Thermal noise in ideal micro-machined levitated gyroscope

Abstract:
In this paper, the thermal noise in an ideal micro-machined levitated gyroscope (MLG) having an axially symmetric rotor is studied. Taking into account the gyroscopic and two-axis nature of such a micro-gyroscope, an effective damping coefficient is obtained as a sum of damping and gyroscopic coupling coefficients. Using the obtained effective damping coefficient, the spectral density of gyroscope noise floor is derived. An investigation of the thermal perturbation of the ideal gyroscope within the entire frequency domain (Johnson noise) shows the restriction in the gyroscope resolution due to preserving an angular position stiffness. Also, using the Ising criterion, an alternative qualitative manner to estimate the resolution is obtained. In turn, the both manners provide an excellent explanation of the mechanism of constraints in current performance of MLG.