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 remained poorly 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 of scientific 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.
