Charging time indicates capacitor value

A comparator changes state when capacitor voltages are equal during rise and fall, which triggers a time measurement.

Vlad Bande and Ioan Ciascai, Technical University of Cluj-Napoca, Cluj-Napoca, Romania; Edited by Martin Rowe and Fran Granville -- EDN, August 11, 2011

The capacitance of every two overlapped copper zones can vary only when the electrical permittivity changes because all other parameters—the plate’s area and the distance between the plates—are constant, as the following equation shows: C_X=(ε₀ε_RA)/D, where ε₀=(8.854×10⁻¹²)F/m, the void electrical permittivity, ε_R is the dielectric’s relative electrical permittivity, D is the total dielectric thickness, C_X is the capacitance of the measured capacitor, and A is every plate’s surface. The relative electrical permittivity strictly depends on which and how many materials are between the capacitor plates. This application uses four kinds of ε_R: air, air-hydro-insulated varnish, water-hydro-insulated varnish, and air-water-hydro-insulated varnish. At this point, you must consider the capacity of the capacitors at the surface-separation line between air and water.

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The pulse width of both OC1A and OC1B must be larger than the maximum capacitor’s charging time, which you obtain when you measure the water’s dielectric capacitor, according to the following equation: PW≥10×R_e×C_MAX. Figure 3 shows the waveforms.

The charging equation in the transient region is:


You can then extract the capacitance using the following equation:

or

You can extract the level on both the left and the right side of the capacitive sensor in Figure 1, resulting in two equations but the same result. The algorithm consists of first measuring all the capacitors—completely immersed, partially immersed, and nonimmersed—and then expressing the surface of both C₇’s and C₃’s capacitor plates at the surface-separation line, using the unknown H variable. You then extract the unknown value of the level, obtaining both capacitive-dependent equations:

From the capacitive-measurement-procedure point of view, the designed system represents a floating measurement method that implies two similar parallel-plate armatures. This method halves the parasitic capacitances that occur during measurement referred to system ground.