An approximate analysis for the dynamics of sigma-delta systems

Sigma-delta modulators are inherently non-linear structures and suffer from many intriguing and unresolved problems. Two approaches are utilized to analyze these structures: analytical and nonlinear approximation techniques. According to the nonlinear approximation analysis, a circle map is proposed to model the dynamics of a third-order sigma-delta modulator and can be extended to include higher-order modulators. The proposed non-linear approximation can be utilized for studying the stability problem and the limit-cycle phenomenon of high-order sigma-delta systems.