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International audience; This paper presents a new method to compute upper and lower bounds of any voltage or current of an arbitrary linear electric circuit model with uncertain parameters. The bounds are in the frequency domain, and when compared to a previously proposed method, this novel approach provides a higher level of guarantee. The reason is that the bounds are not only computed for a set of fixed frequencies but also computed to a set of intervals of frequencies. The details of the proposed approach, especially the equivalent uncertain element models, are given. Additionally, tests are performed on problems with low and high number of uncertain parameters. Contrary to the classical method of Monte Carlo, the results are not based on a random choice of parameters and do not depend on the number of iterations. It is shown on an example that the classical method of Monte Carlo needs a high number of iterations to reach results in agreement with the proposed method. Then, it leads to higher computation times of several orders of magnitude.

International audience; Robustness analysis consists of analyzing if a system performs as it was intended to, even when parametric variations occur. Robustness is particularly interesting in critical applications, where decreased performance or failur cannot be tolerated, such as aerospace or nuclear industry electronic devices. In this context, it is important to develop methodologies to efficiently assess electronic systems robustness, even when the number of parameters or frequency ranges is large.In (Ferber et al, “Systematic LFT Derivation of Uncertain Electrical Circuits for Worst-Case Tolerance Analysis”, IEEE Transactions on EMC, vol. 57, issue 5, pp. 937-946, 2015), the authors presented a methodology to address the aforementioned problem that is efficient for a large number of parameters, since it is based on convex optimization. Upper and lower bounds on the system’s performance for a given frequency can be quickly obtained, even with hundreds of uncertain parameters. However, the computational time can still be large for problems that require a fine frequency grid i.e. a large frequency range with many considered frequencies.The contribution of this new work is to present an alternative methodology that overcomes the necessity of refining the frequency grid by computing bounds for the worst-case over a given frequency range. New forms of modeling the basic electrical components are proposed, such that an analysis on an interval of frequency can be carried out in one optimization run, instead of several runs on a fine frequency grid. Moreover, a new technique to overcome numerical issues is also presented.The method was implemented and tested on different problems related to conducted and radiated electromagnetic interference. The results are in accordance with the classical Monte Carlo method. The two main advantages of the proposed method related to Monte Carlo are: (1) the bounds are formally guaranteed to be respected in any combination of parameter values in a certain range and (2) the computational time required to compute the bounds is orders of magnitude lower than of Monte Carlo.