A 16-MHz Crystal Oscillator With 17.5- $\mu$ s Start-Up Time Under 10 $^{4}$ -ppm- $\Delta $ 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 (
$\Delta$

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
$\Delta$

F
up to 10
$^{{4}}$
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
$\mu $
s with a 16-MHz crystal and a 1.0-V
V

$_{\text{DD}}$
. Furthermore, the start-up time only varies by
$\pm$
1.42% over a
$\Delta$

F
of
$\pm$
10
$^{{4}}$
ppm, and
$\pm$
4.5% amid temperature variations (
$-$
40
$^{\circ}$
C to 85
$^{\circ}$
C), evincing the robustness of the proposed technique. The power consumption and phase noise in the steady state are 84
$\mu$
W and
$-$
139 dBc/Hz at 1-kHz offset, respectively.