Noise transfer function design for delta-sigma modulators using the Gegenbauer polynomial
Abstract An efficient noise transfer function (NTF) is central to the design of a delta-sigma modulator (DSM). A popular method for designing an NTF is based on the placement of its zeros optimally in the frequency band of interest such that the in-band energy is minimized. The poles of the NTF, however, are those of a maximally-flat all-pole filter. The limitation of this method is that when the oversample ratio (OSR) of the DSM is low, the 3-dB cutoff frequency of the denominator polynomial of the NTF may approach the edge of the passband of the NTF. This causes the zeros to no longer be optimal. In this paper, we present a method of designing an NTF based on the Gegenbauer polynomial which does not have this limitation. We show that the signal-to-quantization noise ratio (SQNR) of the NTFs designed with our method is significantly better than that of the NTFs designed using the well-known method.