A general approach to the AC and DC analysis of a class of sigma-delta modulator configurations

This paper is concerned with the determination of the output signal produced in response to AC and DC input signals for a general class of sigma-delta (Σ-Δ) modulator configurations. This is achieved by deriving an input signal bound for “overload-free” operation of the constituent coarse quantizer, and by using the result for the determination of the closed-form solution of the granular quantization error. It is shown that this closed-form solution can be used to replace the Σ-Δ modulator under consideration by an equivalent open-loop system. The resulting open-loop system is then exploited and applied to the determination of the shaped signal and noise components of the modulator output signal. An example is given to illustrate the application of the results to the AC and DC analysis of a conventional double-loop Σ-Δ modulator