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Towards a Procedure for Stability Analysis of High Order Sigma Delta Modulators

One of the greatest unsolved problems in the theory of sigma delta modulation concerns the ability to analytically derive the stability, or boundedness, of a high order sigma delta modulator (SDM). In this work, we describe the existing literature and try to clarify the issues involved. We fully derive the stability of first order sigma delta modulators, and derive some important results for the basic second order sigma delta modulator. For third order sigma delta modulators, we describe interesting simulated results as well as sketch a proof of instability, based on linear programming, for one particular SDM. Finally, we present two theoretical results concerning stability of general high order SDMs that point towards promising directions of future research.

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