A 16MHz X0 with 17.5μs Startup Time Under 10ppm-ΔF Injection Using Automatic Phase-Error Correction Technique

Zhikuang Cai, Xin Wang, Zixuan Wang, Yunjin Yin, Wenjing Zhang, Tailong Xu, Yufeng Guo

Abstract: The start-up time <tex>$(\mathsf{T}_{\mathsf{S}})$</tex> 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 <tex>$(\mathsf{E}_{\mathsf{S}})$</tex> of XOs. Nonetheless, high-efficiency injection is guaranteed only when the frequency mismatch (ΔF) between the injection frequency (F<inf>INJ</inf>) and the XO frequeny <tex>$(\mathsf{F}_{\mathsf{X}0})$</tex> is less than 5000ppm for conventional injection. For best results, <tex>$\Delta \mathsf{F}$</tex> should be within 2500ppm [1]. As shown in Fig. 3.7.1, for each <tex>$\Delta \mathsf{F}$</tex>, there exists a corresponding maximum motional current (i<inf>M</inf>), e.g., 65μA for 5000ppm. This is the limitation to the energy injection and T<inf>S</inf> reduction, especially for large <tex>$\Delta \mathsf{F}$</tex>. Since small <tex>$\Delta \mathsf{F}$</tex> is difficult to achieve across PVT with on-chip oscillators, it is necessary to develop XO circuits with high tolerance for large <tex>$\Delta \mathsf{F}$</tex> In [1]. dithering injection can tolerate ΔF of 2x10⁴ppm but is implemented inefficiently with <tex>$\mathsf{T}_{\mathsf{S}} &gt; 10$</tex> '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 <tex>$\Delta \mathsf{F}$</tex>. 2-step injection [3] employs a phase-locked loop (PLL) to match <tex>$\mathsf{F}_{\mathsf{INJ}}$</tex> with <tex>$\mathsf{F}_{\mathsf{X}0}$</tex>, but it has to inject with <tex>$\Delta \mathsf{F}\leq 5000\mathsf{ppm}$</tex> first. In addition, both [2] and [3] have to suspend the injection during the start-up, which adds to T<inf>s</inf> overhead. Impedance-guided chirp injection [4] calibrates F<inf>'NJ</inf> when chirping inefficiently, which restricts T<inf>s</inf> reduction. Precisely timed injection [5] reduces <tex>$\mathsf{T}_{\mathsf{S}}$</tex> by terminating injection precisely at <tex>$\mathsf{T}_{\mathsf{INJ,OPT}}$</tex> which is significantly influenced by <tex>$\Delta \mathsf{F}$</tex>. The inevitable <tex>$\Delta\mathsf{F}$</tex>: results in the phase error <tex>$\Delta\varphi(\Delta\varphi=\Delta \mathsf{t}\cdot 2\pi \cdot \mathsf{F}_{\mathsf{INJ}},)$</tex> where Δt is the time difference between the voltage peak of crystal resonance and the falling edge of injection signal), <tex>$\Delta \varphi$</tex> 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 <tex>$\Delta\varphi$</tex> automatically, achieving <tex>$\mathsf{T}_{\mathsf{S}}$</tex> of about 18μs with <tex>$\Delta \mathsf{F}{-}$</tex> tolerance up to 104ppm.