Design of sigma-delta modulators with arbitrary transfer functions

This paper addresses the design of sigma-delta modulators with arbitrary signal and noise transfer functions by presenting 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 λ_critical 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 λ_critical while a smaller S reduces the implementation complexity. A genetic algorithm (GA) searches for poles/zeros of the transfer functions to minimize the objective function D+w₁*λ_critical+w2*S, where w₁ and w₂ are two weighing factors. Numerical results demonstrate the effectiveness of the proposed method.