Application of Probabilistic Models for Multitone Electromagnetic Immunity Analysis

The operational environment of modern electronic systems may include multiple frequency electromagnetic disturbances. However, immunity measurements usually employ single-frequency continuous waveforms (i.e.,
single-tones
). The performances of two oscillator circuits with different topologies (one simulated and one measured) were used as case studies to investigate immunity to simultaneous single-tone disturbances (i.e.,
multitones
) using probabilistic Bayesian network models. For the multitone analysis, the noisy-OR model was first used to identify the type of causal interactions between simultaneously occurring single-tones. Probabilistic theories derived from the recursive noisy-OR model, which inherits the independence assumptions of the noisy-OR and any known causal dependence between simultaneously occurring single-tones, were then used to predict the probability of higher order multitone failures. For the two case studies, the probability of three-tone failures was estimated using the single-tone and two-tone failure probability values. An improved adaptive recursive noisy-OR model was also proposed to overcome the practical difficulties of obtaining multitone failure probabilities, from either simulations or measurements.