Monte Carlo simulations of microstrip lines with random substrate impurity

Monte Carlo simulations of microstrip lines with random substrate impurity are performed. Each realization of current distribution on the microstrip line with substrate impurity is calculated by the hybrid finite element method/multilevel fast multipole algorithm. After taking the ensemble average of all the realizations, the super-resolution estimation of signal parameters via rotational invariance technique algorithm is employed to extract the characteristic parameters of the transmission line from the current distribution. Comparisons of our numerical results and previously published results for the conventional microstrip line with homogeneous substrate confirm the validity, accuracy, and efficiency of our simulation tool. Our Monte Carlo simulations demonstrate that the effect of substrate impurity on the characteristics of a microstrip line can be quite accurately estimated by replacing the inhomogeneous substrate with a homogeneous one whose dielectric constant is the averaged value for different materials weighted by their volume ratios. This simple estimation approach, however, does not apply to the attenuation constant of the line due to the effect of finite substrate width.