10.5 A 76 fsrms- Jitter and -65dBc- Fractional-Spur Fractional-N Sampling PLL Using a Nonlinearity-Replication Technique

Sampling PLLs (SPLLs) are currently the most popular architecture for generating ultralow-jitter signals due to their high-gain sampling phase detectors (SPDs) that can significantly reduce in-band phase noise (PN). However, to maintain this advantage even in the fractional- N mode, SPLLs must remove the quantization error (Q-error) of the $\Delta \Sigma \mathrm{M}$ very precisely. The use of a digital-to-time converter (DTC) before the SPD [1] (top left of Fig. 10.5.1) is a common solution, but the inherent non-linearity (NL) of the DTC, i.e., $NL _{\mathrm{DTC}}$, introduces fractional spurs and the leakage of the Q-error, which increases the inband PN. There are two approaches that are used widely to reduce $NL _{\mathrm{DTC}}$. The first approach (①) is to use a typical DTC and then compensate for $NL _{\mathrm{DTC}}$ using a digital pre-distortion (DPD) that modifies the accumulated $\Delta \Sigma \mathrm{M}$ code, i.e., $D_{\mathrm{AQ}}$, to have the inverse function of $NL _{\mathrm{DTC}}$ [2]. However, this technique requires significant design resources (in terms of power and area) to achieve high accuracy. The second approach (②) is to design a linear DTC with an inherently small $NL _{\mathrm{DTC}}$. The constant-slope DTCs (CS-DTCs) reduced $NL _{\mathrm{DTC}}$ by charging a capacitor with the same ramp rate regardless of the initial voltage determined by $D_{\mathrm{AQ}}$. The inverse constant-slope DTC (ICS-DTC) [3] further reduced $NL _{\mathrm{DTC}}$ by generating the initial voltage by controlling the precharging time as a multiple of the VCO period $(T_{\mathrm{VCO}})$, i.e., $k\cdot T_{\mathrm{VCO}}$ (k is an integer), to remove the voltage dependence of the capacitor and the current. However, the downside is that a longer precharge time (or $k\cdot T_{\mathrm{VCO}}$) is required to achieve the higher DTC resolution, which increases the thermal noise of the DTC and hence the in-band PN.