A Systematic Design Methodology for Optimization of Sigma-Delta Modulators Based on an Evolutionary Algorithm

Abstract

In the design of sigma-delta modulators (<inline-formula> <tex-math notation="LaTeX">$\Sigma \Delta $ </tex-math></inline-formula>Ms), different variables need to be optimized together in order to maximize the performance. This design task has the added difficulty of dealing with the non-linear behavior of the quantizer. Although a linearized model of the quantizer can be used, this may result in significant discrepancies between the predicted and actual behavior of the <inline-formula> <tex-math notation="LaTeX">$\Sigma \Delta \text{M}$ </tex-math></inline-formula>. To better predict the behavior of a given design, we propose a design methodology for <inline-formula> <tex-math notation="LaTeX">$\Sigma \Delta $ </tex-math></inline-formula>Ms based on a genetic algorithm (GA) that uses both linear equations and simulations. In order to reduce the computation time, the design solution is initially evaluated using equations and only if the performance is deemed good enough, it is subjected to a more refined simulation. This more precise simulation takes into account thermal noise, finite output swing, and gain (among other non-idealities) of the building blocks of the modulator. Moreover, Monte Carlo (MC) analyses are performed during the optimization in order to assess the sensitivity to component variations of the solutions. In order to demonstrate the validity and robustness of the proposed optimization methodology, several <inline-formula> <tex-math notation="LaTeX">$\Sigma \Delta $ </tex-math></inline-formula>Ms designs are presented, together with the corresponding measured results.