Design of Sigma–Delta Modulators With Arbitrary Transfer Functions

Abstract

This paper addresses the design of sigma-delta modulators with arbitrary signal and noise transfer functions using a genetic algorithm (GA)-based search method. The objective function is defined to include the difference D between the magnitude of the frequency responses of the designed transfer functions and the ideal one, the quantizer gain lambdacritical for which the poles of the modulator start moving out of the unit circle, and the spread of the coefficients S. Stability can be improved by reducing lambdacritical while a smaller S reduces the implementation complexity. A GA searches for poles/zeros of the transfer functions to minimize the objective function D+w1*lambdacritical+w2*S, where w1 and w2 are two weighing factors. Numerical results demonstrate the effectiveness of the proposed method