An $H_{\infty }$ Approach for Robust Calibration of Cascaded Sigma–Delta Modulators

In this paper, we propose a novel robust H _infin optimization approach to the design of digital filters for calibrating 2-1 cascaded sigma-delta (SD) modulators. The main contribution of this paper consists of two parts. First, we develop a new filter design technique based on linear matrix inequalities applied to a model-matching problem with polytopic uncertainties in parameters. The advantage of the proposed method is that it leads to an optimal, less conservative, solution to the robust H _infin filtering problem. The second contribution involves the application of the proposed robust filter design scheme to correct for inevitable and unwelcome analog imperfections typically associated with cascaded SD modulators. For numerical illustration we concentrate on the 2-1 architecture. Simulation results for a range of parameter excursions suggest that our robust H _infin filter guarantees an improved signal-to-noise ratio performance over the nominal filter.