VPT10-H
HART
®
PRESSURE TRANSMITTER
INSTALLATION, OPERATION, CONFIGURATION AND MAINTENANCE MANUAL
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8
However, when the differential capacitance structure is used, the distance between CL and CH plates has a linear
variation with the relation between the difference and the sum of the measured capacitances.
When the displacement of the central diaphragm is inferior than its thickness, there will be a linear relationship between
this displacement and the differential pressure. That is, if the differential pressure (
∆
P) applied to the capacitive cell
does not deflect the sensor diaphragm beyond d/4, we can assume that
∆
P will be proportional to
∆
d.
In short:
P1 and P2 are applied pressures on the high and low pressure sides (H and L), respectively.
CH = capacitance on high pressure side, measured between P1 fixed plate and the central diaphragm.
CL = capacitance on low pressure side, measured between P2 fixed plate and the central diaphragm.
d = distance between the fixed plates of CH and CL.
∆
d = deflection of the central diaphragm due to the application of the differential pressure
∆
P = P1 - P2.
The capacitance of a capacitor of flat and parallel plates can be expressed as a function of the area (A) of the plates
and the distance (d) separating them as:
, where
ϵ
= the dielectric constant of the medium between the capacitor plates.
If we consider CH and CL as capacitances of flat plates of the same area and parallel, when P1> P2 we have:
On the other hand, if the differential pressure (
∆
P) applied to the capacitive cell does not deflect the sensor diaphragm
beyond d/4, we can assume
∆
P proportional to
∆
d.
If we develop the expression (CL-CH) / (CL+CH) we get:
As the distance (d) between the fixed plates of CH and CL is constant, the expression (CL-CH) / (CL+CH) is
proportional to
Δ
d and therefore to the differential pressure to be measured.
Thus, it is concluded that the capacitive cell is a pressure sensor composed of two capacitors of variable capacitances,
according to the applied differential pressure.
These capacitors are part of an oscillator circuit that has its frequency dependent on the applied differential pressure.
This frequency will be inversely proportional to the applied pressure and is measured by the CPU of the pressure
sensor with high resolution, accuracy and processing speed.