A Conceptual Study of Microelectromechanical Disk Resonators

Microelectromechanical systems (MEMS) resonators serve as frequency-selective components in applications ranging from biology to communications. In this paper, the dynamic behavior of an RF MEMS disk resonator is formulated using an analytical method. The resonator is simultaneously subjected to a DC-bias voltage superimposed with an ac harmonic voltage applied across the electrode-to-resonator gap. The governing equation of motion is derived by minimization of the Hamiltonian and generalized to include the viscous damping effect. Periodic solutions are determined by means of a shooting method and their stability is investigated by determining the well-known Floquet exponents of the perturbed motions. The influence of intermolecular forces such as van der Waals and Casimir on the dynamics of each mode of the disk resonator are investigated and the influence of design parameters are discussed. The results indicate that a high quality factor at ultrahigh frequency (UHF), a weak nonlinearity, and a low actuation voltage make polydiamond disk resonators excellent contenders for the next generation of micromechanical RF filters and channelizers. Furthermore, the resonant frequencies observed in the second (1.3 GHz) and third (2.1 GHz) modes allow for power-efficient operation of the disk resonator in the UHF range.