Page 277 - Mechanics of Microelectromechanical Systems

264 Chapter 5
2.1 Transverse Electrostatic Actuation with
Microsuspension

By coupling the transverse (plate-type) electrostatic transduction that has
been introduced in Chapter 4 to one of the microsuspensions presented in
Chapter 3 leads to the model shown in Fig. 5.1.

Figure 5.1 Model of transverse electrostatic actuation and microsuspension

The maximum gap between the fixed and the mobile plates, occurs
initially for y = 0. The static equilibrium sets in when the two opposing
forces, the electrostatic and the spring force, are equal:

The force produced through transverse electrostatic actuation was given in
Chapter 4 and is rewritten here as:

whereas the elastic force is:

Figure 5.2 shows the force-displacement plots of these two forces. As Fig.
5.2 indicates, there are two points of equilibrium, and where the two
forces are equal for specified spring and electrostatic actuation properties.
However, only the first equilibrium point, is stable because of the fact
that the slope of the electrostatic force is smaller than the (constant) slope of
the elastic force, whereas at point the slope of the electrostatic force is
larger than the one of the elastic force.