标题： 弛豫振荡器中再生噪声的微观起源及其宏观电路表现 显示英文标题

标题： Microscopic Origin of Regeneration Noise in Relaxation Oscillator and its Macroscopic Circuit Manifestation

摘要： 本文通过展示弛豫振荡器相位噪声的微观来源，扩充了现有的宏观电路噪声模型，并解释了温度依赖性。 噪声来源于振荡器中器件（晶体管）电容上的多余载流子伴随的能量波动。 这种波动的物理根源来自这些载流子的噪声，从微观上看，它们分布在能级上（费米-狄拉克分布）。 此外，这种能量可以从电路的角度进行解释，使得其梯度相对于电路状态变量对应电流和电压的时间演化，即振荡器的动力学。 三种方法：基于势能（宏观）、基于自由能（微观）、基于朗之万方程，被用来开发噪声模型。 该模型在77K-300K温度范围内的温度变化与在0.13{\mu }m CMOS工艺中制造的振荡器的测量结果进行了比较。 趋势合理一致，在交叉温度以上，相位噪声是温度的单调递增函数，而在交叉温度以下，相位噪声相对恒定，并基于扩展到量子区域的朗之万方程提供了解释。 显示英文摘要

摘要： This paper augments the existing macroscopic circuit noise model for phase noise in relaxation oscillators by showing the microscopic origins of the noise and explains temperature dependency. The noise arises from fluctuation of the energy accompanying the excess carriers on device (transistors) capacitors in the oscillator. Such fluctuation has its physical origin from the noise of such carriers, which, microscopically, are distributed across the energy levels (Fermi-Dirac). Furthermore this energy can be interpreted, circuit-wise, such that its gradient, with respect to circuit state variables, correspond to time evolution of current and voltage i.e. the oscillator dynamics. Three methods: potential energy based (macroscopic), free energy based (microscopic), Langevin equation based, are used to develop the noise model. The model temperature variation over range of 77K-300K was compared to measured results on oscillators fabricated in 0.13 {\mu}m CMOS technology. The trend agree reasonably well, where above a crossover temperature, the phase noise is a monotonic increasing function of temperature, while below the crossover temperature, the phase noise stays relatively constant and an explanation based on Langevin equation, extended to quantum regime, is offered.