# Capacitive Transducers

In this lecture, we are going to learn about the Capacitive Transducers, their advantages, disadvantages of Capacitive Transducers, applications of Capacitive Transducers, equation sensitivity of it, and derivation of it in a very detailed manner. so let’s discuss from the beginning the Capacitive Transducers definition.

## Capacitive Transducers

• The capacitive transducer works on the principle of change of capacitance which may be caused by:
1. Change in the overlapping area of plates (A)
2. Change in the distance between the plates (d)
3. Change in dielectric constant.
• The capacitive transducer is commonly used for the measurement of linear displacement.
Errors in Measurement: Gross Errors, Systematic Errors and Random Errors

## Capacitive Transducers using change in Area of plates

• The formula of capacitance can be given by;

Capacitance (C) =\frac{\epsilon A}{d}=\frac{\epsilon_0 \epsilon_r A}{d}

• Capacitance is directly proportional to the area of the plates.

### 1. For parallel Plate Capacitor

• For a parallel plate capacitor, the capacitance is,

where A= X.W

X = length of overlapping part of plates (m) and W= width of overlapping part of plates (m)

\boxed{Sensitivity=S=\frac{\partial C}{\partial x}=\epsilon\frac{W}{d} \;F/m}

• The sensitivity is constant and therefore is a linear relationship between capacitance and displacement sensitivity for a fractional change in capacitance = S’

S'=\frac{\partial C}{C\partial x} =\frac{1}{x}

• Thie type of capacitive transducer is suitable for linear displacement measurements ranging from 1 mm to 10 mm.
• The accuracy is as high as 0.005%.

### 2. For Cylindrical Plate Capacitor

• For the cylindrical capacitor as shown in the figure above, the capacitor is:

\boxed{C=\frac{2\pi \epsilon x}{\log_{e} \left ( \frac{D_2}{D_1} \right )} \;F}

Where,

• x=length of overlapping part of cylinders (m)
• D2=inner diameter of the outer cylindrical electrode (m)
• D1= outer diameter of the inner cylindrical electrode (m)

\boxed{Sensitivity=S=\frac{\partial C}{\partial x}=\frac{2\pi \epsilon }{\log_{e} \left ( \frac{D_2}{D_1} \right )} \;F/m}

• Its sensitivity is also contacted, and the linear relationship between capacitance and displacement is linear. The principle of change in capacitance with change in the area can be employed for the measurement of angular displacement.
• The capacitance is maximum when the two plates completely overlap each other i.e. when \theta =180^o.
• The maximum value of capacitance = Cmax

\boxed{C_{max}=\frac{\epsilon A}{d} = \frac{\pi \epsilon r^2}{2d}}

• Capacitance at range \thetais,

\boxed{C=\frac{ \epsilon \theta r^2}{2d}}

\boxed{Sensitivity = S = \frac{\partial C}{\partial \theta}= \frac{\epsilon r^2}{2d}}

• This can be used for a maximum angular displacement of 180o
• The variation of capacitance with angular displacement is linear.

## Capacitive Transducers using change in Distance between plates

• In this method, one capacitor is fixed and the displacement to be measured is applied to the other plate which is movable.
• Since, the capacitance, C varies inversely as the distance d between the plates changes and the response of this transducer is not linear, as shown in the figure. Tus this transducer is useful only for the measurement of extremely small displacement.

\boxed{ Sensitivity= S=\frac{\partial C}{\partial x}=-\frac{\epsilon A}{X^2}}

• They are extremely sensitive.
• The loading effect is negligible because of its high input impedance.
• They have a good frequency response (high as 50 kHz). They are very useful for dynamic studies.
• A resolution of the order of 2.5 X 10-3 mm can be obtained with these transducers.
• They require extremely small forces to operate and hence are very useful in small systems.
• Therefore they require small power to operate.

• Their output can be affected by stray capacitances.
• Non-linearity is introduced by the edge effect.
• These are temperature sensitive.

## Application of Capacitive Transducer

• A capacitive transducer can be used for the measurement of force and pressure. The force and pressure to be measured are first converted to displacement which causes a change of capacitance.
• Capacitive transducers can be used for the measurement of both linear and angular displacement.
• Capacitive transducers are commonly used in conjunction with mechanical modifiers for the measurement of volume, density, liquid level, weight, etc.
• Capacitive transducers are used for the measurement of humidity in gases since the dielectric constant of gases changes with the change in humidity thereby producing a change in capacitance.

## Frequently Asked Questions on the capacitive transducer

1. ### What is a capacitive transducer?

Answer: The capacitive transducer is used for measuring the displacement, pressure, and other physical quantities. It is a passive transducer which means it requires external power for operation. The capacitive transducer works on the principle of variable capacitances.

2. ### What is the main use of capacitive transducers?

Answer: The capacitive transducers are used to measure humidity in gases. It is used to measure volume, liquid level, density, etc. It is used for the measurement of linear and angular displacement.

3. ### What are the disadvantages of capacitive transducers?

Answer: The capacitance of this transducer may change because of moisture, dust, etc. These are temperature sensitive, so any modification within temperature can affect their performance badly. This transducer shows non-linear performance many times because of the effect of edges.

4. ### How does capacitive transducer measure pressure?

Answer: Capacitance pressure transducers measure pressure by detecting the changes in electrical capacitance due to the movement of the diaphragm. It has two capacitor plates, a diaphragm, and an electrode fixed to an unpressurized surface.