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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \Sigma $ </tex-math></inline-formula> 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.
Highlights
F RACTIONAL-N frequency synthesizers are capable of generating signals with a precisely-defined frequency
A fractional-N phase locked loops (PLL) can synthesize a frequency that is a rational multiple of the reference fre f
9It is worth specifying that the analysis presented in [9] approximates a piecewise linear (PWL) nonlinearity by a quadratic
Summary
F RACTIONAL-N frequency synthesizers are capable of generating signals with a precisely-defined frequency. A fractional-N PLL can synthesize a frequency that is a rational multiple of the reference fre f This is obtained by modulating the control word of the multi-modulus divider (MMD) that implements frequency division in the feedback path of the loop. If the DDSM is properly designed, its quantization error will be high-pass shaped and spur-free [1], [2], in order not to degrade the close-in phase noise performance of the PLL This works as long as the system is linear but, it does not correspond to reality. The instantaneous division ratio can be expressed as Nint + y[n], where Nint is a fixed integer and y[n] is the time-varying integer output of the DDSM The latter term has an average equal to the fractional value α = X M , where.
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