Sigma delta modulation is a popular form of audio analogue-to-digital and digital-to-analogue conversion, but suffers from stability problems for many designs and many input signals. A general theory of stability in sigma delta modulators has been developed which predicts the stability of a high order one bit sigma delta modulator (SDM) under a variety of designs. In this paper, the theoretical approach to stability as it applies to boundedness of states is explained. Several low pass SDM designs are developed which are intended for audio analogue to digital conversion, and predicted results for stability of these designs are given. Stability is examined both in terms of the maximum allowable DC input amplitude and the theoretical sufficient conditions for stable behavior. Theoretical results are compared with simulated results, and where possible, with experimental results from a realisation of a third order SDM with adjustable parameters. Practical observations are then made concerning the effect of noiseshaping, pole/zero placement, and cut-off frequency on the stability.
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