Improved design of noise transfer functions with monotonic passband response for Delta-Sigma modulators

A method for the design of a noise transfer function (NTF) is presented in which the stopband of a continuous-time high-pass filter with monotonic passband characteristics is minimised by optimally placing an arbitrary number of imaginary-axis zeros. Towards this end, the Papoulis, Halpern, and least-squares monotonic polynomials have been used in the high-pass filter design. The NTF is derived by applying the bilinear transformation on a continuous-time high-pass filter that minimises the in-band energy and satisfies all the realisability constraints of a Delta-Sigma modulator (DSM). By way of examples, it is shown that the signal-to-quantisation noise ratio achieved by the NTF designed by the proposed method is higher than that obtained by the NTF designed using a recently published method. The signal-to-noise ratio of the NTF designed with the proposed method is higher for a wide range of signal amplitude.