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.

Nano- g accelerometers are widely used in space exploration and measurement of the earth's gravitational field. It is essential to precisely evaluate error effects at high orders such as cross-coupling for applications in a dynamic environment. Nevertheless, it remains challenging to meet the precision requirements using conventional calibration measures. In this article, we propose a method to separate the cross-coupling coefficients of a linear single-axis accelerometer by mounting it on a steadily rotating rate table that is tilted at a fixed deviation angle with respect to the horizontal plane. The gravity component is periodically modulated along the input axis per revolution. Simultaneously, a series of centripetal acceleration is applied along the cross axis in sequence while adjusting the rotation frequency of the rate table by steps. Thus, the cross-coupling coefficient can be separated by its dependence both on the modulated gravity acceleration and the centripetal acceleration. In comparison to the static multipoint angular rotation test on a tilted dividing head, the proposed dynamic modulation method demonstrates improved robustness against corruption from bias drift, with an improved uncertainty. This method to separate the cross-coupling coefficient is suitable for testing high-resolution accelerometers, without requiring high bias stability or sensitive response sustaining at ultralow frequency.

The reduction of temperature effect is vitally important for high precision sensors. This paper introduces the theoretical analysis and experimental verification of an in-situ compensation method on the temperature coefficient of the scale factor for a single-axis electromagnetic force-balance feedback MEMS accelerometer. A micro thermistor, fabricated together with the MEMS accelerometer, is integrated to in-situ sense the temperature variation of the accelerometer. The thermistor is connected to the voltage-to-current resistance in series, which compensates the variation of the scale factor of the accelerometer that is influenced by temperature variation. The experimental results reveal that the temperature coefficient of the scale factor of the compensated accelerometer is within 6 ppm/°C for the temperature range from 25°C to 50°C, which is reduced by 68 times compared with the uncompensated accelerometer. Benefiting from the compatible fabrication process and the in-situ compensation, the proposed method is promising to be low-cost and high-efficiency.

High precision accelerometers play a vital role in the measurement of the Earth’s gravitational field. They can be used in the rotating-accelerometer-based gravity gradient instrument to detect the change of the gravity gradient. For that application, the high precision accelerometers should have a noise floor of below 1 ng/ √ Hz and both have a measurement range with dozens of mg for working on a shipborne or airborne moving platform. Therefore, the high precision accelerometers require a wide dynamic range of at least 150 dB. However, the off-the-shelf accelerometers with 150 dB dynamic range cannot meet the requirement of the gravity gradient instrument due to their high self-noise floor. In this paper, a metal flexure electromagnetic rebalance accelerometer with both low noise and wide dynamic range is proposed. For the spring-mass structure design, a pair of metal leaf springs are applied to supported the proof mass with a fundamental frequency of 8.3 Hz and a large cross-axis rejection ratio of 2913.4. The detailed noise analysis of the proposed accelerometer is conducted to ensure the self-noise of the accelerometer can meet the target noise floor. Finally, the proposed accelerometer is evaluated and calibrated with the results showing the scale factor of (398.6±0.2) V/g, the measurement range of ±27 mg, the self-noise of 0.5 ng/ √ Hz@0.4~2 Hz. In this case, the dynamic range of the proposed accelerometer can be derived as 152 dB @0.4~2 Hz, which meets the current requirement of the gravity gradient instrument and other high precision applications.

Accelerometers are required to discern minute gravity-related variations when simultaneously measuring the large disturbing acceleration of the moving platforms in airborne or shipborne gravity gradient measurement. Closed-loop accelerometers with an electromagnetic servo actuator are commonly used to realize such a large dynamic range. However, the noise floor could deteriorate at high inputs and few studies have addressed this issue. This article investigates the noise origins of the electromagnetic actuator under large acceleration excitation using an in situ measurement scheme. The actuation unit is intentionally disconnected from the loop and an independent dc or ac current is fed into the integrated actuator coil to provide a drive force onto the proof mass (PM). The capacitive displacement detection unit independently operates to in situ monitor any induced positional variations of the PM. In order to identify potential actuation noise sources, actuator coils of two identical accelerometers are electrically connected in various configurations and stepwise tested. The common-mode disturbances such as electronic noise sources and ambient vibrations are canceled out by taking the displacement difference of the two PMs, whereas the intrinsic noises in each actuator would superimpose on each other. As a result, we implemented an accelerometer with a noise floor of sub ng/ $\sqrt {\mathrm{ Hz}}$ at any constant input within ±20 mg. On the other hand, our findings indicate that the noise floor deteriorates into a few ng/ $\sqrt {\mathrm{ Hz}}$ at a time-varying input and the deterioration results from the Barkhausen effect of the magnetic material in the actuator.