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.