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A thermodynamical approach to noise in non‐linear networks
Author(s) -
Weiss Laurens,
Mathis Wolfgang
Publication year - 1998
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/(sici)1097-007x(199803/04)26:2<147::aid-cta998>3.0.co;2-e
Subject(s) - noise (video) , master equation , linear map , mathematics , statistical physics , linear system , johnson–nyquist noise , linearity , markov chain , computer science , mathematical analysis , physics , quantum mechanics , pure mathematics , voltage , artificial intelligence , image (mathematics) , quantum , statistics
The physical assumptions on which linear fluctuation theory is based do not apply to internal noise in non‐linear systems. As a consequence, there is still no complete theory for internal (thermal) noise in non‐linear electrical networks. In this paper the authors apply Stratonovich's ‘non‐linear non‐equilibrium thermodynamics’ to describe thermal noise in reciprocal non‐linear RLC‐networks. As an example the (deterministic) Brayton–Moser equations are treated. A stochastic description in terms of master equations for the one‐time probability density related to the Markov processes of the fluctuating electrical quantities is obtained. This decription is a generalization of Nyquist's theorem to non‐linear resistors. When the non‐linear resistances are represented by Taylor polynomials, different master equations are obtained for different degrees of non‐linearity. A transformation of variables is used to apply the theory to non‐linear dynamical network elements. To consider networks including independent sources, the theory is enlarged to open thermodynamical systems. The results are used to derive approximate noise‐equivalent circuits for non‐linear resistors. In this sense, this paper proves the approximate validity of ‘conventional’ noise source models and explicitly fixes the stochastic properties of these noise sources (as far as possible). © 1998 John Wiley & Sons, Ltd.