Recent advances in the analysis, design and optimization of Digital Delta-Sigma Modulators

Abstract

Digital Delta-Sigma Modulators (DDSMs) are almost univerally used in integrated circuits for wireless communications and digital audio, particularly in fractional-N frequency synthesizers and oversampled digital-to-analog converters (DACs). A DDSM is a nonlinear dynamical system which reduces the wordlength of an oversampled digital signal without significantly degrading the SNR in the signal band. DDSMs can exhibit a number of behaviors that are characteristic of nonlinear dynamical systems such as oscillation, coexisting steadystate solutions, sensitivity to initial conditions, and sensitivity to the input. This paper explains the root cause of deterministic spurious and idle tones in DDSMs-short periodic cycles-and describes strategies to eliminate them. The use of a DDSM simplifies the design of analog circuitry in a mixed-signal system. By reducing the bus width in a prescribed way, a DDSM can also permit more efficient downstream digital signal processing-in terms of power and speed-with negligible degradation in performance.

An Exposition of Fractional Spurs Resulting From Nonlinear Distortion

“…Spur-free operation is guaranteed both before and after application of this nonlinearity if the quantizer is designed 4 We expect the quantizer to demonstrate spur-free operation for both the nonlinear mapping function, N : x → x 6 , and the linear mapping function L : x → x. Spur-free operation could be achieved with T = 2 if an accurate description of the transfer function was available in place of an estimate of the nonlinearity, but the solution presented here is robust to scaling inaccuracies in the nonlinearity estimate. 5 While it is entirely possible to implement a quantizer which produces an odd amplitude, for virtually all quantizers described in the literature the amplitude of t is even because the output, y, is full-scale. such that it implements P t (m− nα , n) values which produce a constant µ t [n] and µ tnl [n].…”

“…Fractional spurs sometimes occur as a result of cycles that can arise during the normal operation of the quantizer. Advances in quantizer design over two decades, many of which are summarized in a recent review [5], have eliminated these intrinsic spurs. In this work, we will assume throughout that the output of the quantizer itself is spur-free.…”