This proposal presents a theoretical study and design of two techniques used to reduce start-up time (TS). An analytical study of precise injection on a crystal resonator is introduced, and based on this paper, a relaxation oscillator with a dithered frequency is designed. A prototype integrating these techniques is fabricated in a 180-nm CMOS process and shows a significant improvement compared with the prior art. Specifically, TS can be reduced by 102.7×.