Stable equilibrium study cascaded one bit sigma-delta modulator

TL;DR

This paper establishes a theoretical boundary for the stability zone of cascaded one-bit sigma-delta modulators, aiding design and comparison of different schemes, especially up to fifth order.

Contribution

It provides a theoretical method to determine stability boundaries for sigma-delta modulators of any order, with practical application up to fifth order.

Findings

Stability boundary depends on inner sigma-delta coefficients.

The boundary can be theoretically derived for any order.

Practical derivation is feasible up to fifth order.

Abstract

In the paper defines a boundary of stability zone for sigma-delta modulator. The boundary depends from inner sigma-delta modulator coefficients. For designing purposes such result could be used to find or compare some appropriate schemes with each other. It is proved some statements and showed that boundary could be found theoretically for any order of sigma-delta modulator, but practically till 5-th order.