Hybrid PLLs (HPLLs) leverage the advantages of conventional analog and digital PLLs to cater to the high integration demand inherent with the advanced CMOS nodes, among which the charge-sharing (CS) integrator-based HPLL featuring ultra-compact area and ultra-low power consumption exhibits promising prospects. This work presents a comprehensive analysis concerning the CS integrator-based HPLL for the first time. The behavioral modeling is first conducted with a time-domain event-driven modeling method to simulate the piecewise-linear modulations on the oscillator frequency A noise model considering the slow-fast clock domain transitions and the digital-analog signal transitions inherent with the architecture is further proposed. The proposed models offer precise PN PSD estimations over the specified frequency range under all simulated conditions, whose integrated jitters differ by less than 5 fs compared with circuit simulations. The additional nonlinearity induced by the CS integrator is also considered, and an analytical prediction approach for the nonlinearity-induced spurs is presented, showing a capability of predicting the locations and amplitudes of the most significant spurious tones with a less than 4 % deviation in the relative offset frequency and a less than 5 dBc deviation in the relative amplitude.

This work presents a compact and power-efficient kHz-range relaxation (RC) oscillator with robust performance against temperature and voltage variations. By deliberately introducing a negative-offset voltage into the comparator, an offset cancellation scheme leveraging chopping and piecewise charge-acceleration facilitates a low temperature coefficient. A low-power comparator with a tail resistor and a low oscillation amplitude improves the energy efficiency. The die area is compact by introducing leakage-based temperature compensation that eliminates bulky resistors and complex calibration. Prototyped in a 28-nm CMOS process and measured at 28.5 kHz, our oscillator occupies 0.0046 mm$^{2}$and dissipates 27.6 nW at a 0.8-V supply. The energy efficiency is 0.97 nW/kHz, and the temperature coefficient is 33.3 ppm/$^{\circ}$C over$-$40 to 85$^{\circ}$C with 1-point calibration. The corresponding FoM of 164.9 dB compares favorably with the recent arts. The start-up time is rapid, and the period settling time is within one cycle of$\sim$5.7$\mu$s. The Allan deviation is$\le $40 ppm for measurement intervals of$>$0.5 s.

In this brief, a charge-prestored 21.2-MHz relaxation oscillator is proposed for ultralow-power applications. It occupies only 0.0043 mm2in 0.18-$\mu \text{m}$CMOS by resistor reusing and is reference-free. The simulated temperature coefficient (TC) of the output frequency is 15.2 ppm/° from −30 °C to 125 °C. By generating an asymmetric capacitor charging swing, our charge-prestored technique reduces significantly the power consumed by the swing-boostingRCnetwork during the charging phase. Also, the R-RCstructure further improves the energy efficiency. The total power consumption of the oscillator core is$1.806 \mu \text{W}$at 0.8 V, corresponding to an energy efficiency of$0.085 \mu \text{W}$/MHz that compares favorably with the state of the art.

An accurate performance evaluation of jitter-power figure-of-merit (FOM) for multiplying delay-locked loop (MDLL) is presented. For a typical MDLL employing a single-ended multiplying-delay ring voltage-controlled oscillator (MDVCO), it can be tuned via the capacitive loads to uphold a constant normalized phase noise (PN) across different frequencies for better jitter-power performance. Linear approximation and z-domain PN model are utilized to simplify the analysis with excellent agreement between the time-domain simulation and z-domain approximation. The influences of the asymmetric waveform, flicker noise corner, frequency error and reference noise are also discussed and then ignored based on the reasonable approximation. Under a given process, reference clock frequency and supply voltage, the ideal FOM can be derived theoretically. Based on these insights, the predicted FOM can be the benchmark metric in the design of MDLL for the possible best jitter-power performance.