A THERMODYNAMICAL APPROACH TO NOISE IN NONLINEAR NETWORKS

The physical assumptions on which linear fluctuation theory is based d o 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 Stratonov ich's 'non-linear non-equilibrium thermodynamics' to describe thermal noise in reciprocal non-linear RLC-networks. As an example the (determ inistic) Brayton-Moser equations are treated. A stochastic description in terms of master equations* for the one-time probability density r elated to the Markov processes of the fluctuating electrical quantitie s is obtained. This decription is a generalization of Nyquist's theore m to non-linear resistors. When the non-linear resistances are represe nted by Taylor polynomials, different master equations are obtained fo r 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 enlarg ed to open thermodynamical systems. The results are used to derive app roximate noise-equivalent circuits for non-linear resistors. In this s ense, this paper proves the approximate validity of 'conventional' noi se source models and explicitly fixes the stochastic properties of the se noise sources (as far as possible). (C) 1998 John Wiley & Sons, Ltd .