Vibrational Geometry
Micro-scale inertial sensing structures employ four symmetrically coupled vibrating masses to achieve high motion isolation. A quad-mass resonator operates by driving four proof masses in anti-phase mechanical resonance along balanced orthogonal axes. Symmetric motion cancels reaction forces and moments at the central anchor points, suppressing energy dissipation into the supporting substrate.
High-precision gyroscopes integrate this geometry to achieve high mechanical quality factors and low thermal drift.
Quadrature Drift
Quad-mass architecture couples four identical mass elements through central flexure springs, enforcing symmetrical tuning fork vibration modes. Opposing mass pairs oscillate towards and away from each other simultaneously, eliminating net linear and angular momentum transfer to the package. Coriolis forces induce out-of-plane sensing displacements when rotation occurs around the central perpendicular axis.
High quality factors exceeding one hundred thousand are routinely achieved due to minimal anchor loss in high-vacuum enclosures.
Acceleration Rejection
Manufacturing tolerances cause slight mass mismatches and spring constant asymmetries among the four vibrating bodies. Parameter imbalances generate quadrature error, coupling drive motion into the sense channels without external rotation. External linear acceleration forces act equally on all four masses, canceling out in differential signal detection circuits.
Thermal gradients across the silicon die alter local spring stiffness, requiring integrated micro-heaters to maintain thermal symmetry.
Calibration Tolerance
Mechanical balance specifications dictate maximum permissible frequency mismatch between drive and sense modes.
