4th-order Sigma-delta Modulator Research Articles

WITHDRAWN: A digital low-frequency geophone based on 4th-order sigma-delta modulator and single-coil velocity feedback

The Publisher regrets that this article is an accidental duplication of an article that has already been published, https://doi.org/10.1016/j.sna.2020.112345. The duplicate article has therefore been withdrawn. The full Elsevier Policy on Article Withdrawal can be found at https://www.elsevier.com/about/our-business/policies/article-withdrawal

A digital low-frequency geophone based on 4th-order sigma-delta modulator and single-coil velocity feedback

Widely deployed conventional moving-coil geophones lack the responses needed at low frequencies for detecting long-period seismic waves, and rely heavily on the A/D conversion chips for data acquisition. This work reports on a digital low-frequency geophone based on the PID force balancing technique and a single loop 4th-order sigma-delta modulator. The system is studied by Simulink modeling and is designed to satisfy demanding bandwidth and stability requirements. In addition, the hardware implementation adopts a readout interface for a geophone that consists of two parts: the analog part picks off the coil voltage while driving a control balancing force; and the digital part performs a real-time time DF integrators filtering in an FPGA for high-order noise shaping. The experimental results confirm the design concept of the proposed digital geophone. The balancing loop extends the low-frequency response of a commercial 4.5 Hz geophone down to 0.16 Hz. Within a 200 Hz bandwidth, the sigma-delta modulator achieves an equivalent acceleration noise floor of 4.3 ng/√Hz @ 1.0 Hz and shapes the in-band quantization noise to a level below other noises in the system. This investigation shows its potential to detect low-frequency seismic waves for efficient and high precision deep Earth exploration and hazard predictions.

A 16 Bits Sigma-Delta Modulator Applied in Gyroscope

In this paper, a 4th-order sigma-delta modulator applied in gyroscope is presented. This modulator adopts the 2-1-1 Multi stage noise shaping structure. The bandwidth of signal is 100 KHz, the over sample rate is 64, and sample frequency is 12.8MHz. By the MATLAB Simulink modeling and simulation, when the input signal is 100 KHz, the SNDR of the MASH ADC is 121.8dB, and the effective number of bit is 19.93 in ideal situation. After considering non-ideal factors, the SNDR is 111.6dB, the effective number of bit of ADC is 18.28. Compared with the ideal situation, the noise floor of PSD has increased 40dB. It explains that non-ideal factors have a significant effect on the performance of the sigma-delta ADC. The 4th-order MASH sigma-delta modulator has been implemented under 0.5 um CMOS process and simulated under Cadence. The final simulation results show that SNDR is 112.4 dB and effective number of bits (ENOB) is 18.6.