Page 255 - Introduction to Information Optics

240 4. Switching with Optics

Metal
Membrane

Driving
electrode

Fig. 4.30. A deformabie membrane actuator.

(Fig. 4.32). When voltage is applied, an attractive force develops between the
ringers, which move together. The increase in capacitance is proportional to
the number of fingers. So, to generate large forces, large numbers of fingers can
be used.
To obtain the voltage-displacement relation for the electrostatic comb drive,
we assume that both the left and right elements are constrained from moving
and that the left element is biased at a fixed voltage V. The capacitance for a
single finger face across the gap is given by

c single = — •> (4.51)
v
where the area is given by
(4.52)

Since each finger has two sides, it follows that each finger has two capacitors,
For an n-finger upper actuator, we have In capacitors. The total capacitance is

Bt(L - X)
*- comb (4.53)
ff

Using Eqs. (4.47), (4.48), and (4.53) we obtain the driving force

2
F = m,-V . (4.54)
g
If we set the left element free to move, this force will control the movement