Capacitance transducers are passive transducers that work on the principle of change of capacitance. Here we will discuss the principle, types, applications and advantages of the capacitance transducers.
A capacitor consists of two parallel conducting plates of area A placed at a distance d from each other with any material (insulator) between them. The dielectric constant ε is unique for different medium
Capacitance is defined as the function of the geometric quantities, such as the area of the conducting plate and the distance between them, and the permittivity of the dielectric medium between them.
** 1. Parallel plate capacitance with Rectangular plates** Here one of the plates is fixed while the other is movable, depending on the nature of the movement, there may be variation in the area A or the distance d. The change in capacitance is given as, In case of area variation, where the capacitance plate moves a distance of x,
In case of spatial variation, where the distance between the plates increase by a x,
2. Cylindrical capacitor transducer A cylindrical capacitor is two concentric cylinders with a dielectric in between. The surface area of the cylinder of radius x meters and unit length is given as
The electrical field intensity at a point x meters away from the centre of cylinder is The potential difference developed between the cylinders is given as
In that case the capacitance is given as Considering a length of the cylinders to be L, Numerically substituting D instead of R will give the same result. Sensitivity in this case is S = dC/dL
3. Semi circular parallel plate
Mostly used to measure the angular displacement, the capacitance is maximum when the plates completely overlap.
Area of the plate is given as
180 degree is the maximum displacement of the capacitor.
Sensitivity is given by
4. Change of dielectric between parallel plates The capacitance of the parallel plate with different dielectric is given as
5. Change in distance between circular plates
The capacitance is given by:
With distance between the plates d The relation between the input d and output C are in the powers of 2 and inversely proportional. The output is not linear
With change in area A due to displacement The is a linear relationship between the input and output.
With Angular displacement
|a.||Sensitive is very high|
|b.||High frequency response|
|c.||Minimum loading effect|
|d.||Very good resolution|
|a.||Non linear behaviour due to edge effect|
|c.||Affected by stray capacitance|
Capacitive transducers have the dynamic characteristics similar to high pass filter
Used in pressure, displacement, force and level measurement.
Special capacitance transducers:
Variable capacitance pressure transducer Containing a diaphragm instead of one of the fixed plates, the dielectric material is air. The flexible diaphragm is pulled taut but bends into a curve on pressure.
High precision differential capacitor This uses a three plate differential ( push-pull displacement) sensor consisiting of a movable plate M in between two fixed plates P 1 and 2. X is the displacement of the movable plate, the capacitances is given by, The voltages across C1 and C2 is At midpoint , E1 – E2 = 0 With x being the displacement The differential output is The sensitivity is given as The output varies linearly and gives an accuracy of 0.05 %