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A Phasor-Based Analysis of Sinusoidal Injection Locking in LC and Ring Oscillators

机译:LC和环形振荡器中基于正弦波注入锁定的相量分析

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A new perspective into the locking behavior of LC and ring oscillators is presented. By decomposing a sinusoidal injection current into in-phase and quadrature-phase components, exact expressions for the amplitude and phase of an injection-locked LC oscillator which hold for any injection strength and frequency are derived and confirmed by simulation. The analysis, which can be naturally extended to an arbitrary LC resonator topology, leads to a rigorous understanding of the fundamental physics underlying the locking phenomenon. Furthermore, an investigation of the different necessary and sufficient conditions for injection locking to occur is carried out, leading to a more precise notion of the lock range. The ring oscillator is also analyzed in an analogous fashion, resulting in simple yet accurate closed-form expressions for the fractional lock range in the small-injection and long-ring regimes; the expressions are validated by simulations of single-ended inverter-based ring oscillators in 65-nm CMOS. The mathematics behind how the injection modifies the phase delay contributed by each stage in the ring is discussed. A corollary that generalizes the small-injection lock range to any feedback-based oscillator topology is established. Conceptual and analytical connections to the existing literature are reviewed.
机译:提出了LC和环形振荡器的锁定行为的新观点。通过将正弦波注入电流分解成同相和正交相分量,可以得出并通过仿真确定精确的表达式,该表达式表示了一个注入锁定LC振荡器的振幅和相位,该表达式可以保持任何注入强度和频率。可以自然地扩展到任意LC谐振器拓扑的分析,导致对锁定现象背后的基本物理原理有严格的了解。此外,对用于发生喷射锁定的不同的必要条件和充分条件进行了研究,从而得出了更精确的锁定范围的概念。环形振荡器也以类似的方式进行了分析,从而在小注入和长环情况下得出了分数锁定范围的简单而精确的闭式表达式。这些表达式通过在65 nm CMOS中单端基于反相器的环形振荡器的仿真得到了验证。讨论了注入如何修改环中每个阶段所贡献的相位延迟的背后的数学原理。建立了将小注入锁定范围推广到任何基于反馈的振荡器拓扑的推论。审查了与现有文献的概念和分析联系。

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