Folded Noise Prediction in Nonlinear Fractional-N Frequency Synthesizers

Abstract

The presence of nonlinearities in a fractional-N frequency synthesizer leads to the generation of an additional component of noise that appears in the output phase noise spectrum. This nonlinearity-induced noise component manifests itself as spurious tones and an elevated noise floor, also known as folded noise. This paper presents a mathematical analysis of the folded noise generated in fractional-N phase locked loops (PLL) by the interaction between the quantization noise introduced by the divider controller and a nonlinearity. The analysis is performed for different digital modulators (DDSM) and nonlinearities, providing expressions that allow one to predict the folded noise. These are compared with state-of-the-art predictions and simulation results.

A Family of ΔΣ Modulators With High Spur Immunity and Low Folded Nonlinearity Noise When Used in Fractional- Frequency Synthesizers

“…However, a wider range for the accumulated quantization error would lead to stronger interaction with the nonlinearity and, qualitatively, a higher level of folded noise. The level of the noise floor can be predicted using methods such as those presented in [11], [20] and [29]. For the sake of simplicity, in this paper we will estimate the severity of the generated folded noise with σ 2 e acc , the variance of the accumulated quantization error.…”

“…This assumption about e[n] is only an approximation; however, it allows one to obtain an accurate estimate of the statistical properties of e acc [20]. We will use this assumption later in the paper for evaluating the probability distribution of e acc .…”

“…In particular, the higher the order of the MASH modulator, the higher is the order of the polynomial nonlinearity up to which the modulator is immune from spurs. However, just like the SR, as the order of the MASH DDSM increases, so does the level of folded noise that it introduces [20].…”

“…In this paper, we introduce a family of DDSMs, called Enhanced Nonlinearity-induced nOise Performance digital modulators (ENOP-DDSMs) which, like the SR, can achieve immunity to spurs for memoryless polynomial nonlinearities of up to a certain order. The flexibility of the architecture, underpinned by an analytical evaluation of the spurious behavior [21] and folded noise generation [20], allows one to design an ENOP-DDSM that achieves the same level of spur immunity that can be achieved by the best SRs and PMRs, but with a lower folded noise floor.…”