Application of Probabilistic Models for Multitone Electromagnetic Immunity Analysis

Abstract

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 performance 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.

Synergistic Effect of Multitone EMI on the Conducted Immunity of Integrated Oscillators

“…For single-tone EM disturbance injection at frequencies close to the nominal output frequencies (i.e, 703 MHz for CSVCO, BFD and 950 MHz for RO, BFD) there were very few or no failures. For calculation purposes [11], the absence of failure is considered 0.0001 (shown in Table II as 0.0), whereas the certainty of failure is considered 0.999 (shown in Table II as 1.0) . Further, to identify the sub-type of interactions that were classified as positive causality, i.e., as synergy/asynergy, the two-tone and three-tone probability of failure obtained from the single-tone failure probabilities using (2) were compared with the simulated values.…”

“…A total of 105 two-tone and 455 three-tone cases were obtained from combinations of the 15 arbitrarily selected frequencies shown in Table II [11].…”

“…The noisy-OR model [10] has been used to identify the causal dependence between simultaneously occurring singletone EM disturbances [11]. If n single-tone disturbances, denoted as T i for i ∈ {1, 2, ..., n}, are causally independent when they occur simultaneously, then the probability of failure due to the resulting multi-tone disturbance P N (F | T 1 , ..., T n ) can be estimated using the noisy-OR model [10] as:…”

“…If the probability of failure for multi-tone EM disturbance is less than any of the probabilities for any of the single-tone contributors, then the simultaneous single-tones interact to produce a cancelling effect, which is classified as an inhibition type interaction [11], [18]. By contrast, if the probability for multi-tone EM disturbance is greater than any of the probabilities for any of the single-tone contributors, then the simultaneous single-tones interact to produce a reinforcing effect, classified as positive causality.…”

“…The analysis of the immunity levels of a current-starved voltage controlled oscillator (CSVCO) and a ring oscillator (RO), previously investigated using single-tone disturbances in [9], is extended here to consider multi-tone threats using the probabilistic noisy-OR model [10]. The use of such probabilistic models to predict the impact of multi-tone EM disturbances and to overcome the limitations of multi-tone analysis are discussed in [11].…”