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Johnson–Nyquist noise
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==== Relation to Planck's law ==== Nyquist's formula is essentially the same as that derived by Planck in 1901 for electromagnetic radiation of a blackbody in one dimension—i.e., it is the one-dimensional version of [[Planck's law|Planck's law of blackbody radiation]].<ref>{{cite book |title=Fundamentals of Microwave Photonics |page=63 |url=https://books.google.com/books?id=mg91BgAAQBAJ&pg=PA63 |first1=V. J.|last1=Urick|first2=Keith J.|last2=Williams|first3=Jason D.|last3=McKinney|isbn=9781119029786 |date=2015-01-30 |publisher=John Wiley & Sons }}</ref> In other words, a hot resistor will create electromagnetic waves on a [[transmission line]] just as a hot object will create electromagnetic waves in free space. In 1946, [[Robert H. Dicke]] elaborated on the relationship,<ref>{{Cite journal| doi = 10.1063/1.1770483| volume = 17| issue = 7| pages = 268–275| last = Dicke| first = R. H.| title = The Measurement of Thermal Radiation at Microwave Frequencies| journal = Review of Scientific Instruments| date = 1946-07-01| pmid=20991753| bibcode = 1946RScI...17..268D| s2cid = 26658623| doi-access = free}}</ref> and further connected it to properties of antennas, particularly the fact that the average [[antenna aperture]] over all different directions cannot be larger than <math>\tfrac{\lambda^2}{4\pi}</math>, where λ is wavelength. This comes from the different frequency dependence of 3D versus 1D Planck's law.
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