A Fast Startup CMOS Crystal Oscillator Using Two-Step Injection

Fast startup crystal oscillators (XOs) are needed in heavily duty-cycled communication systems for implementing aggressive dynamic power management schemes. This article presents the ways to improve startup time of XOs. Using a two-step injection technique in a three-step process, the proposed technique reduces the XO startup time to within 1.5 $\times $ the theoretical minimum. By solving the differential equation governing crystal resonator under injection for arbitrary injection frequency, the behavior of energy build-up inside a crystal resonator is analyzed and used to determine optimum injection time as a function of the desired XO steady-state amplitude and injection frequency error. Bounds on tolerable injection frequency error to guarantee the existence of optimal timing are provided. Fabricated in a 65-nm CMOS process, the proposed 54-MHz fast startup XO occupies an active area of 0.075 mm ² and achieves a startup time of less than 20 $\mu \text{s}$ across a temperature range of −40 °C to 85 °C while consuming a startup energy of 34.9 nJ and operating from a 1.0-V supply.