A framework for analysis of high-order sigma-delta modulators

In this paper a framework for the analysis of a family of high-order interpolative sigma-delta modulators is introduced. It is shown that a large number of high-order architectures can be reduced to a diagonal form which facilitates the stability analysis of the system. In addition, the diagonal form is a canonical form which illustrates the equivalence of a variety of sigma-delta architectures. Architectural differences are manifested as differences in parameter values in the diagonal form, providing a convenient method of comparison between systems. It is also shown how transformation to the diagonal form may result in a reduction in order of a system. Finally, there is a brief discussion on the importance of diagonal systems as opposed to nondiagonal systems.