There are many reasons to be interested in phase noise and frequency stability, all related to the fact that randomness in an otherwise perfect periodic signal is goes with spectrum broadening, uncertainty in timing events, and coherence time. Let us go through some examples.

In the superheterodyne receiver, the noise sidebands of the local oscillator make the neighboring channels leak into the IF, and interfere with the desired channel. In digital communi- cations, the clock fluctuations corrupt the eye diagram, which results in increased probability of error. In the chirp radar, the noise sidebands of the oscillator limit the detection of small objects in the clutter. In particle accelerators, time fluctuations in the RF cavities cause intensity loss (leading phase) or energy loss (lagging phase). Frequency fluctuations may be a limiting factor in Josephson voltage standards (frequency- to-voltage conversion). In Very Large Baseline Interferometry (VLBI), short-term time fluctuations cannot be compensated numerically, and limit the detection sensitivity. Phase fluctu- ation limit the maximum frequency in a multiplication chain because of the property of angular modulations that the noise sidebands come at expenses of the carrier power. In quantum computing, the correlation time limits the lifetime of a qubit.

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