On the functioning of a VHF microelectromechanical resonator

We consider a new design of a microelectromechanical resonator with micrometer dimensions operating at gigahertz frequencies, previously proposed by the authors. The article contains a description of technological problems of the realization of a microelectromechanical resonator as well as a rigorous justification of its functioning in a mathematical model. In analytical form, we establish a connection between auto-oscillations of the mobile element of the microresonator generated by electrostatic attraction during startup, and the parameters of the natural oscillations which turn into auto-oscillations at the end of the startup.