SMAR ld301, Инструкция по эксплуатации и техническому обслуживанию

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Section 2
2.1
OPERATION
FUNCTIONAL DESCRIPTION – SENSOR
The LD301 Series Intelligent Pressure Transmitters use capacitive sensors (capacitive cells)
as pressure sensing elements, as shown in Figure 2.1.
Fig. 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,
εεεε
=
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, that is:
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 P
∆ ∆
α
d
d
CH CL
CH CL
P
∆
=
+
−
= ∆
2
and
d d
A
CL
∆ −
∈
=
) 2 / (
.
d d
A
CH
∆ +
∈
=
) 2 / (
.