In this article, we develop the theory of a special type of optoelectronic phase-locked loop (PLL). The output signal of this type of PLL is in the electrical domain and its reference oscillator, typically a mode-locked laser, operates in the optical domain. The PLL uses a balanced optical microwave phase detector (BOMPD). In order to model the optoelectronic PLL, the nonlinear characteristic function and the gain of the BOMPD are derived analytically. Using the results of the phase detector analysis, the theory of an optoelectronic PLL using such a phase detector is developed. Based on the theoretical analysis, a broadband optoelectronic frequency synthesizer with a programmable frequency range from 2 to 20 GHz is designed and implemented. Phase noise measurements show that the optoelectronic PLL frequency synthesizer achieves an integrated rms-jitter (1 kHz–100 MHz) of less than 4 fs in the frequency range from 5 to 20 GHz with a typical value of 4 fs and a minimum of 3 fs. This is the first reported wideband PLL frequency synthesizer achieving sub-10-fs integrated rms-jitter (1 kHz–100 MHz) in the frequency range from 3 to 20 GHz. A comparison with best-in-class laboratory-grade frequency synthesizers in this frequency range shows that this synthesizer achieves lower phase noise than any electronic frequency synthesizer for offset frequencies larger than 2 kHz.

中文翻译：

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使用锁定到锁模激光器的微波振荡器的2–20 GHz超低相位噪声信号源

在本文中，我们将开发一种特殊类型的光电锁相环（PLL）的理论。这种PLL的输出信号在电域中，其参考振荡器（通常为锁模激光器）在光域中工作。PLL使用平衡光学微波相位检测器（BOMPD）。为了对光电锁相环进行建模，需要对非线性特征函数和BOMPD的增益进行解析推导。利用相位检测器分析的结果，开发了使用这种相位检测器的光电PLL理论。根据理论分析，设计并实现了一种可编程频率范围为2至20 GHz的宽带光电频率合成器。相位噪声测量表明，光电PLL频率合成器在5至20 GHz的频率范围内具有小于4 fs的集成均方根抖动（1 kHz– 100 MHz），典型值为4 fs，最小为3 fs 。这是第一个报告的宽带PLL频率合成器，在3至20 GHz的频率范围内实现了低于10fs的集成均方根抖动（1 kHz– 100 MHz）。与该频率范围内同类最佳的实验室级频率合成器进行的比较表明，对于偏移频率大于2 kHz的情况，该合成器比任何电子频率合成器都具有更低的相位噪声。这是第一个报告的宽带PLL频率合成器，在3至20 GHz的频率范围内实现了低于10fs的集成均方根抖动（1 kHz– 100 MHz）。与该频率范围内同类最佳的实验室级频率合成器进行的比较表明，对于偏移频率大于2 kHz的情况，该合成器比任何电子频率合成器都具有更低的相位噪声。这是第一个报告的宽带PLL频率合成器，在3至20 GHz的频率范围内实现了低于10fs的集成均方根抖动（1 kHz– 100 MHz）。与该频率范围内同类最佳的实验室级频率合成器进行的比较表明，对于偏移频率大于2 kHz的情况，该合成器比任何电子频率合成器都具有更低的相位噪声。