High precision nonlinear computer modelling technique for quartz crystal oscillators

The authors present a full nonlinear modeling technique for quartz crystal oscillators. The model computes both an imaginary and a real part of the nonlinear complex polynomial characteristic, giving the frequency and amplitude of the oscillation. It is shown how a computer-aided symbolic calculation can be used to obtain error-free polynomial coefficients. The nonlinear behavior of the active device is described by using nonlinear admittance parameters whose value is a function of the signal level. These functions have been obtained by using a commercially available electrical simulator, and the results are compared with experimental data. Modeling of the oven has also been performed, and the program used to obtain the thermal transfer function of the oven is presented