Uncertainty Quantification of Self-Breakdown Switches in a Circuit Model Using Wiener–Haar Expansion

Abstract

Since many electromagnetic compatibility tests are resourcelimited, it is important to quantify the uncertainties of instruments beforehand. One of the common instruments is the trigger pulse generator with self-breakdown switches. Due to the abrupt changing caused by self-breakdown switches, stochastic methods based on the generalized polynomial chaos suffer from Gibbs-type phenomena and become erroneous around abrupt transition point. This article proposes an effective technique based on the Haar wavelets for quantifying the time delay of self-breakdown switches in stochastic simulations. Wiener–Haar wavelet expansion method is suitable for dealing with abrupt-changing problems and is applied to the nodal-analysis-based circuit model. The stochastic circuit model is expanded to an augmented model with deterministic coefficients by exploiting wavelets’ orthogonality. Furthermore, the distribution of time delay is represented as the mean value of a Heaviside function, which is implemented by an auxiliary circuit in the model. The statistical mean can be directly obtained from the 0th coefficient of Wiener–Haar expansion. A case study of a trigger generator for electromagnetic pulse generators is provided to validate the effectiveness of the proposed method. It is shown that, compared with Monte Carlo methods, Wiener–Haar representation provides robust results with less computational time and a faster convergence rate.