A dynamic element matching technique for multi-bit quadrature delta-sigma modulators

Quadrature multi-bit ¿¿ modulators suffer from a twofold mismatch problem: mismatch between the I-branch DAC and the Q-branch DAC, and mismatch among the elements in each multi-bit DAC. These mismatches occur in the feedback paths and are crucial to the modulators´ performance. In this paper, a new DEM technique, in which the DAC elements of I- and Q-branches are combined into a common element pool, is reported. The DAC elements are dynamically assigned to I- or Q-branch such that their chances of contributing positively/ negatively to I- and Q-branches are equalized. The mismatch-induced DAC error is converted into first-order high-pass-shaped random noise. Behavioral simulations show that, for 1% element mismatch in a third-order 64× over-sampling 3-bit quadrature ¿¿ modulator, a SNDR of 82 dB and an image rejection ratio of 96.6 dB are achieved.