Mechanical Synchronization of MEMS Electrostatically Driven Coupled Beam Filters

Micro-electromechanical systems (MEMS) bandpass filters based on arrays of electrostatically driven coupled beams have been demonstrated at MHz frequencies. High performance follows from the high Q-factor of mechanical resonators, and electrostatic transduction allows tuning, matching and actuation. For high-order filters, there is a conflict between the transduction mechanism and the coupling arrangement needed for dynamic synchronization: it is not possible to achieve synchronization and tuning simultaneously using a single voltage. Here we propose a general solution, based on the addition of mass-loaded beams at the ends of the array. These beams deflect for direct current (DC) voltages, and therefore allow electrostatic tuning, but do not respond to in-band alternating current (AC) voltages and hence do not interfere with synchronization. Spurious modes generated by these beams may be damped, leaving a good approximation to the desired response. The approach is introduced using a lumped element model and verified using stiffness matrix and finite element models for in-plane arrays with parallel plate drives and shown to be tolerant of the exact mass value. The principle may allow compensation of fabrication-induced variations in complex filters.