Capacitance pressure transducers
Fig. 14 presents a transducer for sensing and transmitting differential pressure. Pressures to be measured act on isolating diaphragms 1 and 2 and are transmitted through a silicone oil 3, which fills the system, to a sensing diaphragm 4. This sensing diaphragm is balanced by two forces developed by measured pressures and presents the sensitive element. Capacitor plates 5 and 6 detect the position of the sensing diaphragm, which moves to the left or to the right, and, thus, the differential pressure applied to the sensitive element. The change in electric capacitance is electronically amplified and converted to the standard electrical analog or digital output signal, which is directly proportional to the difference of pressures. In order the capacitance transducer be able to measure comparatively low pressures, the device should produce about 25% change in capacitance for a full-scale pressure change. These transducers have low mass and high resolution. However, they are slightly dependent on temperature variation. Newly developed all-silicon capacitive pressure sensors have better thermal stability.
Figure 14. Variable capacitance differential pressure transducer.
Variable separation capacitance sensors have non-linear relationship between electrical capacitance and the movement of the separating membrane according to the formula:
(84)
where,
C - the electrical capacitance of the pressure sensor, F (Farad);
ε0 = 8.85, pF/m - the permittivity of vacuum, 1pF=10-12 F;
ε - the relative permittivity of the insulating material between plates of the capacitor, this is the dimensionless parameter;
A - the cross-sectional area of the capacitor plate, m2 ;
d - the distance between the capacitor plates, m;
a - variation of the distance between the capacitor plates, m.
A three-plate differential version of the capacitive pressure sensor doesn’t have such disadvantage (see Figure 15).
Two fixed plates form two capacitances with the moving separating plate/membrane as follows:
(85) and 
(86)
Figure 15. Three-plate differential pressure/displacement sensor
Figure 16 shows an a.c. deflection bridge for the detection of variations of capacitances.
Figure 16. a.c. deflection bridge.
In this bridge:
(87) 
,(88) 
,(89)
where,
Z1and Z2 - reactive impedances, Ohm;
Z3 and Z4 - resistive impedances, Ohm.
When Icd = 0, then Vcd is called an open-circuit voltage of the bridge. According to the Kirchoff’s laws we have:
, (90)
Let potential at Vb = 0, then:
(92)
So, the relationship between Vcd and a is linear.
Article Source:: Dr. Alexander Badalyan, University of South Australia
