Study and Design of a Fast Start-Up Crystal Oscillator Using Precise Dithered Injection and

Abstract

This paper presents a theoretical study and design of two techniques used to reduce start-up time ( TS)a n d energy ( ES) of Pierce crystal oscillator (XO). 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. Next, a study of negative resistance of XO’s active circuitry and a method to boost its value beyond the limit set by a crystal static capacitor are presented. A gyrator-C active inductor with high linearity is developed to accelerate the start-up process by boosting the negative resistance. A prototype integrating these techniques is fabricated in a 180-nm CMOS process and shows a significant improvement compared with the prior art. Specifically, T S and ES are reduced by 102.7 × and 2.9×, compared with the XO start-up with no assisting circuitry, to 18 µs and 114.5 nJ for a 48-MHz XO across a temperature range of −40 ◦Ct o9 0 ◦C. The measured steady-state power and the phase noise of the XO are 180 µWa n d −135 dBc/Hz at 1-kHz offset.