Optimal (bandpass) continuous-time ΣΔ modulator

A systematic technique for designing a continuous-time sigma-delta modulator (ΣΔM) is presented. The continuous-time ΣΔ open-loop transfer function is obtained by the pulse-invariant transformation of its discrete-time equivalent. This method results in an inherently stable ΣΔM and does not need any loss factor to make the modulator stable, and so provides the maximum achievable signal-to-noise ratio. Properties of the continuous-time ΣΔM are described. The technique has been applied to-conventional lowpass and bandpass ΣΔMs, and a general-fourth-order bandpass example is given to illustrate the theory