Biomedical Engineering Reference
In-Depth Information
a
b
Fig. 11
Schematic of the pressure square (side length
D
2a) sensor (
a
)3Dviewand(
b
) section
cut B-B
Fig. 12
Cross section of a
generic deflectable diaphragm
P
0
>P
out
P
out
P
0
t
w
0
P
out
a
Equation
1
allows the calculation of the deflection at the center of the diaphragm
for a given pressure load but the deflection along the diaphragm is still required to
model the capacitive changes due to gap variation. Due to the complexity of the
mechanical deflection calculation, trial functions that describe the deflection of the
entire diaphragm are usually used [
27
]. Figure
13
shows the normalized deflection
for a square diaphragm of side-length 2a when the following trial function for large
deflection is used [
27
]:
w
0
h
cos
x
2a
cos
y
2a
i
(2)
w
.x; y/
D
Mechanical deflections caused by pressure changes will originate changes at
the capacitor (electrostatic domain). A capacitor is an electronic component with
two electrodes that are separated by a dielectric. For the simple case of a parallel
plate capacitor, and in the absence of displacements, the model for the capacitor is
(neglecting fringe fields):
w
l
d
0
C
D
"
0
"
r
(3)
