The start-up time of crystal oscillators (T START ) is a major bottleneck in reducing the average power of heavily duty-cycled wireless /wireline communication systems [1]. Among all the reported schemes to reduce T START , techniques that increase initial noise amplitude by injecting a surge of energy into the crystal resonator are shown to be most effective [1–3]. These approaches are proven to be robust if the frequency of the injection signal is equal to the crystal oscillator (XO) frequency (F INJ = F X0 ), which is difficult to achieve across PVT with on-chip oscillators. Any mismatch (ΔF = F INJ − F X0 ) even as small as a few 100 ppm can greatly increase T START . Sweeping the injection frequency using a chirp oscillator [2]or dithering the injection frequency between two values [1]can partially alleviate this issue but because $\Delta \text{F} \neq 0$, this only reduces T START to about 14× the theoretical minimum in [2]. On the other hand, it was shown in [3] that the use of a precise injection period T INJ,OPT can help reduce T START even in the presence of large ΔF. T INJ,OPT must be chosen such that current in the motional branch of the resonator, i m (t), reaches its steady-state value, I m,SS (i m (T INJ, OPT ) = I m,SS ) as shown in Fig. 18.5.1 [3]. However, small T START and large tolerance to ΔF can be achieved only when I m,SS is very small, which translates to small XO output amplitude (V XO < 200mV) and degraded phase noise. For example, as illustrated in Fig. 18.5.1, T START ≈ T INJ,OPT because i m (T INJ, OPT ) = I m,SS1 even when ΔF is as large as 1000ppm. However, for I m,SS2 > I m,SS1 , no TINJ can ensure i m (T INJ ) = I m,SS2 if ΔF > 1000ppm, thus greatly increasing T START . Therefore, ΔF must be small (