On the stability and configuration of sigma delta modulators

A set of ordinary differential equations (ODEs) has been constructed to represent a continuous sigma delta modulator (CΣΔM) [1], i.e. a continuous equivalent of a conventional sigma delta modulator (ΣΔM). This paper is concerned with a stability analysis of these equations with particular reference being made to values representing the gains of the feedback loop and the integrator leakage in the circuit. Conditions for the stability of the equations representing second and third order modulation are derived. The results from this process are used on a conventional simulation of sigma-delta modulation, and the applicability of this method is discussed. The criteria for stable operation are extended to n^th order sigma delta modulation and to a generalised architecture for sigma delta modulation. The results are compared to the conditions for stability derived from the work of various authors