Equilibrium electrical noise, Johnson

Ionic systems, such as water solutions of NaCl, CuS04, K2Cr04, and Ca(NOs)2 and solutions of sulfuric acid in ethyl alcohol, were among the objects of Johnson s experiments (I) that led him to conclude that there exists equilibrium electrical noise of a universal nature that manifests thermal motion of charged particles in conductors on a macroscopic level. Independently of a particular conductivity mechanism, the voltage spectral density, Sv(/), of this noise can be calculated from the real part of the system... 

A noise that has a clearly distinct origin from noise discussed in previous sections is the electric noise that originates in modulation of ion transport by fluctuations in system conductance. These temporal fluctuations can be measured, at least in principle, even in systems at equilibrium. Such a measurement was conducted by Voss and Clark in continuous metal films (44). The idea of the Voss and Clark experiment was to measure low-frequency fluctuations of the mean-square Johnson noise of the object. In accordance with the Nyquist formula, fluctuations in the system conductance result in fluctuations in the spectral density of its equilibrium noise. Measurement of these fluctuations (that is, measurement of the noise of noise) yields information on conductance fluctuations of the system without the application of any external perturbations. The samples used in these experiments require rather large amplitude conductance fluctuations to be distinguished from Johnson noise fluctuations because of the intrinsic limitation of statistics. Voss and... 

Let us first shortly consider velocity fluctuation noise. This is the only noise mechanism that exists without electric bias. It is variably denoted as Johnson noise, thermal noise, Nyquist noise, Johnson-Nyquist noise, resistance noise [59, 60]. It is a consequence of stochastic motion of charge carriers within material with finite resistance, and it represents a mechanism to maintain thermal equilibrium in semiconductor [61]. In a general case the spectral density of thermal noise voltage is 5v(co) = 4J (hv/2 + hv/(c " / - l) = 2/flivch(hv/ i,7 ), which in the case hv becomes Sy = Ak TR, i.e., in this case the squared current due to this noise mechanism is... 

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