# Phase noise

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Phase noise is the frequency domain representation of rapid, short-term, random fluctuations in the phase of a waveform, caused by time domain instabilities ("jitter").[1] Generally speaking, radio frequency engineers speak of the phase noise of an oscillator, whereas digital system engineers work with the jitter of a clock.

Historically there have been two conflicting yet widely used definitions for phase noise. The definition used by some authors defines phase noise to be the Power Spectral Density (PSD) of a signal's phase[2], the other one is based on the PSD of the signal itself[3]. Both definitions yield the same result at offset frequencies well removed from the carrier. At close-in offsets however, characterization results strongly depends on the chosen definition.[4] Recently, the IEEE changed its official definition to $L\left(f\right)=S_{\phi}/2$ where Sφ is the (single-sided) spectral density of a signal's phase fluctuations.[5]

An ideal oscillator would generate a pure sine wave. In the frequency domain, this would be represented as a single pair of delta functions (positive and negative conjugates) at the oscillator's frequency, i.e., all the signal's power is at a single frequency. All real oscillators have phase modulated noise components. The phase noise components spread the power of a signal to adjacent frequencies, resulting in noise sidebands. Oscillator phase noise often includes low frequency flicker noise and may include white noise.

Consider the following noise free signal:

Phase noise is added to this signal by adding a stochastic process represented by φ to the signal as follows:

Phase noise is a type of cyclostationary noise and is closely related to jitter. A particularly important type of phase noise is that produced by oscillators.

Phase noise (L(f)) is typically expressed in units of dBc/Hz, representing the noise power relative to the carrier contained in a 1 Hz bandwidth centered at a certain offsets from the carrier. For example, a certain signal may have a phase noise of -80 dBc/Hz at an offset of 10 kHz and -95 dBc/Hz at an offset of 100 kHz. Phase noise can be measured and expressed as single sideband or double sideband values, but as noted earlier, the IEEE has adapted as its official definition, one-half the double sideband PSD.