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

• Published in: IEEE journal of solid-state circuits Vol. 54; no. 9; pp. 2543 - 2554
• Main Authors: Karimi-Bidhendi, Alireza, Pu, Haoran, Heydari, Payam
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Active inductor (AI); Artificial intelligence; Capacitors; Circuits; CMOS; Crystal oscillators; Crystals; gyrator-C; Inductance; Linearity; motional current; negative resistance; Oscillators; precise injection; quartz crystal; relaxation oscillator (RXO); Relaxation oscillators; Resistance; Resonant frequency; start-up time; static capacitor; Steady-state
• ISSN: 0018-9200; 1558-173X
• DOI: 10.1109/JSSC.2019.2920084

This paper presents a theoretical study and design of two techniques used to reduce start-up time (<inline-formula> <tex-math notation="LaTeX">T_{S} </tex-math></inline-formula>) and energy (<inline-formula> <tex-math notation="LaTeX">E_{S} </tex-math></inline-formula>) 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, <inline-formula> <tex-math notation="LaTeX">T_{S} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">E_{S} </tex-math></inline-formula> are reduced by 102.7<inline-formula> <tex-math notation="LaTeX">\times </tex-math></inline-formula> and 2.9<inline-formula> <tex-math notation="LaTeX">\times </tex-math></inline-formula>, compared with the XO start-up with no assisting circuitry, to 18 <inline-formula> <tex-math notation="LaTeX">\mu \text{s} </tex-math></inline-formula> and 114.5 nJ for a 48-MHz XO across a temperature range of −40 °C to 90 °C. The measured steady-state power and the phase noise of the XO are 180 <inline-formula> <tex-math notation="LaTeX">\mu \text{W} </tex-math></inline-formula> and −135 dBc/Hz at 1-kHz offset.