Parameter Selection of Oscillator Resonant Circuit Based on Stochastic Differential Equation

Because the choice of oscillator resonant circuit parameters depends mostly on experience, we propose nonlinear differential equations to describe an oscillator based on an equivalent circuit of the oscillator and then to describe the internal electrical noise of the oscillator by introducing a stochastic term that establishes a nonlinear stochastic differential equation to analyse the oscillator's behavior.For optimization of the oscillator resonant circuit parameters, first, we used Advanced Design System (simulation software of the Agilent company) to verify the conclusion, and then, using a 10MHz Pierce crystal oscillator, provided experimental evidence.