This article introduces a low-jitter low-spur fractional-N phase-locked loop (PLL) adopting a new concept of a time-mode arithmetic unit (TAU) for phase error extraction. The TAU is a time-signal processor that calculates the weighted sum of input time offsets. It processes two inputs-the period of a digitally controlled oscillator (DCO) and the instantaneous time offset between the DCO and reference clock edges-and then extracts the DCO phase error by calculating their weighted sum. The prototype, implemented in 40-nm CMOS, achieves 182-fs rms jitter with 3.5-mW power consumption. In a near-integer channel, it shows the worst fractional spur below −59 dBc. Under considerable supply or temperature variations, the worst spur still remains below −51.7 dBc without any background calibration tracking. Index Terms-Digital-to-time converter (DTC), fractional spur, phase-locked loop (PLL), process voltage and temperature (PVT), time-mode arithmetic unit (TAU).
I. INTRODUCTIONT HE sub-sampling technique [1], [2], [3], [4], [5] and, more specifically, the narrow-range phase-detection concept [6], [7] have contributed to a significant improvement of phase noise (PN) in phase-locked loops (PLLs). Such techniques ensure that the phase detector (PD) can expect a