Some remarks on the stability and performance of the noise shaper or sigma-delta modulator

Stability Analysis of Higher-Order Delta-Sigma Modulators for Sinusoidal Inputs

“…Since the poles of the denominator (1 +KH(z)) determine the stability of the modulator, for a given H(z), there will be a certain interval [Kmin, Kmax] for which the modulator is stable [4]. Assuming q(k) to be Gaussian white stochastic G(O, Gq2) and the transfer function between q(k) and y(k) to be known, then the output noise variance is given by:…”

A sixth-order continuous-time bandpass sigma-delta modulator for digital radio IF

“…The quantizer model should be adequate for an accurate stability analysis. Commonly, the one-bit quantizer is modeled by a linear, signal-dependent gain [12], [13]. However, when using this model, the describing function method fails to predict small-signal stability issues such as idle patterns and instability under zero-input and zeroinitial state conditions.…”

“…The zero phase error solution set can be simplified by substituting (12) into (10). Using Bezout's theorem [24] gcd (14) Equation (10) is reduced to even odd (15) For input frequencies equal to a rational fraction of the sample frequency, the solutions in are equidistant.…”

Optical oversampled analog-to-digital conversion

“…An Nnh-order error diffusion modulator which uses a transversal filter with coefficient weighting described by Equation (2.13) is shown in Figure 2.9. For modulators with N > 2 and filter weights described by Equation (2.13), stability of the feedback loop is an issue that must be addressed [27].…”