Page 263 - Mechanical design of microresonators _ modeling and applications

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Resonant Micromechanical Systems

262 Chapter Five
actuation

fixed member

mobile member

spiral spring
sensing

Figure 5.39 Rotary comb-type actuation/sensing and spiral-beam microsuspension.

shape memory alloys or fluid. Of all these methods, the electrostatic,
electromagnetic, piezoelectric/piezomagnetic, and bimorph transduc-
tion methods are briefly discussed here, as these procedures, enable us
to obtain excitation and detection frequencies which are within the
range of mechanical microresonators.

5.4.1 Electrostatic transduction
The electrostatic actuation or sensing is one of the most popular tech-
niques used with microresonators. Constructively, the electrostatic
transduction can be implemented in planar and out-of-the-plane res-
onator designs. The comb-type electrostatic transduction is one of the
most employed solutions for both planar and out-of-the-plane resonant
applications. Electrostatic attraction forces can be generated between
a fixed plate and a mobile one in different ways, depending on the
boundary conditions pertaining to the mobile plate. The y motion shown
in Fig. 5.40a can be activated, in the case where the mobile plate moves
parallel to the fixed one, by keeping the gap constant. This type of
transduction is known as comb-finger, and it basically consists of a pla-
nar longitudinal relative motion. The force generated through actua-
tion is constant and can be expressed as

2
İl V
z
F = 2g (5.89)
cf
where İ is the electrical permittivity, l z is the plate overlap length about
the z direction, V is the applied voltage, and g is the constant gap.
Clearly, when a sinusoidal voltage is applied between the mobile and
fixed plates, the resulting force will be sinusoidal as well, and a

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