A symbolic-numeric method to analyse high-Q quartz crystal oscillators in frequency domain

We present a symbolic-numeric method dedicated to the simulation of ultra stable quartz, oscillators entirely in the frequency domain including the nonlinear parts of the circuit. The main idea is to replace, by symbolic computation, the nonlinear differential system describing the oscillator by a system of nonlinear equations of Fourier coefficients whose solution is an approximation of the steady-state solution. This paper explains how to face the two main difficulties of this symbolic computation: the processing of nonlinear components and the management of large number of coefficients