High-performance crystal oscillator circuits: theory and application

A general theory that allows the accurate linear and nonlinear analysis of any crystal oscillator circuit is presented. It is based on the high Q of the resonator and on a very few nonlimiting assumptions. The special case of the three-point oscillator, that includes Peirce and one-pin circuits, is analyzed in more detail. A clear insight into the linear behavior, including the effect of losses, is obtained by means of the circular locus of the circuit impedance. A basic condition for oscillation and simple analytic expressions are derived in the lossless case for frequency pulling, critical transconductance, and start-up time constant. The effects of nonlinearities on amplitude and on frequency stability are analyzed. As an application, a 2-MHz CMOS oscillator which uses amplitude stabilization to minimize power consumption and to eliminate the effects of nonlinearities on frequency is described. The chip, implemented in a 3- mu m p-well low-voltage process, includes a three-stage frequency divider and consumes 0.9 mu A at 1.5 V. The measured frequency stability is 0.05 p.p.m./V in the range 1.1-5 V of supply voltage. Temperature effect on the circuit itself is less than 0.1 p.p.m. from -10 to +60 degrees C.<>