A PIλ controller for a 3rd-order Sigma-Delta Modulator

A 3rd-order Sigma-Delta modulator with a PIλ controller is proposed in this paper to improve the signal to noise ratio (SNR) and system stability. Traditional Sigma-Delta modulator mainly focused on forming an integer high order integrator to improve the SNR, whereas this paper presents a fractional-order controller instead to obtain higher SNR and better stability. Specifically, a 1st-order digital integrator and a fractional-order PIλ controller are inserted between the AFE and the quantizer. The 1st-order digital integrator can increase 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 integrator parts. The parameters of PIλ controller are optimized by using swarm intelligent optimization algorithm. The performance and stability of the proposed 3rd-order Sigma-Delta modulator with PIλ controller are analyzed and demonstrated, respectively.