Scale-factor analysis of a geometrically compensated (100) single-crystal silicon vibratory ring gyroscope

In this paper, we present the rate measurement results, especially the scale factor in a mode-matched geometrically compensated (100) single crystal silicon (SCS) vibratory ring gyroscope (VRG) using closed-loop driving and open-loop sensing test. Compared to the non-compensated (100) VRG with uniform radial width, the smaller frequency split (Δf) of 9 Hz was obtained in the compensated one with non-uniform radial width and optimized suspending beams in simulations. By using electrostatic tuning with multiple electrodes, we realized mode-matching in the as-fabricated compensated VRG with Δf of 126 Hz. Then, considering the dimensions, parameters of read-out circuit and mode-rotation caused by electrostatic tuning, a theoretical model of scale factor is derived. This model adequately considers effect of mode-rotation and dimensions on scale factor of a VRG, especially its radial width, ring radius and capacitance gap, which well explained the reason for the measured values of scale factor and bias stability.