7-4.5 - Typical Specifications
Chapter 8 Variable Capacitance Sensors
Chapter Objectives
1. To review the concept of capacitance.
2. To study the linear motion capacitor.
3. To understand proximity sensing and gaging using the capacitive sensor.
4. To study the rotary capacitor and its multiple-plate designs.
8-1 Introduction
The capacitance sensor is one of the more recent developments in sensor and transducer technology. Its function depends on the characteristics and behavior of the variable capacitor. To understand how the variable capacitance sensor works, we must first review the theory of the capacitor itself.
8-2 Review of Capacitance
A capacitor is comprised of two parallel plates of conducting material separated by an electrical insulating material called a dielectric (Figure 8-1). The plates, along with the
"sandwiched" dielectric, may be either flattened (i.e., parallel with each other) or rolled into some other convenient shape. Electrodes are attached to each capacitive plate for the purpose of making electrical connections within a circuit.
Figure 8-1 Simplified construction of a capacitor.
The purpose of the dielectric is to help the two parallel plates maintain their stored electrical charges. In other words, the dielectric tries to discourage any negative electrical charges stored on one plate from travelling over to the other plate and becoming neutralized. If this segregation of charges can be maintained within the capacitor, the capacitor becomes a very effective device for storing charges until they are needed, much like the behavior of a battery. (However, in a battery, the segregated charges are maintained through an active chemical process rather than through a somewhat passive one in the case of the capacitor.) Equation (8-1) shows the relationship between capacitance, size of capacitor plate, amount of plate separation, and the dielectric, often referred to as the permittivity.
C = A d
ε
(8-1)where
C = capacitance (F) E = permittivity (F/m)
A = area of capacitor plates (m2) d = separation distance of plates (m)
Quite often in discussions of capacitors the term relative permittivity is used, because the permittivities of materials are often compared to the permittivity of a vacuum, the vacuum's value being 8.85 x 10-12 F/m. Table 8-1 lists the relative permittivity values of some of the more common materials used in the manufacture of capacitors. It is important here to emphasize that the amount of capacitance can be varied by altering anyone or all of the three variables shown in eq. (8-1). The only item necessary to measure or record a change in capacitance is, of course, a capacitance-measuring circuit of some sort. However, what is often done is not to measure capacitance or capacitance change directly, but rather to sense some electrical characteristic that is closely associated with this change in capacitance. T his concept is explained in more detail in the next section.
Table 8-1
Relative Permittivity Values for Common Materials in Capacitors
Material Relative permittivity
Vacuum 1.0
Air 1.0006 Paper 2.5
Mica 5.0 Glass 7.5 Ceramic 7500.0
Source: R. L. Boylestad, Introductory Circuit Analysis, 4th ed. (Columbus, OH: Merrill, 1983).
Figure 8-2 Rotary capacitor.
The "active" area of a capacitor is the area that is meshed; this is the area that participates in the determination of the capacitance of that capacitor. To determine this area, one must take into account the surface areas directly opposite the two parallel
plates making up the capacitor, as Figure 8-2 illustrates. Assume that you have a capacitor made up of two plates that rotate relative to each other on the same shaft, as shown in the figure. The area that actually determines the capacitance of this capacitor is the active area, A. The remaining area does not affect the capacitance except for a minor interaction referred to as fringing. Fringing is discussed later in the chapter. For the present, however, we will neglect this characteristic and concentrate on the active areas of a capacitor. The capacitor described in Figure 8-2 is put to good use in at least one displacement-measuring sensor, which we discuss in Section 8-5.
To be sure that the theory of capacitance is fully understood, we will now calculate the distance of separation between two parallel plates using the device in Figure 8-2 as an example.
Example 8-1
The capacitor shown in Figure 8-2 has a capacitance of 38 pF when the two plates are 100% meshed. These plates have a diameter of 20 cm and are rotated so that they are 30% meshed. The dielectric is air. Calculate the amount of separation between the two plates.
Solution: We first calculate the area of each plate in our problem. Since area is found by using the equation area = πd2/4, and since Figure 8-2 shows each plate to be semicircular in shape, we will assume each plate's area to be one-half of the calculated value. Therefore, the active plate area in our capacitor. We must also note that because of the 30%
mesh, we have also reduced the initially stated capacitive value of 38 pF to only 30% of this value, or 11.4 pF.
Having been told that air has a relative permittivity of 1.0006 (Table 8-1) and recalling that the permittivity value for a vacuum is 8.85 x 10-12 F/m, the permittivity of air is then the product of these two figures, or 8.855 x 10-12. We can now use eq. (8-1) to calculate the plates' spacing by solving this equation for d:
(
-12)(
2)
8-3 - Commonly Sensed Measurands
One of the most frequently sensed measurands using capacity-sensing devices is displacement or some variation of displacement. Also, a typical variation of
displacement sensing would be the measurement of force or pressure, in which either would~ cause movement of a variable plate capacitor (Figure 8-3).
Figure 8.3 Capacitor used as a linear displacement device.
Temperature is another measurand that depends on displacement for its detection.
Figure 8-4 shows such an application. In this application we see a bimetallic coil whose expansion and contraction with temperature are converted to a capacitive displacement. In this application the capacitive element has nothing to do with the sensing of temperature. It is used simply as a translation device to convert the motion of the actual sensing device, the bimetallic strip, into an electrical signal.
In the sections that follow we study the detection methods used and obtain a better idea of how capacitive sensors work.
8-4 - Linear Motion Capacitor
The linear motion capacitor is a variable capacitor whose movable plate moves in a straight path toward and away from the fixed plate. At the same time, the faces of both plates are kept parallel to each other, maintaining an evenly spaced gap to allow for a dielectric to be present. The term linear refers to the type of straight-line motion of the movable capacitor plate and does not refer to its output response. We will now describe several of these configurations and discuss how they operate.
Figure 8.4 Using a linear displacement capacitor to indicate temperature with a bimetal coil.