Page 267 - Mechanical design of microresonators _ modeling and applications

0-07-145538-8_CH05_266_08/30/05

Resonant Micromechanical Systems

266 Chapter Five
in-plane about a direction perpendicular to the plates. Out-of-the-plane
motion is also possible when the mobile plate moves about the z axis
due to fringe effects, either in a form of pure translation, as mentioned
10
by Lee and Lin, or as the result of a small relative rotation about a
direction parallel to the x axis, as detailed by Mihailovich and
11
2
MacDonald, or by Selvakumar and Najafi. To increase the
transduction effects, several pairs of digits are utilized in comb-type
microdevices. The force generated by plate-type attraction between two
mating plates can be expressed as
İA V 2
s
F = (5.98)
p 2
2(g + x)
0
where A is the superimposed area, g is the initial gap, and x is the
0
s
distance traveled by the mobile plate, as indicated in Fig. 5.40b. It can
be seen that, unlike the comb-finger actuation, the force in plate-type
actuation varies nonlinearly with the displacement x. In sensing, the
7
capacitance varies with the gap change x (see Lobontiu and Garcia, for
instance) as
İA x
s
C = (5.99)
p
(g í x) 2
0
and the sensitivity [the factor multiplying x in Eq. (5.99)] is not
constant, as it was in comb-finger sensing.
Out-of-the-plane electrostatic transduction can also be achieved by
means of microcantilevers and bridges whose bending motion can be
transduced against a fixed plate. In either of the techniques mentioned
here, the electrostatic variation between two plates can be generated
by the source and control circuit of the device, and this leads to
mechanical motion (in actuation), or the motion can be generated
externally and sensed as a capacity variation by the corresponding
circuit of the device (as in sensing).

5.4.2 Electromagnetic transduction
The principle of electromagnetic transduction in microresonators is
based on the interaction between an external (usually constant) mag-
netic field and an alternating current (ac). The result is a Lorentz-type
force which acts on the conductor carrying the current. Transverse vi-
brations could thus be generated in a fixed-fixed wire, as shown by
12
Husain et al., for instance, according to the sketch of Fig. 5.42.

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.