Loop-Filter Design and Analysis for Delta-Sigma Modulators and Oversampled IIR Filters

Abstract

Delta-sigma modulators spectrally shape quantization noise in discrete systems and are used extensively in communications and signal-processing systems. They are implemented using a loop-filter that processes the input and feed-back signals such that the closed loop behavior has a separate signal transfer function (STF) and noise transfer function (NTF). Loop-filter design often relies on special cases for the NTF or simplified loop-filter structures. This paper presents a method for generalized loop-filter synthesis that can implement a chosen NTF and STF independent of internal loop-filter structure or filter order. The transfer functions are formulated as polynomials of integration, $(z-1)^{-n}$ , instead of delay, $z^{-n}$ , to enable practical numerical loop-filter synthesis even for high-order and highly oversampled loop-filters. An example design shows how to use this synthesis method to design a high-order modulator that directly filters and re-modulates a direct stream digital audio signal.