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. ... Read more

We present a broadband digital PLL (DPLL)-based phase modulator supporting wide frequency modulation (FM) bandwidth (BW). It compensates for the EVM degradation due to the non-uniform period of the retimed updating clock and shortens the nonlinearity calibration time of the digitally controlled oscillator (DCO) with a phase-domain digital pre-distortion (DPD) and an encoding-assisted (EA)-LMS calibration. While generating a 10MHz 64-PSK signal, the prototype can achieve -46dB EVM with less than one-tenth of the calibration samples (time) required by the prior art. ... Read more

In a fractional-N PLL, it is beneficial to minimize the input range of its phase detector (PD) as it promotes better linearity and higher PD gain for suppressing noise contributions of the following loop components. This can be done by canceling the predicted instantaneous time offset between the frequency reference (FREF) and the variable oscillator-clock (CKV) edges prior to the PD. There are currently two main cancellation strategies. The first is to align FREF and CKV by inserting a digital-to-time converter (DTC) on either path. However, due to the DTC nonlinearity and its susceptibility to PVT variations, the PLL can suffer from large fractional spurs. Although system-level techniques, e.g., background calibration [1], supply ripple reduction [2], and DTC code randomization [3], can partially alleviate these DTC issues, the overall system complexity worsens. The second method is to convert and cancel the predicted time offset in the voltage domain [4]. This arrangement is less sensitive to PVT variations. However, the accuracy of the time-to-voltage conversion relies on the strict trade-offs between the power consumption, noise, and linearity of a current source. In this work, we introduce a third solution based on a time-mode arithmetic unit (TAU), which outputs a weighted sum of time delays between the (falling) edges of FREF and CKV, as well as between two consecutive CKV edges. Compared with DTC-based solutions, it is less sensitive to PVT variations, as its output merely varies by the ratio of RC time constants, thus ensuring low fractional spurs with no extra system complexity. Compared to the voltage-domain solutions, the absence of a current source is beneficial for phase-noise optimization and migration to more advanced technology nodes. Moreover, TAU can implicitly provide a time-amplification (TA) gain, thus further suppressing the noise of subsequent blocks. ... Read more