Chains of random impedances

Abstract

The transmission of an electrical wave of frequency ω through a random ladder network is calculated at low frequency in terms of the scaling variables ω and N (the size of the chain). Two classes of disorder are considered : weak disorder where all the moments exist, and strong disorder where no moment can be defined. The characteristic lengths — localization or diffusion — are obtained from the transmission coefficient and the cut-off frequency for the band low-pass filter. For most situations dissipation imposes its characteristic length and frequency dependence on the transmission coefficient. A special situation is found where the localization phenomenon could be observed above the dissipation or diffusion effects