A study on the transient behavior of a single-loop optoelectronic oscillator (OEO) under a single sinusoidal radio frequency (RF) signal injection is presented. Considering only the phase perturbation imposed by the external RF signal, the phase-dynamic equation is solved to analyze the frequency settling behavior of the loop. A closed form expression for the required time of an OEO under RF injection-locking, reaching the steady state condition, is derived in terms of the initial phase difference, beat frequency and injection signal strength. The phase modulated signal, which is responsible for the perturbation of the free running oscillation, is expanded in a Fourier series and the expression for the output RF spectrum of the injection pulled OEO is derived. The injection-pulling dynamics approach is used to describe the phase noise of the OEO and also, the influence of the phase settling time constant on the phase noise of the injection-locked OEO is studied. The experimental results corroborating the theoretical findings are given.

中文翻译：

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射频注入锁定下单回路光电振荡器的瞬态行为

介绍了在单个正弦射频 (RF) 信号注入下单回路光电振荡器 (OEO) 瞬态行为的研究。仅考虑外部射频信号施加的相位扰动，求解相位动态方程以分析环路的频率稳定行为。根据初始相位差、拍频和注入信号强度，推导出在射频注入锁定下 OEO 达到稳态条件所需时间的封闭形式表达式。负责自由振荡扰动的相位调制信号被扩展为傅立叶级数，并导出了注入拉动 OEO 的输出 RF 频谱的表达式。采用注入-拉动动力学方法描述了OEO的相位噪声，并研究了相位稳定时间常数对注入锁定OEO相位噪声的影响。给出了证实理论发现的实验结果。