Computer-aided generation of nonlinear reduced-order dynamic macromodels -I: Non-stress-stiffened case

Reduced-order dynamic macromodels are an effective way to capture device be havior for rapid circuit and system simulation. In this paper, we report th e successful implementation of a methodology for automatically generating r educed-order nonlinear dynamic macromodels from three-dimensional (3-D) phy sical simulations for the conservative-energy-domain behavior of electrosta tically actuated microelectromechanical systems (MEMS) devices. These model s are created with a syntax that is directly usable in circuit- and system- level simulators for complete MEMS system design. This method has been appl ied to several examples of electrostatically actuated microstructures: a su spended clamped beam, with and without residual stress, using both symmetri c and asymmetric positions of the actuation electrode, and an elastically s upported plate with an eccentric electrode and unequal springs, producing t ilting when actuated. When compared to 3-D simulations, this method proves to be accurate for non-stress-stiffened motions, displacements for which th e gradient of the strain energy due to bending is much larger than the corr esponding gradient of the strain energy due to stretching of the neutral su rface. In typical MEMS structures, this corresponds to displacements less t han the element thickness. At larger displacements, the method must be modi fied to account for stress stiffening, which is the subject of part two of this paper.