A 24-MHz Crystal Oscillator with 6.9-µs Startup Time and 2% Injection- $\Delta$ F Tolerance Using Phase-Interpolator-Assisted Synchronized Injection

This article presents a 24-MHz fast startup crystal oscillator with a phase-interpolator-assisted synchronized injection technique. This technique ensures the phase consistency between the injection source and the crystal resonance even with a 2% injection-ΔF. Additionally, a differential peak detection technique is proposed to detect the phase error incurred by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Delta F$</tex>, shortening the auxiliary non-injection period to merely 4 cycles. Fabricated in a 40-nm CMOS process, the proposed XO achieves a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$6.9-\mu \mathrm{s}$</tex> startup time (166 cycles) and a 4.8-nJ startup energy with 2% injection inaccuracy when tested with a 24 MHz off-chip crystal.