Statistical modeling of capacitor mismatch effects for successive approximation register ADCs

This paper presents an efficient modeling method for the effects of capacitor mismatches in SAR ADCs. As the capacitor mismatch can severely degrade accuracy, it is necessary to determine the limitation of the resolution. We statistically analyze the resolution of the SAR ADCs considering both the traditional approach and the proposed advanced analysis, and the concrete relations between the capacitor mismatch ratio and the maximum achievable resolution are carefully derived. In contrast to the numerical approaches performed in the previous literatures, this analysis results in a simple closed-form expression for the relations. Since the unit-capacitor size can be optimally determined according to the proposed relations, the area and energy consumption of the capacitive DAC in SAR ADCs can be minimized. Massive Monte-Carlo simulations are conducted to verify the proposed relations, and the simulation results support the proposed analysis.