Design methodology for Sigma-Delta modulators based on a genetic algorithm using hybrid cost functions

The design of Sigma-Delta modulators (ΣΔMs) encompasses different variables that need to be optimized together in order to maximize the performance. The design task is even more complex due to the non-linear behavior of the quantizer. Typically, a linearized model of the quantizer is used to obtain linear equations that predict the performance of the modulator, which may cause significant discrepancies between the predicted and actual behavior of ΣΔMs. To better predict the behavior of a given design solution, we propose a design methodology for ΣΔMs based on a genetic algorithm (GA) that uses both linear equations and simulations: the design solution is evaluated using the equations and, if the performance is good enough, it will be evaluated trough simulation. This hybrid cost function allows to use a GA with a large population and, therefore, obtains the best possible design solution. The hybrid cost function takes thermal noise, quantization noise, voltage swing variations and stability of the modulator into account. Furthermore, it also selects the design solution that is the most insensitive to component variations. The design of a continuous-time (CT) and a discrete-time (DT) ΣΔM are given as proof-of-concept.