Lecture - 6 - Capacitance Transducers

1 Capacitance TransducersCapacitance is a function of effective area of conductor, the separation between the conductors and the dielectric strength of the Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, S ensor TechnologyA 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 eThe ratio of the amount of charge stored on one of the plates to the amount of voltage across the capacitor is the Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyThe Capacitance is directly proportional to the area of plates and inversely proportional to the distance between themdACe=The constant of proportionality is known as the permittivity is a function of the type of material separating the platesFor a Capacitance with insulating material, the Capacitance between the plates.

2 -edACr0ee= Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor Technology= dielectric constant of the insulating medium ( air = 1)= permittivity of air or free space ( X 10-12F/m)= overlapping area in plates m2= distance between electrodes or platesrere0eAdVariable Capacitance Transducers have applications in the area of liquid level measurement. In chemical plants and in situations where nonconductors are requiredcan be represented asdCD-=DCD2dAdCe-=DDddAdACCCD-=D= Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyAACCdCD=D-=ddAddAdACCCD -=D=Deee2ddCCD-=D1- Capacitance Transducers using change in distance between Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyThe right plate is fixed and the left plate is movable by the displacement that is to be measured Capacitance change due to plate separationdACr0ee=If air is the dielectric medium, then = 1reThe Capacitance is inversely proportional to the distance between platesThe overall response of the transducer is not linear .

3 Transducers of this type are used for the measurement of extremely small displacements where the relationship is approximately Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyVariation of Capacitance with distanceThe sensitivity factor is expressed as ACee- ddCCD-=DddCCD-= Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor Technology20dAdCSree-= =2- Capacitance Transducers Using change in area of platesFor parallel plate capacitors , the Capacitance isdLWdACrr00eeee==L = overlapping part of Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyW = width of overlapping part of platesFor air, =1 the sensitivity of the Capacitance transducer becomesredWlCSr0ee= =Farads per meterThere is a linear relationship between displacement and the Capacitance . The equations showed that.

4 The Capacitance is directly proportional to the area of the plates and varies linearly with changes in the displacement between the platesTransducers of this type are used for the measurement of relatively large Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyTransducers of this type are used for the measurement of relatively large Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyCapacitance Variation by Change in Area3- 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 asD1, the inner radius of the outside cylinder asD2and the length as Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyChange in area based on cylindrical shapesby evaluating the voltage difference between the conductors rqEpe2=Where q = charge /unit lengthVQC= Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyVthe voltage between the cylinders can be found by integrating the electric field =D22212 DDEdrqVpe =D222112 DDdrrqVpe = Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor Technology =D212ln2 DqVpe =D=D12ln12 DDqqVqCpeLDC = Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903.

5 Sensor TechnologyDD 12ln120ln2 DDLC repe=The Capacitance is computed as 4- Capacitance Transducers for angular RotationThe basic principle of change in area can also be used for rotational measurementOne plate is fixed and the other is movableThe angular displacement to be measured is applied to the movable Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyAngular rotation of Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyCapacitance Variation on RotationThe minimum value of the Capacitance is drdACr2/20peee==The Capacitance at angle is r2 Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologydrCr202 =qeeFarads (angular displacement is in radians)qThe relation ship is linear and the maximum angular displacement is 1800. The sensitivity is calculated as 202rdCSreeq= = Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor Technology5- Capacitance Transducers using Variation of Dielectric ConstantThe principal is , change in Capacitance caused by change in dielectric constant of the separating Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyTwo plate separated by a material of different Dielectric constantThe figure shows that.

6 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 l1decreases andl2increasesthe Capacitance value for a dielectric material of thickness dand width w Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologydwldwlCrr2010eeee+={}210lldwCr ee+=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 Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyIf the dielectric material is moved through a distance X, the Capacitance increases from and is shown as (){}xlxldwCCr++-=D+210eeCCD+ Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor Technology(){}1210-++=D+rrxlldwCCeee()dw xCr10-=Dee6- Capacitance Transducers Based on Differential ArrangementDifferential Capacitance Transducers are used for precision displacement Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyDifferential arrangement of platesLet C1and C2be the capacitances of the two plates that are fixed.

7 Plate m is midway between the two alternating voltage Eis applied across the plates P1and P2and the potential difference is measured0eeer=Assume that Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologydACdACee21,=Voltage across C1and C222121 ECCECE=+=22112 ECCECE=+=At the midway point E1-E2is Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyIf X is the displacement of the movable plate, thenxdACxdAC-+=ee21,The differential output voltage is()()EdxdEdxdEEE2221--+=-=DEdxE=DThe output voltage varies linearly with displacement Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyThe output voltage varies linearly with displacement XThe application for use in the range of mm to 10mm and provide accuracy up to sensitivity of the transducer is dExES=D=A capacitive transducer is a displacement sensitive transducer .

8 A suitable processing circuit is necessary to generate a voltage corresponding to the Capacitance losses in the Capacitance are attributed Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyGeneral losses in the Capacitance are attributed to:-- DC leakage resistance- dielectric losses in the insulators- losses in the dielectric gapAdvantages-Require small force to operate - very sensitive -Require low power to frequency response is good up to Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor Technology- 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 Capacitive Gap - A capacitive gap sensor measures the distance between the front face of the sensor and a target target material should have high relative Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903.

9 Sensor TechnologydAC =eoreee == the dielectric constant of the medium separating the sensor and the target material A = the area of the Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyA = the area of the platesd= the distance to be measuredThere is a defined relation ship between the distance (gap ) and the dielectric constant between the sensor head and the target material is a function of the target material typere221rqqKFe =F = the force between the two charged particles21,qq()[] Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor Technologysince the net Capacitance is a function of the target material, the effective distance varies with different target material An excitation circuit for the sensor works to maintain a constant electric field magnitude between the sensor head and the target object.

10 ()[] =ep= Coulomb constant-The capacitive sensors provide only two state ON/OFF output, and sense the change in the oscillation circuit signal the target object enters the field sensing distance of the sensor, the Capacitance increases and the magnitude of the oscillations detection and output circuit then controls the ON/OFF state of a resolution of the capacitive cap sensor is typically in micrometer Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor TechnologyApplications for Capacitive SensorsPrecision Spindle Error Motion (Run out)Precision spindles in disk drives and high-performance machine tools are achieving error motions of less than 100 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 Hisham El-SherifElectronics and Electrical Engineering DepartmentELCT903, Sensor Technologyinductive sensors rotating target errors (electrical run out) when measuring the machine tool application, Two probes each are mounted in the X and Y plane (90 apart).