A method to calculate the statistic characters of the transient electromagnetic pulse coupling into stochastic transmission lines

In this paper, an improved method based on the Gauss-Legendre quadrature and Unscented Transform (UT) is proposed to estimate the statistical characters of the EMC/EMI problems with stochastic parameters. The UT method provides a fast method to propagate mean and covariance information through nonlinear transformations. The Gauss-Legendre quadrature as an efficient numerical integral method is used to select the sigma points and weights. The coupling problem of electromagnetic field and transmission line can be treated as a nonlinear maping. So, we calculate the statistical characters of coupling voltage on the load of the transmission line by the GLUT method. It only needs about five times of FDTD simulation to obtain the mean and standard deviation of the coupling voltage. The Monte Carlo (MC) method has been used to validate the GLUT method. The numerical simulation results indicate that the GL-UT method can reduce the number of FDTD simulation from more than thousands of times to several times.