High-order medium frequency micromechanical electronic filters

Abstract

Abstract-Third-order, high-Q, micromechanical bandpass filters comprised of three ratioed folded-beam resonators coupled by flexural mode springs are demonstrated using an integrated circuit compatible, doped polycrystalline silicon surfacemicromachining technology. A complete design procedure for multiresonator micromechanical filters is presented and solidified via an example design. The use of quarter-wavelength coupling beams attached to resonators at velocity-controllable locations is shown to suppress passband distortion due to finite-mass and process mismatch nonidealities, which become increasingly important on this microscale. In addition, low-velocity coupling methods are shown to greatly alleviate the lithographic resolution required to achieve a given percent bandwidth. Ratioed foldedbeam micromechanical resonators are introduced as the key impedance transforming components that enable the needed low-velocity coupling. Using these design techniques, balanced three-resonator microscale mechanical filters with passband frequencies centered around 340 kHz are demonstrated with percent bandwidths of 0.1%, associated insertion losses as small as 0.1 dB, 20-dB shape factors as low as 1.5, and stopband rejections greater than 64 dB. Measurement and theory are rigorously compared and important limitations, such as thermal susceptibility, the need for passband tuning, and inadequate electromechanical coupling, are addressed. [470]

Mechanical Synchronization of MEMS Electrostatically Driven Coupled Beam Filters

“…However, application of the same DC voltage to each transducer cannot then cause equal beam motion since this would require deflection of the end springs alone. A common approach to such problems is to apply a different DC bias to each transducer [17,25]. However, the correction is extremely tedious.…”

“…Miniaturization using micro-electro-mechanical systems (MEMS) technology allowed operating frequencies to be raised and the fundamental mechanisms limiting Q-factors (gas damping and thermoelastic friction) to be understood [7][8][9][10][11][12]. MEMS filters were initially demonstrated at high kHz frequencies as lumped-element systems driven by electrostatic comb-drives [13][14][15][16][17] and then at MHz frequencies as coupled-beam arrays driven by parallel-plate actuators [15,[18][19][20][21][22][23][24][25]. Matching [20], tuning [26][27][28][29][30] and coupling [31][32][33][34][35] can all be performed electrostatically.…”

“…Electrostatic stiffness modification is thus incompatible with the dynamic synchronization needed for correct collective operation of the array. The effect can be compensated by applying different DC tuning voltages to the inner and outer beams [17]. Unfortunately, it is difficult to establish the voltages needed even in simulation, using either the finite element method (FEM) [51][52][53], which involves accurate results using lengthy run times, or the stiffness matrix method (SMM) [54][55][56][57], which provides approximate results very quickly.…”

Nonlinear couplings and energy transfers in micro- and nano-mechanical resonators: intermodal coupling, internal resonance and synchronization

“…Multimodal functionality of MEMS/NEMS can be achieved either by coupling two or more mechanical resonators via electrostatic, optical and mechanical forces or by nonlinearly coupling two or more vibrational modes within a unitary resonator. In a linear context, coupling two mechanical resonators via an elastic spring has been common in the designs of MEMS filters [13][14][15][16] and inertial sensors [17][18][19] from the early development stage. For mass sensing, multimode measurements of a resonator or coupled resonators have become a new paradigm to improve sensitivity and accuracy [20][21][22][23].…”

Enabling tunable micromechanical bandpass filters through phase-change materials

“…Mechanical coupling requires rather complicated fabrication and precise design for generating multiple pole systems [5][6][7]. Using electrical coupling methods usually involves capacitive coupling or cascading of multiple resonators [8].…”