Editing Phase noise (section)

==Linewidths==
The sinusoidal output of an ideal [[electronic oscillator|oscillator]] is a [[Dirac delta function]] in the power spectral density centered at the frequency of the sinusoid. Such perfect spectral purity is not achievable in a practical oscillator. Spreading of the spectrum line caused by phase noise is characterized by the fundamental linewidth and the integral linewidth. <ref>{{cite thesis |last= Chauhan|first= Nitesh|date= 2024|title= Stabilized Sources in Visible for Atomic, Molecular and Quantum Applications.|url= https://escholarship.org/uc/item/3wk0q2g6 |degree= PhD|publisher=UC Santa Barbara}}</ref>

The '''fundamental linewidth''', also known as the [[White noise]]-limited linewidth or the intrinsic linewidth, is the linewidth of an oscillator's PSD in the presence of only white noise sources (noise with a PSD that follows a <math>f^0</math> trend, ie. equivalent across all frequencies). The fundamental linewidth takes Lorentzian [[spectral line shape]]. White noise provides a <math>1/\sqrt{\tau}</math> Allan Deviation plot at small averaging times.

The '''integral linewidth''', also known as the effective linewidth or the total linewidth, is the linewidth of an oscillator's PSD in the presence of both white noise sources (noise with a PSD that follows a <math>f^0</math> trend) and pink noise sources (noise with a PSD that follows a <math>f^{-1}</math> trend). Pink noise is sometimes called [[Flicker noise]], or simply 1/f noise. The integral linewidth takes Voigt lineshape, a convolution of the white noise-induced Lorentzian lineshape and the pink noise-induced Gaussian lineshape. Pink noise provides a <math>\tau^{0}</math> Allan Deviation plot at moderate averaging times. This flat line on the Allan Deviation plot is also known as the flicker floor.

Additionally, the oscillator might experience [[Frequency drift]] over long periods of time, slowly moving the center frequency of the Voigt lineshape. This drift is a brown noise source (noise with a PSD that follows a <math>f^{-2}</math> trend), and provides a <math>\sqrt{\tau}</math> Allan Deviation plot at large averaging times.