SMAR DT302, Owner'S Operation And Maintenance Manual

Page: 31 / 84

Section 2
2.1
OPERATION
The DT302 Concentration Density Transmitter use capacitive sensors (capacitive cells) as pressure
sensing elements. This is exactly the same sensor as the DT301 series uses, the sensor modules
are therefore interchangeable.
Figure 2.1 - Capacitive Cell
Functional Description - Sensor
Where,
P
1
and P
2
are the pressures and P
1
≥
P
2
CH = Capacitance between the fixed plate on P
1
side and the sensing diaphragm.
CL = Capacitance between the fixed plate on the P
2
side and the sensing diaphragm.
d = Distance between CH and CL fixed plates.
∆
d = Sensing diaphragm's deflection due to the differential pressure
∆
P = P
1
- P
2
.
Knowing that the capacitance of a capacitor with flat, parallel plates may be expressed as a function
of plate area (A) and distance (d) between the plates:
d
A
C
×
≈
ε
Where,
ε
= Dielectric constant of the medium between the capacitor's plates.
CL
d
d
A
d
d
A
CH
≈
∆ −
×
∆ +
×
≈
)
2
(
and
)
2
(
ε ε
However, should CH and CL be considered as capacitances of flat and parallel plates with identical
areas, then:
However, should the differential pressure (
∆
P) applied to the capacitive cell not deflect the sensing
diaphragm beyond d/4, it is possible to assume
∆
P as proportional to
∆
d, that is:
d
∆ ∝ ∆
P
By developing the expression (CL - CH)/(CL + CH), it follows that:
d
d
CH CL
CH CL
∆
=
+
−
2
As the distance (d) between the fixed plates CH and CL is constant. It is possible to conclude that
the expression (CL - CH)/ (CL + CH) is proportional to
∆
d and, therefore, to the differential pressure
to be measured.
Thus it is possible to conclude that the capacitive cell is a pressure sensor formed by two capacitors
whose capacitance varies according to the applied differential pressure.