Nonlinear dynamics of bandpass sigma-delta modulation

Much research attention in recent years has been focussed on the subject of oversampled analogue-to-digital and digital-to-analogue conversion, based on the principle of sigma-delta modulation. Theoretical analysis of these conversion methods has been complicated by their nonlinear nature, precluding the application of standard linear circuit analysis methods. In recent years a number of researchers have undertaken a study of sigma-delta modulation based on nonlinear methods. This paper summarises the results that have been obtained by this study in the case of bandpass sigma-delta modulation, and shows how these results can be extended to handle certain circuit nonidealities.