Performance Modelling of Optimal Combination Algorithms Applied to Arbitrary Data Converter Architectures

The challenge of designing high-accuracy Nyquist-rate data converters with acceptable process yield inevitably leads to adopting ad hoc calibration techniques to overcome random mismatch errors. Optimal Combination Algorithms (OCAs) have emerged as a state-of-art calibration approach for Digital-to-Analog Converters (DACs), mitigating non-linearity errors by optimally rearranging the mapping relations between input code and unit elements in the DAC array. As of today, several OCAs have been demonstrated for specific DAC architectures, but the design space of OCA-compensated DACs remains mostly unexplored. In this work, we provide a wide-range comparison of state-of-art OCAs and, for the first time, we systematically investigate how the DAC nominal resolution affects the effectiveness of OCAs, as for both integral and differential non-linearity performances. The proposed analysis, performed by means of statistical behavioral simulations, uncovers unforeseen relationships between OCAs performances and the DAC architecture. Attained simulation results heuristically suggest novel parameters of merit that may be adopted to characterize OCAs, moving one preliminary step forward in clarifying trade-offs involved in the design of high-resolution OCA-based DACs.