On the DC-Settling Process of the Pierce Crystal Oscillator in Start-Up

This brief presents an analytical treatment of the initial motional current
${i}_{m}{(}{0}{)}$
of the Pierce crystal oscillator (XO), which is critical for determining its start-up time
${T}_{s}$
. Specifically, the limitation of energy injection to boost
${i}_{m}{(}{0}{)}$
is studied, and the dc-settling process (DCS) at the dawn of the start-up for stimulating
${i}_{m}{(}{0}{)}$
is shown. The phases of the DCS process are evaluated under different operation regions, and the theoretical implications are confirmed by detailed simulations. A design guide for an optimal DCS start-up is also proposed, allowing
${i}_{m}{(}{0}{)}$
-boosting via simple voltage and timing controls.