Synthetic modeling of quartz crystal oscillator

This paper presents a new modeling technique to describe the nonlinear behavior of complicated oscillator circuits. The simulation program being developed first removes the resonator from the oscillation loop and call on SPICE to calculate the large signal γ-parameters of the amplifier circuit considered as a nonlinear two-port circuits. The oscillation condition, obtained by reinserting the resonator across the two-port circuit, is expressed under the form of a complex polynomial in the harmonic variable jω, the coefficients of this polynomial being nonlinear functions of the signal amplitude. Solving the real and imaginary parts of this characteristic polynomial by using nonlinear analysis algorithm, it is possible to accurately calculate both amplitude and frequency of the oscillation