Editing Johnson–Nyquist noise (section)

{{Short description|Electronic noise due to thermal vibration within a conductor}}
[[File:Oscilloscope-setup-johnson-noise.svg|thumb|327x327px|Figure 1. [[John Bertrand Johnson|Johnson]]'s 1927 experiment showed that if thermal noise from a [[Resistance (electricity)|resistance]] of <math>\text{R}</math> with [[Absolute Temperature|temperature]] <math>\text{T}</math> is [[bandlimited]] to [[Bandwidth (signal processing)|bandwidth]] <math>\Delta f </math>, then its [[root mean squared]] [[voltage]] <math>(V_\text{rms})</math> is <math>\sqrt{ 4 k_\text{B} \text{T} \, \text{R} \, \Delta f }</math> in general, where <math>k_\text{B}</math> is the [[Boltzmann constant]].]]
'''Johnson–Nyquist noise''' ('''thermal noise''', '''Johnson noise''', or '''Nyquist noise''') is the [[electronic noise]] generated by the [[Thermal energy|thermal agitation]] of the [[charge carrier]]s (usually the [[electron]]s) inside an [[electrical conductor]] at equilibrium, which happens regardless of any applied [[voltage]]. Thermal noise is present in all [[electrical circuit]]s, and in sensitive electronic equipment (such as [[radio receiver]]s) can drown out weak signals, and can be the limiting factor on sensitivity of electrical measuring instruments. Thermal noise is proportional to [[absolute temperature]], so some sensitive electronic equipment such as [[radio telescope]] receivers are cooled to [[cryogenic]] temperatures to improve their [[signal-to-noise ratio]]. The generic, statistical physical derivation of this noise is called the [[fluctuation-dissipation theorem]], where generalized [[Electrical impedance|impedance]] or generalized [[Electric susceptibility|susceptibility]] is used to characterize the medium.
[[File:Johnson-nyquist-noise-power-spectral-density-of-ideal-resistor.svg|thumb|400x400px|Figure 2. Johnson–Nyquist noise has a nearly a constant {{nowrap|{{math|4}}[[Boltzmann constant|{{math|''k''<sub>B</sub>}}]][[Absolute temperature|{{math|T}}]][[Electrical resistance and conductance|{{math|R}}]]}} power spectral density per unit of [[frequency]], but does decay to zero [[Johnson–Nyquist noise#Quantum effects at high frequencies or low temperatures|due to quantum effects]] at high frequencies ([[Terahertz (unit)|terahertz]] for room temperature). This plot's horizontal axis uses a [[log scale]] such that every vertical line corresponds to a [[power of ten]] of frequency in [[hertz]].]]
Thermal noise in an [[ideal resistor]] is approximately [[white noise|white]], meaning that its power [[spectral density]] is nearly constant throughout the [[frequency spectrum]] (Figure 2). When limited to a finite bandwidth and viewed in the [[time domain]] (as sketched in Figure 1), thermal noise has a nearly [[Normal distribution|Gaussian amplitude distribution]].<ref>{{cite book|author1=John R. Barry |author2=Edward A. Lee |author3=David G. Messerschmitt |title=Digital Communications|year=2004|publisher=Sprinter|isbn=9780792375487|page=69|url=https://books.google.com/books?id=hPx70ozDJlwC&q=thermal+johnson+noise+gaussian+filtered+bandwidth&pg=PA69}}</ref> 

For the general case, this definition applies to [[charge carriers]] in any type of conducting [[Transmission medium|medium]] (e.g. [[ion]]s in an [[electrolyte]]), not just [[resistor]]s. Thermal noise is distinct from [[shot noise]], which consists of additional current fluctuations that occur when a voltage is applied and a macroscopic current starts to flow.