An internally non-linear ADC for a ΣΔ accelerometer loop

If an analog-to-digital converter (ADC) is used within a ΣΔ converter such that the loop filter is mixed signal, then the ADC does not need to have the full resolution of the ΣΔ converter, and its input values will not be uniformly distributed over the input range. In this paper, we argue that the best input distribution to use as a general model is the maximum-entropy distribution (for location parameters: the Gaussian distribution). We then describe an externally linear ADC with non-linearly spaced decision boundaries implemented in 0.6μm CMOS and show measurement results of a 19-bit dynamic range ΣΔ accelerometer loop inside which the ADC reaches more than the required 7-bit performance with only 2⁶ decision levels.