A novel genetic algorithm with applications to the design of higher-order sigma-delta D/A converters

The main fundamental problem in the existing genetic-algorithm-based techniques for the optimization of IIR digital filters stems from the fact that after the application of the constituent operations of crossover and mutation to the parent IIR digital filters, the resulting offspring IIR digital filters may cease to be BIBO stable. This paper presents a novel technique for the genetic optimization of IIR digital filters where the offspring IIR digital filters are guaranteed to be (inherently) BIBO stable. The resulting technique is particularly suitable for the optimization of the noise transfer function for Σ-Δ D/A converters. This is due to the fact that the classical IIR digital filter transfer function approximation techniques lead to the formation of delay-free loops in the D/A converter configuration proper. The usefulness of the proposed technique is demonstrated through its application to the design of a set of two 6-th order lowpass Σ-Δ D/A converters employing 64-times oversampling ratios for a final realization incorporating 8-bit multiplier coefficients.