4.3 A 76.7fs-lntegrated-Jitter and −71.9dBc In-Band Fractional-Spur Bang-Bang Digital PLL Based on an Inverse-Constant-Slope DTC and FCW Subtractive Dithering

Ultra-low-jitter and high-spectral-purity frequency synthesizers are key building blocks for high-performance wireless transceivers and $\text{FMCW}$ radars. A bang-bang $\text{PLL} (\text{BBPLL}$ ) is an attractive solution thanks to its small footprint and low power consumption; however, its operation in the $\text{fractional-N}$ mode is hindered by the large quantization error $(\text{Q-error})$ I caused by the non-integer frequency multiplication saturating the narrow input range of the bang-bang phase detector $(\text{BBPD})$ . A digital-to-time converter $(\text{DTC})$ is typically used to cancel the $\text{Q-error}$ in time domain [1] (Fig. 4.3.1 top-left). Unfortunately, the $\text{DTC}$ non-linearity can generate significant fractional spurs, thus corrupting the $\text{PLL}$ spectral purity and integrated jitter. Solutions to this problem rely on either improving the $\text{DTC}$ linearity or adopting a suitable randomization of the $\text{Q-error}$ sequence to generate lower spurs in the presence of the $\text{DTC}$ non-linearity. The constant slope $\text{DTC} (\text{CS-DTC})$ achieves superior linearity among $\text{DTC}$ architectures [2], even if further improvements are limited by the voltage sensitivity of current generators $(\text{CGs})$ and parasitic capacitances as well as by the non-linearity of the digital-to-analog converter $(\text{DAC})$ adopted in the circuit. On the other hand, those randomization techniques to reduce spurs typically require a larger $\text{Q-error}$ range [3], [4] that increases $\text{PLL jitter}$ for two reasons: the higher quantization-noise power and the larger random jitter induced by the wider range needed for the $\text{DTC}$ . This work introduces a $9.25-\text{to}-10.5\text{GHz} \text{fractional-N BBPLL}$ achieving $-71.9\text{dBc}$ fractional spur and a total rms jitter (including spurs) of $76.7\text{fs}$ at near-integer channels leveraging: $(\mathrm{i})$ a $\text{DTC}$ architecture (denoted as $inverse constant-slope DTC)$ I overcoming the $\text{CS-DTC}$ limitations and $(\text{ii})$ a $\text{Q-error}$ randomization technique (denoted as $FCW$ subtractive dithering), which keeps the $\mathrm{Q}- \text{error}$ range constant thus not degrading $\text{PLL jitter}$ .