SMAR LD290, Operation And Maintance Manual

Page: 19 / 66

Section 2
2.1
OPERATION
Functional Description - Sensor
The
LD290 Series Pressure Transmitters use capacitive sensors (capacitive cells) as pressure
sensing elements, as shown in Figure 2.1.
Figure 2.1
– Capacitive Cell
Where,
P
1
and P
2
are the pressures in chambers H and L
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 as:
Where,

=
dielectric constant of the medium between the capacitor's plates.
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.
By developing the expression (CL - CH)/ (CL + CH), it follows that:
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 capacitances vary according to the applied differential pressure.
d
A
C

=
d
d
CH CL
CH CL
P

=
+
−
= 
2
and
d d
A
CL
 −

=
) 2 / (
.
d d
A
CH
 +

=
) 2 / (
.