Abstract
Coupled resonator filters implemented as microelectromechanical systems (MEMS) offer performance advantages as band-pass filters at MHz frequencies. Here new designs based on resonant cavities for acoustic slow waves are developed to allow alternative frequency responses. Derivation of the lumped element model for coupled beam systems with in-plane motion from Rayleigh–Ritz perturbation theory is first reviewed. Departures from ideal behaviour caused by mechanical and electrostatic detuning are resolved. Slow wave theory is then used to develop linear array topologies with novel responses including band-stop and comb filtering with controlled filter roll-off. A systematic procedure is developed to allow rapid identification of design parameters without the need for lengthy numerical simulation, using the lumped element, stiffness matrix and finite element methods to investigate the layout parameters of initial design concepts, detailed mechanical effects and detailed electrostatic effects, respectively. High performance is demonstrated, with good agreement between the models.
Highlights
Microelectromechanical systems (MEMS) have had significant economic impact, with widespread adoption in many industries (Elwenspoek and Jansen 1999; Madou 2011; Beeby et al 2004; Uttamchandani 2013)
A systematic procedure is developed to allow rapid identification of design parameters without the need for lengthy numerical simulation, using the lumped element, stiffness matrix and finite element methods to investigate the layout parameters of initial design concepts, detailed mechanical effects and detailed electrostatic effects, respectively
Analysis of MEMS filters based on arrays of coupled resonant beams has been reviewed, and the factors preventing effective operation of large arrays have been identified
Summary
Microelectromechanical systems (MEMS) have had significant economic impact, with widespread adoption in many industries (Elwenspoek and Jansen 1999; Madou 2011; Beeby et al 2004; Uttamchandani 2013). The super-het uses an intermediate frequency (IF) and requires IF filters with flat passband and small fractional bandwidth Due to their high Q-factors, coupled mechanical resonators have long been used for filtering (Hathaway and Babcock 1957; Johnson et al 1971), and electrostatically driven resonators were among the first MEMS (Tang et al 1989). In this paper we develop a systematic approach for designing new filter architectures based on arrays of electrostatically driven, mechanically coupled in-plane MEMS resonators. 2 by reviewing the use of perturbation theory to derive a suitable LEM and identify the causes of mechanical and electrostatic detuning Resolution of these difficulties is key to effective design of complex filters.
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