On a Non-linear Electronic Circuit Filtering

Abstract

The stochastic versions of non-linear dynamic circuits are formalized using non-linear stochastic differential equations. Stochastic differential equations (SDEs) are exploited to analyse dynamical systems in noisy environments. A potential application of the SDEs can be regarded as `stochastic processes in electronic circuits'. The noisy sampling mixer, a component of digital wireless communications, is an appealing and standard case from the dynamical systems' viewpoint. It assumes the structure of a non-linear SDE, and its linearized version becomes time-varying bilinear SDE. This paper derives the filtering equations for the noisy non-linear sampling mixer circuit utilizing the filtering density evolution equation. The filtering model for the stochastic problem of concern here comprises the following: (1) a non-linear SDE describing the noisy sampling mixer and (2) a non-linear noisy observation equation. It is interesting to note that the filtered estimate accounts for observations. On the other hand, the predicted estimate does not account for the observation terms in evolution equations. As a result of this, the filtered estimate confirms the greater accuracy of estimated state trajectory in contrast to the predicted trajectory. The filtering equation of this paper can be further utilized for control of the noisy sampling mixer, where the observations are available.