Ring oscillators, with capacitive load intended for frequency tuning, can fail to sustain stable oscillations. Failure depends on the size of the load capacitors and their equivalent series resistance. This paper first describes the failing mechanism from an intuitive perspective. It then develops an analytical model and provides the equations for the minimum load capacitance and the range of equivalent series resistance at which the ring oscillator fails. The dependency on the number of stages of the ring oscillator as well as the trans-conductance and impedance of its gain stages are also examined. Confirmed by simulations, the model shows that the failing region reduces significantly for ring oscillators with 7 or more stages but that it can be a serious concern for 5 and especially 3-stage ring oscillators.

中文翻译：

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容性负载环形振荡器的故障


带有用于频率调谐的电容负载的环形振荡器可能无法维持稳定的振荡。故障取决于负载电容器的大小及其等效串联电阻。本文首先从直观的角度描述了失效机制。然后，它开发了一个分析模型，并提供了环形振荡器失效时的最小负载电容和等效串联电阻范围的方程。还检查了对环形振荡器级数的依赖性以及其增益级的跨导和阻抗。经仿真证实，该模型表明，对于 7 级或更多级环形振荡器，故障区域显着减少，但对于 5 级、尤其是 3 级环形振荡器来说，这可能是一个严重问题。