Design of continuous-time sigma-delta modulators with arbitrary feedback waveform

This paper considers the discretization of continuous-time sigma-delta modulators without any constraint on the shape or duration of the feedback signal. A motivation for taking the shape of the feedback signal into account is the system-level compensation of nonidealities encountered in a practical design. Two different discretization approaches based on state-variables and the modified z transform are presented. Explicit formulas for an exact mapping between continuous-time and discrete-time modulators are derived. Subsequently, design of multistage continuous-time modulators using arbitrary feedback waveforms is discussed.