Page 218 - Mechanics of Microelectromechanical Systems

4. Microtransduction: actuation and sensing 205
of distance y (or the increase of the overlap region between two adjacent
plates).
When several pairs of mobile-fixed digits are utilized, the total force
increases to a value which is n times larger than the force of Eq. (4.34),
where n is the number of gaps.

3.3.1.2 Sensing

Conversely, the device sketched in Fig. 4.26 can be utilized as a sensing
tool when the motion of the mobile plate is generated externally through
connection of the mobile digits to a source of motion that is of interest. The
capacitance variation can be calculated similarly to the case of a transverse
sensing device, and its equation is:

where:

is the sensitivity of the linear longitudinal transducer, and is constant, which
is a major advantage of the longitudinal configuration over the transverse
design. Similarly to the transverse sensing case, the change in voltage – Eq.
(4.30) – can be expressed here as:

In the case where n fixed-free digit pairs are used, the total change in
capacitance will be n times the value of Eq. (4.35) because the capacitors are
connected in parallel.

Example 4.6
Compare the voltage gain of an electrostatic transverse sensor with
the one of a longitudinal sensor assuming that the initial overlap length of
the longitudinal sensor is five times larger than the initial gap of the
transverse sensor.

Solution:
By using the subscripts t for transverse and l for longitudinal, the
following voltage gain ratio can be formed by using Eqs. (4.32) and (4.37):

One can take: