A random input-driven resistor-capacitor series circuit

In this paper, we present the noise analysis of simple, but an appealing resistor-capacitor series circuit. As it has found applications in many circuits like RC filter in phase locked loop. The noise originates from the arbitrary thermal motion of carriers and the discreteness of charge. Noise signals are random and must be treated by statistical means. Even though we cannot predict the real noise waveform, we can envisage the statistics such as the mean (average) and variance. Generally, noise contributions to electrical circuits are not accounted for when using deterministic differential equations for their modeling and ignoring noise contributions lead to poor state estimation. A first-order Ordinary Differential Equation (ODE) is used for the response analysis of the circuit. As a result of these, in this paper, the deterministic model is replaced with a stochastic model by adding a noise term as a random voltage source, which drives the RC circuit. The Itô theory is applied to the noise analysis of the noisy dynamic circuit considered here. The Itô theory has found surprising applications in stochastic models arising from diverse field. Numerical simulations of the charge with and without noise, the mean and variance of the charge using MATLAB are discussed.