The synthesis of noise transfer functions for bandpass delta-sigma modulators with tunable center frequency

This paper presents a method to synthesize the noise transfer function (NTF) for tunable bandpass delta-sigma modulators, where the quantization noise stopband can be programmed over the whole Nyquist range. Instead of relying on traditional filter design theory, the proposed method allows to create NTFs of arbitrary order by directly placing the zeros and poles on the z-plane. The advantage is that the NTF can be re-calculated for each center frequency by using simple closed form expressions, thus avoiding the need of large lookup tables to store multiple pre-computed coefficient sets. Extensive system-level simulations show that our method yields equal performance as the Chebyshev-II design method. As an example, the synthesis of a binary 12th-order tunable bandpass delta-sigma modulator is demonstrated, and its stability is proven for any choice of the center frequency.