Stability Analysis of 1-Bit ΣΔ Modulators by Covering State Vector Transition with Hyper Cube for Specified Input Peak Amplitudes and Auto-Correlations

Mitsuhiko YAGYU  Akinori NISHIHARA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A   No.8   pp.1855-1862
Publication Date: 2004/08/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing)
Category: Theory of Signals
Keyword: 
stability,  oversampling ΣΔ modulator,  state vector transition,  optimization,  

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Summary: 
This paper presents an algorithm to analyze the stability and detect an upper-bound of every possible overload of a ΣΔ modulator for a set of input signals that are characterized by specified peak amplitudes and auto-correlations. The approach is to introduce a hyper cube in which all possible state vectors are recursively mapped into a subset of the hyper cube itself for the specified inputs and detect such a hyper cube by iteratively solving linear programming problems. Then the proposed algorithm may not identify every stable ΣΔ modulator but cannot evaluate any unstable ΣΔ modulator as a stable one. In numerical examples, two 1-bit ΣΔ modulators are analyzed, and it is revealed that a band-limitation of inputs to OSR 256 guarantees the rigorous stability even with an extension of input range to at least 240% of conventional range.