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

A 3
^rd
-order Sigma-Delta modulator with a PI
^λ
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 1
^st
-order digital integrator and a fractional-order PI
^λ
controller are inserted between the AFE and the quantizer. The 1
^st
-order digital integrator can increase overall loop order to produce much higher SNR for Sigma-Delta modulator and the fractional-order PI
^λ
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 PI
^λ
controller are optimized by using swarm intelligent optimization algorithm. The performance and stability of the proposed 3
^rd
-order Sigma-Delta modulator with PI
^λ
controller are analyzed and demonstrated, respectively.