Spurious tones in digital delta-sigma modulators resulting from pseudorandom dither

Digital delta-sigma modulators (DDSMs) are finite state machines; their spectra are characterized by strong periodic tones (so-called spurs) when they cycle repeatedly in time through a small number of states. This happens when the input is constant or periodic. Pseudorandom dither generators are widely used to break up periodic cycles in DDSMs in order to eliminate spurs produced by underlying periodic behavior. Unfortunately, pseudorandom dither signals are themselves periodic and therefore can have limited effectiveness. This paper addresses the fundamental limitations of using pseudorandom dither signals that are inherently periodic. We clarify some common misunderstandings in the DDSM literature. We present rigorous mathematical analysis, case studies to illustrate the issues, and insights which can prove useful in design.