1/f^s noise from random R-C networks driven by white noise current, with low frequency characteristics changed by percolation

TL;DR

This study models 1/f^s noise in random R-C networks driven by white noise, showing how network composition and percolation influence the noise exponent and frequency response, bridging the gap between theoretical and real system behaviors.

Contribution

It introduces a model demonstrating how varying resistor and capacitor compositions in R-C networks produce a range of 1/f^s noise exponents, including classic pink noise.

Findings

R-rich networks approach white noise (1/f^0)

C-rich networks approach brown noise (1/f^2)

Equal R and C networks produce 1/f pink noise

Abstract

A model based on thermal fluctuations in conductors in random resistor-capacitor (R-C) networks has been shown to generate a 1/f^s noise with s in between 0 and 1, while in many real systems the noise exponent is between 0 and 2. The wider range of noise exponents is shown here to be generated using a model of random R-C networks driven by white noise current source, and having different compositions of resistors and capacitors. C-rich networks approach a brown noise, 1/f^2 response, while R-rich networks approach a white noise, 1/f^0 response. Random R-C networks containing equal numbers of resistors and capacitors generate the classic, 1/f pink noise. Thus, the composition unbiased R-C networks produce the ubiquitous 1/f noise. Below a limiting frequency, which is a function of the size of the network, the values of individual R and C elements, and their relative numbers in the network, the power-law frequency AC response of the network no longer holds, and the 1/f^s noise response, turns into either capacitor (1/f^2), or resistor (1/f^0) response, depending on the nature of the persistent conductivity structures: series R-C pathways, or pure C and R percolation pathways.