ADOQ: a quartz crystal oscillator simulation software

Abstract

This paper presents the actual state of a computer program especially designed to simulate the behavior of quartz crystal oscillators. The program is based on the fact that the current through the quartz crystal is almost perfectly sinusoidal. Consequently the oscillator can be modeled by a resonator across a nonlinear impedance that depends only on the current magnitude through it. The resonator being replaced by a current source, the nonlinear impedance of the amplifier is computed from a series of transient analyses performed at the resonator frequency. When the steady state is reached, the resonator impedance is exactly equal and of opposite sign to the amplifier impedance. This identity allows one to compute the oscillation amplitude and the frequency shift with respect to the resonator frequency. This computation does not require to perform unacceptable long transient analyses in case of high-Q oscillator. Our program is intended to help the designer in checking or improving oscillator circuit design. From the Spice netlist, it enables the user to compute the steady state features of the oscillator, namely frequency and amplitude. Then, the user can study the effect of temperature change on any components or the influence of quartz characteristic. It is also possible to perform accurate oscillator sensitivity calculation to various parameters (component value, supply voltage, ...) as well as worst case analysis.