Maximum SNR Analysis

Abstract

In this chapter an investigation is made of the apparent limit on the obtainable SNR of a 1-bit look-ahead sigma-delta modulator. The outcome of this investigation is that there is a point of maximal noise shaping, which depends on the filter order. At the point of maximal noise shaping the system is critically stable, and increasing the corner frequency of the loop filter above this point will not change the noise-shaping characteristics, i.e. the look-ahead system forces the same noise shaping as obtained for the critically stable point. If, instead of increasing the loop-filter corner frequency further, a higher filter order is selected in combination with a lower loop-filter corner frequency, a more aggressive noise shaping can be realized that results in a higher SNR. Since the more aggressive noise shaping causes a reduction of the stability of the sigma-delta modulator, more parallel paths are required to stabilize the system. Although with this approach a world-record SNR for a 1-bit noise-shaped signal has been achieved, it is still far away from the limits imposed by information theory. As such, in practice the SNR is only limited by the amount of available computational power that is required to stabilize the higher order filters.