Analysis of a Capacitive Sensing Circuit and Sensitive Structure Based on a Low-Temperature-Drift Planar Transformer

Abstract

'Xin Liu' 'Yongkun Chen' 'Haruo Kobayashi'] In space gravitational-wave-detection missions, inertial sensors are used as the core loads, and their acceleration noise needs to reach $(3\times10-15 \text{ms}-2/\text{Hz})$ at a frequency of $0.1 \text{mHz}$, which corresponds to the capacitive sensing system; the capacitive sensing noise on the sensitive axis needs to reach $(1 \text{aF}/\text{Hz})$. Unlike traditional circuit noise evaluation, the noise in the $\text{mHz}$ frequency band is dominated by the thermal noise and the $(1/f)$ noise of the device, which is a challenging technical goal. In this paper, a low-frequency, high-precision resonant capacitor bridge method based on a planar transformer is used. Compared with the traditional winding transformer, the developed planar transformer has the advantages of low temperature drift and low $(1/f)$ noise. For closed-loop measurements of capacitive sensing circuits and sensitive structures, the minimum capacitive resolution in the time domain is about $3 \text{aF}$, which is far lower than the scientific measurement resolution requirement of $5.8 \text{fF}$ for gravitational wave detection. The capacitive sensing noise is converted to $(1.095 \text{aF}/\text{Hz})$ in the frequency band of $10 \text{mHz}–1 \text{Hz}$. Although there is a gap between the closed-loop measurement results and the final index, the measurement environment is an experimental condition without temperature control on the ground; additionally, in China, the measurement integrity and actual measurement results of the capacitive sensing function have reached a domestic leading level. This is the realization of China’s future space gravitational wave exploration.