title: Analysis of noise in quartz crystal oscillators by using slowly varying functions method.
abstract: By using formal manipulation capability of commercially available symbolic calculation code, it is possible to automatically derive the characteristic polynomial describing the conditions for oscillation of a circuit. The analytical expression of the characteristic polynomial is obtained through an encapsulation process starting from the SPICE netlist description of the circuit: by using a limited number of simple transformations, the initial circuit is progressively transformed in a simplified standard form. In this method, the nonlinear component is described by its large signal admittance parameters obtained from a set of SPICE transient simulations of larger and larger amplitude. The encapsulation process involving linear and nonlinear components as well as noise sources leads to a perturbed characteristic polynomial. In the time domain, the perturbed characteristic polynomial becomes a nonlinear nonautonomous differential equation. By using an extension of the slowly varying functions method, this differential equation is transformed into a nonlinear differential system with perturbation terms as the right-hand side. Eventually, solving this system with classical algorithms allows one to obtain both amplitude and phase noise spectra of the oscillator.
authors.affiliation: CNRS, Univ. de Franche-Comte, Besancon, Cedex, France. brendel@lpmo.univ-fcomte.fr
authors.forename: R
authors.initials: R
authors.lastname: Brendel
authors.forename: N
authors.initials: N
authors.lastname: Ratier
authors.forename: L
authors.initials: L
authors.lastname: Couteleau
authors.forename: G
authors.initials: G
authors.lastname: Marianneau
authors.forename: P
authors.initials: P
authors.lastname: Guillemot