Page 217 - Mechanics of Microelectromechanical Systems

204 Chapter 4
3.3 In-Plane Longitudinal (Comb-Finger) Transduction

3.3.1 Linear Transduction

3.3.1.1 Actuation

The other possibility of in-plane actuation is illustrated in Fig. 4.26,
which shows two adjacent plate digits, one fixed and the other one mobile,
the latter one moving parallel to the former one. By charging the two plates
with equal and opposite charges, +q and –q, the electric field will generate
attractive forces between the two plates, with the net result that the mobile
plate will move to the right in the figure.
In order to simplify notation, no subscript is used to refer the gap because
the gap is constant, as shown in Fig. 4.26. The overlap area will vary this
time, since the engaging distance over the direction of motion changes. The
capacitance is:

where is the plate’s dimension perpendicular to the plane of the drawing.

Figure 4.26 Principle of longitudinal electrostatic actuation

The force that generates the motion to the right can be calculated by means
of the definition given in Eq. (4.20) and its expression is:

It can be seen that the actuation force is constant, as contrasted to the case of
a transverse actuator where the force varied with the distance in a non-linear
manner. The plus sign indicates that the electrostatic force favors the increase