Modeling of quartz crystal oscillators by using nonlinear dipolar method

Time-domain simulation and spectrum measurement of low-noise oscillators

“…As shown in Fig. 1, an oscillator can be thought of as an association between a resonator whose impedance is strongly varying with frequency but weakly varying with the current amplitude and a sustaining active dipole whose impedance strongly vary with the current amplitude but weakly vary with the frequency [1]- [3].…”

“…3 which is a Colpitts-like circuit [3]. The sustaining amplifier is an ideal amplifier except it has a nonlinear cubic transconductance.…”

Symbolic harmonic analysis of quartz crystal oscillators

“…Following [3], these two remarks permit to consider the whole amplifier part (and capacity C p ) as a nonlinear dipole (R d , L d ) that depends only on the current amplitude as shown in Fig. 1 right.…”

“…The transient amplitude and frequency are obtained by solving the first order differential equations (3,4).…”

“…In a previous series of articles [1][2] [3], we have developed a method, called Nonlinear Dipolar Method, which allows to simulate quartz oscillator very efficiently. The calculation needs only a few seconds for a Colpitts oscillator.…”