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Thermal noise in conductors


B.I. Yakubovich

It is considered kinetically thermal noise in conductors. Noise of this type is caused by thermal movement of carriers of an electric charge. Thermal noise is analysed on the basis of following representations about movement electrons in conductors. Collision electron with a lattice leads to change of its speed. And speed after collision does not depend on speed before collision and does not depend on events previous collision. It is considered that interaction between electrons can be neglected. External electric field is not enclosed to a conductor. Conductor is shortly closed by the external circuit. The total current in an external circuit is the sum of the currents connected with movement of separate electrons. In the beginning we will analyse a current caused by one electron. At the representations made above about movement of an electron, the current caused by it is stochastic sequence of pulses with following properties. Pulse parametres statistically are not connected with parametres of previous pulses. There is a statistically connection between pulse parametres: duration of a pulse is statistically connected with its amplitude. Besides, it is natural to consider that uniform distribution of probability of collision free electron with a lattice takes place. We calculate a spectrum of such stochastic sequence of pulses. Further we pass to calculation of a spectrum of the thermal noise defined by set free electrons, available in a conductor. It is considered uniform distribution of energy on freedom degrees. As a result we find expression for a spectrum of fluctuations of a current. Thermal movement of free carriers to similarly fluctuations of a current causes tension fluctuations in a conductor. We calculate a spec-trum of fluctuations of tension. As a result expression for a spectrum of thermal noise is obtained at the rather general assumptions of character of thermal movement of free carriers of a charge in a conductor. Ratios for a spectrum of thermal noise in special cases are considered. Doing simplifications in the carried out kinetic consideration of thermal fluctuations it is possible to pass to known formulas for a spectrum of thermal noise. Having simplified character of statistical connections from the obtained general formula we find the expression earlier resulted for the description of thermal noise. Further at the simplifications made above thermal fluctuations in the field of frequencies a lot of smaller average frequency of collisions electron with a lattice are considered. In this case from the general formula calculated in the article it is obtained widely known formula of Nyquist which is directly calculated as a result of the thermodynamic approach to the analysis of thermal noise. Thus, kinetic consideration of thermal fluctuations in conductors is carried out. A number of formulas for the description of these phenomena is calculated. Expression of a general form for a spectrum of thermal noise is obtained. It is shown, in what special cases such expression passes in known before the formulas for noise of this type.
June 24, 2020
May 29, 2020

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