ANALYSIS OF DELTA-SIGMA MODULATORS WITH ZERO MEAN STOCHASTIC INPUTS

In this paper, a new framework for the analysis of Delta Sigma modulat ors with stochastic inputs is proposed, The framework is based on assu ming that the input to the one-bit quantizer is a Gaussian random proc ess with zero mean and is thus able to interrelate the autocorrelation and cross-correlation of different signals of the modulator, Two main equations describing the behavior of two different Delta Sigma topolo gies are derived. These two equations are generally nonlinear and can be of arbitrary order, hence approximations are used to study some int eresting cases, First, the nonlinear equations are linearized and solv ed analytically for first-order modulator with white inputs and numeri cally for colored inputs both with and without dithering. Also, a nume rical iterative approach is used for second and fourth order modulator s with white and colored inputs, In these cases, the variance of the o ne-bit quantizer input is found as a function of modulator input power , Next, the variance of the one-bit quantizer input is calculated when large amplitude oscillations are present assuming a large amplitude l imit cycle to have a sinusoidal autocorrelation. Finally, an attempt i s made to estimate the modulator's critical input power level beyond w hich these large amplitude limit cycles start.