In space gravitational-wave-detection missions, inertial sensors are used as the core loads, and their acceleration noise needs to reach $3\times {10}^{-15} {\mathrm{ms}}^{-2}/\sqrt{\mathrm{Hz}}$ at a frequency of $0.1 \mathrm{mHz}$, which corresponds to the capacitive sensing system; the capacitive sensing noise on the sensitive axis needs to reach $1 \mathrm{aF}/\sqrt{\mathrm{Hz}}$. Unlike traditional circuit noise evaluation, the noise in the $\mathrm{mHz}$ frequency band is dominated by the thermal noise and the $1/\mathrm{f}$ 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 $1/\mathrm{f}$ noise. For closed-loop measurements of capacitive sensing circuits and sensitive structures, the minimum capacitive resolution in the time domain is about $3 \mathrm{aF}$, which is far lower than the scientific measurement resolution requirement of $5.8 \mathrm{fF}$ for gravitational wave detection. The capacitive sensing noise is converted to $1.095 \mathrm{aF}/\sqrt{\mathrm{Hz}}$ in the frequency band of $10 \mathrm{mHz}–1 \mathrm{Hz}$. 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.

An inertial sensor is a crucial payload in China’s Taiji program for space gravitational wave detection. The performance of the capacitive displacement sensing circuit in the low-frequency band (0.1 mHz to 1 Hz) is extremely important because it directly determines the sensitivity of the space gravitational wave detection missions. Therefore, significant, yet challenging, tasks include decreasing the low-frequency noise in capacitive displacement sensing circuits and improving the capacitive sensing resolution. This study analyzes the noise characteristics of the pre-amplifier circuit within the capacitive sensing circuit, achieves precise tuning of the transformer bridge, and examines how transformer parameters affect noise. In addition, this study introduces a method using a discrete JFET to reduce the operational amplifier current noise and analyzes how feedback resistance and capacitance in TIA circuits affect the overall circuit noise. The proportional relationship between different transformer noises and TIA noise before and after optimization was analyzed and experimentally verified. Finally, an optimized TIA circuit and a superior transformer were utilized to achieve an increase in the capacitive sensing resolution from 1.095 aF/rtHz @ 10 mHz to 0.84 aF/rtHz @ 10 mHz, while improving the performance by 23%. These findings provide valuable insights into further decreasing circuit noise and increasing the capacitive sensing resolution.

In the space gravitational wave detection mission, inertial sensors play the role of providing an inertial reference for the laser interferometric measurement system. Among them, the capacitance sensor serves as the core key technology of the inertial sensor, used to measure the relative position of the test mass (TM) in the electrode cage. The capacitance sensor utilizes synchronous demodulation technology to extract signals from the AC induction signal. When the phase of the demodulation switch signal is aligned, the synchronous demodulator can most effectively filter out noise, thus directly influencing the performance of the capacitance sensor. However, since the TM is in a suspended state, the information read by the capacitance sensor is dynamic, which increases the difficulty of demodulation phase alignment. In light of this, a method is proposed for achieving the phase alignment of the demodulation switch signal in a dynamic environment. This is accomplished by adjusting the phase of the demodulation switch signal, and subsequently computing the phase difference between the AC induction signal and the demodulation switch signal. At the same time, a measurement and evaluation method for phase deviation is also proposed. Ultimately, an automatic phase alignment system for the demodulation switch signal in dynamic environments is successfully implemented on an FPGA platform, and tests are conducted on a hexapod PI console platform to simulate dynamic environments. The experimental results demonstrate that the system accurately achieves phase alignment in the static environment, with a phase deviation of 0.1394 rad. In the simulated dynamic environment, the phase deviation is 0.1395 rad.

Due to the interaction of accumulated charges on the surface of a test mass with the surrounding electric and magnetic fields, the performance of inertial sensors is affected, necessitating charge management for the test mass. Discharge technology based on Ultraviolet LEDs is internationally recognized as the optimal solution for charge management. Precision driving of Ultraviolet LEDs is considered a key technology in charge management. This paper presents the driving control system used for Ultraviolet LEDs, achieving precision pulse-width-modulation-type current output with controllable pulse width and amplitude. The system generates the pulse-width-controllable pulse voltage signal via analog pulse-width modulation, and subsequently regulates the amplitude of the PWM signal through range switching. To convert the voltage into the pulse-width-modulation-type driving current, the improved Howland current source is employed. The test results demonstrate that the driving control system can output controllable current in the range of 0.01 mA to 10 mA, with a minimum step of 0.01 mA. The accuracy of the current reaches 1%, the stability within 1 h is better than 1%, and the load regulation is better than 2%. The driving control system provides an important reference for the integration of charge management system and the precision drive control method for LEDs.

The Taiji program is dedicated to the detection of middle and low-frequency gravitational waves, targeting the 0.1 mHz to 1 Hz frequency band. The project requires an acceleration residual sensitivity of 3 × 10−15 ms−2/Hz1/2, which necessitates a capacitance sensing resolution of 1 aF/Hz1/2 for the capacitive sensing system within the specified frequency range. The noise level of the resonant bridge significantly influences the resolution. Addressing the challenges in enhancing transformer performance parameters in existing resonant capacitance bridges and the constraints on improving the characteristics of resonant capacitance bridges, this study introduces a novel approach to reduce bridge thermal noise without optimizing existing parameters. The simulation results demonstrate that this scheme can reduce the noise to 0.7 times the original level and further reduce bridge thermal noise when other parameters affecting noise are optimized. This not only mitigates the demands for other performance parameters but also increases the range of maximum acceptable resonant frequency deviations and reduces its sensitivity to such variations. Experimental validation confirms that the proposed scheme effectively reduces noise by 0.7 times and improves the resolution of capacitance sensing to 0.6 aF/Hz1/2, thereby advancing the Taiji program gravitational wave detection capabilities.

For space-based gravitational-wave detection, a released test mass in an inertial sensor may retain appreciable residual angular motion, while electrostatic actuation authority is finite. This work investigates single-axis test-mass capture about the suspension-wire axis using a torsion-pendulum platform integrating differential capacitive sensing, electrostatic actuation, and digital control in the same hardware loop. Capacitive-readout calibration, free-oscillation identification, and static torque-balance actuation calibration establish quantitative relations among test-mass motion, suspension dynamics, control voltage, and electrostatic torque, and characterize the nominal near-center actuation authority. At controller activation, the measured angular offset is approximately 15.6 mrad, and the estimated angular velocity is approximately 800 μrad/s. Under limited electrostatic actuation, the control output remains at or near saturation for approximately 110 s during the initial braking stage; the test mass then reverses direction, the output desaturates, and the response converges toward the housing center. The maximum angular displacement after activation is approximately 0.067 rad, with no further test-mass–electrode-housing contact observed. After approximately 550 s, the test mass enters a stable near-center region, where an out-of-loop autocollimator measures an angular RMS of 1.81 μrad. The corresponding command-equivalent electrostatic control torque has an RMS value of $2.6\times {10}^{-11}$ N·m. These results provide a quantitative experimental characterization of single-axis test-mass capture from a large initial dynamic state under limited electrostatic actuation authority.