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CAPACITIVE TRANSDUCERS
Lecture 13Instructor : Dr Alivelu M Parimi
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Introduction
Capacitive sensors basically exploit the change in capacitance
caused by
motion,
chemical composition,
electric fieldand,
indirectly, sense many other variables which can be converted
into change in motion or dielectric constant, such as pressure,
acceleration, level, and fluid composition.
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Introduction
A capacitor is an electrical component made up of two metallic
plates, each of which stores an opposite charge and are separated
by an insulator or dielectric.
When a potential difference is applied across it, one of the plates
becomes positively charged and other negatively charged.
Increasing the potential difference increases the amount of charge
on the plates.
The charge is stored at the surface of the plates, at the boundary
with the dielectric. Because each plate stores an equal but opposite
charge, the total charge in the device is always zero. The property of a capacitor to store electric charge when its plates
are at different potential is referred to as capacitance(C = ).
3
V
Q
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Introduction
The energy (measured inJoules in SIunits) stored in a
capacitor is equal to the amount of work required to establish
the voltage across the capacitor, and therefore the electric
field. This is given by:
4
2
2
1CVEstored
For an ideal capacitor, the capacitor current is proportional to the time rate of change of the
voltage across the capacitor with the constant of proportionality as the capacitance, C
dt
dVCti )(
The impedance in frequency domain (useful for the analysis in electrical circuits) can be
written as
1
CZ
j
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Introduction
The capacitance depends directly on the area of the plates
(the overlap area) and the dielectric constant of the material
between the plates and inversely proportional the distance
between the plates.
The change in capacitance as a function of the threeparameters r, A, d can be employed for the transduction
principle used for measuring various physical quantities.
Figure shows a parallel plate capacitor.
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CONFIGURATIONS AND TYPES OF CAPACITIVE
TRANSDUCERS
Variation in spacing, area and dielectric constant are used for
measuring displacement caused by force, pressure,
acceleration, level change etc.
Capacitive transducers convert physical quantities like motion,change in dielectric constant into change in capacitance, which
is then read as change in voltage/current/frequency.
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CONFIGURATIONS AND TYPES OF CAPACITIVE
TRANSDUCERS:Spacing Variation
8
physical diagram, schematic diagram, variationof capacitance and impedance w.r.t. spacing
variation between plates
This gives a conveniently large value of capacitance at small spacing, but it does
often require signal conditioning that can compensate for the parabolic
capacitance-motion relationship. Measuring impedance rather than capacitance
can also do this.
short range variation in the spacing
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Area variation
For long-range variation in displacement, area variation shown
in Figure is preferred. w is the width of the plates, L is the
length, and if one of the plate moves by distance x laterally,
then the capacitance as a function of x is given by,
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dxLwC r )(0
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Differential capacitor Bridge
Arrangement Circuit
10arrangement of capacitor transducers
connected in Wheatstone bridge.
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Rotary Motion The rotary motion can be converted into capacitance variation
by both spacing and area variation. Spacing variation can be
used when the rotary displacements are small and sensitivity
required is high. Area variation is used for large rotary
movements. Figure shows area variation to detect large rotary
displacement.
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For area variation, the capacitance is maximum when the overlap area is maximum i.e. =
1800 and is given by
d
AC ma xr0
ma x
Where2
rA
2
max
(if plates are semicircular in shape)
Hence the capacitance for any angular displacement is given by the expression,
.CC ma x
d2
rC
2
r0
Sensitivity S =
Kd2rC
2
r0 a constant.
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Example : Capacitance Type
Torque Meter
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Torque meter uses a fixed sleeve
with teeth or serrations cut axially
which surrounds the matching
shaft having similar axially cut
teeth.
Clearance is provided between
tips of teeth.
Torque produces shift in relative
positions of teeth, which changes
the overlapping area.
The resulting change in
capacitance is calibrated in terms
of torque.
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Dielectric Change
If the area, A and the distance d between the plates of a
capacitor remain constant, capacitance will vary only as a
function of the dielectric constant of the substance filling the
gap between the plates
Capacitance varies linearly with change in dielectric constant.
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LINEARIZATION
TECHNIQUES Several sources of nonlinearity corrupt the performance of a
simple parallel plate sensor.
Many techniques exist for removing these nonlinearities.
Either the physical construction of the transducers can be such
that the nonlinearities do not affect the output or thenonlinearities are accounted for in the signal processing part
of the transducer setup.
The non-linearity in the relation between the capacitance and
the distance between the plates can be removed by using
many techniques.
Linearization by Differential Capacitor Arrangement
Linearization by OP amp Circuit
Linearization by Pulse Width Modulation (PWM) Technique
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Linearization by Differential
Capacitor Arrangement The differential arrangement for linearizing the variation of
capacitance with displacement is shown in Figure where the
central plate is movable while upper and lower plates remain
fixed.
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The total potential difference between the two plates is E, which gets divided because of the
central plate which is free to move in the vertical direction. The capacitance associated
between the central plate and the two plates is C1and C2respectively and the corresponding
voltages are E1and E2. (C1 & C2are connected in series)
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2
1
CC
ECE
,21
1
2
CC
ECE
For x = 0, 21 CC and2
EEE 21
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Linearization by Differential
Capacitor Arrangement
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When the central plate is displaced by the measurand, the capacitances C1and C2 change,
changing the voltage E1and E2. When central plate moves up by distance x, C1, C2, E1and
E2become,
xd
AC
xd
AC 21
Ed2xdE1 and E
d2xdE2
If the two capacitances are connected in such a way that we get the difference of the
voltages, then the following relation is obtained which is linear.
12 EEE
EdxE
S = Sensitivity = Kd
E
x
E
= a constant.
Hence the linearization is achieved. Differential arrangement is self-compensating for
thermal expansion effects and to changes in dielectric constants due to humidity and
pressure.
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Linearization by OP amp
Circuit Linearization of the capacitive transducers can also be
obtained by connecting capacitive transducer in feedback path
around Op-amp as shown
The ratio of the output voltage and the input voltage is given
by the following linear equation in x.
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xA
C
C
C
Z
Z
e
e
r0
i
x
i
i
x
x
0
A
C
x
e
r0
i0a constant
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APPLICATIONS OF
CAPACITIVE TRANSDUCER Motion detectors: They can detect 10-14m displacements with good stability,
high speed, and in wide extremes of environment, and capacitive sensors withlarge electrodes can detect an automobile and measure its speed.
Flow: Many types of flow meters convert flow to pressure or displacement, usingan orifice for volume flow or Coriolis effect force for mass flow. Capacitivesensors can then measure the displacement.
Pressure: A diaphragm with stable deflection can measure pressure with a
spacing-variation detector. Liquid Level: Capacitive liquid level detectors sense the liquid level in a tank by
measuring change in capacitance between conducting plates which areimmersed in liquid . Change in dielectric constant is caused by change in liquidlevel.
Shaft angle or linear position: Capacitive sensors can measure angle or positionwith a multi-plate scheme, using principle of change in overlapping area giving
high accuracy. Capacitive sensors in oil refineries measure percent of water-in-oil, and sensors
in grain storage facilities measure the moisture content of wheat, both utilizingeffect of variation in dielectric constant.
Limit switch: Limit switches can detect the proximity of a metal machinecomponent as an increase in capacitance, or the proximity of a plasticcomponent by virtue of its increased dielectric constant over air.
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Advantages and disadvantages
Advantages of Capacitive transducers
The capacitive pickups require extremely small forces to operate.
They are extremely sensitive, can detect 10-14m displacements with good stability.
The frequency response of the capacitive transducers is good upto 50 kHz. For those in MEMS, therange extends upto 5 MHz.
The capacitive transducers have very high input impedance. Hence loading effect is negligible atthe input side thus giving accurate output.
The resolution of the capacitive transducers is of the order of 10-3mm.
They are not susceptible to stray magnetic fields.
Power dissipation in capacitive sensors with gas dielectrics is negligible.
When variable gap sensors are used in transducers with the same responsivity, the excitationforce in the capacitive sensor will be less than in the other sensors such as inductive sensors.
There is more scope to design capacitive sensors which are stable with temperature and time.This is because they can be constructed from a wider range of materials and their geometry issimpler than other sensors.
Disadvantages of Capacitive Transducers
They show nonlinear effect due to the edge fringing effect.
The output impedance is quite high which loads the output side of the measurement side.
Metallic leads and wires may introduce stray capacitances, if not eliminated they distort theoutput signal of the capacitive transducer. So the leads have to be insulated from each other.
Sensitive to humidity variations such as immersion or condensing humidity. 19
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To think and explore
Check whether your smartphone is Resistive or Capacitive
Touchscreens
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Problem
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Find length of rectangular plates in a parallel plate capacitor for making a capacitance of 1F,
having polyester dielectric (r
= 3.4). Width of plates is 2 cm and distance between plates is
13 m.
Solution
C =6
12r0
1015
L26.31085.8
d
A
So L = 25 m ( !)
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Problem
Fig shows a capacitor consisting of 2 plates each 400 mm x
400 mm, spaced 6 mm apart. The space between the metal
plates is filled with a glass plate 5mm thick and a layer of
paper 1 mm thick. Relative permittivities of glass and paper
are 8 and 2 respectively. Find (i) Equivalent capacitance (ii)Electrical field strength in each dielectric due to the potential
difference of 10 kV between the metal plates.
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Paper Glass
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Problem: assignment (No. 13)
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Five square plates of area 1 cm2are connected as shown in Fig.E6.4. The distance d between
the plates is 0.006 cm and air is the dielectric between them. Write expression for
capacitance and calculate the sensitivity of the system.