Frequency Noise Optimization by Operating a Vibrating Beam Accelerometer in the Nonlinear Regime

This letter discusses the results of an optimization study for frequency-modulated inertial sensors, focusing on frequency noise minimization in resonant beam transducers. This is achieved by operating a vibrating beam accelerometer (VBA) in a soft nonlinear regime. This letter builds on prior research, enhancing the signal-to-noise ratio by considering the amplitude–frequency relationship and the impact of spring hardening. A detailed frequency noise analysis is performed, along with an exploration of the effects of additive noise on both the input and output voltage stages. The authors present experimental data validating the model, showing that the noise can be minimized by optimizing the input drive voltage level. This work has significant implications for the design of high-precision inertial sensors used in various applications, including navigation systems. The presented results are measured on a 100-g silicon-based VBA demonstrating an Allan variance result of 0.98 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\upmu {\rm{g}}$</tex-math></inline-formula> @ 1 s of integration time.