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Capacitance Thickness Gauge / Displacement Gauge 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.

The thickness measurement of the insulator using CL-5610 is possible as shown in the figure below, by fixing the VE sensor and the reference surface, and inserting the insulator whose thickness is to be measured between them.

The procedure is as follows:
1. Install the VE sensor on the reference plane of the conductor within the specified gap range of the sensor.
2. Measure the gap between the VE sensor and the reference plane.
3. Set the dielectric constant of the insulating material to be measured in the CL-5610.
4. Insert the insulating material to be measured onto the reference plane without changing the reference gap.
​

Why can the thickness of an insulator be measured by performing such operations?

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

First, let's consider a capacitor as shown in Figure 1.

Let the distance between the plates be d0, the area be S, and the permittivity be ε0 (for air). The permittivity 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 a distance between plates of d0-d and permittivity ε0 (with capacitance C1) is connected in series with a capacitor with a distance of d and permittivity εr (with capacitance C2). (See Figure 2)

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

1／C＝1／C1＋1／C2

here

C1＝ε0・S／（d0-d） C2＝εr・S／d

can be calculated, so,

the combined capacitance C of C1 and C2 is,

C＝ε0・εr・S／（εr・d0－εr・d+ε0・d）
will be.
The relationship formula for 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 when the insulator is inserted. This means that if the dielectric material has a known εr, it is possible to obtain the thickness d. However, since εr is often unknown, the following steps are suggested: 1. Measure the capacitance when nothing is inserted to determine d0. 2. Insert a dielectric of known thickness on the reference plane and measure the capacitance to calculate the relative permittivity εr. 3. Next, place a material of the same type with unknown thickness on the reference plane and use the calculated εr to measure the thickness.

It is also possible to carry it out using the method called.

Last updated: 2013-08-08