (a conductor or a coil) in itself and the current that
produces it. Usually denoted as Lii.
 2. Mutual inductance: the ratio of the flux produced by
circuit i in circuit j and the current in circuit i that produced it.
Denoted as Mij.
 A mutual inductance exists between any two circuits as long
as there a magnetic field (flux) that couples the two.
 This coupling can be large (tightly coupled circuits) or small
(loosely coupled circuits).

Inductors and transformers
 A coil is also called an inductor (having
inductance)
 Transformers are made of two or more
coils, coupled through mutual inductances
 Many sensors are in fact transformers of
one type or another
 Transformer are ac devices

The transformer
 A primary and a secondary circuit
 A magnetic path for the flux (closed or open)
 Transformer ratio is N1/N2

The transformer
 An ac voltage applied to one circuit (or coil)
produces a voltage in any other circuit that couples
to the driving coil as shown in Figure 5.17.
 Coils, of N1 and N2 turns respectively. All flux
produced by coil 1 couples to coil 2 through the
magnetic circuit made of a ferromagnetic material
(iron for example). The voltages and currents
relate as follows (a = N1/N2)
V2 =
N2
N1
V1 = 1
a
V1, I2 =
N1
N2
I1 = aI1

The transformer
 The transformer so defined is a tightly coupled
transformer (all flux links both coils)
 Loosely coupled transformers:
 Only part of the flux produced by one coil links the
second coil
 The magnetic path is said to be open
 These are more often used in sensors than tightly
coupled transformers

Inductive sensors - general
 Most inductive sensors relay on self inductance, mutual
inductance or transformer concepts
 Inductors require currents to sense (passive devices)
 A magnetic field is produced - the sensor can be said to
respond to changes in this magnetic field.
 The most common type of stimuli sensed by inductive
sensors are position (proximity), displacement and
material composition.
 Inductance and induction is often used to sense other
quantities indirectly.

Inductive proximity sensors
 Inductive proximity sensor contain:
 At the very least a coil (inductor)
 Generates a magnetic field
 The coil’s inductance depends on dimensions of the coil, number of
turns and materials around it.
 The current and the diameter of the coil define the extent to which the
field projects away from the coil and therefore the span of the sensor.
• Operation:
 As the sensor gets closer to the sensed surface the inductance of the
coil increases if the sense surface is ferromagnetic
 It is then sufficient to use a means of measuring this inductance to infer
proximity and position

Sensing position and proximity

Inductance - additional details
 Inductance is measured with an ac current source
and a voltmeter or an ac bridge.
 By measuring the voltage across the inductor the
impedance can be evaluated and since Z=R+jL (R is
the ohmic resistance and =2f the angular
frequency) the inductance L is immediately available
as a measure of position of the coil or proximity to the
surface.
 We assumed here that R is constant but even if it is
not, the impedance in air (nothing being sensed) is
known and this can be used for calibration.

Inductance sensor - practical
 A ferromagnetic core is added to increase the
inductance of the sensor.
 Most often iron or a ferrite (a powdered magnetic
material such as Fe2O3, CoO2 in a binding material and
sintered into the shape needed)
 A shield may be placed around the sensor to prevent
sensitivity to objects on the side of the sensor or at its
back
 The net effect of the shield is to project the field in front
of the sensor and hence increase both the field
(inductance) and the span of the sensor.

Practical construction of
inductive sensors

Proximity sensor with reference
coil
 In other sensors, there are two coils, one serving
as reference, the other as a sensor (Figure
5.19b).
 The reference coil’s inductance remains
constant and the two are balanced.
 When a surface is sensed, the sensing coil has
a larger inductance and the imbalance between
the coils serves as a measure of distance.

Closed magnetic circuit
proximity sensor
 Other sensors, like the one is Figure
5.19c may employ a closed magnetic
circuit which tends to concentrate the
magnetic field in the gaps and usually do
not require shielding since within the
sensor, the magnetic field is constrained
within the ferromagnetic material

Eddy current sensors
 Inductive proximity sensors are sensitive
to the presence (proximity) of non-
conducting ferromagnetic materials or to
any conducting media.
 Nonconductors in general do not affect
proximity sensors.
 Many inductive proximity sensors are of
the eddy current type.

 The name eddy current comes from the
fundamental property of ac magnetic fields to
induce currents in conducting media
 There are two related phenomena at work.
 The currents produced in the conductor, called eddy
currents because they flow in closed loops, cause a
field which opposes the original field that produces
them (Lenz’s law). This field reduces the net flux
through the sensor coil.
 Second, the currents flowing in the conductor being
sensed, dissipate power.

 The sensing coil is now forced to supply more
power than it would otherwise supply and
hence, given a constant current, its effective
resistance increases.
 This change in impedance from Z=R+jL to
Z’=R’+jL’ is easily sensed either in absolute
terms or as a change in the phase of the
measured voltage (given a constant current).
 A second effect is the skin effect in
conducting media.

A magnetic field penetrating into a conducting medium
is attenuated exponentially from the surface inwards
(and so are the eddy currents and other quantities):
B = B
0
e
− d / δ
, or : I = I
0
e
− d / δ
B0 and I0 are the flux density and the current density at the surface,
d is depth in the medium
 is the skin depth. Skin depth is defined as the depth at which the field
(or current) is attenuated to 1/e of its value at the surface.

Skin depth
 For planar surfaces, skin depth is given as:
δ =
1
π f μσ
m
f is the frequency of the field.
Penetration depends on frequency, conductivity and
permeability.
The main implication here is that the sensed conductor must be
thick enough compared to skin depth.
Alternatively, operation at higher frequencies may be needed.

Proximity sensors - comments
 Proximity sensors (either capacitive or inductive) can be
used to sense distance.
 Their transfer function is much too nonlinear and their span
too small to be effective except for short spans
 Proximity sensors are usually used as switches to provide a
clear indication when a certain, preset distance is reached.
 Inductive sensors can produce an electric output such as
voltage based on the change in their impedance
 Often the inductor is part of an oscillator (LC oscillator is the
most common) and the frequency of the sensor is then
used as the output.

Position and displacement
sensing
 Position and displacement are usually
understood as measuring the exact distance
from a point or the travel of a point relative to
another.
 Requires accurate measurements and possibly
linear transfer functions of the sensors involved.
 One approach to this task is through the use of
variable inductance sensors, sometimes called
variable reluctance sensors.

Magnetic reluctance
 Magnetic reluctance is the equivalent magnetic
term to resistance and is defined as
R =
L
μ S
1
H
Reluctance is smaller the shorter the magnetic path, the larger its cross
sectional area and the larger its permeability.
Reluctance is then related to inductance through permeability and
reducing reluctance also increases inductance and vice versa.
Typically, the reluctance of a coil can be changed by adding a gap in the
magnetic path and changing the effective length of this gap.

Movable core sensors
 Thus, a simple method of changing inductance of a
coil is to provide it with a movable core:
 The further the movable core moves in, the smaller
the reluctance of the magnetic path and the larger the
change in inductance.
 This type of sensor is called a linear variable
inductance sensor. (Linear here means that the
motion is linear).
 Inductance is a measure of the position of the core
 The same of course may be used to measure force,
pressure, or anything else that can produce linear
displacement.

Variable reluctance (inductance)
sensor - the LVDT

LVDT
 A better displacement sensor is a sensor based
on the idea of the transformer.
 Based on one of two related principles;
 the distance between two coils of a transformer is
varied (the coupling between the coils changes) or
 the coupling coefficient between the two coils is
varied by physically moving the core while the two
coils are fixed.
 Both principles are shown next.

LVDT
 LVDT - Linear Variable Differential
Transformer
 Based on the 2nd principle
 One primary coil, two secondary coils
connected in opposition
 Output is zero if coupling is balanced
 Motion to either side changes the output

Structure and equivalent circuit
of an LVDT
 The output is zero for core centered
 Motion to the right or left changes the output in different
directions (polarity)
 This is a variable reluctance transformer
 Detects both distance and direction of change

LVDT - properties
 LVDTs are very sensitive and useful
 In a relatively small range of motion, the output
is linear.
 The primary coil is driven with a stable
sinusoidal source at a constant frequency and
the core is ferromagnetic.
 The whole sensor is enclosed and shielded so
that no field extends outside it and hence cannot
be influenced by outside fields.

LVDT - properties
 The core slides in and out and that motion is often
used for accurate measurements of displacement for
applications in industrial control and machine tools.
 LVDT sensors are extremely rugged and come in
various dimensions to suit many needs (some as
small as 10mm long).
 In most practical applications, the voltage output is
measured (amplification is usually not needed) while
the phase is detected with a zero-crossing phase
detector (a comparator).

LVDT - properties
 Frequency of the source must be high with respect to the
frequency of motion of the core (a figure of 10 times
higher is common) to avoid errors in the output voltage
due to slow response of the LVDT.
 The operation of LVDTs can be from ac sources or dc
sources (with internal oscillator providing the sinusoidal
voltage).
 Typical voltages are up to about 25V while output is
usually below 5V.
 Resolution can be very high while the linear span is
about 10-20% of the length of the coil assembly

RVDT - Rotary Variable
Differential Transformer
 A variation of the LVDT
 Intended for angular displacement and rotary
position sensing.
 In all respects it is identical in operation to the
LVDT device but the rotary motion imposes
certain restrictions on its construction.
 The span is given in angles and can be up to
±30 to ±40. Beyond that the output is nonlinear.

chapter5-a-Magnetic and electromagnetic.ppt

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