Effective (Spur-Free) dithering of digital delta-sigma modulators with 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 can happen for a range of constant and periodic inputs. 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 produce spurs in the output spectrum. We call pseudorandom dithering effective if it breaks up periodic cycles in the modulator without producing its own spurs in the output spectrum. This paper presents rigorous mathematical analysis and a design methodology to achieve effective dithering.