A statistical technique for the determination of the noise power gain in higher-order Σ-Δ A/D converters excited by DC input signals

The existing techniques available for the statistical determination of the noise power gain (NPG) in general-order Σ-Δ A/D converters are based on the assumption that the quantizer input signal has a Gaussian distribution. However, empirical investigations reveal that this assumption holds true for the special case of the conventional first-order Σ-Δ A/D converters only. This paper presents an alternative technique for a more accurate determination of NPG for higher-order Σ-Δ A/D converters excited by DC input signals. This is achieved by employing the Gram-Charlier series for a (quasi-linear) modelling of the quantizer input signal. The proposed technique is based on the practical assumption that the constituent quantizer operates in its overload-free region. A typical practical application example is given to illustrate the main results.