CHAPTER 7

ELECTROMAGNETICS

In preceding chapters we described the microfabrication and static and dynamic behavior of structures. To design MEMS that function correctly, we need to drive or actuate structures in desired directions and need to detect or measure the movement of the structures. In the macroscale world we live in, electromagnetic motors (also known as electric motors) and engines have been used widely to convert electric and chemical energies into mechanical energy to drive mechanical parts. For sensing physical quantities such as force and displacement, various measuring mechanisms are used (e.g., capacitance detection). In this chapter we describe basic laws for electric circuits, forces, and moments based on electromagnetics, most of which can also be used to detect the motion of a body.

7.1 BASIC ELEMENTS OF ELECTRIC CIRCUITS

Passive elements, defined as elements that cannot generate energy, will be described that are related to mechanical–electrical energy conversion. Active elements such as batteries and amplifiers are capable of delivering energy to electrical circuits connected to them. Many documents and textbooks cover the characteristics and design of active elements, and the reader may refer to them to understand the active elements [e.g., Millman and Grabel (1987)]. Typical passive elements are the resistor, the capacitor, and the inductor, which are shown in Fig. 7.1. A resistor of resistance R in Fig. 7.1a is connected to a voltage source of voltage ...

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