Nonlinear model of crystal resonator and its application to phase noise simulation of oscillator

AT-cut quartz crystal resonators are widely used in communication equipment, measurement instruments, computers and etc. The resonance frequency of AT-cut crystal resonator changes proportional to the square of its driving current. The frequency drive level dependency can be modeled by introducing nonlinearity in the equivalent series capacitance of a crystal resonator. We have determined the nonlinear parameter of a 26MHz crystal resonator from the measured data and simulated its frequency drive level dependency. The simulated results agreed well with the measured frequency drive level dependency. And we simulated the phase noise of a CMOS inverter crystal oscillator using the nonlinear model. We found the increase of phase noise of oscillator in the f^-2 region.