Frequency-multiplexed decoupled multi-degree-of-freedom capacitive sensing for gravitational reference system: design and experimental validation

The multiple degree-of-freedom (DOF) capacitive sensing circuits are among the most critical technologies for the gravitational reference system (GRS) in space-based gravitational wave detection missions. The GRS baseline design in the Laser Interferometer Space Antenna pathfinder (LPF) satellite requires independent injection electrodes to apply a common high-frequency carrier signal to amplitude modulate the attitude signals of the Test Mass (TM), which complicates the electrode distribution and results in low injection efficiency of the carrier signal. In this paper, we present a multi-DOF capacitive sensing circuit architecture that eliminates the need for additional injection electrodes by employing multi-frequency carrier injection and split-frequency modulation for each DOF displacement signal detection. We present a comprehensive analysis of the proposed scheme, including its fundamental principle, cross-channel injection coupling effect, and noise performance. A proof-of-principle experiment demonstrates the feasibility of the design, and the validation results show that the sensing resolution of each channel can still reach 10-7 pF/Hz1/2. The measured cross-channel coupling between the two-DOF channels is less than 0.32% when the TM is in the ±1.0 pF motion range. While imposing stricter requirements on transformer performance and elevating the design complexity of higher-order bandpass filters, the proposed scheme provides a way to simplify the electrode configuration by using the same electrodes to achieve the injection-sensing-feedback function differing from the LPF baseline design, which could also improve the injection efficiency and optimize the GRS performance.