Capacitive Transducers

Capacitive sensors are based on changes in capacitance in response to physical movement. These sensors find their applications mainly in humidity, moisture and displacement sensing.

Reactance of a capacitance C is given by 1/(jωC), since i = C (dv/dt). These sensors have high impedance at low frequencies, as clear from the reactance expression for a capacitor. Also, capacitive sensors are non-contacting devices in the common usage. They require specific signal-conditioning hardware. In addition to analog capacitive sensors, digital (pulse-generating) capacitive transducers such as digital tachometers are also available.

A capacitor is formed by two plates, which can store an electric charge. The stored charge generates a potential difference between the plates. The capacitance C of a two-plate capacitor is given by

where

A is the common /overlapping area of the two plates; m²

d is the gap width between the two plates; m
ε is the dielectric constant or permittivity,  ε = ε_rε_o; F/m
ε_r is the relative permittivity,
ε_o is the permittivity of vacuum; 8.85x10^-12 F/m.

The capacitive transducer work on the principle of change of capacitance which may be caused by:

(i)                 Change in overlapping area A,

(ii)               Change in the distance d between the plates, and

(iii)             Change in dielectric constant

The cause of these changes can be displacement, force and pressure. We will discuss the various types below:

A.    Transducers based on Change in overlapping area

From the characteristic equation of capacitance it is clear that capacitance is directly proportional to the overlapping plate area A. For a parallel plate capacitor, the capacitance is given by-

x = length of overlapping plates; m

w = width of overlapping part of plates; m

Sensitivity

This type of a capacitive transducer is suitable for measurement of linear displacements ranging from 1 mm to 10 mm.

For a cylindrical capacitor, the capacitance is given by-

x = length of overlapping part of cylinders; m

D₂ = inner diameter of outer cylindrical electrode; m

D₁ = outer diameter of inner cylindrical electrode; m

Capacitive transducers can be employed to measure angular displacement also. If we have two plates- one fixed and one rotating, then their overlapping are is a function of angle between the overlapping edges.

The maximum capacitance is when the two plates completely overlap each other.

If the angle of overlap area is θ 

A.    Transducers based on Change in distance between plates

The capacitance between plates is inversely proportional to the distance between them.

The relationship between capacitance C and distance between the plates d is hyperbolic.

The sensitivity increases as x decreases.

The percent change in C is proportional to the percent change in x.

A.    Transducers based on change in Dielectric constant

Measurement of displacement

Normal capacitance when dielectric medium is partially overlapped with metal plates-

If the dielectric material is moved a distance ‘x’ in direction as shown, the capacitance changes by ‘∆C’.

Measurement of Liquid Level

This type of transducer is predominantly used in the form of two concentric cylinders for measuring the level of fluids in tanks. A non-conducting fluid forms the dielectric material. The method is generally based on the difference between the dielectric constant of the liquid and that of the gas or air above it. Two concentric metal cylinders are used for capacitance as shown in Figure below.

Capacitive Differential Transducer

A normal parallel plate capacitive transducer exhibits non-linear response. By using differential arrangement, we can get linear response for capacitive differential transducers. The arrangement is shown below:

It consists of two fixed plates and one moving plate whose displacement is to be measured. It acts like two capacitors in series.

Let C₁ and C₂ be the capacitance of individual parallel plate combination when the movable plate is at middle position. Thus,

For a voltage ‘V’ applied across the fixed plates, the voltage appearing across individual plate combination is equal when the movable plat is at middle position.

 

Differential voltage ∆V= 0.

Let the movable plate is moved by a ‘x’. Therefore the new values of C₁ and C₂ are given as-

This method can have accuracy upto 0.1% and measurement range can be from tens of nm to 10 mm.

Charge Amplifier Circuit

An op-amp circuit with a feedback capacitor Cf, which is similar to a charge amplifier, may be used with a variable-capacitance transducer. A circuit of this type is shown in Figure below. The transducer capacitance is denoted by Cs. The charge balance at node A gives VrefCs + VoCf = 0. The circuit output is given by