High-performance crystal oscillator circuits: theory and application

High-performance crystal oscillator circuits: theory and application. Vittoz, E., Degrauwe, M., & Bitz, S. IEEE Journal of Solid-State Circuits, 23(3):774–783, June, 1988.
doi abstract bibtex

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.\textless\textgreater

@article{vittoz_high-performance_1988,
	title = {High-performance crystal oscillator circuits: theory and application},
	volume = {23},
	issn = {0018-9200},
	shorttitle = {High-performance crystal oscillator circuits},
	doi = {10.1109/4.318},
	abstract = {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.{\textless}{\textgreater}},
	number = {3},
	journal = {IEEE Journal of Solid-State Circuits},
	author = {Vittoz, E.A. and Degrauwe, M.G.R. and Bitz, S.},
	month = jun,
	year = {1988},
	pages = {774--783}
}

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