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Capacitive Thickness Gauges and Displacement Gauges: Frequently Asked Questions

Question number FAQ-0156

Please explain the principle of measuring the thickness of an insulator using the CL-5610 capacitive thickness gauge.

As shown in the diagram below, measuring the thickness of an insulator with the CL-5610 is possible by fixing the VE sensor and the reference surface and placing the insulator whose thickness you want to measure between them.

The procedure is as follows:
1. Install the VE sensor on the reference plane of the conductor within the sensor's specified gap range.
2. Measure the gap between the VE sensor and the reference surface.
3. Set the dielectric constant of the insulator you want to measure in the CL-5610.
4. Without changing the reference gap, insert the insulator to be measured onto the reference surface.
This is the operation.

Why is it possible to measure the thickness of an insulator by performing these operations?

Measuring the thickness of an insulator using the CL-5610 becomes easier to understand if you consider how capacitance can be calculated when a material with a different dielectric constant is inserted into a part of a capacitor.

First, consider a capacitor like the one shown in Figure 1.

Let d0 be the distance between the plates, S be the area, and ε0 be the dielectric constant (air). The dielectric constant of the inserted insulator is εr, and its thickness is d. The capacitance C of this capacitor is the equivalent capacitance when a capacitor with plate distance d0-d and dielectric constant ε0 (let's call it C1) and a capacitor with plate distance d and dielectric constant εr (let's call it C2) are connected in series. (Figure 2)

When capacitors are connected in series, the following relationship holds between the combined capacitance C and the individual capacitances C1 and C2.

1／C＝1／C1＋1／C2

Here

C1＝ε0・S／（d0-d） C2＝εr・S／d

Therefore,

The combined capacity C of C1 and C2 is:

C＝ε0・εr・S／（εr・d0－εr・d+ε0・d）
This is the result.
The relationship between the combined capacity obtained above

C＝ε0・εr・S／（εr・d0－εr・d+ε0・d）＝（ε0・S／d0）・εr／（εr－εr・q+ε0・q） q=d/d0



This also holds true in Figure 3.

Here, ε0 and S are known, and d0 can be measured before inserting the insulator. It is also possible to measure the capacitance C with the insulator inserted. In other words, if the thickness εr of the insulator is known, it is possible to obtain the thickness d. However, since εr is often unknown, 1. Measure the capacitance when nothing is sandwiched and determine d0. 2. Insert an insulator with a known thickness onto a reference surface, measure the capacitance, and calculate the relative permittivity εr. 3. Next, place an object of the same material but with an unknown thickness onto the reference surface and measure the thickness using the calculated εr.

It is also possible to do it using this method.

Last updated: 2013-08-08