Quantization noise consideration and characterization in Sigma-Delta MEMS accelerometer

• Quantization noise model considers the influence of sensing element parameters and the high non-linearity of 1-bit quantizer.
• The formula of quantization noise before noise shaping, the transfer function and its expression in the signal band are presented.
• The influences of electronic noise and sampling frequency on quantization noise are analyzed.

In order to predict the noise performance of a digital capacitive MEMS accelerometer and optimize the parameters of circuits, an improved quantization noise model is presented in this paper. Considering the distortion produced by the nonlinear characteristic of a quantizer, a system model of the Sigma-Delta (ΣΔ) accelerometer is established on the basis of describing function method model of a 1-bit quantizer. On the basis of this model, the formula of quantization noise before noise shaping, the transfer function of quantization noise and its expression in the signal band are presented. The model of quantization noise proposed in this paper includes the influence of sensing element parameters and the high non-linearity of a 1-bit quantizer. DC and AC simulation results show that the model can forecast the quantization noise in the signal band more accurately, compared with the models based on linear and quasi-linear model of a quantizer. The influences of electronic noise and sampling frequency on quantization noise are also analyzed. The results show that in ΣΔ MEMS accelerometer, electronic noise will lead to a reduction of the quantization gain and impact the noise shaping ability seriously. Increasing sampling frequency cannot effectively reduce the output quantization noise, but it will decline with sampling frequency at the slope of −3 dB/oct.