Stability Analysis and Limit Cycles of High Order Sigma-Delta Modulators

In this chapter we present an unified approach for study the stability and validation of potential limit cycles of one bit high order Sigma-Delta modulators. The approach is general because it uses the general form of a Sigma-Delta modulator. It is based on a parallel decomposition of the modulator and a direct nonlinear systems analysis. In this representation, the general N-th order modulator is transformed into a decomposition of low order, generally complex modulators, which interact only through the quantizer function. The developed conditions for stability and for validation of potential limit cycles are very easy for implementation and this procedure is very fast.