Control of MEMS vibration modes with Pulsed Digital Oscillators : Part I — theory

The aim of this paper is to show that it is possible to excite selectively different mechanical resonant modes of a MEMS structure using Pulsed Digital Oscillators (PDOs). This can be done by simply changing the working parameters of the oscillator, namely its sampling frequency or its feedback filter.
A set of iterative maps is formulated to describe the evolution of the spatial modes between two sampling events in PDOs. With this lumped model, it is established that under some circumstances PDO bitstreams related to only one of the resonances can be obtained, and that in the antioscillation regions of the PDO the mechanical energy is absorbed into the electrical domain on average. The possibility of selecting for a given resonant frequency the oscillation and antioscillation behaviour allows one to obtain oscillations at any given resonant mode of the MEMS structure.