A two-stage genetic algorithm for the design and optimization of resonator/integrator based sigma-delta A/D and D/A converters

In preceding papers, a genetic algorithm was developed for the design and optimization of the noise transfer function in higher-order Sigma-Delta A/D and D/A converters having cascade-of-resonators (COR), cascade-of-integrators (COI), and combined cascade-of-integrators-cum-resonators (CRI) configurations. This paper presents a two-stage genetic-algorithm for the optimization of the constituent multiplier coefficient values in COR, COI, and CRI Sigma-Delta D/A converter structures after a corresponding noise transfer function optimization. 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, COR and COI Sigma-Delta A/D converters employing a 64 time oversampling ratio for a final realization incorporating 32-bit multiplier coefficient values