Design of stable high order 1-bit sigma-delta modulators

A method for designing stable 1-b high-order (>or=3) sigma-delta modulators is presented. The stability analysis is based on the root locus and modeling the quantizer for each clock period at a time. The quantizer's gain in the modulator at the present clock period determines the modulator's stability for the next clock period. If the modulator is stable during each clock period, it is unconditionally stable and behaves as a linear analog/digital converter. Examples with third-, fourth-, fifth-, and sixth-order sigma-delta modulators are given to explore the use of the proposed method in practice. With the designed sixth-order modulator it is possible to achieve 23-b signal-to-quantization noise ratio at the oversampling ratio of 64.<>