suggests that the speed–armature current characteristic will take the form of a hyperbola. Similarly, Eq. (20.25) indicates that the torque–armature current characteristic will be approximately parabolic. These general characteristics are illustrated in Fig. 20.62, along with the derived torque–speed charac- teristic in Fig. 20.63. The general characteristics indicate that if the load falls to a particularly low value FIGURE 20.59 The shunt-wound motor load characteristics. FIGURE 20.60 The shunt-wound torque–speed characteristics. FIGURE 20.61 The series-wound motor. Applied voltage, V Speed E Torque Armature current Speed EMF Torque Speed Torque Supply V E M I a R a 0066_Frame_C20 Page 37 Wednesday, January 9, 2002 5:49 PM ©2002 CRC Press LLC suggests that the speed–armature current characteristic will take the form of a hyperbola. Similarly, Eq. (20.25) indicates that the torque–armature current characteristic will be approximately parabolic. These general characteristics are illustrated in Fig. 20.62, along with the derived torque–speed charac- teristic in Fig. 20.63. The general characteristics indicate that if the load falls to a particularly low value FIGURE 20.59 The shunt-wound motor load characteristics. FIGURE 20.60 The shunt-wound torque–speed characteristics. FIGURE 20.61 The series-wound motor. Applied voltage, V Speed E Torque Armature current Speed EMF Torque Speed Torque Supply V E M I a R a 0066_Frame_C20 Page 37 Wednesday, January 9, 2002 5:49 PM ©2002 CRC Press LLC theory and mechanics comprise the fundamentals for analysis, modeling, simulation, design, and opti- mization, while fabrication is based on the micromachining and high-aspect-ratio techniques and pro- cesses, which are the extension of the CMOS technologies developed to fabricate ICs. For many years, the developments in microelectromechanical systems (MEMS) have been concentrated on the fabrica- tion of microstructures adopting, modifying, and redesigning silicon-based processes and technologies commonly used in integrated microelectronics. The reason for refining of conventional processes and technologies as well as application of new materials is simple: in general, microstructures are three- dimensional with high aspect ratios and large structural heights in contrast to two-dimensional planar microelectronic devices. Silicon structures can be formed from bulk silicon micromachining using wet or dry processes, or through surface micromachining. Metallic micromolding techniques, based upon photolithographic processes, are also widely used to fabricate microstructures. Molds are created in polymer films (usually photoresist) on planar surfaces, and then filled by electrodepositing metal (elec- trodeposition plays a key role in the fabrication of the microstructures and microdevices, which are the components of MEMS). High-aspect ratio technologies use optical, e-beam, and x-ray lithography to create trenches up to 1 mm deep in polymethylmethacrylate resist on the electroplating base (called seed layer). Electrodeposition of magnetic materials and conductors, electroplating, electroetching, and lift- off are extremely important processes to fabricate microscale structures and devices. Though it is recog- nized that the ability to use and refine existing microelectronics fabrication technologies and materials is very important, and the development of novel processes to fabricate MEMS is a key factor in the rapid growth of affordable MEMS, other emerging areas arise. In particular, devising, design, modeling, analysis, and optimization of novel MEMS are extremely important. Therefore, recently, the MEMS theory and microengineering fundamentals have been expanded to thoroughly study other critical prob- lems such as the system-level synthesis and integration, synergetic classification and analysis, modeling and design, as well as optimization. This chapter studies the fabrication, analysis, and design problems for electromagnetic microstructures and microdevices (microtransducers with ICs). The descriptions of the fabrication processes are given, modeling and analysis issues are emphasized, and the design is performed. Design and Fabrication In MEMS, the fabrication of thin film magnetic components and microstructures requires deposition of conductors, insulators, and magnetic materials. Some available bulk material constants (conductivity σ , resistivity ρ at 20 ° C, relative permeability µ r , thermal expansion t e , and dielectric constant—relative permittivity ␧ r ) in SI units are given in Table 20.12. TABLE 20.12 Material Constants Material σρ µ r t e × 10 − 6 ␧ r Silver 6.17 × 10 7 0.162 × 10 − 7 0.9999998 NA Copper 5.8 × 10 7 0.172 × 10 − 7 0.99999 16.7 Gold 4.1 × 10 7 0.244 × 10 − 7 0.99999 14 Aluminum 3.82 × 10 7 0.26 × 10 − 7 1.00000065 25 Tungsten 1.82 × 10 7 0.55 × 10 − 7 NA NA Zinc 1.67 × 10 7 0.6 × 10 − 7 NA NA Cobalt NA NA 250 NA Nickel 1.45 × 10 7 0.69 × 10 − 7 600 nonlinear NA Iron 1.03 × 10 7 1 × 10 − 7 4000 nonlinear NA Si 2.65 11.8 SiO 2 0.51 3.8 Si 3 N 4 2.7 7.6 SiC 3.0 6.5 GaAs 6.9 13 Ge 2.2 16.1 0066_Frame_C20.fm Page 97 Wednesday, January 9, 2002 1:44 PM ©2002 CRC Press LLC . extremely important. Therefore, recently, the MEMS theory and microengineering fundamentals have been expanded to thoroughly study other critical prob- lems such as the system-level synthesis and integration,. 0.162 × 10 − 7 0 .99 999 98 NA Copper 5.8 × 10 7 0.172 × 10 − 7 0 .99 999 16.7 Gold 4.1 × 10 7 0.244 × 10 − 7 0 .99 999 14 Aluminum 3.82 × . CRC Press LLC theory and mechanics comprise the fundamentals for analysis, modeling, simulation, design, and opti- mization, while fabrication is based on the micromachining and high-aspect-ratio