3.7 A 16MHz X0 with 17.5μs Startup Time Under 10⁴ppm-ΔF Injection Using Automatic Phase-Error Correction Technique

The start-up time $(\mathsf{T}_{\mathsf{S}})$ of MHz crystal oscillators (XOs) has significantly influenced the power consumption of duty-cycled Internet-of-Things (loT) systems. The injection techniques [1–5] have gained popularity for effectively reducing the start-up time and start-up energy $(\mathsf{E}_{\mathsf{S}})$ of XOs. Nonetheless, high-efficiency injection is guaranteed only when the frequency mismatch (ΔF) between the injection frequency (F INJ ) and the XO frequeny $(\mathsf{F}_{\mathsf{X}0})$ is less than 5000ppm for conventional injection. For best results, $\Delta \mathsf{F}$ should be within 2500ppm [1]. As shown in Fig. 3.7.1, for each $\Delta \mathsf{F}$ , there exists a corresponding maximum motional current (i M ), e.g., 65μA for 5000ppm. This is the limitation to the energy injection and T S reduction, especially for large $\Delta \mathsf{F}$ . Since small $\Delta \mathsf{F}$ is difficult to achieve across PVT with on-chip oscillators, it is necessary to develop XO circuits with high tolerance for large $\Delta \mathsf{F}$ In [1]. dithering injection can tolerate ΔF of 2x10 ⁴ ppm but is implemented inefficiently with $\mathsf{T}_{\mathsf{S}} > 10$ 'cycles. Synchronized signal injection [2] realigns the injection signal with the crystal resonance every fixed time, but every single chip needs to calibrate the cycles of each burst for different $\Delta \mathsf{F}$ . 2-step injection [3] employs a phase-locked loop (PLL) to match $\mathsf{F}_{\mathsf{INJ}}$ with $\mathsf{F}_{\mathsf{X}0}$ , but it has to inject with $\Delta \mathsf{F}\leq 5000\mathsf{ppm}$ first. In addition, both [2] and [3] have to suspend the injection during the start-up, which adds to T s overhead. Impedance-guided chirp injection [4] calibrates F 'NJ when chirping inefficiently, which restricts T s reduction. Precisely timed injection [5] reduces $\mathsf{T}_{\mathsf{S}}$ by terminating injection precisely at $\mathsf{T}_{\mathsf{INJ,OPT}}$ which is significantly influenced by $\Delta \mathsf{F}$ . The inevitable $\Delta\mathsf{F}$ : results in the phase error $\Delta\varphi(\Delta\varphi=\Delta \mathsf{t}\cdot 2\pi \cdot \mathsf{F}_{\mathsf{INJ}},)$ where Δt is the time difference between the voltage peak of crystal resonance and the falling edge of injection signal), $\Delta \varphi$ will accumulate to a point where injection starts to counteract the crystal resonance without any correction. This work presents an automatic phase-error correction (APEC) technique that can correc $\Delta\varphi$ automatically, achieving $\mathsf{T}_{\mathsf{S}}$ of about 18μs with $\Delta \mathsf{F}{-}$ tolerance up to 104ppm.