DAC mismatch shaping for quadrature sigma-delta data converters

An intuitive yet mathematically rigorous procedure for arriving at a DAC element rotation algorithm (ERA) from a given general mismatch transfer function (MTF) is presented for sigma-delta data converters. The approach is validated by deriving low-pass and high-pass ERAs from the corresponding MTFs. Using the proposed approach the ERA for a quadrature sigma-delta ADC is then derived from a quadrature MTF. Simulations show that the new low-complexity quadrature ERA performs better than previously proposed quadrature ERAs of similar complexity. A gain calibration technique is further proposed that works in conjunction to the quadrature ERA to alleviate the image-folding due to mismatches between the quadrature DAC elements.