Symbolic harmonic analysis of quartz crystal oscillators

The nonlinear dipolar method is dedicated to the simulation of quartz crystal oscillators with high quality factor. In this method, the oscillator is considered as a resonator connected across an amplifier that behaves like a nonlinear dipole whose impedance evaluated at the resonator´s frequency depends on the current amplitude. This dipole allows us to compute very quickly the behavior of the oscillator. The computation time of the dipolar impedance by SPICE is of the order of seconds. To gain one order of magnitude in the simulation time of the oscillator, this paper propose a modification of the nonlinear dipolar method by changing the dipolar impedance SPICE calculation. that is the most time consuming part of the program, by a system of equations obtained through a symbolic manipulation of the circuit equations.