Capacitive transducer for liquid level

A capacitive transducer can measure liquid level because the capacitance of a probe depends on how much of it is surrounded by liquid, whose dielectric constant differs from that of air.

Arrangement

          |  <- insulated rod (inner electrode, radius a)
   +------|------+  <- metal tank / outer tube (radius b)
   |      |      |
   |  air |      |  height (H - h), εr = 1
   |~~~~~~|~~~~~~|  <- liquid surface
   |liquid|      |  height h, εr of the liquid
   +------|------+

A cylindrical capacitor is formed by an inner rod (electrode) and an outer concentric tube (or the metal tank wall). The liquid fills the space between them to height h; the total height is H. For a non-conducting liquid, the liquid itself is the dielectric.

Capacitance

The capacitance is that of the part in the liquid plus the part in air (two capacitors in parallel):

C = 2πε0 εr h / ln(b/a) + 2πε0 (H − h) / ln(b/a)

C = [2πε0 / ln(b/a)] · [H + (εr − 1) h]

Here εr is the relative permittivity of the liquid. C is a linear function of h: C = C0 + k h, where C0 = 2πε0H/ln(b/a) is the empty-tank capacitance and k = 2πε0 (εr − 1)/ln(b/a).

Measurement

• The change in capacitance is measured with an AC bridge, an oscillator (whose frequency changes) or a capacitance-to-voltage converter, and the display is calibrated in level.
• For a conducting liquid, the rod is insulated (e.g. Teflon coated) and the liquid acts as the second plate; the capacitance again increases linearly with h.

Advantages: no moving parts, suitable for corrosive liquids and for remote indication. Limitation: εr changes with temperature and with the type of liquid, so calibration is needed.