Analysis of Bilinear Noise Models in Circuits and Devices ”

There are a number of applications in which linear noise models are inappropriate. In this paper, the use of bilinear noise modela in circuits and devices is considered. Several physical problems are studied in this framework. These include circuils involving varying parameters (such as variable resistance circuits constructed using Jieldeffect transistors), the effect of switching jitter on sampled data system performance and communication systems involving voltage-controlled oscillators and phase-lock loops. In addition, several types of analytical techniques for stochastic bilinear systems are considered. Speci$cally, the moment equations of Brockett for bilinear systems driven by white noise are discussed, and closed-form expressions for certain bilinear systema (those that evolve on abelian or solvable Lie groups) driven by white or colored noise are derived. In addition, an approximate statistical technique involving the use of harmonic expansions is described.