Three types of capacitive sensor schematics and their calculation formulas

This paper systematically analyzes three typical application scenarios, revealing the design principles and engineering pathways for capacitive sensing in complex medium level measurement through structural schematics and mathematical models.

A capacitive sensor for conductive liquids

Capacitive level sensors for conductive liquids such as water, acids, alkalis, salts, and various aqueous solutions typically use a stainless steel or copper rod with a diameter d as the electrode. This electrode is either sleeved with a polytetrafluoroethylene (PTFE) plastic insulating tube or coated with enamel for insulation, as shown in Figure 1. The capacitive sensor is inserted into the liquid inside a container with a diameter D₀. The level of the liquid can be determined by detecting the change in the sensor’s capacitance.

As shown in the figure, when the liquid level changes from zero to H, the corresponding change in capacitance C_X of the capacitive sensor can be expressed as:

1. ε represents the dielectric constant of the insulating sleeve or ceramic coating;
2. ε₀’ represents the equivalent dielectric constant of the capacitor formed by the insulating sleeve and air.

3.S represents the sensor sensitivity coefficient.

II. Capacitive Sensor for Non-conductive Liquids
For non-conductive liquids, insulation of the electrode surface is not required. A bare electrode can serve as the inner electrode, enclosed by a metal outer electrode with openings for liquid flow. The sensor is assembled using insulating rings, as illustrated in the figure below:

III. Capacitive Sensor for Granular/Powder Materials
Measuring the material level of non-conductive granular or powdered media—such as ores, alloys, lime, dry cement, and grains—has long been a challenging problem. To date, there is still no consistently accurate and reliable measurement method. The principle of the capacitive level gauge is illustrated in the figure below:

Figure (a) shows a metal silo, while Figure (b) depicts a cement silo:
1 – Inner electrode
2 – Metal container wall electrode
3 – Steel wire rope inner electrode
4 – Reinforcing bar
5 – Insulator