Aspects of EMI, EMC due to Randomness in the Electronic Circuits and the PCB

Good electromagnetic interference (EMI) and electromagnetic compatibility (EMC) performances remain difficult design targets despite several decades of theoretical progresses and the current powerful simulation tools. One of the reasons is constituted by the statistical nature of the parameters of the components and of the printed circuit boards (PCB). We investigate the effect of randomness of these elements and propose versions of the stochastic telegraph equation for the PCB traces. The effects may be increased by the inherent variability of the PCB shape and of the environment, especially in case of wearable systems. The relevance of this study in design for EMI/EMC and in manufacturing consists in providing guidance on the average values and statistical properties of the reflections in circuits on PCBs and on models involving stochastic partial differential equations (SPDEs).