This paper introduces an ultra-low power 1.7-2.7-GHz fractional-N sub-sampling digital PLL (SS-DPLL) for Internet-of-Things (IoT) applications targeting compliance with Bluetooth Low Energy (BLE) and IEEE802.15.4 standards. A snapshot time-to-digital converter (TDC) acts as a digital sub-sampler featuring an increased out-of-range gain and without any assistance from the traditional counting of DCO edges, thus further reducing power consumption. With a proposed DCO-divider phase rotation in the feedback path, the impact of the digital-to-time converter's (DTC's) non-linearity on the PLL is reduced and improves fractional spurs by at least 8 dB across BLE channels. Moreover, a “variable-preconditioned LMS” calibration algorithm is introduced to dynamically correct the DTC gain error with fractional frequency control word (FCW) down to 1/16384. Fabricated in 40 nm CMOS, the SS-DPLL achieves phase noise performance of -109 dBc/Hz at 1 MHz offset, while consuming a record-low power of 1.19 mW.@en