A subnano-g electrostatic force-rebalanced flexure accelerometer is designed for the rotating accelerometer gravity gradient instrument. This accelerometer has a large proof mass, which is supported inversely by two pairs of parallel leaf springs and is centered between two fixed capacitor plates. This novel design enables the proof mass to move exactly along the sensitive direction and exhibits a high rejection ratio at its cross-axis directions. Benefiting from large proof mass, high vacuum packaging, and air-tight sealing, the thermal Brownian noise of the accelerometer is lowered down to less than 0.2 $\mathrm{ng}/\sqrt{\mathrm{Hz}}$ with a quality factor of 15 and a natural resonant frequency of about $7.4\mathrm{Hz}$ . The accelerometer’s designed measurement range is about ±1 mg. Based on the correlation analysis between a commercial triaxial seismometer and our accelerometer, the demonstrated self-noise of our accelerometers is reduced to lower than 0.3 $\mathrm{ng}/\sqrt{\mathrm{Hz}}$ over the frequency ranging from 0.2 to 2 Hz, which meets the requirement of the rotating accelerometer gravity gradiometer.

Capacitive sensing is a key technique to measure the test mass movement with a high resolution for space-borne gravitational wave detectors, such as Laser Interferometer Space Antenna (LISA) and TianQin. The capacitance resolution requirement of TianQin is higher than that of LISA, as the arm length of TianQin is about 15 times shorter. In this paper, the transfer function and capacitance measurement noise of the circuit are modeled and analyzed. Figure-of-merits, including the product of the inductance L and the quality factor Q of the transformer, are proposed to optimize the transformer and the capacitance measurement resolution of the circuit. The LQ product improvement and the resonant frequency augmentation are the key factors to enhance the capacitance measurement resolution. We fabricated a transformer with a high LQ product over a wide frequency band. The evaluation showed that the transformer can generate a capacitance resolution of 0.11 aF/Hz^1/2 at a resonant frequency of 200 kHz, and the amplitude of the injection wave would be 0.6 V. This result supports the potential application of the proposed transformer in space-borne gravitational wave detection and demonstrates that it could relieve the stringent requirements for other parameters in the TianQin mission.

A method for automatic compensation of misalignment angles during matching the scale factors of two pairs of the accelerometers in developing the rotating accelerometer gravity gradient instrument (GGI) is proposed and demonstrated in this paper. The purpose of automatic scale factor matching of the four accelerometers in GGI is to suppress the common mode acceleration of the moving-based platforms. However, taking the full model equation of the accelerometer into consideration, the other two orthogonal axes which is the pendulous axis and the output axis, will also sense the common mode acceleration and reduce the suppression performance. The coefficients from the two axes to the output are δ_O and δ_P respectively, called the misalignment angles. The angle δ_O, coupling with the acceleration along the pendulous axis perpendicular to the rotational plane, will not be modulated by the rotation and gives little contribution to the scale factors matching. On the other hand, because of coupling with the acceleration along the centripetal direction in the rotating plane, the angle δ_P would produce a component with 90 degrees phase delay relative to the scale factor component. Hence, the δ_P component coincides exactly with the sensitive direction of the orthogonal accelerometers. To improve the common mode acceleration rejection, the misalignment angle δ_P is compensated by injecting a trimming current, which is proportional to the output of an orthogonal accelerometer, into the torque coil of the accelerometer during the scale factor matching. The experimental results show that the common linear acceleration suppression achieved three orders after the scale factors balance and five orders after the misalignment angles compensation, which is almost down to the noise level of the used accelerometers of 1~2 × 10⁻⁷ g/√Hz (1 g ≈ 9.8 m/s²).

A new and simple method to adjust the scale factor of a magnetic force feedback accelerometer is presented, which could be used in developing a rotating accelerometer gravity gradient instrument (GGI). Adjusting and matching the acceleration-to-current transfer function of the four accelerometers automatically is one of the basic and necessary technologies for rejecting the common mode accelerations in the development of GGI. In order to adjust the scale factor of the magnetic force rebalance accelerometer, an external current is injected and combined with the normal feedback current; they are then applied together to the torque coil of the magnetic actuator. The injected current could be varied proportionally according to the external adjustment needs, and the change in the acceleration-to-current transfer function then realized dynamically. The new adjustment method has the advantages of no extra assembly and ease of operation. Changes in the scale factors range from 33% smaller to 100% larger are verified experimentally by adjusting the different external coefficients. The static noise of the used accelerometer is compared under conditions with and without the injecting current, and the experimental results find no change at the current noise level, which further confirms the validity of the presented method.