A very high speed method to simulate quartz crystal oscillator

Abstract

International audienceIn this paper, we present the SHA method, a Symbolic Harmonic Analysis method to simulate the behaviour of ultrastable quartz crystal oscillators. This nonlinear method is aimed to compute very quickly the steady state as well as amplitude and frequency transients. The ultimate goal is to see instantaneously the influence of a parameter change on the oscillator's features thank to the computation speed. The method proposed here is a mixing of the nonlinear dipolar method previouly developed in our team and the harmonic method. It allows to replace the set of algebro-differential equation of the circuit by a nonlinear system of the Fourier coefficients of the circuit unknowns