Abstract:
Inertial sensors are important payloads for detecting gravitational waves in space, and precise differential capacitance measurement is an important technology in inertial sensors. Currently, the differential capacitance of the mass block in the middle position is usually calculated based on the ideal plate capacitance formula. However, Nico Brandt et al. pointed out that there is a significant deviation between the theoretical and actual capacitance values obtained from this calculation, which may affect the magnitude of electrostatic forces and interfere with the detection of gravitational waves by inertial sensors. At present, there is no specialized research in China that indicates whether there is an error between the theoretical and actual values of capacitance in inertial sensors, and the specific impact of this error on the magnitude of electrostatic force. Therefore, this article focuses on three aspects: the magnitude and causes of the error between the actual and theoretical values of capacitors, how this error is transmitted through feedback circuits, and how it affects electrostatic forces. Creo Parametric 2.0 is used for modeling, and COMSOL Multiphysics 6.0 is used for multi physics field simulation analysis. Firstly, construct inertial sensor models with multiple structures and conduct capacitance simulation analysis on different models separately. By comparing the capacitance simulation values of different models, analyzing the causes of errors, and verifying the simulation results through experiments. In terms of capacitance simulation values, this article has obtained consistent results with Nico Brandt et al., that is, the capacitance simulation values are about 10% larger than the theoretical capacitance values. Secondly, this article provides the first in-depth analysis of the impact of capacitor simulation values on feedback voltage after feedback control circuit, and finds that this error can increase the feedback voltage by about 10%. Finally, validate the electrostatic force correction formula proposed by Nico Brandt et al. The calculation results indicate that the error between the electrostatic force correction value and the simulated electrostatic force value is only about 2%. Compared to the original formula with a 20% error, the electrostatic force calculated by the electrostatic force correction formula is closer to the simulated value of electrostatic force. It can be seen that the correct application of the electrostatic force correction formula can significantly improve the calculation accuracy of electrostatic force.