A 16-MHz Crystal Oscillator With 17.5- μ s Start-Up Time Under 10⁴-ppm- Δ F Injection Using Automatic Phase-Error Correction

Ast start-up crystal oscillators (XOs) based on energy injection with an auxiliary oscillator (AO) are efficacious in improving the energy consumption of duty-cycled the Internet of Things (IoT) devices. Nonetheless, the frequency mismatch ( <tex-math notation="LaTeX">Δ</tex-math> F ) between the injection frequency and the crystal's resonance frequency restrains the injection efficiency and start-up improvement. This work presents an automatic phase-error correction (APEC) technique for automatically correcting the phase error incurred due to <tex-math notation="LaTeX">Δ</tex-math> F up to 10 <tex-math notation="LaTeX">^4</tex-math> ppm and safeguarding the XO start-up performance. An inflection detector (ID) based on a dynamic comparator (DCMP) traces the crystal resonant signal's peak points and selects the appropriate signals for injection. We fabricated the proposed fast start-up XO in a 40-nm CMOS process. It achieves a start-up time of 17.5 <tex-math notation="LaTeX">μ</tex-math> s with a 16-MHz crystal and a 1.0-V V <tex-math notation="LaTeX">DD</tex-math> . Furthermore, the start-up time only varies by <tex-math notation="LaTeX">±</tex-math> 1.42% over a <tex-math notation="LaTeX">Δ</tex-math> F of <tex-math notation="LaTeX">±</tex-math> 10 <tex-math notation="LaTeX">^4</tex-math> ppm, and <tex-math notation="LaTeX">±</tex-math> 4.5% amid temperature variations ( <tex-math notation="LaTeX">$-$</tex-math> 40 <tex-math notation="LaTeX">∘</tex-math> C to 85 <tex-math notation="LaTeX">∘</tex-math> C), evincing the robustness of the proposed technique. The power consumption and phase noise in the steady state are 84 <tex-math notation="LaTeX">μ</tex-math> W and <tex-math notation="LaTeX">$-$</tex-math> 139 dBc/Hz at 1-kHz offset, respectively.