Design and optimization of a class of oversampled sigma-delta D/A converters by employing genetic algorithms

In a preceding paper, a genetic algorithm was developed for the design and optimization of higher-order oversampled Sigma-Delta digital-to-analog (D/A) converters having cascade-of-resonators and cascade-of-integrators configurations. This paper is concerned with the genetic-algorithm optimization of the corresponding combined cascade-of-resonators/cascade-of-integrators (CRI) Sigma-Delta D/A converters. The salient feature of CRI Sigma-Delta D/A converters is that the constituent signal and noise transfer functions become complimentary by the converter configuration proper, simplifying the design process to the realization of the constituent noise transfer function. Moreover, the configuration proper places the noise transfer function zeros on the unit-circle, making it possible to obtain high signal-to-quantization-noise ratios. The underlying genetic algorithm for the optimization of the noise transfer function guarantees that after the application of the operations of crossover and mutation to the parent noise transfer functions, the resulting offspring noise transfer functions are (inherently) BIBO stable. The usefulness of the proposed technique is demonstrated through its application to the design of a sixth-order lowpass CRI Sigma-Delta D/A converter employing a 64 time oversampling ratio for a final realization incorporating 16-bit multiplier values