An Analysis of Noise in Multi-Bit ΣΔ Modulators with Low-Frequency Input Signals

Digital and smart sensors are commonly implemented using multi-bit Sigma Delta Modulators. Undesired signals can be present at the ADC input, such as low-frequency signals with medium or high amplitude, as a consequence of mechanical artifacts in the MEMS and/or temporary signal overload. Simulations and measurements of those sensors with such signals show temporary increments of in-band noise power. This paper investigates the factors that produce this transient performance loss. Interestingly, noise increments happen when the modulator is forced to toggle between three adjacent levels and is not correlated with the typical tonal behavior of Sigma Delta Modulators. Hence, the sensor performance is sensitive to some specific input patterns even if tonal behavior is decreased by dithering the input of the ADC. Different error sources, such as the mismatch between DAC cells, loop filter linearity error, and quantization error, contribute to the observed noise increments. Our aim is to analyze each of these error sources to understand and quantify in-band noise power increments, and to desensitize the ADC from the undesired input patterns. Some estimation equations are proposed and verified through extensive simulations, by means of deterministic and stochastic methods. These equations are influenced by some modulator parameters and can be used to optimize them in order to reduce such in-band noise power increments.