1/f noise in passive components under time-varying bias

Abstract

A model for the 1/f noise in passive components undergoing time-varying bias is proposed. One-port devices exhibiting 1/f noise are considered, e.g. carbon or polysilicon resistors. Starting from the Hooge’s formula, that holds when the component is operated under DC bias, it is shown that the noise current is simply proportional to the product between the conductivity fluctuation and the time-dependant voltage applied to the component. In other words, the 1/f noise in passive components under time-varying bias arises from the intermodulation between the stochastic process 'conductivity fluctuation' and the voltage applied to the component. Detailed calculations of both autocorrelation function and power spectrum of the resulting noise current are given; different time dependences of the voltage applied to the component are considered. Of particular relevance is the case of sinusoidal voltage; in this case the resulting noise current is a cyclostationary stochastic process and its behaviour can be conveniently described by the cyclic autocorrelation functions or by the cyclic power spectra. A circuit is built to measure the actual power spectra of the noise current of carbon resistors under constant or periodic voltage bias, in order to verify the results obtained from the proposed model. Very good agreement between theory and experiment is observed, and this fact supports the proposed model for 1/f noise in passive components under time-varying bias. The conclusion is that the physical origin of 1/f noise in passive components does not depend on external bias, nor in DC nor when a time-varying signal is applied to the component.