A Universal Platform for Drift Cancellation of MEMS Resonators Based on Hybrid Digital-Physical Synchronization

We present a device-agnostic hybrid (digital-physical) synchronization platform. Starting from a single-DoF AlN BAW resonator measured in ambient air with no compensation, we progressively improve stability by colocking a digitally synthesized resonator in a Huygens-clock-inspired anti-phase mode. A supervisory controller (i) tracks the physical resonator's drift and (ii) regulates the amplitude ratio to$\approx 1$, sustaining synchronization for more than 12 h under uncontrolled ambient conditions, without pressure or temperature compensation or stabilization. This reduces both short-term bias instability and long-term Allan deviation of the physical resonator's frequency (e.g., bias stability improves from$2.04 \times 10^{-8}$to$1.20 \times 10^{-9}$at$\tau \approx 0.16 \mathrm{s}; \sigma \mathrm{y}(\tau)$remains between 1 and 2 decades lower up to 103s). While MEMS synchronization and lock-range engineering are established, our advance is a digital twin that follows drift and preserves gain and frequency symmetry, expanding the usable synchronization range without analog tuning for any resonant MEMS device.