Noise Equilibrium Frequency as a Measure of the Low Noise Devices Quality Involves the Lambert Function

Abstract

We describe a new type of application where the optimization of the noise performance is related to the Lambert W function. The noise-equilibrium (balance) frequency of a physical process (or device) is defined as that upper frequency of the frequency band where the contributions of white and $f^{-1}$ noises are equal, given the lower frequency of the band. The noise-equilibrium frequency is found as the solution expressed with the Lambert function.