This paper proposes a novel algorithm that can be integrated with various design and evaluation tools, to more accuratelyudand rapidly predict stability in multi-bit delta-sigma (Δ-Σ) modulators. Analytical expressions using the nonlinear gains from theudconcept of modified nonlinearity in control theory are incorporated into the mathematical model of multi-bit Δ-Σ modulators to predictudthe stable amplitude limits for sinusoidal input signals. The nonlinear gains lead to a set of equations which can numerically estimateudthe quantizer gain as a function of the input sinusoidal signal amplitude. This method is shown to accurately predict the stableudamplitude limits of sinusoids for 2nd-, 3rd-, 4th-, 5th- and 6th-order 3- and 5-level mid-tread quantizer based Δ-Σ modulators. Theudalgorithm is simple to apply and can be extended to midrise quantizers or to any number of quantizer levels. The only required inputudparameters for this algorithm are the number of quantizer levels and the coefficients of the noise transfer function.
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