ITR: CAD Algorithms for Unified Prediction of Oscillator Mixing and Phase Noise

术语振荡器被广泛用于任何物理系统，可以通过其自身的基本机制产生和维持重复运动。例如，时钟、心脏、内燃机和激光都是振荡器。振荡器是电子学中的基本构建模块，产生时钟信号和重复波形，几乎所有计算机、无线电和通信电路的操作都必不可少。尽管振荡器的普遍存在和长期的科学兴趣，他们的工作的某些方面，如他们的反应，小外部影响或噪音，至今仍知之甚少。噪声使振荡器的重复周期以随机方式漂移，这通常被称为相位噪声或抖动。时钟的准确性，或携带语音或高速数据的无线电信号的纯度，从根本上受到振荡器噪声的限制。因此，能够正确预测振荡器噪声不仅具有相当大的科学价值，而且具有很大的实际意义，因为它可以用来构建对噪声不太敏感的振荡器。这项研究将提供对振荡器噪声机制的严格数学理解，并将这种理解应用于开发定量噪声/抖动预测的计算工具。除了解决一个长期以来一直开放的重要科学问题外，这项研究还将直接用作计算机辅助电路设计工具的模块，例如着名的程序SPICE。虽然这项研究的主要直接好处将是在电子电路的设计，开发的技术将适用于任何类型的振荡器，包括机械，生物，化学和光学的。因此，我们希望这项研究在各种科学学科中产生广泛的长期影响。一个强有力的教育部分是这项工作的一个组成部分，明确的目标是以尽可能可读和易于理解的形式传播成果。为了进一步提高影响力，该研究项目中开发的计算方法将被原型化并作为开源公开提供。

The term oscillator is broadly used for any physical system that can generate and sustain repetitive motions through its own fundamental mechanisms. For example, clocks, hearts, combustion engines, and lasers are all oscillators. Oscillators are fundamental building blocks in electronics, producing the clock signals and repetitive waveforms essential for the operation of virtually all computer, radio and communication circuits. In spite of the ubiquity of and longstanding scientific interest in oscillators, certain aspects of their operation, such as their response to small external influences or noise, have remainedpoorly understood to date. Noise makes an oscillator's repetition period drift in a random fashion this is often referred to as phase noise or jitter. The accuracy of clocks, or the purity of radio signals carrying voice or high-speed data, is fundamentally limited by oscillator noise. Being able to predict oscillator noise correctly is, therefore, not only of considerable scientific value, but also of great practical interest, for it can be used to build oscillators that are less sensitive to noise.This research will provide a rigorous mathematical understanding of oscillator noise mechanisms, and apply this understanding to develop computational tools for quantitative noise/jitter prediction. In addition to solving an important scientific problem that has long been open, this research will be directly useful as a module for computer-aided circuit design tools, such as the well-known program SPICE. Although the principal immediate benefit of this research will be in the design of electronic circuits, the techniques developed will be applicable to any kind of oscillator, including mechanical, biological, chemical and optical ones. Hence we expect this research to have broad long-term impact in a variety ofscientific disciplines. A strong educational component is an integral part of this work, with an explicit goal being to disseminate results in as readable and easily understandable a form as possible. To further increase impact, the computational methods developed in this research project will be prototyped and made publicly available as open source.