The relaxation quartz crystal oscillators-design and performances

Rules are described for analysis and design of relaxation quartz crystal oscillators. Two based topologies for relaxation oscillators and the corresponding mathematical model describing their behavior are presented. Using a phase-space approach the oscillating condition and frequency and the flicker frequency noise level are calculated. The characteristics of an optimal oscillator circuit having a loaded crystal Q-factor close to the unloaded one are determined. Based on the analysis, the design rules for an optimal relaxation circuit are derived. The rules are demonstrated through the design and realization of an optimal relaxation crystal oscillator based on two-transistor negative resistance two-ports. The measured characteristics of the realized oscillator are presented and compared to those of known relaxation circuits. It is concluded that the optimal relaxation crystal oscillator consists of a small number of component circuits having low phase noise and small sensitivity to circuit and ambient parameter variations.