Stability analysis of 1-bit Sigma Delta modulators by covering state vector transition with hyper cube for specified input peak amplitudes and auto-correlations
This paper presents an algorithm to analyze the stability and detect an upper-bound of every possible overload of a SigmaDelta 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 SigmaDelta modulator but cannot evaluate any unstable SigmaDelta modulator as a stable one. In numerical examples, two 1-bit SigmaDelta 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.
stability state vector transition oversampling sigma delta modulator optimization