Simulation of a parametric quartz crystal oscillator by the symbolic harmonic method

The Symbolic Harmonic Analysis (SHA) method is a frequency domain approach for computing the steady state of ultra stable quartz crystal oscillators. First, we present a general method to convert a set of differential equations into a system of non-linear algebraic equations that can be solved for the periodic steady state solution. Then, we apply this method to simulate the behavior of a parametric quartz crystal oscillator currently being developed at FEMTO-ST/LCEP. This oscillator uses a 10 MHz quartz resonator and a 20 MHz signal derived from the oscillator nonlinearities is used to pump a varactor-diode. The quartz resonator time constant induces too long simulation time with classical integration methods. So that the symbolic harmonic analysis offers a good alternative to quickly obtain the periodic steady state. Simulation results are compared with experimental data.