A Study of Deterministic Jitter in Crystal Oscillators

Crystal oscillators are widely used in electronic systems to provide reference timing signals. Even though they are designed to be highly stable, their performance can be deteriorated by several types of random noise sources and deterministic interferences. This paper investigates the phenomenon of timing jitter in crystal oscillators induced by the injection of deterministic interferences. It is shown that timing jitter is closely related to the phase and amplitude modulations of the oscillator response. A closed-form variational macromodel is proposed to quantify timing jitter as well as to qualitatively explain the interference mechanism. Analytical results and efficient numerical simulations are developed to explore how timing jitter depends on the frequency of the interfering signal. The methodology is tested by a crystal Pierce oscillator.