Page 115 - MEMS Mechanical Sensors

104 Mechanical Transduction Techniques

example, to amplifier drift—will cause a shift in the resonant frequency indistin-
guishable from shifts due to the measurand. The analysis of a resonator’s nonlinear
characteristics is therefore important when determining a suitable drive mechanism
and its associated operating variables.
A nonlinear system can exhibit hysteresis if the amplitude of vibration increases
beyond a critical value. Hysteresis occurs when the amplitude has three possible val-
ues at a given frequency. This critical value can be determined by applying

8 h
y > (5.28)
2
0
3ω β
or
where h is the damping coefficient and can be found by measuring the Q-factor of
the resonator at small amplitudes and applying
ω
Q = or (5.29)
2 h

5.6 Actuation Techniques

In Chapter 1 we defined an actuator as a device that responds to the electrical signals
within the transduction system. Specifically, a mechanical actuator is one that trans-
lates a signal from the electrical domain into the mechanical domain. In the ideal
case, we would like the conversion to be 100% efficient. Of course, any real system
cannot achieve a figure anywhere near this, owing to internal and external losses.
Typical micromechanical actuators offer an efficiency between 5% and 35%. Other
factors such as ease of fabrication, robustness, resistance to external effects (i.e.,
temperature, humidity), and range of motion, result in a series of trade-offs for
selecting the appropriate mechanism.
For the purpose of this text, four fundamental approaches for actuator design
will be discussed. Other techniques such as chemical and biological actuation are
not covered here.

5.6.1 Electrostatic
Electrostatic actuators are based on the fundamental principle that two plates of
opposite charge will attract each other. They are quite extensive as they are relatively
straightforward to fabricate. They do, however, have a nonlinear force-to-voltage
relationship. Consider a simple, parallel plate capacitor arrangement again, having a
gap separation, g, and area of overlap, A, as shown in Figure 5.13. Ignoring fringing
effects, the energy stored at a given voltage, V,is

Force
g V

Figure 5.13 A simple planar capacitor electrostatic actuator.