A Fractional-Order Noise-Shaping Integrator for Sigma-Delta Modulator

Abstract

A novel fractional-order Sigma-Delta modulator, which can improve the signal to noise ratio (SNR) and is of robust stability of a high order Sigma-Delta modulator, is presented in the paper. Traditional Sigma-Delta modulator mainly focused on forming an integer high order integrator to improve the SNR, whereas the paper presents a fractional-order integrator instead to obtain higher SNR and better stability. Specifically, a 4th order digital integrator and a fractional-order PIλ controller are inserted between the AFE and the quantizer. The 4th order digital integrator increases overall loop order to produce much higher SNR for Sigma-Delta modulator and the fractional-order PIλ controller allows fine tuning accuracy in seeking the coefficients for Sigma-Delta modulator and provides stability in the placement of poles and zeros for compensating the phase delays caused by system nonlinearity. The parameters of PIλ controller are optimized by using swarm intelligent optimization algorithm. The stability of the proposed fractional-order Sigma-Delta modulator is analyzed and the robustness of the proposed fractional-order Sigma-Delta modulator is demonstrated. Further simulation from the fractional-order Sigma-Delta modulator, results of SNR>145dB and the noise floor under -190dB are obtained in frequency range of [5-150Hz].