Sigma-delta (ΣΔ) closed-loop operation is the best candidate for realizing the interface circuit of MEMS accelerometers. However, stability and reliability problems are still the main obstacles hindering its further development for high-end applications. In situ self-testing and calibration is an alternative way to solve these problems in the current process condition, and thus, has received a lot of attention in recent years. However, circuit methods for self-testing of ΣΔ closed-loop accelerometers are rarely reported. In this paper, we propose a fifth-order ΣΔ closed-loop interface for a capacitive MEMS accelerometer. The nonlinearity problem of the system is detailed discussed, the source of it is analyzed, and the solutions are given. Furthermore, a built-in self-test (BIST) unit is integrated on-chip for in situ self-testing of the loop distortion. In BIST mode, a digital electrostatic excitation is generated by an on-chip digital resonator, which is also ΣΔ modulated. By single-bit ΣΔ-modulation, the noise and linearity of excitation is effectively improved, and a higher detection level for distortion is easily achieved, as opposed to the physical excitation generated by the motion of laboratory equipment.

This paper proposes a low-noise interface application-specific integrated circuit (ASIC) for a microelectromechanical systems (MEMS) disk resonator gyroscope (DRG) which operates in force-to-rebalance (FTR) mode. The ASIC employs an analog closed-loop control scheme which incorporates a self-excited drive loop, a rate loop and a quadrature loop. A ΣΔ modulator and a digital filter are also contained in the design to digitize the analog output besides the control loops. The clocks for the modulator and digital circuits are both generated by the self-clocking circuit, which avoids the requirement of additional quartz crystal. A system-level noise model is established to determine the contribution of each noise source in order to reduce the noise at the output. A noise optimization solution suitable for chip integration is proposed based on system-level analysis, which can effectively avoid the effects of the 1/f noise of the PI amplifier and the white noise of the feedback element. A performance of 0.0075°/√h angle random walk (ARW) and 0.038°/h bias instability (BI) is achieved using the proposed noise optimization method. The ASIC is fabricated in a 0.35 μm process with a die area of 4.4 mm × 4.5 mm and power consumption of 50 mW.

The MEMS sensor converts the physical signal of nature into an electrical signal. The output signal of the MEMS sensor is so weak and basically in the low-frequency band that the MEMS sensor interface circuit has a rigorous requirement for the noise/offset and temperature coefficient, especially in the bandgap reference block. However, the traditional amplifier has low-frequency noise and offset voltage, which will decrease the precision of the bandgap reference. In order to satisfy the need of the MEMS sensor interface circuit, a high-precision and low-noise bandgap reference is proposed in this paper. A novel operational amplifier with a chopper-stabilization technique is adopted to reduce offset and low-frequency noise. At the same time, the V-curve compensation circuit is used to realize the second-order curvature compensation. The circuit is implemented under the 0.18 μm standard of the CMOS process. The test result shows that the temperature coefficient of the bandgap is 2.31 ppm/°C in the range of −40–140 °C, while the output voltage noise is only 616 nV/sqrt(Hz)@1 Hz and the power-supply rejection ratio is 73 dB@10 kHz. The linear adjustment rate is 0.33 mV/V for supply voltages of 1.2–1.8 V at room temperature, the power consumption is only 107 μW at 1.8 V power supply voltage, and the chip active area is 0.21 × 0.28 mm².

Compound word encoding is a widely used method in symbolic music generation tasks. It combines multiple different tokens into a super token, with each time step containing one super token, thereby transforming a long music sequence into multiple shorter subsequences. By applying word embeddings, concatenation, and projection, these subsequences are converted into inputs suitable for neural sequence models, known as compressed representations. Previous research related to compound word encoding has used compressed representations to learn music features directly, but it has not explicitly modeled the relationships between the individual tokens that compose the super tokens (independent representations). In this study, to model both compressed and independent representations, we propose a new multi-level attention transformer model (MLAT). MLAT consists of three main modules: compressed representation modeling (CRM), independent representation modeling (IRM), and feature interaction modeling (FIM). CRM learns the relationships between super tokens by modeling compressed representations, IRM learns the relationships between individual tokens within super tokens by modeling independent representations, and FIM facilitates feature interaction between CRM and IRM. Furthermore, we introduce a new compressive compound word (CCP) encoding method, which significantly reduces the number of ignore tokens in super tokens, thus decreasing the length of independent representations, and further reducing the time steps needed to encode a musical piece, thus decreasing the length of compressed representations. Experimental results show that MLAT can effectively capture multi-level information in compound word encoding, thereby improving the quality of generated music. CCP better models pitch diversity, rhythmic consistency, and chord structure and outperforms mainstream compound word encodings in terms of average inference time when tested on the baseline model.