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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.

    2

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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.

    5

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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.

    7

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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,

    9

    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.

    11

    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

    12

    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.

    13

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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

    14

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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.

    15

    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)

    21

    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.

    17

    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

    20

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    Problem

    21

    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.

    22

    Paper Glass

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    Problem: assignment (No. 13)

    24

    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.