handbook of modern sensors

3.2 Capacitance 49
h 0
(A)
(B)
Fig. 3.8. Capacitive water level sensor (A); capacitance as a function of the water level (B).
where h is height of the water-filled portion of the sensor. If the water is at or below
the level h 0 , the capacitance remains constant
C 0 = 2πε 0
H. (3.27)
ln(b/a)
Figure 3.8B shows a water level-capacitance dependence. 3 It is a straight line from
the level h 0 . Because dielectric constant of water is temperature dependent (Fig. 3.7)
the capacitive sensor will be combined with a temperature sensor—for instance,
a thermistor or resistive temperature detector which monitors water temperature.
The appropriate temperature correction may be performed by the electronic signal
conditioner.
The slope of the transfer function line depends on the liquid. For instance, if
instead of water the sensor measures the level of transformer oil, it is expected to be
22 times less sensitive (see Table A.5).
Another example of a capacitive sensor is a humidity sensor. In such a sensor, a
dielectric between the capacitor plates is fabricated of a material that is hygroscopic;
that is, it can absorb water molecules and change its dielectric constant accordingly.
According to Eq. (3.24), this changes the capacitance that can be measured and related
to relative humidity. Figure 3.9 illustrates the dependence between capacitance and
relative humidity of such a sensor. The dependence is not linear, but this usually can
be taken care of during the signal processing.
3 The sensor’s dimensions are as follows: a = 10 mm, b = 12 mm, H = 200 mm, liquid—
water.