ELECTROSTATIC AND ELECTROMAGNETIC ACTUATORS
Electrostatic actuators utilizing electrostatic attractive force have been used widely in MEMS because their fabrication processes are simple compared to those of other actuators and are compatible with that of existing integrated circuits; that is, an electrostatic actuator can be fabricated with electronic circuits for operating the actuator using the micromachining technologies discussed in Chapter 2. Electromagnetic actuators employing the electromagnetic force are also used. In this chapter we describe a variety of electrostatic and electromagnetic actuators and derive closed-form solutions for their static and dynamic responses.
9.1 ELECTROSTATIC ACTUATORS
Typical electrostatic actuators are shown in Fig. 9.1, in which the structural layers are anchored on substrates and allowed to move in specific directions. In the 1960s, Nathanson et al. demonstrated the cantilever beam with an electronic circuit on a substrate which is illustrated in Fig. 9.1a. The cantilever beam was driven by ac voltage with dc bias and served as a filter or an amplifier for an electronic device. Since the demonstration of the electrostatic cantilever beam actuator with an operating circuit, research on other types of electrostatic actuators as shown in Fig. 9.1b–e has been conducted. A fixed–fixed beam both ends of which are fixed on a substrate (Fig. 9.1b) are actuated electrostatically by applying a time-varying voltage between the beam and a ...