Statistical Analysis of ENOB and Yield in Binary Weighted ADCs and DACS With Random Element Mismatch

Mismatch motivates many of the design decisions for binary weighted, ratiometric converters, such as successive approximation (SAR) analog-to-digital converters (ADC), but the statistical relationship between mismatch and signal-to-noise-plus-distortion ratio (SNDR) has not been precisely quantified. In this paper, we analyze the effects of capacitor mismatch in a binary weighted, charge redistribution SAR ADC and derive a new analytic expression relating capacitor mismatch and the effective-number-of-bits (ENOB). We then explore the statistics of this new expression and develop a model that accurately predicts yield in terms of ENOB. Finally, the major results of this paper are generalized into a simple and compact design equation that relates resolution, mismatch, and ENOB to yield for all binary weighted, ratiometric converters. The expressions derived in this paper offer practical insight into the relationship between mismatch and performance for all binary, weighted ratiometric converters with these results validated through numerical simulations.