Biomedical Engineering Reference
In-Depth Information
FIGURE 2-55
MEMS strain gauge
pressure transducer.
(a) mechanical
layout. (b) Circuit
diagram.
In the pressure transducer shown in Figure 2-55, the total force,
F
(N), applied to the
membrane is equal to the product of differential pressure,
P
(Pa), and the area of the
membrane, A (m
2
)
F
=
PA
(2.54)
The stress introduced in the bridge elements is directly proportional to the applied force,
and its effect on the semiconductor resistors is to alter their resistance by
R
R
R
=
(α
l
σ
l
+
α
t
σ
t
)
(2.55)
where
R
()
is the initial resistance,
α
l
and
α
t
are the piezoresistive coefficients in the
longitudinal and transverse directions, respectively, and
σ
l
and
σ
t
are the stresses in these
directions, respectively (Fraden, 1996).
The magnitudes of these coefficients depends on the orientation of the silicon crys-
tal, and the resistors are positioned on the diaphragm in such a manner (as shown in
Figure 2-55) as to have the longitudinal and transverse coefficients of opposite polarities.
This results in the resistances changing in opposite directions as the pressure alters.
1
2
α
α
l
=−
α
t
=
(2.56)
Therefore
R
1
R
1
=−
R
2
R
2
1
2
α(σ
1
y
−
σ
1
x
)
=
(2.57)
where
σ
lx
and
σ
ly
are the longitudinal stresses in the
x
and
y
directions, respectively.
For the full-bridge configuration shown in Figure 2-55 excited by a voltage
V
ref
, the
output voltage will be
V
ref
2
α(σ
1
y
−
σ
1
x
)
V
out
=
(2.58)
Because
is a function of temperature, the output voltage will change with temperature.
The substrate temperature must therefore be measured and the appropriate corrections
applied.
α
