Transfer function design of stable high-order sigma-delta modulators with root locus inside unit circle

In this paper, a systematic method to design stable high-order sigma-delta modulator (SDM) transfer functions, with no need of stability mechanisms, is proposed. It is shown that a high-order SDM can be absolutely stable if the departure angles of the root locus of its noise-shaping function are properly designed. Tradeoffs between stability and performance of the SDMs are presented.