Multirate formulation for mismatch sensitivity analysis of analog-to-digital converters that utilize parallel S?-modulators

A general formulation based on multirate filterbanktheory for analog-to-digital converters using parallel sigmadeltamodulators in conjunction with modulation sequences ispresented. The time-interleaved modulators (TIMs), Hadamard modulators(HMs), and frequency-band decomposition modulators(FBDMs) can be viewed as special cases of the proposeddescription. The usefulness of the formulation stems from itsability to analyze a system's sensitivity to aliasing due to channel mismatch and modulation sequence level errors. BothNyquist-rate and oversampled systems are considered, and it isshown how the matching requirements between channels canbe reduced for oversampled systems. The new formulation isuseful also for the derivation of new modulation schemes, andan example is given of how it can be used in this context.