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Abstract—Linear time-invariant (LTI) phase noise theories provide important qualitative design insights but are limited in their quantitative predictive power. Part of the difficulty is that device noise undergoes multiple frequency translations to become oscillator phase noise. A quantitative understanding of this process requires abandoning the principle of time invariance assumed in
most older theories of phase noise. Fortunately, the noise-to-phase transfer function of oscillators is still linear, despite the existence of the nonlinearities necessary for amplitude stabilization. In addition to providing a quantitative reconciliation between theory and measurement, the time-varying phase-noise model presented in this tutorial identifies the importance of symmetry in suppressing the upconversion of 1 noise into close-in phase noise, and provides an explicit appreciation of cyclostationary effects and
AM–PM conversion. These insights allow a reinterpretation of why the Colpitts oscillator exhibits good performance, and suggest new oscillator topologies. Tuned LC and ring oscillator circuit examples are presented to reinforce the theoretical considerations developed. Simulation issues and the accommodation of amplitude noise are considered in appendixes.
线性时不变(LTI)相位噪声理论提供了重要的定性设计见解,但其定量预测能力有限。部分困难在于器件噪声经过多次频率平移后成为振荡器相位噪声。对这一过程的定量理解需要放弃大多数旧的相位噪声理论中假定的时不变原理。幸运的是,振荡器的噪声-相位传递函数仍然是线性的,尽管存在振幅稳定所必需的非线性。
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