Effective dithering of digital delta-sigma modulators, with applications to fractional-N frequency synthesis

Abstract

Delta-sigma modulators, both analog and digital, are widely used in a vast range of modern electronic components such as data converters, fractional-N frequency synthesizers, all-digital phase-locked loops and power amplifiers. Digital delta-sigma modulators (DDSMs) have received less attention in the literature in comparison to analog delta-sigma modulators (ADSMs) despite the fact that digital implementations are at least as important as their analog counterparts. This thesis aims to enhance the theoretical understanding of the operation of DDSMs, with a view to developing novel applications for the most popular architectures, namely Error Feedback Modulator (EFM) and Multi stAge noise SHaping (MASH) DDSMs. 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. Over the past decade, much research has been carried out to find ways to reduce the magnitudes of the spurs produced by DDSMs. Dither generators based on linear feedback shift registers (LFSRs) are widely used to break up periodic cycles in DDSMs. Unfortunately, pseudorandom LFSRs are themselves periodic and therefore may have limited effectiveness. This first part of this thesis presents a rigorous mathematical analysis of DDSMs with LFSR-based dither, and a design methodology to achieve effective dithering. The second part of the thesis presents some practical applications arising from our theoretical work. A nested fractional-N frequency synthesizer which uses a bus-splitting DDSM to allow higher clock frequencies is developed. A MASH DDSM employing higher-order dither noise shaping to eliminate spurious tones is investigated. A mechanism for nonlinear distortion in fractional-N frequency synthesizers arising from the modulo nonlinearity of the DDSM is proposed.