Phase noise

In signal processing, phase noise is the frequency-domain representation of random fluctuations in the phase of a waveform, corresponding to time-domain deviations from perfect periodicity (jitter). 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. Some authors define phase noise to be the spectral density of a signal's phase only, while the other definition refers to the phase spectrum (which pairs up with the amplitude spectrum) resulting from the spectral estimation of the signal itself. Both definitions yield the same result at offset frequencies well removed from the carrier. At close-in offsets however, the two definitions differ. The IEEE defines phase noise as L(f) = Sφ(f)/2 where the "phase instability" Sφ(f) is the one-sided spectral density of a signal's phase deviation. Although Sφ(f) is a one-sided function, it represents "the double-sideband spectral density of phase fluctuation". The symbol L is called a (capital or uppercase) script L. An ideal oscillator would generate a pure sine wave. In the frequency domain, this would be represented as a single pair of Dirac 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: v(t) = Acos(2πf0t). Phase noise is added to this signal by adding a stochastic process represented by φ to the signal as follows: v(t) = Acos(2πf0t + φ(t)). Phase noise is a type of cyclostationary noise and is closely related to jitter, a particularly important type of phase noise that is produced by oscillators.