Abstract
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.
Highlights
Because of their intrinsically high Q-factor, electrical filters based on mechanical resonators have long been of interest for signal processing [1,2,3,4,5,6]
mechanical systems (MEMS) filters were initially demonstrated at high kHz frequencies as lumped-element systems driven by electrostatic comb-drives [13,14,15,16,17] and at MHz frequencies as coupled-beam arrays driven by parallel-plate actuators [15,18,19,20,21,22,23,24,25]
A method to compensate for the electrostatic desynchronization of coupled beam arrays has been proposed and confirmed by simulation, with excellent agreement being obtained using lumped element, stiffness matrix and finite element models
Summary
Because of their intrinsically high Q-factor, electrical filters based on mechanical resonators have long been of interest for signal processing [1,2,3,4,5,6]. Electrostatic stiffness modification is incompatible with the dynamic synchronization needed for correct collective operation of the array. Electrostatic stiffness modification is incompatible with the dynamic fect can be compensated by applying different DC tuning voltages to the inner and outer synchronization needed for correct collective operation of the array. Additional resonators are introduced at either end of the array, together nators are mass-loaded so their resonances lie far enough from those of the original array with the coupling elements needed to obtain the correct DC response. These resonators are that they do not in collective.
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