Heuristic finite-impulse-response filter design for cascaded ΣΔ modulators with finite amplifier gain

This study addresses a new digital calibration filter design for cascaded ΣΔ modulators with finite amplifier gain. A recent approach based on the H-infinity loop shaping method to this problem has the merit of obviating the use of an estimation or adaptive digital correction scheme, which thus reduces the complexity of circuit implementation. For the approach to be successful, it is critical to find an appropriate weighting function so as to make the gain responses of the uncertain noise transfer function (NTF) in a proper shape for improving signal-to-noise ratio (SNR). However, the search of such a weighting function is difficult in general. Moreover, the introduced weighting function increases filter order and hence circuit complexity. To circumvent this difficulty and the inherited drawbacks, this study presents a new noise shaping method for the problem. Considering that it is hard to decide the optimal shape of the uncertain NTF a priori, the authors propose a dual-band design to achieve the shape adjustment task. In particular, the range of lower frequency band is determined by SNR performance evaluation rather than being arbitrarily given a priori. This step is crucial and increases the chance of finding a better filter.