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 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 lambda_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 lambda_critical 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*lambda_critical+w₂*S, where w₁ and w₂ are two weighing factors. Numerical results demonstrate the effectiveness of the proposed method