Page 140 - MEMS Mechanical Sensors

6.4 Diaphragm-Based Pressure Sensors 129

2
7 −ν  1 + b 2 + b 4  + ( −ν ) b 2
3



4

3  a 2 a  1 +ν a 2
B =  4   2  (6.28)
p

 
( −ν ) − b 4   1 − b 
1
1


 a   a 2 
The deflection of a bossed diaphragm is shown in Figure 6.13(b). The maxi-
mum radial bending stress occurs at the outer perimeter where the diaphragm is
clamped and the inner perimeter where the boss begins. The stress on the outer
perimeter is equal and opposite to that occurring at the inner, and at the midpoint of
the annulus [r on Figure 6.13(b)] the stress is zero. The radial stress is given by
m
3 P
2
σ = σ =± (a − b 2 ) (6.29)
4 h
r outer r inner 2
6.4.5 Corrugated Diaphragms
Corrugations in a diaphragm enable operation at larger displacements with
improved linearity. The corrugations can have sinusoidal, triangular, rectangular,
trapezoidal, and toroidal profiles. While this has a small influence on the behavior
of the diaphragm, the depth of corrugation (H), material thickness (h), wavelength
(l), and ratio of corrugations to diaphragm radius (l/a) are the main factors. The
characteristic equation of corrugated diaphragms is shown in (6.30). A , B , and q
p p
are given by (6.31), (6.32), and (6.33), respectively.
Pa 4 y y 3
= A + B (6.30)
Eh 4 p h p h 3
( +
)( +
23 q 1 ) q
A = (6.31)
p    
2
ν
  
 31 −  
   q  
32  1 3 −ν 
B =  −  (6.32)
p
2
q − 6 (q −ν )(q+3 )
9
 s  H 2   1 2
q =   115   (6.33)
+ .
 


2
 l  h  
Rigid centers, or bosses, can be incorporated into corrugated diaphragms, and
these will increase the stiffness of the diaphragm if sufficiently large.
6.4.6 Traditional Diaphragm Transduction Mechanisms
The generally small displacements associated with traditional metal diaphragms
typically require electromechanical transduction techniques to sense their magni-
tude. The most common method employed is metal strain gauges located on the face
of the diaphragm. These are positioned at the points of maximum strain in order to