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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 . Generally speaking, radio-frequency engineers speak of the phase noise of an oscillator , whereas digital-system engineers work with the jitter of a clock.
Thus, noise at f 1 is correlated with f 2 if f 2 = f 1 + kf o, where k is an integer, and not otherwise. However, the phase produced by oscillators that exhibit phase noise is not stable. And while the noise produced by oscillators is correlated across frequency, the correlation is not a set of equally spaced impulses as it is with driven systems.
The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same frequency component—perhaps of a different physical phenomenon—appears at the LTI system output.
Leeson's equation is an empirical expression that describes an oscillator's phase noise spectrum. Leeson's expression [1] for single-sideband (SSB) phase noise in dBc/Hz (decibels relative to output level per hertz) and augmented for flicker noise: [2]
The more phase noise the oscillator exhibits, the wider the bandwidth of each harmonic. Phase noise is a noise in the phase of the signal. Consider the following noise free signal: v(t) = Acos(2πf 0 t). Phase noise is added to this signal by adding a stochastic process represented by φ to the signal as follows: v(t) = Acos(2πf 0 t + φ(t)).
In oscillators, however, the low-frequency noise can be mixed up to frequencies close to the carrier, which results in oscillator phase noise. Its contribution to total noise is characterized by the corner frequency f c between the low-frequency region dominated by flicker noise and the higher-frequency region dominated by the flat spectrum of ...
Phase comparison is a comparison of the phase of two waveforms, usually of the same nominal frequency. In time and frequency, the purpose of a phase comparison is generally to determine the frequency offset (difference between signal cycles) with respect to a reference.
The low frequency flicker noise affects the phase noise because the flicker noise is heterodyned to the oscillator output frequency due to the non-linear transfer function of active devices. The effect of flicker noise can be reduced with negative feedback that linearizes the transfer function (for example, emitter degeneration).