Relaxation quartz oscillators with crystal placed in feedback loop: Analysis and design

Our purpose in this paper is to provide a complete theoretical analysis of relaxation quartz oscillators using integrated circuits as active elements and a crystal placed in feedback loop. The general theory of relaxation oscillations is a theoretical background for this analysis, which provides solutions for oscillating conditions, oscillation buildup and period, and a flicker-frequency noise level. The main results are the criteria for the design of an optimal quartz relaxation oscillator having high immunity to circuit and ambient parameter variations and a low phase noise level. The results are derived for oscillators using TTL gates, but they are of a general validity and can be easily modified for every circuit of this kind. The conclusions drawn are discussed and confirmed through experiments.