Lecture - 6 - Capacitance Transducers - German …eee.guc.edu.eg/Courses/Electronics/ELCT903...

Capacitance Transducers

Capacitance is a function of effective area of conductor, the separation between the conductors and the dielectric strength of the material

Dr.-Eng. Hisham El-SherifElectronics and Electrical Engineering Department

ELCT903, S ensor Technology

A change in capacitance can be by varying any of the following parameters

- Changing the distance between the two parallel electrodes. d

- Changing the dielectric constant, permittivity, of the dielectric medium

- Changing the area of the electrode. A

ε

The ratio of the amount of charge stored on one of the plates to the amount of voltage across the capacitor is the capacitance


ELCT903, Sensor Technology

The capacitance is directly proportional to the area of plates and inversely proportional to the distance between them

dA

Cε=

The constant of proportionality is known as the permittivity is a function of the type of material separating the plates

For a capacitance with insulating material, the capacitance between the plates:-

ε

dA

C r 0εε= farad



= dielectric constant of the insulating medium ( air = 1)

= permittivity of air or free space (8.85 X 10-12F/m)

= overlapping area in plates m2

= distance between electrodes or plates

rε rε0ε

A

d

Variable capacitance transducers have applications in the area of liquid level measurement. In chemical plants and in situations where nonconductors are required

can be represented as

dC ∆−=∆

C∆ 2dA

dC ε−=

∆∆

ddA

dAC

CC ∆−=∆=∆

2

εε



AA

CC

dC∆=∆

−= d

dAd

dA

dAC

CC ∆⋅−=∆=∆

εε

ε 2

dd

CC ∆−=∆

1- Capacitance Transducers using change in distance between plates



The right plate is fixed and the left plate is movable by the displacement that is to be measured

Capacitance change due to plate separation

dA

C r 0εε=

If air is the dielectric medium, then = 1rε

The capacitance is inversely proportional to the distance between plates

The overall response of the transducer is not linear. Transducers of this type are used for the measurement of extremely small displacements where the relationship is approximately linear



Variation of capacitance with distance

The sensitivity factor is expressed as

AC εε−∂

dd

CC ∆−=∆

ddC

C∆−=∆



20

dA

dC

S rεε−=∂∂=

2- Capacitance Transducers Using change in area of plates

For parallel plate capacitors , the capacitance is

dLW

dA

C rr 00 εεεε ==

L = overlapping part of plates



W = width of overlapping part of plates

For air, =1 the sensitivity of the capacitance transducer becomesrε

dW

lC

S r 0εε=∂∂= Farads per meter

There is a linear relationship between displacement and the capacitance. The equations showed that:

The capacitance is directly proportional to the area of the plates and varies linearly with changes in the displacement between the plates

Transducers of this type are used for the measurement of relatively large



Transducers of this type are used for the measurement of relatively large displacements


ELCT903, Sensor TechnologyCapacitance Variation by Change in Area

3- Capacitance Transducers Using change in Area ( Cylindrical Shapes)

A cylindrical capacitor consists of two coaxial cylinders with the outer radius of the inner cylinder defined as D1, the inner radius of the outside cylinder as D2and the length as L



Change in area based on cylindrical shapes

by evaluating the voltage difference between the conductors

rq

Eπε2

=

Where q = charge /unit length

VQ

C =



Vthe voltage between the cylinders can be found by integrating the electric field

�=∆22

212

D

D

Edrq

Vπε

�=∆22

21

12

D

D

drr

qV

πε

��

��

=∆ 22

ln

Dq

V



��

��

�

=∆

21

2ln2 Dq

Vπε

��

��

�⋅=

∆=∆

1

2ln

1

2 DDq

qVq

C

πε

LD

C ⋅��

=2

ln

2πε



DD��

��

�

1

2ln

1

2

0

ln

2

DD

LC rεπε=The capacitance is computed as

4- Capacitance Transducers for angular Rotation

The basic principle of change in area can also be used for rotational measurement

One plate is fixed and the other is movable

The angular displacement to be measured is applied to the movable plate.



Angular rotation of plates



Capacitance Variation on Rotation

The minimum value of the capacitance is

dr

dA

C r

2/2

0

πεεε ==

The capacitance at angle is

r2�θ

θ



dr

C r

2

0 2�

��

= θεε Farads (angular displacement is in radians)θ

The relation ship is linear and the maximum angular displacement is 1800.

The sensitivity is calculated as

20

2r

dC

S rεεθ

=∂∂=



5- Capacitance Transducers using Variation of Dielectric Constant

The principal is , change in capacitance caused by change in dielectric constant of the separating material



Two plate separated by a material of different Dielectric constant

The figure shows that; As this material is moved, it causes a variation of dielectric constant in the region separating the two electrodes, resulting in a change in capacitance

As the material moves a distance X , the distance l1 decreases and l2 increases

the capacitance value for a dielectric material of thickness d and width w



dwl

dwl

C rr 2010 εεεε +=

{ }210 lldw

C rεε +=

The equation has two terms

- One represents the capacitance of the two electrodes separated by air

- The other represents the capacitance of the dielectric material between the electrodes



If the dielectric material is moved through a distance X, the capacitance increases from and is shown as

( ){ }xlxldw

CC r ++−=∆+ 210 εε

CC ∆+



( ){ }1210 −++=∆+ rr xlldw

CC εεε

( )d

wxC r 10 −=∆ εε

6- Capacitance Transducers Based on Differential Arrangement

Differential capacitance transducers are used for precision displacement measurement



Differential arrangement of plates

Let C1 and C2 be the capacitances of the two plates that are fixed. Plate m is midway between the two plates.

An alternating voltage E is applied across the plates P1 and P2 and the potential difference is measured

0εεε r=Assume that



dA

CdA

Cεε

21 ,=

Voltage across C1 and C2

221

21

ECC

ECE =

+= 221

12

ECC

ECE =

+=

At the midway point E1 - E2 is zero



If X is the displacement of the movable plate, then

xdA

Cxd

AC

−+= εε

21 ,

The differential output voltage is

( ) ( )E

dxd

Ed

xdEEE

2221

−−+=−=∆

Edx

E =∆

The output voltage varies linearly with displacement X



The output voltage varies linearly with displacement X

The application for use in the range of 0.001 mm to 10mm and provide accuracy up to 0.05%

The sensitivity of the transducer is

dE

xE

S =∆=

A capacitive transducer is a displacement sensitive transducer. A suitable processing circuit is necessary to generate a voltage corresponding to the capacitance change.

General losses in the capacitance are attributed to:-



General losses in the capacitance are attributed to:-

- DC leakage resistance

- dielectric losses in the insulators

- losses in the dielectric gap

Advantages

-Require small force to operate

- very sensitive

-Require low power to operate.

-Their frequency response is good up to 50kHz

-Disadvantages



- the need to insulate metallic parts from each other

- loss of sensitivity due to error sources associated with the cable connecting the transducer to the measuring point.

7 – Capacitive Gap

- A capacitive gap sensor measures the distance between the front face of the sensor and a target object.

The target material should have high relative permittivity



dA

C⋅= ε

or εεε ⋅== the dielectric constant of the medium separating the sensor and the

target material

A = the area of the plates

rε



A = the area of the plates

d = the distance to be measured

There is a defined relation ship between the distance (gap ) and the capacitance.

The dielectric constant between the sensor head and the target material is a function of the target material type

rε

221

rqq

KF e⋅=

F = the force between the two charged particles 21,qq

( ) [ ]2910.9875.81 NmKe ==



since the net capacitance is a function of the target material, the effective distance varies with different target material types.

- An excitation circuit for the sensor works to maintain a constant electric field magnitude between the sensor head and the target object.

( ) [ ]2910.9875.8

41

CNmK

o

e =⋅

=επ

= Coulomb constant

-The capacitive sensors provide only two state ON/OFF output, and sense the change in the oscillation circuit signal amplitude.

-When the target object enters the field sensing distance of the sensor, the capacitance increases and the magnitude of the oscillations increases.

-A detection and output circuit then controls the ON/OFF state of a transistor.

-The resolution of the capacitive cap sensor is typically in micrometer range.



Applications for Capacitive Sensors

Precision Spindle Error Motion (Run out)Precision spindles in disk drives and high-performance machine tools are achieving error motions of less than 100 nanometers.

The only way to properly measure the error motion of these spindles is when they are at full speed. This is a perfect application for capacitive sensing technology because of inductive sensors’ rotating target errors (electrical run out) when measuring ferrous



inductive sensors’ rotating target errors (electrical run out) when measuring ferroustargets.

In the machine tool application, Two probes each are mounted in the X and Y plane (90�apart).While the spindle rotates at operational speeds the outputs of the two channels areviewed on an oscilloscope or analyzed by computer software.

When using an oscilloscope, the X channel is used to drive the horizontal axis and the Y channel is used to drive the vertical axis. This creates a lissajous pattern. The size and shape of the pattern gives indication of the amount and nature of the error motion of the spindle.



Error motions of high precision spindles are measured by capacitive probes in all three axes.



Driving the horizontal and vertical axes of an oscilloscope with the X and Y outputs indicates the motions of the rotating target.

For detailed analysis, computer software is required to calculate measurements forsynchronous error motion (run out) and asynchronous error motion (non repeatingRun out NRR).

Rotor to Stator Gap (Embedded Sensors)Stator to rotor gap can be a critical dimension in precision rotating devices such as airbearings and magnetic bearings. Capacitive probes can be designed to be embeddedin the wall of the stators and monitor the position of the rotor.



Embedded capacitive probes monitor rotor motion in air bearings and magnetic bearings.

Nonconductive Material ThicknessBecause capacitive sensors are sensitive to gap material they are effective at measuringnonconductive targets. Assuming that the composition and density of a nonconductive material are constant, changes in thickness can be measured by capacitivesensors.

The electric field from the sensing area of a capacitive probe must eventually return to ground.



Nonconductors by definition cannot provide a ground. Nonconductive measurement is usually performed while the target material is between the probe and a grounded reference.

The gap between the probe and the grounded reference must be kept constant. Any change in that gap will appear as changes in the thickness of the target material.



A nonconductive target can be measured against a conductive surface but the conductive surface must remain stationary.

-In some applications, measurements of nonconductive targets can bemade without the grounded reference target. -The electric field from the probe wraps back to the grounded outside shell of the probe or the fixturing that is holding it.



Using a fringe field to sense a non-conductor without a conductive back plate.

As the nonconductive target nears the probe it interacts with the electric field causinga change in the output.

But in this case the output will change in response to either changing thickness or changing position of the material.

For measuring thickness, the gap between the probe and either the front or back surface must be held constant.

If the thickness is constant, changes in the output will indicate changes in position.



output will indicate changes in position.

Double Feed Detection (Paper)This may be done in a top-of-the-line copier, a high-volume mailing machine, or a paper currency counter.


ELCT903, Sensor TechnologyCapacitive sensors detect increases in the amount of material in the gap such as paper thickness.

The application is as follows:-As paper is fed through the system, it passes between a capacitive probe and a grounded reference target.

During setup a single thickness of paper is placed under the probe and the sensor is adjusted to some known output, usually zero.

Then a double-thickness is placed under the probe and the sensor gain is adjusted for a known output, maybe 1 V or 5 V.

The Sensor Adjustment



The Sensor AdjustmentThe sensor used in this application will usually include an adjustable set pointoutput. The set point is normally adjusted to activate at about half of the double sheet output.

For example, if the double sheet output was 1 V, the set point would be adjusted to activate at 0.5 V. In this way, any output over 0.5 V would trigger a fault in the system.

Label SensingThe current state of the art in label sensing employs capacitive technology. Duringthe process of placing labels on containers such as bottles, the location of the leadingedge of the label is critical to locating the label in the center of the bottle.



Differential capacitive measurementsenses the gap between labels on a web.

The detection of the label edge is accomplished using a differential sensor.

The sensor actually has two sensing areas that are driven by the same circuit.

The sensor only activates its output when there is a difference between the two sensors.

The advantage to the differential configuration is that the sensor is much more immune to changes in the gap between the sensor and the grounded reference. Any changes in the gap size are common to both sensors so there is no



difference between them and the change does not affect the output.

Glue or Paper Additive SensingThe presence and/or amount of glue or other material deposited on a nonconductivematerial has been solved in many industries using capacitive technology. If the thickness/density of the underlying material is constant, changes in the amount of glue or other material is easily detected with capacitive sensors.



Capacitive sensors’sensitivity to varying amounts of nonconductive material make themideal glue, adhesive, or additive sensors.

-The probe is mounted in a position such that the applied material passes through its sensing area.

-Tests are performed to determine the sensor’s sensitivity to the material and gain adjustments are made to an appropriate level.

-The output of the sensor is then monitored by the control system and either warns an operator if the material is no longer present, or in more sophisticated systems, the output is used to control the flow of the applied material.



Level Measurement

The principle is used in devices for measuring levels in non-conducting liquids.


ELCT903, Sensor TechnologyThe change in capacitance is proportional to the displacement X.

-The electrodes are two concentric cylinders.

-The non conducting liquid provides a dielectric medium between them.

-At the lower end the outer cylinder are holes that allow passage of liquid.

-As the fluid level changes, the dielectric constant between the electrodes changes.

-This results in a change in capacitance



Capacitance Based Pressure Sensor

- The diaphragm pressure sensing concept can also be used to change the capacitance between two charged plates inside the sensor.

-The displacement of the diaphragm results in a proportional change in capacitance.

- by using the operational amplifier, reference capacitance and reference voltage.

- the change in the capacitance of the sensor can be converted to a voltage output signal proportionally.



PKd ∆⋅= 1

dA

C⋅= ε



��

��

�⋅=CC

VVr

rout

i

�= idtq

Cq

V =

Cq

VV CO ==r

crrCq

VV ==



C rC

r

r

cr

cr

CC

CqCq

VV

V ===

��

��

�⋅=CC

VVr

rout

xACV

Vrr

out ⋅��

��

�

⋅⋅=

ε

PA

KCVV

rrout ∆⋅

⋅⋅⋅=

ε1



PA

V ∆⋅⋅

=ε

The signal flow for the sensor operation is as follows, where the pressure differential results in change in the distance between two plates of the capacitive sensor with is in turn changes the capacitance of the sensor.

OutVCdP →→→∆

Lecture - 6 - Capacitance Transducers - German …eee.guc.edu.eg/Courses/Electronics/ELCT903...

Documents

Transcript of Lecture - 6 - Capacitance Transducers - German …eee.guc.edu.eg/Courses/Electronics/ELCT903...