Robust Calibration of an Improved Delta-Sigma Data Converter Using Convex Optimization

In this paper, we analyze that analog circuit imperfections in the cascaded delta-sigma modulators may lead to the incomplete noise cancellation from the earlier stages, as well as non-unit transfer function from the input signal to the output, resulting in the degradation of signal-to-noise ratio (SNR) performance. It is difficult to design one digital filter to compensate the effects from both the incomplete noise cancellation and non-unit transfer function. We therefore proposed a novel architecture of cascaded delta-sigma modulators which consist of feedforward and feedback loops. Under this structure, the transfer function from the input signal to the output is always unit even though there exist analog circuit imperfections. The rest of the design therefore, is only to consider to reduce the effect of the incomplete noise cancellation as small as possible, which is formed as a robust H₂ optimization problem. This problem can be recast as a convex optimization problem by the change of variables, congruence transformations and Schur complement, which is easily solved by reliable and efficient numerical algorithms. To prove the advantages of the architecture and the design method, we conduct numerical simulations on 2-2 cascaded delta-sigma modulators. Simulation results for a range of parameter excursions show that our proposed filter improves SNR performance over the nominal filter greatly.