Computer aided design of quartz crystal oscillators

The last development of a simulation program specialized in the quartz crystal oscillator analysis is presented in this paper. The simulator actually being developed is using the full nonlinear Barkhausen criterion method. It consists in finding the frequency ω₀ and the amplitude u₀ which nullify both the real and imaginary parts of a characteristic complex polynomial P(u,jω) describing the oscillator behavior. The main nonlinearities come from the amplifying transistor described by using large signal admittance parameters y(u) obtained by means of an analog circuit simulator (SPICE). The paper presents the method used to derive and code the characteristic polynomial coefficients. This method has been successfully implemented for a Colpitts oscillator and is currently being used to build an oscillator library covering the most widely used structures. The validity and the predictive power of the model have been checked by using a circuit board and the comparison between experimental results and simulation is presented and discussed