Unified Analysis of Digital Delta-Sigma Modulators for Fractional-N Frequency Synthesis: Introducing the PASS Family of DDSMs
Unified Analysis of Digital Delta-Sigma Modulators for Fractional-N Frequency Synthesis: Introducing the PASS Family of DDSMs
Abstract
To enable fractional-N frequency synthesis in a phase locked loop (PLL), the instantaneous division ratio of a multi-modulus divider is usually controlled by a digital ∆-Σ modulator (DDSM). The accumulated quantization error (AQE) of the DDSM is injected into the loop. When distorted by inevitable nonlinearities within the loop, the distorted AQE gives rise to fractional spurs; these degrade the spectral purity and jitter of the synthesized signal. In this paper, we present a unified analysis of representative DDSMs in terms of their architectures and working principles. Their AQE’s variation range, variance (power), statistical distribution, spectral signature, and immunity to fractional spurs in the presence of nonlinear distortions are also characterized. In particular, we study and compare the classic family of Multi-stAge noise-SHaping (MASH) DDSMs and two state-of-the-art families: probability-density-shaping (PDS) and Enhanced Nonlinearity-induced nOise Performance (ENOP) DDSMs. Building on the prior art, we propose a novel family of Probability density And Spectral envelope Shaping (PASS) DDSMs which, while guaranteeing the maximum spur immunity for a given variation range of the AQE, also provide optimized shaping for fractional-N frequency synthesis in terms of both the probability distribution and spectral envelope of the AQE to avoid high frequency phase noise “bumps†and/or “plateausâ€.
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